diff --git a/README.md b/README.md
index a0f9b20773..afd127433d 100644
--- a/README.md
+++ b/README.md
@@ -18,7 +18,7 @@ Hecke is part of the [OSCAR](https://oscar.computeralgebra.de/) project and the
- (Online documentation)
So far, Hecke provides the following features:
-
+
- Number fields (absolute, relative, simple and non-simple)
- Orders and ideals in number fields
- Class and unit group computations of orders
@@ -72,16 +72,16 @@ Here is a quick example of using Hecke:
julia> using Hecke
...
-Welcome to
+Welcome to
- _ _ _
- | | | | | |
- | |__| | ___ ___| | _____
+ _ _ _
+ | | | | | |
+ | |__| | ___ ___| | _____
| __ |/ _ \/ __| |/ / _ \
| | | | __/ (__| < __/
|_| |_|\___|\___|_|\_\___|
-
-Version 0.10.12...
+
+Version 0.10.12...
... which comes with absolutely no warrant whatsoever
(c) 2015-2019 by Claus Fieker, Tommy Hofmann and Carlo Sircana
@@ -90,7 +90,7 @@ julia> f = x^3 + 2;
julia> K, a = NumberField(f, "a");
julia> O = maximal_order(K);
julia> O
-Maximal order of Number field over Rational Field with defining polynomial x^3 + 2
+Maximal order of Number field over Rational Field with defining polynomial x^3 + 2
with basis [1,a,a^2]
```
diff --git a/TODO.md b/TODO.md
index 6e319b3458..60aef40082 100644
--- a/TODO.md
+++ b/TODO.md
@@ -10,7 +10,7 @@
* [ ] implement Montes--Nart algorithm
* [ ] composite Dedekind criterion
* [ ] composite Round Two algorithm
- * [ ] implement information about containment (O_1 \sub O_2)
+ * [ ] implement information about containment (O_1 \sub O_2)
* [ ] save prime factors of discriminant
* [x] `princ_gen` should be cached
* [ ] Clean up uniformizer (p-uniformizer? strong uniformizer?)
@@ -37,13 +37,13 @@
* [ ] `coeff(z, i)` and `coefficients(z)` "inconsistencies"
## Renaming
-
+
* [x] `DiagonalGroup` and `AbelianGroup` to `abelian_group`.
* [x] `princ_gen` to `principal_generator`
* [ ] `nf` to `number_field`
* [x] Group algebra renaming
* [ ] Make `has*` and `*_known` consistent.
-
+
## Misc
* [ ] `exp_map_unit_grp_mod`
* [ ] `charpoly` should have `parent = ` keyword.
diff --git a/deps/_build.jl b/deps/_build.jl
index 96d35e8680..7950e8abb6 100644
--- a/deps/_build.jl
+++ b/deps/_build.jl
@@ -3,7 +3,7 @@ using Pkg, Nemo, Libdl
oldwdir = pwd()
nemo_pkgdir = joinpath(dirname(pathof(Nemo)), "..")
-#nemo_pkgdir = Pkg.dir("Nemo")
+#nemo_pkgdir = Pkg.dir("Nemo")
nemo_wdir = joinpath(nemo_pkgdir, "deps")
nemo_vdir = joinpath(nemo_pkgdir, "local")
diff --git a/deps/hecke/Makefile.in b/deps/hecke/Makefile.in
index df9ff25c6f..16ec309987 100644
--- a/deps/hecke/Makefile.in
+++ b/deps/hecke/Makefile.in
@@ -14,11 +14,11 @@ AT=@
BUILD_DIRS = antic \
$(EXTRA_BUILD_DIRS)
-TEMPLATE_DIRS =
+TEMPLATE_DIRS =
export
-SOURCES =
+SOURCES =
LIB_SOURCES = $(wildcard $(patsubst %, %/*.c, $(BUILD_DIRS))) $(patsubst %, %/*.c, $(TEMPLATE_DIRS))
HEADERS = $(patsubst %, %.h, $(BUILD_DIRS))
diff --git a/deps/hecke/configure b/deps/hecke/configure
index d0be70e8f6..72ab2bbc03 100755
--- a/deps/hecke/configure
+++ b/deps/hecke/configure
@@ -375,7 +375,7 @@ case "$OS" in
;;
*)
;;
-esac
+esac
#test for popcnt flag and set needed CFLAGS
@@ -383,12 +383,12 @@ mkdir -p build
rm -f build/test-popcnt > /dev/null 2>&1
MSG="Testing __builtin_popcountl..."
printf "%s" "$MSG"
-echo "int main(int argc, char ** argv) {
+echo "int main(int argc, char ** argv) {
#if defined(_WIN64)
return __builtin_popcountll(argc) == 100;
#else
return __builtin_popcountl(argc) == 100;
-#endif
+#endif
}" > build/test-popcnt.c
$CC build/test-popcnt.c -o ./build/test-popcnt > /dev/null 2>&1
if [ $? -eq 0 ]; then
diff --git a/docs/src/FacElem.md b/docs/src/FacElem.md
index 98fffcf1d2..daa45ae700 100644
--- a/docs/src/FacElem.md
+++ b/docs/src/FacElem.md
@@ -15,16 +15,16 @@ products of smaller elements, allowing the computer to handle them.
Mathematically, one can think of factored elements to formally
live in the ring $Z[K]$ the group ring of the non-zero field
elements. Thus elements are of the form $ \prod a_i^{e_i}$ where
-$a_i$ are elements in $K$, typically _small_ and the $e_i\in Z$ are frequently
-large exponents. We refer to the $a_i$ as the *base* and the $e_i$ as the
+$a_i$ are elements in $K$, typically _small_ and the $e_i\in Z$ are frequently
+large exponents. We refer to the $a_i$ as the *base* and the $e_i$ as the
*exponents* of the factored element.
Since $K$ is, in general, no PID, this presentation
is non-unique, elements in this form can easily be multiplied, raised
to large powers, but in general not compared and not added.
-In Hecke, this is caputured more generally by the type `FacElem`,
-parametrized by the type of the elements in the base and the type of their
+In Hecke, this is caputured more generally by the type `FacElem`,
+parametrized by the type of the elements in the base and the type of their
parent.
Important special cases are
@@ -32,12 +32,12 @@ Important special cases are
* ```FacElem{nf_elem, AnticNumberField}```, factored algerbaic numbers
* ```FacElem{NfAbsOrdIdl, NfAbsOrdIdlSet}```, factored ideals
-It should be noted that an object of type ```FacElem{fmpz, FlintIntegerRing}``
+It should be noted that an object of type ```FacElem{fmpz, FlintIntegerRing}``
will, in general, not represent an integer as the exponents can be
negative.
-## Construction
-In general one can define factored elements by giving 2 arrays, the
+## Construction
+In general one can define factored elements by giving 2 arrays, the
base and the exponent, or a dictionary containing the pairs:
```@docs
diff --git a/docs/src/abelian/elements.md b/docs/src/abelian/elements.md
index 39296b101a..b44750b575 100644
--- a/docs/src/abelian/elements.md
+++ b/docs/src/abelian/elements.md
@@ -40,5 +40,5 @@ G = abelian_group(fmpz[1 2; 3 4])
for g = G
println(g)
end
-```
+```
diff --git a/docs/src/abelian/maps.md b/docs/src/abelian/maps.md
index 396eb2bb77..fc1d54954d 100644
--- a/docs/src/abelian/maps.md
+++ b/docs/src/abelian/maps.md
@@ -4,7 +4,7 @@ and can be created in a variety of situations.
## Maps
Maps between abelian groups can be constructed via
- images of the generators
- - pairs of elements
+ - pairs of elements
- via composition
- and isomorphism/ inclusion testing
diff --git a/docs/src/abelian/structural.md b/docs/src/abelian/structural.md
index 7e59fa1c0e..461b69af3e 100644
--- a/docs/src/abelian/structural.md
+++ b/docs/src/abelian/structural.md
@@ -62,7 +62,7 @@ quo(G::GrpAbFinGen, n::fmpz)
quo(G::GrpAbFinGen, U::GrpAbFinGen)
```
-For 2 subgroups `U` and `V` of the same group `G`, `U+V` returns
+For 2 subgroups `U` and `V` of the same group `G`, `U+V` returns
the smallest subgroup of `G` containing both. Similarly, $U\cap V$
computes the intersection and `U \subset V` tests for inclusion.
The difference between `issubset =` $\subset$ and
diff --git a/docs/src/class_fields/intro.md b/docs/src/class_fields/intro.md
index 8684f0571e..878530c981 100644
--- a/docs/src/class_fields/intro.md
+++ b/docs/src/class_fields/intro.md
@@ -101,10 +101,10 @@ maximal_abelian_subfield(K::NfRel{nf_elem})
## Invariants
```@docs
degree(C::ClassField)
-base_ring(A::Hecke.ClassField)
-base_field(A::Hecke.ClassField)
+base_ring(A::Hecke.ClassField)
+base_field(A::Hecke.ClassField)
discriminant(C::Hecke.ClassField)
-conductor(C::Hecke.ClassField)
+conductor(C::Hecke.ClassField)
defining_modulus(C::ClassField)
iscyclic(C::ClassField)
isconductor(C::Hecke.ClassField, m::NfOrdIdl, inf_plc::Vector{InfPlc})
@@ -122,7 +122,7 @@ prime_decomposition_type(C::Hecke.ClassField, p::Hecke.NfAbsOrdIdl)
Hecke.issubfield(a::ClassField, b::ClassField)
Hecke.islocal_norm(r::Hecke.ClassField, a::Hecke.NfAbsOrdElem)
Hecke.islocal_norm(r::Hecke.ClassField, a::Hecke.NfAbsOrdElem, p::Hecke.NfAbsOrdIdl)
-Hecke.normal_closure(r::Hecke.ClassField)
+Hecke.normal_closure(r::Hecke.ClassField)
subfields(r::ClassField)
subfields(r::ClassField, d::Int)
```
diff --git a/docs/src/function_fields/elements.md b/docs/src/function_fields/elements.md
index 9caa38eac8..6a749a42c7 100644
--- a/docs/src/function_fields/elements.md
+++ b/docs/src/function_fields/elements.md
@@ -5,5 +5,5 @@ CurrentModule = Hecke
```
For details on element arithmetic in rational function fields and extensions, refer
-to the AbstractAlgebra documentation which can be found at
+to the AbstractAlgebra documentation which can be found at
[https://nemocas.github.io/AbstractAlgebra.jl/latest/function_field/](https://nemocas.github.io/AbstractAlgebra.jl/latest/function_field/).
diff --git a/docs/src/function_fields/intro.md b/docs/src/function_fields/intro.md
index 94a611c1ea..de150e1496 100644
--- a/docs/src/function_fields/intro.md
+++ b/docs/src/function_fields/intro.md
@@ -6,7 +6,7 @@ CurrentModule = Hecke
## [Introduction](@id FunctionFieldsLink)
-By definition, a (univariate) function field can be written as a finite extension of a rational
+By definition, a (univariate) function field can be written as a finite extension of a rational
function field $k(x)$ for a field $k$ (commonly $k = \mathbb{Q}$ or $k = \mathbb{F}_p$).
In Hecke, a function field $L$ is currently defined as being a (univariate) rational function
field $k(x)$ or a finite extension thereof. In other words, the extension
diff --git a/docs/src/index.md b/docs/src/index.md
index 2f004a58e2..051d74ff4a 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -44,16 +44,16 @@ Here is a quick example of using Hecke:
julia> using Hecke
...
-Welcome to
+Welcome to
- _ _ _
- | | | | | |
- | |__| | ___ ___| | _____
+ _ _ _
+ | | | | | |
+ | |__| | ___ ___| | _____
| __ |/ _ \/ __| |/ / _ \
| | | | __/ (__| < __/
|_| |_|\___|\___|_|\_\___|
-
-Version 0.9.0 ...
+
+Version 0.9.0 ...
... which comes with absolutely no warranty whatsoever
(c) 2015-2018 by Claus Fieker, Tommy Hofmann and Carlo Sircana
@@ -62,7 +62,7 @@ julia> f = x^3 + 2;
julia> K, a = NumberField(f, "a");
julia> O = maximal_order(K);
julia> O
-Maximal order of Number field over Rational Field with defining polynomial x^3 + 2
+Maximal order of Number field over Rational Field with defining polynomial x^3 + 2
with basis [1,a,a^2]
```
diff --git a/docs/src/number_fields/conventions.md b/docs/src/number_fields/conventions.md
index ee3dcb006b..f40760c0f8 100644
--- a/docs/src/number_fields/conventions.md
+++ b/docs/src/number_fields/conventions.md
@@ -44,7 +44,7 @@ determinant $\det(B)^{-1}$ is in fact equal to $[ \mathcal O : \mathbf Z[\alpha]
and is called the *index* of $\mathcal O$.
The matrix
```math
-\begin{pmatrix}
+\begin{pmatrix}
\sigma_1(\omega_1) & \dotsc & \sigma_r(\omega_1) & \sqrt{2}\operatorname{Re}(\sigma_{r+1}(\omega_1)) & \sqrt{2}\operatorname{Im}(\sigma_{r+1}(\omega_1)) & \dotsc & \sqrt{2}\operatorname{Im}(\sigma_{r+s}(\omega_1)) \\\\
\sigma_1(\omega_2) & \dotsc & \sigma_r(\omega_2) & \sqrt{2}\operatorname{Re}(\sigma_{r+1}(\omega_2)) & \sqrt{2}\operatorname{Im}(\sigma_{r+1}(\omega_2)) & \dotsc & \sqrt{2}\operatorname{Im}(\sigma_{r+s}(\omega_2)) \\\\
\vdots & \ddots & \vdots & \vdots & \vdots & \ddots & \vdots\\\\
diff --git a/docs/src/number_fields/fields.md b/docs/src/number_fields/fields.md
index 4b51654cd5..588a09e65f 100644
--- a/docs/src/number_fields/fields.md
+++ b/docs/src/number_fields/fields.md
@@ -138,7 +138,7 @@ inertia_subgroup(::AnticNumberField, ::NfOrdIdl, ::Map)
infinite_places(K::NumField)
real_places(K::AnticNumberField)
complex_places(K::AnticNumberField)
-isreal(::Plc)
+isreal(::Plc)
iscomplex(::Plc)
infinite_places_uniformizers(::AnticNumberField)
```
diff --git a/docs/src/number_fields/internal.md b/docs/src/number_fields/internal.md
index 0073b7d199..5c7d7c6dbb 100644
--- a/docs/src/number_fields/internal.md
+++ b/docs/src/number_fields/internal.md
@@ -12,7 +12,7 @@ different types:
- `NfAbsNS`: a finite extension of $\mathbf{Q}$ given by several polynomials.
We will refer to this as a non-simple field - even though mathematically
we can find a primitive elements.
- - `NfRel`: a finite simple extension of a number field. This is
+ - `NfRel`: a finite simple extension of a number field. This is
actually parametried by the (element) type of the coefficient field.
The complete type of an extension of an absolute field (`AnticNumberField`)
is `NfRel{nf_elem}`. The next extension thus will be
@@ -28,7 +28,7 @@ called absolute.
Internally, simple fields are essentially just (univariate) polynomial
quotients in a dense representation, while non-simple fields are
multivariate quotient rings, thus have a sparse presentation.
-In general, simple fields allow much faster arithmetic, while
+In general, simple fields allow much faster arithmetic, while
the non-simple fields give easy access to large degree fields.
## Absolute simple fields
diff --git a/docs/src/orders/elements.md b/docs/src/orders/elements.md
index 12c657f9b9..94b47159c1 100644
--- a/docs/src/orders/elements.md
+++ b/docs/src/orders/elements.md
@@ -4,18 +4,18 @@ CurrentModule = Hecke
```
-Elements in orders have two representations: they can be viewed as
+Elements in orders have two representations: they can be viewed as
elements in the $Z^n$ giving the coefficients wrt to the order basis
where they are elements in. On the other hand, as every order is
in a field, they also have a representation as number field elements.
-Since, asymptotically, operations are more efficient in the
+Since, asymptotically, operations are more efficient in the
field (due to fast polynomial arithmetic) than in the order, the primary
representation is that as a field element.
## Creation
Elements are constructed either as linear combinations of basis elements
-or via explicit coercion. Elements will be of type `NfOrdElem`,
+or via explicit coercion. Elements will be of type `NfOrdElem`,
the type if actually parametrized by the type of the surrounding field and
the type of the field elements. E.g. the type of any element in any
order of an absolute simple field will be
diff --git a/docs/src/orders/ideals.md b/docs/src/orders/ideals.md
index 6f2b45e83d..9dfefd0a04 100644
--- a/docs/src/orders/ideals.md
+++ b/docs/src/orders/ideals.md
@@ -6,7 +6,7 @@ CurrentModule = Hecke
(Integral) ideals in orders are always free $Z$-module of the same rank as the
order, hence have a representation via a $Z$-basis. This can be made unique
-by normalising the corresponding matrix to be in reduced row echelon form
+by normalising the corresponding matrix to be in reduced row echelon form
(HNF).
For ideals in maximal orders $Z_K$, we also have a second presentation coming
@@ -89,7 +89,7 @@ mc \ ans
The class group, or more precisely the information used to compute it
-also allows for principal ideal testing and related tasks.
+also allows for principal ideal testing and related tasks.
In general, due to the size of the objetcs, the ```fac_elem``` versions are
more effcient.
diff --git a/docs/src/orders/introduction.md b/docs/src/orders/introduction.md
index 2872b5acb0..4dd6a0ba74 100644
--- a/docs/src/orders/introduction.md
+++ b/docs/src/orders/introduction.md
@@ -3,7 +3,7 @@
CurrentModule = Hecke
```
-This chapter deals with number fields and orders there of.
+This chapter deals with number fields and orders there of.
We follow the common terminology and conventions as e.g. used in
[Cohen1](@cite), [Cohen2](@cite), [PoZa](@cite) or [Marcus](@cite).
@@ -16,7 +16,7 @@ and of relative number fields is the same.
## Orders of absolute number fields
-Assume that $K$ is defined as an absolute field.
+Assume that $K$ is defined as an absolute field.
An order $\mathcal O$ of such a field are constructed (implicitely) by
specifying a $\mathbf Z$-basis, which is refered to as the *basis* of $\mathcal
O$. If $(\omega_1,\dotsc,\omega_d)$ is the basis of $\mathcal O$ and
@@ -40,7 +40,7 @@ finitly generated torsion-free module over the Dedekind domain $\mathcal O_K$. A
the order $\mathcal O$ is unitary and has $L$ as a fraction field.
Due to $\mathcal O_K$ in general not being a principal
ideal domain, the module structure is more complicated
-and requires so called pseudo-matrices. See
+and requires so called pseudo-matrices. See
[here](@ref PMatLink) for details on pseudo-matrices, or [Cohen2](@cite),
Chapter 1 for an introduction.
diff --git a/docs/src/orders/orders.md b/docs/src/orders/orders.md
index c7d9360d77..8eda1f4417 100644
--- a/docs/src/orders/orders.md
+++ b/docs/src/orders/orders.md
@@ -101,7 +101,7 @@ All of the functions have a very similar interface: they return
an abelian group and a map converting elements of the group
into the objects required. The maps also
allow a point-wise inverse to server as the *discrete logarithm* map.
-For more information on abelian group, see [here](@ref AbelianGroupLink),
+For more information on abelian group, see [here](@ref AbelianGroupLink),
for ideals, [here](@ref NfOrdIdlLink).
- [`torsion_unit_group(::NfOrd)`](@ref)
diff --git a/docs/src/pmat/introduction.md b/docs/src/pmat/introduction.md
index e084dbd609..45dd239dc0 100644
--- a/docs/src/pmat/introduction.md
+++ b/docs/src/pmat/introduction.md
@@ -13,7 +13,7 @@ Let $R$ be a Dedekind domain, typically, the maximal order of
some number field $K$, further fix some finite dimensional
$K$-vectorspace $V$ (with some basis), frequently $K^n$ or the $K$-structure of
some extension of $K$. Since in general $R$ is not a PID, the $R$-modules
-in $V$ are usually not free, but still projective.
+in $V$ are usually not free, but still projective.
Any finitely generated $R$-module $M\subset V$
can be represented as a pseudo-matrix `PMat` as follows:
@@ -26,7 +26,7 @@ Following Cohen we call modules of the form $\mathfrak A\omega$ for
some ideal $\mathfrak A$ and $\omega \in V$ a *pseudo element*.
A system $(\mathfrak A_i, \omega_i)$ is called a pseudo-generating
system for $M$ if $\langle \mathfrak A_i\omega_i|i\langle = M$.
-A pseudo-generating system is called a pseudo-basis if the
+A pseudo-generating system is called a pseudo-basis if the
$\omega_i$ are $K$-linear independent.
A *pseudo-matrix* $X$ is a tuple containing a vector of ideals
diff --git a/docs/src/quad_forms/basics.md b/docs/src/quad_forms/basics.md
index ceb20e7b0b..98efb52939 100644
--- a/docs/src/quad_forms/basics.md
+++ b/docs/src/quad_forms/basics.md
@@ -1,4 +1,4 @@
-# Basics
+# Basics
```@meta
CurrentModule = Hecke
```
diff --git a/docs/src/quad_forms/introduction.md b/docs/src/quad_forms/introduction.md
index d7190d5bfb..9bb02909f5 100644
--- a/docs/src/quad_forms/introduction.md
+++ b/docs/src/quad_forms/introduction.md
@@ -4,11 +4,11 @@ CurrentModule = Hecke
```
-This chapter deals with quadratic and Hermitian spaces and lattices there of.
+This chapter deals with quadratic and Hermitian spaces and lattices there of.
## Definitions and vocabulary
-We begin by collecting the necessary definitions and vocabulary.
+We begin by collecting the necessary definitions and vocabulary.
The terminology follows mainly [Kir16]
### Quadratic and Hermitian spaces
@@ -28,7 +28,7 @@ If $V$ is a Hermitian space, we call the matrix $G = (\Phi(e_i, e_j))_{1 \leq i,
the *Gram matrix* of $V$. We call $\overline{\phantom{x}}$ the *involution* of $V$.
In both cases we refer to the field $E$ as the *base ring* $V$. In this chapter
-we will refer to quadratic and Hermitian spaces also just as *spaces*.
+we will refer to quadratic and Hermitian spaces also just as *spaces*.
For Hermitian lattices, the field $K$ will be refered to as the *fixed field* of $V$.
### Quadratic and Hermitian lattices
diff --git a/docs/src/quad_forms/lattices.md b/docs/src/quad_forms/lattices.md
index 7d061fe617..b0fe98f0b1 100644
--- a/docs/src/quad_forms/lattices.md
+++ b/docs/src/quad_forms/lattices.md
@@ -1,4 +1,4 @@
-# Quadratic and hermitian lattices
+# Quadratic and hermitian lattices
```@meta
CurrentModule = Hecke
```
diff --git a/docs/src/sparse/intro.md b/docs/src/sparse/intro.md
index 3f00b124d7..a401d05f4f 100644
--- a/docs/src/sparse/intro.md
+++ b/docs/src/sparse/intro.md
@@ -8,7 +8,7 @@ CurrentModule = Hecke
This chapter deals with sparse linear algebra over commutative rings and fields.
-Sparse linear algebra, that is, linear algebra with sparse matrices,
+Sparse linear algebra, that is, linear algebra with sparse matrices,
plays an important role in various algorithms in algebraic number theory. For
example, it is one of the key ingredients in the computation of class groups
and discrete logarithms using index calculus methods.
@@ -84,7 +84,7 @@ For example, `SMat{fmpz}` is the type for sparse matrices over the integers.
In constrast to sparse rows, sparse matrices have a fixed number of rows and columns,
that is, they represent elements of the matrices space $\mathrm{Mat}_{n\times m}(R)$.
-Internally, sparse matrices are implemented as an array of sparse rows.
+Internally, sparse matrices are implemented as an array of sparse rows.
As a consequence, unlike their dense counterparts, sparse matrices have a mutable number of rows and it is very performant to add additional rows.
### Construction
diff --git a/examples/FieldEnumeration/FieldEnumeration.jl b/examples/FieldEnumeration/FieldEnumeration.jl
index 48a7e7b1a1..2431044739 100644
--- a/examples/FieldEnumeration/FieldEnumeration.jl
+++ b/examples/FieldEnumeration/FieldEnumeration.jl
@@ -43,139 +43,139 @@ function _read_fields(filename::String)
end
close(f)
return identity.(pols)
-end
+end
-global small_solvable_groups =
-[ (1, 1), (2, 1), (3, 1), (4, 1), (4, 2), (5, 1), (6, 1), (6, 2), (7, 1), (8,
-1), (8, 2), (8, 3), (8, 4), (8, 5), (9, 1), (9, 2), (10, 1), (10, 2), (11, 1),
+global small_solvable_groups =
+[ (1, 1), (2, 1), (3, 1), (4, 1), (4, 2), (5, 1), (6, 1), (6, 2), (7, 1), (8,
+1), (8, 2), (8, 3), (8, 4), (8, 5), (9, 1), (9, 2), (10, 1), (10, 2), (11, 1),
(12, 1), (12, 2), (12, 3), (12, 4), (12, 5), (13, 1), (14, 1), (14, 2), (15, 1),
(16, 1), (16, 2), (16, 3), (16, 4), (16, 5), (16, 6), (16, 7), (16, 8), (16, 9),
-(16, 10), (16, 11), (16, 12), (16, 13), (16, 14), (17, 1), (18, 1), (18, 2),
+(16, 10), (16, 11), (16, 12), (16, 13), (16, 14), (17, 1), (18, 1), (18, 2),
(18, 3), (18, 4), (18, 5), (19, 1), (20, 1), (20, 2), (20, 3), (20, 4), (20, 5),
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-(96, 217), (96, 218), (96, 219), (96, 220), (96, 221), (96, 222), (96, 223),
-(96, 224), (96, 225), (96, 226), (96, 227), (96, 228), (96, 229), (96, 230),
-(96, 231), (97, 1), (98, 1), (98, 2), (98, 3), (98, 4), (98, 5), (99, 1), (99,
-2), (100, 1), (100, 2), (100, 3), (100, 4), (100, 5), (100, 6), (100, 7), (100,
-8), (100, 9), (100, 10), (100, 11), (100, 12), (100, 13), (100, 14), (100, 15),
+9), (96, 10), (96, 11), (96, 12), (96, 13), (96, 14), (96, 15), (96, 16), (96,
+17), (96, 18), (96, 19), (96, 20), (96, 21), (96, 22), (96, 23), (96, 24), (96,
+25), (96, 26), (96, 27), (96, 28), (96, 29), (96, 30), (96, 31), (96, 32), (96,
+33), (96, 34), (96, 35), (96, 36), (96, 37), (96, 38), (96, 39), (96, 40), (96,
+41), (96, 42), (96, 43), (96, 44), (96, 45), (96, 46), (96, 47), (96, 48), (96,
+49), (96, 50), (96, 51), (96, 52), (96, 53), (96, 54), (96, 55), (96, 56), (96,
+57), (96, 58), (96, 59), (96, 60), (96, 61), (96, 62), (96, 63), (96, 64), (96,
+65), (96, 66), (96, 67), (96, 68), (96, 69), (96, 70), (96, 71), (96, 72), (96,
+73), (96, 74), (96, 75), (96, 76), (96, 77), (96, 78), (96, 79), (96, 80), (96,
+81), (96, 82), (96, 83), (96, 84), (96, 85), (96, 86), (96, 87), (96, 88), (96,
+89), (96, 90), (96, 91), (96, 92), (96, 93), (96, 94), (96, 95), (96, 96), (96,
+97), (96, 98), (96, 99), (96, 100), (96, 101), (96, 102), (96, 103), (96, 104),
+(96, 105), (96, 106), (96, 107), (96, 108), (96, 109), (96, 110), (96, 111),
+(96, 112), (96, 113), (96, 114), (96, 115), (96, 116), (96, 117), (96, 118),
+(96, 119), (96, 120), (96, 121), (96, 122), (96, 123), (96, 124), (96, 125),
+(96, 126), (96, 127), (96, 128), (96, 129), (96, 130), (96, 131), (96, 132),
+(96, 133), (96, 134), (96, 135), (96, 136), (96, 137), (96, 138), (96, 139),
+(96, 140), (96, 141), (96, 142), (96, 143), (96, 144), (96, 145), (96, 146),
+(96, 147), (96, 148), (96, 149), (96, 150), (96, 151), (96, 152), (96, 153),
+(96, 154), (96, 155), (96, 156), (96, 157), (96, 158), (96, 159), (96, 160),
+(96, 161), (96, 162), (96, 163), (96, 164), (96, 165), (96, 166), (96, 167),
+(96, 168), (96, 169), (96, 170), (96, 171), (96, 172), (96, 173), (96, 174),
+(96, 175), (96, 176), (96, 177), (96, 178), (96, 179), (96, 180), (96, 181),
+(96, 182), (96, 183), (96, 184), (96, 185), (96, 186), (96, 187), (96, 188),
+(96, 189), (96, 190), (96, 191), (96, 192), (96, 193), (96, 194), (96, 195),
+(96, 196), (96, 197), (96, 198), (96, 199), (96, 200), (96, 201), (96, 202),
+(96, 203), (96, 204), (96, 205), (96, 206), (96, 207), (96, 208), (96, 209),
+(96, 210), (96, 211), (96, 212), (96, 213), (96, 214), (96, 215), (96, 216),
+(96, 217), (96, 218), (96, 219), (96, 220), (96, 221), (96, 222), (96, 223),
+(96, 224), (96, 225), (96, 226), (96, 227), (96, 228), (96, 229), (96, 230),
+(96, 231), (97, 1), (98, 1), (98, 2), (98, 3), (98, 4), (98, 5), (99, 1), (99,
+2), (100, 1), (100, 2), (100, 3), (100, 4), (100, 5), (100, 6), (100, 7), (100,
+8), (100, 9), (100, 10), (100, 11), (100, 12), (100, 13), (100, 14), (100, 15),
(100, 16) ]
diff --git a/examples/FieldEnumeration/abelian_extensions.jl b/examples/FieldEnumeration/abelian_extensions.jl
index c188dac12d..463aa88f61 100644
--- a/examples/FieldEnumeration/abelian_extensions.jl
+++ b/examples/FieldEnumeration/abelian_extensions.jl
@@ -121,7 +121,7 @@ function main()
@info "Only real fields: $only_real"
@info "Only complex fields: $only_complex"
@info "Input from: $input"
-
+
if old_output == ""
@info "Output to: $output (default)"
else
@@ -157,7 +157,7 @@ function main()
ending = String(split(basename(input), ".")[2])
- relative_deg = prod(type)
+ relative_deg = prod(type)
if ending == "nfdb"
DBin = Base.read(input, Hecke.NFDB)
diff --git a/examples/FieldEnumeration/absolute_abelian.jl b/examples/FieldEnumeration/absolute_abelian.jl
index 3c81a6b2f2..1798be1df6 100644
--- a/examples/FieldEnumeration/absolute_abelian.jl
+++ b/examples/FieldEnumeration/absolute_abelian.jl
@@ -2,7 +2,7 @@ using Hecke
Base.:*(x::Hecke.NfRelNSElem{Nemo.nf_elem}) = x
-function _get_simple_extension_and_maximal_order(K)
+function _get_simple_extension_and_maximal_order(K)
@assert degree(base_ring(K)) == 1
pol = K.pol
k = length(pol)
@@ -114,7 +114,7 @@ for (i, k) in enumerate(l_conductors)
L=number_field(C)
LL = _get_simple_extension_and_maximal_order(L)
LLdisc = discriminant(maximal_order(LL))
-
+
if LLdisc != prod( p^e for (p, e) in C.absolute_discriminant)
println("Ups")
@show LLdisc
diff --git a/examples/FieldEnumeration/absolute_abelian_with_conductors.jl b/examples/FieldEnumeration/absolute_abelian_with_conductors.jl
index a4268a3194..2f8d4b7cbb 100644
--- a/examples/FieldEnumeration/absolute_abelian_with_conductors.jl
+++ b/examples/FieldEnumeration/absolute_abelian_with_conductors.jl
@@ -113,7 +113,7 @@ function main()
ls = subgroups(r, quotype = gtype, fun = (x, y) -> quo(x, y, false)[2])
for s in ls
C = ray_class_field(mr, s)::Hecke.ClassField{Hecke.MapRayClassGrp, GrpAbFinGenMap}
- if Hecke._is_conductor_minQQ(C, n)
+ if Hecke._is_conductor_minQQ(C, n)
push!(class_fields, C)
end
end
@@ -149,7 +149,7 @@ function main()
f = Qx(fmpq[coeff(coeff(fK, j), 0) for j = 0:degree(fK)])
polys[t] = f
end
- NS, gNS = number_field(polys, check = false, cached = false)
+ NS, gNS = number_field(polys, check = false, cached = false)
push!(fields, (NS, Hecke.discriminantQQ(O, C, Int(minimum(defining_modulus(C)[1])))))
end
end
diff --git a/examples/FieldEnumeration/all_fields.jl b/examples/FieldEnumeration/all_fields.jl
index 3e7540b6e3..ed82054653 100644
--- a/examples/FieldEnumeration/all_fields.jl
+++ b/examples/FieldEnumeration/all_fields.jl
@@ -56,7 +56,7 @@ function parse_commandline()
help = "Only CM fields"
action = :store_true
"--max-ab-subfields"
- help = "File containing maximal abelian subextensions"
+ help = "File containing maximal abelian subextensions"
"--simplify"
help = "Simplify the field"
action = :store_true
@@ -233,7 +233,7 @@ function main()
DBout = Hecke.NFDB(res)
t = "fields($n, $i, $dbound, only_real = $only_real, simplify = $simplify)"
- if rdbound !== nothing
+ if rdbound !== nothing
t = t * " (rd bound $rdbound)"
end
if maxabsubfields isa String
diff --git a/examples/FieldEnumeration/compute_class_groups.jl b/examples/FieldEnumeration/compute_class_groups.jl
index 2c2ba89128..e8e6a3c29f 100644
--- a/examples/FieldEnumeration/compute_class_groups.jl
+++ b/examples/FieldEnumeration/compute_class_groups.jl
@@ -78,7 +78,7 @@ function has_obviously_not_relative_class_number_one(K::AnticNumberField)
for (k,_) in subs
if degree(k) == degree(K)
continue
- end
+ end
fl, tau = Hecke.iscm_field(k)
if !fl
continue
@@ -90,8 +90,8 @@ function has_obviously_not_relative_class_number_one(K::AnticNumberField)
hminus = divexact(h, hplus)
if hminus > 4 || hminus == 3
return true
- end
- end
+ end
+ end
return false
end
@@ -178,7 +178,7 @@ function main()
r = Hecke._create_record(K)
if _relative_class_number
- if hrelative == 0
+ if hrelative == 0
hK = _fancy_class_number(OK)
fl, tau = Hecke.iscm_field(K)
k, = fixed_field(K, tau, simplify = true)
diff --git a/examples/FieldEnumeration/cubic.jl b/examples/FieldEnumeration/cubic.jl
index c3f89e955e..842eb5c150 100644
--- a/examples/FieldEnumeration/cubic.jl
+++ b/examples/FieldEnumeration/cubic.jl
@@ -38,7 +38,7 @@ end
#Note: this is not optimised, but hopefully correct.
#if you need more, analyse Hasse...
-function induce_action(phi::Hecke.NfToNfMor, mR::T) where T <: Map{GrpAbFinGen,
+function induce_action(phi::Hecke.NfToNfMor, mR::T) where T <: Map{GrpAbFinGen,
Hecke.FacElemMon{Hecke.NfOrdIdlSet}}
#function induce_action(phi::Hecke.NfToNfMor, mR::Hecke.MapRayClassGrpFacElem{Hecke.GrpAbFinGen})
lp, x = Hecke.find_gens(
@@ -116,7 +116,7 @@ function s3_with_discriminant(I::NfOrdIdl)
println("need to try $D and $F as conductors")
#all quadratics with conductor D:
r, mr = ray_class_group(D, n_quo = 2)
-
+
for s in index_p_subgroups(r, fmpz(2), (A,x) -> quo(A, x)[2])
a = ray_class_field(mr*pseudo_inv(s))
# println(a, " with cond ", conductor(a))
@@ -134,7 +134,7 @@ function s3_with_discriminant(I::NfOrdIdl)
k = base_ring(Kr)
Ka, m1 = absolute_simple_field(Kr)
m2 = restrict(inv(m1), k)
- sigma = hom(Ka, Ka, m1\(conj(m1(gen(Ka)))))
+ sigma = hom(Ka, Ka, m1\(conj(m1(gen(Ka)))))
#m1: Kr -> Ka, m2: base_ring(Kr) -> Ka
M = lll(maximal_order(Ka))
FF = ideal(M, F.gen_one, M(m2(k(F.gen_two))))
@@ -146,7 +146,7 @@ function s3_with_discriminant(I::NfOrdIdl)
sigma_R = induce_action(sigma, mR)
# println(sigma_R)
-
+
for S = Hecke.stable_subgroups(R, [3], [sigma_R], op=quo)
@assert order(S[1]) == 3
s, ms = snf(S[1])
diff --git a/examples/FieldEnumeration/smallest_field.jl b/examples/FieldEnumeration/smallest_field.jl
index 562d32ab9f..8bb20e068a 100644
--- a/examples/FieldEnumeration/smallest_field.jl
+++ b/examples/FieldEnumeration/smallest_field.jl
@@ -27,7 +27,7 @@ function _read_fields(filename::String)
end
close(f)
return pols
-end
+end
function parse_commandline()
s = ArgParseSettings()
diff --git a/examples/IsPower.jl b/examples/IsPower.jl
index 7522bdf46c..4aa8805831 100644
--- a/examples/IsPower.jl
+++ b/examples/IsPower.jl
@@ -129,7 +129,7 @@ function ispower_mod_p(a::nf_elem, i::Int)
the "correct" one will have no_fac ones in the front
rear (a+b) < bd => (a+b)/c < bd/c
round((a+b)/c) - round(a/c) - round(b/c)
- =#
+ =#
no_rt, trafo = lll_with_removal(trafo, fmpz(p)^2*fmpz(2*no_fac)) #THINK
trafo = sub(trafo, 1:no_rt, 1:ncols(trafo))
d = Dict{fmpz_mat, Vector{Int}}()
@@ -175,7 +175,7 @@ function ispower_mod_p(a::nf_elem, i::Int)
end
if j > 40 error("") end
end
-end
+end
function Hecke.crt(A::Vector{<:NfAbsOrdElem}, I::Vector{<:NfAbsOrdIdl})
while length(I) > 1
@@ -251,7 +251,7 @@ function Hecke.roots(a::qadic, i::Int)
end
local zeta
- j = gcd(size(k)-1, i)
+ j = gcd(size(k)-1, i)
if j != 1
while true
zeta = rand(k)^(divexact(size(k)-1, j))
diff --git a/examples/MultDep.jl b/examples/MultDep.jl
index 0862317657..f894668bfe 100644
--- a/examples/MultDep.jl
+++ b/examples/MultDep.jl
@@ -128,7 +128,7 @@ mutable struct GeIdeal
end
end
-import Hecke.gcd, Hecke.isone, Hecke.*, Hecke.gcd_into!, Hecke.copy, Hecke.divexact,
+import Hecke.gcd, Hecke.isone, Hecke.*, Hecke.gcd_into!, Hecke.copy, Hecke.divexact,
Hecke.isunit, Hecke.coprime_base, Hecke.valuation
function make_compatible!(a::GeIdeal, b::GeIdeal)
@@ -257,7 +257,7 @@ function mult_syzygies_units(A::Vector{FacElem{nf_elem, AnticNumberField}})
continue
end
d = reduce(lcm, map(denominator, s))
- gamma = fmpz[FlintZZ(x*d)::fmpz for x = s]
+ gamma = fmpz[FlintZZ(x*d)::fmpz for x = s]
@assert reduce(gcd, gamma) == 1 # should be a primitive relation
@time if !verify_gamma(push!(copy(u), a), gamma, fmpz(p)^prec)
prec *= 2
@@ -274,7 +274,7 @@ function mult_syzygies_units(A::Vector{FacElem{nf_elem, AnticNumberField}})
end
#=
let u_1, .., u_n be units and
- has rank s and
+ has rank s and
r_i in Z^n be such that
prod u_i^r_i = 1 (OK, sum of the logs is zero)
rank = s as well
@@ -288,7 +288,7 @@ function mult_syzygies_units(A::Vector{FacElem{nf_elem, AnticNumberField}})
[H | 0] [v_i | i] = 0
so, since H is triangular(!!) v_1, ... v_n-s = 0
and =
-
+
for the case of n=s+1 this is mostly the "normal" construction.
Note: as a side, the relations do not have to be primitive.
If they are, (and n=s+1), then H = 1
@@ -352,7 +352,7 @@ function lift_reco(::FlintRationalField, a::padic; reco::Bool = false)
R = parent(a)
fl, c, d = rational_reconstruction(u, prime(R, N-v))
!fl && return nothing
-
+
x = FlintQQ(c, d)
if v < 0
return x//prime(R, -v)
diff --git a/examples/MultiQuad.jl b/examples/MultiQuad.jl
index fccfc5021f..d8315e3891 100644
--- a/examples/MultiQuad.jl
+++ b/examples/MultiQuad.jl
@@ -111,7 +111,7 @@ function multi_quad(d::Vector{fmpz}, B::Int)
lp = prime_ideals_up_to(zk, Int(B), complete = false, degree_limit = 1)
#only need split primes ...
lp = [ x for x = lp if minimum(x) in cp]
- @assert all(x->minimum(x) == norm(x), lp)
+ @assert all(x->minimum(x) == norm(x), lp)
if length(lp) > 0
S, mS = Hecke.sunit_group_fac_elem(lp)
else
@@ -140,7 +140,7 @@ function multi_quad(d::Vector{fmpz}, B::Int)
return c
end
-function dlog(dl::Dict, x, p::Int)
+function dlog(dl::Dict, x, p::Int)
if iszero(x)
throw(Hecke.BadPrime(1))
end
@@ -215,7 +215,7 @@ function _nullspace(A::nmod_mat)
end
else
A = sub(A, i:r, c+1:ncols(A))
- end
+ end
A = A'
@assert iszero(A_orig * A)
for i = keys(factor(p).fac)
@@ -336,12 +336,12 @@ function saturate_exp(c::Hecke.ClassGrpCtx, p::Int, stable = 1.5)
AA = sub(AA, 1:i, 1:ncols(AA))'
else
@assert rank(AA') == ncols(AA)
- end
+ end
# @show cAA, pp, q, size(AA)
- if cAA == ncols(AA)
+ if cAA == ncols(AA)
break #the other ideals are going to give the same info
#for multi-quad as the field is normal
- end
+ end
catch e
@show "BadPrime"
if !isa(e, Hecke.BadPrime)
@@ -349,7 +349,7 @@ function saturate_exp(c::Hecke.ClassGrpCtx, p::Int, stable = 1.5)
end
end
end
- if cAA == ncols(AA)
+ if cAA == ncols(AA)
#println("good $i")
i += 1
else
@@ -428,7 +428,7 @@ function saturate(c::Hecke.ClassGrpCtx, n::Int, stable = 3.5)
g = content(r)
g = gcd(g, n)
divexact!(r, r, g)
-# g == 1 || println("non triv. content $g in ", e[:, i])
+# g == 1 || println("non triv. content $g in ", e[:, i])
a = fe(c.R_gen[1])^r[1, 1]
fac_a = r[1, 1] * c.M.bas_gens[1]
for j = 2:length(c.R_gen)
@@ -443,7 +443,7 @@ function saturate(c::Hecke.ClassGrpCtx, n::Int, stable = 3.5)
@assert length(c.R_gen) + length(c.R_rel) + 1 == nrows(e)
a *= fe(zeta)^r[nrows(e), 1]
end
-
+
decom = Dict((c.FB.ideals[k], v) for (k,v) = fac_a)
if n == g
fl = true
@@ -465,7 +465,7 @@ function saturate(c::Hecke.ClassGrpCtx, n::Int, stable = 3.5)
error("not a power")
end
end
-
+
#= Idea - before I forget:
we have generators g_1, ..., g_n on input and enlarge by
h_1, ..., h_r
@@ -496,7 +496,7 @@ function saturate(c::Hecke.ClassGrpCtx, n::Int, stable = 3.5)
push!(R, zeta)
end
R = vcat(R, n_gen)
- @assert ncols(Ti) == length(R)
+ @assert ncols(Ti) == length(R)
d = Hecke.class_group_init(c.FB, SMat{fmpz}, add_rels = false)
@@ -508,7 +508,7 @@ function saturate(c::Hecke.ClassGrpCtx, n::Int, stable = 3.5)
#TODO remove zeta from relations!!
Hecke.class_group_add_relation(d, a)
end
-
+
return d
end
@@ -550,7 +550,7 @@ function simplify(c::Hecke.ClassGrpCtx)
Hecke._add_unit(U, c.R_rel[i])
end
end
- for i=1:length(U.units)
+ for i=1:length(U.units)
Hecke.class_group_add_relation(d, U.units[i], SRow(FlintZZ))
end
return d
@@ -589,12 +589,12 @@ end
# units: we have new^n = prod old. use this to obtain new basis
#
# track the torsion as well
-# if n is divisible by 8, then, generically, the saturation needs to
+# if n is divisible by 8, then, generically, the saturation needs to
# be followed by a second saturation at 2:
# Elements look like (locally) an 8-th power but are only a 4-th
# so I can only extract a 4-th.
# However, it might be an 8-th (or the product of 2 might be an 8-th)
# Darn. Math is unfair.
-#
+#
# extend to gen. mult group...
end
diff --git a/examples/NFDB.jl b/examples/NFDB.jl
index b5c14173fc..8a10800051 100644
--- a/examples/NFDB.jl
+++ b/examples/NFDB.jl
@@ -3,7 +3,7 @@ function _class_group(c::Vector{BigInt})
f = Qx(c)
K, a = number_field(f, cached = false)
OK = lll(maximal_order(K))
- C, mC = class_group(OK)
+ C, mC = class_group(OK)
return BigInt(order(C))
end
@@ -32,7 +32,7 @@ end
# mmap::Vector{UInt}
# hash::UInt
# field_names::Vector{Symbol}
-#
+#
# function NFDB(path::String)
# metadata = Dict()
# f = open(path)
@@ -191,7 +191,7 @@ const properties_comp = Dict(:id => (Int, x -> UInt(hash(x))),
:isabelian => (Bool, x -> isabelian(automorphism_group(x)[1])),
:non_simple => (Vector{fmpq_poly}, x -> non_simple_extension(x)),
:galois_group => (Tuple{Int, Int}, x -> error()))
-
+
for (k, v) in properties_comp
@eval ($k)(D::NFDBRecord) = D[Symbol($k)]::($(v[1]))
diff --git a/examples/Petri.jl b/examples/Petri.jl
index 8468e7b9ca..94d7443385 100644
--- a/examples/Petri.jl
+++ b/examples/Petri.jl
@@ -139,7 +139,7 @@ function fire(P::Petri)
end
# println(stderr, p)
# println(stderr, P.d)
-end
+end
function fire()
global pe, M, c, pe
@@ -272,7 +272,7 @@ function petri(P::Petri)
end
# push!(n[2], callback("PetriNet.trigger", "(:"*n[2].s[:id]*", 1)"))
push!(c, g)
- return c
+ return c
end
node_index(s::Symbol) = findfirst(x -> x.s[:id] == String(s), n)
@@ -310,7 +310,7 @@ function trigger(t::Tuple)
j = node_index(i)
n[j].s[:title] = string(Char(Int(n[j].s[:title][1])+1))
end
-
+
display(Francy.FrancyMimeString, c)
end
diff --git a/examples/Plesken.jl b/examples/Plesken.jl
index 5c2bad0935..5e974cc8b8 100644
--- a/examples/Plesken.jl
+++ b/examples/Plesken.jl
@@ -15,7 +15,7 @@
# residueRing creation: rename generator to prefix with r or so
#
# Padic -> pAdic
-# gen for ResidueRing(Poly)
+# gen for ResidueRing(Poly)
#################################################
@@ -259,7 +259,7 @@ function plesken_kummer(p::fmpz, r::Int, s::Int)
if descent
b = f_tr(a, f, ord)
#println("$i: trace of $a is $b")
-# pol = minpoly_aut(b, x->x^(p^(r^(i-1))))
+# pol = minpoly_aut(b, x->x^(p^(r^(i-1))))
pol = minpoly_pow(b, r) ## does not work: expo too large
#println(pol)
arr = Array{typeof(zero(T))}(degree(pol)+1)
diff --git a/examples/PolyRoot.jl b/examples/PolyRoot.jl
index 68e7193ce2..bd561ad87a 100644
--- a/examples/PolyRoot.jl
+++ b/examples/PolyRoot.jl
@@ -24,7 +24,7 @@ function ispower(f::PolyElem{T}, n::Int) where {T <: FieldElem}
p *= 2
end
r = (f*r) % gen(parent(f))^d
- #this is the ONLY possible candidate
+ #this is the ONLY possible candidate
#(think about n-th roots of 1 - maybe only other roots lift?)
#NO: this is a purely transcendental extension, roots of unity are in
#base_ring or don't come in.
diff --git a/examples/RayClass.jl b/examples/RayClass.jl
index ed8c05d1a2..2585ec5f7e 100644
--- a/examples/RayClass.jl
+++ b/examples/RayClass.jl
@@ -4,7 +4,7 @@ mutable struct MapRayClassGrpNew{T} #<: Hecke.Map{T, Hecke.NfOrdIdlSet}
header::Hecke.MapHeader
modulus_fin::Hecke.NfOrdIdl
modulus_inf::Vector{Hecke.InfPlc}
-
+
function MapRayClassGrpNew{T}() where {T}
return new{T}()
end
@@ -13,10 +13,10 @@ end
#
# Modify the map of the class group so that the chosen representatives are coprime to m
-#
+#
function _coprime_ideal(C::GrpAbFinGen, mC::Map, m::NfOrdIdl)
-
+
O=parent(m).order
K=nf(O)
L=NfOrdIdl[]
@@ -24,14 +24,14 @@ function _coprime_ideal(C::GrpAbFinGen, mC::Map, m::NfOrdIdl)
a=mC(C[i])
if iscoprime(a,m)
push!(L,a)
- else
+ else
J=inv(a)
s=K(rand(J.num,5))//J.den # Is the bound acceptable?
I=s*a
simplify(I)
I = numerator(I)
while !iscoprime(I,m)
- s=K(rand(J.num,5))//J.den
+ s=K(rand(J.num,5))//J.den
I=s*a
simplify(I)
I = numerator(I)
@@ -39,7 +39,7 @@ function _coprime_ideal(C::GrpAbFinGen, mC::Map, m::NfOrdIdl)
push!(L,I)
end
end
-
+
function exp(a::GrpAbFinGenElem)
I=ideal(O,1)
for i=1:ngens(C)
@@ -49,13 +49,13 @@ function _coprime_ideal(C::GrpAbFinGen, mC::Map, m::NfOrdIdl)
end
return I
end
-
+
mp=Hecke.MapClassGrp{typeof(C)}()
mp.header=Hecke.MapHeader(C,Hecke.NfOrdIdlSet(O),exp, mC.header.preimage)
-
+
return mp
-
-end
+
+end
@doc Markdown.doc"""
@@ -63,7 +63,7 @@ end
ray_class_group(m::NfOrdIdl, A::Vector{InfPlc}=[]) -> FinGenGrpAb, Map
> Compute the ray class group of the maximal order $L$ with respect to the modulus given by $m$ (the finite part) and the infinite primes of $A$
-> and return an abstract group isomorphic to the ray class group with a map
+> and return an abstract group isomorphic to the ray class group with a map
> from the group to the ideals of $L$
"""
@@ -72,17 +72,17 @@ function ray_class_group_std(m::NfOrdIdl, primes::Vector{InfPlc}=InfPlc[])
#
# We compute the group using the sequence U -> (O/m)^* _> Cl^m -> Cl -> 1
# First of all, we compute all these groups with their own maps
-#
+#
O=parent(m).order
K=nf(O)
-
+
C, mC = class_group(O)
mC=_coprime_ideal(C,mC,m)
U, mU = unit_group(O)
M, pi= quo(O,m)
G, mG=unit_group(M)
-
+
p = [ x for x in primes if isreal(x) ]
if !isempty(p)
H,lH,eH=_infinite_primes(O,p,m)
@@ -99,7 +99,7 @@ function ray_class_group_std(m::NfOrdIdl, primes::Vector{InfPlc}=InfPlc[])
A=vcat(RC, MatrixSpace(FlintZZ, ngens(G)+ngens(U), ncols(RC))())
B=vcat(MatrixSpace(FlintZZ, ngens(C), ncols(RG))(), RG)
B=vcat(B, MatrixSpace(FlintZZ, ngens(U) , ncols(RG))())
-
+
#
# We compute the relation matrix given by the image of the map U -> (O/m)^*
#
@@ -108,11 +108,11 @@ function ray_class_group_std(m::NfOrdIdl, primes::Vector{InfPlc}=InfPlc[])
a=(mG\(pi(u))).coeff
if !isempty(primes)
a=hcat(a, (lH(K(u))).coeff)
- end
+ end
for j=1:ngens(G)
B[i+nrows(RC)+nrows(RG),j]=a[1,j]
end
- end
+ end
#
# We compute the relation between generators of Cl and (O/m)^* in Cl^m
@@ -124,10 +124,10 @@ function ray_class_group_std(m::NfOrdIdl, primes::Vector{InfPlc}=InfPlc[])
b=(mG\(pi(y))).coeff
if primes != []
b=hcat(b, (lH(K(y))).coeff)
- end
+ end
for j=1: ngens(G)
B[i,j]=-b[1,j]
- end
+ end
end
end
@@ -153,10 +153,10 @@ function ray_class_group_std(m::NfOrdIdl, primes::Vector{InfPlc}=InfPlc[])
if primes!=[]
z=lH(K(gamma))
y=hcat(y, z.coeff)
- end
+ end
return X(hcat(L.coeff,y))
end
- end
+ end
#
# Exp map
@@ -168,7 +168,7 @@ function ray_class_group_std(m::NfOrdIdl, primes::Vector{InfPlc}=InfPlc[])
if isempty(primes)
c=G([a.coeff[1,i] for i=ngens(C)+1:ngens(X)])
return mC(b)*(pi\(mG(c)))
- else
+ else
c=T([a.coeff[1,i] for i=ngens(C)+1:ngens(T)+ngens(C)])
d=H([a.coeff[1,i] for i=ngens(T)+ngens(C)+1: ngens(X)])
el=pi\(mG(c))
@@ -176,7 +176,7 @@ function ray_class_group_std(m::NfOrdIdl, primes::Vector{InfPlc}=InfPlc[])
vect=(lH(K(el))).coeff
if vect==d.coeff
return el*mC(b)
- else
+ else
correction=O(1)
for i=1:ngens(H)
if d.coeff[1,i]==1
@@ -188,17 +188,17 @@ function ray_class_group_std(m::NfOrdIdl, primes::Vector{InfPlc}=InfPlc[])
vect=(lH(K(el))).coeff
end
return el*mC(b)
- end
+ end
end
- end
+ end
mp=MapRayClassGrpNew{typeof(X)}()
mp.header = Hecke.MapHeader(X, Hecke.NfOrdIdlSet(O), expo, disclog)
mp.modulus_fin=m
mp.modulus_inf=p
-
+
return X, mp
-
+
end
@@ -215,8 +215,8 @@ function ray_class_group_p_part(p::Integer, m::NfOrdIdl, inf_plc::Vector{InfPlc}
G, mG, lp = Hecke._mult_grp(Q,p)
C, mC = class_group(O)
Hecke._assure_princ_gen(mC)
-
- if p==2
+
+ if p==2
pr = [ x for x in inf_plc if isreal(x) ]
if !isempty(pr)
H,eH,lH=Hecke._infinite_primes(O,pr,m)
@@ -224,34 +224,34 @@ function ray_class_group_p_part(p::Integer, m::NfOrdIdl, inf_plc::Vector{InfPlc}
G =Hecke.direct_product(G,H)
end
end
-
+
valclassp=Int(p^(valuation(order(C[ngens(C)]),p)))
nonppartclass=div(order(C[ngens(C)]),valclassp)
-
+
if valclassp==1 && order(G)==1
return Hecke.empty_ray_class(m)
end
-
+
C, mC, vect = Hecke._class_group_mod_n(C,mC,valclassp)
U, mU = unit_group_fac_elem(O)
exp_class, Kel = Hecke._elements_to_coprime_ideal(C,mC,m)
-
+
if order(G)==1
- return Hecke.class_as_ray_class(C,mC,exp_class,m)
+ return Hecke.class_as_ray_class(C,mC,exp_class,m)
end
n=ideal(O,1)
for (q,vq) in lp
n*=q^vq
end
-
+
#
# We start to construct the relation matrix
#
expo=exponent(G)
inverse_d=gcdx(nonppartclass,expo)[2]
-
+
R=zero_matrix(FlintZZ, ngens(C)+ngens(U)+ngens(G), ngens(C)+ngens(G))
for i=1:ngens(C)
R[i,i]=C.snf[i]
@@ -265,7 +265,7 @@ function ray_class_group_p_part(p::Integer, m::NfOrdIdl, inf_plc::Vector{InfPlc}
R[i+ngens(C),i+ngens(C)]=G.rels[i,i]
end
end
-
+
#
# We compute the relation matrix given by the image of the map U -> (O/m)^*
#
@@ -280,21 +280,21 @@ function ray_class_group_p_part(p::Integer, m::NfOrdIdl, inf_plc::Vector{InfPlc}
else
push!(tobeeval, mU(U[1]))
end
- else
+ else
push!(evals, Q(1))
end
append!(tobeeval,[mU(U[i]) for i=2:ngens(U)])
-
+
@vprint :RayFacElem 1 "then principal ideal generators \n"
for i=1:ngens(C)
@vtime :RayFacElem 1 push!(tobeeval, mC.princ_gens[i][2]*Kel[i])
end
-
+
@vprint :RayFacElem 1 "Time for elements evaluation: "
ev,quots,idemps= Hecke.fac_elems_eval(O,Q,tobeeval,lp,expo)
@vtime :RayFacElem 1 append!(evals, ev)
@vprint :RayFacElem 1 "\n"
-
+
for i=1:ngens(U)
@vprint :RayFacElem 1 "Disclog of unit $i \n"
a=(mG\(evals[i])).coeff
@@ -309,7 +309,7 @@ function ray_class_group_p_part(p::Integer, m::NfOrdIdl, inf_plc::Vector{InfPlc}
for j=1:ngens(G)
R[i+ngens(G)+ngens(C),ngens(C)+j]=a[1,j]
end
- end
+ end
#
# We compute the relation between generators of Cl and (O/m)^* in Cl^m
@@ -325,12 +325,12 @@ function ray_class_group_p_part(p::Integer, m::NfOrdIdl, inf_plc::Vector{InfPlc}
end
for j=1: ngens(G)
R[i,ngens(C)+j]=-a[1,j]
- end
+ end
end
-
+
X=abelian_group(R)
-
-
+
+
#
# Discrete logarithm
#
@@ -342,7 +342,7 @@ function ray_class_group_p_part(p::Integer, m::NfOrdIdl, inf_plc::Vector{InfPlc}
end
return a
end
-
+
function disclog(J::NfOrdIdl)
if isone(J)
return X([0 for i=1:ngens(X)])
@@ -360,7 +360,7 @@ function ray_class_group_p_part(p::Integer, m::NfOrdIdl, inf_plc::Vector{InfPlc}
end
return X(hcat(L.coeff,y))
end
- end
+ end
#
# Exp map
@@ -371,7 +371,7 @@ function ray_class_group_p_part(p::Integer, m::NfOrdIdl, inf_plc::Vector{InfPlc}
if p!=2 || isempty(pr)
c=G([a.coeff[1,i] for i=ngens(C)+1:ngens(X)])
return exp_class(b)*ideal(O,pi\(mG(c)))
- else
+ else
c=T([a.coeff[1,i] for i=ngens(C)+1:ngens(T)+ngens(C)])
d=H([a.coeff[1,i] for i=ngens(T)+ngens(C)+1: ngens(X)])
el=pi\(mG(c))
@@ -379,16 +379,16 @@ function ray_class_group_p_part(p::Integer, m::NfOrdIdl, inf_plc::Vector{InfPlc}
vect=(lH(K(el))).coeff
if vect==d.coeff
return exp_class(b)*ideal(O,el)
- else
+ else
correction=eH(d)
while vect!=d.coeff
el=el+correction
vect=(lH(K(el))).coeff
end
return exp_class(b)*ideal(O,el)
- end
+ end
end
- end
+ end
mp=Hecke.MapRayClassGrpNew{typeof(X)}()
mp.header = Hecke.MapHeader(X, FacElemMon(parent(m)) , expon, disclog)
@@ -400,5 +400,5 @@ function ray_class_group_p_part(p::Integer, m::NfOrdIdl, inf_plc::Vector{InfPlc}
mp.defining_modulus = (m, inf_plc)
return X,mp
-end
+end
diff --git a/examples/RelNeq.jl b/examples/RelNeq.jl
index 32ef8c7516..23eee2b251 100644
--- a/examples/RelNeq.jl
+++ b/examples/RelNeq.jl
@@ -21,7 +21,7 @@ struct RelNeq
Qt = parent(K.pol)
h = gcd(gen(k) - evaluate(Qt(mp(gen(k))), t), evaluate(K.pol, t))
Kk, _ = number_field(h)
- return new(k, K, Kk, mp, mp)
+ return new(k, K, Kk, mp, mp)
end
function RelNeq(m::Map)
@@ -48,8 +48,8 @@ end
Next Q: Let N^1 be the subgroup of Cl_M defined above. Then
- X_M the ray class field mod M = Z_K m
- |
+ X_M the ray class field mod M = Z_K m
+ |
|
X the class field for N^1, thus the norm group is Cl_M/N^1
Y | the norm group of Y is the norm of X_M over k.
@@ -70,17 +70,17 @@ end
Alternatively: use Jan Albert's thesis to get bound on the generation...
For K/k normal this should reduce(?) to Scholz' paper (or Jehne's version) on Zahlknoten/ number knots
- In this case N(I) = 1 iff I = prod A^(1-sigma a) thus it can be computed from the Galois action on
+ In this case N(I) = 1 iff I = prod A^(1-sigma a) thus it can be computed from the Galois action on
ideal (classes), then Cl/N^1 is fixed pointwise by Gal(K/k) (trivial action) (in fact this should be the
largest/ smallest such quotient)
hence the group extension (exact sequence)
-
- 1 -> Cl/N^1 -> Gal(X/k) -> Gal(K/k) -> 1
+
+ 1 -> Cl/N^1 -> Gal(X/k) -> Gal(K/k) -> 1
is split(?) direct(?) (nice?) (special?)
My memory of Scholz is that there is a second field lurking around...
-=#
+=#
function norm_1_subgroup(A::RelNeq)
k = A.k
K = A.K
@@ -111,7 +111,7 @@ function norm_1_subgroup(A::RelNeq)
lp = prime_decomposition(maximal_order(k), p)
for P = lp
- if d % p == 0
+ if d % p == 0
@show "expensive", p
lP = collect(factor(IdealSet(ZK)(A.m_k_K, P[1])))
else
@@ -146,41 +146,41 @@ function norm_1_subgroup(A::RelNeq)
end
#= The idea
- we have
- 1
-
- |
+ we have
+ 1
+
+ |
V
-
+
U_K {N(a) in U_k} {N(I) = 1}
1 -> ---------- -> ------------- -> ---------- -> Cl
{N(u) = 1} {N(a) = 1} {N(a) = 1}
| N
V
-
+
U_k
-
- So what we want is a group extension of a sub-group of a quotient of U_k
+
+ So what we want is a group extension of a sub-group of a quotient of U_k
by a subgroup of Cl:
- 1
-
- |
+ 1
+
+ |
V
-
+
{N(a) in U_k} {N(I) = 1}
1 -> ---------------- -> ---------- -> Cl
N(U_K){N(a) = 1} {N(a) = 1}
| N
V
-
+
U_k
-----
N(U_K)
-
+
=#
mutable struct Norm1Group
@@ -206,7 +206,7 @@ mutable struct Norm1Group
r.U = q, pseudo_inv(mq)*mu
r.sU = sub(u, elem_type(u)[])
r.gC = [(ideal(maximal_order(A.K), 1)//1, 0*c[1])]
- r.gU = [(FacElem(A.k(1)), 0*q[1])]
+ r.gU = [(FacElem(A.k(1)), 0*q[1])]
r.gens = []
return r
end
@@ -265,7 +265,7 @@ function Base.push!(N::Norm1Group, I::Hecke.NfOrdFracIdl)
@assert fl
ng = norm(A.m_k_K, g)
@assert isunit(maximal_order(N.A.k)(evaluate(ng)))
- r = mu\ng
+ r = mu\ng
fl, _ = haspreimage(N.sU[2], r)
if fl
return false # nothing new
@@ -298,7 +298,7 @@ function Hecke.evaluate(N::Norm1Group)
s2, ms2 = snf(N.sU[1])
R = [rels(s2) zero_matrix(FlintZZ, ngens(s2), ngens(s1));
zero_matrix(FlintZZ, ngens(s1), ngens(s2)) rels(s1)]
-
+
for i = 1:ngens(s1)
x = ms1(s1[i])
I = FacElem(Dict((N.gC[j][1], x[j]) for j=1:ngens(N.sC[1])))
@@ -307,7 +307,7 @@ function Hecke.evaluate(N::Norm1Group)
@assert fl
ng = norm(N.A.m_k_K, g)
@assert isunit(maximal_order(N.A.k)(evaluate(ng)))
- r = N.U[2]\ng
+ r = N.U[2]\ng
fl, x = haspreimage(N.sU[2], r)
for j=1:ngens(s2)
R[ngens(s2) + i, j] = -x[j]
@@ -336,7 +336,7 @@ function Hecke.evaluate(N::Norm1Group)
@assert fl
ng = norm(N.A.m_k_K, g)
@assert isunit(maximal_order(N.A.k)(evaluate(ng)))
- r = N.U[2]\ng
+ r = N.U[2]\ng
fl, r = haspreimage(N.sU[2], r)
@assert fl
return A(hcat((ms2\r).coeff, (ms1\s).coeff))
@@ -358,7 +358,7 @@ function n1group(A::RelNeq, B::Int)
function single_prime(P::NfAbsOrdIdl)
p = minimum(P)
- if numerator(discriminant(K)) % p == 0 ||
+ if numerator(discriminant(K)) % p == 0 ||
numerator(discriminant(k)) % p == 0
@show "expensive", p
lq = collect(factor(IdealSet(ZK)(A.m_k_K, P)))
@@ -437,7 +437,7 @@ function doit(n::String)
if i % 10 == 0
flush(fo)
end
- end
+ end
end
diff --git a/examples/Round2.jl b/examples/Round2.jl
index e0ad686830..05ac32207e 100644
--- a/examples/Round2.jl
+++ b/examples/Round2.jl
@@ -13,7 +13,7 @@ Support for generic maximal orders over any PID
given a in Frac(R), decompose into num, den
(all Localisations of Z have QQ as quotient field,
Q[x], Z[x] and Localisation(Q(x), degree) use Q(t))
- - isdomain_type
+ - isdomain_type
Seems to work for
- R = ZZ, F = AnticNumberField
@@ -288,7 +288,7 @@ function radical_basis_power(O::Order, p::RingElem)
while q < degree(O)
q *= characteristic(F)
end
-
+
b = basis(O)
m = zero_matrix(F, degree(O), degree(O))
for i=1:degree(O)
@@ -315,7 +315,7 @@ function radical_basis_trace(O::Order, p::RingElem)
R = t
mR = MapFromFunc(x->R(x), y->lift(y), parent(p), R)
end
-
+
TT = map_entries(mR, T)
k, B = kernel(TT)
M2 = map_entries(x->preimage(mR, x), B[:, 1:k])'
@@ -338,7 +338,7 @@ function radical_basis_power_non_perfect(O::Order, p::RingElem)
while q < degree(O)
q *= characteristic(F)
end
-
+
q = Int(q)
b = basis(O)
m = zero_matrix(F, q*degree(O), degree(O))
@@ -477,7 +477,7 @@ function Hecke.maximal_order(O::Order)
end
T = integral_split(OO.trans, S)
isone(T[2]) && continue
- if first
+ if first
Op = T
first = false
else
@@ -570,7 +570,7 @@ function Hecke.integral_split(a::fmpq, R::Loc{fmpz})
return R(numerator(a)//q), R(w)
else
return R(numerator(a)//w), R(q)
- end
+ end
end
Hecke.denominator(a::fmpq, R::Loc{fmpz}) = integral_split(a, R)[2]
Hecke.numerator(a::fmpq, R::Loc{fmpz}) = integral_split(a, R)[1]
@@ -883,11 +883,11 @@ function divrem(a::HessQRElem, b::HessQRElem)
g(cx?+1) = cg x^? + g and cont(cg mod d = 1)...
- af/g -d/(cx^?+1) now has a denominator with cont( mod d) = 1
- af/g - (af - du)/(g - dv) =
- (af(g-dv) -g(af-du))/(g(g-dv)) = d*..., so once cont(g %d) =1,
+ (af(g-dv) -g(af-du))/(g(g-dv)) = d*..., so once cont(g %d) =1,
we can replace f and g mod d (and figure out the quotient afterwards)
- - for d = p a prime, the rep is unqiue, thus F_p(t)
- =#
+ - for d = p a prime, the rep is unqiue, thus F_p(t)
+ =#
r = rem(a,b)
return divexact(a-r, b), r
@@ -959,7 +959,7 @@ function Nemo.ResidueField(a::HessQR, b::HessQRElem)
F = GF(b.c)
Ft, t = RationalFunctionField(F, String(var(a.R)), cached = false)
R = parent(numerator(t))
- return Ft, MapFromFunc(x->F(x.c)*Ft(map_coefficients(F, x.f, parent = R))//Ft(map_coefficients(F, x.g, parent = R)),
+ return Ft, MapFromFunc(x->F(x.c)*Ft(map_coefficients(F, x.f, parent = R))//Ft(map_coefficients(F, x.g, parent = R)),
y->HessQRElem(a, fmpz(1), map_coefficients(lift, numerator(y)), map_coefficients(lift, denominator(y))), a, Ft)
end
diff --git a/examples/Suri.jl b/examples/Suri.jl
index 86696c40be..082d3a22d9 100644
--- a/examples/Suri.jl
+++ b/examples/Suri.jl
@@ -9,7 +9,7 @@ import Base: +, -, *, ^
assume, at least for now, the alpha_i are independent.
assume sum gamma_i alpha_i + gamma alpha = 0
(gamma are the dependency)
- Now P :=
+ Now P :=
(inv(A_i) gamma_i)
( inv(A) gamma )
is a (n+1) x 1 pseudo matrix. Using the (pseudo) HNF we find a matrix
@@ -67,7 +67,7 @@ end
function extend(M::Hecke.PMat, b::Generic.MatSpaceElem{nf_elem}, gamma::Generic.MatSpaceElem{nf_elem})
- @assert iszero(hcat(M.matrix', b)*gamma)
+ @assert iszero(hcat(M.matrix', b)*gamma)
zk = base_ring(M)
nc = ncols(gamma)
n = nrows(gamma) - 1
@@ -353,7 +353,7 @@ Hecke.fmpz(a::RRSelem) = Hecke.crt(a.x, a.R.ce)
# a random invertable matrix with coeffs in R
-#start with identity, do i rounds of random elementary row and column
+#start with identity, do i rounds of random elementary row and column
#operations
function rand_gl(R::Hecke.Ring, n::Int, u, i::Int)
A = identity_matrix(R, n)
diff --git a/examples/pAdicConj.jl b/examples/pAdicConj.jl
index 7b27fef85f..d1595500ea 100644
--- a/examples/pAdicConj.jl
+++ b/examples/pAdicConj.jl
@@ -15,7 +15,7 @@ function mult_syzygies_units(a::Vector{FacElem{nf_elem, AnticNumberField}})
u = FacElem{nf_elem, AnticNumberField}[]
la = [conjugates_pAdic_log(e, p, 300) for e = a] #can loose precision
# needs to be traced
- # precision needs to be updated.
+ # precision needs to be updated.
n = ncols(la[1])
Qp = base_ring(la[1])
lu = matrix(Qp, 0, n, [])
@@ -51,17 +51,17 @@ function mult_syzygies_units(a::Vector{FacElem{nf_elem, AnticNumberField}})
As an example, det U
det U = :
and using universal lower bounds on the size of units (Dobrowski)
- and the successive minimal, we can get a lower bound on the
+ and the successive minimal, we can get a lower bound on the
regulator of . Hadramat gives an upper bound on reg()
(regulator in the sence of lattice disciminant)
Think: can we use the p-adic regulator to help???
possibly increase precision until we either have
- indepence or a relation
+ indepence or a relation
ignore bounds?
- =#
+ =#
d = reduce(lcm, map(denominator, r))
- gamma = [FlintZZ(x*d) for x = r]
+ gamma = [FlintZZ(x*d) for x = r]
#technically, this relations needs to be verified.
#=
we have a relation mod p^k, which means
@@ -82,10 +82,10 @@ function mult_syzygies_units(a::Vector{FacElem{nf_elem, AnticNumberField}})
Dobrowski. Hence this can be evaluated with low precision.
Not done.
- =#
+ =#
@assert reduce(gcd, gamma) == 1 # should be a primitive relation
_, U = hnf_with_trafo(matrix(FlintZZ, length(r), 1, gamma))
- U = inv(U)
+ U = inv(U)
U = sub(U, 1:nrows(U), 2:ncols(U))
#new basis is the cols of U
push!(u, a[i])
@@ -145,7 +145,7 @@ function regulator_lower_bound(R::NfOrd, B::Int = 2*degree(R))
Ms, _ = unit_lower_bound(R, B)
r1, r2 = signature(R)
r = r1+r2-1
- n = degree(R)
+ n = degree(R)
return Ms^r * 2^r2 /n / Hecke.hermite_constant(r)
end
diff --git a/examples/polymake.jl b/examples/polymake.jl
index 817f3b5e8a..7f28dec459 100644
--- a/examples/polymake.jl
+++ b/examples/polymake.jl
@@ -142,7 +142,7 @@ function norm_equation2_fac_elem(R::NfAbsOrd, k::fmpz; abs::Bool = false)
lp = factor(k*R)
s, ms = Hecke.sunit_mod_units_group_fac_elem(collect(keys(lp)))
C = vcat([matrix(FlintZZ, 1, ngens(s), [valuation(ms(s[i]), p) for i=1:ngens(s)]) for p = keys(lp)])
-
+
lp = factor(k)
A = vcat([matrix(FlintZZ, 1, ngens(s), [valuation(Hecke.factored_norm(ms(s[i])), p) for i=1:ngens(s)]) for p = keys(lp.fac)])
b = matrix(FlintZZ, length(lp.fac), 1, [valuation(k, p) for p = keys(lp.fac)])
@@ -197,7 +197,7 @@ function norm_equation_fac_elem(R::NfAbsOrd, k::fmpz; abs::Bool = false)
return sol
end
-norm_equation_fac_elem(R::NfAbsOrd, k::Integer; abs::Bool = false) =
+norm_equation_fac_elem(R::NfAbsOrd, k::Integer; abs::Bool = false) =
norm_equation_fac_elem(R, fmpz(k), abs = abs)
function norm_equation(R::NfAbsOrd, k::fmpz; abs::Bool = false)
@@ -226,7 +226,7 @@ function norm_equation_fac_elem(R::Hecke.NfRelOrd{nf_elem,Hecke.NfOrdFracIdl}, a
mq = mq*inv(mms)
C = vcat([matrix(FlintZZ, 1, ngens(q), [valuation(mS(preimage(mq, q[i])), p) for i=1:ngens(q)]) for p = keys(lp)])
-
+
A = vcat([matrix(FlintZZ, 1, ngens(q), [valuation(norm(mkK, mS(preimage(mq, g))), p) for g in gens(q)]) for p = keys(la)])
b = matrix(FlintZZ, length(la), 1, [valuation(a, p) for p = keys(la)])
@@ -296,8 +296,8 @@ function irreducibles(S::Vector{NfAbsOrdIdl{AnticNumberField,nf_elem}})
end
@assert all(isprime, S)
#TODO: try to get a better bound - in general if S is too large
- # it cannot work
-
+ # it cannot work
+
O = order(S[1])
@assert all(x-> order(x) == O, S)
diff --git a/src/AlgAss/AlgGrp.jl b/src/AlgAss/AlgGrp.jl
index f83fae1232..327f689fdf 100644
--- a/src/AlgAss/AlgGrp.jl
+++ b/src/AlgAss/AlgGrp.jl
@@ -719,7 +719,7 @@ function decompose(A::AlgGrp)
return res
end
G = group(A)
- res = __decompose(A)
+ res = __decompose(A)
#if !isdefined(res[1][1], :isomorphic_full_matrix_algebra)
# if order(G) == 24 && find_small_group(G)[1] == (24, 12) &&
@@ -727,7 +727,7 @@ function decompose(A::AlgGrp)
# @assert G.isfromdb
# _compute_matrix_algebras_from_reps(A, res, _reps[1])
# end
- #
+ #
# if order(G) == 48 && find_small_group(G)[1] == (48, 48) &&
# base_ring(A) isa FlintRationalField
# @assert G.isfromdb
@@ -897,7 +897,7 @@ function _absolute_basis(A)
v[i] = zero(K)
end
v[j] = bK[j]
- push!(B, A(v))
+ push!(B, A(v))
end
end
return B
@@ -1024,7 +1024,7 @@ function isfree_a5_fabi(K::AnticNumberField)
println("fabi 2")
return false
end
-
+
if !(istamely_ramified(K, fmpz(5)) || !isalmost_maximally_ramified(K, fmpz(5)))
println("fabi 3")
return false
diff --git a/src/AlgAss/AlgQuat.jl b/src/AlgAss/AlgQuat.jl
index e0e7325a82..3b067d1c43 100644
--- a/src/AlgAss/AlgQuat.jl
+++ b/src/AlgAss/AlgQuat.jl
@@ -281,7 +281,7 @@ function Base.enumerate(O::Union{AlgAssRelOrd, AlgAssAbsOrd}, b::Int, equal::Boo
# TODO: Replace this by short_vectors_gram(M, nrr) once it works
@assert !iszero(det(G))
- V = _short_vectors_gram(G, fmpz(b), hard = true)
+ V = _short_vectors_gram(G, fmpz(b), hard = true)
res = elem_type(O)[]
for i in 1:length(V)
y = sum(V[i][1][j] * B[j] for j in 1:d)
@@ -296,7 +296,7 @@ function Base.enumerate(O::Union{AlgAssRelOrd, AlgAssAbsOrd}, b::Int, equal::Boo
end
return res
-end
+end
# Thanks Aurel!
# https://mathoverflow.net/questions/250753/finite-group-of-units-in-quaternion-orders
@@ -334,7 +334,7 @@ function unit_group_modulo_scalars(O::AlgAssRelOrd)
push!(norms, n)
end
end
-
+
@assert all(isunit(u) for u in gens)
return gens
@@ -465,7 +465,7 @@ function _is_principal_maximal_quaternion_generic_proper(a, M, side = :right)
alpha = inv(Nnu)
_d = denominator(alpha, maximal_order(K))
- alpha = _d * alpha
+ alpha = _d * alpha
#@show isintegral(alpha)
@@ -484,7 +484,7 @@ function _is_principal_maximal_quaternion_generic_proper(a, M, side = :right)
#@show denominator(G)
#_d = degree(base_ring(A))
-
+
#@show B
v = _short_vectors_gram_integral(G, FlintZZ(B), hard = true)
diff --git a/src/AlgAss/Elem.jl b/src/AlgAss/Elem.jl
index f6141c4fa3..80e4aa6637 100644
--- a/src/AlgAss/Elem.jl
+++ b/src/AlgAss/Elem.jl
@@ -16,7 +16,7 @@ function (K::AnticNumberField)(a::AbsAlgAssElem{nf_elem})
@assert K == base_ring(parent(a))
@assert has_one(parent(a))
o = one(parent(a))
-
+
if iszero(a)
return zero(K)
end
@@ -24,7 +24,7 @@ function (K::AnticNumberField)(a::AbsAlgAssElem{nf_elem})
i = findfirst(!iszero, o.coeffs)
fl, c = divides(a.coeffs[i], o.coeffs[i])
-
+
if fl
if c * o == a
return c
@@ -38,7 +38,7 @@ function (K::FlintRationalField)(a::AbsAlgAssElem{fmpq})
@assert K == base_ring(parent(a))
@assert has_one(parent(a))
o = one(parent(a))
-
+
if iszero(a)
return zero(K)
end
@@ -46,7 +46,7 @@ function (K::FlintRationalField)(a::AbsAlgAssElem{fmpq})
i = findfirst(!iszero, o.coeffs)
fl, c = divides(a.coeffs[i], o.coeffs[i])
-
+
if fl
if c * o == a
return c
diff --git a/src/AlgAss/Types.jl b/src/AlgAss/Types.jl
index 0b62d5cf48..05c15f715c 100644
--- a/src/AlgAss/Types.jl
+++ b/src/AlgAss/Types.jl
@@ -70,8 +70,8 @@ mutable struct AlgQuat{T} <: AbsAlgAss{T}
trace_basis_elem::Vector{T}
maximal_order
std_inv# standard involution
-
- function AlgQuat{T}() where {T}
+
+ function AlgQuat{T}() where {T}
z = new{T}()
z.issimple = 1
return z
diff --git a/src/AlgAssAbsOrd/Conjugacy/Conjugacy.jl b/src/AlgAssAbsOrd/Conjugacy/Conjugacy.jl
index 83d8470b87..3e0f6f0e2c 100644
--- a/src/AlgAssAbsOrd/Conjugacy/Conjugacy.jl
+++ b/src/AlgAssAbsOrd/Conjugacy/Conjugacy.jl
@@ -589,7 +589,7 @@ function isGLZ_conjugate(A::Vector{fmpq_mat}, B::Vector{fmpq_mat})
d = lcm(d1, d2)
return _isGLZ_conjugate(d .* A, d .* B)
end
-
+
function _isGLZ_conjugate(A::Vector{fmpq_mat}, B::Vector{fmpq_mat})
if A == B
@@ -647,7 +647,7 @@ function _isGLZ_conjugate(A::Vector{fmpq_mat}, B::Vector{fmpq_mat})
S, AtoS = quo(AA, J)
@info "Semisimple quotient has dimension $(dim(S))"
!iscommutative(S) && error("Semisimple quotient must be commutative")
- IS = ideal_from_lattice_gens(S, [AtoS(b) for b in basis(OI)])
+ IS = ideal_from_lattice_gens(S, [AtoS(b) for b in basis(OI)])
OS = Order(S, [AtoS(elem_in_algebra(b)) for b in basis(OO)])
@info "Algebra is commutative"
IS.order = OS
diff --git a/src/AlgAssAbsOrd/Conjugacy/Husert.jl b/src/AlgAssAbsOrd/Conjugacy/Husert.jl
index eff700a637..21d8c91928 100644
--- a/src/AlgAssAbsOrd/Conjugacy/Husert.jl
+++ b/src/AlgAssAbsOrd/Conjugacy/Husert.jl
@@ -11,7 +11,7 @@ function _issimilar_husert(A::fmpz_mat, B::fmpz_mat)
return fl, change_base_ring(FlintZZ, QC)
end
-# If successful, returns X such that X * A * X^-1 == B
+# If successful, returns X such that X * A * X^-1 == B
function _issimilar_husert_generic(A, B)
@assert issquarefree(minpoly(A))
m = nrows(A)
@@ -65,7 +65,7 @@ function _issimilar_husert_generic(A, B)
end
# Now construct the colon ideal
- # First the Q-basis of \prod Mat(n_i, K_i)
+ # First the Q-basis of \prod Mat(n_i, K_i)
actions = Vector{fmpq_mat}()
another_basis_of_actions = Vector{Vector{dense_matrix_type(nf_elem)}}()
@@ -112,9 +112,9 @@ function _issimilar_husert_generic(A, B)
# So D is a Q-basis of Mat_n(K)
# Now determine the colon ideal
-
+
la = length(actions)
-
+
M = zero_matrix(FlintQQ, la, 0)
for a in absolute_basis_vec_A
diff --git a/src/AlgAssAbsOrd/Conjugacy/Lifting.jl b/src/AlgAssAbsOrd/Conjugacy/Lifting.jl
index a059cb122d..1c089d981f 100644
--- a/src/AlgAssAbsOrd/Conjugacy/Lifting.jl
+++ b/src/AlgAssAbsOrd/Conjugacy/Lifting.jl
@@ -85,7 +85,7 @@ function _lift2(MM)
k += 1
#@show M
else # no unit there # I could do this in one go by putting a unit in the first position
- _, l = findmin(abs.(v))
+ _, l = findmin(abs.(v))
l = l + (k - 1)
#@show l
#@show euclid(M[l, k])
diff --git a/src/AlgAssAbsOrd/Conjugacy/Random.jl b/src/AlgAssAbsOrd/Conjugacy/Random.jl
index 57fd4581a6..c9ce734d7b 100644
--- a/src/AlgAssAbsOrd/Conjugacy/Random.jl
+++ b/src/AlgAssAbsOrd/Conjugacy/Random.jl
@@ -108,7 +108,7 @@ end
function _similarity_test_setup(R, n; max_block = 4, same = false)
block_shape = Tuple{Int, Int, Int}[]
nn = n
-
+
if same
AA = _random_matrix_special(R, div(n, 3), rand(1:max_block))
nn = n - nrows(AA)
diff --git a/src/AlgAssAbsOrd/Ideal.jl b/src/AlgAssAbsOrd/Ideal.jl
index 034a159f31..a01e1ef0f1 100644
--- a/src/AlgAssAbsOrd/Ideal.jl
+++ b/src/AlgAssAbsOrd/Ideal.jl
@@ -56,7 +56,7 @@ Returns the ideal in $A$ with basis matrix $M$.
If `M_in_hnf == true`, it is assumed that $M$ is already in lower left HNF.
"""
function ideal(A::AbsAlgAss{fmpq}, M::FakeFmpqMat, M_in_hnf::Bool = false)
- if !M_in_hnf
+ if !M_in_hnf
if false #issquare(M) && (dim(A) > 50 || sum(nbits, numerator(M)) > 1000)
M = hnf(M, :lowerleft, compute_det = true)
else
diff --git a/src/AlgAssAbsOrd/LocallyFreeClassGroup.jl b/src/AlgAssAbsOrd/LocallyFreeClassGroup.jl
index fad1c332eb..0a044722e9 100644
--- a/src/AlgAssAbsOrd/LocallyFreeClassGroup.jl
+++ b/src/AlgAssAbsOrd/LocallyFreeClassGroup.jl
@@ -376,7 +376,7 @@ mutable struct DiscLogLocallyFreeClassGroup{S, T} <: Map{S, T, HeckeMap, DiscLog
end
end
m.primes_in_fields = primes_in_fields
-
+
_image = x -> x
m.header = MapHeader{S, T}(IdlSet, C, _image)
@@ -390,8 +390,8 @@ function image(m::DiscLogLocallyFreeClassGroup, I::AlgAssAbsOrdIdl)
A = algebra(O)
RtoC = m.RtoC
- mR = m.mR
- FinZ = m.FinZ
+ mR = m.mR
+ FinZ = m.FinZ
fields_and_maps = m.fields_and_maps::Vector{Tuple{AnticNumberField, AbsAlgAssToNfAbsMor{AlgAss{fmpq}, elem_type(AlgAss{fmpq}), AnticNumberField, fmpq_mat}}}
ZtoA = m.ZtoA::morphism_type(AlgAss{fmpq}, typeof(A))
_T = _ext_type(elem_type(base_ring(A)))
diff --git a/src/AlgAssAbsOrd/PIP.jl b/src/AlgAssAbsOrd/PIP.jl
index eeb5b303c2..ec722285db 100644
--- a/src/AlgAssAbsOrd/PIP.jl
+++ b/src/AlgAssAbsOrd/PIP.jl
@@ -35,7 +35,7 @@ function _isprincipal_maximal(a::AlgAssAbsOrdIdl, M, side = :right)
res = decompose(A)
abas = basis(a)
Mbas = basis(M)
-
+
@hassert :PIP 1 all(b in M for b in abas)
gens = elem_type(A)[]
#@show A
@@ -111,7 +111,7 @@ function _is_principal_maximal_quaternion_generic(a, M, side = :right)
#@show u
#@show istotally_positive(u * c)
-
+
Babs = absolute_basis(b)::Vector{elem_type(B)}
d = length(Babs)
G = zero_matrix(FlintQQ, d, d)
@@ -512,9 +512,9 @@ function _isprincipal(a::AlgAssAbsOrdIdl, O, side = :right)
UU = _solve_norm_equation_over_center(OA, ZtoA(elem_in_algebra(_u::elem_type(OZ))))
fll, uu = haspreimage(mSS, mQuni\(mQ(OZ(normred_over_center(elem_in_algebra(UU), ZtoA)))) - ttt)
-
+
@assert fll
-
+
elemA = one(A)
for i in 1:length(uu.coeff)
if !iszero(uu.coeff[1, i])
@@ -593,7 +593,7 @@ function _solve_norm_equation_over_center_quaternion(M, x)
end
end
#@show nrm
- V = _short_vectors_gram(G, nrm)
+ V = _short_vectors_gram(G, nrm)
for i in 1:length(V)
if V[i][2] == nrm
y = sum(V[i][1][j] * B[j] for j in 1:4)
@@ -726,7 +726,7 @@ function _lift_norm_one_unit_quaternion(x, F)
#@show normred(elem_in_algebra(x))
# TODO: Replace this by short_vectors_gram(M, nrr) once it works
- V = _short_vectors_gram(G, fmpz(1))
+ V = _short_vectors_gram(G, fmpz(1))
for i in 1:length(V)
y = sum(V[i][1][j] * B[j] for j in 1:4)
@assert normred(y) == 1
@@ -776,7 +776,7 @@ function _lift_norm_one_unit_full_matrix_algebra_nice(x, F)
el, id = pseudo_basis(FinZA)[1]
fl, el2 = isprincipal(id)
if false fl
- @assert fl
+ @assert fl
n = el.coeffs[1] * el2
OK = base_ring(M)
@assert basis_pmatrix(M).matrix == identity_matrix(base_ring(A), dim(A))
@@ -825,7 +825,7 @@ function _lift_norm_one_unit_full_matrix_algebra_nice(x, F)
@assert li - x in id * M
#@show (li - x) in id * M
-
+
return elem_in_algebra(li)
end
end
@@ -848,7 +848,7 @@ function _lift_norm_one_unit_full_rational_matrix_algebra(x, F)
xwrtR = c * elem_in_algebra(x) * inv(c)
# Now x is in M_n(Z) and I want to lift from M_n(Z/nn)
-
+
@assert mod(FlintZZ(det(matrix((xwrtR)))), nn) == 1
R = ResidueRing(FlintZZ, nn, cached = false)
@@ -996,7 +996,7 @@ function _normalize_column(N, i)
if isunit(N[i, i])
ainv = inv(N[i, i])
for j in n:-1:(i + 1)
- E = elementary_matrix(R, n, j, i, -ainv * N[j, i])
+ E = elementary_matrix(R, n, j, i, -ainv * N[j, i])
#@show N
N = mul!(N, E, N)
#@show N
@@ -1178,12 +1178,12 @@ function _lift_unimodular_matrix(N, n, R)
Mwithout1stcolumn = sub(M, 1:nrows(M), 2:ncols(M))
for i in 2:r
I[1, i] = (-1)^(i + 1) * det(remove_row(Mwithout1stcolumn, i))
- end
+ end
#@show "asdsd", I
M = I * M
@assert det(M) == 1
push!(left_elementary, I)
-
+
I = identity_matrix(R, r)
for i in 2:r
I[i, 1] = -M[i, 1]
@@ -1321,7 +1321,7 @@ function lift_two_by_two_matrix(M)
end
#@show left_elementary
-
+
a1 = inv(B[1,1])
D1 = identity_matrix(A, 2)
D1[1, 2] += a1
@@ -1380,7 +1380,7 @@ function lift_two_by_two_elementary_matrix(E)
#@show E, z
@assert matrix(base_ring(E), 2, 2, [z[1, 1], z[1, 2], z[2, 1], z[2, 2]]) == E
return z
-end
+end
function _gcdx(a::NfOrdElem, b::NfOrdElem)
OK = parent(a)
@@ -1553,7 +1553,7 @@ function _SLn_generators(OK, n)
# This is the case n >= 3
# Follows from Bass, "K-Theory and stable algebra", Corollary 1.5
d = degree(K)
- #
+ #
# We find a small generating set of OK as Z-algebra
found = false
for i in 1:d
@@ -1614,7 +1614,7 @@ function _GLn_generators(OK, n)
s1[i, i - 1] = 1
end
s1[1, n] = 1
-
+
s3 = identity_matrix(K, n)
s3[1, 2] = 1
@@ -1712,7 +1712,7 @@ function _isfree_Q32(K::AnticNumberField)
# N = _colon_raw(OKasideal, ideal(QG, ZG, FakeFmpqMat(representation_matrix(theta, :left))), :left)
# #N = _colon_raw(OKasideal, ideal(QG, ZG, FakeFmpqMat(identity_matrix(FlintQQ, n))), :left)
# # Johannes convention is the other way around
- #
+ #
# Atheta = ideal(QG, ZG, N)
# @assert all(theta * lambda in OKasideal for lambda in basis(Atheta))
@@ -1745,7 +1745,7 @@ function _isfree_Q32(K::AnticNumberField)
# X = order(G) * Athetaprime
-
+
res = __decompose(QG)
#Z, mZ = subgroups(G, order = 2)[1]
#k, mk = fixed_field(K, [mG(mZ(z)) for z in Z])
@@ -1803,7 +1803,7 @@ function _isfree_Q32(K::AnticNumberField)
#allunitsLambda = map(x -> BtoA(CtoB(QtoC(elem_in_algebra(x)))), (closure(Lambda_star, *)))
# I want to make sure that Lambda_star = eZG^times
-
+
QoverQQ, QtoQoverQQ, theother = restrict_scalars(Q, FlintQQ)
#@show Q
@@ -1855,7 +1855,7 @@ function _isfree_Q32(K::AnticNumberField)
#@assert sum(eZG(QtoC\(BtoC(BtoA\(d * e * b)))) * eZG for b in basis(OKasideal)) == (d * x) * eZG
# Now move Lambda_star (which is in fact (eZG)^\times back to ZG)
-
+
#Lambda_star_in_QGalmost = [BtoA(CtoB(QtoC(elem_in_algebra(u)))) for u in Lambda_star]
Lambda_star_in_QGalmost = [BtoA(CtoB(QtoC(u))) for u in eZGstar]
@@ -2007,7 +2007,7 @@ function _is_D16_subfield_free(K, KtoQG, QG::AlgGrp)
#@show [isdefined(B, :isomorphic_full_matrix_algebra) for (B, mB) in res]
fl, x = _isprincipal(Ok, ZD16, :right)
- if !fl return
+ if !fl return
false
end
diff --git a/src/AlgAssAbsOrd/PicardGroup.jl b/src/AlgAssAbsOrd/PicardGroup.jl
index f35c67a1a8..892872259d 100644
--- a/src/AlgAssAbsOrd/PicardGroup.jl
+++ b/src/AlgAssAbsOrd/PicardGroup.jl
@@ -983,7 +983,7 @@ function _coprime_integral_ideal_class_deterministic(a::AlgAssAbsOrdIdl, b::AlgA
#@show res_ideal + b
#@show one(A) * O
-
+
@assert res_elem * aorig == res_ideal
@assert res_ideal + b == one(A) * O
return res_ideal, res_elem
diff --git a/src/Assertions.jl b/src/Assertions.jl
index 9961ae91db..2442011e74 100644
--- a/src/Assertions.jl
+++ b/src/Assertions.jl
@@ -33,7 +33,7 @@
export @vprint, @hassert, @vtime, add_verbose_scope, get_verbose_level,
set_verbose_level, add_assert_scope, get_assert_level, set_assert_level
-
+
################################################################################
#
# Verbose
@@ -42,17 +42,17 @@ export @vprint, @hassert, @vtime, add_verbose_scope, get_verbose_level,
# Example:
# julia> add_verbose_scope(:Test)
-#
+#
# julia> function f()
# @vprint :Test 1 "test"
# end
# f (generic function with 1 method)
-#
+#
# julia> f()
-#
+#
# julia> set_verbose_level(:Test, 1)
# 1
-#
+#
# julia> f()
# test
@@ -143,34 +143,34 @@ end
# Example:
# julia> add_assert_scope(:Test)
-#
+#
# julia> function f()
# @hassert :Test true == false # the default level is 1
# end
# f (generic function with 1 method)
-#
+#
# julia> f()
-#
+#
# julia> set_assert_level(:Test, 1)
# 1
-#
+#
# julia> f()
# ERROR: AssertionError: $(Expr(:escape, :(true == false)))
# Stacktrace:
# [1] macro expansion at /home/thofmann/.julia/dev/Hecke/src/Hecke.jl:482 [inlined]
# [2] f() at ./REPL[6]:2
# [3] top-level scope at REPL[11]:1
-#
+#
# julia> function f()
# @hassert :Test 2 true == false
# end
# f (generic function with 1 method)
-#
+#
# julia> f()
-#
+#
# julia> set_assert_level(:Test, 3)
# 3
-#
+#
# julia> f()
# ERROR: AssertionError: $(Expr(:escape, :(true == false)))
# Stacktrace:
diff --git a/src/Deprecations.jl b/src/Deprecations.jl
index 21deb9f4cd..f4014d9382 100644
--- a/src/Deprecations.jl
+++ b/src/Deprecations.jl
@@ -30,7 +30,7 @@ else
@doc Markdown.doc"""
simplest_between(l::fmpq, r::fmpq)
-
+
> Return the simplest fraction in the closed interval `[l, r]`. A canonical >
> fraction `a_1/b_1` is defined to be simpler than `a_2/b_2` iff `b_1 < b_2` or
> `b_1 = b_2` and `a_1 < a_2`.
diff --git a/src/EllCrv/Misc.jl b/src/EllCrv/Misc.jl
index ed4deaf1c2..07297fa9f7 100644
--- a/src/EllCrv/Misc.jl
+++ b/src/EllCrv/Misc.jl
@@ -151,7 +151,7 @@ end
# @doc Markdown.doc"""
# quadroots(a::fmpz, b::fmpz, c::fmpz, p::fmpz) -> Bool
-#
+#
# Returns true if the quadratic congruence of the quadratic polynomial
# $ax^2 + bx + c = 0$ has a root modulo $p$.
# """
@@ -231,7 +231,7 @@ end
@doc Markdown.doc"""
characteristic(R::ResRing{fmpz}) -> Nemo.fmpz
-
+
Returns the characteristic of $R$
"""
function characteristic(R::ResRing{fmpz})
diff --git a/src/EllCrv/QQ.jl b/src/EllCrv/QQ.jl
index 8fb20fae90..1aa31e7161 100644
--- a/src/EllCrv/QQ.jl
+++ b/src/EllCrv/QQ.jl
@@ -966,7 +966,7 @@ end
@doc Markdown.doc"""
get_b_c_integral(E::EllCrv{fmpz}) -> Nemo.fmpz
-
+
Computes the invariants $b2$, $b4$, $b6$, $b8$, $c4$, $c6$ of an elliptic curve $E$ with integer coefficients.
"""
function get_b_c_integral(E)
diff --git a/src/FieldFactory/ab_exts.jl b/src/FieldFactory/ab_exts.jl
index 0ac70c4e51..637a8aefad 100644
--- a/src/FieldFactory/ab_exts.jl
+++ b/src/FieldFactory/ab_exts.jl
@@ -58,14 +58,14 @@ function abelian_fields(gtype::Vector{Int}, conds::Vector{Int}, absolute_discrim
end
function abelian_fields(O::NfOrd, gtype::Vector{Int}, absolute_discriminant_bound::fmpz; only_real::Bool = false, only_complex::Bool = false, tame::Bool = false)
- K = nf(O)
+ K = nf(O)
@assert degree(K)==1
gtype = map(Int, snf(abelian_group(gtype))[1].snf)
n = prod(gtype)
real = only_real
-
+
expo = lcm(gtype)
-
+
#Getting conductors
l_conductors = conductorsQQ(O, gtype, absolute_discriminant_bound, tame)
@vprint :AbExt 1 "Number of conductors: $(length(l_conductors)) \n"
@@ -99,17 +99,17 @@ end
function abelian_normal_extensions(K::AnticNumberField, gtype::Vector{Int}, absolute_discriminant_bound::fmpz; only_real::Bool = false, only_complex::Bool = false, tame::Bool = false, absolute_galois_group::Tuple{Int, Int} = (0, 0))
-
+
@assert !(only_real && only_complex)
O = maximal_order(K)
d = degree(K)
if d == 1
- return abelian_fields(O, gtype, absolute_discriminant_bound, only_real = only_real, tame = tame)
+ return abelian_fields(O, gtype, absolute_discriminant_bound, only_real = only_real, tame = tame)
end
gtype = map(Int, snf(abelian_group(gtype))[1].snf)
n = prod(gtype)
inf_plc = InfPlc[]
-
+
fields = ClassField{MapRayClassGrp, GrpAbFinGenMap}[]
bound = div(absolute_discriminant_bound, abs(discriminant(O))^n)
@@ -120,7 +120,7 @@ function abelian_normal_extensions(K::AnticNumberField, gtype::Vector{Int}, abso
if iseven(n) && !only_real
inf_plc = real_places(K)
end
-
+
Aut = automorphisms(K)
@assert length(Aut) == d #The field is normal over Q
gs = Hecke.small_generating_set(Aut)
@@ -133,7 +133,7 @@ function abelian_normal_extensions(K::AnticNumberField, gtype::Vector{Int}, abso
#Getting conductors
l_conductors = conductors(O, gtype, bound, tame)
@vprint :AbExt 1 "Number of conductors: $(length(l_conductors)) \n"
-
+
ctx = rayclassgrp_ctx(O, expo)
#Now, the big loop
for (i, k) in enumerate(l_conductors)
@@ -186,7 +186,7 @@ function abelian_extensions(K::AnticNumberField, gtype::Vector{Int}, absolute_di
gtype = map(Int, snf(abelian_group(gtype))[1].snf)
n = prod(gtype)
inf_plc = InfPlc[]
-
+
fields = ClassField{MapRayClassGrp, GrpAbFinGenMap}[]
bound = div(absolute_discriminant_bound, abs(discriminant(OK))^n)
if iszero(bound)
@@ -213,7 +213,7 @@ function abelian_extensions(K::AnticNumberField, gtype::Vector{Int}, absolute_di
l_conductors = _sieve_conjugates(auts, l_conductors)
end
@vprint :AbExt 1 "Number of conductors: $(length(l_conductors)) \n"
-
+
ctx = rayclassgrp_ctx(OK, expo)
fsub = (x, y) -> quo(x, y, false)[2]
fsub_distinct = (x, y) -> (quo(x, y, false)[2], sub(x, y, false)[2])
@@ -380,8 +380,8 @@ function valuation_bound_discriminant(n::Int, p::Union{Integer, fmpz})
end
return b
-end
-
+end
+
###########################################################################
#
# Some useful functions
@@ -393,7 +393,7 @@ end
# In output, we get the quotient group as a ZpnGModule
function _action_on_quo(mq::GrpAbFinGenMap, act::Vector{GrpAbFinGenMap})
-
+
q=mq.header.codomain
S,mS=snf(q)
n=Int(S.snf[end])
@@ -443,7 +443,7 @@ function quadratic_fields(bound::Int; tame::Bool=false, real::Bool=false, comple
end
function _quad_ext(bound::Int, only_real::Bool = false; unramified_outside::Vector{fmpz} = fmpz[])
-
+
Qx, x = PolynomialRing(FlintQQ, "x", cached = false)
K = NumberField(x-1, cached = false, check = false)[1]
sqf = squarefree_up_to(bound, prime_base = unramified_outside)
@@ -501,8 +501,8 @@ end
###############################################################################
function C22_extensions(bound::Int)
-
-
+
+
Qx, x=PolynomialRing(FlintZZ, "x")
K, _=NumberField(x-1, cached = false)
Kx,x=PolynomialRing(K,"x", cached=false)
@@ -510,11 +510,11 @@ function C22_extensions(bound::Int)
n=2*b1+1
pairs = _find_pairs(bound)
return (_ext(Kx,x,i,j) for (i, j) in pairs)
-
+
end
function _ext(Ox,x,i,j)
-
+
y=mod(i,4)
pol1 = x^2
if y != 1
@@ -607,12 +607,12 @@ function _C22_with_max_ord(l)
O = NfAbsOrd(S, FakeFmpqMat(M.num, M.den))
O.disc = d1^2*d2^2
d3 = numerator(discriminant(S))
- if d3 < 0
+ if d3 < 0
O.disc = -O.disc
end
O.index = divexact(d3, O.disc)
O.ismaximal = 1
- Hecke._set_maximal_order_of_nf(S, O)
+ Hecke._set_maximal_order_of_nf(S, O)
else
maximal_order(S)
end
@@ -733,14 +733,14 @@ function _find_pairs(bound::Int, only_real::Bool = false; unramified_outside::Ve
for I in it
res[ind] = (ls1[I[1]], ls[I[2]])
ind += 1
- end
+ end
return vcat(res, real_exts)
end
function _from_relative_to_abs(L::NfRelNS{T}, auts::Vector{<: NumFieldMor{NfRelNS{T}, NfRelNS{T}}}) where T
-
+
@vtime :AbExt 2 Ks, mKs = simplified_absolute_field(L, cached = false)
#Now, we have to construct the maximal order of this field.
#I am computing the preimages of mKs by hand, by inverting the matrix.
@@ -754,7 +754,7 @@ function _from_relative_to_abs(L::NfRelNS{T}, auts::Vector{<: NumFieldMor{NfRelN
_set_automorphisms_nf(Ks, closure(autos, degree(Ks)))
@vprint :AbExt 2 "Finished\n"
return Ks, autos
-end
+end
#######################################################################################
@@ -768,8 +768,8 @@ function discriminant_conductor(C::ClassField{MapClassGrp, GrpAbFinGenMap}, boun
end
function discriminant_conductor(C::ClassField, bound::fmpz; lwp::Dict{Tuple{Int, Int}, Vector{GrpAbFinGenElem}} = Dict{Tuple{Int, Int}, Vector{GrpAbFinGenElem}}())
-
- mr = C.rayclassgroupmap
+
+ mr = C.rayclassgroupmap
O = base_ring(C)
n = degree(C)
e = Int(exponent(C))
@@ -801,17 +801,17 @@ function discriminant_conductor(C::ClassField, bound::fmpz; lwp::Dict{Tuple{Int,
else
if haskey(abs_disc, p.minimum)
abs_disc[p.minimum] += qw
- else
+ else
abs_disc[p.minimum] = qw
end
end
end
return true
end
-
+
powers = mr.powers
groups_and_maps = mr.groups_and_maps
-
+
for i = 1:length(powers)
p, q = powers[i]
if p.minimum in primes_done
@@ -832,7 +832,7 @@ function discriminant_conductor(C::ClassField, bound::fmpz; lwp::Dict{Tuple{Int,
else
if haskey(abs_disc, p.minimum)
abs_disc[p.minimum] += qw
- else
+ else
abs_disc[p.minimum] = qw
end
end
@@ -843,7 +843,7 @@ function discriminant_conductor(C::ClassField, bound::fmpz; lwp::Dict{Tuple{Int,
s = lp[p]
@hassert :AbExt 1 s>=2
els=GrpAbFinGenElem[]
- for k=2:lp[p]
+ for k=2:lp[p]
s = s-1
pk = p^s
pv = pk*p
@@ -883,7 +883,7 @@ function discriminant_conductor(C::ClassField, bound::fmpz; lwp::Dict{Tuple{Int,
else
if haskey(abs_disc, p.minimum)
abs_disc[p.minimum] += ap*divexact(d, p.splitting_type[1])
- else
+ else
abs_disc[p.minimum] = ap*divexact(d, p.splitting_type[1])
end
end
@@ -896,20 +896,20 @@ end
#same function but for ray class groups over QQ
function discriminant_conductorQQ(O::NfOrd, C::ClassField, m::Int, bound::fmpz)
-
+
n = degree(C)
discr=fmpz(1)
mp = pseudo_inv(C.quotientmap) * C.rayclassgroupmap
G=domain(mp)
-
+
cyc_prime= isprime(n)==true
-
+
lp=factor(m).fac
abs_disc=Dict{fmpz,Int}()
R=ResidueRing(FlintZZ, m, cached=false)
- for (p,v) in lp
+ for (p,v) in lp
if v==1
ap=n
if cyc_prime
@@ -939,14 +939,14 @@ function discriminant_conductorQQ(O::NfOrd, C::ClassField, m::Int, bound::fmpz)
else
if isodd(p)
s=divexact(m,pow)
- d,a,b=gcdx(pow,s)
+ d,a,b=gcdx(pow,s)
s1=R(1+p)^(p-1)
el=G[1]
if v==2
el=mp\ideal(O,Int((b*s*R(s1)+a*pow).data))
ap-=order(quo(G,GrpAbFinGenElem[el], false)[1])
else
- for k=0:v-2
+ for k=0:v-2
el=mp\ideal(O,Int((b*s*R(s1)^(p^k)+a*pow).data))
ap-=order(quo(G, GrpAbFinGenElem[el], false)[1])
@hassert :AbExt 1 ap>0
@@ -961,7 +961,7 @@ function discriminant_conductorQQ(O::NfOrd, C::ClassField, m::Int, bound::fmpz)
end
else
s=divexact(m,2^v)
- d,a,b=gcdx(2^v,s)
+ d,a,b=gcdx(2^v,s)
el=0*G[1]
for k=v-3:-1:0
el=mp\ideal(O,Int((R(5)^(2^k)*b*s+a*2^v).data))
@@ -985,20 +985,20 @@ function discriminant_conductorQQ(O::NfOrd, C::ClassField, m::Int, bound::fmpz)
end
function discriminantQQ(O::NfOrd, C::ClassField, m::Int)
-
+
discr=fmpz(1)
n = degree(C)
mp = pseudo_inv(C.quotientmap) * C.rayclassgroupmap
G = domain(mp)
-
+
cyc_prime= isprime(n)==true
-
+
lp=factor(m).fac
abs_disc=Dict{fmpz,Int}()
R=ResidueRing(FlintZZ, m, cached=false)
- for (p,v) in lp
+ for (p,v) in lp
if v==1
ap=n
if cyc_prime
@@ -1023,14 +1023,14 @@ function discriminantQQ(O::NfOrd, C::ClassField, m::Int)
else
if isodd(p)
s=divexact(m,pow)
- d,a,b=gcdx(pow,s)
+ d,a,b=gcdx(pow,s)
s1=R(1+p)^(p-1)
el=G[1]
if v==2
el=mp\ideal(O,Int((b*s*R(s1)+a*pow).data))
ap-=order(quo(G,GrpAbFinGenElem[el], false)[1])
else
- for k=0:v-2
+ for k=0:v-2
el=mp\ideal(O,Int((b*s*R(s1)^(p^k)+a*pow).data))
ap-=order(quo(G, GrpAbFinGenElem[el], false)[1])
@hassert :AbExt 1 ap>0
@@ -1045,7 +1045,7 @@ function discriminantQQ(O::NfOrd, C::ClassField, m::Int)
end
else
s=divexact(m,2^v)
- d,a,b=gcdx(2^v,s)
+ d,a,b=gcdx(2^v,s)
el=0*G[1]
for k=v-3:-1:0
el=mp\ideal(O,Int((R(5)^(2^k)*b*s+a*2^v).data))
@@ -1082,9 +1082,9 @@ function _is_conductor_min_normal(C::Hecke.ClassField; lwp::Dict{Int, Vector{Grp
if isempty(lp)
return true
end
-
+
a = minimum(defining_modulus(mr)[1])
- mp = pseudo_inv(C.quotientmap) * mr
+ mp = pseudo_inv(C.quotientmap) * mr
R = domain(mp)
e = Int(exponent(C))
O = base_ring(C)
@@ -1096,7 +1096,7 @@ function _is_conductor_min_normal(C::Hecke.ClassField; lwp::Dict{Int, Vector{Grp
primes_done = fmpz[]
for i = 1:length(powers)
p, q = powers[i]
- if p.minimum in primes_done
+ if p.minimum in primes_done
continue
end
push!(primes_done, p.minimum)
@@ -1134,7 +1134,7 @@ function _is_conductor_min_normal(C::Hecke.ClassField; lwp::Dict{Int, Vector{Grp
end
end
return true
-end
+end
#
# Same function as above, but in the assumption that the map comes from a ray class group over QQ
@@ -1147,10 +1147,10 @@ function _is_conductor_minQQ(C::Hecke.ClassField, n::Int)
m = defining_modulus(mr)[1]
mm = Int(minimum(m))
lp = factor(mm)
-
+
O=order(m)
K=nf(O)
-
+
R=ResidueRing(FlintZZ, mm, cached=false)
for (p,v) in lp.fac
if isodd(p)
@@ -1158,11 +1158,11 @@ function _is_conductor_minQQ(C::Hecke.ClassField, n::Int)
x=_unit_grp_residue_field_mod_n(Int(p), n)[1]
s=divexact(mm,Int(p))
d,a,b=gcdx(s,Int(p))
- l=a*s*R(x)+p*b
+ l=a*s*R(x)+p*b
if iszero(mp\(ideal(O,Int(l.data))))
return false
end
- else
+ else
s=divexact(mm,p^v)
d,a,b=gcdx(s,p^v)
x=a*s*R(1+p)^((p-1)*p^(v-2))+p^v*b
@@ -1193,7 +1193,7 @@ function _is_conductor_minQQ(C::Hecke.ClassField, n::Int)
end
return true
-end
+end
#Returns the cyclic extension of prime degree i with minimal discriminant
diff --git a/src/FieldFactory/abelian_layer.jl b/src/FieldFactory/abelian_layer.jl
index 98e6dccfe9..3eb3eba794 100644
--- a/src/FieldFactory/abelian_layer.jl
+++ b/src/FieldFactory/abelian_layer.jl
@@ -11,10 +11,10 @@ function _real_level(L::GAP.GapObj)
G = L[1]
ElemsG = GAP.Globals.Elements(G)
for i = 1:length(ElemsG)
- g = ElemsG[i]
+ g = ElemsG[i]
if GAP.Globals.Order(g) == 2
push!(lElem, g)
- end
+ end
end
S = GAP.Globals.Subgroup(G, GAP.julia_to_gap(lElem))
#Now, I check containment.
@@ -36,7 +36,7 @@ end
###############################################################################
function abelian_extensionsQQ(gtype::Vector{Int}, bound::fmpz, only_real::Bool = false; unramified_outside::Vector{fmpz} = fmpz[])
-
+
gtype = map(Int, snf(abelian_group(gtype))[1].snf)
#Easy case: quadratic and biquadratic extensions
if gtype == [2]
@@ -94,31 +94,31 @@ function abelian_extensionsQQ(gtype::Vector{Int}, bound::fmpz, only_real::Bool =
end
@vprint :Fields 1 "\e[1F$(Hecke.set_cursor_col())$(Hecke.clear_to_eol())"
return list1
-
+
end
function _abelian_extensionsQQ(gtype::Vector{Int}, absolute_discriminant_bound::fmpz, only_real::Bool = false; unramified_outside::Vector{fmpz} = fmpz[])
-
+
Qx, x = PolynomialRing(FlintQQ, "x", cached = false)
K, _ = NumberField(x-1, "a", cached = false)
O = maximal_order(K)
n = prod(gtype)
expo = lcm(gtype)
-
+
#Getting conductors
l_conductors = Hecke.conductorsQQ(O, gtype, absolute_discriminant_bound; unramified_outside = unramified_outside)
sort!(l_conductors, rev = true)
len = length(l_conductors)
@vprint :Fields 1 "Number of conductors: $(len) \n\n"
@vprint :FieldsNonFancy 1 "Number of conductors: $(len) \n"
-
-
+
+
complex = iseven(expo) && !only_real
-
+
#Now, the big loop
class_fields = Vector{Hecke.ClassField{MapRayClassGrp, GrpAbFinGenMap}}()
for (i, k) in enumerate(l_conductors)
- if iszero(mod(i, 1000))
+ if iszero(mod(i, 1000))
pt = len - i
@vprint :Fields 1 "\e[1F$(Hecke.set_cursor_col())$(Hecke.clear_to_eol()) Conductors to test: $(pt)\n"
end
@@ -158,9 +158,9 @@ function check_extension(C::Hecke.ClassField, bound::fmpz, Dcond::Dict, Ddisc::D
if !fl2
return false
end
- @vtime :Fields 3 fl3 = Hecke.discriminant_conductor(C, bound, lwp = Ddisc)
+ @vtime :Fields 3 fl3 = Hecke.discriminant_conductor(C, bound, lwp = Ddisc)
return fl3
-
+
end
function _construct_grp(IdH::GAP.GapObj, uncom::Int)
@@ -173,7 +173,7 @@ function _construct_grp(IdH::GAP.GapObj, uncom::Int)
for i = 1:length(gens)
o = GAP.Globals.Order(gens[i])
ex = ppio(o, uncom)[1]
- push!(new_gens, gens[i]^ex)
+ push!(new_gens, gens[i]^ex)
end
S = GAP.Globals.Subgroup(G, GAP.julia_to_gap(new_gens))
Q = GAP.Globals.FactorGroup(G, S)
@@ -186,14 +186,14 @@ function max_ramified_prime(O::NfOrd, gtype::Vector{Int}, bound::fmpz)
fac = factor(n)
m = Int(minimum(keys(fac.fac)))
k = divexact(n, m)
- b1 = Int(root(bound, degree(O)*(m-1)*k))
+ b1 = Int(root(bound, degree(O)*(m-1)*k))
return b1
end
function _abelian_normal_extensions(F::FieldsTower, gtype::Vector{Int}, absbound::fmpz, IdCheck::GAP.GapObj, only_real::Bool, IdG::GAP.GapObj; unramified_outside::Vector{fmpz} = fmpz[])
K = F.field
- O = maximal_order(K)
+ O = maximal_order(K)
n = prod(gtype)
inf_plc = Vector{InfPlc}()
if abs(discriminant(O))^n > absbound
@@ -270,7 +270,7 @@ function _abelian_normal_extensions(F::FieldsTower, gtype::Vector{Int}, absbound
end
end
@vprint :Fields 3 "\n\n"
- end
+ end
if isempty(class_fields_with_act)
return Vector{Hecke.ClassField{Hecke.MapRayClassGrp, GrpAbFinGenMap}}[]
end
@@ -289,10 +289,10 @@ end
################################################################################
function from_class_fields_to_fields(class_fields::Vector{ClassField{MapRayClassGrp, GrpAbFinGenMap}}, autos::Vector{NfToNfMor}, grp_to_be_checked::Dict{Int, GAP.GapObj}, target_group::GAP.GapObj)
-
+
if isempty(class_fields)
@vprint :Fields 1 "\e[1F$(Hecke.set_cursor_col())$(Hecke.clear_to_eol())"
- return Tuple{Hecke.NfRelNS{nf_elem}, Vector{Hecke.NfRelNSToNfRelNSMor_nf_elem}}[]
+ return Tuple{Hecke.NfRelNS{nf_elem}, Vector{Hecke.NfRelNSToNfRelNSMor_nf_elem}}[]
end
K = base_ring(class_fields[1])
divisors_of_n = collect(keys(grp_to_be_checked))
@@ -311,7 +311,7 @@ function from_class_fields_to_fields(class_fields::Vector{ClassField{MapRayClass
end
idE = grp_to_be_checked[p]
if iszero(mod(order(torsion_unit_group(maximal_order(K))[1]), p^(valuation(exponent(class_fields[1]), p))))
- #In this case, since we already know the class group of K and the RCF requires K(zeta_p^v) = K,
+ #In this case, since we already know the class group of K and the RCF requires K(zeta_p^v) = K,
#we compute the class field directly over K
compute_fields(cfieldsp, autos, idE, right_grp)
pclassfields[ind] = cfieldsp
@@ -321,7 +321,7 @@ function from_class_fields_to_fields(class_fields::Vector{ClassField{MapRayClass
#Now, we check whether the abelian extensions can be realized over a subfield from a group theoretical point of view.
E = GAP.Globals.SmallGroup(idE)
S, H, ab_inv = max_ab_norm_sub_containing(E)
- if S == H
+ if S == H
#No, it can't.
compute_fields(cfieldsp, autos, idE, right_grp)
pclassfields[ind] = cfieldsp
@@ -370,11 +370,11 @@ function from_class_fields_to_fields(class_fields::Vector{ClassField{MapRayClass
end
end
return fields
-
+
end
function compute_fields(class_fields::Vector{Hecke.ClassField{Hecke.MapRayClassGrp, GrpAbFinGenMap}}, autos::Vector{NfToNfMor}, grp_to_be_checked::GAP.GapObj, right_grp)
-
+
use_brauer = true
it = findall(right_grp)
K = base_field(class_fields[it[1]])
@@ -385,7 +385,7 @@ function compute_fields(class_fields::Vector{Hecke.ClassField{Hecke.MapRayClassG
fields = Tuple{Hecke.NfRelNS{nf_elem}, Vector{Hecke.NfRelNSToNfRelNSMor_nf_elem}}[]
expo = Int(exponent(codomain(class_fields[it[1]].quotientmap)))
-
+
if !use_brauer
set_up_cycl_ext(K, expo, autos)
end
@@ -394,7 +394,7 @@ function compute_fields(class_fields::Vector{Hecke.ClassField{Hecke.MapRayClassG
C = class_fields[i]
L = number_field(C, using_norm_relation = use_brauer)
autL = Hecke.absolute_automorphism_group(C, autos)
- if !isone(gcd(degree(K), expo))
+ if !isone(gcd(degree(K), expo))
Cpperm = permutation_group(autL)
if GAP.Globals.IdGroup(Cpperm) != grp_to_be_checked
right_grp[i] = false
@@ -427,7 +427,7 @@ function _ext_and_autos(resul::Vector{Hecke.ClassField{S, T}}, autos::Vector{NfT
w = 1
while mod(degree(pols[w]), p) != 0
w += 1
- end
+ end
auts = Cp.AbsAutGrpA
for phi in auts
if (isdefined(phi.image_data.base_field_map_data, :prim_image) ? phi.image_data.base_field_map_data.prim_image : codomain(phi)(gen(base_field(codomain(phi))))) == codomain(phi)(gen(K))
@@ -478,7 +478,7 @@ function set_up_cycl_ext(K::AnticNumberField, n::Int, autK::Vector{NfToNfMor})
end
function _action(t::Hecke.GrpAbFinGenMap, act::Vector{Hecke.GrpAbFinGenMap})
-
+
T = codomain(t)
S, mS = snf(T)
new_act = Vector{Hecke.GrpAbFinGenMap}(undef, length(act))
@@ -487,7 +487,7 @@ function _action(t::Hecke.GrpAbFinGenMap, act::Vector{Hecke.GrpAbFinGenMap})
new_act[i] = Hecke.GrpAbFinGenMap(S, S, res)
end
return new_act
-
+
end
################################################################################
@@ -497,7 +497,7 @@ end
################################################################################
function max_ab_norm_sub_containing(G::GAP.GapObj)
-
+
D = GAP.Globals.DerivedSeries(G)
H = D[end-1]
G1 = GAP.Globals.Centralizer(G, H)
@@ -602,7 +602,7 @@ function computing_over_subfields(class_fields, subfields, idE, autos, right_grp
fields[ind] = (C.A, C.AbsAutGrpA)
ind += 1
end
- return fields
+ return fields
end
@@ -640,7 +640,7 @@ function translate_extensions(mL::NfToNfMor, class_fields, new_class_fields, ctx
for (p, v) in fM0
p1 = Hecke.intersect_prime(mL, p)
if !haskey(fm0, p1)
- if iscoprime(minimum(p1, copy = false), n)
+ if iscoprime(minimum(p1, copy = false), n)
fm0[p1] = 1
else
fm0[p1] = v
@@ -652,14 +652,14 @@ function translate_extensions(mL::NfToNfMor, class_fields, new_class_fields, ctx
#Now, I have problems, so I need to add the ramification of the other extension.
for (p, v) in f
if !haskey(fm0, p)
- if isone(gcd(minimum(p), n))
+ if isone(gcd(minimum(p), n))
fm0[p] = 1
else
fm0[p] = v
end
else
- if !isone(gcd(minimum(p), n))
- fm0[p] = max(v, fm0[p])
+ if !isone(gcd(minimum(p), n))
+ fm0[p] = max(v, fm0[p])
end
end
lPP = prime_decomposition(mL, p)
@@ -672,7 +672,7 @@ function translate_extensions(mL::NfToNfMor, class_fields, new_class_fields, ctx
end
end
infplc = InfPlc[]
- if iszero(mod(n, 2))
+ if iszero(mod(n, 2))
infplc = real_places(L)
end
@vprint :Fields 3 "Checking if I can compute $(indclf) over a subfield\n\n "
@@ -680,10 +680,10 @@ function translate_extensions(mL::NfToNfMor, class_fields, new_class_fields, ctx
if exponent(r) < n || order(r) < degree(C)
push!(to_be_done, indclf)
continue
- end
+ end
#Now, the norm group of K over L
@vtime :Fields 3 ngL, mngL = Hecke.norm_group(mL, mr, prod(ab_invariants_mod))
- @hassert :Fields 1 divisible(divexact(fmpz(degree(codomain(mL))), degree(domain(mL))), divexact(order(r), order(ngL)))
+ @hassert :Fields 1 divisible(divexact(fmpz(degree(codomain(mL))), degree(domain(mL))), divexact(order(r), order(ngL)))
if !divisible(order(ngL), degree(C)) || !divisible(exponent(C), n)
push!(to_be_done, indclf)
continue
@@ -698,7 +698,7 @@ function translate_extensions(mL::NfToNfMor, class_fields, new_class_fields, ctx
fM0[p] = max(v, fM0[p])
else
fM0[p] = v
- end
+ end
end
end
inf_plc2 = InfPlc[]
@@ -727,7 +727,7 @@ function translate_extensions(mL::NfToNfMor, class_fields, new_class_fields, ctx
@hassert :Fields 1 isisomorphic(cokernel(mk, false)[1], codomain(C.quotientmap))
mp = mk*proj
ck, mck = cokernel(mp, false)
- #If everything could work, then ck should be the direct product of the abelian extension I am searching for and
+ #If everything could work, then ck should be the direct product of the abelian extension I am searching for and
#the maximal abelian subextension of K/L
G1 = snf(cokernel(mngL, false)[1])[1]
G2 = snf(codomain(C.quotientmap))[1]
@@ -740,7 +740,7 @@ function translate_extensions(mL::NfToNfMor, class_fields, new_class_fields, ctx
fl, ms1 = has_complement(ms)
@assert fl
mq1 = cokernel(ms1, false)[2]
- mqq = mck * mq1
+ mqq = mck * mq1
@hassert :Fields 1 domain(mqq) == r
C1 = ray_class_field(mr, mqq)
number_field(C1)
@@ -749,7 +749,7 @@ function translate_extensions(mL::NfToNfMor, class_fields, new_class_fields, ctx
end
@vprint :Fields 1 "$(Hecke.set_cursor_col())$(Hecke.clear_to_eol())"
return to_be_done
-
+
end
function create_sub(ss, iso, PermGAP, auts, K)
@@ -765,7 +765,7 @@ function create_sub(ss, iso, PermGAP, auts, K)
end
function compute_subfields(K::AnticNumberField, E, H, S)
-
+
proj = GAP.Globals.NaturalHomomorphismByNormalSubgroup(E, H)
Hn = GAP.Globals.ImagesSource(proj)
imgsS = GAP.Globals.Image(proj, S)
@@ -776,7 +776,7 @@ function compute_subfields(K::AnticNumberField, E, H, S)
Sn = GAP.Globals.Image(varphi, imgsS)
if !(Sn in orbitS)
push!(orbitS, Sn)
- end
+ end
end
auts = automorphisms(K, copy = false)
Hperm = _from_autos_to_perm(auts)
@@ -801,7 +801,7 @@ function translate_class_field_down(subfields, class_fields, it, ab_invariants)
for mL in subfields
push!(created_subfields, mL)
to_be_done_new = translate_extensions(mL, class_fields, new_class_fields, ctxK, it, ab_invariants)
- if length(to_be_done_new) == 0
+ if length(to_be_done_new) == 0
return new_class_fields, created_subfields, to_be_done_new
end
to_be_done = to_be_done_new
@@ -836,7 +836,7 @@ function translate_fields_up(class_fields, new_class_fields, subfields, it)
mul!(img, img, gen(CEK.Kr))
end
end
- mrel = hom(CEL.Kr, CEK.Kr, mL, img)
+ mrel = hom(CEL.Kr, CEK.Kr, mL, img)
#@hassert :Fields 1 isconsistent(mrel)
g = mrel(CEL.mp[1](gen(CEL.Ka)))
mp = hom(CEL.Ka, CEK.Ka, CEK.mp[1]\(g), check = false)
@@ -871,7 +871,7 @@ function translate_fields_up(class_fields, new_class_fields, subfields, it)
mrel2 = hom(Ccyc.K, Cpp.K, D[d], gen(Cpp.K))
#@hassert :Fields 1 isconsistent(mrel2)
@hassert :Fields 1 parent(Ccyc.pe) == domain(mrel2)
- Cpp.pe = mrel2(Ccyc.pe)
+ Cpp.pe = mrel2(Ccyc.pe)
CEKK = cyclotomic_extension(K, d)
@hassert :Fields 1 iszero(map_coefficients(CEKK.mp[2], fdef, cached = false)(Cpp.pe))
Cpp.o = d1
diff --git a/src/FieldFactory/brauer.jl b/src/FieldFactory/brauer.jl
index 9d02c6f2eb..5844c1d765 100644
--- a/src/FieldFactory/brauer.jl
+++ b/src/FieldFactory/brauer.jl
@@ -4,12 +4,12 @@ add_verbose_scope(:BrauerObst)
################################################################################
#
# Obstruction Interface
-#
+#
################################################################################
function check_obstruction(list::Vector{FieldsTower}, L::GAP.GapObj,
i::Int, invariants::Vector{Int})
-
+
d = degree(list[1])
common_degree = ppio(invariants[end], d)[1]
@vprint :BrauerObst 1 "Computing cocycles\n"
@@ -56,12 +56,12 @@ function check_obstruction(list::Vector{FieldsTower}, L::GAP.GapObj,
end
for (p, v) in fac
@vprint :BrauerObst 1 "Checking obstructions at $p \n"
- cocycles_p_start = cocycle_ctx[_to_prime_power_kernel(x, Int(p)) for x in cocycles]
+ cocycles_p_start = cocycle_ctx[_to_prime_power_kernel(x, Int(p)) for x in cocycles]
indices_non_split = Int[]
for i = 1:length(cocycles_p_start)
@vprint :BrauerObst 1 "Checking if cocycle $i splits \n"
if !iszero(cocycles_p_start[i])
- push!(indices_non_split, i)
+ push!(indices_non_split, i)
end
end
if isempty(indices_non_split)
@@ -72,7 +72,7 @@ function check_obstruction(list::Vector{FieldsTower}, L::GAP.GapObj,
for i = 1:length(list)
@vprint :Fields 1 "$(Hecke.set_cursor_col())$(Hecke.clear_to_eol())Fields to test: $(length(list)-i+1)"
if !all(obstructions[i])
- obstructions_i = check_obstruction(list[i], cocycles_p, Int(p), obstructions[i])
+ obstructions_i = check_obstruction(list[i], cocycles_p, Int(p), obstructions[i])
for j = 1:length(obstructions_i)
obstructions[i][indices_non_split[j]] = obstructions_i[j]
end
@@ -87,7 +87,7 @@ function check_obstruction(list::Vector{FieldsTower}, L::GAP.GapObj,
for i = 1:length(list)
@vprint :Fields 1 "$(Hecke.set_cursor_col())$(Hecke.clear_to_eol())Fields to test: $(length(list)-i+1)"
if !all(obstructions[i])
- obstructions_i = check_obstruction_non_cyclic(list[i], all_cocycles, Int(p), obstructions[i])
+ obstructions_i = check_obstruction_non_cyclic(list[i], all_cocycles, Int(p), obstructions[i])
for j = 1:length(obstructions_i)
obstructions[i][indices_non_split[j]] = obstructions_i[j]
end
@@ -111,10 +111,10 @@ function check_obstruction(list::Vector{FieldsTower}, L::GAP.GapObj,
end
-function check_obstruction(F::FieldsTower, cocycles::Vector{cocycle_ctx},
+function check_obstruction(F::FieldsTower, cocycles::Vector{cocycle_ctx},
p::Int, obstruction_at::Vector{Bool})
#I assume that the kernel of the embedding problem is a p-group
- @assert isprime(p)
+ @assert isprime(p)
indices = [i for i = 1:length(obstruction_at) if !obstruction_at[i]]
cocycles_to_test = cocycles[indices]
for i = 1:length(cocycles)
@@ -193,9 +193,9 @@ end
#
################################################################################
-function check_obstruction_non_cyclic(F::FieldsTower, cocycles::Vector{Vector{cocycle_ctx}},
+function check_obstruction_non_cyclic(F::FieldsTower, cocycles::Vector{Vector{cocycle_ctx}},
p::Int, obstruction_at::Vector{Bool})
-
+
indices = Int[i for i = 1:length(obstruction_at) if !obstruction_at[i]]
new_cocycles = cocycles[indices]
for j = 1:length(new_cocycles)
@@ -275,7 +275,7 @@ function _cocycles_with_cyclic_kernel(old_cocycle::cocycle_ctx, p::Int)
np = remove(order, p)[2]
if isone(np) && GAP.Globals.IsCyclic(fg)
push!(normal_cyclic_and_contained, prmg)
- end
+ end
end
#Almost done. I only want the minimal ones, so I need to sieve.
res = GAP.GapObj[]
@@ -319,7 +319,7 @@ function _to_subgroup_of_kernel(cocycle::cocycle_ctx, S)
for i = 1:length(gensA_new)
el_A = GAP.Globals.PreImagesRepresentative(pr, gensA_new[i])
el_E = GAP.Globals.Image(cocycle.inclusion, el_A)
- push!(images_inclusion, GAP.Globals.Image(pr1, el_E))
+ push!(images_inclusion, GAP.Globals.Image(pr1, el_E))
end
inclusion = GAP.Globals.GroupHomomorphismByImages(A_new, E_new, gensA_new, GAP.julia_to_gap(images_inclusion))
gensE_new = GAP.Globals.GeneratorsOfGroup(E_new)
@@ -330,7 +330,7 @@ function _to_subgroup_of_kernel(cocycle::cocycle_ctx, S)
end
projection = GAP.Globals.GroupHomomorphismByImages(E_new, G, gensE_new, GAP.julia_to_gap(images_proj))
local new_coc
- let cocycle = cocycle, pr = pr
+ let cocycle = cocycle, pr = pr
function new_coc(x::GAP.GapObj, y::GAP.GapObj)
return GAP.Globals.Image(pr, cocycle.cocycle(x, y))
end
@@ -370,7 +370,7 @@ function _to_prime_power_kernel(cocycle::cocycle_ctx, p::Int)
for i = 1:length(gensA_new)
el_A = GAP.Globals.PreImagesRepresentative(pr, gensA_new[i])
el_E = GAP.Globals.Image(cocycle.inclusion, el_A)
- push!(images_inclusion, GAP.Globals.Image(pr1, el_E))
+ push!(images_inclusion, GAP.Globals.Image(pr1, el_E))
end
inclusion = GAP.Globals.GroupHomomorphismByImages(A_new, E_new, gensA_new, GAP.julia_to_gap(images_inclusion))
gensE_new = GAP.Globals.GeneratorsOfGroup(E_new)
@@ -381,7 +381,7 @@ function _to_prime_power_kernel(cocycle::cocycle_ctx, p::Int)
end
projection = GAP.Globals.GroupHomomorphismByImages(E_new, G, gensE_new, GAP.julia_to_gap(images_proj))
local new_coc
- let cocycle = cocycle, pr = pr
+ let cocycle = cocycle, pr = pr
function new_coc(x::GAP.GapObj, y::GAP.GapObj)
return GAP.Globals.Image(pr, cocycle.cocycle(x, y))
end
@@ -499,7 +499,7 @@ function cocycles_computation(GG, HH, KK)
mH1 = GAP.Globals.NaturalHomomorphismByNormalSubgroup(target_grp, GAP.Globals.Image(proj, KK))
H1 = GAP.Globals.ImagesSource(mH1)
K = GAP.Globals.Kernel(mH1)
-
+
Elems = GAP.Globals.Elements(H1)
MatCoc = Matrix{GAP.GapObj}(undef, length(Elems), length(Elems))
Preimags = Vector{GAP.GapObj}(undef, length(Elems))
@@ -519,7 +519,7 @@ function cocycles_computation(GG, HH, KK)
MatCoc[i, j] = x1*y1*GAP.Globals.Inverse(xy1)
end
end
-
+
@vprint :BrauerObst 1 "Listing automorphisms \n"
autos = _autos_to_check(H1, K, target_grp, mH1)
cocycles = Vector{cocycle_ctx}(undef, length(autos))
@@ -527,7 +527,7 @@ function cocycles_computation(GG, HH, KK)
aut1, aut2 = autos[i]
local cocycle
let Elems = Elems, MatCoc = MatCoc, aut1 = aut1, aut2 = aut2, Elems = Elems
- function cocycle(x::GAP.GapObj, y::GAP.GapObj)
+ function cocycle(x::GAP.GapObj, y::GAP.GapObj)
new_x = GAP.Globals.PreImagesRepresentative(aut1, x)
new_y = GAP.Globals.PreImagesRepresentative(aut1, y)
ind1 = 1
@@ -544,7 +544,7 @@ function cocycles_computation(GG, HH, KK)
#I change aut2 so that its codomain is really target_grp
new_aut2 = aut2*GAP.Globals.GroupHomomorphismByImages(K, target_grp, GAP.Globals.GeneratorsOfGroup(K), GAP.Globals.GeneratorsOfGroup(K))
cocycles[i] = cocycle_ctx(mH1*aut1, new_aut2, cocycle)
- end
+ end
return cocycles
end
@@ -575,7 +575,7 @@ function _find_exp(x::GAP.GapObj, y::GAP.GapObj)
while z != y
z = z*x
i += 1
- end
+ end
#@assert x^i == y
return i
end
@@ -604,7 +604,7 @@ function pSylow(Gperm::GAP.GapObj, permGAP::Vector{GAP.GapObj}, G::Vector{NfToNf
j += 1
end
end
- return Gp
+ return Gp
end
function pSylow(G::Vector{NfToNfMor}, p::Int)
@@ -612,7 +612,7 @@ function pSylow(G::Vector{NfToNfMor}, p::Int)
if uncom == 1
return G
end
- permGC = _from_autos_to_perm(G)
+ permGC = _from_autos_to_perm(G)
Gperm = _perm_to_gap_grp(permGC)
PermGAP = Vector{GAP.GapObj}(undef, length(permGC))
for w = 1:length(permGC)
@@ -692,8 +692,8 @@ function _obstruction_prime_no_extend(x::FieldsTower, cocycles, p::Int)
pol = Rx(image_primitive_element(g))
el = D[g]
D1[pol] = el
- end
- obstruction = falses(length(cocycles))
+ end
+ obstruction = falses(length(cocycles))
for i = 1:length(obstruction)
if isdefined(cocycles[i], :inclusion_of_pSylow)
#I need to assert that I took the right pSylow.
@@ -738,7 +738,7 @@ function _obstruction_prime(x::FieldsTower, cocycles::Vector{cocycle_ctx}, p)
autsK1 = automorphisms(K1, copy = false)
restr = restriction(autsK1, autsK, Kc.mp[2])
#I construct the group and the isomorphisms between the automorphisms and the gap group.
- permGC = _from_autos_to_perm(autsK)
+ permGC = _from_autos_to_perm(autsK)
Gperm = _perm_to_gap_grp(permGC)
Pcomp = 2
R = GF(Pcomp, cached = false)
@@ -756,7 +756,7 @@ function _obstruction_prime(x::FieldsTower, cocycles::Vector{cocycle_ctx}, p)
dautsK1 = Dict{gfp_poly, Int}()
for w = 1:length(autsK1)
dautsK1[Rx(image_primitive_element(autsK1[w]))] = w
- end
+ end
#Restrict to the p-Sylow
#Unfortunately, I need to compute the group structure.
Gp = pSylow(autsK1, p)
@@ -783,7 +783,7 @@ function _obstruction_prime(x::FieldsTower, cocycles::Vector{cocycle_ctx}, p)
return mod(rescoc, p)::Int
end
end
-
+
if !issplit_cpa(x, Gp, cocycle, p, 1, Rx)
obstruction[i] = true
end
@@ -888,7 +888,7 @@ function check_obstruction_pp(F::FieldsTower, cocycles::Vector{cocycle_ctx}, n::
#=
lp = ramified_primes(F)
assure_automorphisms(F)
-
+
v, p = ispower(n)
if all(x -> (isone(mod(x, n)) || x == p), lp)
return _obstruction_pp_no_extend(F, cocycles, n)
@@ -914,7 +914,7 @@ function _obstruction_pp(F::FieldsTower, cocycles::Vector{cocycle_ctx}, pv::Int)
autsK1 = automorphisms(K1, copy = false)
restr = restriction(autsK1, autsK, Kc.mp[2])
#I construct the group and the isomorphisms between the automorphisms and the gap group.
- permGC = _from_autos_to_perm(autsK)
+ permGC = _from_autos_to_perm(autsK)
Gperm = _perm_to_gap_grp(permGC)
Pcomp = 7
R = GF(Pcomp, cached = false)
@@ -931,7 +931,7 @@ function _obstruction_pp(F::FieldsTower, cocycles::Vector{cocycle_ctx}, pv::Int)
dautsK1 = Dict{gfp_poly, Int}()
for w = 1:length(autsK1)
dautsK1[Rx(image_primitive_element(autsK1[w]))] = w
- end
+ end
#Restrict to the p-Sylow
#Unfortunately, I need to compute the group structure.
Gp = pSylow(autsK1, p)
@@ -970,7 +970,7 @@ function _obstruction_pp(F::FieldsTower, cocycles::Vector{cocycle_ctx}, pv::Int)
return mod(rescoc, pv)::Int
end
end
- #I have to find the subgroup of Gp such that the action of Gp on the roots of unity
+ #I have to find the subgroup of Gp such that the action of Gp on the roots of unity
#coincides with the action on the kernel
Stab = NfToNfMor[]
inclusion = cocycles[i].inclusion
@@ -996,7 +996,7 @@ function _obstruction_pp(F::FieldsTower, cocycles::Vector{cocycle_ctx}, pv::Int)
if !fl
obstruction[i] = true
end
-
+
end
return obstruction
end
@@ -1006,7 +1006,7 @@ function _obstruction_pp_no_extend(F::FieldsTower, cocycles::Vector{cocycle_ctx}
K = F.field
autsK = automorphisms(K, copy = false)
#I construct the group and the isomorphisms between the automorphisms and the gap group.
- permGC = _from_autos_to_perm(autsK)
+ permGC = _from_autos_to_perm(autsK)
Gperm = _perm_to_gap_grp(permGC)
Pcomp = 7
R = GF(Pcomp, cached = false)
@@ -1021,7 +1021,7 @@ function _obstruction_pp_no_extend(F::FieldsTower, cocycles::Vector{cocycle_ctx}
dautsK = Dict{gfp_poly, Int}()
for w = 1:length(autsK)
dautsK[Rx(image_primitive_element(autsK[w]))] = w
- end
+ end
H = GAP.Globals.ImagesSource(cocycles[1].projection)
iso = GAP.Globals.IsomorphismGroups(Gperm, H)
ElemGAP = Vector{GAP.GapObj}(undef, length(permGC))
@@ -1042,7 +1042,7 @@ function _obstruction_pp_no_extend(F::FieldsTower, cocycles::Vector{cocycle_ctx}
return mod(rescoc, pv)::Int
end
end
- #I have to find the subgroup of Gp such that the action of Gp on the roots of unity
+ #I have to find the subgroup of Gp such that the action of Gp on the roots of unity
#coincides with the action on the kernel
Stab = NfToNfMor[]
inclusion = cocycles[i].inclusion
@@ -1064,10 +1064,10 @@ function _obstruction_pp_no_extend(F::FieldsTower, cocycles::Vector{cocycle_ctx}
if !issplit_cpa(F, Stab, cocycle, p, v, Rx)
obstruction[i] = true
end
-
+
end
- return obstruction
+ return obstruction
end
################################################################################
@@ -1079,7 +1079,7 @@ end
function issplit_cpa(F::FieldsTower, G::Vector{NfToNfMor}, Coc::Function, p::Int, v::Int, Rx::GFPPolyRing)
K = F.field
@vtime :BrauerObst 1 if p == 2 && istotally_complex(K) && !is_split_at_infinity(K, G, Coc, Rx)
- return false
+ return false
end
# Now, the finite primes.
# The crossed product algebra is ramified at the ramified primes of the field (and at the primes dividing the values
@@ -1090,7 +1090,7 @@ function issplit_cpa(F::FieldsTower, G::Vector{NfToNfMor}, Coc::Function, p::Int
lp = ramified_primes(F)
if p in lp || !(F.isabelian || (length(G) == degree(K)))
for q in lp
- if q != p
+ if q != p
@vtime :BrauerObst 1 fl = issplit_at_p(F, G, Coc, Int(q), p^v, Rx)
if !fl
return false
@@ -1106,7 +1106,7 @@ function issplit_cpa(F::FieldsTower, G::Vector{NfToNfMor}, Coc::Function, p::Int
end
end
end
- return true
+ return true
end
function is_split_at_infinity(K::AnticNumberField, G::Vector{NfToNfMor}, Coc::Function, Rx::GFPPolyRing)
@@ -1167,7 +1167,7 @@ function _find_theta(G::Vector{NfToNfMor}, F::FqNmodFiniteField, mF::Hecke.NfOrd
#img = compose_mod(theta_q, igFq, fmod)
#res = O(lift(K, img), false)
#I make sure that the element is a generator of the inertia subgroup
- if mF(res) == gF
+ if mF(res) == gF
theta_q = Rt(image_primitive_element(theta))
pp = theta_q
for i = 2:t
@@ -1213,7 +1213,7 @@ function _find_frob(G::Vector{NfToNfMor}, F::FqNmodFiniteField, mF::Hecke.NfOrdT
end
frob_q = Rt(image_primitive_element(frob))
#Now, I check the relation
- #gc = frob * theta
+ #gc = frob * theta
gc = compose_mod(frob_q, theta_q, fmod)
#gq = (theta^expo) * frob
#TODO: Binary powering
@@ -1268,7 +1268,7 @@ function issplit_at_P(O::NfOrd, G::Vector{NfToNfMor}, Coc::Function, P::NfOrdIdl
if f == 1 && iszero(mod(c, n))
return true
end
- end
+ end
@vtime :BrauerObst 1 Gp = decomposition_group(P, G = G, orderG = e*f)
InGrp = inertia_subgroup(P, G = Gp)
e = length(InGrp)
@@ -1280,7 +1280,7 @@ function issplit_at_P(O::NfOrd, G::Vector{NfToNfMor}, Coc::Function, P::NfOrdIdl
c = divexact(norm(P)-1, e)
if f == 1 && iszero(mod(c, n))
return true
- end
+ end
p = Int(minimum(P))
@assert mod(degree(P), f) == 0
f1 = divexact(degree(P), f)
@@ -1304,7 +1304,7 @@ function issplit_at_P(O::NfOrd, G::Vector{NfToNfMor}, Coc::Function, P::NfOrdIdl
return false
end
end
-
+
if f == 1
return true
end
diff --git a/src/FieldFactory/chain.jl b/src/FieldFactory/chain.jl
index d597334576..9aea2cd0a9 100644
--- a/src/FieldFactory/chain.jl
+++ b/src/FieldFactory/chain.jl
@@ -73,7 +73,7 @@ function get_chain(G::GAP.GapObj, H::GAP.GapObj)
res = possible_subs[i]
break
elseif occ < best_occ
- res = possible_subs[i]
+ res = possible_subs[i]
end
end
end
diff --git a/src/FieldFactory/conductors.jl b/src/FieldFactory/conductors.jl
index 72befd1a2e..fd1820c1e5 100644
--- a/src/FieldFactory/conductors.jl
+++ b/src/FieldFactory/conductors.jl
@@ -41,7 +41,7 @@ function must_be_ramified(L::GAP.GapObj, i::Int)
S = GAP.Globals.Representative(lS[i])
if !GAP.Globals.IsCyclic(S) || isone(GAP.Globals.Size(S))
continue
- end
+ end
g = GAP.Globals.MinimalGeneratingSet(S)[1]
n = GAP.Globals.Order(g)
preimgs = GAP.Globals.List(GAP.Globals.PreImages(mH1, g))
@@ -61,7 +61,7 @@ function must_be_ramified(L::GAP.GapObj, i::Int)
break
end
end
- return found_all, found_one
+ return found_all, found_one
end
################################################################################
@@ -116,7 +116,7 @@ function _conductors_using_cocycles(F::FieldsTower, st::Vector{Int}, l_cond::Vec
push!(ramify_here, p)
elseif maximum(sizes_preimages) == ord && !divides(fmpz(n), p)[1]
push!(not_ramify_here, p)
- end
+ end
end
if isempty(ramify_here) && isempty(not_ramify_here)
return l_cond
@@ -212,12 +212,12 @@ function conductors_with_restrictions(F::FieldsTower, st::Vector{Int}, IdG::GAP.
#Regardless of the exponents, the norm of the discriminant will be a square
if issquare && is_square_disc_base_field
return new_conds
- elseif issquare
+ elseif issquare
return typeof(new_conds)()
else
return new_conds
end
- end
+ end
#Now, p must be 2.
if issquare && is_square_disc_base_field
#Only the even exponents are allowed!
@@ -226,7 +226,7 @@ function conductors_with_restrictions(F::FieldsTower, st::Vector{Int}, IdG::GAP.
if isempty(new_conds[i][2])
push!(newer_conds, new_conds[i])
continue
- end
+ end
if iszero(mod(first(values(new_conds[i][2])), 2))
push!(newer_conds, new_conds[i])
end
@@ -269,7 +269,7 @@ function conductors_with_restrictions(F::FieldsTower, st::Vector{Int}, IdG::GAP.
else
continue
end
- end
+ end
#Now, p must be 2.
if issquare && is_square_disc_base_field
#Only the even exponents are allowed!
diff --git a/src/FieldFactory/conductors_generic.jl b/src/FieldFactory/conductors_generic.jl
index d981531fb4..1754d4d813 100644
--- a/src/FieldFactory/conductors_generic.jl
+++ b/src/FieldFactory/conductors_generic.jl
@@ -30,7 +30,7 @@ function tame_conductors_degree_2(O::NfOrd, bound::fmpz; unramified_outside::Vec
push!(extra_list, (extra_list[i][1]*q, n))
end
end
-
+
final_list=Tuple{Int,fmpz}[]
l = length(list)
for (el,norm) in extra_list
@@ -42,15 +42,15 @@ function tame_conductors_degree_2(O::NfOrd, bound::fmpz; unramified_outside::Vec
end
end
return final_list
-
+
end
function squarefree_for_conductors(O::NfOrd, n::Int, deg::Int; coprime_to::Vector{fmpz}=fmpz[], prime_base::Vector{fmpz} = fmpz[])
-
+
sqf = trues(n)
primes = trues(n)
-
+
#remove primes that can be wildly ramified or
#that are ramified in the base field
for x in coprime_to
@@ -65,9 +65,9 @@ function squarefree_for_conductors(O::NfOrd, n::Int, deg::Int; coprime_to::Vecto
t += el
end
end
-
+
#sieving procedure
-
+
if !(2 in coprime_to)
dt = prime_decomposition_type(O,2)
if isone(gcd(2^dt[1][1]-1, deg))
@@ -77,7 +77,7 @@ function squarefree_for_conductors(O::NfOrd, n::Int, deg::Int; coprime_to::Vecto
@inbounds primes[j] = false
j += 2
end
- else
+ else
i=2
s=4
while s <= n
@@ -94,7 +94,7 @@ function squarefree_for_conductors(O::NfOrd, n::Int, deg::Int; coprime_to::Vecto
i = 3
b = isqrt(n)
while i <= b
- if primes[i]
+ if primes[i]
if gcd(i-1, deg) != 1 && (!isempty(prime_base) && (i in prime_base))
j = i
while j <= n
@@ -116,7 +116,7 @@ function squarefree_for_conductors(O::NfOrd, n::Int, deg::Int; coprime_to::Vecto
@inbounds sqf[j] = false
j+=i
end
- else
+ else
j=i
while j <= n
@inbounds primes[j]=false
@@ -147,7 +147,7 @@ function squarefree_for_conductors(O::NfOrd, n::Int, deg::Int; coprime_to::Vecto
end
i+=2
end
-
+
if degree(O)==1
i=2
while i<=length(sqf)
@@ -165,9 +165,9 @@ function conductors_tame(O::NfOrd, n::Int, bound::fmpz; unramified_outside::Vect
return tame_conductors_degree_2(O, bound, unramified_outside = unramified_outside)
end
#
- # First, conductors coprime to the ramified primes and to the
+ # First, conductors coprime to the ramified primes and to the
# degree of the extension we are searching for.
- #
+ #
d = degree(O)
K = nf(O)
wild_ram = collect(keys(factor(fmpz(n)).fac))
@@ -180,7 +180,7 @@ function conductors_tame(O::NfOrd, n::Int, bound::fmpz; unramified_outside::Vect
e = Int((m-1)*k)
b1 = Int(root(bound, degree(O)*e))
list = squarefree_for_conductors(O, b1, n, coprime_to = coprime_to, prime_base = unramified_outside)
-
+
extra_list = Tuple{Int, fmpz}[(1, fmpz(1))]
for q in ram_primes
if !isempty(unramified_outside) && !(q in unramified_outside)
@@ -188,7 +188,7 @@ function conductors_tame(O::NfOrd, n::Int, bound::fmpz; unramified_outside::Vect
end
tr = prime_decomposition_type(O, Int(q))
f = tr[1][1]
- nq = q^f
+ nq = q^f
if iscoprime(nq - 1, fmpz(n))
continue
end
@@ -205,7 +205,7 @@ function conductors_tame(O::NfOrd, n::Int, bound::fmpz; unramified_outside::Vect
push!(extra_list, (extra_list[i][1]*q, no))
end
end
-
+
final_list = Tuple{Int, fmpz}[]
l = length(list)
e = Int((m-1)*k)
@@ -217,12 +217,12 @@ function conductors_tame(O::NfOrd, n::Int, bound::fmpz; unramified_outside::Vect
push!(final_list, (list[i]*el, (fmpz(list[i])^(e*d))*norm))
end
end
-
+
return final_list
end
function conductors(O::NfOrd, a::Vector{Int}, bound::fmpz, tame::Bool=false; unramified_outside::Vector{fmpz} = fmpz[])
-
+
#Careful: I am assuming that a is in snf!
K = nf(O)
d = degree(O)
@@ -238,10 +238,10 @@ function conductors(O::NfOrd, a::Vector{Int}, bound::fmpz, tame::Bool=false; unr
if tame
reverse!(list)
- return Tuple{Int, Dict{NfOrdIdl, Int}}[(x[1], Dict{NfOrdIdl, Int}()) for x in list]
+ return Tuple{Int, Dict{NfOrdIdl, Int}}[(x[1], Dict{NfOrdIdl, Int}()) for x in list]
end
#
- # now, we have to multiply the obtained conductors by proper powers of wildly ramified ideals.
+ # now, we have to multiply the obtained conductors by proper powers of wildly ramified ideals.
#
wild_list = Tuple{Int, Dict{NfOrdIdl, Int}, fmpz}[(1, Dict{NfOrdIdl, Int}(), fmpz(1))]
for q in wild_ram
@@ -254,9 +254,9 @@ function conductors(O::NfOrd, a::Vector{Int}, bound::fmpz, tame::Bool=false; unr
sq = q^(divexact(d,lp[1][2])) #norm of the squarefree part of the integer q
#=
we have to use the conductor discriminant formula to understand the maximal possible exponent of q.
- Let ap be the exponent of p in the relative discriminant, let m be the conductor and h_(m,C) the cardinality of the
+ Let ap be the exponent of p in the relative discriminant, let m be the conductor and h_(m,C) the cardinality of the
quotient of ray class group by its subgroup C.
- Then
+ Then
ap= v_p(m)h_(m,C)- sum_{i=1:v_p(m)} h_(m/p^i, C)
Since m is the conductor, h_(m/p^i, C)<= h_(m,C)/q.
Consequently, we get
@@ -264,26 +264,26 @@ function conductors(O::NfOrd, a::Vector{Int}, bound::fmpz, tame::Bool=false; unr
=#
v = valuation(expo, q)
# First, we compute the bound coming from the bound on the discriminant
- boundsubext = root(bound, Int(divexact(n, q^v))) #The bound on the norm of the discriminant on the subextension
+ boundsubext = root(bound, Int(divexact(n, q^v))) #The bound on the norm of the discriminant on the subextension
# of order q^v
#Bound coming from the bound on the discriminant
- obound = fmpz(flog(boundsubext, sq))
-
+ obound = fmpz(flog(boundsubext, sq))
+
#Bound coming from the analysis on the different in a local extension
nbound = q^v + lp[1][2] * v * q^v - 1
bound_max_ap = min(nbound, obound) #bound on ap
bound_max_exp = div(bound_max_ap, (q-1)*q^(v-1)) #bound on the exponent in the conductor
-
+
#Ramification groups bound
max_nontrivial_ramification_group = div(lp[1][2]*(q^v), q-1)
if v > 1
- ram_groups_bound = max_nontrivial_ramification_group - sum(q^i for i = 1:v-1) + v
+ ram_groups_bound = max_nontrivial_ramification_group - sum(q^i for i = 1:v-1) + v
else
- ram_groups_bound = max_nontrivial_ramification_group + 1
+ ram_groups_bound = max_nontrivial_ramification_group + 1
end
bound_max_exp = min(ram_groups_bound, bound_max_exp)
-
+
#The prime may be also tamely ramified!
nisc = gcd(q^(fq)-1, fmpz(expo))
if nisc != 1
@@ -309,7 +309,7 @@ function conductors(O::NfOrd, a::Vector{Int}, bound::fmpz, tame::Bool=false; unr
if nn>bound
continue
end
- d2 = merge(max, d1, wild_list[s][2])
+ d2 = merge(max, d1, wild_list[s][2])
if nisc!=1
push!(wild_list, (q*wild_list[s][1], d2, nn))
else
@@ -318,7 +318,7 @@ function conductors(O::NfOrd, a::Vector{Int}, bound::fmpz, tame::Bool=false; unr
end
end
end
-
+
#the final list
final_list=Tuple{Int, Dict{NfOrdIdl, Int}}[]
for (el, nm) in list
@@ -331,7 +331,7 @@ function conductors(O::NfOrd, a::Vector{Int}, bound::fmpz, tame::Bool=false; unr
end
reverse!(final_list)
return final_list
-
+
end
###############################################################################
@@ -341,7 +341,7 @@ end
###############################################################################
function squarefree_for_conductorsQQ(O::NfOrd, n::Int, a::Vector{Int}; coprime_to::Vector{fmpz}=fmpz[], unramified_outside::Vector{fmpz} = fmpz[])
-
+
G = map(Int, snf(abelian_group(a))[1].snf)
sqf= trues(n)
primes= trues(n)
@@ -359,11 +359,11 @@ function squarefree_for_conductorsQQ(O::NfOrd, n::Int, a::Vector{Int}; coprime_t
t += el
end
end
-
+
single = Vector{Int}()
push!(single, 1)
multiple = Vector{Int}()
-
+
#sieving procedure
#First, I can remove all the multiples of 2
if !(2 in coprime_to)
@@ -372,7 +372,7 @@ function squarefree_for_conductorsQQ(O::NfOrd, n::Int, a::Vector{Int}; coprime_t
@inbounds sqf[i] = false
i+=2
end
- end
+ end
i=3
b = isqrt(n)
@@ -387,7 +387,7 @@ function squarefree_for_conductorsQQ(O::NfOrd, n::Int, a::Vector{Int}; coprime_t
@inbounds sqf[j]=false
j+=i
end
- else
+ else
j=i
while j<= n
@inbounds primes[j]=false
@@ -431,7 +431,7 @@ function squarefree_for_conductorsQQ(O::NfOrd, n::Int, a::Vector{Int}; coprime_t
elseif !isprime(deg)
i = 3
while i < n
- if primes[i]
+ if primes[i]
if rem(i-1, deg) == 0
push!(multiple, i)
else
@@ -445,9 +445,9 @@ function squarefree_for_conductorsQQ(O::NfOrd, n::Int, a::Vector{Int}; coprime_t
else
multiple = Int[i for i = 2:length(sqf) if sqf[i]]
end
-
- return single, multiple
-
+
+ return single, multiple
+
end
@@ -455,21 +455,21 @@ end
function conductors_tameQQ(O::NfOrd, a::Vector{Int}, bound::fmpz; unramified_outside::Vector{fmpz} = fmpz[])
#
- # First, conductors coprime to the ramified primes and to the
+ # First, conductors coprime to the ramified primes and to the
# degree of the extension we are searching for.
- #
+ #
n = prod(a)
wild_ram = collect(keys(factor(fmpz(n)).fac))
m = minimum(wild_ram)
k = divexact(n, m)
- b1 = Int(root(fmpz(bound),Int((m-1)*k)))
-
+ b1 = Int(root(fmpz(bound),Int((m-1)*k)))
+
return squarefree_for_conductorsQQ(O, b1, a, coprime_to = wild_ram, unramified_outside = unramified_outside)
end
function conductorsQQ(O::NfOrd, a::Vector{Int}, bound::fmpz, tame::Bool=false; unramified_outside::Vector{fmpz} = fmpz[])
-
+
K = nf(O)
d = degree(O)
n = prod(a)
@@ -483,10 +483,10 @@ function conductorsQQ(O::NfOrd, a::Vector{Int}, bound::fmpz, tame::Bool=false; u
single, multiple = conductors_tameQQ(O, a, bound, unramified_outside = unramified_outside)
if tame
- return multiple
+ return multiple
end
#
- # now, we have to multiply the obtained conductors by proper powers of wildly ramified ideals.
+ # now, we have to multiply the obtained conductors by proper powers of wildly ramified ideals.
#
wild_list=Tuple{Int, Int, fmpz}[(1, 1, 1)]
for q in wild_ram
@@ -496,9 +496,9 @@ function conductorsQQ(O::NfOrd, a::Vector{Int}, bound::fmpz, tame::Bool=false; u
l = length(wild_list)
#=
we have to use the conductor discriminant formula to understand the maximal possible exponent of q.
- Let ap be the exponent of p in the relative discriminant, let m be the conductor and h_(m,C) the cardinality of the
+ Let ap be the exponent of p in the relative discriminant, let m be the conductor and h_(m,C) the cardinality of the
quotient of ray class group by its subgroup C.
- Then
+ Then
ap= v_p(m)h_(m,C)- sum_{i=1:v_p(m)} h_(m/p^i, C)
Since m is the conductor, h_(m/p^i, C)<= h_(m,C)/q.
Consequently, we get
@@ -506,7 +506,7 @@ function conductorsQQ(O::NfOrd, a::Vector{Int}, bound::fmpz, tame::Bool=false; u
To find ap, it is enough to compute a logarithm.
=#
v = valuation(expo, q)
-
+
#I don't need to give a bound for a_p on the big extension but only on the maximum extension of q-power order
#This is the only thing that matters for the exponent of the conductor
nisc = gcd(q-1,n)
@@ -544,7 +544,7 @@ function conductorsQQ(O::NfOrd, a::Vector{Int}, bound::fmpz, tame::Bool=false; u
end
end
end
-
+
#the final list
final_list = Int[]
exps = Int((minimum(wild_ram)-1)*divexact(n, minimum(wild_ram)))
@@ -556,7 +556,7 @@ function conductorsQQ(O::NfOrd, a::Vector{Int}, bound::fmpz, tame::Bool=false; u
push!(final_list, (el*q*d))
end
end
-
+
for el in single
for j = 2:length(wild_list)
q,d,nm2 = wild_list[j]
@@ -567,7 +567,7 @@ function conductorsQQ(O::NfOrd, a::Vector{Int}, bound::fmpz, tame::Bool=false; u
end
end
return final_list
-
+
end
################################################################################
@@ -599,17 +599,17 @@ function conductors_generic(K::AnticNumberField, gtype::Vector{Int}, absolute_bo
if nP > bound
continue
end
- gn = gcd(nP-1, gtype[end])
+ gn = gcd(nP-1, gtype[end])
if !isone(gn)
starting_power = 1
end
vp = valuation(gtype[end], p)
# First, we compute the bound coming from the bound on the discriminant
- boundsubext = root(bound, Int(divexact(n, p^vp))) #The bound on the norm of the discriminant on the subextension
+ boundsubext = root(bound, Int(divexact(n, p^vp))) #The bound on the norm of the discriminant on the subextension
# of order q^v
#Bound coming from the bound on the discriminant
- obound = flog(boundsubext, nP)
-
+ obound = flog(boundsubext, nP)
+
#Bound coming from the analysis on the different in a local extension
nbound = p^vp + v * vp * p^vp - 1
diff --git a/src/FieldFactory/fields.jl b/src/FieldFactory/fields.jl
index ee389e8c4f..70493d880d 100644
--- a/src/FieldFactory/fields.jl
+++ b/src/FieldFactory/fields.jl
@@ -19,7 +19,7 @@ mutable struct cocycle_ctx
values_cyclic::Function
gen_kernel::GAP.GapObj
inclusion_of_pSylow::GAP.GapObj
-
+
function cocycle_ctx(proj::GAP.GapObj, incl::GAP.GapObj, cocycle::Function)
z = new()
z.projection = proj
@@ -41,7 +41,7 @@ mutable struct FieldsTower
isomorphism::Dict{NfToNfMor, GAP.GapObj}
admissible_cocycles::Vector{cocycle_ctx}
projections_for_conductors::Vector{GAP.GapObj}
-
+
function FieldsTower(K::AnticNumberField, auts::Vector{NfToNfMor}, subfields::Vector{NfToNfMor})
z = new()
z.field = K
@@ -275,7 +275,7 @@ function permutation_group(G::Vector{Hecke.NfToNfMor})
end
function _from_autos_to_perm(G::Vector{Hecke.NfToNfMor})
-
+
K = domain(G[1])
@assert degree(K) == length(G)
n = length(G)
@@ -304,7 +304,7 @@ function _from_autos_to_perm(G::Vector{Hecke.NfToNfMor})
permutations[s] = perm
end
return permutations
-
+
end
function _perm_to_gap_grp(perm::Vector{Vector{Int}})
@@ -314,7 +314,7 @@ function _perm_to_gap_grp(perm::Vector{Vector{Int}})
push!(g, z)
end
g1 = GAP.julia_to_gap(g)
- return GAP.Globals.Group(g1)
+ return GAP.Globals.Group(g1)
end
function _perm_to_gap_perm(x::Vector{Int})
@@ -335,7 +335,7 @@ end
###############################################################################
function _split_extension(G::Vector{Hecke.NfToNfMor}, mats::Vector{Hecke.GrpAbFinGenMap})
-
+
gtype = map(Int, domain(mats[1]).snf)
G1 = permutation_group(G)
gensG1 = GAP.Globals.GeneratorsOfGroup(G1)
@@ -354,7 +354,7 @@ function _split_extension(G::Vector{Hecke.NfToNfMor}, mats::Vector{Hecke.GrpAbFi
images[j] = g
end
auts[i] = GAP.Globals.GroupHomomorphismByImages(A, A, gens, GAP.julia_to_gap(images))
- end
+ end
AutGrp = GAP.Globals.Group(GAP.julia_to_gap(auts))
mp = GAP.Globals.GroupHomomorphismByImages(G1, AutGrp, gensG1, GAP.julia_to_gap(auts))
return GAP.Globals.SplitExtension(G1, mp, A)
@@ -375,8 +375,8 @@ function check_group_extension(TargetGroup::GAP.GapObj, autos::Vector{NfToNfMor}
K = domain(autos[1])
d = degree(K)
com, uncom = ppio(expo, d)
-
- if com == 1
+
+ if com == 1
# I only need to check the split extension, since the second cohomology group is
# trivial, regardless of the action
if length(res_act) == 1 && isprime(order(GS)) == 1 && isprime(degree(K)) && iscoprime(d, order(GS))
@@ -390,12 +390,12 @@ function check_group_extension(TargetGroup::GAP.GapObj, autos::Vector{NfToNfMor}
return false
end
end
-
+
if uncom == 1
#Need a cohomological check. Only useful in the prime power case.
return true
end
-
+
# I check the split extension related to only uncom
#Now, I have to check if the split extension is isomorphic to IdH
Qn, mQn = quo(GS, uncom, false)
@@ -412,7 +412,7 @@ function check_group_extension(TargetGroup::GAP.GapObj, autos::Vector{NfToNfMor}
else
return false
end
-
+
end
@@ -438,17 +438,17 @@ function field_extensions(list::Vector{FieldsTower}, bound::fmpz, IsoE1::GAP.Gap
IsoCheck = IsoE1
end
final_list = FieldsTower[]
- for (j, x) in enumerate(list)
+ for (j, x) in enumerate(list)
@vprint :Fields 1 "Field $(j)/$(length(list)): $(x.field.pol)"
@vprint :FieldsNonFancy 1 "Field $(j)/$(length(list)): $(x.field.pol)\n"
append!(final_list, field_extensions(x, bound, IsoCheck, l, only_real, grp_to_be_checked, IsoE1, unramified_outside = unramified_outside))
- end
+ end
return final_list
end
function field_extensions(x::FieldsTower, bound::fmpz, IsoE1::GAP.GapObj, l::Vector{Int}, only_real::Bool, grp_to_be_checked::Dict{Int, GAP.GapObj}, IsoG::GAP.GapObj; unramified_outside::Vector{fmpz} = fmpz[])
-
+
list_cfields = _abelian_normal_extensions(x, l, bound, IsoE1, only_real, IsoG, unramified_outside = unramified_outside)
if isempty(list_cfields)
@vprint :Fields 1 "\e[1F$(Hecke.set_cursor_col())$(Hecke.clear_to_eol())Number of new fields found: 0\n\n"
@@ -466,7 +466,7 @@ function field_extensions(x::FieldsTower, bound::fmpz, IsoE1::GAP.GapObj, l::Vec
for s = 1:length(x.subfields)
previous_fields[s] = x.subfields[s]
end
- previous_fields[end] = embed
+ previous_fields[end] = embed
final_list[j] = FieldsTower(fld, autos, previous_fields)
end
@@ -474,7 +474,7 @@ function field_extensions(x::FieldsTower, bound::fmpz, IsoE1::GAP.GapObj, l::Vec
@vprint :Fields 1 "Number of new fields found: $(length(final_list))\n\n"
@vprint :FieldsNonFancy 1 "Number of new fields found: $(length(final_list))\n\n"
return final_list
-
+
end
###############################################################################
@@ -497,20 +497,20 @@ function fields(a::Int, b::Int, list::Vector{FieldsTower}, absolute_bound::fmpz;
E1 = GAP.Globals.FactorGroup(L[1], L[i+1])
H1 = GAP.Globals.FactorGroup(L[i], L[i+1])
l = GAP.gap_to_julia(Vector{Int64}, GAP.Globals.AbelianInvariants(H1))
- @vprint :Fields 1 "contructing abelian extensions with invariants $l \n"
- @vprint :FieldsNonFancy 1 "contructing abelian extensions with invariants $l \n"
+ @vprint :Fields 1 "contructing abelian extensions with invariants $l \n"
+ @vprint :FieldsNonFancy 1 "contructing abelian extensions with invariants $l \n"
o = divexact(GAP.Globals.Size(G), GAP.Globals.Size(E1))
bound = root(absolute_bound, o)
IsoE1 = GAP.Globals.IdGroup(E1)
@vprint :Fields 1 "Number of fields at the $i -th step: $(length(list)) \n"
@vprint :FieldsNonFancy 1 "Number of fields at the $i -th step: $(length(list)) \n"
lG = snf(abelian_group(l))[1]
- invariants = map(Int, lG.snf)
+ invariants = map(Int, lG.snf)
onlyreal = (lvl > i || only_real)
#First, I search for obstruction.
@vprint :Fields 1 "Computing obstructions\n"
@vprint :FieldsNonFancy 1 "Computing obstructions\n"
- #@vtime :Fields 1
+ #@vtime :Fields 1
list = check_obstruction(list, L, i, invariants)
@vprint :Fields 1 "Fields to check: $(length(list))\n\n"
@vprint :FieldsNonFancy 1 "Fields to check: $(length(list))\n\n"
@@ -559,8 +559,8 @@ function fields(a::Int, b::Int, absolute_bound::fmpz; using_direct_product::Bool
G = GAP.Globals.SmallGroup(a, b)
if using_direct_product
g1, g2, red, redfirst = direct_product_decomposition(G, (a, b))
- if g2 != (1, 1)
- @vprint :Fields 1 "computing extensions with Galois group ($a, $b) and bound ~10^$(clog(absolute_bound, 10))\n"
+ if g2 != (1, 1)
+ @vprint :Fields 1 "computing extensions with Galois group ($a, $b) and bound ~10^$(clog(absolute_bound, 10))\n"
return fields_direct_product(g1, g2, red, redfirst, absolute_bound; only_real = only_real, unramified_outside = unramified_outside)
end
end
@@ -590,7 +590,7 @@ function fields(a::Int, b::Int, absolute_bound::fmpz; using_direct_product::Bool
#2 is not wildly ramified. Then we only have the boring bound...
d = minimum(keys(factor(invariants[end]).fac))
cd = 2^((d-1)*div(pinvariants, d))
- end
+ end
#But I want the minimum. So I have to look at the other primes..
SP = PrimesSet(3, -1)
for p in SP
@@ -612,7 +612,7 @@ function fields(a::Int, b::Int, absolute_bound::fmpz; using_direct_product::Bool
if cd > cd1
cd = cd1
end
- end
+ end
end
bound = root(div(absolute_bound, cd), prod(invariants))
else
@@ -626,10 +626,10 @@ function fields(a::Int, b::Int, absolute_bound::fmpz; using_direct_product::Bool
@vprint :Fields 1 "Abelian invariants of the relative extension: $(invariants)\n"
@vprint :Fields 1 "Number of fields at this step: $(length(list)) \n"
@vprint :FieldsNonFancy 1 "Number of fields at this step: $(length(list)) \n"
-
+
@vprint :Fields 1 "Computing obstructions\n"
@vprint :FieldsNonFancy 1 "Computing obstructions\n"
- #@vtime :Fields 1
+ #@vtime :Fields 1
list = check_obstruction(list, L, length(L)-1, invariants)
@vprint :Fields 1 "Fields to check: $(length(list))\n\n"
@vprint :FieldsNonFancy 1 "Fields to check: $(length(list))\n\n"
diff --git a/src/FieldFactory/maximal_abelian_subextension.jl b/src/FieldFactory/maximal_abelian_subextension.jl
index 1e0516d2a6..01f25ed45c 100644
--- a/src/FieldFactory/maximal_abelian_subextension.jl
+++ b/src/FieldFactory/maximal_abelian_subextension.jl
@@ -47,7 +47,7 @@ function check_abelian_extensions(class_fields::Vector{Tuple{ClassField{MapRayCl
com, uncom = ppio(Int(expo), d)
if com == 1
return trues(length(class_fields))
- end
+ end
#I extract the generators that restricted to the domain of emb_sub are the identity.
#Notice that I can do this only because I know the way I am constructing the generators of the group.
expG_arr = Int[]
@@ -73,10 +73,10 @@ function check_abelian_extensions(class_fields::Vector{Tuple{ClassField{MapRayCl
expG = lcm(expG_arr)
expG1 = ppio(expG, com)[1]
@vprint :MaxAbExt 3 "Context for ray class groups\n"
-
+
OK = maximal_order(K)
rcg_ctx = Hecke.rayclassgrp_ctx(OK, com*expG1)
-
+
cfields = trues(length(class_fields))
for i = 1:length(class_fields)
@vprint :MaxAbExt 3 "Class Field $i\n"
@@ -88,7 +88,7 @@ function check_abelian_extensions(class_fields::Vector{Tuple{ClassField{MapRayCl
cfields[i] = check_abelian_extension(C, res_act_new, emb_sub, rcg_ctx, expG)
end
return cfields
-
+
end
@@ -107,7 +107,7 @@ function check_abelian_extension(C::Hecke.ClassField, res_act::Vector{GrpAbFinGe
if !isfixed_point_free(act_sub)
push!(prime_to_test, P)
end
- end
+ end
if isempty(prime_to_test)
return true
end
@@ -117,10 +117,10 @@ function check_abelian_extension(C::Hecke.ClassField, res_act::Vector{GrpAbFinGe
# Now, I compute the maximal abelian subextension of the n-part of C
Q, mQ = quo(G, n1, false)
C1 = ray_class_field(C.rayclassgroupmap, C.quotientmap*mQ)
- #@vtime :MaxAbExt 1
+ #@vtime :MaxAbExt 1
fl = _maximal_abelian_subfield(C1, emb_sub, rcg_ctx, exponent_extension)
else
- #@vtime :MaxAbExt 1
+ #@vtime :MaxAbExt 1
fl = _maximal_abelian_subfield(C, emb_sub, rcg_ctx, exponent_extension)
end
return fl
@@ -130,7 +130,7 @@ end
function _bound_exp_conductor_wild(O::NfOrd, n::Int, q::Int, bound::fmpz)
d = degree(O)
lp = prime_decomposition_type(O, q)
- f_times_r = divexact(d, lp[1][2])
+ f_times_r = divexact(d, lp[1][2])
sq = fmpz(q)^f_times_r
nbound = n+n*lp[1][2]*valuation(n,q)-div(fmpz(n), q^(valuation(n,q)))
obound = flog(bound, sq)
@@ -182,7 +182,7 @@ function _maximal_abelian_subfield(A::Hecke.ClassField, mp::Hecke.NfToNfMor, ctx
for (P, e) in mR1.fact_mod
p = intersect_prime(mp, P)
if !haskey(fm0, p)
- if !iscoprime(minimum(P, copy = false), expo)
+ if !iscoprime(minimum(P, copy = false), expo)
if e > 1
fm0[p] = e
end
@@ -272,7 +272,7 @@ function _maximal_abelian_subfield(A::Hecke.ClassField, mp::Hecke.NfToNfMor, ctx
end
@vtime :MaxAbExt 1 r, mr = Hecke.ray_class_groupQQ(zk, Int(wrp), rel_plc, ctx.n)
end
- @vtime :MaxAbExt 1 lP, gS = Hecke.find_gens(mR, coprime_to = minimum(defining_modulus(mR1)[1]))
+ @vtime :MaxAbExt 1 lP, gS = Hecke.find_gens(mR, coprime_to = minimum(defining_modulus(mR1)[1]))
listn = NfOrdIdl[norm(mp, x) for x in lP]
# Create the map between R and r by taking norms
preimgs = Vector{GrpAbFinGenElem}(undef, length(listn))
diff --git a/src/FieldFactory/merge.jl b/src/FieldFactory/merge.jl
index 710a03d407..c3f85fa8b1 100644
--- a/src/FieldFactory/merge.jl
+++ b/src/FieldFactory/merge.jl
@@ -38,22 +38,22 @@ function direct_product_decomposition(G::GAP.GapObj, ab::Tuple{Int, Int})
if isempty(decompositions)
return ab, (1, 1) , 1, 1
end
-
+
#We pass to the list with the group ID
grp_id_list = Vector{Tuple{Tuple{Int, Int}, Tuple{Int, Int}}}(undef, length(decompositions))
for i = 1:length(grp_id_list)
- grp_id_list[i] = (GAP.gap_to_julia(Tuple{Int, Int}, GAP.Globals.IdGroup(decompositions[i][1])), GAP.gap_to_julia(Tuple{Int, Int}, GAP.Globals.IdGroup(decompositions[i][2])))
+ grp_id_list[i] = (GAP.gap_to_julia(Tuple{Int, Int}, GAP.Globals.IdGroup(decompositions[i][1])), GAP.gap_to_julia(Tuple{Int, Int}, GAP.Globals.IdGroup(decompositions[i][2])))
end
-
+
possible_decompositions = Set(grp_id_list)
#First, I want to choose which decomposition to consider.
#In general, a balanced one is the best, so that pair maximising the minimum of the two orders.
#However, we also want to maximise the order of the abelian factor, if it exists.
res = first(possible_decompositions)
has_abelian_decomposition = 0
- if GAP.Globals.IsAbelian(GAP.Globals.SmallGroup(res[1]...))
+ if GAP.Globals.IsAbelian(GAP.Globals.SmallGroup(res[1]...))
has_abelian_decomposition = 1
- elseif GAP.Globals.IsAbelian(GAP.Globals.SmallGroup(res[2]...))
+ elseif GAP.Globals.IsAbelian(GAP.Globals.SmallGroup(res[2]...))
has_abelian_decomposition = 2
end
for x in possible_decompositions
@@ -66,9 +66,9 @@ function direct_product_decomposition(G::GAP.GapObj, ab::Tuple{Int, Int})
end
else
has_abelian_decx = 0
- if GAP.Globals.IsAbelian(GAP.Globals.SmallGroup(x[1]...))
+ if GAP.Globals.IsAbelian(GAP.Globals.SmallGroup(x[1]...))
has_abelian_decx = 1
- elseif GAP.Globals.IsAbelian(GAP.Globals.SmallGroup(x[2]...))
+ elseif GAP.Globals.IsAbelian(GAP.Globals.SmallGroup(x[2]...))
has_abelian_decx = 2
end
if !iszero(has_abelian_decx)
@@ -83,12 +83,12 @@ function direct_product_decomposition(G::GAP.GapObj, ab::Tuple{Int, Int})
res1 = res[1]
res2 = res[2]
#I count the redundancy, i.e. the number of possible decompositions of the same type.
- red = 0
+ red = 0
for i = 1:length(grp_id_list)
l1 = grp_id_list[i][1]
l2 = grp_id_list[i][2]
if l1 == res1 && l2 == res2
- red += 1
+ red += 1
end
end
#Finally, I count the numer of times a single subgroup appears in the lists.
@@ -142,7 +142,7 @@ function _to_composite(x::FieldsTower, y::FieldsTower, abs_disc::fmpz)
ima = mK\(autns(el))
autK[j+length(x.generators_of_automorphisms)] = hom(K, K, ima, check = false)
end
-
+
#Last thing: I have to add the maps of the subfields!
#I want to merge the information for the last embedding.
i = 1
@@ -195,11 +195,11 @@ function _easy_merge(list1, list2, absolute_bound::fmpz)
@vprint :Fields 1 "$(Hecke.set_cursor_col())$(Hecke.clear_to_eol())"
end
return res
-
+
end
function _disjoint_ab_subs(list1::Vector{FieldsTower}, list2::Vector{FieldsTower})
-
+
deg_ab_sub1 = 1
deg_ab_sub2 = 1
for i = 1:length(list1[1].subfields)
@@ -211,9 +211,9 @@ function _disjoint_ab_subs(list1::Vector{FieldsTower}, list2::Vector{FieldsTower
if degree(domain(list2[1].subfields[i])) == 1
deg_ab_sub2 *= degree(codomain(list2[1].subfields[i]))
end
- end
+ end
return deg_ab_sub1, deg_ab_sub2, gcd(deg_ab_sub1, deg_ab_sub2) == 1
-
+
end
function check_bound_disc(K::FieldsTower, L::FieldsTower, bound::fmpz)
@@ -315,7 +315,7 @@ function new_check_disc(K::FieldsTower, L::FieldsTower, absolute_bound::fmpz)
for (q, v) in lwild
v1 = valuation(d1, q)
v2 = valuation(d2, q)
- valnum = degree(Lf)*v1 + degree(Kf)*v2
+ valnum = degree(Lf)*v1 + degree(Kf)*v2
valden = valuation(g1, q)
if iseven(valden)
valden = divexact(valden, 2)
@@ -445,7 +445,7 @@ function _first_sieve(list1::Vector{FieldsTower}, list2::Vector{FieldsTower}, ab
ar[j] = (i1, v[j])
end
if haskey(D, (k[1], k[2], false))
- append!(ar, D[(k[1], k[2], false)])
+ append!(ar, D[(k[1], k[2], false)])
end
D[(k[1], k[2], false)] = ar
else
@@ -460,13 +460,13 @@ function _first_sieve(list1::Vector{FieldsTower}, list2::Vector{FieldsTower}, ab
end
if !isempty(ar_real)
if haskey(D, (k[1], k[2], true))
- append!(ar_real, D[(k[1], k[2], true)])
+ append!(ar_real, D[(k[1], k[2], true)])
end
D[(k[1], k[2], true)] = ar_real
end
if !isempty(ar_not_real)
if haskey(D, (k[1], k[2], false))
- append!(ar_not_real, D[(k[1], k[2], false)])
+ append!(ar_not_real, D[(k[1], k[2], false)])
end
D[(k[1], k[2], false)] = ar_not_real
end
@@ -520,7 +520,7 @@ function sieve_by_discriminant(list1, list2, v)
d1 = degree(list1[1].field)
d2 = degree(list2[1].field)
D = Dict{fmpz, Vector{Int}}()
-
+
for i = 1:length(v)
candidate = abs(discriminant(maximal_order(list1[v[i][1]].field))^d2)*abs(discriminant(maximal_order(list2[v[i][2]].field))^d1)
found = false
@@ -530,7 +530,7 @@ function sieve_by_discriminant(list1, list2, v)
found = true
break
end
- end
+ end
if !found
D[candidate] = Int[i]
end
@@ -656,7 +656,7 @@ function _merge(list1::Vector{FieldsTower}, list2::Vector{FieldsTower}, absolute
end
clusters = Vector{Tuple{Int, Int}}[x for x in values(D1)]
@vprint :Fields 1 "$(Hecke.set_cursor_col())$(Hecke.clear_to_eol())Candidates after first sieve: $(sum(length(x) for x in clusters))\n"
-
+
@vprint :Fields 1 "Sieving by discriminant\n"
#Now, I sieve by discriminant
clusters1 = Vector{Vector{Tuple{Int, Int}}}()
@@ -671,7 +671,7 @@ function _merge(list1::Vector{FieldsTower}, list2::Vector{FieldsTower}, absolute
@vprint :Fields 1 "Candidates: $(sum(length(x) for x in clusters1))\n"
@vprint :Fields 1 "Sieving by prime_splitting\n"
fields_to_be_computed = _sieve_by_prime_splitting(list1, list2, clusters1, red, redfirst, redsecond)
-
+
@vprint :Fields 1 "Computing maximal order of $(length(fields_to_be_computed)) fields\n"
for i = 1:length(fields_to_be_computed)
@vprint :Fields 1 "Doing $(i) / $(length(fields_to_be_computed))"
@@ -760,7 +760,7 @@ function _sieve_by_prime_splitting(list1, list2, clusters, red, redfirst, redsec
p = next_prime(p)
end
end
- end
+ end
end
@vprint :Fields 1 "$(Hecke.set_cursor_col())$(Hecke.clear_to_eol())"
return fields_to_be_computed
diff --git a/src/FieldFactory/non_normal.jl b/src/FieldFactory/non_normal.jl
index 5467502c71..79f271864c 100644
--- a/src/FieldFactory/non_normal.jl
+++ b/src/FieldFactory/non_normal.jl
@@ -27,7 +27,7 @@ function fixed_field(x::FieldsTower, H::GAP.GapObj)
gH = GAP.Globals.SmallGeneratingSet(H)
auts = NfToNfMor[]
- found = 0
+ found = 0
D = x.isomorphism
autsx = automorphisms(number_field(x))
i = 0
@@ -68,7 +68,7 @@ function _find_discriminant_bound(n, i, disc)
H = GAP.Globals.Representative(cg)
conjs = GAP.Globals.Elements(cg)
#I check if it is a Frobenius group!
- isfrobenius = true
+ isfrobenius = true
for i = 1:length(conjs)
for j = i+1:length(conjs)
if GAP.Globals.Size(GAP.Globals.Intersection(conjs[i], conjs[j])) != 1
diff --git a/src/FieldFactory/rayclassgrp.jl b/src/FieldFactory/rayclassgrp.jl
index da9ee02a1f..02d2dbba51 100644
--- a/src/FieldFactory/rayclassgrp.jl
+++ b/src/FieldFactory/rayclassgrp.jl
@@ -6,15 +6,15 @@
mutable struct ctx_rayclassgrp
order::NfOrd
- class_group_map::MapClassGrp #The class group mod n map
+ class_group_map::MapClassGrp #The class group mod n map
n::Int #the n for n_quo
diffC::fmpz #exponent of the full class group, divided by n
units::Vector{FacElem{nf_elem, AnticNumberField}}
princ_gens::Vector{FacElem{nf_elem, AnticNumberField}}
-
+
computed::Vector{Tuple{Dict{NfOrdIdl, Int}, Bool, MapRayClassGrp}}
multiplicative_groups::Dict{NfOrdIdl, GrpAbFinGenToAbsOrdQuoRingMultMap}
-
+
function ctx_rayclassgrp()
z = new()
return z
@@ -73,13 +73,13 @@ function ray_class_group_quo(m::NfOrdIdl, y1::Dict{NfOrdIdl,Int}, y2::Dict{NfOrd
end
return class_as_ray_class(C, mC, exp_c, m, ctx.n)
end
-
+
O = ctx.order
K = nf(O)
n_quo = ctx.n
lp = merge(max, y1, y2)
-
+
powers = Vector{Tuple{NfOrdIdl, NfOrdIdl}}()
quo_rings = Tuple{NfOrdQuoRing, Hecke.AbsOrdQuoMap{NfAbsOrd{AnticNumberField,nf_elem},NfAbsOrdIdl{AnticNumberField,nf_elem},NfAbsOrdElem{AnticNumberField,nf_elem}}}[]
groups_and_maps = Tuple{GrpAbFinGen, Hecke.GrpAbFinGenToAbsOrdQuoRingMultMap{NfAbsOrd{AnticNumberField,nf_elem},NfAbsOrdIdl{AnticNumberField,nf_elem},NfAbsOrdElem{AnticNumberField,nf_elem}}}[]
@@ -96,7 +96,7 @@ function ray_class_group_quo(m::NfOrdIdl, y1::Dict{NfOrdIdl,Int}, y2::Dict{NfOrd
end
end
QQ = PP^ee
-
+
push!(powers, (PP, QQ))
if haskey(ctx.multiplicative_groups, QQ)
cached_map = ctx.multiplicative_groups[QQ]
@@ -123,16 +123,16 @@ function ray_class_group_quo(m::NfOrdIdl, y1::Dict{NfOrdIdl,Int}, y2::Dict{NfOrd
push!(groups_and_maps, gandm)
end
end
-
+
if isempty(groups_and_maps)
nG = 0
expon = fmpz(1)
- else
+ else
nG = sum(ngens(x[1]) for x in groups_and_maps)
expon = lcm([exponent(x[1]) for x in groups_and_maps])
end
-
-
+
+
if iseven(n_quo)
p = InfPlc[ x for x in inf_plc if isreal(x) ]
else
@@ -140,19 +140,19 @@ function ray_class_group_quo(m::NfOrdIdl, y1::Dict{NfOrdIdl,Int}, y2::Dict{NfOrd
end
H, lH = log_infinite_primes(O, p)
expon = lcm(expon, exponent(H))
-
+
if exponent(C)*expon < n_quo && check
return empty_ray_class(m)
end
-
+
assure_elements_to_be_eval(ctx)
exp_class, Kel = find_coprime_representatives(mC, m, lp)
-
-
- nU = length(ctx.units)
+
+
+ nU = length(ctx.units)
# We construct the relation matrix and evaluate units and relations with the class group in the quotient by m
- # Then we compute the discrete logarithms
-
+ # Then we compute the discrete logarithms
+
R = zero_matrix(FlintZZ, 2*(ngens(C)+nG+ngens(H))+nU, ngens(C)+ngens(H)+nG)
for i = 1:ncols(R)
R[i+ngens(C)+nG+ngens(H)+nU, i] = n_quo
@@ -161,7 +161,7 @@ function ray_class_group_quo(m::NfOrdIdl, y1::Dict{NfOrdIdl,Int}, y2::Dict{NfOrd
R[i, i] = C.snf[i]
end
ind = 1
- for s = 1:length(quo_rings)
+ for s = 1:length(quo_rings)
G = groups_and_maps[s][1]
@assert issnf(G)
for i = 1:ngens(G)
@@ -195,7 +195,7 @@ function ray_class_group_quo(m::NfOrdIdl, y1::Dict{NfOrdIdl,Int}, y2::Dict{NfOrd
R[j+nG+ngens(H)+ngens(C), ngens(C)+s+ind-1] = a[1, s]
end
end
-
+
for j = 1:ngens(C)
a = (mG\Qr(evals[j+nU])).coeff
for s = 1:ncols(a)
@@ -203,23 +203,23 @@ function ray_class_group_quo(m::NfOrdIdl, y1::Dict{NfOrdIdl,Int}, y2::Dict{NfOrd
end
end
ind += ngens(groups_and_maps[i][1])
- end
-
+ end
+
if !isempty(p)
for j = 1:nU
aa = lH(tobeeval[j])::GrpAbFinGenElem
for s = 1:ngens(H)
- R[j+nG+ngens(C)+ngens(H), ngens(C)+ind-1+s] = aa[s]
+ R[j+nG+ngens(C)+ngens(H), ngens(C)+ind-1+s] = aa[s]
end
end
for j = 1:ngens(C)
aa = lH(tobeeval[j+nU])::GrpAbFinGenElem
for s = 1:ngens(H)
- R[j, ngens(C)+ind-1+s] = -aa[s]
+ R[j, ngens(C)+ind-1+s] = -aa[s]
end
end
- end
-
+ end
+
X = abelian_group(R)
X.exponent = n_quo
if isone(order(X))
@@ -227,11 +227,11 @@ function ray_class_group_quo(m::NfOrdIdl, y1::Dict{NfOrdIdl,Int}, y2::Dict{NfOrd
mp.header = MapHeader(X, FacElemMon(parent(m)))
return X, mp
end
-
+
invd = invmod(fmpz(diffC), expon)
local disclog
let X = X, mC = mC, invd = invd, C = C, exp_class = exp_class, powers = powers, groups_and_maps = groups_and_maps, quo_rings = quo_rings, lH = lH, diffC = diffC, n_quo = n_quo, m = m, p = p, expon = expon
-
+
# Discrete logarithm
function disclog(J::FacElem{NfOrdIdl, NfOrdIdlSet})
@vprint :RayFacElem 1 "Disc log of element $J \n"
@@ -241,7 +241,7 @@ function ray_class_group_quo(m::NfOrdIdl, y1::Dict{NfOrdIdl,Int}, y2::Dict{NfOrd
end
return a1
end
-
+
function disclog(J::NfOrdIdl)
@hassert :RayFacElem 1 iscoprime(J, m)
if isone(J)
@@ -259,7 +259,7 @@ function ray_class_group_quo(m::NfOrdIdl, y1::Dict{NfOrdIdl,Int}, y2::Dict{NfOrd
@vprint :RayFacElem 1 "Disc log of element J in the Class Group: $(L.coeff) \n"
eL = exp_class(L)
inv!(eL)
- add_to_key!(eL.fac, J, 1)
+ add_to_key!(eL.fac, J, 1)
pow!(eL, diffC)
@vprint :RayFacElem 1 "This ideal is principal: $eL \n"
z = principal_generator_fac_elem(eL)
@@ -281,11 +281,11 @@ function ray_class_group_quo(m::NfOrdIdl, y1::Dict{NfOrdIdl,Int}, y2::Dict{NfOrd
for s = 1:ncols(b)
coeffs[1, ii-1+s+ngens(C)] = b[1, s]
end
- end
+ end
return GrpAbFinGenElem(X, coeffs)
- end
+ end
end
-
+
Dgens = Tuple{NfOrdElem, GrpAbFinGenElem}[]
ind = 1
#We need generators of the full multiplicative group
@@ -313,7 +313,7 @@ function ray_class_group_quo(m::NfOrdIdl, y1::Dict{NfOrdIdl,Int}, y2::Dict{NfOrd
d, u1, v1 = gcdx(minimum(QQ, copy = false), mins)
i1 = i1*(u1*minimum(QQ, copy = false) + v1*mins) + u1*minimum(QQ, copy = false) *i2
i2 = v1*mins*i2
- end
+ end
@hassert :RayFacElem 1 isone(i1+i2)
@hassert :RayFacElem 1 i1 in QQ
@hassert :RayFacElem 1 i2 in J
@@ -378,7 +378,7 @@ function ray_class_group_quo(m::NfOrdIdl, y1::Dict{NfOrdIdl,Int}, y2::Dict{NfOrd
end
end
end
-
+
ind = 1
for i = 1:length(powers)
mG = groups_and_maps[i][2]
@@ -394,14 +394,14 @@ function ray_class_group_quo(m::NfOrdIdl, y1::Dict{NfOrdIdl,Int}, y2::Dict{NfOrd
end
ind += ngens(domain(mG))
end
-
+
disc_log_inf = Dict{InfPlc, GrpAbFinGenElem}()
for i = 1:length(p)
eldi = zero_matrix(FlintZZ, 1, ngens(X))
eldi[1, ngens(X) - length(inf_plc) + i] = 1
disc_log_inf[p[i]] = GrpAbFinGenElem(X, eldi)
end
-
+
mp = MapRayClassGrp()
mp.header = MapHeader(X, FacElemMon(parent(m)))
mp.header.preimage = disclog
@@ -414,23 +414,23 @@ function ray_class_group_quo(m::NfOrdIdl, y1::Dict{NfOrdIdl,Int}, y2::Dict{NfOrd
mp.clgrpmap = mC
X.exponent = fmpz(n_quo)
return X, mp
-
+
end
function log_infinite_primes(O::NfOrd, p::Vector{InfPlc})
if isempty(p)
S = abelian_group(Int[])
-
+
local log1
let S = S
function log1(B::T) where T <: Union{nf_elem ,FacElem{nf_elem, AnticNumberField}}
return id(S)
end
- end
+ end
return S, log1
end
-
+
S = abelian_group(Int[2 for i=1:length(p)])
local log
let S = S, p = p
@@ -444,19 +444,19 @@ function log_infinite_primes(O::NfOrd, p::Vector{InfPlc})
end
return GrpAbFinGenElem(S, ar)
end
- end
+ end
return S, log
end
function ray_class_group_quo(O::NfOrd, m::Int, wprimes::Dict{NfOrdIdl,Int}, inf_plc::Vector{InfPlc}, ctx::ctx_rayclassgrp; GRH::Bool = true)
-
+
d1 = Dict{NfOrdIdl, Int}()
lp = factor(m)
I = ideal(O, 1)
minI = fmpz(1)
for q in keys(lp.fac)
- lq = prime_decomposition(O, q)
+ lq = prime_decomposition(O, q)
for (P, e) in lq
if !haskey(wprimes, P)
I *= P
@@ -464,7 +464,7 @@ function ray_class_group_quo(O::NfOrd, m::Int, wprimes::Dict{NfOrdIdl,Int}, inf_
else
d1[P] = 1
end
- end
+ end
minI = q*minI
end
if !isempty(wprimes)
@@ -476,13 +476,13 @@ function ray_class_group_quo(O::NfOrd, m::Int, wprimes::Dict{NfOrdIdl,Int}, inf_
end
I.minimum = minI
return ray_class_group_quo(I, d1, wprimes, inf_plc, ctx, GRH = GRH)
-
+
end
function ray_class_group_quo(O::NfOrd, y::Dict{NfOrdIdl, Int}, inf_plc::Vector{InfPlc}, ctx::ctx_rayclassgrp; GRH::Bool = true, check::Bool = true)
-
+
y1=Dict{NfOrdIdl,Int}()
y2=Dict{NfOrdIdl,Int}()
n = ctx.n
diff --git a/src/FieldFactory/read_write.jl b/src/FieldFactory/read_write.jl
index 12a94eb029..09d49b5bd7 100644
--- a/src/FieldFactory/read_write.jl
+++ b/src/FieldFactory/read_write.jl
@@ -163,7 +163,7 @@ function _parse_array_of_tuples_of_arrays(s)
i += 1
k = _find_closing_sbraket(s, i)
vec1 = _parse_as_fmpq_vector(s[i-1:k-1])
- i = k
+ i = k
while s[i] != ','
i += 1
end
diff --git a/src/FunField/DegreeLocalization.jl b/src/FunField/DegreeLocalization.jl
index a5ae8dc48b..b4b404d084 100644
--- a/src/FunField/DegreeLocalization.jl
+++ b/src/FunField/DegreeLocalization.jl
@@ -12,7 +12,7 @@ export KInftyRing, KInftyElem, function_field
###############################################################################
#
# Declaration types
-# KInftyRing / KInftyElem
+# KInftyRing / KInftyElem
#
###############################################################################
@@ -265,7 +265,7 @@ end
- = <1/t^n>, the canonical rep
- translate via t-> 1/t into the "normal" world
- a rep of a/b mod t^n is ((a % t^n)*invmod(b, t^n) % t^n)
- - translate back
+ - translate back
The "canonical" rep should be r/t^l for deg(r) < n and l = deg(r)
In particular, for n=1, this is a scalar.
@@ -274,7 +274,7 @@ end
so a/b -> a(1/t)/b(1/t) and this needs to be expanded by t^max/t^max to
make both num and den polynomials
a/b -> reverse(a, max)//reverse(b, max)
-=#
+=#
function mod(a::KInftyElem{T}, b::KInftyElem{T}, checked::Bool=true) where T <: FieldElement
check_parent(a, b)
@@ -292,7 +292,7 @@ function mod(a::KInftyElem{T}, b::KInftyElem{T}, checked::Bool=true) where T <:
end
t = gen(parent(na))
tn = t^n
- r = mod(mod(na, tn) * invmod(da, tn), tn)
+ r = mod(mod(na, tn) * invmod(da, tn), tn)
Qt = parent(a.d)
return parent(a)(Qt(reverse(r))//Qt(t)^degree(r))
else
@@ -359,7 +359,7 @@ function gcdx(a::KInftyElem{T}, b::KInftyElem{T}, checked::Bool=true) where T <:
K = parent(a)
t = gen(K)
- if iszero(a)
+ if iszero(a)
iszero(b) && a, a, one(K)
g = t^-degree(b)
return g, zero(K), inv(canonical_unit(b))
@@ -499,7 +499,7 @@ function ResidueField(K::KInftyRing{T}, a::KInftyElem{T}) where {T <: FieldEleme
F = base_ring(K.K)
@assert degree(a) == -1
#TODO: can be optimized, see blurb of euc. div. above
- return F, MapFromFunc(x -> leading_coefficient(numerator(mod(x, a))), y-> K(y), K, F)
+ return F, MapFromFunc(x -> leading_coefficient(numerator(mod(x, a))), y-> K(y), K, F)
end
#TODO: ResidueRing is probably "just" poly of deg < n, think about it
diff --git a/src/Grp/8T.jl b/src/Grp/8T.jl
index bdb0e2bd57..e81c223d50 100644
--- a/src/Grp/8T.jl
+++ b/src/Grp/8T.jl
@@ -21,7 +21,7 @@ x^8 - 2*x^7 + 2*x^6 - 6*x^5 + 14*x^4 - 30*x^3 + 50*x^2 - 50*x + 25]
q8fields = [ x^8 + 12*x^6 + 36*x^4 + 36*x^2 + 9,
x^8 - 12*x^6 + 36*x^4 - 36*x^2 + 9,
- x^8 - x^7 - 34*x^6 + 29*x^5 + 361*x^4 - 305*x^3 - 1090*x^2 + 1345*x - 395,
+ x^8 - x^7 - 34*x^6 + 29*x^5 + 361*x^4 - 305*x^3 - 1090*x^2 + 1345*x - 395,
x^8 - 3*x^7 + 22*x^6 - 60*x^5 + 201*x^4 - 450*x^3 + 1528*x^2 - 3069*x + 4561,
x^8 + 60*x^6 + 900*x^4 + 4500*x^2 + 5625,
x^8 - 60*x^6 + 900*x^4 - 4500*x^2 + 5625,
diff --git a/src/Grp/SmallGroups.jl b/src/Grp/SmallGroups.jl
index 4f07d78760..d0435ca927 100644
--- a/src/Grp/SmallGroups.jl
+++ b/src/Grp/SmallGroups.jl
@@ -104,7 +104,7 @@ function SmallGroupDBLegacy(path::String)
db = Hecke.eval(Meta.parse(Base.read(path, String)))
for i in 1:length(db)
- push!(dbnew, eltype(dbnew)(undef, length(db[i])))
+ push!(dbnew, eltype(dbnew)(undef, length(db[i])))
for j in 1:length(db[i])
v = db[i][j]
vv = map(f, v)
diff --git a/src/Grp/small_groups_1_63 b/src/Grp/small_groups_1_63
index 25e602fdfe..65fecc8c67 100644
--- a/src/Grp/small_groups_1_63
+++ b/src/Grp/small_groups_1_63
@@ -112,7 +112,7 @@ const small_groups_1_63 = Vector{Tuple{Vector{Perm{Int64}}, Vector{Vector{Int}},
], [
[ -1, -1, 2 ],
[ -1, -3, 1, -3 ]
-], [ (1, 1), (2, 1), (3, 2), (4, 6), (6, 2) ], [ (1, 1), (2, 1), (3, 1), (4, 3), (6, 1), (12, 1) ], false, false, true, false, 12), ([ perm"(1, 8, 2, 7)(3, 10, 4, 9)(5, 12, 6, 11)", perm"(1, 5, 3)(2,
+], [ (1, 1), (2, 1), (3, 2), (4, 6), (6, 2) ], [ (1, 1), (2, 1), (3, 1), (4, 3), (6, 1), (12, 1) ], false, false, true, false, 12), ([ perm"(1, 8, 2, 7)(3, 10, 4, 9)(5, 12, 6, 11)", perm"(1, 5, 3)(2,
6, 4)(7, 11, 9)(8, 12, 10)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)" ], [
[ 2, 2, 2 ],
[ 3, 3 ],
@@ -121,7 +121,7 @@ const small_groups_1_63 = Vector{Tuple{Vector{Perm{Int64}}, Vector{Vector{Int}},
], [
[ -1, -1, 3 ],
[ -1, -2, 1, 2 ]
-], [ (1, 1), (2, 1), (3, 2), (4, 2), (6, 2), (12, 4) ], [ (1, 1), (2, 1), (3, 1), (4, 1), (6, 1), (12, 1) ], true, true, true, true, 4), ([ perm"(1, 9, 5)(2, 10, 6)(3, 11, 7)(4, 12, 8)", perm"(1,
+], [ (1, 1), (2, 1), (3, 2), (4, 2), (6, 2), (12, 4) ], [ (1, 1), (2, 1), (3, 1), (4, 1), (6, 1), (12, 1) ], true, true, true, true, 4), ([ perm"(1, 9, 5)(2, 10, 6)(3, 11, 7)(4, 12, 8)", perm"(1,
3)(2, 4)(5, 6)(7, 8)(9, 12)(10, 11)", perm"(1, 2)(3, 4)(5, 8)(6, 7)(9, 11)(10, 12)" ], [
[ 1, 1, 1 ],
[ 2, 2 ],
@@ -133,7 +133,7 @@ const small_groups_1_63 = Vector{Tuple{Vector{Perm{Int64}}, Vector{Vector{Int}},
[ -1, 2, 1, 3 ],
[ 2, 3, 2, 3 ],
[ 1, 2, -1, 2, 3 ]
-], [ (1, 1), (2, 3), (3, 8) ], [ (1, 1), (2, 3), (3, 4), (4, 1), (12, 1) ], false, false, true, false, 24), ([ perm"(1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9,
+], [ (1, 1), (2, 3), (3, 8) ], [ (1, 1), (2, 3), (3, 4), (4, 1), (12, 1) ], false, false, true, false, 24), ([ perm"(1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9,
12)", perm"(1, 3, 2)(4, 6, 5)(7, 8, 9)(10, 11, 12)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -165,21 +165,21 @@ const small_groups_1_63 = Vector{Tuple{Vector{Perm{Int64}}, Vector{Vector{Int}},
[ -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -2, 1, -2, 1 ]
-], [ (1, 1), (2, 7), (7, 6) ], [ (1, 1), (2, 7), (7, 1), (14, 1) ], false, false, true, false, 42), ([ perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12,
+], [ (1, 1), (2, 7), (7, 6) ], [ (1, 1), (2, 7), (7, 1), (14, 1) ], false, false, true, false, 42), ([ perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12,
11, 10, 9)" ], [
[ 1, 1 ],
[ -2, 1, 2, 1 ],
[ -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -2, 1, 2, 1 ]
-], [ (1, 1), (2, 1), (7, 6), (14, 6) ], [ (1, 1), (2, 1), (7, 1), (14, 1) ], true, true, true, true, 6) ], [ ([ perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)", perm"(1, 5, 4, 3, 2)(6, 10,
+], [ (1, 1), (2, 1), (7, 6), (14, 6) ], [ (1, 1), (2, 1), (7, 1), (14, 1) ], true, true, true, true, 6) ], [ ([ perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)", perm"(1, 5, 4, 3, 2)(6, 10,
9, 8, 7)(11, 15, 14, 13, 12)" ], [
[ 1, 1, 1 ],
[ -1, -2, 1, 2 ],
[ -2, -2, -2, -2, -2 ]
], [
[ -1, -2, 1, 2 ]
-], [ (1, 1), (3, 2), (5, 4), (15, 8) ], [ (1, 1), (3, 1), (5, 1), (15, 1) ], true, true, true, true, 8) ], [ ([ perm"(1, 16, 8, 12, 4, 14, 6, 10, 2, 15, 7, 11, 3, 13, 5, 9)", perm"(1, 8, 4, 6, 2, 7,
+], [ (1, 1), (3, 2), (5, 4), (15, 8) ], [ (1, 1), (3, 1), (5, 1), (15, 1) ], true, true, true, true, 8) ], [ ([ perm"(1, 16, 8, 12, 4, 14, 6, 10, 2, 15, 7, 11, 3, 13, 5, 9)", perm"(1, 8, 4, 6, 2, 7,
3, 5)(9, 16, 12, 14, 10, 15, 11, 13)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)" ], [
[ 3, 3, 3, 3 ],
[ 4, 4 ],
@@ -190,7 +190,7 @@ const small_groups_1_63 = Vector{Tuple{Vector{Perm{Int64}}, Vector{Vector{Int}},
[ -1, -1, 2 ],
[ 2, 1, 1, -3 ],
[ 3, 2, 2, 4 ]
-], [ (1, 1), (2, 1), (4, 2), (8, 4), (16, 8) ], [ (1, 1), (2, 1), (4, 1), (8, 1), (16, 1) ], true, true, true, true, 8), ([ perm"(1, 11, 3, 9)(2, 12, 4, 10)(5, 15, 7, 13)(6, 16, 8, 14)", perm"(1, 6,
+], [ (1, 1), (2, 1), (4, 2), (8, 4), (16, 8) ], [ (1, 1), (2, 1), (4, 1), (8, 1), (16, 1) ], true, true, true, true, 8), ([ perm"(1, 11, 3, 9)(2, 12, 4, 10)(5, 15, 7, 13)(6, 16, 8, 14)", perm"(1, 6,
2, 5)(3, 8, 4, 7)(9, 14, 10, 13)(11, 16, 12, 15)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -203,7 +203,7 @@ const small_groups_1_63 = Vector{Tuple{Vector{Perm{Int64}}, Vector{Vector{Int}},
[ -1, -1, 3 ],
[ -1, -2, 1, 2 ],
[ -2, -2, 4 ]
-], [ (1, 1), (2, 3), (4, 12) ], [ (1, 1), (2, 3), (4, 7), (8, 3), (16, 1) ], true, false, true, true, 96), ([ perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)", perm"(1, 5)(2, 6)(3, 7)(4,
+], [ (1, 1), (2, 3), (4, 12) ], [ (1, 1), (2, 3), (4, 7), (8, 3), (16, 1) ], true, false, true, true, 96), ([ perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)", perm"(1, 5)(2, 6)(3, 7)(4,
8)(9, 15)(10, 16)(11, 13)(12, 14)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -259,7 +259,7 @@ const small_groups_1_63 = Vector{Tuple{Vector{Perm{Int64}}, Vector{Vector{Int}},
[ 3, 1, 1, 4 ],
[ 2, -3, 2, 3 ],
[ -1, 2, -1, 2, -3 ]
-], [ (1, 1), (2, 3), (4, 4), (8, 8) ], [ (1, 1), (2, 3), (4, 3), (8, 3), (16, 1) ], false, false, true, true, 16), ([ perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)", perm"(1, 5)(2,
+], [ (1, 1), (2, 3), (4, 4), (8, 8) ], [ (1, 1), (2, 3), (4, 3), (8, 3), (16, 1) ], false, false, true, true, 16), ([ perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 15)(10, 16)(11, 14)(12, 13)", perm"(1, 4, 2, 3)(5, 7, 6, 8)(9, 11, 10, 12)(13, 16, 14, 15)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -274,7 +274,7 @@ const small_groups_1_63 = Vector{Tuple{Vector{Perm{Int64}}, Vector{Vector{Int}},
[ 2, -3, 2, -3 ],
[ -3, -3, 4 ],
[ 1, 2, 1, 2, 3 ]
-], [ (1, 1), (2, 9), (4, 2), (8, 4) ], [ (1, 1), (2, 9), (4, 5), (8, 3), (16, 1) ], false, false, true, true, 32), ([ perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)", perm"(1, 5)(2,
+], [ (1, 1), (2, 9), (4, 2), (8, 4) ], [ (1, 1), (2, 9), (4, 5), (8, 3), (16, 1) ], false, false, true, true, 32), ([ perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 15)(10, 16)(11, 14)(12, 13)", perm"(1, 4, 2, 3)(5, 7, 6, 8)(9, 11, 10, 12)(13, 16, 14, 15)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -291,7 +291,7 @@ const small_groups_1_63 = Vector{Tuple{Vector{Perm{Int64}}, Vector{Vector{Int}},
[ -1, -3, 1, -3 ],
[ 2, -3, 2, -3 ],
[ -1, 2, -1, 2, -3 ]
-], [ (1, 1), (2, 5), (4, 6), (8, 4) ], [ (1, 1), (2, 5), (4, 5), (8, 3), (16, 1) ], false, false, true, true, 16), ([ perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)", perm"(1, 6, 2,
+], [ (1, 1), (2, 5), (4, 6), (8, 4) ], [ (1, 1), (2, 5), (4, 5), (8, 3), (16, 1) ], false, false, true, true, 16), ([ perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)", perm"(1, 6, 2,
5)(3, 8, 4, 7)(9, 16, 10, 15)(11, 13, 12, 14)", perm"(1, 4, 2, 3)(5, 7, 6, 8)(9, 11, 10, 12)(13, 16, 14, 15)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -310,7 +310,7 @@ const small_groups_1_63 = Vector{Tuple{Vector{Perm{Int64}}, Vector{Vector{Int}},
[ -1, -3, 1, -3 ],
[ -2, -3, 2, -3 ],
[ -1, -2, -1, 2, -3 ]
-], [ (1, 1), (2, 1), (4, 10), (8, 4) ], [ (1, 1), (2, 1), (4, 5), (8, 3), (16, 1) ], false, false, true, true, 32), ([ perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)", perm"(1, 5)(2,
+], [ (1, 1), (2, 1), (4, 10), (8, 4) ], [ (1, 1), (2, 1), (4, 5), (8, 3), (16, 1) ], false, false, true, true, 32), ([ perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -344,7 +344,7 @@ const small_groups_1_63 = Vector{Tuple{Vector{Perm{Int64}}, Vector{Vector{Int}},
[ 2, 4, 2, 4 ],
[ 3, 4, 3, 4 ],
[ 1, 2, 1, 2, 4 ]
-], [ (1, 1), (2, 11), (4, 4) ], [ (1, 1), (2, 11), (4, 15), (8, 7), (16, 1) ], false, false, true, true, 64), ([ perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)", perm"(1, 6, 2, 5)(3, 8,
+], [ (1, 1), (2, 11), (4, 4) ], [ (1, 1), (2, 11), (4, 15), (8, 7), (16, 1) ], false, false, true, true, 64), ([ perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)", perm"(1, 6, 2, 5)(3, 8,
4, 7)(9, 13, 10, 14)(11, 15, 12, 16)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -361,7 +361,7 @@ const small_groups_1_63 = Vector{Tuple{Vector{Perm{Int64}}, Vector{Vector{Int}},
[ -1, -2, 1, -2 ],
[ -1, 3, 1, 3 ],
[ -2, 3, 2, 3 ]
-], [ (1, 1), (2, 3), (4, 12) ], [ (1, 1), (2, 3), (4, 7), (8, 7), (16, 1) ], false, false, true, true, 192), ([ perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)", perm"(1, 5)(2, 6)(3,
+], [ (1, 1), (2, 3), (4, 12) ], [ (1, 1), (2, 3), (4, 7), (8, 7), (16, 1) ], false, false, true, true, 192), ([ perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)", perm"(1, 5)(2, 6)(3,
7)(4, 8)(9, 14)(10, 13)(11, 16)(12, 15)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -376,7 +376,7 @@ const small_groups_1_63 = Vector{Tuple{Vector{Perm{Int64}}, Vector{Vector{Int}},
[ 2, -3, 2, 3 ],
[ -3, -3, 4 ],
[ 1, 2, 1, 2, 4 ]
-], [ (1, 1), (2, 7), (4, 8) ], [ (1, 1), (2, 7), (4, 7), (8, 7), (16, 1) ], false, false, true, true, 48), ([ perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)", perm"(1, 5)(2, 6)(3, 7)(4,
+], [ (1, 1), (2, 7), (4, 8) ], [ (1, 1), (2, 7), (4, 7), (8, 7), (16, 1) ], false, false, true, true, 48), ([ perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)", perm"(1, 5)(2, 6)(3, 7)(4,
8)(9, 13)(10, 14)(11, 15)(12, 16)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -397,7 +397,7 @@ const small_groups_1_63 = Vector{Tuple{Vector{Perm{Int64}}, Vector{Vector{Int}},
[ 3, 4, 3, 4 ]
], [ (1, 1), (2, 15) ], [ (1, 1), (2, 15), (4, 35), (8, 15), (16, 1) ], true, false, true, true, 20160) ], [ ([ perm"(1, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)" ], [
[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 ]
-], [], [ (1, 1), (17, 16) ], [ (1, 1), (17, 1) ], true, true, true, true, 16) ], [ ([ perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)", perm"(1, 9, 6, 3, 8, 5, 2, 7, 4)(10, 13,
+], [], [ (1, 1), (17, 16) ], [ (1, 1), (17, 1) ], true, true, true, true, 16) ], [ ([ perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)", perm"(1, 9, 6, 3, 8, 5, 2, 7, 4)(10, 13,
16, 11, 14, 17, 12, 15, 18)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 11, 12)(13, 14, 15)(16, 17, 18)" ], [
[ 1, 1 ],
[ 3, 3, 3 ],
@@ -406,7 +406,7 @@ const small_groups_1_63 = Vector{Tuple{Vector{Perm{Int64}}, Vector{Vector{Int}},
], [
[ 2, 2, 2, -3 ],
[ -2, 1, -2, 1 ]
-], [ (1, 1), (2, 9), (3, 2), (9, 6) ], [ (1, 1), (2, 9), (3, 1), (6, 3), (9, 1), (18, 1) ], false, false, true, false, 54), ([ perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)",
+], [ (1, 1), (2, 9), (3, 2), (9, 6) ], [ (1, 1), (2, 9), (3, 1), (6, 3), (9, 1), (18, 1) ], false, false, true, false, 54), ([ perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)",
perm"(1, 9, 6, 3, 8, 5, 2, 7, 4)(10, 18, 15, 12, 17, 14, 11, 16, 13)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)" ], [
[ 1, 1 ],
[ 3, 3, 3 ],
@@ -415,7 +415,7 @@ perm"(1, 9, 6, 3, 8, 5, 2, 7, 4)(10, 18, 15, 12, 17, 14, 11, 16, 13)", perm"(1,
], [
[ 2, 2, 2, -3 ],
[ -2, 1, 2, 1 ]
-], [ (1, 1), (2, 1), (3, 2), (6, 2), (9, 6), (18, 6) ], [ (1, 1), (2, 1), (3, 1), (6, 1), (9, 1), (18, 1) ], true, true, true, true, 6), ([ perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8,
+], [ (1, 1), (2, 1), (3, 2), (6, 2), (9, 6), (18, 6) ], [ (1, 1), (2, 1), (3, 1), (6, 1), (9, 1), (18, 1) ], true, true, true, true, 6), ([ perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8,
17)(9, 18)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 11, 12)(13, 14, 15)(16, 17, 18)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -427,7 +427,7 @@ perm"(1, 9, 6, 3, 8, 5, 2, 7, 4)(10, 18, 15, 12, 17, 14, 11, 16, 13)", perm"(1,
[ -2, 1, 2, 1 ],
[ -2, -3, 2, 3 ],
[ 1, -3, 1, -3 ]
-], [ (1, 1), (2, 3), (3, 8), (6, 6) ], [ (1, 1), (2, 3), (3, 4), (6, 4), (9, 1), (18, 1) ], false, false, true, false, 12), ([ perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)",
+], [ (1, 1), (2, 3), (3, 8), (6, 6) ], [ (1, 1), (2, 3), (3, 4), (6, 4), (9, 1), (18, 1) ], false, false, true, false, 12), ([ perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)",
perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 13, 16)(11, 14, 17)(12, 15, 18)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 11, 12)(13, 14, 15)(16, 17, 18)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -451,10 +451,10 @@ perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 13, 16)(11, 14, 17)(12, 15, 18)", perm"(1,
[ -2, 1, 2, 1 ],
[ -2, -3, 2, 3 ],
[ 1, -3, 1, 3 ]
-], [ (1, 1), (2, 1), (3, 8), (6, 8) ], [ (1, 1), (2, 1), (3, 4), (6, 4), (9, 1), (18, 1) ], true, false, true, true, 48) ], [ ([ perm"(1, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3,
+], [ (1, 1), (2, 1), (3, 8), (6, 8) ], [ (1, 1), (2, 1), (3, 4), (6, 4), (9, 1), (18, 1) ], true, false, true, true, 48) ], [ ([ perm"(1, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3,
2)" ], [
[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 ]
-], [], [ (1, 1), (19, 18) ], [ (1, 1), (19, 1) ], true, true, true, true, 18) ], [ ([ perm"(1, 16, 6, 11)(2, 17, 7, 12)(3, 18, 8, 13)(4, 19, 9, 14)(5, 20, 10, 15)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5,
+], [], [ (1, 1), (19, 18) ], [ (1, 1), (19, 1) ], true, true, true, true, 18) ], [ ([ perm"(1, 16, 6, 11)(2, 17, 7, 12)(3, 18, 8, 13)(4, 19, 9, 14)(5, 20, 10, 15)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5,
10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 12, 13, 14, 15)(16, 17, 18, 19, 20)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -464,7 +464,7 @@ perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 13, 16)(11, 14, 17)(12, 15, 18)", perm"(1,
], [
[ -1, -1, 2 ],
[ -1, -3, 1, -3 ]
-], [ (1, 1), (2, 1), (4, 10), (5, 4), (10, 4) ], [ (1, 1), (2, 1), (4, 5), (5, 1), (10, 1), (20, 1) ], false, false, true, false, 40), ([ perm"(1, 12, 2, 11)(3, 14, 4, 13)(5, 16, 6, 15)(7, 18, 8,
+], [ (1, 1), (2, 1), (4, 10), (5, 4), (10, 4) ], [ (1, 1), (2, 1), (4, 5), (5, 1), (10, 1), (20, 1) ], false, false, true, false, 40), ([ perm"(1, 12, 2, 11)(3, 14, 4, 13)(5, 16, 6, 15)(7, 18, 8,
17)(9, 20, 10, 19)", perm"(1, 9, 7, 5, 3)(2, 10, 8, 6, 4)(11, 19, 17, 15, 13)(12, 20, 18, 16, 14)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)" ], [
[ 1, 1, 1, 1 ],
[ 3, 3 ],
@@ -474,7 +474,7 @@ perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 13, 16)(11, 14, 17)(12, 15, 18)", perm"(1,
], [
[ -1, -1, 3 ],
[ -1, -2, 1, 2 ]
-], [ (1, 1), (2, 1), (4, 2), (5, 4), (10, 4), (20, 8) ], [ (1, 1), (2, 1), (4, 1), (5, 1), (10, 1), (20, 1) ], true, true, true, true, 8), ([ perm"(1, 16, 6, 11)(2, 17, 7, 12)(3, 18, 8, 13)(4, 19, 9,
+], [ (1, 1), (2, 1), (4, 2), (5, 4), (10, 4), (20, 8) ], [ (1, 1), (2, 1), (4, 1), (5, 1), (10, 1), (20, 1) ], true, true, true, true, 8), ([ perm"(1, 16, 6, 11)(2, 17, 7, 12)(3, 18, 8, 13)(4, 19, 9,
14)(5, 20, 10, 15)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)", perm"(1, 5, 4, 3, 2)(6, 7, 8, 9, 10)(11, 14, 12, 15, 13)(16, 18, 20, 17, 19)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -485,7 +485,7 @@ perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 13, 16)(11, 14, 17)(12, 15, 18)", perm"(1,
[ -1, -1, 2 ],
[ 2, -3, 2, -3 ],
[ 1, -3, -1, -3, -3 ]
-], [ (1, 1), (2, 5), (4, 10), (5, 4) ], [ (1, 1), (2, 5), (4, 5), (5, 1), (10, 1), (20, 1) ], false, false, true, false, 20), ([ perm"(1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9,
+], [ (1, 1), (2, 5), (4, 10), (5, 4) ], [ (1, 1), (2, 5), (4, 5), (5, 1), (10, 1), (20, 1) ], false, false, true, false, 20), ([ perm"(1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9,
19)(10, 20)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 12, 13, 14, 15)(16, 17, 18, 19, 20)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -497,7 +497,7 @@ perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 13, 16)(11, 14, 17)(12, 15, 18)", perm"(1,
[ 1, 2, 1, 2 ],
[ 1, -3, 1, -3 ],
[ 2, -3, 2, 3 ]
-], [ (1, 1), (2, 11), (5, 4), (10, 4) ], [ (1, 1), (2, 11), (4, 5), (5, 1), (10, 3), (20, 1) ], false, false, true, false, 40), ([ perm"(1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9,
+], [ (1, 1), (2, 11), (5, 4), (10, 4) ], [ (1, 1), (2, 11), (4, 5), (5, 1), (10, 3), (20, 1) ], false, false, true, false, 40), ([ perm"(1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9,
19)(10, 20)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -509,13 +509,13 @@ perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 13, 16)(11, 14, 17)(12, 15, 18)", perm"(1,
[ 1, 2, 1, 2 ],
[ 1, -3, 1, 3 ],
[ 2, -3, 2, 3 ]
-], [ (1, 1), (2, 3), (5, 4), (10, 12) ], [ (1, 1), (2, 3), (4, 1), (5, 1), (10, 3), (20, 1) ], true, false, true, true, 24) ], [ ([ perm"(1, 15, 8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6, 20,
+], [ (1, 1), (2, 3), (5, 4), (10, 12) ], [ (1, 1), (2, 3), (4, 1), (5, 1), (10, 3), (20, 1) ], true, false, true, true, 24) ], [ ([ perm"(1, 15, 8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6, 20,
13)(7, 21, 14)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 13, 11, 9, 14, 12, 10)(15, 18, 21, 17, 20, 16, 19)" ], [
[ 1, 1, 1 ],
[ -2, -2, -1, 2, 1 ]
], [
[ -2, -2, -1, 2, 1 ]
-], [ (1, 1), (3, 14), (7, 6) ], [ (1, 1), (3, 7), (7, 1), (21, 1) ], false, false, true, false, 42), ([ perm"(1, 15, 8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6, 20, 13)(7, 21, 14)", perm"(1, 7,
+], [ (1, 1), (3, 14), (7, 6) ], [ (1, 1), (3, 7), (7, 1), (21, 1) ], false, false, true, false, 42), ([ perm"(1, 15, 8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6, 20, 13)(7, 21, 14)", perm"(1, 7,
6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)" ], [
[ 1, 1, 1 ],
[ -1, -2, 1, 2 ],
@@ -529,17 +529,17 @@ perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
[ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -2, 1, -2, 1 ]
-], [ (1, 1), (2, 11), (11, 10) ], [ (1, 1), (2, 11), (11, 1), (22, 1) ], false, false, true, false, 110), ([ perm"(1, 12)(2, 13)(3, 14)(4, 15)(5, 16)(6, 17)(7, 18)(8, 19)(9, 20)(10, 21)(11, 22)",
+], [ (1, 1), (2, 11), (11, 10) ], [ (1, 1), (2, 11), (11, 1), (22, 1) ], false, false, true, false, 110), ([ perm"(1, 12)(2, 13)(3, 14)(4, 15)(5, 16)(6, 17)(7, 18)(8, 19)(9, 20)(10, 21)(11, 22)",
perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13)" ], [
[ 1, 1 ],
[ -2, 1, 2, 1 ],
[ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -2, 1, 2, 1 ]
-], [ (1, 1), (2, 1), (11, 10), (22, 10) ], [ (1, 1), (2, 1), (11, 1), (22, 1) ], true, true, true, true, 10) ], [ ([ perm"(1, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4,
+], [ (1, 1), (2, 1), (11, 10), (22, 10) ], [ (1, 1), (2, 1), (11, 1), (22, 1) ], true, true, true, true, 10) ], [ ([ perm"(1, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4,
3, 2)" ], [
[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 ]
-], [], [ (1, 1), (23, 22) ], [ (1, 1), (23, 1) ], true, true, true, true, 22) ], [ ([ perm"(1, 22, 10, 16, 4, 19, 7, 13)(2, 23, 11, 17, 5, 20, 8, 14)(3, 24, 12, 18, 6, 21, 9, 15)", perm"(1, 10, 4,
+], [], [ (1, 1), (23, 22) ], [ (1, 1), (23, 1) ], true, true, true, true, 22) ], [ ([ perm"(1, 22, 10, 16, 4, 19, 7, 13)(2, 23, 11, 17, 5, 20, 8, 14)(3, 24, 12, 18, 6, 21, 9, 15)", perm"(1, 10, 4,
7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)", perm"(1, 3, 2)(4, 6, 5)(7,
9, 8)(10, 12, 11)(13, 14, 15)(16, 17, 18)(19, 20, 21)(22, 23, 24)" ], [
[ 2, 2, 2, 2 ],
@@ -552,7 +552,7 @@ perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14,
[ -1, -1, 2 ],
[ 2, 1, 1, 3 ],
[ -1, -4, 1, -4 ]
-], [ (1, 1), (2, 1), (3, 2), (4, 2), (6, 2), (8, 12), (12, 4) ], [ (1, 1), (2, 1), (3, 1), (4, 1), (6, 1), (8, 3), (12, 1), (24, 1) ], false, false, true, false, 24), ([ perm"(1, 16, 4, 14, 2, 15, 3,
+], [ (1, 1), (2, 1), (3, 2), (4, 2), (6, 2), (8, 12), (12, 4) ], [ (1, 1), (2, 1), (3, 1), (4, 1), (6, 1), (8, 3), (12, 1), (24, 1) ], false, false, true, false, 24), ([ perm"(1, 16, 4, 14, 2, 15, 3,
13)(5, 20, 8, 18, 6, 19, 7, 17)(9, 24, 12, 22, 10, 23, 11, 21)", perm"(1, 9, 5)(2, 10, 6)(3, 11, 7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10,
11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22, 23)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)" ], [
[ 2, 2, 2 ],
@@ -565,8 +565,8 @@ perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14,
[ -1, -1, 3 ],
[ 3, 1, 1, 4 ],
[ -1, -2, 1, 2 ]
-], [ (1, 1), (2, 1), (3, 2), (4, 2), (6, 2), (8, 4), (12, 4), (24, 8) ], [ (1, 1), (2, 1), (3, 1), (4, 1), (6, 1), (8, 1), (12, 1), (24, 1) ], true, true, true, true, 8), ([ perm"(1, 17, 9)(2, 18,
-10)(3, 19, 11)(4, 20, 12)(5, 21, 13)(6, 22, 14)(7, 23, 15)(8, 24, 16)", perm"(1, 6, 2, 5)(3, 8, 4, 7)(9, 12, 10, 11)(13, 15, 14, 16)(17, 24, 18, 23)(19, 21, 20, 22)", perm"(1, 4, 2, 3)(5, 7, 6, 8)(9,
+], [ (1, 1), (2, 1), (3, 2), (4, 2), (6, 2), (8, 4), (12, 4), (24, 8) ], [ (1, 1), (2, 1), (3, 1), (4, 1), (6, 1), (8, 1), (12, 1), (24, 1) ], true, true, true, true, 8), ([ perm"(1, 17, 9)(2, 18,
+10)(3, 19, 11)(4, 20, 12)(5, 21, 13)(6, 22, 14)(7, 23, 15)(8, 24, 16)", perm"(1, 6, 2, 5)(3, 8, 4, 7)(9, 12, 10, 11)(13, 15, 14, 16)(17, 24, 18, 23)(19, 21, 20, 22)", perm"(1, 4, 2, 3)(5, 7, 6, 8)(9,
16, 10, 15)(11, 13, 12, 14)(17, 22, 18, 21)(19, 24, 20, 23)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)" ], [
[ 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -583,8 +583,8 @@ perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14,
[ -3, 2, 2, -3 ],
[ -2, -3, 2, -3 ],
[ 1, -2, -1, 2, 3 ]
-], [ (1, 1), (2, 1), (3, 8), (4, 6), (6, 8) ], [ (1, 1), (2, 1), (3, 4), (4, 3), (6, 4), (8, 1), (24, 1) ], false, false, true, false, 24), ([ perm"(1, 16, 4, 13)(2, 17, 5, 14)(3, 18, 6, 15)(7, 22,
-10, 19)(8, 23, 11, 20)(9, 24, 12, 21)", perm"(1, 10, 4, 7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 19, 16, 22)(14, 20, 17, 23)(15, 21, 18, 24)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15,
+], [ (1, 1), (2, 1), (3, 8), (4, 6), (6, 8) ], [ (1, 1), (2, 1), (3, 4), (4, 3), (6, 4), (8, 1), (24, 1) ], false, false, true, false, 24), ([ perm"(1, 16, 4, 13)(2, 17, 5, 14)(3, 18, 6, 15)(7, 22,
+10, 19)(8, 23, 11, 20)(9, 24, 12, 21)", perm"(1, 10, 4, 7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 19, 16, 22)(14, 20, 17, 23)(15, 21, 18, 24)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15,
18)(19, 22)(20, 23)(21, 24)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 14, 15)(16, 17, 18)(19, 20, 21)(22, 23, 24)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -601,8 +601,8 @@ perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14,
[ -1, -2, 1, -2 ],
[ -1, -4, 1, -4 ],
[ -2, -4, 2, 4 ]
-], [ (1, 1), (2, 1), (3, 2), (4, 14), (6, 2), (12, 4) ], [ (1, 1), (2, 1), (3, 1), (4, 7), (6, 1), (8, 3), (12, 3), (24, 1) ], false, false, true, false, 48), ([ perm"(1, 13)(2, 14)(3, 15)(4, 16)(5,
-17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)", perm"(1, 10, 4, 7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9,
+], [ (1, 1), (2, 1), (3, 2), (4, 14), (6, 2), (12, 4) ], [ (1, 1), (2, 1), (3, 1), (4, 7), (6, 1), (8, 3), (12, 3), (24, 1) ], false, false, true, false, 48), ([ perm"(1, 13)(2, 14)(3, 15)(4, 16)(5,
+17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)", perm"(1, 10, 4, 7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9,
12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 14, 15)(16, 17, 18)(19, 20, 21)(22, 23, 24)" ], [
[ 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -617,8 +617,8 @@ perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14,
[ -2, 1, 2, 1 ],
[ -2, -4, 2, 4 ],
[ 1, -4, 1, -4 ]
-], [ (1, 1), (2, 7), (3, 2), (4, 8), (6, 2), (12, 4) ], [ (1, 1), (2, 7), (3, 1), (4, 7), (6, 3), (8, 3), (12, 3), (24, 1) ], false, false, true, false, 24), ([ perm"(1, 13)(2, 14)(3, 15)(4, 16)(5,
-17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)", perm"(1, 10, 4, 7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 19, 16, 22)(14, 20, 17, 23)(15, 21, 18, 24)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9,
+], [ (1, 1), (2, 7), (3, 2), (4, 8), (6, 2), (12, 4) ], [ (1, 1), (2, 7), (3, 1), (4, 7), (6, 3), (8, 3), (12, 3), (24, 1) ], false, false, true, false, 24), ([ perm"(1, 13)(2, 14)(3, 15)(4, 16)(5,
+17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)", perm"(1, 10, 4, 7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 19, 16, 22)(14, 20, 17, 23)(15, 21, 18, 24)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9,
12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 14, 15)(16, 17, 18)(19, 20, 21)(22, 23, 24)" ], [
[ 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -633,8 +633,8 @@ perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14,
[ -2, 1, -2, 1 ],
[ -2, -4, 2, 4 ],
[ 1, -4, 1, -4 ]
-], [ (1, 1), (2, 13), (3, 2), (4, 2), (6, 2), (12, 4) ], [ (1, 1), (2, 13), (3, 1), (4, 7), (6, 5), (8, 3), (12, 3), (24, 1) ], false, false, true, false, 48), ([ perm"(1, 16, 4, 13)(2, 17, 5, 14)(3,
-18, 6, 15)(7, 22, 10, 19)(8, 23, 11, 20)(9, 24, 12, 21)", perm"(1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9,
+], [ (1, 1), (2, 13), (3, 2), (4, 2), (6, 2), (12, 4) ], [ (1, 1), (2, 13), (3, 1), (4, 7), (6, 5), (8, 3), (12, 3), (24, 1) ], false, false, true, false, 48), ([ perm"(1, 16, 4, 13)(2, 17, 5, 14)(3,
+18, 6, 15)(7, 22, 10, 19)(8, 23, 11, 20)(9, 24, 12, 21)", perm"(1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9,
12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 14, 15)(16, 17, 18)(19, 20, 21)(22, 23, 24)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -649,8 +649,8 @@ perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14,
[ -1, 2, 1, 2 ],
[ -1, -4, 1, -4 ],
[ 2, -4, 2, 4 ]
-], [ (1, 1), (2, 3), (3, 2), (4, 12), (6, 6) ], [ (1, 1), (2, 3), (3, 1), (4, 7), (6, 3), (8, 3), (12, 3), (24, 1) ], false, false, true, false, 48), ([ perm"(1, 13)(2, 14)(3, 15)(4, 16)(5, 17)(6,
-18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)", perm"(1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 22)(14, 23)(15, 24)(16, 19)(17, 20)(18, 21)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13,
+], [ (1, 1), (2, 3), (3, 2), (4, 12), (6, 6) ], [ (1, 1), (2, 3), (3, 1), (4, 7), (6, 3), (8, 3), (12, 3), (24, 1) ], false, false, true, false, 48), ([ perm"(1, 13)(2, 14)(3, 15)(4, 16)(5, 17)(6,
+18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)", perm"(1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 22)(14, 23)(15, 24)(16, 19)(17, 20)(18, 21)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13,
16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 14, 15)(16, 17, 18)(19, 20, 21)(22, 23, 24)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -669,8 +669,8 @@ perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14,
[ 2, -4, 2, 4 ],
[ 3, -4, 3, 4 ],
[ 1, 2, 1, 2, 3 ]
-], [ (1, 1), (2, 9), (3, 2), (4, 6), (6, 6) ], [ (1, 1), (2, 9), (3, 1), (4, 7), (6, 5), (8, 3), (12, 3), (24, 1) ], false, false, true, false, 24), ([ perm"(1, 14, 2, 13)(3, 16, 4, 15)(5, 18, 6,
-17)(7, 20, 8, 19)(9, 22, 10, 21)(11, 24, 12, 23)", perm"(1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)", perm"(1, 5, 3)(2, 6, 4)(7, 11, 9)(8, 12, 10)(13, 17,
+], [ (1, 1), (2, 9), (3, 2), (4, 6), (6, 6) ], [ (1, 1), (2, 9), (3, 1), (4, 7), (6, 5), (8, 3), (12, 3), (24, 1) ], false, false, true, false, 24), ([ perm"(1, 14, 2, 13)(3, 16, 4, 15)(5, 18, 6,
+17)(7, 20, 8, 19)(9, 22, 10, 21)(11, 24, 12, 23)", perm"(1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)", perm"(1, 5, 3)(2, 6, 4)(7, 11, 9)(8, 12, 10)(13, 17,
15)(14, 18, 16)(19, 23, 21)(20, 24, 22)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -685,8 +685,8 @@ perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14,
[ -1, 2, 1, 2 ],
[ -1, -3, 1, 3 ],
[ 2, -3, 2, 3 ]
-], [ (1, 1), (2, 3), (3, 2), (4, 4), (6, 6), (12, 8) ], [ (1, 1), (2, 3), (3, 1), (4, 3), (6, 3), (8, 1), (12, 3), (24, 1) ], true, false, true, true, 16), ([ perm"(1, 13)(2, 14)(3, 15)(4, 16)(5,
-17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)", perm"(1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 20)(14, 19)(15, 22)(16, 21)(17, 24)(18, 23)", perm"(1, 5, 3)(2, 6, 4)(7, 11, 9)(8, 12,
+], [ (1, 1), (2, 3), (3, 2), (4, 4), (6, 6), (12, 8) ], [ (1, 1), (2, 3), (3, 1), (4, 3), (6, 3), (8, 1), (12, 3), (24, 1) ], true, false, true, true, 16), ([ perm"(1, 13)(2, 14)(3, 15)(4, 16)(5,
+17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)", perm"(1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 20)(14, 19)(15, 22)(16, 21)(17, 24)(18, 23)", perm"(1, 5, 3)(2, 6, 4)(7, 11, 9)(8, 12,
10)(13, 17, 15)(14, 18, 16)(19, 23, 21)(20, 24, 22)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -705,8 +705,8 @@ perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14,
[ 2, 4, 2, 4 ],
[ -3, 4, 3, 4 ],
[ 1, 2, 1, 2, 4 ]
-], [ (1, 1), (2, 5), (3, 2), (4, 2), (6, 10), (12, 4) ], [ (1, 1), (2, 5), (3, 1), (4, 3), (6, 5), (8, 1), (12, 3), (24, 1) ], false, false, true, true, 16), ([ perm"(1, 14, 2, 13)(3, 16, 4, 15)(5,
-18, 6, 17)(7, 20, 8, 19)(9, 22, 10, 21)(11, 24, 12, 23)", perm"(1, 8, 2, 7)(3, 10, 4, 9)(5, 12, 6, 11)(13, 19, 14, 20)(15, 21, 16, 22)(17, 23, 18, 24)", perm"(1, 5, 3)(2, 6, 4)(7, 11, 9)(8, 12,
+], [ (1, 1), (2, 5), (3, 2), (4, 2), (6, 10), (12, 4) ], [ (1, 1), (2, 5), (3, 1), (4, 3), (6, 5), (8, 1), (12, 3), (24, 1) ], false, false, true, true, 16), ([ perm"(1, 14, 2, 13)(3, 16, 4, 15)(5,
+18, 6, 17)(7, 20, 8, 19)(9, 22, 10, 21)(11, 24, 12, 23)", perm"(1, 8, 2, 7)(3, 10, 4, 9)(5, 12, 6, 11)(13, 19, 14, 20)(15, 21, 16, 22)(17, 23, 18, 24)", perm"(1, 5, 3)(2, 6, 4)(7, 11, 9)(8, 12,
10)(13, 17, 15)(14, 18, 16)(19, 23, 21)(20, 24, 22)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -723,8 +723,8 @@ perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14,
[ -1, -2, 1, -2 ],
[ -1, -3, 1, 3 ],
[ -2, -3, 2, 3 ]
-], [ (1, 1), (2, 1), (3, 2), (4, 6), (6, 2), (12, 12) ], [ (1, 1), (2, 1), (3, 1), (4, 3), (6, 1), (8, 1), (12, 3), (24, 1) ], false, false, true, true, 48), ([ perm"(1, 13)(2, 14)(3, 15)(4, 16)(5,
-17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)", perm"(1, 9, 5)(2, 10, 6)(3, 11, 7)(4, 12, 8)(13, 17, 21)(14, 18, 22)(15, 19, 23)(16, 20, 24)", perm"(1, 3)(2, 4)(5, 6)(7, 8)(9, 12)(10,
+], [ (1, 1), (2, 1), (3, 2), (4, 6), (6, 2), (12, 12) ], [ (1, 1), (2, 1), (3, 1), (4, 3), (6, 1), (8, 1), (12, 3), (24, 1) ], false, false, true, true, 48), ([ perm"(1, 13)(2, 14)(3, 15)(4, 16)(5,
+17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)", perm"(1, 9, 5)(2, 10, 6)(3, 11, 7)(4, 12, 8)(13, 17, 21)(14, 18, 22)(15, 19, 23)(16, 20, 24)", perm"(1, 3)(2, 4)(5, 6)(7, 8)(9, 12)(10,
11)(13, 14)(15, 16)(17, 20)(18, 19)(21, 23)(22, 24)", perm"(1, 2)(3, 4)(5, 8)(6, 7)(9, 11)(10, 12)(13, 15)(14, 16)(17, 18)(19, 20)(21, 24)(22, 23)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -741,8 +741,8 @@ perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14,
[ 1, 3, 1, 4 ],
[ 3, 4, 3, 4 ],
[ 2, 3, -2, 3, 4 ]
-], [ (1, 1), (2, 9), (3, 8), (4, 6) ], [ (1, 1), (2, 9), (3, 4), (4, 7), (6, 4), (8, 3), (12, 1), (24, 1) ], false, false, true, false, 24), ([ perm"(1, 13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7,
-19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)", perm"(1, 9, 5)(2, 10, 6)(3, 11, 7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)", perm"(1, 3)(2, 4)(5, 6)(7, 8)(9, 12)(10, 11)(13, 15)(14,
+], [ (1, 1), (2, 9), (3, 8), (4, 6) ], [ (1, 1), (2, 9), (3, 4), (4, 7), (6, 4), (8, 3), (12, 1), (24, 1) ], false, false, true, false, 24), ([ perm"(1, 13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7,
+19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)", perm"(1, 9, 5)(2, 10, 6)(3, 11, 7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)", perm"(1, 3)(2, 4)(5, 6)(7, 8)(9, 12)(10, 11)(13, 15)(14,
16)(17, 18)(19, 20)(21, 24)(22, 23)", perm"(1, 2)(3, 4)(5, 8)(6, 7)(9, 11)(10, 12)(13, 14)(15, 16)(17, 20)(18, 19)(21, 23)(22, 24)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -759,8 +759,8 @@ perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14,
[ 1, 3, 1, 3 ],
[ 3, 4, 3, 4 ],
[ 2, 3, -2, 3, 4 ]
-], [ (1, 1), (2, 7), (3, 8), (6, 8) ], [ (1, 1), (2, 7), (3, 4), (4, 7), (6, 4), (8, 1), (12, 1), (24, 1) ], false, false, true, false, 24), ([ perm"(1, 13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7,
-19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)", perm"(1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13, 16)(14,
+], [ (1, 1), (2, 7), (3, 8), (6, 8) ], [ (1, 1), (2, 7), (3, 4), (4, 7), (6, 4), (8, 1), (12, 1), (24, 1) ], false, false, true, false, 24), ([ perm"(1, 13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7,
+19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)", perm"(1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13, 16)(14,
17)(15, 18)(19, 22)(20, 23)(21, 24)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 14, 15)(16, 17, 18)(19, 20, 21)(22, 23, 24)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -779,8 +779,8 @@ perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14,
[ 1, -4, 1, -4 ],
[ 2, -4, 2, 4 ],
[ 3, -4, 3, 4 ]
-], [ (1, 1), (2, 15), (3, 2), (6, 6) ], [ (1, 1), (2, 15), (3, 1), (4, 19), (6, 7), (8, 3), (12, 7), (24, 1) ], false, false, true, false, 144), ([ perm"(1, 13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7,
-19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)", perm"(1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13, 16)(14,
+], [ (1, 1), (2, 15), (3, 2), (6, 6) ], [ (1, 1), (2, 15), (3, 1), (4, 19), (6, 7), (8, 3), (12, 7), (24, 1) ], false, false, true, false, 144), ([ perm"(1, 13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7,
+19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)", perm"(1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13, 16)(14,
17)(15, 18)(19, 22)(20, 23)(21, 24)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -799,7 +799,7 @@ perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14,
[ 1, -4, 1, 4 ],
[ 2, -4, 2, 4 ],
[ 3, -4, 3, 4 ]
-], [ (1, 1), (2, 7), (3, 2), (6, 14) ], [ (1, 1), (2, 7), (3, 1), (4, 7), (6, 7), (8, 1), (12, 7), (24, 1) ], true, false, true, true, 336) ], [ ([ perm"(1, 25, 20, 15, 10, 5, 24, 19, 14, 9, 4, 23,
+], [ (1, 1), (2, 7), (3, 2), (6, 14) ], [ (1, 1), (2, 7), (3, 1), (4, 7), (6, 7), (8, 1), (12, 7), (24, 1) ], true, false, true, true, 336) ], [ ([ perm"(1, 25, 20, 15, 10, 5, 24, 19, 14, 9, 4, 23,
18, 13, 8, 3, 22, 17, 12, 7, 2, 21, 16, 11, 6)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 25, 24, 23, 22)" ], [
[ -1, -2, 1, 2 ],
[ 1, 1, 1, 1, 1, -2 ],
@@ -807,29 +807,29 @@ perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14,
], [
[ -1, -2, 1, 2 ],
[ 1, 1, 1, 1, 1, -2 ]
-], [ (1, 1), (5, 4), (25, 20) ], [ (1, 1), (5, 1), (25, 1) ], true, true, true, true, 20), ([ perm"(1, 21, 16, 11, 6)(2, 22, 17, 12, 7)(3, 23, 18, 13, 8)(4, 24, 19, 14, 9)(5, 25, 20, 15, 10)",
+], [ (1, 1), (5, 4), (25, 20) ], [ (1, 1), (5, 1), (25, 1) ], true, true, true, true, 20), ([ perm"(1, 21, 16, 11, 6)(2, 22, 17, 12, 7)(3, 23, 18, 13, 8)(4, 24, 19, 14, 9)(5, 25, 20, 15, 10)",
perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 25, 24, 23, 22)" ], [
[ -1, -2, 1, 2 ],
[ -1, -1, -1, -1, -1 ],
[ -2, -2, -2, -2, -2 ]
], [
[ -1, -2, 1, 2 ]
-], [ (1, 1), (5, 24) ], [ (1, 1), (5, 6), (25, 1) ], true, false, true, true, 480) ], [ ([ perm"(1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7, 20)(8, 21)(9, 22)(10, 23)(11, 24)(12, 25)(13, 26)",
+], [ (1, 1), (5, 24) ], [ (1, 1), (5, 6), (25, 1) ], true, false, true, true, 480) ], [ ([ perm"(1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7, 20)(8, 21)(9, 22)(10, 23)(11, 24)(12, 25)(13, 26)",
perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26)" ], [
[ 1, 1 ],
[ -2, 1, -2, 1 ],
[ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -2, 1, -2, 1 ]
-], [ (1, 1), (2, 13), (13, 12) ], [ (1, 1), (2, 13), (13, 1), (26, 1) ], false, false, true, false, 156), ([ perm"(1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7, 20)(8, 21)(9, 22)(10, 23)(11, 24)(12,
+], [ (1, 1), (2, 13), (13, 12) ], [ (1, 1), (2, 13), (13, 1), (26, 1) ], false, false, true, false, 156), ([ perm"(1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7, 20)(8, 21)(9, 22)(10, 23)(11, 24)(12,
25)(13, 26)", perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15)" ], [
[ 1, 1 ],
[ -2, 1, 2, 1 ],
[ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -2, 1, 2, 1 ]
-], [ (1, 1), (2, 1), (13, 12), (26, 12) ], [ (1, 1), (2, 1), (13, 1), (26, 1) ], true, true, true, true, 12) ], [ ([ perm"(1, 27, 18, 9, 24, 15, 6, 21, 12, 3, 26, 17, 8, 23, 14, 5, 20, 11, 2, 25, 16,
-7, 22, 13, 4, 19, 10)", perm"(1, 9, 6, 3, 8, 5, 2, 7, 4)(10, 18, 15, 12, 17, 14, 11, 16, 13)(19, 27, 24, 21, 26, 23, 20, 25, 22)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18,
+], [ (1, 1), (2, 1), (13, 12), (26, 12) ], [ (1, 1), (2, 1), (13, 1), (26, 1) ], true, true, true, true, 12) ], [ ([ perm"(1, 27, 18, 9, 24, 15, 6, 21, 12, 3, 26, 17, 8, 23, 14, 5, 20, 11, 2, 25, 16,
+7, 22, 13, 4, 19, 10)", perm"(1, 9, 6, 3, 8, 5, 2, 7, 4)(10, 18, 15, 12, 17, 14, 11, 16, 13)(19, 27, 24, 21, 26, 23, 20, 25, 22)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18,
17)(19, 21, 20)(22, 24, 23)(25, 27, 26)" ], [
[ 3, 3, 3 ],
[ 1, 1, 1, -2 ],
@@ -837,7 +837,7 @@ perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(14, 15, 16, 17, 18, 19, 20, 21,
], [
[ 1, 1, 1, -2 ],
[ 2, 2, 2, -3 ]
-], [ (1, 1), (3, 2), (9, 6), (27, 18) ], [ (1, 1), (3, 1), (9, 1), (27, 1) ], true, true, true, true, 18), ([ perm"(1, 21, 12, 3, 20, 11, 2, 19, 10)(4, 24, 15, 6, 23, 14, 5, 22, 13)(7, 27, 18, 9, 26,
+], [ (1, 1), (3, 2), (9, 6), (27, 18) ], [ (1, 1), (3, 1), (9, 1), (27, 1) ], true, true, true, true, 18), ([ perm"(1, 21, 12, 3, 20, 11, 2, 19, 10)(4, 24, 15, 6, 23, 14, 5, 22, 13)(7, 27, 18, 9, 26,
17, 8, 25, 16)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21,
20)(22, 24, 23)(25, 27, 26)" ], [
[ 2, 2, 2 ],
@@ -847,8 +847,8 @@ perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(14, 15, 16, 17, 18, 19, 20, 21,
], [
[ 1, 1, 1, -3 ],
[ -1, -2, 1, 2 ]
-], [ (1, 1), (3, 8), (9, 18) ], [ (1, 1), (3, 4), (9, 4), (27, 1) ], true, false, true, true, 108), ([ perm"(1, 19, 10)(2, 20, 11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9,
-27, 18)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 18, 14)(11, 16, 15)(12, 17, 13)(19, 26, 24)(20, 27, 22)(21, 25, 23)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21,
+], [ (1, 1), (3, 8), (9, 18) ], [ (1, 1), (3, 4), (9, 4), (27, 1) ], true, false, true, true, 108), ([ perm"(1, 19, 10)(2, 20, 11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9,
+27, 18)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 18, 14)(11, 16, 15)(12, 17, 13)(19, 26, 24)(20, 27, 22)(21, 25, 23)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21,
20)(22, 24, 23)(25, 27, 26)" ], [
[ 1, 1, 1 ],
[ 2, 2, 2 ],
@@ -860,8 +860,8 @@ perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(14, 15, 16, 17, 18, 19, 20, 21,
[ -1, -3, 1, 3 ],
[ -2, -3, 2, 3 ],
[ 1, -2, -1, 2, -3 ]
-], [ (1, 1), (3, 26) ], [ (1, 1), (3, 13), (9, 4), (27, 1) ], false, false, true, true, 432), ([ perm"(1, 21, 12, 3, 20, 11, 2, 19, 10)(4, 24, 15, 6, 23, 14, 5, 22, 13)(7, 27, 18, 9, 26, 17, 8, 25,
-16)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 18, 14)(11, 16, 15)(12, 17, 13)(19, 26, 24)(20, 27, 22)(21, 25, 23)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22,
+], [ (1, 1), (3, 26) ], [ (1, 1), (3, 13), (9, 4), (27, 1) ], false, false, true, true, 432), ([ perm"(1, 21, 12, 3, 20, 11, 2, 19, 10)(4, 24, 15, 6, 23, 14, 5, 22, 13)(7, 27, 18, 9, 26, 17, 8, 25,
+16)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 18, 14)(11, 16, 15)(12, 17, 13)(19, 26, 24)(20, 27, 22)(21, 25, 23)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22,
24, 23)(25, 27, 26)" ], [
[ 2, 2, 2 ],
[ 3, 3, 3 ],
@@ -872,8 +872,8 @@ perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(14, 15, 16, 17, 18, 19, 20, 21,
[ 1, 1, 1, -3 ],
[ -2, -3, 2, 3 ],
[ 2, -1, -1, -2, -1 ]
-], [ (1, 1), (3, 8), (9, 18) ], [ (1, 1), (3, 4), (9, 4), (27, 1) ], false, false, true, true, 54), ([ perm"(1, 19, 10)(2, 20, 11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9,
-27, 18)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21,
+], [ (1, 1), (3, 8), (9, 18) ], [ (1, 1), (3, 4), (9, 4), (27, 1) ], false, false, true, true, 54), ([ perm"(1, 19, 10)(2, 20, 11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9,
+27, 18)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21,
20)(22, 24, 23)(25, 27, 26)" ], [
[ 1, 1, 1 ],
[ 2, 2, 2 ],
@@ -885,8 +885,8 @@ perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(14, 15, 16, 17, 18, 19, 20, 21,
[ -1, -2, 1, 2 ],
[ -1, -3, 1, 3 ],
[ -2, -3, 2, 3 ]
-], [ (1, 1), (3, 26) ], [ (1, 1), (3, 13), (9, 13), (27, 1) ], true, false, true, true, 11232) ], [ ([ perm"(1, 22, 8, 15)(2, 23, 9, 16)(3, 24, 10, 17)(4, 25, 11, 18)(5, 26, 12, 19)(6, 27, 13, 20)(7,
-28, 14, 21)", perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 16, 17, 18, 19,
+], [ (1, 1), (3, 26) ], [ (1, 1), (3, 13), (9, 13), (27, 1) ], true, false, true, true, 11232) ], [ ([ perm"(1, 22, 8, 15)(2, 23, 9, 16)(3, 24, 10, 17)(4, 25, 11, 18)(5, 26, 12, 19)(6, 27, 13, 20)(7,
+28, 14, 21)", perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 16, 17, 18, 19,
20, 21)(22, 23, 24, 25, 26, 27, 28)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -896,8 +896,8 @@ perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(14, 15, 16, 17, 18, 19, 20, 21,
], [
[ -1, -1, 2 ],
[ -1, -3, 1, -3 ]
-], [ (1, 1), (2, 1), (4, 14), (7, 6), (14, 6) ], [ (1, 1), (2, 1), (4, 7), (7, 1), (14, 1), (28, 1) ], false, false, true, false, 84), ([ perm"(1, 16, 2, 15)(3, 18, 4, 17)(5, 20, 6, 19)(7, 22, 8,
-21)(9, 24, 10, 23)(11, 26, 12, 25)(13, 28, 14, 27)", perm"(1, 13, 11, 9, 7, 5, 3)(2, 14, 12, 10, 8, 6, 4)(15, 27, 25, 23, 21, 19, 17)(16, 28, 26, 24, 22, 20, 18)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9,
+], [ (1, 1), (2, 1), (4, 14), (7, 6), (14, 6) ], [ (1, 1), (2, 1), (4, 7), (7, 1), (14, 1), (28, 1) ], false, false, true, false, 84), ([ perm"(1, 16, 2, 15)(3, 18, 4, 17)(5, 20, 6, 19)(7, 22, 8,
+21)(9, 24, 10, 23)(11, 26, 12, 25)(13, 28, 14, 27)", perm"(1, 13, 11, 9, 7, 5, 3)(2, 14, 12, 10, 8, 6, 4)(15, 27, 25, 23, 21, 19, 17)(16, 28, 26, 24, 22, 20, 18)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9,
10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)" ], [
[ 1, 1, 1, 1 ],
[ 3, 3 ],
@@ -907,7 +907,7 @@ perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(14, 15, 16, 17, 18, 19, 20, 21,
], [
[ -1, -1, 3 ],
[ -1, -2, 1, 2 ]
-], [ (1, 1), (2, 1), (4, 2), (7, 6), (14, 6), (28, 12) ], [ (1, 1), (2, 1), (4, 1), (7, 1), (14, 1), (28, 1) ], true, true, true, true, 12), ([ perm"(1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7,
+], [ (1, 1), (2, 1), (4, 2), (7, 6), (14, 6), (28, 12) ], [ (1, 1), (2, 1), (4, 1), (7, 1), (14, 1), (28, 1) ], true, true, true, true, 12), ([ perm"(1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7,
21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)", perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)", perm"(1, 7, 6, 5, 4, 3, 2)(8,
14, 13, 12, 11, 10, 9)(15, 16, 17, 18, 19, 20, 21)(22, 23, 24, 25, 26, 27, 28)" ], [
[ 1, 1 ],
@@ -920,8 +920,8 @@ perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(14, 15, 16, 17, 18, 19, 20, 21,
[ 1, 2, 1, 2 ],
[ 1, -3, 1, -3 ],
[ 2, -3, 2, 3 ]
-], [ (1, 1), (2, 15), (7, 6), (14, 6) ], [ (1, 1), (2, 15), (4, 7), (7, 1), (14, 3), (28, 1) ], false, false, true, false, 84), ([ perm"(1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9,
-23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)", perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12,
+], [ (1, 1), (2, 15), (7, 6), (14, 6) ], [ (1, 1), (2, 15), (4, 7), (7, 1), (14, 3), (28, 1) ], false, false, true, false, 84), ([ perm"(1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9,
+23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)", perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12,
11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -936,8 +936,8 @@ perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(14, 15, 16, 17, 18, 19, 20, 21,
], [ (1, 1), (2, 3), (7, 6), (14, 18) ], [ (1, 1), (2, 3), (4, 1), (7, 1), (14, 3), (28, 1) ], true, false, true, true, 36) ], [ ([ perm"(1, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15,
14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)" ], [
[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 ]
-], [], [ (1, 1), (29, 28) ], [ (1, 1), (29, 1) ], true, true, true, true, 28) ], [ ([ perm"(1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15,
-30)", perm"(1, 13, 10, 7, 4)(2, 14, 11, 8, 5)(3, 15, 12, 9, 6)(16, 28, 25, 22, 19)(17, 29, 26, 23, 20)(18, 30, 27, 24, 21)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 17, 18)(19,
+], [], [ (1, 1), (29, 28) ], [ (1, 1), (29, 1) ], true, true, true, true, 28) ], [ ([ perm"(1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15,
+30)", perm"(1, 13, 10, 7, 4)(2, 14, 11, 8, 5)(3, 15, 12, 9, 6)(16, 28, 25, 22, 19)(17, 29, 26, 23, 20)(18, 30, 27, 24, 21)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 17, 18)(19,
20, 21)(22, 23, 24)(25, 26, 27)(28, 29, 30)" ], [
[ 1, 1 ],
[ 3, 3, 3 ],
@@ -962,7 +962,7 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 17, 18, 19, 20)(21,
[ -2, 1, 2, 1 ],
[ -2, -3, 2, 3 ],
[ 1, -3, 1, -3 ]
-], [ (1, 1), (2, 5), (3, 2), (5, 4), (6, 10), (15, 8) ], [ (1, 1), (2, 5), (3, 1), (5, 1), (6, 5), (10, 1), (15, 1), (30, 1) ], false, false, true, false, 40), ([ perm"(1, 16)(2, 17)(3, 18)(4, 19)(5,
+], [ (1, 1), (2, 5), (3, 2), (5, 4), (6, 10), (15, 8) ], [ (1, 1), (2, 5), (3, 1), (5, 1), (6, 5), (10, 1), (15, 1), (30, 1) ], false, false, true, false, 40), ([ perm"(1, 16)(2, 17)(3, 18)(4, 19)(5,
20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)", perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)(16, 21, 26)(17, 22, 27)(18, 23, 28)(19, 24, 29)(20, 25, 30)",
perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 17, 18, 19, 20)(21, 22, 23, 24, 25)(26, 27, 28, 29, 30)" ], [
[ 1, 1 ],
@@ -976,7 +976,7 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 17, 18, 19, 20)(21,
[ -2, -3, 2, 3 ],
[ 1, -3, 1, -3 ]
], [ (1, 1), (2, 15), (3, 2), (5, 4), (15, 8) ], [ (1, 1), (2, 15), (3, 1), (5, 1), (6, 5), (10, 3), (15, 1), (30, 1) ], false, false, true, false, 120), ([ perm"(1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6,
-21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)", perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)(16, 26, 21)(17, 27, 22)(18, 28, 23)(19, 29, 24)(20, 30, 25)",
+21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)", perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)(16, 26, 21)(17, 27, 22)(18, 28, 23)(19, 29, 24)(20, 30, 25)",
perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 25, 24, 23, 22)(26, 30, 29, 28, 27)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -991,9 +991,9 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
], [ (1, 1), (2, 1), (3, 2), (5, 4), (6, 2), (10, 4), (15, 8), (30, 8) ], [ (1, 1), (2, 1), (3, 1), (5, 1), (6, 1), (10, 1), (15, 1), (30, 1) ], true, true, true, true, 8) ], [ ([ perm"(1, 31, 30, 29,
28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)" ], [
[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 ]
-], [], [ (1, 1), (31, 30) ], [ (1, 1), (31, 1) ], true, true, true, true, 30) ], [ ([ perm"(1, 32, 16, 24, 8, 28, 12, 20, 4, 30, 14, 22, 6, 26, 10, 18, 2, 31, 15, 23, 7, 27, 11, 19, 3, 29, 13, 21, 5,
-25, 9, 17)", perm"(1, 16, 8, 12, 4, 14, 6, 10, 2, 15, 7, 11, 3, 13, 5, 9)(17, 32, 24, 28, 20, 30, 22, 26, 18, 31, 23, 27, 19, 29, 21, 25)", perm"(1, 8, 4, 6, 2, 7, 3, 5)(9, 16, 12, 14, 10, 15, 11,
-13)(17, 24, 20, 22, 18, 23, 19, 21)(25, 32, 28, 30, 26, 31, 27, 29)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22, 23)(25, 28, 26, 27)(29, 32, 30, 31)",
+], [], [ (1, 1), (31, 30) ], [ (1, 1), (31, 1) ], true, true, true, true, 30) ], [ ([ perm"(1, 32, 16, 24, 8, 28, 12, 20, 4, 30, 14, 22, 6, 26, 10, 18, 2, 31, 15, 23, 7, 27, 11, 19, 3, 29, 13, 21, 5,
+25, 9, 17)", perm"(1, 16, 8, 12, 4, 14, 6, 10, 2, 15, 7, 11, 3, 13, 5, 9)(17, 32, 24, 28, 20, 30, 22, 26, 18, 31, 23, 27, 19, 29, 21, 25)", perm"(1, 8, 4, 6, 2, 7, 3, 5)(9, 16, 12, 14, 10, 15, 11,
+13)(17, 24, 20, 22, 18, 23, 19, 21)(25, 32, 28, 30, 26, 31, 27, 29)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22, 23)(25, 28, 26, 27)(29, 32, 30, 31)",
perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 4, 4, 4, 4 ],
[ 5, 5 ],
@@ -1006,9 +1006,9 @@ perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21,
[ 2, 1, 1, -3 ],
[ 3, 2, 2, -4 ],
[ 4, 3, 3, 5 ]
-], [ (1, 1), (2, 1), (4, 2), (8, 4), (16, 8), (32, 16) ], [ (1, 1), (2, 1), (4, 1), (8, 1), (16, 1), (32, 1) ], true, true, true, true, 16), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24,
-8, 22)(9, 27, 11, 25)(10, 28, 12, 26)(13, 31, 15, 29)(14, 32, 16, 30)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 30, 18, 29)(19, 32, 20, 31)(21, 26, 22, 25)(23, 28, 24, 27)",
-perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18,
+], [ (1, 1), (2, 1), (4, 2), (8, 4), (16, 8), (32, 16) ], [ (1, 1), (2, 1), (4, 1), (8, 1), (16, 1), (32, 1) ], true, true, true, true, 16), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24,
+8, 22)(9, 27, 11, 25)(10, 28, 12, 26)(13, 31, 15, 29)(14, 32, 16, 30)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 30, 18, 29)(19, 32, 20, 31)(21, 26, 22, 25)(23, 28, 24, 27)",
+perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18,
20)(21, 23)(22, 24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -1030,9 +1030,9 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -2, 4, 2, 4 ],
[ -1, 5, 1, 5 ],
[ 1, -2, -1, 2, 3 ]
-], [ (1, 1), (2, 7), (4, 24) ], [ (1, 1), (2, 7), (4, 19), (8, 19), (16, 3), (32, 1) ], false, false, true, true, 384), ([ perm"(1, 22, 6, 18, 2, 21, 5, 17)(3, 24, 8, 20, 4, 23, 7, 19)(9, 30, 14, 26,
+], [ (1, 1), (2, 7), (4, 24) ], [ (1, 1), (2, 7), (4, 19), (8, 19), (16, 3), (32, 1) ], false, false, true, true, 384), ([ perm"(1, 22, 6, 18, 2, 21, 5, 17)(3, 24, 8, 20, 4, 23, 7, 19)(9, 30, 14, 26,
10, 29, 13, 25)(11, 32, 16, 28, 12, 31, 15, 27)", perm"(1, 11, 3, 9)(2, 12, 4, 10)(5, 15, 7, 13)(6, 16, 8, 14)(17, 27, 19, 25)(18, 28, 20, 26)(21, 31, 23, 29)(22, 32, 24, 30)", perm"(1, 6, 2, 5)(3, 8,
-4, 7)(9, 14, 10, 13)(11, 16, 12, 15)(17, 22, 18, 21)(19, 24, 20, 23)(25, 30, 26, 29)(27, 32, 28, 31)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22, 24)(25,
+4, 7)(9, 14, 10, 13)(11, 16, 12, 15)(17, 22, 18, 21)(19, 24, 20, 23)(25, 30, 26, 29)(27, 32, 28, 31)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22, 24)(25,
27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 2, 2, 2, 2 ],
[ 3, 3, 3, 3 ],
@@ -1047,8 +1047,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 3, 1, 1, 5 ],
[ -1, -2, 1, 2 ],
[ -2, -2, 4 ]
-], [ (1, 1), (2, 3), (4, 12), (8, 16) ], [ (1, 1), (2, 3), (4, 7), (8, 7), (16, 3), (32, 1) ], true, false, true, true, 128), ([ perm"(1, 22, 6, 18, 2, 21, 5, 17)(3, 24, 8, 20, 4, 23, 7, 19)(9, 30,
-14, 26, 10, 29, 13, 25)(11, 32, 16, 28, 12, 31, 15, 27)", perm"(1, 11, 3, 9)(2, 12, 4, 10)(5, 15, 7, 13)(6, 16, 8, 14)(17, 28, 19, 26)(18, 27, 20, 25)(21, 32, 23, 30)(22, 31, 24, 29)", perm"(1, 6, 2,
+], [ (1, 1), (2, 3), (4, 12), (8, 16) ], [ (1, 1), (2, 3), (4, 7), (8, 7), (16, 3), (32, 1) ], true, false, true, true, 128), ([ perm"(1, 22, 6, 18, 2, 21, 5, 17)(3, 24, 8, 20, 4, 23, 7, 19)(9, 30,
+14, 26, 10, 29, 13, 25)(11, 32, 16, 28, 12, 31, 15, 27)", perm"(1, 11, 3, 9)(2, 12, 4, 10)(5, 15, 7, 13)(6, 16, 8, 14)(17, 28, 19, 26)(18, 27, 20, 25)(21, 32, 23, 30)(22, 31, 24, 29)", perm"(1, 6, 2,
5)(3, 8, 4, 7)(9, 14, 10, 13)(11, 16, 12, 15)(17, 22, 18, 21)(19, 24, 20, 23)(25, 30, 26, 29)(27, 32, 28, 31)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 2, 2, 2, 2 ],
@@ -1068,8 +1068,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -2, -3, 2, 3 ],
[ -1, 4, 1, 4 ],
[ -1, -2, -1, 2, -3 ]
-], [ (1, 1), (2, 3), (4, 12), (8, 16) ], [ (1, 1), (2, 3), (4, 7), (8, 7), (16, 3), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 20, 4, 18, 2, 19, 3, 17)(5, 24, 8, 22, 6, 23, 7, 21)(9, 28,
-12, 26, 10, 27, 11, 25)(13, 32, 16, 30, 14, 31, 15, 29)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 29)(18, 30)(19, 31)(20, 32)(21, 25)(22, 26)(23, 27)(24, 28)", perm"(1, 5)(2,
+], [ (1, 1), (2, 3), (4, 12), (8, 16) ], [ (1, 1), (2, 3), (4, 7), (8, 7), (16, 3), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 20, 4, 18, 2, 19, 3, 17)(5, 24, 8, 22, 6, 23, 7, 21)(9, 28,
+12, 26, 10, 27, 11, 25)(13, 32, 16, 30, 14, 31, 15, 29)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 29)(18, 30)(19, 31)(20, 32)(21, 25)(22, 26)(23, 27)(24, 28)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22,
23)(25, 28, 26, 27)(29, 32, 30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 2, 2 ],
@@ -1089,8 +1089,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 2, 3, 2, 3 ],
[ 2, -4, 2, 4 ],
[ 1, 2, -1, 2, 3 ]
-], [ (1, 1), (2, 7), (4, 8), (8, 16) ], [ (1, 1), (2, 7), (4, 11), (8, 11), (16, 3), (32, 1) ], false, false, true, true, 64), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24, 8, 22)(9, 28,
-12, 25)(10, 27, 11, 26)(13, 32, 16, 29)(14, 31, 15, 30)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 29)(18, 30)(19, 31)(20, 32)(21, 25)(22, 26)(23, 27)(24, 28)", perm"(1, 5)(2,
+], [ (1, 1), (2, 7), (4, 8), (8, 16) ], [ (1, 1), (2, 7), (4, 11), (8, 11), (16, 3), (32, 1) ], false, false, true, true, 64), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24, 8, 22)(9, 28,
+12, 25)(10, 27, 11, 26)(13, 32, 16, 29)(14, 31, 15, 30)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 29)(18, 30)(19, 31)(20, 32)(21, 25)(22, 26)(23, 27)(24, 28)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 22)(18, 21)(19, 24)(20, 23)(25, 30)(26, 29)(27, 32)(28, 31)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 12)(10, 11)(13, 16)(14, 15)(17, 19)(18, 20)(21, 23)(22,
24)(25, 28)(26, 27)(29, 32)(30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
@@ -1116,8 +1116,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 3, 2, -1, 2, 1 ],
[ 1, 3, -1, 3, 5 ]
], [ (1, 1), (2, 11), (4, 20) ], [ (1, 1), (2, 11), (4, 23), (8, 11), (16, 3), (32, 1) ], false, false, true, true, 64), ([ perm"(1, 20, 4, 18, 2, 19, 3, 17)(5, 24, 8, 22, 6, 23, 7, 21)(9, 27, 11, 26,
-10, 28, 12, 25)(13, 31, 15, 30, 14, 32, 16, 29)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 29)(18, 30)(19, 31)(20, 32)(21, 25)(22, 26)(23, 27)(24, 28)", perm"(1, 5)(2, 6)(3,
-7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 22)(18, 21)(19, 24)(20, 23)(25, 30)(26, 29)(27, 32)(28, 31)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 20, 18, 19)(21, 24, 22,
+10, 28, 12, 25)(13, 31, 15, 30, 14, 32, 16, 29)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 29)(18, 30)(19, 31)(20, 32)(21, 25)(22, 26)(23, 27)(24, 28)", perm"(1, 5)(2, 6)(3,
+7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 22)(18, 21)(19, 24)(20, 23)(25, 30)(26, 29)(27, 32)(28, 31)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 20, 18, 19)(21, 24, 22,
23)(25, 27, 26, 28)(29, 31, 30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 2, 2 ],
[ 3, 3 ],
@@ -1136,9 +1136,9 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 2, -4, 2, -4 ],
[ 3, -4, 3, 4 ],
[ 3, 2, -1, 2, 1 ]
-], [ (1, 1), (2, 11), (4, 4), (8, 16) ], [ (1, 1), (2, 11), (4, 15), (8, 11), (16, 3), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 20, 4, 18, 2, 19, 3, 17)(5, 24, 8, 22, 6, 23, 7, 21)(9,
-27, 11, 26, 10, 28, 12, 25)(13, 31, 15, 30, 14, 32, 16, 29)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 30, 18, 29)(19, 32, 20, 31)(21, 26, 22, 25)(23, 28, 24, 27)", perm"(1,
-5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 22)(18, 21)(19, 24)(20, 23)(25, 30)(26, 29)(27, 32)(28, 31)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 20, 18, 19)(21,
+], [ (1, 1), (2, 11), (4, 4), (8, 16) ], [ (1, 1), (2, 11), (4, 15), (8, 11), (16, 3), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 20, 4, 18, 2, 19, 3, 17)(5, 24, 8, 22, 6, 23, 7, 21)(9,
+27, 11, 26, 10, 28, 12, 25)(13, 31, 15, 30, 14, 32, 16, 29)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 30, 18, 29)(19, 32, 20, 31)(21, 26, 22, 25)(23, 28, 24, 27)", perm"(1,
+5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 22)(18, 21)(19, 24)(20, 23)(25, 30)(26, 29)(27, 32)(28, 31)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 20, 18, 19)(21,
24, 22, 23)(25, 27, 26, 28)(29, 31, 30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 2, 2, 2, 2 ],
[ 3, 3 ],
@@ -1159,8 +1159,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -2, -4, 2, -4 ],
[ 3, -4, 3, 4 ],
[ 1, -2, -1, -2, 3 ]
-], [ (1, 1), (2, 3), (4, 12), (8, 16) ], [ (1, 1), (2, 3), (4, 7), (8, 11), (16, 3), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24, 8, 22)(9, 27,
-11, 25)(10, 28, 12, 26)(13, 31, 15, 29)(14, 32, 16, 30)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 29)(18, 30)(19, 31)(20, 32)(21, 26)(22, 25)(23, 28)(24, 27)", perm"(1, 6, 2,
+], [ (1, 1), (2, 3), (4, 12), (8, 16) ], [ (1, 1), (2, 3), (4, 7), (8, 11), (16, 3), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24, 8, 22)(9, 27,
+11, 25)(10, 28, 12, 26)(13, 31, 15, 29)(14, 32, 16, 30)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 29)(18, 30)(19, 31)(20, 32)(21, 26)(22, 25)(23, 28)(24, 27)", perm"(1, 6, 2,
5)(3, 8, 4, 7)(9, 13, 10, 14)(11, 15, 12, 16)(17, 21, 18, 22)(19, 23, 20, 24)(25, 30, 26, 29)(27, 32, 28, 31)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
@@ -1182,7 +1182,7 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 2, 4, 2, 4 ],
[ 1, 2, -1, 2, 3 ]
], [ (1, 1), (2, 11), (4, 12), (8, 8) ], [ (1, 1), (2, 11), (4, 19), (8, 11), (16, 3), (32, 1) ], false, false, true, true, 64), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24, 8, 22)(9, 27,
-11, 25)(10, 28, 12, 26)(13, 31, 15, 29)(14, 32, 16, 30)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 30, 18, 29)(19, 32, 20, 31)(21, 25, 22, 26)(23, 27, 24, 28)", perm"(1, 6, 2,
+11, 25)(10, 28, 12, 26)(13, 31, 15, 29)(14, 32, 16, 30)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 30, 18, 29)(19, 32, 20, 31)(21, 25, 22, 26)(23, 27, 24, 28)", perm"(1, 6, 2,
5)(3, 8, 4, 7)(9, 13, 10, 14)(11, 15, 12, 16)(17, 21, 18, 22)(19, 23, 20, 24)(25, 30, 26, 29)(27, 32, 28, 31)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
@@ -1205,8 +1205,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -2, -3, 2, -3 ],
[ -2, 4, 2, 4 ],
[ 1, -2, -1, 2, 3 ]
-], [ (1, 1), (2, 3), (4, 20), (8, 8) ], [ (1, 1), (2, 3), (4, 11), (8, 11), (16, 3), (32, 1) ], false, false, true, true, 64), ([ perm"(1, 20, 4, 18, 2, 19, 3, 17)(5, 24, 8, 22, 6, 23, 7, 21)(9, 28,
-12, 26, 10, 27, 11, 25)(13, 32, 16, 30, 14, 31, 15, 29)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 29)(18, 30)(19, 31)(20, 32)(21, 26)(22, 25)(23, 28)(24, 27)", perm"(1, 6, 2,
+], [ (1, 1), (2, 3), (4, 20), (8, 8) ], [ (1, 1), (2, 3), (4, 11), (8, 11), (16, 3), (32, 1) ], false, false, true, true, 64), ([ perm"(1, 20, 4, 18, 2, 19, 3, 17)(5, 24, 8, 22, 6, 23, 7, 21)(9, 28,
+12, 26, 10, 27, 11, 25)(13, 32, 16, 30, 14, 31, 15, 29)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 29)(18, 30)(19, 31)(20, 32)(21, 26)(22, 25)(23, 28)(24, 27)", perm"(1, 6, 2,
5)(3, 8, 4, 7)(9, 13, 10, 14)(11, 15, 12, 16)(17, 21, 18, 22)(19, 23, 20, 24)(25, 30, 26, 29)(27, 32, 28, 31)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22,
23)(25, 28, 26, 27)(29, 32, 30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 2, 2 ],
@@ -1228,8 +1228,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -3, -3, 5 ],
[ 2, -4, 2, 4 ],
[ 1, 2, -1, 2, 3 ]
-], [ (1, 1), (2, 7), (4, 16), (8, 8) ], [ (1, 1), (2, 7), (4, 11), (8, 11), (16, 3), (32, 1) ], false, false, true, true, 32), ([ perm"(1, 20, 4, 18, 2, 19, 3, 17)(5, 24, 8, 22, 6, 23, 7, 21)(9, 28,
-12, 26, 10, 27, 11, 25)(13, 32, 16, 30, 14, 31, 15, 29)", perm"(1, 13, 5, 9)(2, 14, 6, 10)(3, 15, 7, 11)(4, 16, 8, 12)(17, 25, 21, 29)(18, 26, 22, 30)(19, 27, 23, 31)(20, 28, 24, 32)", perm"(1, 5)(2,
+], [ (1, 1), (2, 7), (4, 16), (8, 8) ], [ (1, 1), (2, 7), (4, 11), (8, 11), (16, 3), (32, 1) ], false, false, true, true, 32), ([ perm"(1, 20, 4, 18, 2, 19, 3, 17)(5, 24, 8, 22, 6, 23, 7, 21)(9, 28,
+12, 26, 10, 27, 11, 25)(13, 32, 16, 30, 14, 31, 15, 29)", perm"(1, 13, 5, 9)(2, 14, 6, 10)(3, 15, 7, 11)(4, 16, 8, 12)(17, 25, 21, 29)(18, 26, 22, 30)(19, 27, 23, 31)(20, 28, 24, 32)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22,
23)(25, 28, 26, 27)(29, 32, 30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 2, 2, 2, 2 ],
@@ -1245,8 +1245,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 4, 1, 1, 5 ],
[ -1, -2, 1, -2 ],
[ -2, -2, 3 ]
-], [ (1, 1), (2, 3), (4, 12), (8, 16) ], [ (1, 1), (2, 3), (4, 7), (8, 7), (16, 3), (32, 1) ], false, false, true, true, 64), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24, 8, 22)(9, 27,
-11, 25)(10, 28, 12, 26)(13, 31, 15, 29)(14, 32, 16, 30)", perm"(1, 14, 6, 10, 2, 13, 5, 9)(3, 16, 8, 12, 4, 15, 7, 11)(17, 26, 21, 30, 18, 25, 22, 29)(19, 28, 23, 32, 20, 27, 24, 31)", perm"(1, 6, 2,
+], [ (1, 1), (2, 3), (4, 12), (8, 16) ], [ (1, 1), (2, 3), (4, 7), (8, 7), (16, 3), (32, 1) ], false, false, true, true, 64), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24, 8, 22)(9, 27,
+11, 25)(10, 28, 12, 26)(13, 31, 15, 29)(14, 32, 16, 30)", perm"(1, 14, 6, 10, 2, 13, 5, 9)(3, 16, 8, 12, 4, 15, 7, 11)(17, 26, 21, 30, 18, 25, 22, 29)(19, 28, 23, 32, 20, 27, 24, 31)", perm"(1, 6, 2,
5)(3, 8, 4, 7)(9, 14, 10, 13)(11, 16, 12, 15)(17, 21, 18, 22)(19, 23, 20, 24)(25, 29, 26, 30)(27, 31, 28, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
@@ -1266,8 +1266,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -1, -3, 1, -3 ],
[ -2, 4, 2, 4 ],
[ 1, -2, -1, 2, 3 ]
-], [ (1, 1), (2, 3), (4, 20), (8, 8) ], [ (1, 1), (2, 3), (4, 11), (8, 7), (16, 3), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24, 8, 22)(9, 27,
-11, 25)(10, 28, 12, 26)(13, 31, 15, 29)(14, 32, 16, 30)", perm"(1, 13, 5, 10, 2, 14, 6, 9)(3, 15, 7, 12, 4, 16, 8, 11)(17, 25, 22, 30, 18, 26, 21, 29)(19, 27, 24, 32, 20, 28, 23, 31)", perm"(1, 6, 2,
+], [ (1, 1), (2, 3), (4, 20), (8, 8) ], [ (1, 1), (2, 3), (4, 11), (8, 7), (16, 3), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24, 8, 22)(9, 27,
+11, 25)(10, 28, 12, 26)(13, 31, 15, 29)(14, 32, 16, 30)", perm"(1, 13, 5, 10, 2, 14, 6, 9)(3, 15, 7, 12, 4, 16, 8, 11)(17, 25, 22, 30, 18, 26, 21, 29)(19, 27, 24, 32, 20, 28, 23, 31)", perm"(1, 6, 2,
5)(3, 8, 4, 7)(9, 14, 10, 13)(11, 16, 12, 15)(17, 21, 18, 22)(19, 23, 20, 24)(25, 29, 26, 30)(27, 31, 28, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
@@ -1283,8 +1283,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -1, -2, 1, -2 ],
[ -2, -2, -3 ],
[ -3, 2, 2, 5 ]
-], [ (1, 1), (2, 3), (4, 20), (8, 8) ], [ (1, 1), (2, 3), (4, 11), (8, 7), (16, 3), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 20, 4, 18, 2, 19, 3, 17)(5, 24, 8, 22, 6, 23, 7, 21)(9, 28,
-12, 26, 10, 27, 11, 25)(13, 32, 16, 30, 14, 31, 15, 29)", perm"(1, 14, 6, 10, 2, 13, 5, 9)(3, 16, 8, 12, 4, 15, 7, 11)(17, 26, 21, 30, 18, 25, 22, 29)(19, 28, 23, 32, 20, 27, 24, 31)", perm"(1, 6, 2,
+], [ (1, 1), (2, 3), (4, 20), (8, 8) ], [ (1, 1), (2, 3), (4, 11), (8, 7), (16, 3), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 20, 4, 18, 2, 19, 3, 17)(5, 24, 8, 22, 6, 23, 7, 21)(9, 28,
+12, 26, 10, 27, 11, 25)(13, 32, 16, 30, 14, 31, 15, 29)", perm"(1, 14, 6, 10, 2, 13, 5, 9)(3, 16, 8, 12, 4, 15, 7, 11)(17, 26, 21, 30, 18, 25, 22, 29)(19, 28, 23, 32, 20, 27, 24, 31)", perm"(1, 6, 2,
5)(3, 8, 4, 7)(9, 14, 10, 13)(11, 16, 12, 15)(17, 21, 18, 22)(19, 23, 20, 24)(25, 29, 26, 30)(27, 31, 28, 32)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22,
23)(25, 28, 26, 27)(29, 32, 30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 3, 3, 3, 3 ],
@@ -1306,8 +1306,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -2, -4, 2, 4 ],
[ -1, -2, -1, -2, -4 ]
], [ (1, 1), (2, 3), (4, 4), (8, 24) ], [ (1, 1), (2, 3), (4, 3), (8, 7), (16, 3), (32, 1) ], false, false, true, true, 64), ([ perm"(1, 24, 8, 20, 4, 22, 6, 18, 2, 23, 7, 19, 3, 21, 5, 17)(9, 32, 16,
-28, 12, 30, 14, 26, 10, 31, 15, 27, 11, 29, 13, 25)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)", perm"(1, 8, 4, 6,
-2, 7, 3, 5)(9, 16, 12, 14, 10, 15, 11, 13)(17, 24, 20, 22, 18, 23, 19, 21)(25, 32, 28, 30, 26, 31, 27, 29)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22,
+28, 12, 30, 14, 26, 10, 31, 15, 27, 11, 29, 13, 25)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)", perm"(1, 8, 4, 6,
+2, 7, 3, 5)(9, 16, 12, 14, 10, 15, 11, 13)(17, 24, 20, 22, 18, 23, 19, 21)(25, 32, 28, 30, 26, 31, 27, 29)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22,
23)(25, 28, 26, 27)(29, 32, 30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 2, 2 ],
[ 4, 4, 4, 4 ],
@@ -1323,7 +1323,7 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 4, 3, 3, 5 ]
], [ (1, 1), (2, 3), (4, 4), (8, 8), (16, 16) ], [ (1, 1), (2, 3), (4, 3), (8, 3), (16, 3), (32, 1) ], true, false, true, true, 32), ([ perm"(1, 24, 8, 20, 4, 22, 6, 18, 2, 23, 7, 19, 3, 21, 5, 17)(9,
32, 16, 28, 12, 30, 14, 26, 10, 31, 15, 27, 11, 29, 13, 25)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 26)(18, 25)(19, 28)(20, 27)(21, 30)(22, 29)(23, 32)(24, 31)", perm"(1, 8,
-4, 6, 2, 7, 3, 5)(9, 16, 12, 14, 10, 15, 11, 13)(17, 24, 20, 22, 18, 23, 19, 21)(25, 32, 28, 30, 26, 31, 27, 29)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24,
+4, 6, 2, 7, 3, 5)(9, 16, 12, 14, 10, 15, 11, 13)(17, 24, 20, 22, 18, 23, 19, 21)(25, 32, 28, 30, 26, 31, 27, 29)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24,
22, 23)(25, 28, 26, 27)(29, 32, 30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 2, 2 ],
[ 4, 4, 4, 4 ],
@@ -1339,9 +1339,9 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 2, -3, 2, 3 ],
[ 4, 3, 3, 5 ],
[ 1, 2, -1, 2, 5 ]
-], [ (1, 1), (2, 3), (4, 4), (8, 8), (16, 16) ], [ (1, 1), (2, 3), (4, 3), (8, 3), (16, 3), (32, 1) ], false, false, true, true, 32), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8,
-24)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 29)(18, 30)(19, 31)(20, 32)(21, 28)(22, 27)(23, 25)(24, 26)",
-perm"(1, 7, 3, 6, 2, 8, 4, 5)(9, 13, 12, 16, 10, 14, 11, 15)(17, 21, 20, 24, 18, 22, 19, 23)(25, 31, 27, 30, 26, 32, 28, 29)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 19, 18,
+], [ (1, 1), (2, 3), (4, 4), (8, 8), (16, 16) ], [ (1, 1), (2, 3), (4, 3), (8, 3), (16, 3), (32, 1) ], false, false, true, true, 32), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8,
+24)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 29)(18, 30)(19, 31)(20, 32)(21, 28)(22, 27)(23, 25)(24, 26)",
+perm"(1, 7, 3, 6, 2, 8, 4, 5)(9, 13, 12, 16, 10, 14, 11, 15)(17, 21, 20, 24, 18, 22, 19, 23)(25, 31, 27, 30, 26, 32, 28, 29)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 19, 18,
20)(21, 23, 22, 24)(25, 28, 26, 27)(29, 32, 30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -1358,9 +1358,9 @@ perm"(1, 7, 3, 6, 2, 8, 4, 5)(9, 13, 12, 16, 10, 14, 11, 15)(17, 21, 20, 24, 18,
[ -3, -3, -4 ],
[ -4, 3, 3, 5 ],
[ 1, 2, 1, 2, 3 ]
-], [ (1, 1), (2, 17), (4, 2), (8, 4), (16, 8) ], [ (1, 1), (2, 17), (4, 9), (8, 5), (16, 3), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8,
-23)(9, 26, 10, 25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 29)(18, 30)(19, 31)(20, 32)(21, 28)(22, 27)(23, 25)(24, 26)",
-perm"(1, 7, 3, 6, 2, 8, 4, 5)(9, 13, 12, 16, 10, 14, 11, 15)(17, 21, 20, 24, 18, 22, 19, 23)(25, 31, 27, 30, 26, 32, 28, 29)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 19, 18,
+], [ (1, 1), (2, 17), (4, 2), (8, 4), (16, 8) ], [ (1, 1), (2, 17), (4, 9), (8, 5), (16, 3), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8,
+23)(9, 26, 10, 25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 29)(18, 30)(19, 31)(20, 32)(21, 28)(22, 27)(23, 25)(24, 26)",
+perm"(1, 7, 3, 6, 2, 8, 4, 5)(9, 13, 12, 16, 10, 14, 11, 15)(17, 21, 20, 24, 18, 22, 19, 23)(25, 31, 27, 30, 26, 32, 28, 29)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 19, 18,
20)(21, 23, 22, 24)(25, 28, 26, 27)(29, 32, 30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -1379,9 +1379,9 @@ perm"(1, 7, 3, 6, 2, 8, 4, 5)(9, 13, 12, 16, 10, 14, 11, 15)(17, 21, 20, 24, 18,
[ 2, -3, 2, -3 ],
[ -3, -3, -4 ],
[ 1, 2, -1, 2, 3 ]
-], [ (1, 1), (2, 9), (4, 10), (8, 4), (16, 8) ], [ (1, 1), (2, 9), (4, 9), (8, 5), (16, 3), (32, 1) ], false, false, true, true, 64), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8,
-23)(9, 26, 10, 25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 30, 18, 29)(19, 32, 20, 31)(21, 27, 22, 28)(23, 26, 24, 25)",
-perm"(1, 7, 3, 6, 2, 8, 4, 5)(9, 13, 12, 16, 10, 14, 11, 15)(17, 21, 20, 24, 18, 22, 19, 23)(25, 31, 27, 30, 26, 32, 28, 29)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 19, 18,
+], [ (1, 1), (2, 9), (4, 10), (8, 4), (16, 8) ], [ (1, 1), (2, 9), (4, 9), (8, 5), (16, 3), (32, 1) ], false, false, true, true, 64), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8,
+23)(9, 26, 10, 25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 30, 18, 29)(19, 32, 20, 31)(21, 27, 22, 28)(23, 26, 24, 25)",
+perm"(1, 7, 3, 6, 2, 8, 4, 5)(9, 13, 12, 16, 10, 14, 11, 15)(17, 21, 20, 24, 18, 22, 19, 23)(25, 31, 27, 30, 26, 32, 28, 29)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 19, 18,
20)(21, 23, 22, 24)(25, 28, 26, 27)(29, 32, 30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -1402,9 +1402,9 @@ perm"(1, 7, 3, 6, 2, 8, 4, 5)(9, 13, 12, 16, 10, 14, 11, 15)(17, 21, 20, 24, 18,
[ -2, -3, 2, -3 ],
[ -3, -3, -4 ],
[ -1, -2, -1, -2, 3 ]
-], [ (1, 1), (2, 1), (4, 18), (8, 4), (16, 8) ], [ (1, 1), (2, 1), (4, 9), (8, 5), (16, 3), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24, 8,
-22)(9, 27, 11, 25)(10, 28, 12, 26)(13, 31, 15, 29)(14, 32, 16, 30)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 26, 18, 25)(19, 28, 20, 27)(21, 30, 22, 29)(23, 32, 24, 31)",
-perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18,
+], [ (1, 1), (2, 1), (4, 18), (8, 4), (16, 8) ], [ (1, 1), (2, 1), (4, 9), (8, 5), (16, 3), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24, 8,
+22)(9, 27, 11, 25)(10, 28, 12, 26)(13, 31, 15, 29)(14, 32, 16, 30)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 26, 18, 25)(19, 28, 20, 27)(21, 30, 22, 29)(23, 32, 24, 31)",
+perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18,
20)(21, 23)(22, 24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -1422,8 +1422,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -2, -2, 5 ],
[ -1, 3, 1, 3 ],
[ -2, 3, 2, 3 ]
-], [ (1, 1), (2, 7), (4, 24) ], [ (1, 1), (2, 7), (4, 19), (8, 19), (16, 7), (32, 1) ], true, false, true, true, 1536), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8, 23)(9, 26, 10,
-25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 27)(18, 28)(19, 25)(20, 26)(21, 31)(22, 32)(23, 29)(24, 30)", perm"(1, 5)(2,
+], [ (1, 1), (2, 7), (4, 24) ], [ (1, 1), (2, 7), (4, 19), (8, 19), (16, 7), (32, 1) ], true, false, true, true, 1536), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8, 23)(9, 26, 10,
+25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 27)(18, 28)(19, 25)(20, 26)(21, 31)(22, 32)(23, 29)(24, 30)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
@@ -1448,8 +1448,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 3, 4, 3, 4 ],
[ 2, 5, 2, 5 ],
[ 1, 2, -1, 2, 4 ]
-], [ (1, 1), (2, 15), (4, 16) ], [ (1, 1), (2, 15), (4, 43), (8, 27), (16, 7), (32, 1) ], false, false, true, true, 512), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8, 23)(9, 26, 10,
-25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 11, 3, 9)(2, 12, 4, 10)(5, 15, 7, 13)(6, 16, 8, 14)(17, 25, 19, 27)(18, 26, 20, 28)(21, 29, 23, 31)(22, 30, 24, 32)", perm"(1, 5)(2,
+], [ (1, 1), (2, 15), (4, 16) ], [ (1, 1), (2, 15), (4, 43), (8, 27), (16, 7), (32, 1) ], false, false, true, true, 512), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8, 23)(9, 26, 10,
+25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 11, 3, 9)(2, 12, 4, 10)(5, 15, 7, 13)(6, 16, 8, 14)(17, 25, 19, 27)(18, 26, 20, 28)(21, 29, 23, 31)(22, 30, 24, 32)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
@@ -1468,8 +1468,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -2, -2, 4 ],
[ -1, 3, 1, 3 ],
[ -2, 3, 2, 3 ]
-], [ (1, 1), (2, 7), (4, 24) ], [ (1, 1), (2, 7), (4, 19), (8, 19), (16, 7), (32, 1) ], false, false, true, true, 512), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8, 23)(9, 26, 10,
-25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 27)(18, 28)(19, 25)(20, 26)(21, 31)(22, 32)(23, 29)(24, 30)", perm"(1, 7, 3,
+], [ (1, 1), (2, 7), (4, 24) ], [ (1, 1), (2, 7), (4, 19), (8, 19), (16, 7), (32, 1) ], false, false, true, true, 512), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8, 23)(9, 26, 10,
+25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 27)(18, 28)(19, 25)(20, 26)(21, 31)(22, 32)(23, 29)(24, 30)", perm"(1, 7, 3,
5)(2, 8, 4, 6)(9, 15, 11, 13)(10, 16, 12, 14)(17, 23, 19, 21)(18, 24, 20, 22)(25, 31, 27, 29)(26, 32, 28, 30)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
@@ -1490,8 +1490,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -3, -3, 4 ],
[ 2, 5, 2, 5 ],
[ 1, 2, -1, 2, 4 ]
-], [ (1, 1), (2, 7), (4, 24) ], [ (1, 1), (2, 7), (4, 19), (8, 11), (16, 7), (32, 1) ], false, false, true, true, 256), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8, 23)(9, 26, 10,
-25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 27)(18, 28)(19, 25)(20, 26)(21, 31)(22, 32)(23, 29)(24, 30)", perm"(1, 6, 2,
+], [ (1, 1), (2, 7), (4, 24) ], [ (1, 1), (2, 7), (4, 19), (8, 11), (16, 7), (32, 1) ], false, false, true, true, 256), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8, 23)(9, 26, 10,
+25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 27)(18, 28)(19, 25)(20, 26)(21, 31)(22, 32)(23, 29)(24, 30)", perm"(1, 6, 2,
5)(3, 8, 4, 7)(9, 14, 10, 13)(11, 16, 12, 15)(17, 22, 18, 21)(19, 24, 20, 23)(25, 30, 26, 29)(27, 32, 28, 31)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
@@ -1516,8 +1516,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 2, 4, 2, 4 ],
[ -3, 4, 3, 4 ],
[ 1, 2, -1, 2, 4 ]
-], [ (1, 1), (2, 11), (4, 20) ], [ (1, 1), (2, 11), (4, 23), (8, 19), (16, 7), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8, 23)(9, 26, 10,
-25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 11, 3, 9)(2, 12, 4, 10)(5, 15, 7, 13)(6, 16, 8, 14)(17, 25, 19, 27)(18, 26, 20, 28)(21, 29, 23, 31)(22, 30, 24, 32)", perm"(1, 8, 4,
+], [ (1, 1), (2, 11), (4, 20) ], [ (1, 1), (2, 11), (4, 23), (8, 19), (16, 7), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8, 23)(9, 26, 10,
+25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 11, 3, 9)(2, 12, 4, 10)(5, 15, 7, 13)(6, 16, 8, 14)(17, 25, 19, 27)(18, 26, 20, 28)(21, 29, 23, 31)(22, 30, 24, 32)", perm"(1, 8, 4,
5)(2, 7, 3, 6)(9, 16, 12, 13)(10, 15, 11, 14)(17, 24, 20, 21)(18, 23, 19, 22)(25, 32, 28, 29)(26, 31, 27, 30)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
@@ -1538,8 +1538,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -1, -3, 1, 3 ],
[ -2, -3, 2, 3 ],
[ 4, 3, 3, 5 ]
-], [ (1, 1), (2, 3), (4, 28) ], [ (1, 1), (2, 3), (4, 15), (8, 11), (16, 7), (32, 1) ], false, false, true, true, 384), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
-26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 27)(18, 28)(19, 25)(20, 26)(21, 31)(22, 32)(23, 29)(24, 30)", perm"(1, 5)(2,
+], [ (1, 1), (2, 3), (4, 28) ], [ (1, 1), (2, 3), (4, 15), (8, 11), (16, 7), (32, 1) ], false, false, true, true, 384), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
+26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 27)(18, 28)(19, 25)(20, 26)(21, 31)(22, 32)(23, 29)(24, 30)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 22)(18, 21)(19, 24)(20, 23)(25, 30)(26, 29)(27, 32)(28, 31)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1 ],
@@ -1568,8 +1568,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 4, 5, 4, 5 ],
[ 1, 2, 1, 2, 4 ],
[ 1, 3, 1, 3, 5 ]
-], [ (1, 1), (2, 19), (4, 12) ], [ (1, 1), (2, 19), (4, 47), (8, 31), (16, 7), (32, 1) ], false, false, true, true, 384), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
-26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 11, 3, 9)(2, 12, 4, 10)(5, 15, 7, 13)(6, 16, 8, 14)(17, 25, 19, 27)(18, 26, 20, 28)(21, 29, 23, 31)(22, 30, 24, 32)", perm"(1, 5)(2,
+], [ (1, 1), (2, 19), (4, 12) ], [ (1, 1), (2, 19), (4, 47), (8, 31), (16, 7), (32, 1) ], false, false, true, true, 384), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
+26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 11, 3, 9)(2, 12, 4, 10)(5, 15, 7, 13)(6, 16, 8, 14)(17, 25, 19, 27)(18, 26, 20, 28)(21, 29, 23, 31)(22, 30, 24, 32)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 22)(18, 21)(19, 24)(20, 23)(25, 30)(26, 29)(27, 32)(28, 31)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1 ],
@@ -1592,8 +1592,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 1, 5, 1, 5 ],
[ 3, 5, 3, 5 ],
[ 1, 3, 1, 3, 5 ]
-], [ (1, 1), (2, 15), (4, 16) ], [ (1, 1), (2, 15), (4, 27), (8, 23), (16, 7), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24, 8, 22)(9, 27, 11,
-25)(10, 28, 12, 26)(13, 31, 15, 29)(14, 32, 16, 30)", perm"(1, 11, 3, 9)(2, 12, 4, 10)(5, 15, 7, 13)(6, 16, 8, 14)(17, 25, 19, 27)(18, 26, 20, 28)(21, 29, 23, 31)(22, 30, 24, 32)", perm"(1, 5)(2,
+], [ (1, 1), (2, 15), (4, 16) ], [ (1, 1), (2, 15), (4, 27), (8, 23), (16, 7), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24, 8, 22)(9, 27, 11,
+25)(10, 28, 12, 26)(13, 31, 15, 29)(14, 32, 16, 30)", perm"(1, 11, 3, 9)(2, 12, 4, 10)(5, 15, 7, 13)(6, 16, 8, 14)(17, 25, 19, 27)(18, 26, 20, 28)(21, 29, 23, 31)(22, 30, 24, 32)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 22)(18, 21)(19, 24)(20, 23)(25, 30)(26, 29)(27, 32)(28, 31)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
@@ -1618,8 +1618,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -2, 5, 2, 5 ],
[ 3, 5, 3, 5 ],
[ 1, 3, -1, 3, 5 ]
-], [ (1, 1), (2, 7), (4, 24) ], [ (1, 1), (2, 7), (4, 19), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
-26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 27)(18, 28)(19, 25)(20, 26)(21, 31)(22, 32)(23, 29)(24, 30)", perm"(1, 7, 3,
+], [ (1, 1), (2, 7), (4, 24) ], [ (1, 1), (2, 7), (4, 19), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
+26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 27)(18, 28)(19, 25)(20, 26)(21, 31)(22, 32)(23, 29)(24, 30)", perm"(1, 7, 3,
5)(2, 8, 4, 6)(9, 15, 11, 13)(10, 16, 12, 14)(17, 24, 19, 22)(18, 23, 20, 21)(25, 32, 27, 30)(26, 31, 28, 29)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1 ],
@@ -1644,8 +1644,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -3, 5, 3, 5 ],
[ 1, 2, 1, 2, 4 ],
[ 1, -3, 1, 3, 5 ]
-], [ (1, 1), (2, 11), (4, 20) ], [ (1, 1), (2, 11), (4, 23), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
-26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 28, 18, 27)(19, 26, 20, 25)(21, 32, 22, 31)(23, 30, 24, 29)", perm"(1, 7, 3,
+], [ (1, 1), (2, 11), (4, 20) ], [ (1, 1), (2, 11), (4, 23), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
+26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 28, 18, 27)(19, 26, 20, 25)(21, 32, 22, 31)(23, 30, 24, 29)", perm"(1, 7, 3,
5)(2, 8, 4, 6)(9, 15, 11, 13)(10, 16, 12, 14)(17, 24, 19, 22)(18, 23, 20, 21)(25, 32, 27, 30)(26, 31, 28, 29)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1 ],
@@ -1668,8 +1668,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 1, 5, 1, 5 ],
[ 2, 1, -2, 1, 4 ],
[ -3, 1, 2, 2, 3, 1 ]
-], [ (1, 1), (2, 11), (4, 20) ], [ (1, 1), (2, 11), (4, 23), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 256), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24, 8, 22)(9, 27, 11,
-25)(10, 28, 12, 26)(13, 31, 15, 29)(14, 32, 16, 30)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 28, 18, 27)(19, 26, 20, 25)(21, 32, 22, 31)(23, 30, 24, 29)", perm"(1, 7, 3,
+], [ (1, 1), (2, 11), (4, 20) ], [ (1, 1), (2, 11), (4, 23), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 256), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24, 8, 22)(9, 27, 11,
+25)(10, 28, 12, 26)(13, 31, 15, 29)(14, 32, 16, 30)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 28, 18, 27)(19, 26, 20, 25)(21, 32, 22, 31)(23, 30, 24, 29)", perm"(1, 7, 3,
5)(2, 8, 4, 6)(9, 15, 11, 13)(10, 16, 12, 14)(17, 24, 19, 22)(18, 23, 20, 21)(25, 32, 27, 30)(26, 31, 28, 29)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
@@ -1690,8 +1690,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -2, -2, 5 ],
[ -2, -3, 2, 3 ],
[ -1, -3, -1, -3, 5 ]
-], [ (1, 1), (2, 3), (4, 28) ], [ (1, 1), (2, 3), (4, 15), (8, 7), (16, 7), (32, 1) ], false, false, true, true, 256), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
-26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 12, 4, 9)(2, 11, 3, 10)(5, 16, 8, 13)(6, 15, 7, 14)(17, 26, 20, 27)(18, 25, 19, 28)(21, 30, 24, 31)(22, 29, 23, 32)", perm"(1, 7, 3,
+], [ (1, 1), (2, 3), (4, 28) ], [ (1, 1), (2, 3), (4, 15), (8, 7), (16, 7), (32, 1) ], false, false, true, true, 256), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
+26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 12, 4, 9)(2, 11, 3, 10)(5, 16, 8, 13)(6, 15, 7, 14)(17, 26, 20, 27)(18, 25, 19, 28)(21, 30, 24, 31)(22, 29, 23, 32)", perm"(1, 7, 3,
5)(2, 8, 4, 6)(9, 15, 11, 13)(10, 16, 12, 14)(17, 24, 19, 22)(18, 23, 20, 21)(25, 32, 27, 30)(26, 31, 28, 29)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1 ],
@@ -1714,8 +1714,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 1, 5, 1, 5 ],
[ -2, 1, -2, 1, 5 ],
[ -3, 1, 2, 2, -3, 1 ]
-], [ (1, 1), (2, 7), (4, 24) ], [ (1, 1), (2, 7), (4, 19), (8, 7), (16, 7), (32, 1) ], false, false, true, true, 192), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
-26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 11, 3, 9)(2, 12, 4, 10)(5, 15, 7, 13)(6, 16, 8, 14)(17, 25, 19, 27)(18, 26, 20, 28)(21, 29, 23, 31)(22, 30, 24, 32)", perm"(1, 6, 2,
+], [ (1, 1), (2, 7), (4, 24) ], [ (1, 1), (2, 7), (4, 19), (8, 7), (16, 7), (32, 1) ], false, false, true, true, 192), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
+26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 11, 3, 9)(2, 12, 4, 10)(5, 15, 7, 13)(6, 16, 8, 14)(17, 25, 19, 27)(18, 26, 20, 28)(21, 29, 23, 31)(22, 30, 24, 32)", perm"(1, 6, 2,
5)(3, 8, 4, 7)(9, 14, 10, 13)(11, 16, 12, 15)(17, 21, 18, 22)(19, 23, 20, 24)(25, 29, 26, 30)(27, 31, 28, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1 ],
@@ -1734,8 +1734,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -2, -3, 2, 3 ],
[ 1, -3, 1, -3 ],
[ -3, -3, 5 ]
-], [ (1, 1), (2, 19), (4, 12) ], [ (1, 1), (2, 19), (4, 31), (8, 31), (16, 7), (32, 1) ], false, false, true, true, 1536), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24, 8, 22)(9, 27, 11,
-25)(10, 28, 12, 26)(13, 31, 15, 29)(14, 32, 16, 30)", perm"(1, 11, 3, 9)(2, 12, 4, 10)(5, 15, 7, 13)(6, 16, 8, 14)(17, 25, 19, 27)(18, 26, 20, 28)(21, 29, 23, 31)(22, 30, 24, 32)", perm"(1, 6, 2,
+], [ (1, 1), (2, 19), (4, 12) ], [ (1, 1), (2, 19), (4, 31), (8, 31), (16, 7), (32, 1) ], false, false, true, true, 1536), ([ perm"(1, 19, 3, 17)(2, 20, 4, 18)(5, 23, 7, 21)(6, 24, 8, 22)(9, 27, 11,
+25)(10, 28, 12, 26)(13, 31, 15, 29)(14, 32, 16, 30)", perm"(1, 11, 3, 9)(2, 12, 4, 10)(5, 15, 7, 13)(6, 16, 8, 14)(17, 25, 19, 27)(18, 26, 20, 28)(21, 29, 23, 31)(22, 30, 24, 32)", perm"(1, 6, 2,
5)(3, 8, 4, 7)(9, 14, 10, 13)(11, 16, 12, 15)(17, 21, 18, 22)(19, 23, 20, 24)(25, 29, 26, 30)(27, 31, 28, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
@@ -1756,9 +1756,9 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -1, -3, 1, -3 ],
[ -2, -3, 2, 3 ],
[ -3, -3, 5 ]
-], [ (1, 1), (2, 3), (4, 28) ], [ (1, 1), (2, 3), (4, 15), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 512), ([ perm"(1, 20, 4, 18, 2, 19, 3, 17)(5, 24, 8, 22, 6, 23, 7, 21)(9, 28, 12, 26,
-10, 27, 11, 25)(13, 32, 16, 30, 14, 31, 15, 29)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)", perm"(1, 5)(2, 6)(3,
-7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22,
+], [ (1, 1), (2, 3), (4, 28) ], [ (1, 1), (2, 3), (4, 15), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 512), ([ perm"(1, 20, 4, 18, 2, 19, 3, 17)(5, 24, 8, 22, 6, 23, 7, 21)(9, 28, 12, 26,
+10, 27, 11, 25)(13, 32, 16, 30, 14, 31, 15, 29)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)", perm"(1, 5)(2, 6)(3,
+7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22,
23)(25, 28, 26, 27)(29, 32, 30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 2, 2 ],
[ 3, 3 ],
@@ -1775,8 +1775,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -1, 2, 1, 2 ],
[ -1, 3, 1, 3 ],
[ 2, 3, 2, 3 ]
-], [ (1, 1), (2, 7), (4, 8), (8, 16) ], [ (1, 1), (2, 7), (4, 11), (8, 11), (16, 7), (32, 1) ], true, false, true, true, 384), ([ perm"(1, 20, 4, 18, 2, 19, 3, 17)(5, 24, 8, 22, 6, 23, 7, 21)(9, 28,
-12, 26, 10, 27, 11, 25)(13, 32, 16, 30, 14, 31, 15, 29)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 26)(18, 25)(19, 28)(20, 27)(21, 30)(22, 29)(23, 32)(24, 31)", perm"(1, 5)(2,
+], [ (1, 1), (2, 7), (4, 8), (8, 16) ], [ (1, 1), (2, 7), (4, 11), (8, 11), (16, 7), (32, 1) ], true, false, true, true, 384), ([ perm"(1, 20, 4, 18, 2, 19, 3, 17)(5, 24, 8, 22, 6, 23, 7, 21)(9, 28,
+12, 26, 10, 27, 11, 25)(13, 32, 16, 30, 14, 31, 15, 29)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 26)(18, 25)(19, 28)(20, 27)(21, 30)(22, 29)(23, 32)(24, 31)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22,
23)(25, 28, 26, 27)(29, 32, 30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 2, 2 ],
@@ -1796,8 +1796,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 2, 3, 2, 3 ],
[ 2, -4, 2, 4 ],
[ -1, 2, -1, 2, -4 ]
-], [ (1, 1), (2, 7), (4, 8), (8, 16) ], [ (1, 1), (2, 7), (4, 11), (8, 11), (16, 7), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 20, 4, 18, 2, 19, 3, 17)(5, 24, 8, 22, 6, 23, 7, 21)(9, 28,
-12, 26, 10, 27, 11, 25)(13, 32, 16, 30, 14, 31, 15, 29)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)", perm"(1, 5)(2,
+], [ (1, 1), (2, 7), (4, 8), (8, 16) ], [ (1, 1), (2, 7), (4, 11), (8, 11), (16, 7), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 20, 4, 18, 2, 19, 3, 17)(5, 24, 8, 22, 6, 23, 7, 21)(9, 28,
+12, 26, 10, 27, 11, 25)(13, 32, 16, 30, 14, 31, 15, 29)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 14)(10, 13)(11, 16)(12, 15)(17, 21)(18, 22)(19, 23)(20, 24)(25, 30)(26, 29)(27, 32)(28, 31)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22,
23)(25, 28, 26, 27)(29, 32, 30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 2, 2 ],
@@ -1815,9 +1815,9 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -1, 2, 1, 2 ],
[ -1, 3, 1, 3 ],
[ 2, 3, 2, 3, 5 ]
-], [ (1, 1), (2, 7), (4, 8), (8, 16) ], [ (1, 1), (2, 7), (4, 7), (8, 11), (16, 7), (32, 1) ], false, false, true, true, 96), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9,
-25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 27)(18, 28)(19, 26)(20, 25)(21, 31)(22, 32)(23, 30)(24, 29)", perm"(1,
-5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 19, 18, 20)(21,
+], [ (1, 1), (2, 7), (4, 8), (8, 16) ], [ (1, 1), (2, 7), (4, 7), (8, 11), (16, 7), (32, 1) ], false, false, true, true, 96), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9,
+25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 27)(18, 28)(19, 26)(20, 25)(21, 31)(22, 32)(23, 30)(24, 29)", perm"(1,
+5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 19, 18, 20)(21,
23, 22, 24)(25, 28, 26, 27)(29, 32, 30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -1840,7 +1840,7 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -4, -4, 5 ],
[ 1, 2, 1, 2, 4 ]
], [ (1, 1), (2, 19), (4, 4), (8, 8) ], [ (1, 1), (2, 19), (4, 27), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 256), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8, 23)(9, 26,
-10, 25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 27)(18, 28)(19, 26)(20, 25)(21, 31)(22, 32)(23, 30)(24, 29)", perm"(1, 5)(2,
+10, 25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 27)(18, 28)(19, 26)(20, 25)(21, 31)(22, 32)(23, 30)(24, 29)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 19, 18, 20)(21, 23, 22,
24)(25, 28, 26, 27)(29, 32, 30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
@@ -1865,9 +1865,9 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 2, -4, 2, -4 ],
[ 3, -4, 3, 4 ],
[ -1, 2, -1, 2, -4 ]
-], [ (1, 1), (2, 11), (4, 12), (8, 8) ], [ (1, 1), (2, 11), (4, 19), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8, 23)(9,
-26, 10, 25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 28, 18, 27)(19, 25, 20, 26)(21, 32, 22, 31)(23, 29, 24, 30)", perm"(1,
-5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 19, 18, 20)(21,
+], [ (1, 1), (2, 11), (4, 12), (8, 8) ], [ (1, 1), (2, 11), (4, 19), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 128), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8, 23)(9,
+26, 10, 25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 28, 18, 27)(19, 25, 20, 26)(21, 32, 22, 31)(23, 29, 24, 30)", perm"(1,
+5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 19, 18, 20)(21,
23, 22, 24)(25, 28, 26, 27)(29, 32, 30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -1893,9 +1893,9 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -2, -4, 2, -4 ],
[ 3, -4, 3, 4 ],
[ -1, -2, -1, 2, -4 ]
-], [ (1, 1), (2, 3), (4, 20), (8, 8) ], [ (1, 1), (2, 3), (4, 11), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 256), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9,
+], [ (1, 1), (2, 3), (4, 20), (8, 8) ], [ (1, 1), (2, 3), (4, 11), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 256), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9,
25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 27)(18, 28)(19, 26)(20, 25)(21, 31)(22, 32)(23, 30)(24, 29)", perm"(1, 6,
-2, 5)(3, 8, 4, 7)(9, 14, 10, 13)(11, 16, 12, 15)(17, 22, 18, 21)(19, 24, 20, 23)(25, 30, 26, 29)(27, 32, 28, 31)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 19, 18, 20)(21, 23,
+2, 5)(3, 8, 4, 7)(9, 14, 10, 13)(11, 16, 12, 15)(17, 22, 18, 21)(19, 24, 20, 23)(25, 30, 26, 29)(27, 32, 28, 31)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 19, 18, 20)(21, 23,
22, 24)(25, 28, 26, 27)(29, 32, 30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -1919,9 +1919,9 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 2, -4, 2, -4 ],
[ -3, -4, 3, 4 ],
[ 1, 2, 1, 2, 4 ]
-], [ (1, 1), (2, 11), (4, 12), (8, 8) ], [ (1, 1), (2, 11), (4, 11), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 64), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9,
-25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 27)(18, 28)(19, 26)(20, 25)(21, 31)(22, 32)(23, 30)(24, 29)", perm"(1,
-5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 22)(18, 21)(19, 24)(20, 23)(25, 30)(26, 29)(27, 32)(28, 31)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 19, 18, 20)(21,
+], [ (1, 1), (2, 11), (4, 12), (8, 8) ], [ (1, 1), (2, 11), (4, 11), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 64), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9,
+25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 27)(18, 28)(19, 26)(20, 25)(21, 31)(22, 32)(23, 30)(24, 29)", perm"(1,
+5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 22)(18, 21)(19, 24)(20, 23)(25, 30)(26, 29)(27, 32)(28, 31)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 19, 18, 20)(21,
23, 22, 24)(25, 28, 26, 27)(29, 32, 30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -1943,9 +1943,9 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -4, -4, 5 ],
[ 1, 2, 1, 2, 4 ],
[ 1, 3, 1, 3, 5 ]
-], [ (1, 1), (2, 15), (4, 8), (8, 8) ], [ (1, 1), (2, 15), (4, 19), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 64), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9,
-25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 28, 18, 27)(19, 25, 20, 26)(21, 32, 22, 31)(23, 29, 24, 30)", perm"(1,
-5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 22)(18, 21)(19, 24)(20, 23)(25, 30)(26, 29)(27, 32)(28, 31)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 19, 18, 20)(21,
+], [ (1, 1), (2, 15), (4, 8), (8, 8) ], [ (1, 1), (2, 15), (4, 19), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 64), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9,
+25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 28, 18, 27)(19, 25, 20, 26)(21, 32, 22, 31)(23, 29, 24, 30)", perm"(1,
+5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 22)(18, 21)(19, 24)(20, 23)(25, 30)(26, 29)(27, 32)(28, 31)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 11, 10, 12)(13, 15, 14, 16)(17, 19, 18, 20)(21,
23, 22, 24)(25, 28, 26, 27)(29, 32, 30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -1969,8 +1969,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 3, -4, 3, 4 ],
[ -2, 1, -2, 1, 4 ],
[ 3, 1, 2, 2, 3, 1 ]
-], [ (1, 1), (2, 7), (4, 16), (8, 8) ], [ (1, 1), (2, 7), (4, 11), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 64), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8, 23)(9, 26,
-10, 25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)", perm"(1, 5)(2,
+], [ (1, 1), (2, 7), (4, 16), (8, 8) ], [ (1, 1), (2, 7), (4, 11), (8, 15), (16, 7), (32, 1) ], false, false, true, true, 64), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8, 23)(9, 26,
+10, 25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
@@ -1993,8 +1993,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -1, 4, 1, 4 ],
[ 2, 4, 2, 4 ],
[ 3, 4, 3, 4 ]
-], [ (1, 1), (2, 15), (4, 16) ], [ (1, 1), (2, 15), (4, 43), (8, 43), (16, 15), (32, 1) ], true, false, true, true, 21504), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
-26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 26)(18, 25)(19, 28)(20, 27)(21, 30)(22, 29)(23, 32)(24, 31)", perm"(1, 5)(2,
+], [ (1, 1), (2, 15), (4, 16) ], [ (1, 1), (2, 15), (4, 43), (8, 43), (16, 15), (32, 1) ], true, false, true, true, 21504), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
+26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 26)(18, 25)(19, 28)(20, 27)(21, 30)(22, 29)(23, 32)(24, 31)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1 ],
@@ -2023,8 +2023,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 3, 5, 3, 5 ],
[ 4, 5, 4, 5 ],
[ 1, 2, 1, 2, 5 ]
-], [ (1, 1), (2, 23), (4, 8) ], [ (1, 1), (2, 23), (4, 67), (8, 51), (16, 15), (32, 1) ], false, false, true, true, 3072), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8, 23)(9, 26, 10,
-25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 25, 18, 26)(19, 27, 20, 28)(21, 29, 22, 30)(23, 31, 24, 32)", perm"(1, 5)(2,
+], [ (1, 1), (2, 23), (4, 8) ], [ (1, 1), (2, 23), (4, 67), (8, 51), (16, 15), (32, 1) ], false, false, true, true, 3072), ([ perm"(1, 18, 2, 17)(3, 20, 4, 19)(5, 22, 6, 21)(7, 24, 8, 23)(9, 26, 10,
+25)(11, 28, 12, 27)(13, 30, 14, 29)(15, 32, 16, 31)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 25, 18, 26)(19, 27, 20, 28)(21, 29, 22, 30)(23, 31, 24, 32)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1, 1, 1 ],
@@ -2049,8 +2049,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -1, 4, 1, 4 ],
[ -2, 4, 2, 4 ],
[ 3, 4, 3, 4 ]
-], [ (1, 1), (2, 7), (4, 24) ], [ (1, 1), (2, 7), (4, 19), (8, 35), (16, 15), (32, 1) ], false, false, true, true, 9216), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
-26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 26)(18, 25)(19, 28)(20, 27)(21, 30)(22, 29)(23, 32)(24, 31)", perm"(1, 6, 2,
+], [ (1, 1), (2, 7), (4, 24) ], [ (1, 1), (2, 7), (4, 19), (8, 35), (16, 15), (32, 1) ], false, false, true, true, 9216), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
+26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 26)(18, 25)(19, 28)(20, 27)(21, 30)(22, 29)(23, 32)(24, 31)", perm"(1, 6, 2,
5)(3, 8, 4, 7)(9, 14, 10, 13)(11, 16, 12, 15)(17, 22, 18, 21)(19, 24, 20, 23)(25, 30, 26, 29)(27, 32, 28, 31)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1 ],
@@ -2073,8 +2073,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 2, 4, 2, 4 ],
[ -3, 4, 3, 4 ],
[ 1, 2, 1, 2, 5 ]
-], [ (1, 1), (2, 15), (4, 16) ], [ (1, 1), (2, 15), (4, 27), (8, 35), (16, 15), (32, 1) ], false, false, true, true, 768), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
-26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 26)(18, 25)(19, 28)(20, 27)(21, 30)(22, 29)(23, 32)(24, 31)", perm"(1, 5)(2,
+], [ (1, 1), (2, 15), (4, 16) ], [ (1, 1), (2, 15), (4, 27), (8, 35), (16, 15), (32, 1) ], false, false, true, true, 768), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
+26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 26)(18, 25)(19, 28)(20, 27)(21, 30)(22, 29)(23, 32)(24, 31)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 14)(10, 13)(11, 16)(12, 15)(17, 21)(18, 22)(19, 23)(20, 24)(25, 30)(26, 29)(27, 32)(28, 31)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 20)(18, 19)(21, 24)(22,
23)(25, 28)(26, 27)(29, 32)(30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1 ],
@@ -2103,8 +2103,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ 1, 2, 1, 2, 5 ],
[ 1, 4, 1, 4, 5 ],
[ 3, 1, 2, 1, 3, 2 ]
-], [ (1, 1), (2, 19), (4, 12) ], [ (1, 1), (2, 19), (4, 39), (8, 35), (16, 15), (32, 1) ], false, false, true, true, 1152), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
-26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 25, 18, 26)(19, 27, 20, 28)(21, 29, 22, 30)(23, 31, 24, 32)", perm"(1, 6, 2,
+], [ (1, 1), (2, 19), (4, 12) ], [ (1, 1), (2, 19), (4, 39), (8, 35), (16, 15), (32, 1) ], false, false, true, true, 1152), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
+26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 10, 2, 9)(3, 12, 4, 11)(5, 14, 6, 13)(7, 16, 8, 15)(17, 25, 18, 26)(19, 27, 20, 28)(21, 29, 22, 30)(23, 31, 24, 32)", perm"(1, 6, 2,
5)(3, 8, 4, 7)(9, 13, 10, 14)(11, 15, 12, 16)(17, 22, 18, 21)(19, 24, 20, 23)(25, 29, 26, 30)(27, 31, 28, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 20)(18, 19)(21, 24)(22,
23)(25, 28)(26, 27)(29, 32)(30, 31)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1 ],
@@ -2129,8 +2129,8 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -2, 4, 2, 4 ],
[ -3, 4, 3, 4 ],
[ 4, 1, 2, 2, 4, 1 ]
-], [ (1, 1), (2, 11), (4, 20) ], [ (1, 1), (2, 11), (4, 15), (8, 35), (16, 15), (32, 1) ], false, false, true, true, 1920), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
-26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)", perm"(1, 5)(2,
+], [ (1, 1), (2, 11), (4, 20) ], [ (1, 1), (2, 11), (4, 15), (8, 35), (16, 15), (32, 1) ], false, false, true, true, 1920), ([ perm"(1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10,
+26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32)", perm"(1, 5)(2,
6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22,
24)(25, 27)(26, 28)(29, 31)(30, 32)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)" ], [
[ 1, 1 ],
@@ -2166,30 +2166,30 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -1, -2, 1, 2 ]
-], [ (1, 1), (3, 2), (11, 10), (33, 20) ], [ (1, 1), (3, 1), (11, 1), (33, 1) ], true, true, true, true, 20) ], [ ([ perm"(1, 18)(2, 19)(3, 20)(4, 21)(5, 22)(6, 23)(7, 24)(8, 25)(9, 26)(10, 27)(11,
+], [ (1, 1), (3, 2), (11, 10), (33, 20) ], [ (1, 1), (3, 1), (11, 1), (33, 1) ], true, true, true, true, 20) ], [ ([ perm"(1, 18)(2, 19)(3, 20)(4, 21)(5, 22)(6, 23)(7, 24)(8, 25)(9, 26)(10, 27)(11,
28)(12, 29)(13, 30)(14, 31)(15, 32)(16, 33)(17, 34)", perm"(1, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34)" ], [
[ 1, 1 ],
[ -2, 1, -2, 1 ],
[ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -2, 1, -2, 1 ]
-], [ (1, 1), (2, 17), (17, 16) ], [ (1, 1), (2, 17), (17, 1), (34, 1) ], false, false, true, false, 272), ([ perm"(1, 18)(2, 19)(3, 20)(4, 21)(5, 22)(6, 23)(7, 24)(8, 25)(9, 26)(10, 27)(11, 28)(12,
+], [ (1, 1), (2, 17), (17, 16) ], [ (1, 1), (2, 17), (17, 1), (34, 1) ], false, false, true, false, 272), ([ perm"(1, 18)(2, 19)(3, 20)(4, 21)(5, 22)(6, 23)(7, 24)(8, 25)(9, 26)(10, 27)(11, 28)(12,
29)(13, 30)(14, 31)(15, 32)(16, 33)(17, 34)", perm"(1, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(18, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19)" ], [
[ 1, 1 ],
[ -2, 1, 2, 1 ],
[ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -2, 1, 2, 1 ]
-], [ (1, 1), (2, 1), (17, 16), (34, 16) ], [ (1, 1), (2, 1), (17, 1), (34, 1) ], true, true, true, true, 16) ], [ ([ perm"(1, 29, 22, 15, 8)(2, 30, 23, 16, 9)(3, 31, 24, 17, 10)(4, 32, 25, 18, 11)(5,
+], [ (1, 1), (2, 1), (17, 16), (34, 16) ], [ (1, 1), (2, 1), (17, 1), (34, 1) ], true, true, true, true, 16) ], [ ([ perm"(1, 29, 22, 15, 8)(2, 30, 23, 16, 9)(3, 31, 24, 17, 10)(4, 32, 25, 18, 11)(5,
33, 26, 19, 12)(6, 34, 27, 20, 13)(7, 35, 28, 21, 14)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)(29, 35, 34, 33, 32, 31, 30)" ], [
[ 1, 1, 1, 1, 1 ],
[ -1, -2, 1, 2 ],
[ -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -1, -2, 1, 2 ]
-], [ (1, 1), (5, 4), (7, 6), (35, 24) ], [ (1, 1), (5, 1), (7, 1), (35, 1) ], true, true, true, true, 24) ], [ ([ perm"(1, 28, 10, 19)(2, 29, 11, 20)(3, 30, 12, 21)(4, 31, 13, 22)(5, 32, 14, 23)(6,
-33, 15, 24)(7, 34, 16, 25)(8, 35, 17, 26)(9, 36, 18, 27)", perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 28)(20, 29)(21, 30)(22, 31)(23, 32)(24, 33)(25, 34)(26, 35)(27,
-36)", perm"(1, 8, 5, 2, 9, 6, 3, 7, 4)(10, 17, 14, 11, 18, 15, 12, 16, 13)(19, 22, 25, 21, 24, 27, 20, 23, 26)(28, 31, 34, 30, 33, 36, 29, 32, 35)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13,
+], [ (1, 1), (5, 4), (7, 6), (35, 24) ], [ (1, 1), (5, 1), (7, 1), (35, 1) ], true, true, true, true, 24) ], [ ([ perm"(1, 28, 10, 19)(2, 29, 11, 20)(3, 30, 12, 21)(4, 31, 13, 22)(5, 32, 14, 23)(6,
+33, 15, 24)(7, 34, 16, 25)(8, 35, 17, 26)(9, 36, 18, 27)", perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 28)(20, 29)(21, 30)(22, 31)(23, 32)(24, 33)(25, 34)(26, 35)(27,
+36)", perm"(1, 8, 5, 2, 9, 6, 3, 7, 4)(10, 17, 14, 11, 18, 15, 12, 16, 13)(19, 22, 25, 21, 24, 27, 20, 23, 26)(28, 31, 34, 30, 33, 36, 29, 32, 35)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13,
15, 14)(16, 18, 17)(19, 20, 21)(22, 23, 24)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -2201,9 +2201,9 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -1, -1, 2 ],
[ -1, -3, 1, -3 ],
[ 3, 3, 3, 4 ]
-], [ (1, 1), (2, 1), (3, 2), (4, 18), (6, 2), (9, 6), (18, 6) ], [ (1, 1), (2, 1), (3, 1), (4, 9), (6, 1), (9, 1), (12, 3), (18, 1), (36, 1) ], false, false, true, false, 108), ([ perm"(1, 22, 4,
-19)(2, 23, 5, 20)(3, 24, 6, 21)(7, 28, 10, 25)(8, 29, 11, 26)(9, 30, 12, 27)(13, 34, 16, 31)(14, 35, 17, 32)(15, 36, 18, 33)", perm"(1, 15, 9, 3, 14, 8, 2, 13, 7)(4, 18, 12, 6, 17, 11, 5, 16, 10)(19,
-33, 27, 21, 32, 26, 20, 31, 25)(22, 36, 30, 24, 35, 29, 23, 34, 28)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32,
+], [ (1, 1), (2, 1), (3, 2), (4, 18), (6, 2), (9, 6), (18, 6) ], [ (1, 1), (2, 1), (3, 1), (4, 9), (6, 1), (9, 1), (12, 3), (18, 1), (36, 1) ], false, false, true, false, 108), ([ perm"(1, 22, 4,
+19)(2, 23, 5, 20)(3, 24, 6, 21)(7, 28, 10, 25)(8, 29, 11, 26)(9, 30, 12, 27)(13, 34, 16, 31)(14, 35, 17, 32)(15, 36, 18, 33)", perm"(1, 15, 9, 3, 14, 8, 2, 13, 7)(4, 18, 12, 6, 17, 11, 5, 16, 10)(19,
+33, 27, 21, 32, 26, 20, 31, 25)(22, 36, 30, 24, 35, 29, 23, 34, 28)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32,
35)(33, 36)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 33, 32)(34, 36, 35)" ], [
[ 1, 1, 1, 1 ],
[ 3, 3 ],
@@ -2215,9 +2215,9 @@ perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19,
[ -1, -1, 3 ],
[ -1, -2, 1, 2 ],
[ 2, 2, 2, -4 ]
-], [ (1, 1), (2, 1), (3, 2), (4, 2), (6, 2), (9, 6), (12, 4), (18, 6), (36, 12) ], [ (1, 1), (2, 1), (3, 1), (4, 1), (6, 1), (9, 1), (12, 1), (18, 1), (36, 1) ], true, true, true, true, 12), ([
-perm"(1, 33, 21, 9, 29, 17, 5, 25, 13)(2, 34, 22, 10, 30, 18, 6, 26, 14)(3, 35, 23, 11, 31, 19, 7, 27, 15)(4, 36, 24, 12, 32, 20, 8, 28, 16)", perm"(1, 9, 5)(2, 10, 6)(3, 11, 7)(4, 12, 8)(13, 21,
-17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 28)(26,
+], [ (1, 1), (2, 1), (3, 2), (4, 2), (6, 2), (9, 6), (12, 4), (18, 6), (36, 12) ], [ (1, 1), (2, 1), (3, 1), (4, 1), (6, 1), (9, 1), (12, 1), (18, 1), (36, 1) ], true, true, true, true, 12), ([
+perm"(1, 33, 21, 9, 29, 17, 5, 25, 13)(2, 34, 22, 10, 30, 18, 6, 26, 14)(3, 35, 23, 11, 31, 19, 7, 27, 15)(4, 36, 24, 12, 32, 20, 8, 28, 16)", perm"(1, 9, 5)(2, 10, 6)(3, 11, 7)(4, 12, 8)(13, 21,
+17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 28)(26,
27)(29, 32)(30, 31)(33, 36)(34, 35)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 16)(14, 15)(17, 20)(18, 19)(21, 24)(22, 23)(25, 27)(26, 28)(29, 31)(30, 32)(33, 35)(34, 36)" ], [
[ 2, 2, 2 ],
[ 3, 3 ],
@@ -2233,8 +2233,8 @@ perm"(1, 33, 21, 9, 29, 17, 5, 25, 13)(2, 34, 22, 10, 30, 18, 6, 26, 14)(3, 35,
[ -2, 3, 2, 3 ],
[ 3, 4, 3, 4 ],
[ 1, 3, -1, 3, 4 ]
-], [ (1, 1), (2, 3), (3, 2), (6, 6), (9, 24) ], [ (1, 1), (2, 3), (3, 1), (4, 1), (6, 3), (9, 4), (12, 1), (36, 1) ], false, false, true, false, 72), ([ perm"(1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6,
-24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)", perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 28)(20, 29)(21, 30)(22,
+], [ (1, 1), (2, 3), (3, 2), (6, 6), (9, 24) ], [ (1, 1), (2, 3), (3, 1), (4, 1), (6, 3), (9, 4), (12, 1), (36, 1) ], false, false, true, false, 72), ([ perm"(1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6,
+24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)", perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 28)(20, 29)(21, 30)(22,
31)(23, 32)(24, 33)(25, 34)(26, 35)(27, 36)", perm"(1, 8, 5, 2, 9, 6, 3, 7, 4)(10, 17, 14, 11, 18, 15, 12, 16, 13)(19, 22, 25, 21, 24, 27, 20, 23, 26)(28, 31, 34, 30, 33, 36, 29, 32, 35)", perm"(1, 3,
2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 20, 21)(22, 23, 24)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)" ], [
[ 1, 1 ],
@@ -2249,9 +2249,9 @@ perm"(1, 33, 21, 9, 29, 17, 5, 25, 13)(2, 34, 22, 10, 30, 18, 6, 26, 14)(3, 35,
[ 1, -3, 1, -3 ],
[ 2, -3, 2, 3 ],
[ 3, 3, 3, 4 ]
-], [ (1, 1), (2, 19), (3, 2), (6, 2), (9, 6), (18, 6) ], [ (1, 1), (2, 19), (3, 1), (4, 9), (6, 7), (9, 1), (12, 3), (18, 3), (36, 1) ], false, false, true, false, 108), ([ perm"(1, 19)(2, 20)(3,
+], [ (1, 1), (2, 19), (3, 2), (6, 2), (9, 6), (18, 6) ], [ (1, 1), (2, 19), (3, 1), (4, 9), (6, 7), (9, 1), (12, 3), (18, 3), (36, 1) ], false, false, true, false, 108), ([ perm"(1, 19)(2, 20)(3,
21)(4, 22)(5, 23)(6, 24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)", perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 28)(20,
-29)(21, 30)(22, 31)(23, 32)(24, 33)(25, 34)(26, 35)(27, 36)", perm"(1, 9, 6, 3, 8, 5, 2, 7, 4)(10, 18, 15, 12, 17, 14, 11, 16, 13)(19, 27, 24, 21, 26, 23, 20, 25, 22)(28, 36, 33, 30, 35, 32, 29, 34,
+29)(21, 30)(22, 31)(23, 32)(24, 33)(25, 34)(26, 35)(27, 36)", perm"(1, 9, 6, 3, 8, 5, 2, 7, 4)(10, 18, 15, 12, 17, 14, 11, 16, 13)(19, 27, 24, 21, 26, 23, 20, 25, 22)(28, 36, 33, 30, 35, 32, 29, 34,
31)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 33, 32)(34, 36, 35)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -2265,8 +2265,8 @@ perm"(1, 33, 21, 9, 29, 17, 5, 25, 13)(2, 34, 22, 10, 30, 18, 6, 26, 14)(3, 35,
[ 1, -3, 1, 3 ],
[ 2, -3, 2, 3 ],
[ 3, 3, 3, -4 ]
-], [ (1, 1), (2, 3), (3, 2), (6, 6), (9, 6), (18, 18) ], [ (1, 1), (2, 3), (3, 1), (4, 1), (6, 3), (9, 1), (12, 1), (18, 3), (36, 1) ], true, false, true, true, 36), ([ perm"(1, 22, 4, 19)(2, 23, 5,
-20)(3, 24, 6, 21)(7, 28, 10, 25)(8, 29, 11, 26)(9, 30, 12, 27)(13, 34, 16, 31)(14, 35, 17, 32)(15, 36, 18, 33)", perm"(1, 13, 7)(2, 14, 8)(3, 15, 9)(4, 16, 10)(5, 17, 11)(6, 18, 12)(19, 31, 25)(20,
+], [ (1, 1), (2, 3), (3, 2), (6, 6), (9, 6), (18, 18) ], [ (1, 1), (2, 3), (3, 1), (4, 1), (6, 3), (9, 1), (12, 1), (18, 3), (36, 1) ], true, false, true, true, 36), ([ perm"(1, 22, 4, 19)(2, 23, 5,
+20)(3, 24, 6, 21)(7, 28, 10, 25)(8, 29, 11, 26)(9, 30, 12, 27)(13, 34, 16, 31)(14, 35, 17, 32)(15, 36, 18, 33)", perm"(1, 13, 7)(2, 14, 8)(3, 15, 9)(4, 16, 10)(5, 17, 11)(6, 18, 12)(19, 31, 25)(20,
32, 26)(21, 33, 27)(22, 34, 28)(23, 35, 29)(24, 36, 30)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)",
perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 20, 21)(22, 23, 24)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)" ], [
[ 1, 1, 1, 1 ],
@@ -2282,9 +2282,9 @@ perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 20, 21)
[ -1, -2, 1, 2 ],
[ -1, -4, 1, -4 ],
[ -2, -4, 2, 4 ]
-], [ (1, 1), (2, 1), (3, 8), (4, 6), (6, 8), (12, 12) ], [ (1, 1), (2, 1), (3, 4), (4, 3), (6, 4), (9, 1), (12, 4), (18, 1), (36, 1) ], false, false, true, false, 24), ([ perm"(1, 28, 10, 19)(2, 29,
-11, 20)(3, 30, 12, 21)(4, 31, 13, 22)(5, 32, 14, 23)(6, 33, 15, 24)(7, 34, 16, 25)(8, 35, 17, 26)(9, 36, 18, 27)", perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 28)(20,
-29)(21, 30)(22, 31)(23, 32)(24, 33)(25, 34)(26, 35)(27, 36)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 22, 25)(20, 23, 26)(21, 24, 27)(28, 31, 34)(29, 32, 35)(30, 33,
+], [ (1, 1), (2, 1), (3, 8), (4, 6), (6, 8), (12, 12) ], [ (1, 1), (2, 1), (3, 4), (4, 3), (6, 4), (9, 1), (12, 4), (18, 1), (36, 1) ], false, false, true, false, 24), ([ perm"(1, 28, 10, 19)(2, 29,
+11, 20)(3, 30, 12, 21)(4, 31, 13, 22)(5, 32, 14, 23)(6, 33, 15, 24)(7, 34, 16, 25)(8, 35, 17, 26)(9, 36, 18, 27)", perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 28)(20,
+29)(21, 30)(22, 31)(23, 32)(24, 33)(25, 34)(26, 35)(27, 36)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 22, 25)(20, 23, 26)(21, 24, 27)(28, 31, 34)(29, 32, 35)(30, 33,
36)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 20, 21)(22, 23, 24)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -2300,8 +2300,8 @@ perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 20, 21)
[ -1, -4, 1, -4 ],
[ -3, -4, 3, 4 ]
], [ (1, 1), (2, 1), (3, 8), (4, 18), (6, 8) ], [ (1, 1), (2, 1), (3, 4), (4, 9), (6, 4), (9, 1), (12, 12), (18, 1), (36, 1) ], false, false, true, false, 864), ([ perm"(1, 20, 2, 19)(3, 22, 4, 21)(5,
-24, 6, 23)(7, 26, 8, 25)(9, 28, 10, 27)(11, 30, 12, 29)(13, 32, 14, 31)(15, 34, 16, 33)(17, 36, 18, 35)", perm"(1, 13, 7)(2, 14, 8)(3, 15, 9)(4, 16, 10)(5, 17, 11)(6, 18, 12)(19, 31, 25)(20, 32,
-26)(21, 33, 27)(22, 34, 28)(23, 35, 29)(24, 36, 30)", perm"(1, 5, 3)(2, 6, 4)(7, 11, 9)(8, 12, 10)(13, 17, 15)(14, 18, 16)(19, 23, 21)(20, 24, 22)(25, 29, 27)(26, 30, 28)(31, 35, 33)(32, 36, 34)",
+24, 6, 23)(7, 26, 8, 25)(9, 28, 10, 27)(11, 30, 12, 29)(13, 32, 14, 31)(15, 34, 16, 33)(17, 36, 18, 35)", perm"(1, 13, 7)(2, 14, 8)(3, 15, 9)(4, 16, 10)(5, 17, 11)(6, 18, 12)(19, 31, 25)(20, 32,
+26)(21, 33, 27)(22, 34, 28)(23, 35, 29)(24, 36, 30)", perm"(1, 5, 3)(2, 6, 4)(7, 11, 9)(8, 12, 10)(13, 17, 15)(14, 18, 16)(19, 23, 21)(20, 24, 22)(25, 29, 27)(26, 30, 28)(31, 35, 33)(32, 36, 34)",
perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2 ],
@@ -2317,8 +2317,8 @@ perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21,
[ -1, -3, 1, 3 ],
[ -2, -3, 2, 3 ]
], [ (1, 1), (2, 1), (3, 8), (4, 2), (6, 8), (12, 16) ], [ (1, 1), (2, 1), (3, 4), (4, 1), (6, 4), (9, 1), (12, 4), (18, 1), (36, 1) ], true, false, true, true, 96), ([ perm"(1, 28, 10, 19)(2, 29, 11,
-20)(3, 30, 12, 21)(4, 31, 13, 22)(5, 32, 14, 23)(6, 33, 15, 24)(7, 34, 16, 25)(8, 35, 17, 26)(9, 36, 18, 27)", perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 28)(20, 29)(21,
-30)(22, 31)(23, 32)(24, 33)(25, 34)(26, 35)(27, 36)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 13, 16)(11, 14, 17)(12, 15, 18)(19, 26, 24)(20, 27, 22)(21, 25, 23)(28, 33, 35)(29, 31, 36)(30, 32, 34)",
+20)(3, 30, 12, 21)(4, 31, 13, 22)(5, 32, 14, 23)(6, 33, 15, 24)(7, 34, 16, 25)(8, 35, 17, 26)(9, 36, 18, 27)", perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 28)(20, 29)(21,
+30)(22, 31)(23, 32)(24, 33)(25, 34)(26, 35)(27, 36)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 13, 16)(11, 14, 17)(12, 15, 18)(19, 26, 24)(20, 27, 22)(21, 25, 23)(28, 33, 35)(29, 31, 36)(30, 32, 34)",
perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 11, 12)(13, 14, 15)(16, 17, 18)(19, 23, 27)(20, 24, 25)(21, 22, 26)(28, 36, 32)(29, 34, 33)(30, 35, 31)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -2335,9 +2335,9 @@ perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 11, 12)(13, 14, 15)(16, 17, 18)(19, 23, 27)
[ 2, -4, 2, -4 ],
[ -3, -4, 3, 4 ],
[ 1, -3, -1, -3, 4 ]
-], [ (1, 1), (2, 9), (3, 8), (4, 18) ], [ (1, 1), (2, 9), (3, 4), (4, 9), (6, 12), (9, 1), (18, 1), (36, 1) ], false, false, true, false, 144), ([ perm"(1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6, 24)(7,
-25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)", perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 28)(20, 29)(21, 30)(22, 31)(23,
-32)(24, 33)(25, 34)(26, 35)(27, 36)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 13, 16)(11, 14, 17)(12, 15, 18)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 31, 34)(29, 32, 35)(30, 33, 36)", perm"(1, 3, 2)(4,
+], [ (1, 1), (2, 9), (3, 8), (4, 18) ], [ (1, 1), (2, 9), (3, 4), (4, 9), (6, 12), (9, 1), (18, 1), (36, 1) ], false, false, true, false, 144), ([ perm"(1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6, 24)(7,
+25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)", perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 28)(20, 29)(21, 30)(22, 31)(23,
+32)(24, 33)(25, 34)(26, 35)(27, 36)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 13, 16)(11, 14, 17)(12, 15, 18)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 31, 34)(29, 32, 35)(30, 33, 36)", perm"(1, 3, 2)(4,
6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 20, 21)(22, 23, 24)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -2356,9 +2356,9 @@ perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 11, 12)(13, 14, 15)(16, 17, 18)(19, 23, 27)
[ 1, -4, 1, -4 ],
[ 2, -4, 2, 4 ],
[ -3, -4, 3, 4 ]
-], [ (1, 1), (2, 15), (3, 8), (6, 12) ], [ (1, 1), (2, 15), (3, 4), (4, 9), (6, 20), (9, 1), (12, 6), (18, 3), (36, 1) ], false, false, true, false, 72), ([ perm"(1, 25, 13)(2, 26, 14)(3, 27, 15)(4,
-28, 16)(5, 29, 17)(6, 30, 18)(7, 31, 19)(8, 32, 20)(9, 33, 21)(10, 34, 22)(11, 35, 23)(12, 36, 24)", perm"(1, 9, 5)(2, 10, 6)(3, 11, 7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25,
-33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 28)(26, 27)(29, 32)(30, 31)(33, 36)(34, 35)", perm"(1,
+], [ (1, 1), (2, 15), (3, 8), (6, 12) ], [ (1, 1), (2, 15), (3, 4), (4, 9), (6, 20), (9, 1), (12, 6), (18, 3), (36, 1) ], false, false, true, false, 72), ([ perm"(1, 25, 13)(2, 26, 14)(3, 27, 15)(4,
+28, 16)(5, 29, 17)(6, 30, 18)(7, 31, 19)(8, 32, 20)(9, 33, 21)(10, 34, 22)(11, 35, 23)(12, 36, 24)", perm"(1, 9, 5)(2, 10, 6)(3, 11, 7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25,
+33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 28)(26, 27)(29, 32)(30, 31)(33, 36)(34, 35)", perm"(1,
2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 16)(14, 15)(17, 20)(18, 19)(21, 24)(22, 23)(25, 27)(26, 28)(29, 31)(30, 32)(33, 35)(34, 36)" ], [
[ 1, 1, 1 ],
[ 2, 2, 2 ],
@@ -2375,9 +2375,9 @@ perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 11, 12)(13, 14, 15)(16, 17, 18)(19, 23, 27)
[ -2, 3, 2, 3 ],
[ 3, 4, 3, 4 ],
[ 1, 3, -1, 3, 4 ]
-], [ (1, 1), (2, 3), (3, 26), (6, 6) ], [ (1, 1), (2, 3), (3, 13), (4, 1), (6, 3), (9, 4), (12, 4), (36, 1) ], false, false, true, false, 144), ([ perm"(1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6, 24)(7,
-25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)", perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 28)(20, 29)(21, 30)(22, 31)(23,
-32)(24, 33)(25, 34)(26, 35)(27, 36)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 34, 31)(29, 35, 32)(30, 36, 33)", perm"(1, 3, 2)(4,
+], [ (1, 1), (2, 3), (3, 26), (6, 6) ], [ (1, 1), (2, 3), (3, 13), (4, 1), (6, 3), (9, 4), (12, 4), (36, 1) ], false, false, true, false, 144), ([ perm"(1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6, 24)(7,
+25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)", perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 28)(20, 29)(21, 30)(22, 31)(23,
+32)(24, 33)(25, 34)(26, 35)(27, 36)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 34, 31)(29, 35, 32)(30, 36, 33)", perm"(1, 3, 2)(4,
6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 20, 21)(22, 23, 24)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -2396,8 +2396,8 @@ perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 11, 12)(13, 14, 15)(16, 17, 18)(19, 23, 27)
[ 1, -4, 1, -4 ],
[ 2, -4, 2, 4 ],
[ -3, -4, 3, 4 ]
-], [ (1, 1), (2, 7), (3, 8), (6, 20) ], [ (1, 1), (2, 7), (3, 4), (4, 3), (6, 12), (9, 1), (12, 4), (18, 3), (36, 1) ], false, false, true, false, 24), ([ perm"(1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6,
-24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)", perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 28)(20, 29)(21, 30)(22,
+], [ (1, 1), (2, 7), (3, 8), (6, 20) ], [ (1, 1), (2, 7), (3, 4), (4, 3), (6, 12), (9, 1), (12, 4), (18, 3), (36, 1) ], false, false, true, false, 24), ([ perm"(1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6,
+24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)", perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 28)(20, 29)(21, 30)(22,
31)(23, 32)(24, 33)(25, 34)(26, 35)(27, 36)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 22, 25)(20, 23, 26)(21, 24, 27)(28, 31, 34)(29, 32, 35)(30, 33, 36)", perm"(1, 3,
2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 20, 21)(22, 23, 24)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)" ], [
[ 1, 1 ],
@@ -2417,9 +2417,9 @@ perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 11, 12)(13, 14, 15)(16, 17, 18)(19, 23, 27)
[ 1, -4, 1, -4 ],
[ 2, -4, 2, 4 ],
[ -3, -4, 3, 4 ]
-], [ (1, 1), (2, 19), (3, 8), (6, 8) ], [ (1, 1), (2, 19), (3, 4), (4, 9), (6, 28), (9, 1), (12, 12), (18, 3), (36, 1) ], false, false, true, false, 864), ([ perm"(1, 19)(2, 20)(3, 21)(4, 22)(5,
-23)(6, 24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)", perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 28)(20, 29)(21,
-30)(22, 31)(23, 32)(24, 33)(25, 34)(26, 35)(27, 36)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 34, 31)(29, 35, 32)(30, 36, 33)",
+], [ (1, 1), (2, 19), (3, 8), (6, 8) ], [ (1, 1), (2, 19), (3, 4), (4, 9), (6, 28), (9, 1), (12, 12), (18, 3), (36, 1) ], false, false, true, false, 864), ([ perm"(1, 19)(2, 20)(3, 21)(4, 22)(5,
+23)(6, 24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)", perm"(1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 28)(20, 29)(21,
+30)(22, 31)(23, 32)(24, 33)(25, 34)(26, 35)(27, 36)", perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 34, 31)(29, 35, 32)(30, 36, 33)",
perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 33, 32)(34, 36, 35)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -2438,25 +2438,25 @@ perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)
[ 1, -4, 1, 4 ],
[ 2, -4, 2, 4 ],
[ -3, -4, 3, 4 ]
-], [ (1, 1), (2, 3), (3, 8), (6, 24) ], [ (1, 1), (2, 3), (3, 4), (4, 1), (6, 12), (9, 1), (12, 4), (18, 3), (36, 1) ], true, false, true, true, 288) ], [ ([ perm"(1, 37, 36, 35, 34, 33, 32, 31, 30,
+], [ (1, 1), (2, 3), (3, 8), (6, 24) ], [ (1, 1), (2, 3), (3, 4), (4, 1), (6, 12), (9, 1), (12, 4), (18, 3), (36, 1) ], true, false, true, true, 288) ], [ ([ perm"(1, 37, 36, 35, 34, 33, 32, 31, 30,
29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)" ], [
[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 ]
-], [], [ (1, 1), (37, 36) ], [ (1, 1), (37, 1) ], true, true, true, true, 36) ], [ ([ perm"(1, 20)(2, 21)(3, 22)(4, 23)(5, 24)(6, 25)(7, 26)(8, 27)(9, 28)(10, 29)(11, 30)(12, 31)(13, 32)(14, 33)(15,
+], [], [ (1, 1), (37, 36) ], [ (1, 1), (37, 1) ], true, true, true, true, 36) ], [ ([ perm"(1, 20)(2, 21)(3, 22)(4, 23)(5, 24)(6, 25)(7, 26)(8, 27)(9, 28)(10, 29)(11, 30)(12, 31)(13, 32)(14, 33)(15,
34)(16, 35)(17, 36)(18, 37)(19, 38)", perm"(1, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38)" ], [
[ 1, 1 ],
[ -2, 1, -2, 1 ],
[ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -2, 1, -2, 1 ]
-], [ (1, 1), (2, 19), (19, 18) ], [ (1, 1), (2, 19), (19, 1), (38, 1) ], false, false, true, false, 342), ([ perm"(1, 20)(2, 21)(3, 22)(4, 23)(5, 24)(6, 25)(7, 26)(8, 27)(9, 28)(10, 29)(11, 30)(12,
-31)(13, 32)(14, 33)(15, 34)(16, 35)(17, 36)(18, 37)(19, 38)", perm"(1, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(20, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24,
+], [ (1, 1), (2, 19), (19, 18) ], [ (1, 1), (2, 19), (19, 1), (38, 1) ], false, false, true, false, 342), ([ perm"(1, 20)(2, 21)(3, 22)(4, 23)(5, 24)(6, 25)(7, 26)(8, 27)(9, 28)(10, 29)(11, 30)(12,
+31)(13, 32)(14, 33)(15, 34)(16, 35)(17, 36)(18, 37)(19, 38)", perm"(1, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(20, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24,
23, 22, 21)" ], [
[ 1, 1 ],
[ -2, 1, 2, 1 ],
[ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -2, 1, 2, 1 ]
-], [ (1, 1), (2, 1), (19, 18), (38, 18) ], [ (1, 1), (2, 1), (19, 1), (38, 1) ], true, true, true, true, 18) ], [ ([ perm"(1, 27, 14)(2, 28, 15)(3, 29, 16)(4, 30, 17)(5, 31, 18)(6, 32, 19)(7, 33,
+], [ (1, 1), (2, 1), (19, 18), (38, 18) ], [ (1, 1), (2, 1), (19, 1), (38, 1) ], true, true, true, true, 18) ], [ ([ perm"(1, 27, 14)(2, 28, 15)(3, 29, 16)(4, 30, 17)(5, 31, 18)(6, 32, 19)(7, 33,
20)(8, 34, 21)(9, 35, 22)(10, 36, 23)(11, 37, 24)(12, 38, 25)(13, 39, 26)", perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(14, 24, 21, 18, 15, 25, 22, 19, 16, 26, 23, 20, 17)(27, 31, 35, 39, 30, 34,
38, 29, 33, 37, 28, 32, 36)" ], [
[ 1, 1, 1 ],
@@ -2465,8 +2465,8 @@ perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)
], [
[ -2, -1, -2, -1, -2, -1 ],
[ 2, -1, -2, 1, 2, 2 ]
-], [ (1, 1), (3, 26), (13, 12) ], [ (1, 1), (3, 13), (13, 1), (39, 1) ], false, false, true, false, 156), ([ perm"(1, 27, 14)(2, 28, 15)(3, 29, 16)(4, 30, 17)(5, 31, 18)(6, 32, 19)(7, 33, 20)(8, 34,
-21)(9, 35, 22)(10, 36, 23)(11, 37, 24)(12, 38, 25)(13, 39, 26)", perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15)(27, 39, 38, 37, 36, 35, 34, 33,
+], [ (1, 1), (3, 26), (13, 12) ], [ (1, 1), (3, 13), (13, 1), (39, 1) ], false, false, true, false, 156), ([ perm"(1, 27, 14)(2, 28, 15)(3, 29, 16)(4, 30, 17)(5, 31, 18)(6, 32, 19)(7, 33, 20)(8, 34,
+21)(9, 35, 22)(10, 36, 23)(11, 37, 24)(12, 38, 25)(13, 39, 26)", perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15)(27, 39, 38, 37, 36, 35, 34, 33,
32, 31, 30, 29, 28)" ], [
[ 1, 1, 1 ],
[ -1, -2, 1, 2 ],
@@ -2474,8 +2474,8 @@ perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)
], [
[ -1, -2, 1, 2 ]
], [ (1, 1), (3, 2), (13, 12), (39, 24) ], [ (1, 1), (3, 1), (13, 1), (39, 1) ], true, true, true, true, 24) ], [ ([ perm"(1, 36, 16, 26, 6, 31, 11, 21)(2, 37, 17, 27, 7, 32, 12, 22)(3, 38, 18, 28, 8,
-33, 13, 23)(4, 39, 19, 29, 9, 34, 14, 24)(5, 40, 20, 30, 10, 35, 15, 25)", perm"(1, 16, 6, 11)(2, 17, 7, 12)(3, 18, 8, 13)(4, 19, 9, 14)(5, 20, 10, 15)(21, 36, 26, 31)(22, 37, 27, 32)(23, 38, 28,
-33)(24, 39, 29, 34)(25, 40, 30, 35)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24, 29)(25, 30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)",
+33, 13, 23)(4, 39, 19, 29, 9, 34, 14, 24)(5, 40, 20, 30, 10, 35, 15, 25)", perm"(1, 16, 6, 11)(2, 17, 7, 12)(3, 18, 8, 13)(4, 19, 9, 14)(5, 20, 10, 15)(21, 36, 26, 31)(22, 37, 27, 32)(23, 38, 28,
+33)(24, 39, 29, 34)(25, 40, 30, 35)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24, 29)(25, 30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)",
perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 22, 23, 24, 25)(26, 27, 28, 29, 30)(31, 32, 33, 34, 35)(36, 37, 38, 39, 40)" ], [
[ 2, 2, 2, 2 ],
[ 3, 3 ],
@@ -2487,10 +2487,10 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ -1, -1, 2 ],
[ 2, 1, 1, 3 ],
[ -1, -4, 1, -4 ]
-], [ (1, 1), (2, 1), (4, 2), (5, 4), (8, 20), (10, 4), (20, 8) ], [ (1, 1), (2, 1), (4, 1), (5, 1), (8, 5), (10, 1), (20, 1), (40, 1) ], false, false, true, false, 80), ([ perm"(1, 24, 4, 22, 2, 23,
-3, 21)(5, 28, 8, 26, 6, 27, 7, 25)(9, 32, 12, 30, 10, 31, 11, 29)(13, 36, 16, 34, 14, 35, 15, 33)(17, 40, 20, 38, 18, 39, 19, 37)", perm"(1, 17, 13, 9, 5)(2, 18, 14, 10, 6)(3, 19, 15, 11, 7)(4, 20,
-16, 12, 8)(21, 37, 33, 29, 25)(22, 38, 34, 30, 26)(23, 39, 35, 31, 27)(24, 40, 36, 32, 28)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22, 23)(25, 28, 26,
-27)(29, 32, 30, 31)(33, 36, 34, 35)(37, 40, 38, 39)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37,
+], [ (1, 1), (2, 1), (4, 2), (5, 4), (8, 20), (10, 4), (20, 8) ], [ (1, 1), (2, 1), (4, 1), (5, 1), (8, 5), (10, 1), (20, 1), (40, 1) ], false, false, true, false, 80), ([ perm"(1, 24, 4, 22, 2, 23,
+3, 21)(5, 28, 8, 26, 6, 27, 7, 25)(9, 32, 12, 30, 10, 31, 11, 29)(13, 36, 16, 34, 14, 35, 15, 33)(17, 40, 20, 38, 18, 39, 19, 37)", perm"(1, 17, 13, 9, 5)(2, 18, 14, 10, 6)(3, 19, 15, 11, 7)(4, 20,
+16, 12, 8)(21, 37, 33, 29, 25)(22, 38, 34, 30, 26)(23, 39, 35, 31, 27)(24, 40, 36, 32, 28)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22, 23)(25, 28, 26,
+27)(29, 32, 30, 31)(33, 36, 34, 35)(37, 40, 38, 39)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37,
38)(39, 40)" ], [
[ 2, 2, 2, 2, 2 ],
[ 3, 3, 3, 3 ],
@@ -2502,10 +2502,10 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ -1, -1, 3 ],
[ 3, 1, 1, 4 ],
[ -1, -2, 1, 2 ]
-], [ (1, 1), (2, 1), (4, 2), (5, 4), (8, 4), (10, 4), (20, 8), (40, 16) ], [ (1, 1), (2, 1), (4, 1), (5, 1), (8, 1), (10, 1), (20, 1), (40, 1) ], true, true, true, true, 16), ([ perm"(1, 36, 16, 26,
-6, 31, 11, 21)(2, 37, 17, 27, 7, 32, 12, 22)(3, 38, 18, 28, 8, 33, 13, 23)(4, 39, 19, 29, 9, 34, 14, 24)(5, 40, 20, 30, 10, 35, 15, 25)", perm"(1, 16, 6, 11)(2, 17, 7, 12)(3, 18, 8, 13)(4, 19, 9,
-14)(5, 20, 10, 15)(21, 36, 26, 31)(22, 37, 27, 32)(23, 38, 28, 33)(24, 39, 29, 34)(25, 40, 30, 35)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23,
-28)(24, 29)(25, 30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 12, 13, 14, 15)(16, 17, 18, 19, 20)(21, 24, 22, 25, 23)(26, 29, 27, 30, 28)(31, 33, 35, 32,
+], [ (1, 1), (2, 1), (4, 2), (5, 4), (8, 4), (10, 4), (20, 8), (40, 16) ], [ (1, 1), (2, 1), (4, 1), (5, 1), (8, 1), (10, 1), (20, 1), (40, 1) ], true, true, true, true, 16), ([ perm"(1, 36, 16, 26,
+6, 31, 11, 21)(2, 37, 17, 27, 7, 32, 12, 22)(3, 38, 18, 28, 8, 33, 13, 23)(4, 39, 19, 29, 9, 34, 14, 24)(5, 40, 20, 30, 10, 35, 15, 25)", perm"(1, 16, 6, 11)(2, 17, 7, 12)(3, 18, 8, 13)(4, 19, 9,
+14)(5, 20, 10, 15)(21, 36, 26, 31)(22, 37, 27, 32)(23, 38, 28, 33)(24, 39, 29, 34)(25, 40, 30, 35)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23,
+28)(24, 29)(25, 30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 12, 13, 14, 15)(16, 17, 18, 19, 20)(21, 24, 22, 25, 23)(26, 29, 27, 30, 28)(31, 33, 35, 32,
34)(36, 38, 40, 37, 39)" ], [
[ 2, 2, 2, 2 ],
[ 3, 3 ],
@@ -2520,9 +2520,9 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ -2, -4, 2, -4 ],
[ 1, -4, -1, -4, -4 ]
], [ (1, 1), (2, 1), (4, 10), (5, 4), (8, 20), (10, 4) ], [ (1, 1), (2, 1), (4, 5), (5, 1), (8, 5), (10, 1), (20, 1), (40, 1) ], false, false, true, false, 40), ([ perm"(1, 26, 6, 21)(2, 27, 7, 22)(3,
-28, 8, 23)(4, 29, 9, 24)(5, 30, 10, 25)(11, 36, 16, 31)(12, 37, 17, 32)(13, 38, 18, 33)(14, 39, 19, 34)(15, 40, 20, 35)", perm"(1, 16, 6, 11)(2, 17, 7, 12)(3, 18, 8, 13)(4, 19, 9, 14)(5, 20, 10,
-15)(21, 31, 26, 36)(22, 32, 27, 37)(23, 33, 28, 38)(24, 34, 29, 39)(25, 35, 30, 40)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24, 29)(25,
-30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 22, 23, 24, 25)(26, 27, 28, 29, 30)(31, 32, 33, 34, 35)(36, 37, 38, 39,
+28, 8, 23)(4, 29, 9, 24)(5, 30, 10, 25)(11, 36, 16, 31)(12, 37, 17, 32)(13, 38, 18, 33)(14, 39, 19, 34)(15, 40, 20, 35)", perm"(1, 16, 6, 11)(2, 17, 7, 12)(3, 18, 8, 13)(4, 19, 9, 14)(5, 20, 10,
+15)(21, 31, 26, 36)(22, 32, 27, 37)(23, 33, 28, 38)(24, 34, 29, 39)(25, 35, 30, 40)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24, 29)(25,
+30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 22, 23, 24, 25)(26, 27, 28, 29, 30)(31, 32, 33, 34, 35)(36, 37, 38, 39,
40)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -2539,10 +2539,10 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ -1, -2, 1, -2 ],
[ -1, -4, 1, -4 ],
[ -2, -4, 2, 4 ]
-], [ (1, 1), (2, 1), (4, 22), (5, 4), (10, 4), (20, 8) ], [ (1, 1), (2, 1), (4, 11), (5, 1), (8, 5), (10, 1), (20, 3), (40, 1) ], false, false, true, false, 160), ([ perm"(1, 21)(2, 22)(3, 23)(4,
-24)(5, 25)(6, 26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)", perm"(1, 16, 6, 11)(2, 17, 7, 12)(3, 18, 8, 13)(4, 19, 9, 14)(5, 20,
-10, 15)(21, 36, 26, 31)(22, 37, 27, 32)(23, 38, 28, 33)(24, 39, 29, 34)(25, 40, 30, 35)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24,
-29)(25, 30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 22, 23, 24, 25)(26, 27, 28, 29, 30)(31, 32, 33, 34, 35)(36, 37,
+], [ (1, 1), (2, 1), (4, 22), (5, 4), (10, 4), (20, 8) ], [ (1, 1), (2, 1), (4, 11), (5, 1), (8, 5), (10, 1), (20, 3), (40, 1) ], false, false, true, false, 160), ([ perm"(1, 21)(2, 22)(3, 23)(4,
+24)(5, 25)(6, 26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)", perm"(1, 16, 6, 11)(2, 17, 7, 12)(3, 18, 8, 13)(4, 19, 9, 14)(5, 20,
+10, 15)(21, 36, 26, 31)(22, 37, 27, 32)(23, 38, 28, 33)(24, 39, 29, 34)(25, 40, 30, 35)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24,
+29)(25, 30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 22, 23, 24, 25)(26, 27, 28, 29, 30)(31, 32, 33, 34, 35)(36, 37,
38, 39, 40)" ], [
[ 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -2557,10 +2557,10 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ -2, 1, 2, 1 ],
[ -2, -4, 2, 4 ],
[ 1, -4, 1, -4 ]
-], [ (1, 1), (2, 11), (4, 12), (5, 4), (10, 4), (20, 8) ], [ (1, 1), (2, 11), (4, 11), (5, 1), (8, 5), (10, 3), (20, 3), (40, 1) ], false, false, true, false, 80), ([ perm"(1, 21)(2, 22)(3, 23)(4,
-24)(5, 25)(6, 26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)", perm"(1, 16, 6, 11)(2, 17, 7, 12)(3, 18, 8, 13)(4, 19, 9, 14)(5, 20,
-10, 15)(21, 31, 26, 36)(22, 32, 27, 37)(23, 33, 28, 38)(24, 34, 29, 39)(25, 35, 30, 40)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24,
-29)(25, 30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 22, 23, 24, 25)(26, 27, 28, 29, 30)(31, 32, 33, 34, 35)(36, 37,
+], [ (1, 1), (2, 11), (4, 12), (5, 4), (10, 4), (20, 8) ], [ (1, 1), (2, 11), (4, 11), (5, 1), (8, 5), (10, 3), (20, 3), (40, 1) ], false, false, true, false, 80), ([ perm"(1, 21)(2, 22)(3, 23)(4,
+24)(5, 25)(6, 26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)", perm"(1, 16, 6, 11)(2, 17, 7, 12)(3, 18, 8, 13)(4, 19, 9, 14)(5, 20,
+10, 15)(21, 31, 26, 36)(22, 32, 27, 37)(23, 33, 28, 38)(24, 34, 29, 39)(25, 35, 30, 40)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24,
+29)(25, 30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 22, 23, 24, 25)(26, 27, 28, 29, 30)(31, 32, 33, 34, 35)(36, 37,
38, 39, 40)" ], [
[ 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -2575,10 +2575,10 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ -2, 1, -2, 1 ],
[ -2, -4, 2, 4 ],
[ 1, -4, 1, -4 ]
-], [ (1, 1), (2, 21), (4, 2), (5, 4), (10, 4), (20, 8) ], [ (1, 1), (2, 21), (4, 11), (5, 1), (8, 5), (10, 5), (20, 3), (40, 1) ], false, false, true, false, 160), ([ perm"(1, 26, 6, 21)(2, 27, 7,
-22)(3, 28, 8, 23)(4, 29, 9, 24)(5, 30, 10, 25)(11, 36, 16, 31)(12, 37, 17, 32)(13, 38, 18, 33)(14, 39, 19, 34)(15, 40, 20, 35)", perm"(1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9,
-19)(10, 20)(21, 31)(22, 32)(23, 33)(24, 34)(25, 35)(26, 36)(27, 37)(28, 38)(29, 39)(30, 40)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24,
-29)(25, 30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 22, 23, 24, 25)(26, 27, 28, 29, 30)(31, 32, 33, 34, 35)(36, 37,
+], [ (1, 1), (2, 21), (4, 2), (5, 4), (10, 4), (20, 8) ], [ (1, 1), (2, 21), (4, 11), (5, 1), (8, 5), (10, 5), (20, 3), (40, 1) ], false, false, true, false, 160), ([ perm"(1, 26, 6, 21)(2, 27, 7,
+22)(3, 28, 8, 23)(4, 29, 9, 24)(5, 30, 10, 25)(11, 36, 16, 31)(12, 37, 17, 32)(13, 38, 18, 33)(14, 39, 19, 34)(15, 40, 20, 35)", perm"(1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9,
+19)(10, 20)(21, 31)(22, 32)(23, 33)(24, 34)(25, 35)(26, 36)(27, 37)(28, 38)(29, 39)(30, 40)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24,
+29)(25, 30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 22, 23, 24, 25)(26, 27, 28, 29, 30)(31, 32, 33, 34, 35)(36, 37,
38, 39, 40)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -2593,10 +2593,10 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ -1, 2, 1, 2 ],
[ -1, -4, 1, -4 ],
[ 2, -4, 2, 4 ]
-], [ (1, 1), (2, 3), (4, 20), (5, 4), (10, 12) ], [ (1, 1), (2, 3), (4, 11), (5, 1), (8, 5), (10, 3), (20, 3), (40, 1) ], false, false, true, false, 160), ([ perm"(1, 21)(2, 22)(3, 23)(4, 24)(5,
-25)(6, 26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)", perm"(1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10,
-20)(21, 36)(22, 37)(23, 38)(24, 39)(25, 40)(26, 31)(27, 32)(28, 33)(29, 34)(30, 35)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24, 29)(25,
-30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 22, 23, 24, 25)(26, 27, 28, 29, 30)(31, 32, 33, 34, 35)(36, 37, 38, 39,
+], [ (1, 1), (2, 3), (4, 20), (5, 4), (10, 12) ], [ (1, 1), (2, 3), (4, 11), (5, 1), (8, 5), (10, 3), (20, 3), (40, 1) ], false, false, true, false, 160), ([ perm"(1, 21)(2, 22)(3, 23)(4, 24)(5,
+25)(6, 26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)", perm"(1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10,
+20)(21, 36)(22, 37)(23, 38)(24, 39)(25, 40)(26, 31)(27, 32)(28, 33)(29, 34)(30, 35)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24, 29)(25,
+30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 22, 23, 24, 25)(26, 27, 28, 29, 30)(31, 32, 33, 34, 35)(36, 37, 38, 39,
40)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -2615,9 +2615,9 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ 2, -4, 2, 4 ],
[ 3, -4, 3, 4 ],
[ 1, 2, 1, 2, 3 ]
-], [ (1, 1), (2, 13), (4, 10), (5, 4), (10, 12) ], [ (1, 1), (2, 13), (4, 11), (5, 1), (8, 5), (10, 5), (20, 3), (40, 1) ], false, false, true, false, 80), ([ perm"(1, 22, 2, 21)(3, 24, 4, 23)(5, 26,
-6, 25)(7, 28, 8, 27)(9, 30, 10, 29)(11, 32, 12, 31)(13, 34, 14, 33)(15, 36, 16, 35)(17, 38, 18, 37)(19, 40, 20, 39)", perm"(1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10, 20)(21,
-31)(22, 32)(23, 33)(24, 34)(25, 35)(26, 36)(27, 37)(28, 38)(29, 39)(30, 40)", perm"(1, 9, 7, 5, 3)(2, 10, 8, 6, 4)(11, 19, 17, 15, 13)(12, 20, 18, 16, 14)(21, 29, 27, 25, 23)(22, 30, 28, 26, 24)(31,
+], [ (1, 1), (2, 13), (4, 10), (5, 4), (10, 12) ], [ (1, 1), (2, 13), (4, 11), (5, 1), (8, 5), (10, 5), (20, 3), (40, 1) ], false, false, true, false, 80), ([ perm"(1, 22, 2, 21)(3, 24, 4, 23)(5, 26,
+6, 25)(7, 28, 8, 27)(9, 30, 10, 29)(11, 32, 12, 31)(13, 34, 14, 33)(15, 36, 16, 35)(17, 38, 18, 37)(19, 40, 20, 39)", perm"(1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10, 20)(21,
+31)(22, 32)(23, 33)(24, 34)(25, 35)(26, 36)(27, 37)(28, 38)(29, 39)(30, 40)", perm"(1, 9, 7, 5, 3)(2, 10, 8, 6, 4)(11, 19, 17, 15, 13)(12, 20, 18, 16, 14)(21, 29, 27, 25, 23)(22, 30, 28, 26, 24)(31,
39, 37, 35, 33)(32, 40, 38, 36, 34)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -2632,10 +2632,10 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ -1, 2, 1, 2 ],
[ -1, -3, 1, 3 ],
[ 2, -3, 2, 3 ]
-], [ (1, 1), (2, 3), (4, 4), (5, 4), (10, 12), (20, 16) ], [ (1, 1), (2, 3), (4, 3), (5, 1), (8, 1), (10, 3), (20, 3), (40, 1) ], true, false, true, true, 32), ([ perm"(1, 21)(2, 22)(3, 23)(4, 24)(5,
-25)(6, 26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)", perm"(1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10,
-20)(21, 32)(22, 31)(23, 34)(24, 33)(25, 36)(26, 35)(27, 38)(28, 37)(29, 40)(30, 39)", perm"(1, 9, 7, 5, 3)(2, 10, 8, 6, 4)(11, 19, 17, 15, 13)(12, 20, 18, 16, 14)(21, 29, 27, 25, 23)(22, 30, 28, 26,
-24)(31, 39, 37, 35, 33)(32, 40, 38, 36, 34)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39,
+], [ (1, 1), (2, 3), (4, 4), (5, 4), (10, 12), (20, 16) ], [ (1, 1), (2, 3), (4, 3), (5, 1), (8, 1), (10, 3), (20, 3), (40, 1) ], true, false, true, true, 32), ([ perm"(1, 21)(2, 22)(3, 23)(4, 24)(5,
+25)(6, 26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)", perm"(1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10,
+20)(21, 32)(22, 31)(23, 34)(24, 33)(25, 36)(26, 35)(27, 38)(28, 37)(29, 40)(30, 39)", perm"(1, 9, 7, 5, 3)(2, 10, 8, 6, 4)(11, 19, 17, 15, 13)(12, 20, 18, 16, 14)(21, 29, 27, 25, 23)(22, 30, 28, 26,
+24)(31, 39, 37, 35, 33)(32, 40, 38, 36, 34)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39,
40)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -2654,10 +2654,10 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ 2, 4, 2, 4 ],
[ -3, 4, 3, 4 ],
[ 1, 2, 1, 2, 4 ]
-], [ (1, 1), (2, 5), (4, 2), (5, 4), (10, 20), (20, 8) ], [ (1, 1), (2, 5), (4, 3), (5, 1), (8, 1), (10, 5), (20, 3), (40, 1) ], false, false, true, true, 32), ([ perm"(1, 22, 2, 21)(3, 24, 4, 23)(5,
-26, 6, 25)(7, 28, 8, 27)(9, 30, 10, 29)(11, 32, 12, 31)(13, 34, 14, 33)(15, 36, 16, 35)(17, 38, 18, 37)(19, 40, 20, 39)", perm"(1, 12, 2, 11)(3, 14, 4, 13)(5, 16, 6, 15)(7, 18, 8, 17)(9, 20, 10,
-19)(21, 31, 22, 32)(23, 33, 24, 34)(25, 35, 26, 36)(27, 37, 28, 38)(29, 39, 30, 40)", perm"(1, 9, 7, 5, 3)(2, 10, 8, 6, 4)(11, 19, 17, 15, 13)(12, 20, 18, 16, 14)(21, 29, 27, 25, 23)(22, 30, 28, 26,
-24)(31, 39, 37, 35, 33)(32, 40, 38, 36, 34)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39,
+], [ (1, 1), (2, 5), (4, 2), (5, 4), (10, 20), (20, 8) ], [ (1, 1), (2, 5), (4, 3), (5, 1), (8, 1), (10, 5), (20, 3), (40, 1) ], false, false, true, true, 32), ([ perm"(1, 22, 2, 21)(3, 24, 4, 23)(5,
+26, 6, 25)(7, 28, 8, 27)(9, 30, 10, 29)(11, 32, 12, 31)(13, 34, 14, 33)(15, 36, 16, 35)(17, 38, 18, 37)(19, 40, 20, 39)", perm"(1, 12, 2, 11)(3, 14, 4, 13)(5, 16, 6, 15)(7, 18, 8, 17)(9, 20, 10,
+19)(21, 31, 22, 32)(23, 33, 24, 34)(25, 35, 26, 36)(27, 37, 28, 38)(29, 39, 30, 40)", perm"(1, 9, 7, 5, 3)(2, 10, 8, 6, 4)(11, 19, 17, 15, 13)(12, 20, 18, 16, 14)(21, 29, 27, 25, 23)(22, 30, 28, 26,
+24)(31, 39, 37, 35, 33)(32, 40, 38, 36, 34)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39,
40)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -2674,10 +2674,10 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ -1, -2, 1, -2 ],
[ -1, -3, 1, 3 ],
[ -2, -3, 2, 3 ]
-], [ (1, 1), (2, 1), (4, 6), (5, 4), (10, 4), (20, 24) ], [ (1, 1), (2, 1), (4, 3), (5, 1), (8, 1), (10, 1), (20, 3), (40, 1) ], false, false, true, true, 96), ([ perm"(1, 26, 6, 21)(2, 27, 7, 22)(3,
-28, 8, 23)(4, 29, 9, 24)(5, 30, 10, 25)(11, 36, 16, 31)(12, 37, 17, 32)(13, 38, 18, 33)(14, 39, 19, 34)(15, 40, 20, 35)", perm"(1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10,
-20)(21, 31)(22, 32)(23, 33)(24, 34)(25, 35)(26, 36)(27, 37)(28, 38)(29, 39)(30, 40)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24, 29)(25,
-30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)", perm"(1, 5, 4, 3, 2)(6, 7, 8, 9, 10)(11, 15, 14, 13, 12)(16, 17, 18, 19, 20)(21, 24, 22, 25, 23)(26, 28, 30, 27, 29)(31, 34, 32, 35, 33)(36, 38, 40, 37,
+], [ (1, 1), (2, 1), (4, 6), (5, 4), (10, 4), (20, 24) ], [ (1, 1), (2, 1), (4, 3), (5, 1), (8, 1), (10, 1), (20, 3), (40, 1) ], false, false, true, true, 96), ([ perm"(1, 26, 6, 21)(2, 27, 7, 22)(3,
+28, 8, 23)(4, 29, 9, 24)(5, 30, 10, 25)(11, 36, 16, 31)(12, 37, 17, 32)(13, 38, 18, 33)(14, 39, 19, 34)(15, 40, 20, 35)", perm"(1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10,
+20)(21, 31)(22, 32)(23, 33)(24, 34)(25, 35)(26, 36)(27, 37)(28, 38)(29, 39)(30, 40)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24, 29)(25,
+30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)", perm"(1, 5, 4, 3, 2)(6, 7, 8, 9, 10)(11, 15, 14, 13, 12)(16, 17, 18, 19, 20)(21, 24, 22, 25, 23)(26, 28, 30, 27, 29)(31, 34, 32, 35, 33)(36, 38, 40, 37,
39)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -2694,10 +2694,10 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ 2, -4, 2, 4 ],
[ 3, -4, 3, -4 ],
[ 1, -4, -1, -4, -4 ]
-], [ (1, 1), (2, 11), (4, 20), (5, 4), (10, 4) ], [ (1, 1), (2, 11), (4, 15), (5, 1), (8, 5), (10, 3), (20, 3), (40, 1) ], false, false, true, false, 40), ([ perm"(1, 21)(2, 22)(3, 23)(4, 24)(5,
-25)(6, 26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)", perm"(1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10,
-20)(21, 31)(22, 32)(23, 33)(24, 34)(25, 35)(26, 36)(27, 37)(28, 38)(29, 39)(30, 40)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24, 29)(25,
-30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 22, 23, 24, 25)(26, 27, 28, 29, 30)(31, 32, 33, 34, 35)(36, 37, 38, 39,
+], [ (1, 1), (2, 11), (4, 20), (5, 4), (10, 4) ], [ (1, 1), (2, 11), (4, 15), (5, 1), (8, 5), (10, 3), (20, 3), (40, 1) ], false, false, true, false, 40), ([ perm"(1, 21)(2, 22)(3, 23)(4, 24)(5,
+25)(6, 26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)", perm"(1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10,
+20)(21, 31)(22, 32)(23, 33)(24, 34)(25, 35)(26, 36)(27, 37)(28, 38)(29, 39)(30, 40)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24, 29)(25,
+30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 22, 23, 24, 25)(26, 27, 28, 29, 30)(31, 32, 33, 34, 35)(36, 37, 38, 39,
40)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -2716,9 +2716,9 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ 1, -4, 1, -4 ],
[ 2, -4, 2, 4 ],
[ 3, -4, 3, 4 ]
-], [ (1, 1), (2, 23), (5, 4), (10, 12) ], [ (1, 1), (2, 23), (4, 31), (5, 1), (8, 5), (10, 7), (20, 7), (40, 1) ], false, false, true, false, 480), ([ perm"(1, 21)(2, 22)(3, 23)(4, 24)(5, 25)(6,
-26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)", perm"(1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10, 20)(21,
-31)(22, 32)(23, 33)(24, 34)(25, 35)(26, 36)(27, 37)(28, 38)(29, 39)(30, 40)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24, 29)(25, 30)(31,
+], [ (1, 1), (2, 23), (5, 4), (10, 12) ], [ (1, 1), (2, 23), (4, 31), (5, 1), (8, 5), (10, 7), (20, 7), (40, 1) ], false, false, true, false, 480), ([ perm"(1, 21)(2, 22)(3, 23)(4, 24)(5, 25)(6,
+26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)", perm"(1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10, 20)(21,
+31)(22, 32)(23, 33)(24, 34)(25, 35)(26, 36)(27, 37)(28, 38)(29, 39)(30, 40)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24, 29)(25, 30)(31,
36)(32, 37)(33, 38)(34, 39)(35, 40)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 25, 24, 23, 22)(26, 30, 29, 28, 27)(31, 35, 34, 33, 32)(36, 40, 39, 38, 37)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -2737,11 +2737,11 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ 1, -4, 1, 4 ],
[ 2, -4, 2, 4 ],
[ 3, -4, 3, 4 ]
-], [ (1, 1), (2, 7), (5, 4), (10, 28) ], [ (1, 1), (2, 7), (4, 7), (5, 1), (8, 1), (10, 7), (20, 7), (40, 1) ], true, false, true, true, 672) ], [ ([ perm"(1, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32,
+], [ (1, 1), (2, 7), (5, 4), (10, 28) ], [ (1, 1), (2, 7), (4, 7), (5, 1), (8, 1), (10, 7), (20, 7), (40, 1) ], true, false, true, true, 672) ], [ ([ perm"(1, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32,
31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)" ], [
[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 ]
-], [], [ (1, 1), (41, 40) ], [ (1, 1), (41, 1) ], true, true, true, true, 40) ], [ ([ perm"(1, 22)(2, 23)(3, 24)(4, 25)(5, 26)(6, 27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15,
-36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)", perm"(1, 15, 8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6, 20, 13)(7, 21, 14)(22, 36, 29)(23, 37, 30)(24, 38, 31)(25, 39, 32)(26, 40, 33)(27,
+], [], [ (1, 1), (41, 40) ], [ (1, 1), (41, 1) ], true, true, true, true, 40) ], [ ([ perm"(1, 22)(2, 23)(3, 24)(4, 25)(5, 26)(6, 27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15,
+36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)", perm"(1, 15, 8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6, 20, 13)(7, 21, 14)(22, 36, 29)(23, 37, 30)(24, 38, 31)(25, 39, 32)(26, 40, 33)(27,
41, 34)(28, 42, 35)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 13, 11, 9, 14, 12, 10)(15, 18, 21, 17, 20, 16, 19)(22, 23, 24, 25, 26, 27, 28)(29, 31, 33, 35, 30, 32, 34)(36, 40, 37, 41, 38, 42, 39)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -2752,9 +2752,9 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ -2, 1, 2, 1 ],
[ 1, -3, 1, -3 ],
[ -3, -3, -2, 3, 2 ]
-], [ (1, 1), (2, 7), (3, 14), (6, 14), (7, 6) ], [ (1, 1), (2, 7), (3, 7), (6, 7), (7, 1), (14, 1), (21, 1), (42, 1) ], false, false, true, false, 42), ([ perm"(1, 22)(2, 23)(3, 24)(4, 25)(5, 26)(6,
-27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15, 36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)", perm"(1, 15, 8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6, 20, 13)(7, 21,
-14)(22, 36, 29)(23, 37, 30)(24, 38, 31)(25, 39, 32)(26, 40, 33)(27, 41, 34)(28, 42, 35)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 13, 11, 9, 14, 12, 10)(15, 18, 21, 17, 20, 16, 19)(22, 28, 27, 26, 25, 24,
+], [ (1, 1), (2, 7), (3, 14), (6, 14), (7, 6) ], [ (1, 1), (2, 7), (3, 7), (6, 7), (7, 1), (14, 1), (21, 1), (42, 1) ], false, false, true, false, 42), ([ perm"(1, 22)(2, 23)(3, 24)(4, 25)(5, 26)(6,
+27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15, 36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)", perm"(1, 15, 8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6, 20, 13)(7, 21,
+14)(22, 36, 29)(23, 37, 30)(24, 38, 31)(25, 39, 32)(26, 40, 33)(27, 41, 34)(28, 42, 35)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 13, 11, 9, 14, 12, 10)(15, 18, 21, 17, 20, 16, 19)(22, 28, 27, 26, 25, 24,
23)(29, 34, 32, 30, 35, 33, 31)(36, 39, 42, 38, 41, 37, 40)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -2767,7 +2767,7 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ -3, -3, -2, 3, 2 ]
], [ (1, 1), (2, 1), (3, 14), (6, 14), (7, 6), (14, 6) ], [ (1, 1), (2, 1), (3, 7), (6, 7), (7, 1), (14, 1), (21, 1), (42, 1) ], false, false, true, false, 42), ([ perm"(1, 22)(2, 23)(3, 24)(4, 25)(5,
26)(6, 27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15, 36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)", perm"(1, 19, 16, 13, 10, 7, 4)(2, 20, 17, 14, 11, 8, 5)(3, 21, 18, 15,
-12, 9, 6)(22, 40, 37, 34, 31, 28, 25)(23, 41, 38, 35, 32, 29, 26)(24, 42, 39, 36, 33, 30, 27)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 23, 24)(25, 26,
+12, 9, 6)(22, 40, 37, 34, 31, 28, 25)(23, 41, 38, 35, 32, 29, 26)(24, 42, 39, 36, 33, 30, 27)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 23, 24)(25, 26,
27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)" ], [
[ 1, 1 ],
[ 3, 3, 3 ],
@@ -2779,9 +2779,9 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ -2, 1, 2, 1 ],
[ -2, -3, 2, 3 ],
[ 1, -3, 1, -3 ]
-], [ (1, 1), (2, 3), (3, 2), (7, 6), (14, 18), (21, 12) ], [ (1, 1), (2, 3), (3, 1), (6, 1), (7, 1), (14, 3), (21, 1), (42, 1) ], false, false, true, false, 36), ([ perm"(1, 22)(2, 23)(3, 24)(4,
-25)(5, 26)(6, 27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15, 36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)", perm"(1, 15, 8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6,
-20, 13)(7, 21, 14)(22, 36, 29)(23, 37, 30)(24, 38, 31)(25, 39, 32)(26, 40, 33)(27, 41, 34)(28, 42, 35)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 23, 24,
+], [ (1, 1), (2, 3), (3, 2), (7, 6), (14, 18), (21, 12) ], [ (1, 1), (2, 3), (3, 1), (6, 1), (7, 1), (14, 3), (21, 1), (42, 1) ], false, false, true, false, 36), ([ perm"(1, 22)(2, 23)(3, 24)(4,
+25)(5, 26)(6, 27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15, 36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)", perm"(1, 15, 8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6,
+20, 13)(7, 21, 14)(22, 36, 29)(23, 37, 30)(24, 38, 31)(25, 39, 32)(26, 40, 33)(27, 41, 34)(28, 42, 35)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 23, 24,
25, 26, 27, 28)(29, 30, 31, 32, 33, 34, 35)(36, 37, 38, 39, 40, 41, 42)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -2794,8 +2794,8 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ -2, -3, 2, 3 ],
[ 1, -3, 1, -3 ]
], [ (1, 1), (2, 7), (3, 2), (6, 14), (7, 6), (21, 12) ], [ (1, 1), (2, 7), (3, 1), (6, 7), (7, 1), (14, 1), (21, 1), (42, 1) ], false, false, true, false, 84), ([ perm"(1, 22)(2, 23)(3, 24)(4, 25)(5,
-26)(6, 27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15, 36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)", perm"(1, 15, 8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6, 20,
-13)(7, 21, 14)(22, 29, 36)(23, 30, 37)(24, 31, 38)(25, 32, 39)(26, 33, 40)(27, 34, 41)(28, 35, 42)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 23, 24, 25,
+26)(6, 27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15, 36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)", perm"(1, 15, 8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6, 20,
+13)(7, 21, 14)(22, 29, 36)(23, 30, 37)(24, 31, 38)(25, 32, 39)(26, 33, 40)(27, 34, 41)(28, 35, 42)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 23, 24, 25,
26, 27, 28)(29, 30, 31, 32, 33, 34, 35)(36, 37, 38, 39, 40, 41, 42)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -2807,9 +2807,9 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ -2, 1, -2, 1 ],
[ -2, -3, 2, 3 ],
[ 1, -3, 1, -3 ]
-], [ (1, 1), (2, 21), (3, 2), (7, 6), (21, 12) ], [ (1, 1), (2, 21), (3, 1), (6, 7), (7, 1), (14, 3), (21, 1), (42, 1) ], false, false, true, false, 252), ([ perm"(1, 22)(2, 23)(3, 24)(4, 25)(5,
-26)(6, 27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15, 36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)", perm"(1, 15, 8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6, 20,
-13)(7, 21, 14)(22, 36, 29)(23, 37, 30)(24, 38, 31)(25, 39, 32)(26, 40, 33)(27, 41, 34)(28, 42, 35)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26,
+], [ (1, 1), (2, 21), (3, 2), (7, 6), (21, 12) ], [ (1, 1), (2, 21), (3, 1), (6, 7), (7, 1), (14, 3), (21, 1), (42, 1) ], false, false, true, false, 252), ([ perm"(1, 22)(2, 23)(3, 24)(4, 25)(5,
+26)(6, 27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15, 36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)", perm"(1, 15, 8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6, 20,
+13)(7, 21, 14)(22, 36, 29)(23, 37, 30)(24, 38, 31)(25, 39, 32)(26, 40, 33)(27, 41, 34)(28, 42, 35)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26,
25, 24, 23)(29, 35, 34, 33, 32, 31, 30)(36, 42, 41, 40, 39, 38, 37)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -2821,12 +2821,12 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ -2, 1, 2, 1 ],
[ -2, -3, 2, 3 ],
[ 1, -3, 1, 3 ]
-], [ (1, 1), (2, 1), (3, 2), (6, 2), (7, 6), (14, 6), (21, 12), (42, 12) ], [ (1, 1), (2, 1), (3, 1), (6, 1), (7, 1), (14, 1), (21, 1), (42, 1) ], true, true, true, true, 12) ], [ ([ perm"(1, 43, 42,
+], [ (1, 1), (2, 1), (3, 2), (6, 2), (7, 6), (14, 6), (21, 12), (42, 12) ], [ (1, 1), (2, 1), (3, 1), (6, 1), (7, 1), (14, 1), (21, 1), (42, 1) ], true, true, true, true, 12) ], [ ([ perm"(1, 43, 42,
41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)" ], [
[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 ]
-], [], [ (1, 1), (43, 42) ], [ (1, 1), (43, 1) ], true, true, true, true, 42) ], [ ([ perm"(1, 34, 12, 23)(2, 35, 13, 24)(3, 36, 14, 25)(4, 37, 15, 26)(5, 38, 16, 27)(6, 39, 17, 28)(7, 40, 18, 29)(8,
-41, 19, 30)(9, 42, 20, 31)(10, 43, 21, 32)(11, 44, 22, 33)", perm"(1, 12)(2, 13)(3, 14)(4, 15)(5, 16)(6, 17)(7, 18)(8, 19)(9, 20)(10, 21)(11, 22)(23, 34)(24, 35)(25, 36)(26, 37)(27, 38)(28, 39)(29,
-40)(30, 41)(31, 42)(32, 43)(33, 44)", perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13)(23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33)(34, 35, 36, 37, 38, 39, 40, 41,
+], [], [ (1, 1), (43, 42) ], [ (1, 1), (43, 1) ], true, true, true, true, 42) ], [ ([ perm"(1, 34, 12, 23)(2, 35, 13, 24)(3, 36, 14, 25)(4, 37, 15, 26)(5, 38, 16, 27)(6, 39, 17, 28)(7, 40, 18, 29)(8,
+41, 19, 30)(9, 42, 20, 31)(10, 43, 21, 32)(11, 44, 22, 33)", perm"(1, 12)(2, 13)(3, 14)(4, 15)(5, 16)(6, 17)(7, 18)(8, 19)(9, 20)(10, 21)(11, 22)(23, 34)(24, 35)(25, 36)(26, 37)(27, 38)(28, 39)(29,
+40)(30, 41)(31, 42)(32, 43)(33, 44)", perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13)(23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33)(34, 35, 36, 37, 38, 39, 40, 41,
42, 43, 44)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -2836,8 +2836,8 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
], [
[ -1, -1, 2 ],
[ -1, -3, 1, -3 ]
-], [ (1, 1), (2, 1), (4, 22), (11, 10), (22, 10) ], [ (1, 1), (2, 1), (4, 11), (11, 1), (22, 1), (44, 1) ], false, false, true, false, 220), ([ perm"(1, 24, 2, 23)(3, 26, 4, 25)(5, 28, 6, 27)(7, 30,
-8, 29)(9, 32, 10, 31)(11, 34, 12, 33)(13, 36, 14, 35)(15, 38, 16, 37)(17, 40, 18, 39)(19, 42, 20, 41)(21, 44, 22, 43)", perm"(1, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3)(2, 22, 20, 18, 16, 14, 12, 10, 8,
+], [ (1, 1), (2, 1), (4, 22), (11, 10), (22, 10) ], [ (1, 1), (2, 1), (4, 11), (11, 1), (22, 1), (44, 1) ], false, false, true, false, 220), ([ perm"(1, 24, 2, 23)(3, 26, 4, 25)(5, 28, 6, 27)(7, 30,
+8, 29)(9, 32, 10, 31)(11, 34, 12, 33)(13, 36, 14, 35)(15, 38, 16, 37)(17, 40, 18, 39)(19, 42, 20, 41)(21, 44, 22, 43)", perm"(1, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3)(2, 22, 20, 18, 16, 14, 12, 10, 8,
6, 4)(23, 43, 41, 39, 37, 35, 33, 31, 29, 27, 25)(24, 44, 42, 40, 38, 36, 34, 32, 30, 28, 26)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27,
28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)" ], [
[ 1, 1, 1, 1 ],
@@ -2848,9 +2848,9 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
], [
[ -1, -1, 3 ],
[ -1, -2, 1, 2 ]
-], [ (1, 1), (2, 1), (4, 2), (11, 10), (22, 10), (44, 20) ], [ (1, 1), (2, 1), (4, 1), (11, 1), (22, 1), (44, 1) ], true, true, true, true, 20), ([ perm"(1, 23)(2, 24)(3, 25)(4, 26)(5, 27)(6, 28)(7,
-29)(8, 30)(9, 31)(10, 32)(11, 33)(12, 34)(13, 35)(14, 36)(15, 37)(16, 38)(17, 39)(18, 40)(19, 41)(20, 42)(21, 43)(22, 44)", perm"(1, 12)(2, 13)(3, 14)(4, 15)(5, 16)(6, 17)(7, 18)(8, 19)(9, 20)(10,
-21)(11, 22)(23, 34)(24, 35)(25, 36)(26, 37)(27, 38)(28, 39)(29, 40)(30, 41)(31, 42)(32, 43)(33, 44)", perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13)(23, 24, 25,
+], [ (1, 1), (2, 1), (4, 2), (11, 10), (22, 10), (44, 20) ], [ (1, 1), (2, 1), (4, 1), (11, 1), (22, 1), (44, 1) ], true, true, true, true, 20), ([ perm"(1, 23)(2, 24)(3, 25)(4, 26)(5, 27)(6, 28)(7,
+29)(8, 30)(9, 31)(10, 32)(11, 33)(12, 34)(13, 35)(14, 36)(15, 37)(16, 38)(17, 39)(18, 40)(19, 41)(20, 42)(21, 43)(22, 44)", perm"(1, 12)(2, 13)(3, 14)(4, 15)(5, 16)(6, 17)(7, 18)(8, 19)(9, 20)(10,
+21)(11, 22)(23, 34)(24, 35)(25, 36)(26, 37)(27, 38)(28, 39)(29, 40)(30, 41)(31, 42)(32, 43)(33, 44)", perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13)(23, 24, 25,
26, 27, 28, 29, 30, 31, 32, 33)(34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -2862,9 +2862,9 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ 1, 2, 1, 2 ],
[ 1, -3, 1, -3 ],
[ 2, -3, 2, 3 ]
-], [ (1, 1), (2, 23), (11, 10), (22, 10) ], [ (1, 1), (2, 23), (4, 11), (11, 1), (22, 3), (44, 1) ], false, false, true, false, 220), ([ perm"(1, 23)(2, 24)(3, 25)(4, 26)(5, 27)(6, 28)(7, 29)(8,
-30)(9, 31)(10, 32)(11, 33)(12, 34)(13, 35)(14, 36)(15, 37)(16, 38)(17, 39)(18, 40)(19, 41)(20, 42)(21, 43)(22, 44)", perm"(1, 12)(2, 13)(3, 14)(4, 15)(5, 16)(6, 17)(7, 18)(8, 19)(9, 20)(10, 21)(11,
-22)(23, 34)(24, 35)(25, 36)(26, 37)(27, 38)(28, 39)(29, 40)(30, 41)(31, 42)(32, 43)(33, 44)", perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13)(23, 33, 32, 31, 30,
+], [ (1, 1), (2, 23), (11, 10), (22, 10) ], [ (1, 1), (2, 23), (4, 11), (11, 1), (22, 3), (44, 1) ], false, false, true, false, 220), ([ perm"(1, 23)(2, 24)(3, 25)(4, 26)(5, 27)(6, 28)(7, 29)(8,
+30)(9, 31)(10, 32)(11, 33)(12, 34)(13, 35)(14, 36)(15, 37)(16, 38)(17, 39)(18, 40)(19, 41)(20, 42)(21, 43)(22, 44)", perm"(1, 12)(2, 13)(3, 14)(4, 15)(5, 16)(6, 17)(7, 18)(8, 19)(9, 20)(10, 21)(11,
+22)(23, 34)(24, 35)(25, 36)(26, 37)(27, 38)(28, 39)(29, 40)(30, 41)(31, 42)(32, 43)(33, 44)", perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13)(23, 33, 32, 31, 30,
29, 28, 27, 26, 25, 24)(34, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -2876,9 +2876,9 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ 1, 2, 1, 2 ],
[ 1, -3, 1, 3 ],
[ 2, -3, 2, 3 ]
-], [ (1, 1), (2, 3), (11, 10), (22, 30) ], [ (1, 1), (2, 3), (4, 1), (11, 1), (22, 3), (44, 1) ], true, false, true, true, 60) ], [ ([ perm"(1, 33, 18, 3, 32, 17, 2, 31, 16)(4, 36, 21, 6, 35, 20, 5,
-34, 19)(7, 39, 24, 9, 38, 23, 8, 37, 22)(10, 42, 27, 12, 41, 26, 11, 40, 25)(13, 45, 30, 15, 44, 29, 14, 43, 28)", perm"(1, 13, 10, 7, 4)(2, 14, 11, 8, 5)(3, 15, 12, 9, 6)(16, 28, 25, 22, 19)(17, 29,
-26, 23, 20)(18, 30, 27, 24, 21)(31, 43, 40, 37, 34)(32, 44, 41, 38, 35)(33, 45, 42, 39, 36)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27,
+], [ (1, 1), (2, 3), (11, 10), (22, 30) ], [ (1, 1), (2, 3), (4, 1), (11, 1), (22, 3), (44, 1) ], true, false, true, true, 60) ], [ ([ perm"(1, 33, 18, 3, 32, 17, 2, 31, 16)(4, 36, 21, 6, 35, 20, 5,
+34, 19)(7, 39, 24, 9, 38, 23, 8, 37, 22)(10, 42, 27, 12, 41, 26, 11, 40, 25)(13, 45, 30, 15, 44, 29, 14, 43, 28)", perm"(1, 13, 10, 7, 4)(2, 14, 11, 8, 5)(3, 15, 12, 9, 6)(16, 28, 25, 22, 19)(17, 29,
+26, 23, 20)(18, 30, 27, 24, 21)(31, 43, 40, 37, 34)(32, 44, 41, 38, 35)(33, 45, 42, 39, 36)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27,
26)(28, 30, 29)(31, 33, 32)(34, 36, 35)(37, 39, 38)(40, 42, 41)(43, 45, 44)" ], [
[ 2, 2, 2, 2, 2 ],
[ 3, 3, 3 ],
@@ -2888,8 +2888,8 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ 1, 1, 1, -3 ],
[ -1, -2, 1, 2 ]
], [ (1, 1), (3, 2), (5, 4), (9, 6), (15, 8), (45, 24) ], [ (1, 1), (3, 1), (5, 1), (9, 1), (15, 1), (45, 1) ], true, true, true, true, 24), ([ perm"(1, 31, 16)(2, 32, 17)(3, 33, 18)(4, 34, 19)(5, 35,
-20)(6, 36, 21)(7, 37, 22)(8, 38, 23)(9, 39, 24)(10, 40, 25)(11, 41, 26)(12, 42, 27)(13, 43, 28)(14, 44, 29)(15, 45, 30)", perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)(16, 26, 21)(17, 27,
-22)(18, 28, 23)(19, 29, 24)(20, 30, 25)(31, 41, 36)(32, 42, 37)(33, 43, 38)(34, 44, 39)(35, 45, 40)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 25, 24, 23,
+20)(6, 36, 21)(7, 37, 22)(8, 38, 23)(9, 39, 24)(10, 40, 25)(11, 41, 26)(12, 42, 27)(13, 43, 28)(14, 44, 29)(15, 45, 30)", perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)(16, 26, 21)(17, 27,
+22)(18, 28, 23)(19, 29, 24)(20, 30, 25)(31, 41, 36)(32, 42, 37)(33, 43, 38)(34, 44, 39)(35, 45, 40)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 25, 24, 23,
22)(26, 30, 29, 28, 27)(31, 35, 34, 33, 32)(36, 40, 39, 38, 37)(41, 45, 44, 43, 42)" ], [
[ 1, 1, 1 ],
[ 2, 2, 2 ],
@@ -2901,7 +2901,7 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ -1, -2, 1, 2 ],
[ -1, -3, 1, 3 ],
[ -2, -3, 2, 3 ]
-], [ (1, 1), (3, 8), (5, 4), (15, 32) ], [ (1, 1), (3, 4), (5, 1), (9, 1), (15, 4), (45, 1) ], true, false, true, true, 192) ], [ ([ perm"(1, 24)(2, 25)(3, 26)(4, 27)(5, 28)(6, 29)(7, 30)(8, 31)(9,
+], [ (1, 1), (3, 8), (5, 4), (15, 32) ], [ (1, 1), (3, 4), (5, 1), (9, 1), (15, 4), (45, 1) ], true, false, true, true, 192) ], [ ([ perm"(1, 24)(2, 25)(3, 26)(4, 27)(5, 28)(6, 29)(7, 30)(8, 31)(9,
32)(10, 33)(11, 34)(12, 35)(13, 36)(14, 37)(15, 38)(16, 39)(17, 40)(18, 41)(19, 42)(20, 43)(21, 44)(22, 45)(23, 46)", perm"(1, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4,
3, 2)(24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46)" ], [
[ 1, 1 ],
@@ -2909,22 +2909,22 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -2, 1, -2, 1 ]
-], [ (1, 1), (2, 23), (23, 22) ], [ (1, 1), (2, 23), (23, 1), (46, 1) ], false, false, true, false, 506), ([ perm"(1, 24)(2, 25)(3, 26)(4, 27)(5, 28)(6, 29)(7, 30)(8, 31)(9, 32)(10, 33)(11, 34)(12,
-35)(13, 36)(14, 37)(15, 38)(16, 39)(17, 40)(18, 41)(19, 42)(20, 43)(21, 44)(22, 45)(23, 46)", perm"(1, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(24, 46, 45, 44,
+], [ (1, 1), (2, 23), (23, 22) ], [ (1, 1), (2, 23), (23, 1), (46, 1) ], false, false, true, false, 506), ([ perm"(1, 24)(2, 25)(3, 26)(4, 27)(5, 28)(6, 29)(7, 30)(8, 31)(9, 32)(10, 33)(11, 34)(12,
+35)(13, 36)(14, 37)(15, 38)(16, 39)(17, 40)(18, 41)(19, 42)(20, 43)(21, 44)(22, 45)(23, 46)", perm"(1, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(24, 46, 45, 44,
43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25)" ], [
[ 1, 1 ],
[ -2, 1, 2, 1 ],
[ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -2, 1, 2, 1 ]
-], [ (1, 1), (2, 1), (23, 22), (46, 22) ], [ (1, 1), (2, 1), (23, 1), (46, 1) ], true, true, true, true, 22) ], [ ([ perm"(1, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30,
+], [ (1, 1), (2, 1), (23, 22), (46, 22) ], [ (1, 1), (2, 1), (23, 1), (46, 1) ], true, true, true, true, 22) ], [ ([ perm"(1, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30,
29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)" ], [
[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 ]
-], [], [ (1, 1), (47, 46) ], [ (1, 1), (47, 1) ], true, true, true, true, 46) ], [ ([ perm"(1, 46, 22, 34, 10, 40, 16, 28, 4, 43, 19, 31, 7, 37, 13, 25)(2, 47, 23, 35, 11, 41, 17, 29, 5, 44, 20, 32,
-8, 38, 14, 26)(3, 48, 24, 36, 12, 42, 18, 30, 6, 45, 21, 33, 9, 39, 15, 27)", perm"(1, 22, 10, 16, 4, 19, 7, 13)(2, 23, 11, 17, 5, 20, 8, 14)(3, 24, 12, 18, 6, 21, 9, 15)(25, 46, 34, 40, 28, 43, 31,
-37)(26, 47, 35, 41, 29, 44, 32, 38)(27, 48, 36, 42, 30, 45, 33, 39)", perm"(1, 10, 4, 7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 34, 28, 31)(26, 35, 29, 32)(27,
-36, 30, 33)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33,
-36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37,
+], [], [ (1, 1), (47, 46) ], [ (1, 1), (47, 1) ], true, true, true, true, 46) ], [ ([ perm"(1, 46, 22, 34, 10, 40, 16, 28, 4, 43, 19, 31, 7, 37, 13, 25)(2, 47, 23, 35, 11, 41, 17, 29, 5, 44, 20, 32,
+8, 38, 14, 26)(3, 48, 24, 36, 12, 42, 18, 30, 6, 45, 21, 33, 9, 39, 15, 27)", perm"(1, 22, 10, 16, 4, 19, 7, 13)(2, 23, 11, 17, 5, 20, 8, 14)(3, 24, 12, 18, 6, 21, 9, 15)(25, 46, 34, 40, 28, 43, 31,
+37)(26, 47, 35, 41, 29, 44, 32, 38)(27, 48, 36, 42, 30, 45, 33, 39)", perm"(1, 10, 4, 7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 34, 28, 31)(26, 35, 29, 32)(27,
+36, 30, 33)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33,
+36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37,
38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 3, 3, 3, 3 ],
[ 4, 4 ],
@@ -2938,11 +2938,11 @@ perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21,
[ 2, 1, 1, -3 ],
[ 3, 2, 2, 4 ],
[ -1, -5, 1, -5 ]
-], [ (1, 1), (2, 1), (3, 2), (4, 2), (6, 2), (8, 4), (12, 4), (16, 24), (24, 8) ], [ (1, 1), (2, 1), (3, 1), (4, 1), (6, 1), (8, 1), (12, 1), (16, 3), (24, 1), (48, 1) ], false, false, true, false,
-48), ([ perm"(1, 32, 8, 28, 4, 30, 6, 26, 2, 31, 7, 27, 3, 29, 5, 25)(9, 40, 16, 36, 12, 38, 14, 34, 10, 39, 15, 35, 11, 37, 13, 33)(17, 48, 24, 44, 20, 46, 22, 42, 18, 47, 23, 43, 19, 45, 21, 41)",
-perm"(1, 17, 9)(2, 18, 10)(3, 19, 11)(4, 20, 12)(5, 21, 13)(6, 22, 14)(7, 23, 15)(8, 24, 16)(25, 41, 33)(26, 42, 34)(27, 43, 35)(28, 44, 36)(29, 45, 37)(30, 46, 38)(31, 47, 39)(32, 48, 40)", perm"(1,
-8, 4, 6, 2, 7, 3, 5)(9, 16, 12, 14, 10, 15, 11, 13)(17, 24, 20, 22, 18, 23, 19, 21)(25, 32, 28, 30, 26, 31, 27, 29)(33, 40, 36, 38, 34, 39, 35, 37)(41, 48, 44, 46, 42, 47, 43, 45)", perm"(1, 4, 2,
-3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22, 23)(25, 28, 26, 27)(29, 32, 30, 31)(33, 36, 34, 35)(37, 40, 38, 39)(41, 44, 42, 43)(45, 48, 46, 47)", perm"(1, 2)(3, 4)(5,
+], [ (1, 1), (2, 1), (3, 2), (4, 2), (6, 2), (8, 4), (12, 4), (16, 24), (24, 8) ], [ (1, 1), (2, 1), (3, 1), (4, 1), (6, 1), (8, 1), (12, 1), (16, 3), (24, 1), (48, 1) ], false, false, true, false,
+48), ([ perm"(1, 32, 8, 28, 4, 30, 6, 26, 2, 31, 7, 27, 3, 29, 5, 25)(9, 40, 16, 36, 12, 38, 14, 34, 10, 39, 15, 35, 11, 37, 13, 33)(17, 48, 24, 44, 20, 46, 22, 42, 18, 47, 23, 43, 19, 45, 21, 41)",
+perm"(1, 17, 9)(2, 18, 10)(3, 19, 11)(4, 20, 12)(5, 21, 13)(6, 22, 14)(7, 23, 15)(8, 24, 16)(25, 41, 33)(26, 42, 34)(27, 43, 35)(28, 44, 36)(29, 45, 37)(30, 46, 38)(31, 47, 39)(32, 48, 40)", perm"(1,
+8, 4, 6, 2, 7, 3, 5)(9, 16, 12, 14, 10, 15, 11, 13)(17, 24, 20, 22, 18, 23, 19, 21)(25, 32, 28, 30, 26, 31, 27, 29)(33, 40, 36, 38, 34, 39, 35, 37)(41, 48, 44, 46, 42, 47, 43, 45)", perm"(1, 4, 2,
+3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22, 23)(25, 28, 26, 27)(29, 32, 30, 31)(33, 36, 34, 35)(37, 40, 38, 39)(41, 44, 42, 43)(45, 48, 46, 47)", perm"(1, 2)(3, 4)(5,
6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)" ], [
[ 2, 2, 2 ],
[ 4, 4, 4, 4 ],
@@ -2956,11 +2956,11 @@ perm"(1, 17, 9)(2, 18, 10)(3, 19, 11)(4, 20, 12)(5, 21, 13)(6, 22, 14)(7, 23, 15
[ 3, 1, 1, -4 ],
[ -1, -2, 1, 2 ],
[ 4, 3, 3, 5 ]
-], [ (1, 1), (2, 1), (3, 2), (4, 2), (6, 2), (8, 4), (12, 4), (16, 8), (24, 8), (48, 16) ], [ (1, 1), (2, 1), (3, 1), (4, 1), (6, 1), (8, 1), (12, 1), (16, 1), (24, 1), (48, 1) ], true, true, true,
-true, 16), ([ perm"(1, 33, 17)(2, 34, 18)(3, 35, 19)(4, 36, 20)(5, 37, 21)(6, 38, 22)(7, 39, 23)(8, 40, 24)(9, 41, 25)(10, 42, 26)(11, 43, 27)(12, 44, 28)(13, 45, 29)(14, 46, 30)(15, 47, 31)(16, 48,
-32)", perm"(1, 12, 4, 9)(2, 11, 3, 10)(5, 16, 8, 13)(6, 15, 7, 14)(17, 23, 19, 21)(18, 24, 20, 22)(25, 31, 27, 29)(26, 32, 28, 30)(33, 45, 34, 46)(35, 47, 36, 48)(37, 43, 38, 44)(39, 41, 40, 42)",
-perm"(1, 7, 3, 5)(2, 8, 4, 6)(9, 15, 11, 13)(10, 16, 12, 14)(17, 29, 18, 30)(19, 31, 20, 32)(21, 27, 22, 28)(23, 25, 24, 26)(33, 44, 36, 41)(34, 43, 35, 42)(37, 48, 40, 45)(38, 47, 39, 46)", perm"(1,
-3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 36)(34, 35)(37, 40)(38, 39)(41, 44)(42, 43)(45, 48)(46, 47)", perm"(1, 2)(3,
+], [ (1, 1), (2, 1), (3, 2), (4, 2), (6, 2), (8, 4), (12, 4), (16, 8), (24, 8), (48, 16) ], [ (1, 1), (2, 1), (3, 1), (4, 1), (6, 1), (8, 1), (12, 1), (16, 1), (24, 1), (48, 1) ], true, true, true,
+true, 16), ([ perm"(1, 33, 17)(2, 34, 18)(3, 35, 19)(4, 36, 20)(5, 37, 21)(6, 38, 22)(7, 39, 23)(8, 40, 24)(9, 41, 25)(10, 42, 26)(11, 43, 27)(12, 44, 28)(13, 45, 29)(14, 46, 30)(15, 47, 31)(16, 48,
+32)", perm"(1, 12, 4, 9)(2, 11, 3, 10)(5, 16, 8, 13)(6, 15, 7, 14)(17, 23, 19, 21)(18, 24, 20, 22)(25, 31, 27, 29)(26, 32, 28, 30)(33, 45, 34, 46)(35, 47, 36, 48)(37, 43, 38, 44)(39, 41, 40, 42)",
+perm"(1, 7, 3, 5)(2, 8, 4, 6)(9, 15, 11, 13)(10, 16, 12, 14)(17, 29, 18, 30)(19, 31, 20, 32)(21, 27, 22, 28)(23, 25, 24, 26)(33, 44, 36, 41)(34, 43, 35, 42)(37, 48, 40, 45)(38, 47, 39, 46)", perm"(1,
+3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 36)(34, 35)(37, 40)(38, 39)(41, 44)(42, 43)(45, 48)(46, 47)", perm"(1, 2)(3,
4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 20)(18, 19)(21, 24)(22, 23)(25, 28)(26, 27)(29, 32)(30, 31)(33, 35)(34, 36)(37, 39)(38, 40)(41, 43)(42, 44)(45, 47)(46, 48)" ], [
[ 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -2980,11 +2980,11 @@ perm"(1, 7, 3, 5)(2, 8, 4, 6)(9, 15, 11, 13)(10, 16, 12, 14)(17, 29, 18, 30)(19,
[ -3, -3, 4 ],
[ -1, 4, 1, 5 ],
[ 1, -2, -1, -2, -3 ]
-], [ (1, 1), (2, 3), (3, 32), (4, 12) ], [ (1, 1), (2, 3), (3, 16), (4, 7), (8, 3), (12, 4), (16, 1), (48, 1) ], false, false, true, false, 384), ([ perm"(1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7,
-31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 22, 10, 16, 4, 19, 7, 13)(2, 23, 11, 17, 5, 20, 8,
-14)(3, 24, 12, 18, 6, 21, 9, 15)(25, 46, 34, 40, 28, 43, 31, 37)(26, 47, 35, 41, 29, 44, 32, 38)(27, 48, 36, 42, 30, 45, 33, 39)", perm"(1, 10, 4, 7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23,
-17, 20)(15, 24, 18, 21)(25, 34, 28, 31)(26, 35, 29, 32)(27, 36, 30, 33)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19,
-22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21,
+], [ (1, 1), (2, 3), (3, 32), (4, 12) ], [ (1, 1), (2, 3), (3, 16), (4, 7), (8, 3), (12, 4), (16, 1), (48, 1) ], false, false, true, false, 384), ([ perm"(1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7,
+31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 22, 10, 16, 4, 19, 7, 13)(2, 23, 11, 17, 5, 20, 8,
+14)(3, 24, 12, 18, 6, 21, 9, 15)(25, 46, 34, 40, 28, 43, 31, 37)(26, 47, 35, 41, 29, 44, 32, 38)(27, 48, 36, 42, 30, 45, 33, 39)", perm"(1, 10, 4, 7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23,
+17, 20)(15, 24, 18, 21)(25, 34, 28, 31)(26, 35, 29, 32)(27, 36, 30, 33)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19,
+22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21,
20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1 ],
[ 3, 3, 3, 3 ],
@@ -3001,11 +3001,11 @@ perm"(1, 7, 3, 5)(2, 8, 4, 6)(9, 15, 11, 13)(10, 16, 12, 14)(17, 29, 18, 30)(19,
[ -2, 1, 2, 1 ],
[ -2, -5, 2, 5 ],
[ 1, -5, 1, -5 ]
-], [ (1, 1), (2, 7), (3, 2), (4, 8), (6, 2), (8, 16), (12, 4), (24, 8) ], [ (1, 1), (2, 7), (3, 1), (4, 7), (6, 3), (8, 7), (12, 3), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 48), ([
-perm"(1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1,
-22, 10, 16, 4, 19, 7, 13)(2, 23, 11, 17, 5, 20, 8, 14)(3, 24, 12, 18, 6, 21, 9, 15)(25, 43, 34, 37, 28, 46, 31, 40)(26, 44, 35, 38, 29, 47, 32, 41)(27, 45, 36, 39, 30, 48, 33, 42)", perm"(1, 10, 4,
-7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 34, 28, 31)(26, 35, 29, 32)(27, 36, 30, 33)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3,
-6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9,
+], [ (1, 1), (2, 7), (3, 2), (4, 8), (6, 2), (8, 16), (12, 4), (24, 8) ], [ (1, 1), (2, 7), (3, 1), (4, 7), (6, 3), (8, 7), (12, 3), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 48), ([
+perm"(1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1,
+22, 10, 16, 4, 19, 7, 13)(2, 23, 11, 17, 5, 20, 8, 14)(3, 24, 12, 18, 6, 21, 9, 15)(25, 43, 34, 37, 28, 46, 31, 40)(26, 44, 35, 38, 29, 47, 32, 41)(27, 45, 36, 39, 30, 48, 33, 42)", perm"(1, 10, 4,
+7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 34, 28, 31)(26, 35, 29, 32)(27, 36, 30, 33)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3,
+6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9,
8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1 ],
[ 3, 3, 3, 3 ],
@@ -3024,11 +3024,11 @@ perm"(1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11,
[ -2, -5, 2, 5 ],
[ 1, -5, 1, -5 ],
[ -2, 1, -2, 1, -3 ]
-], [ (1, 1), (2, 7), (3, 2), (4, 8), (6, 2), (8, 16), (12, 4), (24, 8) ], [ (1, 1), (2, 7), (3, 1), (4, 7), (6, 3), (8, 7), (12, 3), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 48), ([
-perm"(1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1,
-22, 10, 16, 4, 19, 7, 13)(2, 23, 11, 17, 5, 20, 8, 14)(3, 24, 12, 18, 6, 21, 9, 15)(25, 40, 31, 46, 28, 37, 34, 43)(26, 41, 32, 47, 29, 38, 35, 44)(27, 42, 33, 48, 30, 39, 36, 45)", perm"(1, 10, 4,
-7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 43, 40, 46)(38, 44, 41, 47)(39, 45, 42, 48)", perm"(1, 4)(2, 5)(3,
-6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9,
+], [ (1, 1), (2, 7), (3, 2), (4, 8), (6, 2), (8, 16), (12, 4), (24, 8) ], [ (1, 1), (2, 7), (3, 1), (4, 7), (6, 3), (8, 7), (12, 3), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 48), ([
+perm"(1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1,
+22, 10, 16, 4, 19, 7, 13)(2, 23, 11, 17, 5, 20, 8, 14)(3, 24, 12, 18, 6, 21, 9, 15)(25, 40, 31, 46, 28, 37, 34, 43)(26, 41, 32, 47, 29, 38, 35, 44)(27, 42, 33, 48, 30, 39, 36, 45)", perm"(1, 10, 4,
+7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 43, 40, 46)(38, 44, 41, 47)(39, 45, 42, 48)", perm"(1, 4)(2, 5)(3,
+6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9,
8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1 ],
[ 3, 3, 3, 3 ],
@@ -3047,11 +3047,11 @@ perm"(1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11,
[ -2, -5, 2, 5 ],
[ 1, -5, 1, -5 ],
[ -2, 1, -2, 1, 4 ]
-], [ (1, 1), (2, 13), (3, 2), (4, 14), (6, 2), (8, 4), (12, 4), (24, 8) ], [ (1, 1), (2, 13), (3, 1), (4, 13), (6, 5), (8, 7), (12, 5), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 96), ([
-perm"(1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1,
-19, 7, 16, 4, 22, 10, 13)(2, 20, 8, 17, 5, 23, 11, 14)(3, 21, 9, 18, 6, 24, 12, 15)(25, 37, 34, 46, 28, 40, 31, 43)(26, 38, 35, 47, 29, 41, 32, 44)(27, 39, 36, 48, 30, 42, 33, 45)", perm"(1, 10, 4,
-7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 43, 40, 46)(38, 44, 41, 47)(39, 45, 42, 48)", perm"(1, 4)(2, 5)(3,
-6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9,
+], [ (1, 1), (2, 13), (3, 2), (4, 14), (6, 2), (8, 4), (12, 4), (24, 8) ], [ (1, 1), (2, 13), (3, 1), (4, 13), (6, 5), (8, 7), (12, 5), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 96), ([
+perm"(1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1,
+19, 7, 16, 4, 22, 10, 13)(2, 20, 8, 17, 5, 23, 11, 14)(3, 21, 9, 18, 6, 24, 12, 15)(25, 37, 34, 46, 28, 40, 31, 43)(26, 38, 35, 47, 29, 41, 32, 44)(27, 39, 36, 48, 30, 42, 33, 45)", perm"(1, 10, 4,
+7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 43, 40, 46)(38, 44, 41, 47)(39, 45, 42, 48)", perm"(1, 4)(2, 5)(3,
+6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9,
8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1 ],
[ 3, 3, 3, 3 ],
@@ -3068,11 +3068,11 @@ perm"(1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11,
[ -2, 1, -2, 1 ],
[ -2, -5, 2, 5 ],
[ 1, -5, 1, -5 ]
-], [ (1, 1), (2, 25), (3, 2), (4, 2), (6, 2), (8, 4), (12, 4), (24, 8) ], [ (1, 1), (2, 25), (3, 1), (4, 13), (6, 9), (8, 7), (12, 5), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 192), ([
-perm"(1, 28, 4, 25)(2, 29, 5, 26)(3, 30, 6, 27)(7, 34, 10, 31)(8, 35, 11, 32)(9, 36, 12, 33)(13, 40, 16, 37)(14, 41, 17, 38)(15, 42, 18, 39)(19, 46, 22, 43)(20, 47, 23, 44)(21, 48, 24, 45)", perm"(1,
-19, 7, 16, 4, 22, 10, 13)(2, 20, 8, 17, 5, 23, 11, 14)(3, 21, 9, 18, 6, 24, 12, 15)(25, 37, 34, 46, 28, 40, 31, 43)(26, 38, 35, 47, 29, 41, 32, 44)(27, 39, 36, 48, 30, 42, 33, 45)", perm"(1, 10, 4,
-7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 43, 40, 46)(38, 44, 41, 47)(39, 45, 42, 48)", perm"(1, 4)(2, 5)(3,
-6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9,
+], [ (1, 1), (2, 25), (3, 2), (4, 2), (6, 2), (8, 4), (12, 4), (24, 8) ], [ (1, 1), (2, 25), (3, 1), (4, 13), (6, 9), (8, 7), (12, 5), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 192), ([
+perm"(1, 28, 4, 25)(2, 29, 5, 26)(3, 30, 6, 27)(7, 34, 10, 31)(8, 35, 11, 32)(9, 36, 12, 33)(13, 40, 16, 37)(14, 41, 17, 38)(15, 42, 18, 39)(19, 46, 22, 43)(20, 47, 23, 44)(21, 48, 24, 45)", perm"(1,
+19, 7, 16, 4, 22, 10, 13)(2, 20, 8, 17, 5, 23, 11, 14)(3, 21, 9, 18, 6, 24, 12, 15)(25, 37, 34, 46, 28, 40, 31, 43)(26, 38, 35, 47, 29, 41, 32, 44)(27, 39, 36, 48, 30, 42, 33, 45)", perm"(1, 10, 4,
+7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 43, 40, 46)(38, 44, 41, 47)(39, 45, 42, 48)", perm"(1, 4)(2, 5)(3,
+6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9,
8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1, 1, 1 ],
[ 3, 3, 3, 3 ],
@@ -3091,11 +3091,11 @@ perm"(1, 28, 4, 25)(2, 29, 5, 26)(3, 30, 6, 27)(7, 34, 10, 31)(8, 35, 11, 32)(9,
[ -2, -2, -3 ],
[ -1, -5, 1, -5 ],
[ -2, -5, 2, 5 ]
-], [ (1, 1), (2, 1), (3, 2), (4, 26), (6, 2), (8, 4), (12, 4), (24, 8) ], [ (1, 1), (2, 1), (3, 1), (4, 13), (6, 1), (8, 7), (12, 5), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 192), ([
-perm"(1, 34, 10, 28, 4, 31, 7, 25)(2, 35, 11, 29, 5, 32, 8, 26)(3, 36, 12, 30, 6, 33, 9, 27)(13, 46, 22, 40, 16, 43, 19, 37)(14, 47, 23, 41, 17, 44, 20, 38)(15, 48, 24, 42, 18, 45, 21, 39)", perm"(1,
-13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 10, 4,
-7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 34, 28, 31)(26, 35, 29, 32)(27, 36, 30, 33)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3,
-6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9,
+], [ (1, 1), (2, 1), (3, 2), (4, 26), (6, 2), (8, 4), (12, 4), (24, 8) ], [ (1, 1), (2, 1), (3, 1), (4, 13), (6, 1), (8, 7), (12, 5), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 192), ([
+perm"(1, 34, 10, 28, 4, 31, 7, 25)(2, 35, 11, 29, 5, 32, 8, 26)(3, 36, 12, 30, 6, 33, 9, 27)(13, 46, 22, 40, 16, 43, 19, 37)(14, 47, 23, 41, 17, 44, 20, 38)(15, 48, 24, 42, 18, 45, 21, 39)", perm"(1,
+13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 10, 4,
+7)(2, 11, 5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 34, 28, 31)(26, 35, 29, 32)(27, 36, 30, 33)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3,
+6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9,
8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 2, 2 ],
[ 3, 3, 3, 3 ],
@@ -3114,9 +3114,9 @@ perm"(1, 34, 10, 28, 4, 31, 7, 25)(2, 35, 11, 29, 5, 32, 8, 26)(3, 36, 12, 30, 6
[ 2, -5, 2, 5 ]
], [ (1, 1), (2, 3), (3, 2), (4, 4), (6, 6), (8, 24), (12, 8) ], [ (1, 1), (2, 3), (3, 1), (4, 3), (6, 3), (8, 7), (12, 3), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 96), ([ perm"(1, 34,
10, 28, 4, 31, 7, 25)(2, 35, 11, 29, 5, 32, 8, 26)(3, 36, 12, 30, 6, 33, 9, 27)(13, 46, 22, 40, 16, 43, 19, 37)(14, 47, 23, 41, 17, 44, 20, 38)(15, 48, 24, 42, 18, 45, 21, 39)", perm"(1, 13)(2, 14)(3,
-15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 40)(26, 41)(27, 42)(28, 37)(29, 38)(30, 39)(31, 46)(32, 47)(33, 48)(34, 43)(35, 44)(36, 45)", perm"(1, 10, 4, 7)(2, 11, 5,
-8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 34, 28, 31)(26, 35, 29, 32)(27, 36, 30, 33)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
-11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
+15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 40)(26, 41)(27, 42)(28, 37)(29, 38)(30, 39)(31, 46)(32, 47)(33, 48)(34, 43)(35, 44)(36, 45)", perm"(1, 10, 4, 7)(2, 11, 5,
+8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 34, 28, 31)(26, 35, 29, 32)(27, 36, 30, 33)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
+11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 2, 2 ],
[ 3, 3, 3, 3 ],
@@ -3137,9 +3137,9 @@ perm"(1, 34, 10, 28, 4, 31, 7, 25)(2, 35, 11, 29, 5, 32, 8, 26)(3, 36, 12, 30, 6
[ -1, 2, -1, 2, -3 ]
], [ (1, 1), (2, 3), (3, 2), (4, 4), (6, 6), (8, 24), (12, 8) ], [ (1, 1), (2, 3), (3, 1), (4, 3), (6, 3), (8, 7), (12, 3), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 96), ([ perm"(1, 31,
7, 25)(2, 32, 8, 26)(3, 33, 9, 27)(4, 34, 10, 28)(5, 35, 11, 29)(6, 36, 12, 30)(13, 43, 19, 37)(14, 44, 20, 38)(15, 45, 21, 39)(16, 46, 22, 40)(17, 47, 23, 41)(18, 48, 24, 42)", perm"(1, 16, 4, 13)(2,
-17, 5, 14)(3, 18, 6, 15)(7, 22, 10, 19)(8, 23, 11, 20)(9, 24, 12, 21)(25, 40, 28, 37)(26, 41, 29, 38)(27, 42, 30, 39)(31, 46, 34, 43)(32, 47, 35, 44)(33, 48, 36, 45)", perm"(1, 7)(2, 8)(3, 9)(4,
-10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
-11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
+17, 5, 14)(3, 18, 6, 15)(7, 22, 10, 19)(8, 23, 11, 20)(9, 24, 12, 21)(25, 40, 28, 37)(26, 41, 29, 38)(27, 42, 30, 39)(31, 46, 34, 43)(32, 47, 35, 44)(33, 48, 36, 45)", perm"(1, 7)(2, 8)(3, 9)(4,
+10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
+11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -3157,11 +3157,11 @@ perm"(1, 34, 10, 28, 4, 31, 7, 25)(2, 35, 11, 29, 5, 32, 8, 26)(3, 36, 12, 30, 6
[ -2, -2, 4 ],
[ -1, -5, 1, -5 ],
[ -2, -5, 2, 5 ]
-], [ (1, 1), (2, 3), (3, 2), (4, 28), (6, 6), (12, 8) ], [ (1, 1), (2, 3), (3, 1), (4, 15), (6, 3), (8, 7), (12, 7), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 192), ([ perm"(1, 28, 4,
-25)(2, 29, 5, 26)(3, 30, 6, 27)(7, 34, 10, 31)(8, 35, 11, 32)(9, 36, 12, 33)(13, 40, 16, 37)(14, 41, 17, 38)(15, 42, 18, 39)(19, 46, 22, 43)(20, 47, 23, 44)(21, 48, 24, 45)", perm"(1, 19, 7, 13)(2,
-20, 8, 14)(3, 21, 9, 15)(4, 22, 10, 16)(5, 23, 11, 17)(6, 24, 12, 18)(25, 46, 31, 40)(26, 47, 32, 41)(27, 48, 33, 42)(28, 43, 34, 37)(29, 44, 35, 38)(30, 45, 36, 39)", perm"(1, 7)(2, 8)(3, 9)(4,
-10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
-11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
+], [ (1, 1), (2, 3), (3, 2), (4, 28), (6, 6), (12, 8) ], [ (1, 1), (2, 3), (3, 1), (4, 15), (6, 3), (8, 7), (12, 7), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 192), ([ perm"(1, 28, 4,
+25)(2, 29, 5, 26)(3, 30, 6, 27)(7, 34, 10, 31)(8, 35, 11, 32)(9, 36, 12, 33)(13, 40, 16, 37)(14, 41, 17, 38)(15, 42, 18, 39)(19, 46, 22, 43)(20, 47, 23, 44)(21, 48, 24, 45)", perm"(1, 19, 7, 13)(2,
+20, 8, 14)(3, 21, 9, 15)(4, 22, 10, 16)(5, 23, 11, 17)(6, 24, 12, 18)(25, 46, 31, 40)(26, 47, 32, 41)(27, 48, 33, 42)(28, 43, 34, 37)(29, 44, 35, 38)(30, 45, 36, 39)", perm"(1, 7)(2, 8)(3, 9)(4,
+10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
+11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -3179,11 +3179,11 @@ perm"(1, 34, 10, 28, 4, 31, 7, 25)(2, 35, 11, 29, 5, 32, 8, 26)(3, 36, 12, 30, 6
[ -2, -2, 3 ],
[ -1, -5, 1, -5 ],
[ -2, -5, 2, 5 ]
-], [ (1, 1), (2, 3), (3, 2), (4, 28), (6, 6), (12, 8) ], [ (1, 1), (2, 3), (3, 1), (4, 15), (6, 3), (8, 7), (12, 7), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 96), ([ perm"(1, 31, 7,
-25)(2, 32, 8, 26)(3, 33, 9, 27)(4, 34, 10, 28)(5, 35, 11, 29)(6, 36, 12, 30)(13, 43, 19, 37)(14, 44, 20, 38)(15, 45, 21, 39)(16, 46, 22, 40)(17, 47, 23, 41)(18, 48, 24, 42)", perm"(1, 16, 4, 13)(2,
-17, 5, 14)(3, 18, 6, 15)(7, 22, 10, 19)(8, 23, 11, 20)(9, 24, 12, 21)(25, 37, 28, 40)(26, 38, 29, 41)(27, 39, 30, 42)(31, 43, 34, 46)(32, 44, 35, 47)(33, 45, 36, 48)", perm"(1, 7)(2, 8)(3, 9)(4,
-10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
-11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
+], [ (1, 1), (2, 3), (3, 2), (4, 28), (6, 6), (12, 8) ], [ (1, 1), (2, 3), (3, 1), (4, 15), (6, 3), (8, 7), (12, 7), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 96), ([ perm"(1, 31, 7,
+25)(2, 32, 8, 26)(3, 33, 9, 27)(4, 34, 10, 28)(5, 35, 11, 29)(6, 36, 12, 30)(13, 43, 19, 37)(14, 44, 20, 38)(15, 45, 21, 39)(16, 46, 22, 40)(17, 47, 23, 41)(18, 48, 24, 42)", perm"(1, 16, 4, 13)(2,
+17, 5, 14)(3, 18, 6, 15)(7, 22, 10, 19)(8, 23, 11, 20)(9, 24, 12, 21)(25, 37, 28, 40)(26, 38, 29, 41)(27, 39, 30, 42)(31, 43, 34, 46)(32, 44, 35, 47)(33, 45, 36, 48)", perm"(1, 7)(2, 8)(3, 9)(4,
+10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
+11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -3201,11 +3201,11 @@ perm"(1, 34, 10, 28, 4, 31, 7, 25)(2, 35, 11, 29, 5, 32, 8, 26)(3, 36, 12, 30, 6
[ -2, -2, 4 ],
[ -1, -5, 1, -5 ],
[ -2, -5, 2, 5 ]
-], [ (1, 1), (2, 3), (3, 2), (4, 28), (6, 6), (12, 8) ], [ (1, 1), (2, 3), (3, 1), (4, 15), (6, 3), (8, 7), (12, 7), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 192), ([ perm"(1, 25)(2,
-26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 19, 7, 13)(2,
-20, 8, 14)(3, 21, 9, 15)(4, 22, 10, 16)(5, 23, 11, 17)(6, 24, 12, 18)(25, 46, 31, 40)(26, 47, 32, 41)(27, 48, 33, 42)(28, 43, 34, 37)(29, 44, 35, 38)(30, 45, 36, 39)", perm"(1, 7)(2, 8)(3, 9)(4,
-10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
-11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
+], [ (1, 1), (2, 3), (3, 2), (4, 28), (6, 6), (12, 8) ], [ (1, 1), (2, 3), (3, 1), (4, 15), (6, 3), (8, 7), (12, 7), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 192), ([ perm"(1, 25)(2,
+26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 19, 7, 13)(2,
+20, 8, 14)(3, 21, 9, 15)(4, 22, 10, 16)(5, 23, 11, 17)(6, 24, 12, 18)(25, 46, 31, 40)(26, 47, 32, 41)(27, 48, 33, 42)(28, 43, 34, 37)(29, 44, 35, 38)(30, 45, 36, 39)", perm"(1, 7)(2, 8)(3, 9)(4,
+10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
+11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -3229,11 +3229,11 @@ perm"(1, 34, 10, 28, 4, 31, 7, 25)(2, 35, 11, 29, 5, 32, 8, 26)(3, 36, 12, 30, 6
[ 1, -5, 1, -5 ],
[ 4, -5, 4, 5 ],
[ 2, 1, -2, 1, 4 ]
-], [ (1, 1), (2, 15), (3, 2), (4, 16), (6, 6), (12, 8) ], [ (1, 1), (2, 15), (3, 1), (4, 27), (6, 7), (8, 7), (12, 11), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 96), ([ perm"(1, 25)(2,
-26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3,
-15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 43)(26, 44)(27, 45)(28, 46)(29, 47)(30, 48)(31, 40)(32, 41)(33, 42)(34, 37)(35, 38)(36, 39)", perm"(1, 10, 4, 7)(2, 11, 5,
-8)(3, 12, 6, 9)(13, 19, 16, 22)(14, 20, 17, 23)(15, 21, 18, 24)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
-11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
+], [ (1, 1), (2, 15), (3, 2), (4, 16), (6, 6), (12, 8) ], [ (1, 1), (2, 15), (3, 1), (4, 27), (6, 7), (8, 7), (12, 11), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 96), ([ perm"(1, 25)(2,
+26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3,
+15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 43)(26, 44)(27, 45)(28, 46)(29, 47)(30, 48)(31, 40)(32, 41)(33, 42)(34, 37)(35, 38)(36, 39)", perm"(1, 10, 4, 7)(2, 11, 5,
+8)(3, 12, 6, 9)(13, 19, 16, 22)(14, 20, 17, 23)(15, 21, 18, 24)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
+11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -3255,11 +3255,11 @@ perm"(1, 34, 10, 28, 4, 31, 7, 25)(2, 35, 11, 29, 5, 32, 8, 26)(3, 36, 12, 30, 6
[ 2, -5, 2, 5 ],
[ -3, -5, 3, 5 ],
[ 1, 2, 1, 2, 3 ]
-], [ (1, 1), (2, 17), (3, 2), (4, 2), (6, 10), (8, 12), (12, 4) ], [ (1, 1), (2, 17), (3, 1), (4, 9), (6, 9), (8, 7), (12, 5), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 96), ([ perm"(1,
-28, 4, 25)(2, 29, 5, 26)(3, 30, 6, 27)(7, 34, 10, 31)(8, 35, 11, 32)(9, 36, 12, 33)(13, 40, 16, 37)(14, 41, 17, 38)(15, 42, 18, 39)(19, 46, 22, 43)(20, 47, 23, 44)(21, 48, 24, 45)", perm"(1, 13)(2,
+], [ (1, 1), (2, 17), (3, 2), (4, 2), (6, 10), (8, 12), (12, 4) ], [ (1, 1), (2, 17), (3, 1), (4, 9), (6, 9), (8, 7), (12, 5), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 96), ([ perm"(1,
+28, 4, 25)(2, 29, 5, 26)(3, 30, 6, 27)(7, 34, 10, 31)(8, 35, 11, 32)(9, 36, 12, 33)(13, 40, 16, 37)(14, 41, 17, 38)(15, 42, 18, 39)(19, 46, 22, 43)(20, 47, 23, 44)(21, 48, 24, 45)", perm"(1, 13)(2,
14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 43)(26, 44)(27, 45)(28, 46)(29, 47)(30, 48)(31, 40)(32, 41)(33, 42)(34, 37)(35, 38)(36, 39)", perm"(1, 10, 4, 7)(2, 11,
-5, 8)(3, 12, 6, 9)(13, 19, 16, 22)(14, 20, 17, 23)(15, 21, 18, 24)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
-11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
+5, 8)(3, 12, 6, 9)(13, 19, 16, 22)(14, 20, 17, 23)(15, 21, 18, 24)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
+11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -3283,11 +3283,11 @@ perm"(1, 34, 10, 28, 4, 31, 7, 25)(2, 35, 11, 29, 5, 32, 8, 26)(3, 36, 12, 30, 6
[ 2, -5, 2, 5 ],
[ -3, -5, 3, 5 ],
[ -1, 2, -1, 2, -3 ]
-], [ (1, 1), (2, 5), (3, 2), (4, 14), (6, 10), (8, 12), (12, 4) ], [ (1, 1), (2, 5), (3, 1), (4, 9), (6, 5), (8, 7), (12, 5), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 96), ([ perm"(1,
-25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 16, 4,
+], [ (1, 1), (2, 5), (3, 2), (4, 14), (6, 10), (8, 12), (12, 4) ], [ (1, 1), (2, 5), (3, 1), (4, 9), (6, 5), (8, 7), (12, 5), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 96), ([ perm"(1,
+25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 16, 4,
13)(2, 17, 5, 14)(3, 18, 6, 15)(7, 22, 10, 19)(8, 23, 11, 20)(9, 24, 12, 21)(25, 46, 28, 43)(26, 47, 29, 44)(27, 48, 30, 45)(31, 37, 34, 40)(32, 38, 35, 41)(33, 39, 36, 42)", perm"(1, 10, 4, 7)(2, 11,
-5, 8)(3, 12, 6, 9)(13, 19, 16, 22)(14, 20, 17, 23)(15, 21, 18, 24)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
-11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
+5, 8)(3, 12, 6, 9)(13, 19, 16, 22)(14, 20, 17, 23)(15, 21, 18, 24)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
+11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -3311,11 +3311,11 @@ perm"(1, 34, 10, 28, 4, 31, 7, 25)(2, 35, 11, 29, 5, 32, 8, 26)(3, 36, 12, 30, 6
[ 1, -5, 1, -5 ],
[ -3, -5, 3, 5 ],
[ -2, 1, -2, 1, 3 ]
-], [ (1, 1), (2, 13), (3, 2), (4, 6), (6, 2), (8, 12), (12, 12) ], [ (1, 1), (2, 13), (3, 1), (4, 9), (6, 5), (8, 7), (12, 5), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 96), ([ perm"(1,
-28, 4, 25)(2, 29, 5, 26)(3, 30, 6, 27)(7, 34, 10, 31)(8, 35, 11, 32)(9, 36, 12, 33)(13, 40, 16, 37)(14, 41, 17, 38)(15, 42, 18, 39)(19, 46, 22, 43)(20, 47, 23, 44)(21, 48, 24, 45)", perm"(1, 16, 4,
+], [ (1, 1), (2, 13), (3, 2), (4, 6), (6, 2), (8, 12), (12, 12) ], [ (1, 1), (2, 13), (3, 1), (4, 9), (6, 5), (8, 7), (12, 5), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 96), ([ perm"(1,
+28, 4, 25)(2, 29, 5, 26)(3, 30, 6, 27)(7, 34, 10, 31)(8, 35, 11, 32)(9, 36, 12, 33)(13, 40, 16, 37)(14, 41, 17, 38)(15, 42, 18, 39)(19, 46, 22, 43)(20, 47, 23, 44)(21, 48, 24, 45)", perm"(1, 16, 4,
13)(2, 17, 5, 14)(3, 18, 6, 15)(7, 22, 10, 19)(8, 23, 11, 20)(9, 24, 12, 21)(25, 46, 28, 43)(26, 47, 29, 44)(27, 48, 30, 45)(31, 37, 34, 40)(32, 38, 35, 41)(33, 39, 36, 42)", perm"(1, 10, 4, 7)(2, 11,
-5, 8)(3, 12, 6, 9)(13, 19, 16, 22)(14, 20, 17, 23)(15, 21, 18, 24)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
-11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
+5, 8)(3, 12, 6, 9)(13, 19, 16, 22)(14, 20, 17, 23)(15, 21, 18, 24)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
+11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -3341,10 +3341,10 @@ perm"(1, 34, 10, 28, 4, 31, 7, 25)(2, 35, 11, 29, 5, 32, 8, 26)(3, 36, 12, 30, 6
[ -2, -5, 2, 5 ],
[ -3, -5, 3, 5 ],
[ -1, -2, -1, 2, -3 ]
-], [ (1, 1), (2, 1), (3, 2), (4, 18), (6, 2), (8, 12), (12, 12) ], [ (1, 1), (2, 1), (3, 1), (4, 9), (6, 1), (8, 7), (12, 5), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 96), ([ perm"(1,
-31, 7, 25)(2, 32, 8, 26)(3, 33, 9, 27)(4, 34, 10, 28)(5, 35, 11, 29)(6, 36, 12, 30)(13, 43, 19, 37)(14, 44, 20, 38)(15, 45, 21, 39)(16, 46, 22, 40)(17, 47, 23, 41)(18, 48, 24, 42)", perm"(1, 13)(2,
-14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 40)(26, 41)(27, 42)(28, 37)(29, 38)(30, 39)(31, 46)(32, 47)(33, 48)(34, 43)(35, 44)(36, 45)", perm"(1, 7)(2, 8)(3,
-9)(4, 10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 4)(2, 5)(3, 6)(7,
+], [ (1, 1), (2, 1), (3, 2), (4, 18), (6, 2), (8, 12), (12, 12) ], [ (1, 1), (2, 1), (3, 1), (4, 9), (6, 1), (8, 7), (12, 5), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 96), ([ perm"(1,
+31, 7, 25)(2, 32, 8, 26)(3, 33, 9, 27)(4, 34, 10, 28)(5, 35, 11, 29)(6, 36, 12, 30)(13, 43, 19, 37)(14, 44, 20, 38)(15, 45, 21, 39)(16, 46, 22, 40)(17, 47, 23, 41)(18, 48, 24, 42)", perm"(1, 13)(2,
+14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 40)(26, 41)(27, 42)(28, 37)(29, 38)(30, 39)(31, 46)(32, 47)(33, 48)(34, 43)(35, 44)(36, 45)", perm"(1, 7)(2, 8)(3,
+9)(4, 10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 4)(2, 5)(3, 6)(7,
10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10,
12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1, 1, 1 ],
@@ -3369,11 +3369,11 @@ perm"(1, 34, 10, 28, 4, 31, 7, 25)(2, 35, 11, 29, 5, 32, 8, 26)(3, 36, 12, 30, 6
[ 2, -5, 2, 5 ],
[ 4, -5, 4, 5 ],
[ 1, 2, -1, 2, 4 ]
-], [ (1, 1), (2, 7), (3, 2), (4, 24), (6, 14) ], [ (1, 1), (2, 7), (3, 1), (4, 19), (6, 7), (8, 7), (12, 11), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 192), ([ perm"(1, 27, 3, 25)(2,
-28, 4, 26)(5, 31, 7, 29)(6, 32, 8, 30)(9, 35, 11, 33)(10, 36, 12, 34)(13, 39, 15, 37)(14, 40, 16, 38)(17, 43, 19, 41)(18, 44, 20, 42)(21, 47, 23, 45)(22, 48, 24, 46)", perm"(1, 14, 2, 13)(3, 16, 4,
-15)(5, 18, 6, 17)(7, 20, 8, 19)(9, 22, 10, 21)(11, 24, 12, 23)(25, 38, 26, 37)(27, 40, 28, 39)(29, 42, 30, 41)(31, 44, 32, 43)(33, 46, 34, 45)(35, 48, 36, 47)", perm"(1, 9, 5)(2, 10, 6)(3, 11, 7)(4,
-12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)(37, 45, 41)(38, 46, 42)(39, 47, 43)(40, 48, 44)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10,
-12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22, 24)(25, 27)(26, 28)(29, 31)(30, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 43)(42, 44)(45, 47)(46, 48)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13,
+], [ (1, 1), (2, 7), (3, 2), (4, 24), (6, 14) ], [ (1, 1), (2, 7), (3, 1), (4, 19), (6, 7), (8, 7), (12, 11), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 192), ([ perm"(1, 27, 3, 25)(2,
+28, 4, 26)(5, 31, 7, 29)(6, 32, 8, 30)(9, 35, 11, 33)(10, 36, 12, 34)(13, 39, 15, 37)(14, 40, 16, 38)(17, 43, 19, 41)(18, 44, 20, 42)(21, 47, 23, 45)(22, 48, 24, 46)", perm"(1, 14, 2, 13)(3, 16, 4,
+15)(5, 18, 6, 17)(7, 20, 8, 19)(9, 22, 10, 21)(11, 24, 12, 23)(25, 38, 26, 37)(27, 40, 28, 39)(29, 42, 30, 41)(31, 44, 32, 43)(33, 46, 34, 45)(35, 48, 36, 47)", perm"(1, 9, 5)(2, 10, 6)(3, 11, 7)(4,
+12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)(37, 45, 41)(38, 46, 42)(39, 47, 43)(40, 48, 44)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10,
+12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22, 24)(25, 27)(26, 28)(29, 31)(30, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 43)(42, 44)(45, 47)(46, 48)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13,
14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -3391,11 +3391,11 @@ perm"(1, 34, 10, 28, 4, 31, 7, 25)(2, 35, 11, 29, 5, 32, 8, 26)(3, 36, 12, 30, 6
[ -2, -2, 5 ],
[ -1, -3, 1, 3 ],
[ -2, -3, 2, 3 ]
-], [ (1, 1), (2, 3), (3, 2), (4, 12), (6, 6), (12, 24) ], [ (1, 1), (2, 3), (3, 1), (4, 7), (6, 3), (8, 3), (12, 7), (16, 1), (24, 3), (48, 1) ], true, false, true, true, 192), ([ perm"(1, 26, 2,
-25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11, 36, 12, 35)(13, 38, 14, 37)(15, 40, 16, 39)(17, 42, 18, 41)(19, 44, 20, 43)(21, 46, 22, 45)(23, 48, 24, 47)", perm"(1, 13)(2, 14)(3,
-15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 39)(26, 40)(27, 37)(28, 38)(29, 43)(30, 44)(31, 41)(32, 42)(33, 47)(34, 48)(35, 45)(36, 46)", perm"(1, 9, 5)(2, 10, 6)(3, 11,
-7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)(37, 45, 41)(38, 46, 42)(39, 47, 43)(40, 48, 44)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10,
-12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22, 24)(25, 27)(26, 28)(29, 31)(30, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 43)(42, 44)(45, 47)(46, 48)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13,
+], [ (1, 1), (2, 3), (3, 2), (4, 12), (6, 6), (12, 24) ], [ (1, 1), (2, 3), (3, 1), (4, 7), (6, 3), (8, 3), (12, 7), (16, 1), (24, 3), (48, 1) ], true, false, true, true, 192), ([ perm"(1, 26, 2,
+25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11, 36, 12, 35)(13, 38, 14, 37)(15, 40, 16, 39)(17, 42, 18, 41)(19, 44, 20, 43)(21, 46, 22, 45)(23, 48, 24, 47)", perm"(1, 13)(2, 14)(3,
+15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 39)(26, 40)(27, 37)(28, 38)(29, 43)(30, 44)(31, 41)(32, 42)(33, 47)(34, 48)(35, 45)(36, 46)", perm"(1, 9, 5)(2, 10, 6)(3, 11,
+7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)(37, 45, 41)(38, 46, 42)(39, 47, 43)(40, 48, 44)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10,
+12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22, 24)(25, 27)(26, 28)(29, 31)(30, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 43)(42, 44)(45, 47)(46, 48)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13,
14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -3419,11 +3419,11 @@ perm"(1, 34, 10, 28, 4, 31, 7, 25)(2, 35, 11, 29, 5, 32, 8, 26)(3, 36, 12, 30, 6
[ -3, 4, 3, 4 ],
[ 2, 5, 2, 5 ],
[ 1, 2, -1, 2, 4 ]
-], [ (1, 1), (2, 7), (3, 2), (4, 8), (6, 14), (12, 16) ], [ (1, 1), (2, 7), (3, 1), (4, 11), (6, 7), (8, 3), (12, 11), (16, 1), (24, 3), (48, 1) ], false, false, true, true, 64), ([ perm"(1, 26, 2,
-25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11, 36, 12, 35)(13, 38, 14, 37)(15, 40, 16, 39)(17, 42, 18, 41)(19, 44, 20, 43)(21, 46, 22, 45)(23, 48, 24, 47)", perm"(1, 15, 3, 13)(2,
-16, 4, 14)(5, 19, 7, 17)(6, 20, 8, 18)(9, 23, 11, 21)(10, 24, 12, 22)(25, 37, 27, 39)(26, 38, 28, 40)(29, 41, 31, 43)(30, 42, 32, 44)(33, 45, 35, 47)(34, 46, 36, 48)", perm"(1, 9, 5)(2, 10, 6)(3, 11,
-7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)(37, 45, 41)(38, 46, 42)(39, 47, 43)(40, 48, 44)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10,
-12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22, 24)(25, 27)(26, 28)(29, 31)(30, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 43)(42, 44)(45, 47)(46, 48)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13,
+], [ (1, 1), (2, 7), (3, 2), (4, 8), (6, 14), (12, 16) ], [ (1, 1), (2, 7), (3, 1), (4, 11), (6, 7), (8, 3), (12, 11), (16, 1), (24, 3), (48, 1) ], false, false, true, true, 64), ([ perm"(1, 26, 2,
+25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11, 36, 12, 35)(13, 38, 14, 37)(15, 40, 16, 39)(17, 42, 18, 41)(19, 44, 20, 43)(21, 46, 22, 45)(23, 48, 24, 47)", perm"(1, 15, 3, 13)(2,
+16, 4, 14)(5, 19, 7, 17)(6, 20, 8, 18)(9, 23, 11, 21)(10, 24, 12, 22)(25, 37, 27, 39)(26, 38, 28, 40)(29, 41, 31, 43)(30, 42, 32, 44)(33, 45, 35, 47)(34, 46, 36, 48)", perm"(1, 9, 5)(2, 10, 6)(3, 11,
+7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)(37, 45, 41)(38, 46, 42)(39, 47, 43)(40, 48, 44)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10,
+12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 23)(22, 24)(25, 27)(26, 28)(29, 31)(30, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 43)(42, 44)(45, 47)(46, 48)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13,
14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -3441,11 +3441,11 @@ perm"(1, 34, 10, 28, 4, 31, 7, 25)(2, 35, 11, 29, 5, 32, 8, 26)(3, 36, 12, 30, 6
[ -2, -2, 4 ],
[ -1, -3, 1, 3 ],
[ -2, -3, 2, 3 ]
-], [ (1, 1), (2, 3), (3, 2), (4, 12), (6, 6), (12, 24) ], [ (1, 1), (2, 3), (3, 1), (4, 7), (6, 3), (8, 3), (12, 7), (16, 1), (24, 3), (48, 1) ], false, false, true, true, 64), ([ perm"(1, 28, 4, 26,
+], [ (1, 1), (2, 3), (3, 2), (4, 12), (6, 6), (12, 24) ], [ (1, 1), (2, 3), (3, 1), (4, 7), (6, 3), (8, 3), (12, 7), (16, 1), (24, 3), (48, 1) ], false, false, true, true, 64), ([ perm"(1, 28, 4, 26,
2, 27, 3, 25)(5, 32, 8, 30, 6, 31, 7, 29)(9, 36, 12, 34, 10, 35, 11, 33)(13, 40, 16, 38, 14, 39, 15, 37)(17, 44, 20, 42, 18, 43, 19, 41)(21, 48, 24, 46, 22, 47, 23, 45)", perm"(1, 13)(2, 14)(3, 15)(4,
-16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 9, 5)(2, 10, 6)(3, 11, 7)(4,
-12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)(37, 45, 41)(38, 46, 42)(39, 47, 43)(40, 48, 44)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10,
-11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22, 23)(25, 28, 26, 27)(29, 32, 30, 31)(33, 36, 34, 35)(37, 40, 38, 39)(41, 44, 42, 43)(45, 48, 46, 47)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13,
+16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 9, 5)(2, 10, 6)(3, 11, 7)(4,
+12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)(37, 45, 41)(38, 46, 42)(39, 47, 43)(40, 48, 44)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10,
+11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22, 23)(25, 28, 26, 27)(29, 32, 30, 31)(33, 36, 34, 35)(37, 40, 38, 39)(41, 44, 42, 43)(45, 48, 46, 47)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13,
14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)" ], [
[ 2, 2 ],
[ 3, 3, 3 ],
@@ -3462,11 +3462,11 @@ perm"(1, 34, 10, 28, 4, 31, 7, 25)(2, 35, 11, 29, 5, 32, 8, 26)(3, 36, 12, 30, 6
[ -1, 2, 1, 2 ],
[ -1, -3, 1, 3 ],
[ 2, -3, 2, 3 ]
-], [ (1, 1), (2, 3), (3, 2), (4, 4), (6, 6), (8, 8), (12, 8), (24, 16) ], [ (1, 1), (2, 3), (3, 1), (4, 3), (6, 3), (8, 3), (12, 3), (16, 1), (24, 3), (48, 1) ], true, false, true, true, 32), ([
-perm"(1, 28, 4, 26, 2, 27, 3, 25)(5, 32, 8, 30, 6, 31, 7, 29)(9, 36, 12, 34, 10, 35, 11, 33)(13, 40, 16, 38, 14, 39, 15, 37)(17, 44, 20, 42, 18, 43, 19, 41)(21, 48, 24, 46, 22, 47, 23, 45)", perm"(1,
-13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 38)(26, 37)(27, 40)(28, 39)(29, 42)(30, 41)(31, 44)(32, 43)(33, 46)(34, 45)(35, 48)(36, 47)", perm"(1, 9, 5)(2,
-10, 6)(3, 11, 7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)(37, 45, 41)(38, 46, 42)(39, 47, 43)(40, 48, 44)", perm"(1, 4, 2, 3)(5, 8, 6,
-7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22, 23)(25, 28, 26, 27)(29, 32, 30, 31)(33, 36, 34, 35)(37, 40, 38, 39)(41, 44, 42, 43)(45, 48, 46, 47)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9,
+], [ (1, 1), (2, 3), (3, 2), (4, 4), (6, 6), (8, 8), (12, 8), (24, 16) ], [ (1, 1), (2, 3), (3, 1), (4, 3), (6, 3), (8, 3), (12, 3), (16, 1), (24, 3), (48, 1) ], true, false, true, true, 32), ([
+perm"(1, 28, 4, 26, 2, 27, 3, 25)(5, 32, 8, 30, 6, 31, 7, 29)(9, 36, 12, 34, 10, 35, 11, 33)(13, 40, 16, 38, 14, 39, 15, 37)(17, 44, 20, 42, 18, 43, 19, 41)(21, 48, 24, 46, 22, 47, 23, 45)", perm"(1,
+13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 38)(26, 37)(27, 40)(28, 39)(29, 42)(30, 41)(31, 44)(32, 43)(33, 46)(34, 45)(35, 48)(36, 47)", perm"(1, 9, 5)(2,
+10, 6)(3, 11, 7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)(37, 45, 41)(38, 46, 42)(39, 47, 43)(40, 48, 44)", perm"(1, 4, 2, 3)(5, 8, 6,
+7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22, 23)(25, 28, 26, 27)(29, 32, 30, 31)(33, 36, 34, 35)(37, 40, 38, 39)(41, 44, 42, 43)(45, 48, 46, 47)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9,
10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)" ], [
[ 2, 2 ],
[ 3, 3, 3 ],
@@ -3485,11 +3485,11 @@ perm"(1, 28, 4, 26, 2, 27, 3, 25)(5, 32, 8, 30, 6, 31, 7, 29)(9, 36, 12, 34, 10,
[ 2, -3, 2, 3 ],
[ 2, -4, 2, 4 ],
[ -1, 2, -1, 2, -4 ]
-], [ (1, 1), (2, 3), (3, 2), (4, 4), (6, 6), (8, 8), (12, 8), (24, 16) ], [ (1, 1), (2, 3), (3, 1), (4, 3), (6, 3), (8, 3), (12, 3), (16, 1), (24, 3), (48, 1) ], false, false, true, true, 32), ([
-perm"(1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1,
-13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 39)(26, 40)(27, 38)(28, 37)(29, 43)(30, 44)(31, 42)(32, 41)(33, 47)(34, 48)(35, 46)(36, 45)", perm"(1, 9, 5)(2,
-10, 6)(3, 11, 7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)(37, 45, 41)(38, 46, 42)(39, 47, 43)(40, 48, 44)", perm"(1, 4, 2, 3)(5, 8, 6,
-7)(9, 12, 10, 11)(13, 15, 14, 16)(17, 19, 18, 20)(21, 23, 22, 24)(25, 27, 26, 28)(29, 31, 30, 32)(33, 35, 34, 36)(37, 40, 38, 39)(41, 44, 42, 43)(45, 48, 46, 47)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9,
+], [ (1, 1), (2, 3), (3, 2), (4, 4), (6, 6), (8, 8), (12, 8), (24, 16) ], [ (1, 1), (2, 3), (3, 1), (4, 3), (6, 3), (8, 3), (12, 3), (16, 1), (24, 3), (48, 1) ], false, false, true, true, 32), ([
+perm"(1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1,
+13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 39)(26, 40)(27, 38)(28, 37)(29, 43)(30, 44)(31, 42)(32, 41)(33, 47)(34, 48)(35, 46)(36, 45)", perm"(1, 9, 5)(2,
+10, 6)(3, 11, 7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)(37, 45, 41)(38, 46, 42)(39, 47, 43)(40, 48, 44)", perm"(1, 4, 2, 3)(5, 8, 6,
+7)(9, 12, 10, 11)(13, 15, 14, 16)(17, 19, 18, 20)(21, 23, 22, 24)(25, 27, 26, 28)(29, 31, 30, 32)(33, 35, 34, 36)(37, 40, 38, 39)(41, 44, 42, 43)(45, 48, 46, 47)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9,
10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -3511,11 +3511,11 @@ perm"(1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11,
[ -3, -4, 3, 4 ],
[ -4, -4, 5 ],
[ 1, 2, 1, 2, 4 ]
-], [ (1, 1), (2, 9), (3, 2), (4, 2), (6, 18), (8, 4), (12, 4), (24, 8) ], [ (1, 1), (2, 9), (3, 1), (4, 5), (6, 9), (8, 3), (12, 5), (16, 1), (24, 3), (48, 1) ], false, false, true, true, 64), ([
-perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11, 36, 12, 35)(13, 38, 14, 37)(15, 40, 16, 39)(17, 42, 18, 41)(19, 44, 20, 43)(21, 46, 22, 45)(23, 48, 24, 47)", perm"(1,
-13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 39)(26, 40)(27, 38)(28, 37)(29, 43)(30, 44)(31, 42)(32, 41)(33, 47)(34, 48)(35, 46)(36, 45)", perm"(1, 9, 5)(2,
-10, 6)(3, 11, 7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)(37, 45, 41)(38, 46, 42)(39, 47, 43)(40, 48, 44)", perm"(1, 4, 2, 3)(5, 8, 6,
-7)(9, 12, 10, 11)(13, 15, 14, 16)(17, 19, 18, 20)(21, 23, 22, 24)(25, 27, 26, 28)(29, 31, 30, 32)(33, 35, 34, 36)(37, 40, 38, 39)(41, 44, 42, 43)(45, 48, 46, 47)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9,
+], [ (1, 1), (2, 9), (3, 2), (4, 2), (6, 18), (8, 4), (12, 4), (24, 8) ], [ (1, 1), (2, 9), (3, 1), (4, 5), (6, 9), (8, 3), (12, 5), (16, 1), (24, 3), (48, 1) ], false, false, true, true, 64), ([
+perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11, 36, 12, 35)(13, 38, 14, 37)(15, 40, 16, 39)(17, 42, 18, 41)(19, 44, 20, 43)(21, 46, 22, 45)(23, 48, 24, 47)", perm"(1,
+13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 39)(26, 40)(27, 38)(28, 37)(29, 43)(30, 44)(31, 42)(32, 41)(33, 47)(34, 48)(35, 46)(36, 45)", perm"(1, 9, 5)(2,
+10, 6)(3, 11, 7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)(37, 45, 41)(38, 46, 42)(39, 47, 43)(40, 48, 44)", perm"(1, 4, 2, 3)(5, 8, 6,
+7)(9, 12, 10, 11)(13, 15, 14, 16)(17, 19, 18, 20)(21, 23, 22, 24)(25, 27, 26, 28)(29, 31, 30, 32)(33, 35, 34, 36)(37, 40, 38, 39)(41, 44, 42, 43)(45, 48, 46, 47)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9,
10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -3539,11 +3539,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ 2, -4, 2, -4 ],
[ -3, -4, 3, 4 ],
[ -1, 2, -1, 2, -4 ]
-], [ (1, 1), (2, 5), (3, 2), (4, 6), (6, 10), (8, 4), (12, 12), (24, 8) ], [ (1, 1), (2, 5), (3, 1), (4, 5), (6, 5), (8, 3), (12, 5), (16, 1), (24, 3), (48, 1) ], false, false, true, true, 32), ([
-perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11, 36, 12, 35)(13, 38, 14, 37)(15, 40, 16, 39)(17, 42, 18, 41)(19, 44, 20, 43)(21, 46, 22, 45)(23, 48, 24, 47)", perm"(1,
-14, 2, 13)(3, 16, 4, 15)(5, 18, 6, 17)(7, 20, 8, 19)(9, 22, 10, 21)(11, 24, 12, 23)(25, 40, 26, 39)(27, 37, 28, 38)(29, 44, 30, 43)(31, 41, 32, 42)(33, 48, 34, 47)(35, 45, 36, 46)", perm"(1, 9, 5)(2,
-10, 6)(3, 11, 7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)(37, 45, 41)(38, 46, 42)(39, 47, 43)(40, 48, 44)", perm"(1, 4, 2, 3)(5, 8, 6,
-7)(9, 12, 10, 11)(13, 15, 14, 16)(17, 19, 18, 20)(21, 23, 22, 24)(25, 27, 26, 28)(29, 31, 30, 32)(33, 35, 34, 36)(37, 40, 38, 39)(41, 44, 42, 43)(45, 48, 46, 47)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9,
+], [ (1, 1), (2, 5), (3, 2), (4, 6), (6, 10), (8, 4), (12, 12), (24, 8) ], [ (1, 1), (2, 5), (3, 1), (4, 5), (6, 5), (8, 3), (12, 5), (16, 1), (24, 3), (48, 1) ], false, false, true, true, 32), ([
+perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11, 36, 12, 35)(13, 38, 14, 37)(15, 40, 16, 39)(17, 42, 18, 41)(19, 44, 20, 43)(21, 46, 22, 45)(23, 48, 24, 47)", perm"(1,
+14, 2, 13)(3, 16, 4, 15)(5, 18, 6, 17)(7, 20, 8, 19)(9, 22, 10, 21)(11, 24, 12, 23)(25, 40, 26, 39)(27, 37, 28, 38)(29, 44, 30, 43)(31, 41, 32, 42)(33, 48, 34, 47)(35, 45, 36, 46)", perm"(1, 9, 5)(2,
+10, 6)(3, 11, 7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)(37, 45, 41)(38, 46, 42)(39, 47, 43)(40, 48, 44)", perm"(1, 4, 2, 3)(5, 8, 6,
+7)(9, 12, 10, 11)(13, 15, 14, 16)(17, 19, 18, 20)(21, 23, 22, 24)(25, 27, 26, 28)(29, 31, 30, 32)(33, 35, 34, 36)(37, 40, 38, 39)(41, 44, 42, 43)(45, 48, 46, 47)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9,
10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -3569,11 +3569,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -2, -4, 2, -4 ],
[ -3, -4, 3, 4 ],
[ -1, -2, -1, 2, -4 ]
-], [ (1, 1), (2, 1), (3, 2), (4, 10), (6, 2), (8, 4), (12, 20), (24, 8) ], [ (1, 1), (2, 1), (3, 1), (4, 5), (6, 1), (8, 3), (12, 5), (16, 1), (24, 3), (48, 1) ], false, false, true, true, 64), ([
-perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11, 36, 12, 35)(13, 38, 14, 37)(15, 40, 16, 39)(17, 42, 18, 41)(19, 44, 20, 43)(21, 46, 22, 45)(23, 48, 24, 47)", perm"(1,
-17, 9)(2, 18, 10)(3, 19, 11)(4, 20, 12)(5, 21, 13)(6, 22, 14)(7, 23, 15)(8, 24, 16)(25, 33, 41)(26, 34, 42)(27, 35, 43)(28, 36, 44)(29, 37, 45)(30, 38, 46)(31, 39, 47)(32, 40, 48)", perm"(1, 6, 2,
-5)(3, 8, 4, 7)(9, 11, 10, 12)(13, 16, 14, 15)(17, 23, 18, 24)(19, 22, 20, 21)(25, 28, 26, 27)(29, 31, 30, 32)(33, 40, 34, 39)(35, 37, 36, 38)(41, 45, 42, 46)(43, 47, 44, 48)", perm"(1, 4, 2, 3)(5, 7,
-6, 8)(9, 16, 10, 15)(11, 13, 12, 14)(17, 21, 18, 22)(19, 23, 20, 24)(25, 30, 26, 29)(27, 32, 28, 31)(33, 35, 34, 36)(37, 40, 38, 39)(41, 47, 42, 48)(43, 46, 44, 45)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9,
+], [ (1, 1), (2, 1), (3, 2), (4, 10), (6, 2), (8, 4), (12, 20), (24, 8) ], [ (1, 1), (2, 1), (3, 1), (4, 5), (6, 1), (8, 3), (12, 5), (16, 1), (24, 3), (48, 1) ], false, false, true, true, 64), ([
+perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11, 36, 12, 35)(13, 38, 14, 37)(15, 40, 16, 39)(17, 42, 18, 41)(19, 44, 20, 43)(21, 46, 22, 45)(23, 48, 24, 47)", perm"(1,
+17, 9)(2, 18, 10)(3, 19, 11)(4, 20, 12)(5, 21, 13)(6, 22, 14)(7, 23, 15)(8, 24, 16)(25, 33, 41)(26, 34, 42)(27, 35, 43)(28, 36, 44)(29, 37, 45)(30, 38, 46)(31, 39, 47)(32, 40, 48)", perm"(1, 6, 2,
+5)(3, 8, 4, 7)(9, 11, 10, 12)(13, 16, 14, 15)(17, 23, 18, 24)(19, 22, 20, 21)(25, 28, 26, 27)(29, 31, 30, 32)(33, 40, 34, 39)(35, 37, 36, 38)(41, 45, 42, 46)(43, 47, 44, 48)", perm"(1, 4, 2, 3)(5, 7,
+6, 8)(9, 16, 10, 15)(11, 13, 12, 14)(17, 21, 18, 22)(19, 23, 20, 24)(25, 30, 26, 29)(27, 32, 28, 31)(33, 35, 34, 36)(37, 40, 38, 39)(41, 47, 42, 48)(43, 46, 44, 45)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9,
10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2 ],
@@ -3597,11 +3597,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -2, -3, 2, -4 ],
[ -3, -4, 3, -4 ],
[ 2, -3, -2, 3, -4 ]
-], [ (1, 1), (2, 1), (3, 8), (4, 18), (6, 8), (8, 12) ], [ (1, 1), (2, 1), (3, 4), (4, 9), (6, 4), (8, 7), (12, 4), (16, 3), (24, 1), (48, 1) ], false, false, true, false, 48), ([ perm"(1, 25)(2,
-26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 17, 9)(2, 18,
+], [ (1, 1), (2, 1), (3, 8), (4, 18), (6, 8), (8, 12) ], [ (1, 1), (2, 1), (3, 4), (4, 9), (6, 4), (8, 7), (12, 4), (16, 3), (24, 1), (48, 1) ], false, false, true, false, 48), ([ perm"(1, 25)(2,
+26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 17, 9)(2, 18,
10)(3, 19, 11)(4, 20, 12)(5, 21, 13)(6, 22, 14)(7, 23, 15)(8, 24, 16)(25, 33, 41)(26, 34, 42)(27, 35, 43)(28, 36, 44)(29, 37, 45)(30, 38, 46)(31, 39, 47)(32, 40, 48)", perm"(1, 6, 2, 5)(3, 8, 4, 7)(9,
-11, 10, 12)(13, 16, 14, 15)(17, 23, 18, 24)(19, 22, 20, 21)(25, 28, 26, 27)(29, 31, 30, 32)(33, 40, 34, 39)(35, 37, 36, 38)(41, 45, 42, 46)(43, 47, 44, 48)", perm"(1, 4, 2, 3)(5, 7, 6, 8)(9, 16, 10,
-15)(11, 13, 12, 14)(17, 21, 18, 22)(19, 23, 20, 24)(25, 30, 26, 29)(27, 32, 28, 31)(33, 35, 34, 36)(37, 40, 38, 39)(41, 47, 42, 48)(43, 46, 44, 45)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13,
+11, 10, 12)(13, 16, 14, 15)(17, 23, 18, 24)(19, 22, 20, 21)(25, 28, 26, 27)(29, 31, 30, 32)(33, 40, 34, 39)(35, 37, 36, 38)(41, 45, 42, 46)(43, 47, 44, 48)", perm"(1, 4, 2, 3)(5, 7, 6, 8)(9, 16, 10,
+15)(11, 13, 12, 14)(17, 21, 18, 22)(19, 23, 20, 24)(25, 30, 26, 29)(27, 32, 28, 31)(33, 35, 34, 36)(37, 40, 38, 39)(41, 47, 42, 48)(43, 46, 44, 45)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13,
14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -3623,11 +3623,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -4, 3, 3, -4 ],
[ -3, -4, 3, -4 ],
[ 2, -3, -2, 3, -4 ]
-], [ (1, 1), (2, 13), (3, 8), (4, 6), (6, 8), (8, 12) ], [ (1, 1), (2, 13), (3, 4), (4, 9), (6, 12), (8, 7), (12, 4), (16, 3), (24, 1), (48, 1) ], false, false, true, false, 48), ([ perm"(1, 37, 13,
-25)(2, 38, 14, 26)(3, 39, 15, 27)(4, 40, 16, 28)(5, 41, 17, 29)(6, 42, 18, 30)(7, 43, 19, 31)(8, 44, 20, 32)(9, 45, 21, 33)(10, 46, 22, 34)(11, 47, 23, 35)(12, 48, 24, 36)", perm"(1, 13)(2, 14)(3,
-15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 9, 5)(2, 10, 6)(3, 11,
-7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 29, 33)(26, 30, 34)(27, 31, 35)(28, 32, 36)(37, 41, 45)(38, 42, 46)(39, 43, 47)(40, 44, 48)", perm"(1, 3)(2, 4)(5, 6)(7, 8)(9, 12)(10,
-11)(13, 15)(14, 16)(17, 18)(19, 20)(21, 24)(22, 23)(25, 26)(27, 28)(29, 32)(30, 31)(33, 35)(34, 36)(37, 38)(39, 40)(41, 44)(42, 43)(45, 47)(46, 48)", perm"(1, 2)(3, 4)(5, 8)(6, 7)(9, 11)(10, 12)(13,
+], [ (1, 1), (2, 13), (3, 8), (4, 6), (6, 8), (8, 12) ], [ (1, 1), (2, 13), (3, 4), (4, 9), (6, 12), (8, 7), (12, 4), (16, 3), (24, 1), (48, 1) ], false, false, true, false, 48), ([ perm"(1, 37, 13,
+25)(2, 38, 14, 26)(3, 39, 15, 27)(4, 40, 16, 28)(5, 41, 17, 29)(6, 42, 18, 30)(7, 43, 19, 31)(8, 44, 20, 32)(9, 45, 21, 33)(10, 46, 22, 34)(11, 47, 23, 35)(12, 48, 24, 36)", perm"(1, 13)(2, 14)(3,
+15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 9, 5)(2, 10, 6)(3, 11,
+7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 29, 33)(26, 30, 34)(27, 31, 35)(28, 32, 36)(37, 41, 45)(38, 42, 46)(39, 43, 47)(40, 44, 48)", perm"(1, 3)(2, 4)(5, 6)(7, 8)(9, 12)(10,
+11)(13, 15)(14, 16)(17, 18)(19, 20)(21, 24)(22, 23)(25, 26)(27, 28)(29, 32)(30, 31)(33, 35)(34, 36)(37, 38)(39, 40)(41, 44)(42, 43)(45, 47)(46, 48)", perm"(1, 2)(3, 4)(5, 8)(6, 7)(9, 11)(10, 12)(13,
14)(15, 16)(17, 20)(18, 19)(21, 23)(22, 24)(25, 27)(26, 28)(29, 30)(31, 32)(33, 36)(34, 35)(37, 39)(38, 40)(41, 42)(43, 44)(45, 48)(46, 47)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -3649,11 +3649,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -3, 4, 3, 5 ],
[ 4, 5, 4, 5 ],
[ 3, 4, -3, 4, 5 ]
-], [ (1, 1), (2, 7), (3, 8), (4, 24), (6, 8) ], [ (1, 1), (2, 7), (3, 4), (4, 19), (6, 4), (8, 7), (12, 5), (16, 3), (24, 1), (48, 1) ], false, false, true, false, 48), ([ perm"(1, 29, 5, 25)(2, 30,
-6, 26)(3, 31, 7, 27)(4, 32, 8, 28)(9, 37, 13, 33)(10, 38, 14, 34)(11, 39, 15, 35)(12, 40, 16, 36)(17, 45, 21, 41)(18, 46, 22, 42)(19, 47, 23, 43)(20, 48, 24, 44)", perm"(1, 17, 9)(2, 18, 10)(3, 19,
-11)(4, 20, 12)(5, 21, 13)(6, 22, 14)(7, 23, 15)(8, 24, 16)(25, 41, 33)(26, 42, 34)(27, 43, 35)(28, 44, 36)(29, 45, 37)(30, 46, 38)(31, 47, 39)(32, 48, 40)", perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10,
-14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 10)(11, 12)(13,
-14)(15, 16)(17, 20)(18, 19)(21, 24)(22, 23)(25, 27)(26, 28)(29, 31)(30, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 44)(42, 43)(45, 48)(46, 47)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 12)(10, 11)(13, 16)(14,
+], [ (1, 1), (2, 7), (3, 8), (4, 24), (6, 8) ], [ (1, 1), (2, 7), (3, 4), (4, 19), (6, 4), (8, 7), (12, 5), (16, 3), (24, 1), (48, 1) ], false, false, true, false, 48), ([ perm"(1, 29, 5, 25)(2, 30,
+6, 26)(3, 31, 7, 27)(4, 32, 8, 28)(9, 37, 13, 33)(10, 38, 14, 34)(11, 39, 15, 35)(12, 40, 16, 36)(17, 45, 21, 41)(18, 46, 22, 42)(19, 47, 23, 43)(20, 48, 24, 44)", perm"(1, 17, 9)(2, 18, 10)(3, 19,
+11)(4, 20, 12)(5, 21, 13)(6, 22, 14)(7, 23, 15)(8, 24, 16)(25, 41, 33)(26, 42, 34)(27, 43, 35)(28, 44, 36)(29, 45, 37)(30, 46, 38)(31, 47, 39)(32, 48, 40)", perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10,
+14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 10)(11, 12)(13,
+14)(15, 16)(17, 20)(18, 19)(21, 24)(22, 23)(25, 27)(26, 28)(29, 31)(30, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 44)(42, 43)(45, 48)(46, 47)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 12)(10, 11)(13, 16)(14,
15)(17, 19)(18, 20)(21, 23)(22, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 36)(34, 35)(37, 40)(38, 39)(41, 43)(42, 44)(45, 47)(46, 48)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2 ],
@@ -3673,11 +3673,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -2, 4, 2, 5 ],
[ 4, 5, 4, 5 ],
[ 2, 4, -2, 4, 5 ]
-], [ (1, 1), (2, 7), (3, 8), (4, 8), (6, 8), (12, 16) ], [ (1, 1), (2, 7), (3, 4), (4, 11), (6, 4), (8, 7), (12, 5), (16, 1), (24, 1), (48, 1) ], false, false, true, false, 48), ([ perm"(1, 25)(2,
-26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 17, 9)(2, 18,
+], [ (1, 1), (2, 7), (3, 8), (4, 8), (6, 8), (12, 16) ], [ (1, 1), (2, 7), (3, 4), (4, 11), (6, 4), (8, 7), (12, 5), (16, 1), (24, 1), (48, 1) ], false, false, true, false, 48), ([ perm"(1, 25)(2,
+26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 17, 9)(2, 18,
10)(3, 19, 11)(4, 20, 12)(5, 21, 13)(6, 22, 14)(7, 23, 15)(8, 24, 16)(25, 41, 33)(26, 42, 34)(27, 43, 35)(28, 44, 36)(29, 45, 37)(30, 46, 38)(31, 47, 39)(32, 48, 40)", perm"(1, 6, 2, 5)(3, 8, 4, 7)(9,
-12, 10, 11)(13, 15, 14, 16)(17, 24, 18, 23)(19, 21, 20, 22)(25, 30, 26, 29)(27, 32, 28, 31)(33, 36, 34, 35)(37, 39, 38, 40)(41, 48, 42, 47)(43, 45, 44, 46)", perm"(1, 4, 2, 3)(5, 7, 6, 8)(9, 16, 10,
-15)(11, 13, 12, 14)(17, 22, 18, 21)(19, 24, 20, 23)(25, 28, 26, 27)(29, 31, 30, 32)(33, 40, 34, 39)(35, 37, 36, 38)(41, 46, 42, 45)(43, 48, 44, 47)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13,
+12, 10, 11)(13, 15, 14, 16)(17, 24, 18, 23)(19, 21, 20, 22)(25, 30, 26, 29)(27, 32, 28, 31)(33, 36, 34, 35)(37, 39, 38, 40)(41, 48, 42, 47)(43, 45, 44, 46)", perm"(1, 4, 2, 3)(5, 7, 6, 8)(9, 16, 10,
+15)(11, 13, 12, 14)(17, 22, 18, 21)(19, 24, 20, 23)(25, 28, 26, 27)(29, 31, 30, 32)(33, 40, 34, 39)(35, 37, 36, 38)(41, 46, 42, 45)(43, 48, 44, 47)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13,
14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -3699,11 +3699,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -4, 3, 3, -4 ],
[ -3, -4, 3, -4 ],
[ 2, -3, -2, 3, 4 ]
-], [ (1, 1), (2, 3), (3, 8), (4, 12), (6, 24) ], [ (1, 1), (2, 3), (3, 4), (4, 7), (6, 12), (8, 7), (12, 4), (16, 1), (24, 1), (48, 1) ], false, false, true, false, 48), ([ perm"(1, 26, 2, 25)(3, 28,
-4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11, 36, 12, 35)(13, 38, 14, 37)(15, 40, 16, 39)(17, 42, 18, 41)(19, 44, 20, 43)(21, 46, 22, 45)(23, 48, 24, 47)", perm"(1, 17, 9)(2, 18, 10)(3, 19,
-11)(4, 20, 12)(5, 21, 13)(6, 22, 14)(7, 23, 15)(8, 24, 16)(25, 41, 33)(26, 42, 34)(27, 43, 35)(28, 44, 36)(29, 45, 37)(30, 46, 38)(31, 47, 39)(32, 48, 40)", perm"(1, 6, 2, 5)(3, 8, 4, 7)(9, 12, 10,
-11)(13, 15, 14, 16)(17, 24, 18, 23)(19, 21, 20, 22)(25, 30, 26, 29)(27, 32, 28, 31)(33, 36, 34, 35)(37, 39, 38, 40)(41, 48, 42, 47)(43, 45, 44, 46)", perm"(1, 4, 2, 3)(5, 7, 6, 8)(9, 16, 10, 15)(11,
-13, 12, 14)(17, 22, 18, 21)(19, 24, 20, 23)(25, 28, 26, 27)(29, 31, 30, 32)(33, 40, 34, 39)(35, 37, 36, 38)(41, 46, 42, 45)(43, 48, 44, 47)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15,
+], [ (1, 1), (2, 3), (3, 8), (4, 12), (6, 24) ], [ (1, 1), (2, 3), (3, 4), (4, 7), (6, 12), (8, 7), (12, 4), (16, 1), (24, 1), (48, 1) ], false, false, true, false, 48), ([ perm"(1, 26, 2, 25)(3, 28,
+4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11, 36, 12, 35)(13, 38, 14, 37)(15, 40, 16, 39)(17, 42, 18, 41)(19, 44, 20, 43)(21, 46, 22, 45)(23, 48, 24, 47)", perm"(1, 17, 9)(2, 18, 10)(3, 19,
+11)(4, 20, 12)(5, 21, 13)(6, 22, 14)(7, 23, 15)(8, 24, 16)(25, 41, 33)(26, 42, 34)(27, 43, 35)(28, 44, 36)(29, 45, 37)(30, 46, 38)(31, 47, 39)(32, 48, 40)", perm"(1, 6, 2, 5)(3, 8, 4, 7)(9, 12, 10,
+11)(13, 15, 14, 16)(17, 24, 18, 23)(19, 21, 20, 22)(25, 30, 26, 29)(27, 32, 28, 31)(33, 36, 34, 35)(37, 39, 38, 40)(41, 48, 42, 47)(43, 45, 44, 46)", perm"(1, 4, 2, 3)(5, 7, 6, 8)(9, 16, 10, 15)(11,
+13, 12, 14)(17, 22, 18, 21)(19, 24, 20, 23)(25, 28, 26, 27)(29, 31, 30, 32)(33, 40, 34, 39)(35, 37, 36, 38)(41, 46, 42, 45)(43, 48, 44, 47)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15,
16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2 ],
@@ -3727,11 +3727,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -2, -3, 2, 4 ],
[ -3, -4, 3, -4 ],
[ 2, -3, -2, 3, 4 ]
-], [ (1, 1), (2, 7), (3, 8), (4, 8), (6, 8), (12, 16) ], [ (1, 1), (2, 7), (3, 4), (4, 7), (6, 4), (8, 7), (12, 4), (16, 1), (24, 1), (48, 1) ], false, false, true, false, 48), ([ perm"(1, 28, 4,
-25)(2, 29, 5, 26)(3, 30, 6, 27)(7, 34, 10, 31)(8, 35, 11, 32)(9, 36, 12, 33)(13, 40, 16, 37)(14, 41, 17, 38)(15, 42, 18, 39)(19, 46, 22, 43)(20, 47, 23, 44)(21, 48, 24, 45)", perm"(1, 13)(2, 14)(3,
-15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 10, 4, 7)(2, 11, 5,
-8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 43, 40, 46)(38, 44, 41, 47)(39, 45, 42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
-11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
+], [ (1, 1), (2, 7), (3, 8), (4, 8), (6, 8), (12, 16) ], [ (1, 1), (2, 7), (3, 4), (4, 7), (6, 4), (8, 7), (12, 4), (16, 1), (24, 1), (48, 1) ], false, false, true, false, 48), ([ perm"(1, 28, 4,
+25)(2, 29, 5, 26)(3, 30, 6, 27)(7, 34, 10, 31)(8, 35, 11, 32)(9, 36, 12, 33)(13, 40, 16, 37)(14, 41, 17, 38)(15, 42, 18, 39)(19, 46, 22, 43)(20, 47, 23, 44)(21, 48, 24, 45)", perm"(1, 13)(2, 14)(3,
+15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 10, 4, 7)(2, 11, 5,
+8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 43, 40, 46)(38, 44, 41, 47)(39, 45, 42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
+11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -3755,11 +3755,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -1, -5, 1, -5 ],
[ 2, -5, 2, 5 ],
[ -3, -5, 3, 5 ]
-], [ (1, 1), (2, 3), (3, 2), (4, 28), (6, 6), (12, 8) ], [ (1, 1), (2, 3), (3, 1), (4, 15), (6, 3), (8, 19), (12, 7), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 384), ([ perm"(1, 25)(2,
-26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3,
-15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 10, 4, 7)(2, 11, 5,
-8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 34, 28, 31)(26, 35, 29, 32)(27, 36, 30, 33)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
-11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
+], [ (1, 1), (2, 3), (3, 2), (4, 28), (6, 6), (12, 8) ], [ (1, 1), (2, 3), (3, 1), (4, 15), (6, 3), (8, 19), (12, 7), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 384), ([ perm"(1, 25)(2,
+26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3,
+15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 10, 4, 7)(2, 11, 5,
+8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 34, 28, 31)(26, 35, 29, 32)(27, 36, 30, 33)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
+11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -3781,11 +3781,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ 1, -5, 1, -5 ],
[ 2, -5, 2, 5 ],
[ -3, -5, 3, 5 ]
-], [ (1, 1), (2, 15), (3, 2), (4, 16), (6, 6), (12, 8) ], [ (1, 1), (2, 15), (3, 1), (4, 27), (6, 7), (8, 19), (12, 11), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 192), ([ perm"(1,
-25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2,
+], [ (1, 1), (2, 15), (3, 2), (4, 16), (6, 6), (12, 8) ], [ (1, 1), (2, 15), (3, 1), (4, 27), (6, 7), (8, 19), (12, 11), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 192), ([ perm"(1,
+25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2,
14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 10, 4, 7)(2, 11,
-5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 43, 40, 46)(38, 44, 41, 47)(39, 45, 42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
-11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
+5, 8)(3, 12, 6, 9)(13, 22, 16, 19)(14, 23, 17, 20)(15, 24, 18, 21)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 43, 40, 46)(38, 44, 41, 47)(39, 45, 42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
+11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -3807,10 +3807,10 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ 1, -5, 1, -5 ],
[ 2, -5, 2, 5 ],
[ -3, -5, 3, 5 ]
-], [ (1, 1), (2, 27), (3, 2), (4, 4), (6, 6), (12, 8) ], [ (1, 1), (2, 27), (3, 1), (4, 39), (6, 11), (8, 19), (12, 15), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 384), ([ perm"(1,
-25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 16, 4,
-13)(2, 17, 5, 14)(3, 18, 6, 15)(7, 22, 10, 19)(8, 23, 11, 20)(9, 24, 12, 21)(25, 40, 28, 37)(26, 41, 29, 38)(27, 42, 30, 39)(31, 46, 34, 43)(32, 47, 35, 44)(33, 48, 36, 45)", perm"(1, 7)(2, 8)(3,
-9)(4, 10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 34)(26, 35)(27, 36)(28, 31)(29, 32)(30, 33)(37, 46)(38, 47)(39, 48)(40, 43)(41, 44)(42, 45)", perm"(1, 4)(2, 5)(3, 6)(7,
+], [ (1, 1), (2, 27), (3, 2), (4, 4), (6, 6), (12, 8) ], [ (1, 1), (2, 27), (3, 1), (4, 39), (6, 11), (8, 19), (12, 15), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 384), ([ perm"(1,
+25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 16, 4,
+13)(2, 17, 5, 14)(3, 18, 6, 15)(7, 22, 10, 19)(8, 23, 11, 20)(9, 24, 12, 21)(25, 40, 28, 37)(26, 41, 29, 38)(27, 42, 30, 39)(31, 46, 34, 43)(32, 47, 35, 44)(33, 48, 36, 45)", perm"(1, 7)(2, 8)(3,
+9)(4, 10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 34)(26, 35)(27, 36)(28, 31)(29, 32)(30, 33)(37, 46)(38, 47)(39, 48)(40, 43)(41, 44)(42, 45)", perm"(1, 4)(2, 5)(3, 6)(7,
10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10,
12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1 ],
@@ -3833,11 +3833,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ 1, -5, 1, -5 ],
[ 3, -5, 3, 5 ],
[ 3, 1, 2, 2, 3, 1 ]
-], [ (1, 1), (2, 15), (3, 2), (4, 16), (6, 6), (12, 8) ], [ (1, 1), (2, 15), (3, 1), (4, 15), (6, 7), (8, 19), (12, 7), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 96), ([ perm"(1, 25)(2,
-26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3,
-15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 7)(2, 8)(3, 9)(4,
-10)(5, 11)(6, 12)(13, 22)(14, 23)(15, 24)(16, 19)(17, 20)(18, 21)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 46)(38, 47)(39, 48)(40, 43)(41, 44)(42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
-11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
+], [ (1, 1), (2, 15), (3, 2), (4, 16), (6, 6), (12, 8) ], [ (1, 1), (2, 15), (3, 1), (4, 15), (6, 7), (8, 19), (12, 7), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 96), ([ perm"(1, 25)(2,
+26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3,
+15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 7)(2, 8)(3, 9)(4,
+10)(5, 11)(6, 12)(13, 22)(14, 23)(15, 24)(16, 19)(17, 20)(18, 21)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 46)(38, 47)(39, 48)(40, 43)(41, 44)(42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
+11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -3865,10 +3865,10 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ 3, -5, 3, 5 ],
[ 4, -5, 4, 5 ],
[ 2, 3, 2, 3, 4 ]
-], [ (1, 1), (2, 23), (3, 2), (4, 8), (6, 10), (12, 4) ], [ (1, 1), (2, 23), (3, 1), (4, 39), (6, 11), (8, 19), (12, 15), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 96), ([ perm"(1,
-25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 16, 4,
-13)(2, 17, 5, 14)(3, 18, 6, 15)(7, 22, 10, 19)(8, 23, 11, 20)(9, 24, 12, 21)(25, 40, 28, 37)(26, 41, 29, 38)(27, 42, 30, 39)(31, 46, 34, 43)(32, 47, 35, 44)(33, 48, 36, 45)", perm"(1, 7)(2, 8)(3,
-9)(4, 10)(5, 11)(6, 12)(13, 22)(14, 23)(15, 24)(16, 19)(17, 20)(18, 21)(25, 34)(26, 35)(27, 36)(28, 31)(29, 32)(30, 33)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 4)(2, 5)(3, 6)(7,
+], [ (1, 1), (2, 23), (3, 2), (4, 8), (6, 10), (12, 4) ], [ (1, 1), (2, 23), (3, 1), (4, 39), (6, 11), (8, 19), (12, 15), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 96), ([ perm"(1,
+25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 16, 4,
+13)(2, 17, 5, 14)(3, 18, 6, 15)(7, 22, 10, 19)(8, 23, 11, 20)(9, 24, 12, 21)(25, 40, 28, 37)(26, 41, 29, 38)(27, 42, 30, 39)(31, 46, 34, 43)(32, 47, 35, 44)(33, 48, 36, 45)", perm"(1, 7)(2, 8)(3,
+9)(4, 10)(5, 11)(6, 12)(13, 22)(14, 23)(15, 24)(16, 19)(17, 20)(18, 21)(25, 34)(26, 35)(27, 36)(28, 31)(29, 32)(30, 33)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 4)(2, 5)(3, 6)(7,
10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10,
12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1 ],
@@ -3892,10 +3892,10 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ 3, -5, 3, 5 ],
[ 3, 1, 2, 2, 3, 1 ]
], [ (1, 1), (2, 11), (3, 2), (4, 20), (6, 10), (12, 4) ], [ (1, 1), (2, 11), (3, 1), (4, 15), (6, 7), (8, 19), (12, 7), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 96), ([ perm"(1, 25)(2,
-26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 16, 4, 13)(2,
-17, 5, 14)(3, 18, 6, 15)(7, 22, 10, 19)(8, 23, 11, 20)(9, 24, 12, 21)(25, 40, 28, 37)(26, 41, 29, 38)(27, 42, 30, 39)(31, 46, 34, 43)(32, 47, 35, 44)(33, 48, 36, 45)", perm"(1, 10, 4, 7)(2, 11, 5,
-8)(3, 12, 6, 9)(13, 19, 16, 22)(14, 20, 17, 23)(15, 21, 18, 24)(25, 34, 28, 31)(26, 35, 29, 32)(27, 36, 30, 33)(37, 43, 40, 46)(38, 44, 41, 47)(39, 45, 42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
-11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
+26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 16, 4, 13)(2,
+17, 5, 14)(3, 18, 6, 15)(7, 22, 10, 19)(8, 23, 11, 20)(9, 24, 12, 21)(25, 40, 28, 37)(26, 41, 29, 38)(27, 42, 30, 39)(31, 46, 34, 43)(32, 47, 35, 44)(33, 48, 36, 45)", perm"(1, 10, 4, 7)(2, 11, 5,
+8)(3, 12, 6, 9)(13, 19, 16, 22)(14, 20, 17, 23)(15, 21, 18, 24)(25, 34, 28, 31)(26, 35, 29, 32)(27, 36, 30, 33)(37, 43, 40, 46)(38, 44, 41, 47)(39, 45, 42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
+11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -3919,11 +3919,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -2, -5, 2, 5 ],
[ 1, -5, 1, -5 ],
[ -3, -5, 3, 5 ]
-], [ (1, 1), (2, 7), (3, 2), (4, 24), (6, 2), (12, 12) ], [ (1, 1), (2, 7), (3, 1), (4, 15), (6, 3), (8, 19), (12, 7), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 288), ([ perm"(1, 25)(2,
-26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 16, 4, 13)(2,
-17, 5, 14)(3, 18, 6, 15)(7, 22, 10, 19)(8, 23, 11, 20)(9, 24, 12, 21)(25, 40, 28, 37)(26, 41, 29, 38)(27, 42, 30, 39)(31, 46, 34, 43)(32, 47, 35, 44)(33, 48, 36, 45)", perm"(1, 10, 4, 7)(2, 11, 5,
-8)(3, 12, 6, 9)(13, 19, 16, 22)(14, 20, 17, 23)(15, 21, 18, 24)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
-11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
+], [ (1, 1), (2, 7), (3, 2), (4, 24), (6, 2), (12, 12) ], [ (1, 1), (2, 7), (3, 1), (4, 15), (6, 3), (8, 19), (12, 7), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 288), ([ perm"(1, 25)(2,
+26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 16, 4, 13)(2,
+17, 5, 14)(3, 18, 6, 15)(7, 22, 10, 19)(8, 23, 11, 20)(9, 24, 12, 21)(25, 40, 28, 37)(26, 41, 29, 38)(27, 42, 30, 39)(31, 46, 34, 43)(32, 47, 35, 44)(33, 48, 36, 45)", perm"(1, 10, 4, 7)(2, 11, 5,
+8)(3, 12, 6, 9)(13, 19, 16, 22)(14, 20, 17, 23)(15, 21, 18, 24)(25, 31, 28, 34)(26, 32, 29, 35)(27, 33, 30, 36)(37, 46, 40, 43)(38, 47, 41, 44)(39, 48, 42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
+11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -3947,11 +3947,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -2, -5, 2, 5 ],
[ 1, -5, 1, -5 ],
[ -3, -5, 3, 5 ]
-], [ (1, 1), (2, 19), (3, 2), (4, 12), (6, 2), (12, 12) ], [ (1, 1), (2, 19), (3, 1), (4, 15), (6, 7), (8, 19), (12, 7), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 288), ([ perm"(1, 28,
+], [ (1, 1), (2, 19), (3, 2), (4, 12), (6, 2), (12, 12) ], [ (1, 1), (2, 19), (3, 1), (4, 15), (6, 7), (8, 19), (12, 7), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 288), ([ perm"(1, 28,
4, 25)(2, 29, 5, 26)(3, 30, 6, 27)(7, 34, 10, 31)(8, 35, 11, 32)(9, 36, 12, 33)(13, 40, 16, 37)(14, 41, 17, 38)(15, 42, 18, 39)(19, 46, 22, 43)(20, 47, 23, 44)(21, 48, 24, 45)", perm"(1, 13)(2, 14)(3,
-15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 7)(2, 8)(3, 9)(4,
-10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
-11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
+15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 7)(2, 8)(3, 9)(4,
+10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
+11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12,
11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -3973,11 +3973,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -1, -5, 1, -5 ],
[ 2, -5, 2, 5 ],
[ 3, -5, 3, 5 ]
-], [ (1, 1), (2, 7), (3, 2), (4, 24), (6, 14) ], [ (1, 1), (2, 7), (3, 1), (4, 19), (6, 7), (8, 19), (12, 11), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 1152), ([ perm"(1, 25)(2, 26)(3,
-27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3, 15)(4,
-16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 7)(2, 8)(3, 9)(4, 10)(5,
-11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 34)(26, 35)(27, 36)(28, 31)(29, 32)(30, 33)(37, 46)(38, 47)(39, 48)(40, 43)(41, 44)(42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9,
-12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13,
+], [ (1, 1), (2, 7), (3, 2), (4, 24), (6, 14) ], [ (1, 1), (2, 7), (3, 1), (4, 19), (6, 7), (8, 19), (12, 11), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 1152), ([ perm"(1, 25)(2, 26)(3,
+27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3, 15)(4,
+16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 7)(2, 8)(3, 9)(4, 10)(5,
+11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 34)(26, 35)(27, 36)(28, 31)(29, 32)(30, 33)(37, 46)(38, 47)(39, 48)(40, 43)(41, 44)(42, 45)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9,
+12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13,
15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -4005,11 +4005,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ 3, -5, 3, 5 ],
[ 4, -5, 4, 5 ],
[ 1, 3, 1, 3, 4 ]
-], [ (1, 1), (2, 19), (3, 2), (4, 12), (6, 14) ], [ (1, 1), (2, 19), (3, 1), (4, 31), (6, 11), (8, 19), (12, 15), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 192), ([ perm"(1, 26, 2,
-25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11, 36, 12, 35)(13, 38, 14, 37)(15, 40, 16, 39)(17, 42, 18, 41)(19, 44, 20, 43)(21, 46, 22, 45)(23, 48, 24, 47)", perm"(1, 13)(2, 14)(3,
-15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 7)(2, 8)(3, 9)(4,
+], [ (1, 1), (2, 19), (3, 2), (4, 12), (6, 14) ], [ (1, 1), (2, 19), (3, 1), (4, 31), (6, 11), (8, 19), (12, 15), (16, 3), (24, 7), (48, 1) ], false, false, true, false, 192), ([ perm"(1, 26, 2,
+25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11, 36, 12, 35)(13, 38, 14, 37)(15, 40, 16, 39)(17, 42, 18, 41)(19, 44, 20, 43)(21, 46, 22, 45)(23, 48, 24, 47)", perm"(1, 13)(2, 14)(3,
+15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 7)(2, 8)(3, 9)(4,
10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 5, 3)(2, 6, 4)(7, 11, 9)(8,
-12, 10)(13, 17, 15)(14, 18, 16)(19, 23, 21)(20, 24, 22)(25, 29, 27)(26, 30, 28)(31, 35, 33)(32, 36, 34)(37, 41, 39)(38, 42, 40)(43, 47, 45)(44, 48, 46)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11,
+12, 10)(13, 17, 15)(14, 18, 16)(19, 23, 21)(20, 24, 22)(25, 29, 27)(26, 30, 28)(31, 35, 33)(32, 36, 34)(37, 41, 39)(38, 42, 40)(43, 47, 45)(44, 48, 46)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11,
12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -4031,11 +4031,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -1, -4, 1, 4 ],
[ 2, -4, 2, 4 ],
[ 3, -4, 3, 4 ]
-], [ (1, 1), (2, 7), (3, 2), (4, 8), (6, 14), (12, 16) ], [ (1, 1), (2, 7), (3, 1), (4, 11), (6, 7), (8, 7), (12, 11), (16, 1), (24, 7), (48, 1) ], true, false, true, true, 384), ([ perm"(1, 25)(2,
-26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3,
-15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 38)(26, 37)(27, 40)(28, 39)(29, 42)(30, 41)(31, 44)(32, 43)(33, 46)(34, 45)(35, 48)(36, 47)", perm"(1, 7)(2, 8)(3, 9)(4,
+], [ (1, 1), (2, 7), (3, 2), (4, 8), (6, 14), (12, 16) ], [ (1, 1), (2, 7), (3, 1), (4, 11), (6, 7), (8, 7), (12, 11), (16, 1), (24, 7), (48, 1) ], true, false, true, true, 384), ([ perm"(1, 25)(2,
+26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3,
+15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 38)(26, 37)(27, 40)(28, 39)(29, 42)(30, 41)(31, 44)(32, 43)(33, 46)(34, 45)(35, 48)(36, 47)", perm"(1, 7)(2, 8)(3, 9)(4,
10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 5, 3)(2, 6, 4)(7, 11, 9)(8,
-12, 10)(13, 17, 15)(14, 18, 16)(19, 23, 21)(20, 24, 22)(25, 29, 27)(26, 30, 28)(31, 35, 33)(32, 36, 34)(37, 41, 39)(38, 42, 40)(43, 47, 45)(44, 48, 46)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11,
+12, 10)(13, 17, 15)(14, 18, 16)(19, 23, 21)(20, 24, 22)(25, 29, 27)(26, 30, 28)(31, 35, 33)(32, 36, 34)(37, 41, 39)(38, 42, 40)(43, 47, 45)(44, 48, 46)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11,
12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -4064,10 +4064,10 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -4, 5, 4, 5 ],
[ 1, 2, 1, 2, 5 ]
], [ (1, 1), (2, 11), (3, 2), (4, 4), (6, 22), (12, 8) ], [ (1, 1), (2, 11), (3, 1), (4, 15), (6, 11), (8, 7), (12, 15), (16, 1), (24, 7), (48, 1) ], false, false, true, true, 128), ([ perm"(1, 26, 2,
-25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11, 36, 12, 35)(13, 38, 14, 37)(15, 40, 16, 39)(17, 42, 18, 41)(19, 44, 20, 43)(21, 46, 22, 45)(23, 48, 24, 47)", perm"(1, 14, 2, 13)(3,
-16, 4, 15)(5, 18, 6, 17)(7, 20, 8, 19)(9, 22, 10, 21)(11, 24, 12, 23)(25, 37, 26, 38)(27, 39, 28, 40)(29, 41, 30, 42)(31, 43, 32, 44)(33, 45, 34, 46)(35, 47, 36, 48)", perm"(1, 7)(2, 8)(3, 9)(4,
+25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11, 36, 12, 35)(13, 38, 14, 37)(15, 40, 16, 39)(17, 42, 18, 41)(19, 44, 20, 43)(21, 46, 22, 45)(23, 48, 24, 47)", perm"(1, 14, 2, 13)(3,
+16, 4, 15)(5, 18, 6, 17)(7, 20, 8, 19)(9, 22, 10, 21)(11, 24, 12, 23)(25, 37, 26, 38)(27, 39, 28, 40)(29, 41, 30, 42)(31, 43, 32, 44)(33, 45, 34, 46)(35, 47, 36, 48)", perm"(1, 7)(2, 8)(3, 9)(4,
10)(5, 11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 5, 3)(2, 6, 4)(7, 11, 9)(8,
-12, 10)(13, 17, 15)(14, 18, 16)(19, 23, 21)(20, 24, 22)(25, 29, 27)(26, 30, 28)(31, 35, 33)(32, 36, 34)(37, 41, 39)(38, 42, 40)(43, 47, 45)(44, 48, 46)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11,
+12, 10)(13, 17, 15)(14, 18, 16)(19, 23, 21)(20, 24, 22)(25, 29, 27)(26, 30, 28)(31, 35, 33)(32, 36, 34)(37, 41, 39)(38, 42, 40)(43, 47, 45)(44, 48, 46)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11,
12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -4091,11 +4091,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -1, -4, 1, 4 ],
[ -2, -4, 2, 4 ],
[ 3, -4, 3, 4 ]
-], [ (1, 1), (2, 3), (3, 2), (4, 12), (6, 6), (12, 24) ], [ (1, 1), (2, 3), (3, 1), (4, 7), (6, 3), (8, 7), (12, 7), (16, 1), (24, 7), (48, 1) ], false, false, true, true, 384), ([ perm"(1, 25)(2,
-26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3,
-15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 38)(26, 37)(27, 40)(28, 39)(29, 42)(30, 41)(31, 44)(32, 43)(33, 46)(34, 45)(35, 48)(36, 47)", perm"(1, 8, 2, 7)(3, 10, 4,
-9)(5, 12, 6, 11)(13, 20, 14, 19)(15, 22, 16, 21)(17, 24, 18, 23)(25, 32, 26, 31)(27, 34, 28, 33)(29, 36, 30, 35)(37, 44, 38, 43)(39, 46, 40, 45)(41, 48, 42, 47)", perm"(1, 5, 3)(2, 6, 4)(7, 11, 9)(8,
-12, 10)(13, 17, 15)(14, 18, 16)(19, 23, 21)(20, 24, 22)(25, 29, 27)(26, 30, 28)(31, 35, 33)(32, 36, 34)(37, 41, 39)(38, 42, 40)(43, 47, 45)(44, 48, 46)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11,
+], [ (1, 1), (2, 3), (3, 2), (4, 12), (6, 6), (12, 24) ], [ (1, 1), (2, 3), (3, 1), (4, 7), (6, 3), (8, 7), (12, 7), (16, 1), (24, 7), (48, 1) ], false, false, true, true, 384), ([ perm"(1, 25)(2,
+26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3,
+15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 38)(26, 37)(27, 40)(28, 39)(29, 42)(30, 41)(31, 44)(32, 43)(33, 46)(34, 45)(35, 48)(36, 47)", perm"(1, 8, 2, 7)(3, 10, 4,
+9)(5, 12, 6, 11)(13, 20, 14, 19)(15, 22, 16, 21)(17, 24, 18, 23)(25, 32, 26, 31)(27, 34, 28, 33)(29, 36, 30, 35)(37, 44, 38, 43)(39, 46, 40, 45)(41, 48, 42, 47)", perm"(1, 5, 3)(2, 6, 4)(7, 11, 9)(8,
+12, 10)(13, 17, 15)(14, 18, 16)(19, 23, 21)(20, 24, 22)(25, 29, 27)(26, 30, 28)(31, 35, 33)(32, 36, 34)(37, 41, 39)(38, 42, 40)(43, 47, 45)(44, 48, 46)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11,
12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -4117,11 +4117,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ 2, -4, 2, 4 ],
[ -3, -4, 3, 4 ],
[ 1, 2, 1, 2, 5 ]
-], [ (1, 1), (2, 7), (3, 2), (4, 8), (6, 14), (12, 16) ], [ (1, 1), (2, 7), (3, 1), (4, 7), (6, 7), (8, 7), (12, 7), (16, 1), (24, 7), (48, 1) ], false, false, true, true, 96), ([ perm"(1, 25)(2,
-26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3,
-15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 9, 5)(2, 10, 6)(3, 11,
-7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 29, 33)(26, 30, 34)(27, 31, 35)(28, 32, 36)(37, 41, 45)(38, 42, 46)(39, 43, 47)(40, 44, 48)", perm"(1, 3)(2, 4)(5, 6)(7, 8)(9, 12)(10,
-11)(13, 15)(14, 16)(17, 18)(19, 20)(21, 24)(22, 23)(25, 26)(27, 28)(29, 32)(30, 31)(33, 35)(34, 36)(37, 38)(39, 40)(41, 44)(42, 43)(45, 47)(46, 48)", perm"(1, 2)(3, 4)(5, 8)(6, 7)(9, 11)(10, 12)(13,
+], [ (1, 1), (2, 7), (3, 2), (4, 8), (6, 14), (12, 16) ], [ (1, 1), (2, 7), (3, 1), (4, 7), (6, 7), (8, 7), (12, 7), (16, 1), (24, 7), (48, 1) ], false, false, true, true, 96), ([ perm"(1, 25)(2,
+26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3,
+15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 9, 5)(2, 10, 6)(3, 11,
+7)(4, 12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 29, 33)(26, 30, 34)(27, 31, 35)(28, 32, 36)(37, 41, 45)(38, 42, 46)(39, 43, 47)(40, 44, 48)", perm"(1, 3)(2, 4)(5, 6)(7, 8)(9, 12)(10,
+11)(13, 15)(14, 16)(17, 18)(19, 20)(21, 24)(22, 23)(25, 26)(27, 28)(29, 32)(30, 31)(33, 35)(34, 36)(37, 38)(39, 40)(41, 44)(42, 43)(45, 47)(46, 48)", perm"(1, 2)(3, 4)(5, 8)(6, 7)(9, 11)(10, 12)(13,
14)(15, 16)(17, 20)(18, 19)(21, 23)(22, 24)(25, 27)(26, 28)(29, 30)(31, 32)(33, 36)(34, 35)(37, 39)(38, 40)(41, 42)(43, 44)(45, 48)(46, 47)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -4145,11 +4145,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -3, 4, 3, 5 ],
[ 4, 5, 4, 5 ],
[ 3, 4, -3, 4, 5 ]
-], [ (1, 1), (2, 19), (3, 8), (4, 12), (6, 8) ], [ (1, 1), (2, 19), (3, 4), (4, 31), (6, 12), (8, 19), (12, 5), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 48), ([ perm"(1, 25)(2, 26)(3,
-27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3, 15)(4,
-16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 9, 5)(2, 10, 6)(3, 11, 7)(4,
-12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)(37, 45, 41)(38, 46, 42)(39, 47, 43)(40, 48, 44)", perm"(1, 3)(2, 4)(5, 6)(7, 8)(9, 12)(10,
-11)(13, 15)(14, 16)(17, 18)(19, 20)(21, 24)(22, 23)(25, 27)(26, 28)(29, 30)(31, 32)(33, 36)(34, 35)(37, 39)(38, 40)(41, 42)(43, 44)(45, 48)(46, 47)", perm"(1, 2)(3, 4)(5, 8)(6, 7)(9, 11)(10, 12)(13,
+], [ (1, 1), (2, 19), (3, 8), (4, 12), (6, 8) ], [ (1, 1), (2, 19), (3, 4), (4, 31), (6, 12), (8, 19), (12, 5), (16, 3), (24, 3), (48, 1) ], false, false, true, false, 48), ([ perm"(1, 25)(2, 26)(3,
+27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3, 15)(4,
+16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 9, 5)(2, 10, 6)(3, 11, 7)(4,
+12, 8)(13, 21, 17)(14, 22, 18)(15, 23, 19)(16, 24, 20)(25, 33, 29)(26, 34, 30)(27, 35, 31)(28, 36, 32)(37, 45, 41)(38, 46, 42)(39, 47, 43)(40, 48, 44)", perm"(1, 3)(2, 4)(5, 6)(7, 8)(9, 12)(10,
+11)(13, 15)(14, 16)(17, 18)(19, 20)(21, 24)(22, 23)(25, 27)(26, 28)(29, 30)(31, 32)(33, 36)(34, 35)(37, 39)(38, 40)(41, 42)(43, 44)(45, 48)(46, 47)", perm"(1, 2)(3, 4)(5, 8)(6, 7)(9, 11)(10, 12)(13,
14)(15, 16)(17, 20)(18, 19)(21, 23)(22, 24)(25, 26)(27, 28)(29, 32)(30, 31)(33, 35)(34, 36)(37, 38)(39, 40)(41, 44)(42, 43)(45, 47)(46, 48)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -4173,11 +4173,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -3, 4, 3, 5 ],
[ 4, 5, 4, 5 ],
[ 3, 4, -3, 4, 5 ]
-], [ (1, 1), (2, 15), (3, 8), (6, 24) ], [ (1, 1), (2, 15), (3, 4), (4, 35), (6, 12), (8, 15), (12, 5), (16, 1), (24, 3), (48, 1) ], false, false, true, false, 144), ([ perm"(1, 33, 17)(2, 34, 18)(3,
-35, 19)(4, 36, 20)(5, 37, 21)(6, 38, 22)(7, 39, 23)(8, 40, 24)(9, 41, 25)(10, 42, 26)(11, 43, 27)(12, 44, 28)(13, 45, 29)(14, 46, 30)(15, 47, 31)(16, 48, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5,
-13)(6, 14)(7, 15)(8, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 45)(34, 46)(35, 47)(36, 48)(37, 41)(38, 42)(39, 43)(40, 44)", perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10,
-14)(11, 15)(12, 16)(17, 29)(18, 30)(19, 31)(20, 32)(21, 25)(22, 26)(23, 27)(24, 28)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13,
-15)(14, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 36)(34, 35)(37, 40)(38, 39)(41, 44)(42, 43)(45, 48)(46, 47)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15,
+], [ (1, 1), (2, 15), (3, 8), (6, 24) ], [ (1, 1), (2, 15), (3, 4), (4, 35), (6, 12), (8, 15), (12, 5), (16, 1), (24, 3), (48, 1) ], false, false, true, false, 144), ([ perm"(1, 33, 17)(2, 34, 18)(3,
+35, 19)(4, 36, 20)(5, 37, 21)(6, 38, 22)(7, 39, 23)(8, 40, 24)(9, 41, 25)(10, 42, 26)(11, 43, 27)(12, 44, 28)(13, 45, 29)(14, 46, 30)(15, 47, 31)(16, 48, 32)", perm"(1, 9)(2, 10)(3, 11)(4, 12)(5,
+13)(6, 14)(7, 15)(8, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 45)(34, 46)(35, 47)(36, 48)(37, 41)(38, 42)(39, 43)(40, 44)", perm"(1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10,
+14)(11, 15)(12, 16)(17, 29)(18, 30)(19, 31)(20, 32)(21, 25)(22, 26)(23, 27)(24, 28)(33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13,
+15)(14, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 36)(34, 35)(37, 40)(38, 39)(41, 44)(42, 43)(45, 48)(46, 47)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15,
16)(17, 20)(18, 19)(21, 24)(22, 23)(25, 28)(26, 27)(29, 32)(30, 31)(33, 35)(34, 36)(37, 39)(38, 40)(41, 43)(42, 44)(45, 47)(46, 48)" ], [
[ 1, 1, 1 ],
[ 2, 2 ],
@@ -4203,11 +4203,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ 4, 5, 4, 5 ],
[ 1, 2, -1, 2, 3 ],
[ 1, 4, -1, 4, 5 ]
-], [ (1, 1), (2, 15), (3, 32) ], [ (1, 1), (2, 15), (3, 16), (4, 35), (8, 15), (12, 20), (16, 1), (48, 1) ], false, false, true, false, 5760), ([ perm"(1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7,
-31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8,
-20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 19)(14, 20)(15,
-21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19,
-22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21,
+], [ (1, 1), (2, 15), (3, 32) ], [ (1, 1), (2, 15), (3, 16), (4, 35), (8, 15), (12, 20), (16, 1), (48, 1) ], false, false, true, false, 5760), ([ perm"(1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7,
+31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8,
+20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12)(13, 19)(14, 20)(15,
+21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9, 12)(13, 16)(14, 17)(15, 18)(19,
+22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21,
20)(22, 24, 23)(25, 26, 27)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -4235,11 +4235,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ 2, -5, 2, 5 ],
[ 3, -5, 3, 5 ],
[ 4, -5, 4, 5 ]
-], [ (1, 1), (2, 31), (3, 2), (6, 14) ], [ (1, 1), (2, 31), (3, 1), (4, 91), (6, 15), (8, 43), (12, 35), (16, 3), (24, 15), (48, 1) ], false, false, true, false, 8064), ([ perm"(1, 25)(2, 26)(3,
-27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3, 15)(4,
-16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 7)(2, 8)(3, 9)(4, 10)(5,
-11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9,
-12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13,
+], [ (1, 1), (2, 31), (3, 2), (6, 14) ], [ (1, 1), (2, 31), (3, 1), (4, 91), (6, 15), (8, 43), (12, 35), (16, 3), (24, 15), (48, 1) ], false, false, true, false, 8064), ([ perm"(1, 25)(2, 26)(3,
+27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)", perm"(1, 13)(2, 14)(3, 15)(4,
+16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)", perm"(1, 7)(2, 8)(3, 9)(4, 10)(5,
+11)(6, 12)(13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24)(25, 31)(26, 32)(27, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8, 11)(9,
+12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13,
15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 33, 32)(34, 36, 35)(37, 39, 38)(40, 42, 41)(43, 45, 44)(46, 48, 47)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -4267,8 +4267,8 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ 2, -5, 2, 5 ],
[ 3, -5, 3, 5 ],
[ 4, -5, 4, 5 ]
-], [ (1, 1), (2, 15), (3, 2), (6, 30) ], [ (1, 1), (2, 15), (3, 1), (4, 35), (6, 15), (8, 15), (12, 35), (16, 1), (24, 15), (48, 1) ], true, false, true, true, 40320) ], [ ([ perm"(1, 49, 42, 35, 28,
-21, 14, 7, 48, 41, 34, 27, 20, 13, 6, 47, 40, 33, 26, 19, 12, 5, 46, 39, 32, 25, 18, 11, 4, 45, 38, 31, 24, 17, 10, 3, 44, 37, 30, 23, 16, 9, 2, 43, 36, 29, 22, 15, 8)", perm"(1, 7, 6, 5, 4, 3, 2)(8,
+], [ (1, 1), (2, 15), (3, 2), (6, 30) ], [ (1, 1), (2, 15), (3, 1), (4, 35), (6, 15), (8, 15), (12, 35), (16, 1), (24, 15), (48, 1) ], true, false, true, true, 40320) ], [ ([ perm"(1, 49, 42, 35, 28,
+21, 14, 7, 48, 41, 34, 27, 20, 13, 6, 47, 40, 33, 26, 19, 12, 5, 46, 39, 32, 25, 18, 11, 4, 45, 38, 31, 24, 17, 10, 3, 44, 37, 30, 23, 16, 9, 2, 43, 36, 29, 22, 15, 8)", perm"(1, 7, 6, 5, 4, 3, 2)(8,
14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)(29, 35, 34, 33, 32, 31, 30)(36, 42, 41, 40, 39, 38, 37)(43, 49, 48, 47, 46, 45, 44)" ], [
[ -1, -2, 1, 2 ],
[ 1, 1, 1, 1, 1, 1, 1, -2 ],
@@ -4276,17 +4276,17 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
], [
[ -1, -2, 1, 2 ],
[ 1, 1, 1, 1, 1, 1, 1, -2 ]
-], [ (1, 1), (7, 6), (49, 42) ], [ (1, 1), (7, 1), (49, 1) ], true, true, true, true, 42), ([ perm"(1, 43, 36, 29, 22, 15, 8)(2, 44, 37, 30, 23, 16, 9)(3, 45, 38, 31, 24, 17, 10)(4, 46, 39, 32, 25,
-18, 11)(5, 47, 40, 33, 26, 19, 12)(6, 48, 41, 34, 27, 20, 13)(7, 49, 42, 35, 28, 21, 14)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24,
+], [ (1, 1), (7, 6), (49, 42) ], [ (1, 1), (7, 1), (49, 1) ], true, true, true, true, 42), ([ perm"(1, 43, 36, 29, 22, 15, 8)(2, 44, 37, 30, 23, 16, 9)(3, 45, 38, 31, 24, 17, 10)(4, 46, 39, 32, 25,
+18, 11)(5, 47, 40, 33, 26, 19, 12)(6, 48, 41, 34, 27, 20, 13)(7, 49, 42, 35, 28, 21, 14)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24,
23)(29, 35, 34, 33, 32, 31, 30)(36, 42, 41, 40, 39, 38, 37)(43, 49, 48, 47, 46, 45, 44)" ], [
[ -1, -2, 1, 2 ],
[ -1, -1, -1, -1, -1, -1, -1 ],
[ -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -1, -2, 1, 2 ]
-], [ (1, 1), (7, 48) ], [ (1, 1), (7, 8), (49, 1) ], true, false, true, true, 2016) ], [ ([ perm"(1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9, 34)(10, 35)(11, 36)(12, 37)(13, 38)(14,
-39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50)", perm"(1, 25, 20, 15, 10, 5, 24, 19, 14, 9, 4, 23, 18, 13, 8, 3, 22, 17, 12, 7, 2, 21, 16, 11, 6)(26, 31,
-36, 41, 46, 27, 32, 37, 42, 47, 28, 33, 38, 43, 48, 29, 34, 39, 44, 49, 30, 35, 40, 45, 50)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 25, 24, 23, 22)(26, 27,
+], [ (1, 1), (7, 48) ], [ (1, 1), (7, 8), (49, 1) ], true, false, true, true, 2016) ], [ ([ perm"(1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9, 34)(10, 35)(11, 36)(12, 37)(13, 38)(14,
+39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50)", perm"(1, 25, 20, 15, 10, 5, 24, 19, 14, 9, 4, 23, 18, 13, 8, 3, 22, 17, 12, 7, 2, 21, 16, 11, 6)(26, 31,
+36, 41, 46, 27, 32, 37, 42, 47, 28, 33, 38, 43, 48, 29, 34, 39, 44, 49, 30, 35, 40, 45, 50)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 25, 24, 23, 22)(26, 27,
28, 29, 30)(31, 32, 33, 34, 35)(36, 37, 38, 39, 40)(41, 42, 43, 44, 45)(46, 47, 48, 49, 50)" ], [
[ 1, 1 ],
[ 3, 3, 3, 3, 3 ],
@@ -4299,9 +4299,9 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -2, -3, 2, 3 ],
[ 1, -3, 1, -3 ],
[ 2, 2, 2, 2, 2, -3 ]
-], [ (1, 1), (2, 25), (5, 4), (25, 20) ], [ (1, 1), (2, 25), (5, 1), (10, 5), (25, 1), (50, 1) ], false, false, true, false, 500), ([ perm"(1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9,
-34)(10, 35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50)", perm"(1, 25, 20, 15, 10, 5, 24, 19, 14, 9, 4, 23, 18, 13, 8, 3,
-22, 17, 12, 7, 2, 21, 16, 11, 6)(26, 50, 45, 40, 35, 30, 49, 44, 39, 34, 29, 48, 43, 38, 33, 28, 47, 42, 37, 32, 27, 46, 41, 36, 31)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20,
+], [ (1, 1), (2, 25), (5, 4), (25, 20) ], [ (1, 1), (2, 25), (5, 1), (10, 5), (25, 1), (50, 1) ], false, false, true, false, 500), ([ perm"(1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9,
+34)(10, 35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50)", perm"(1, 25, 20, 15, 10, 5, 24, 19, 14, 9, 4, 23, 18, 13, 8, 3,
+22, 17, 12, 7, 2, 21, 16, 11, 6)(26, 50, 45, 40, 35, 30, 49, 44, 39, 34, 29, 48, 43, 38, 33, 28, 47, 42, 37, 32, 27, 46, 41, 36, 31)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20,
19, 18, 17)(21, 25, 24, 23, 22)(26, 30, 29, 28, 27)(31, 35, 34, 33, 32)(36, 40, 39, 38, 37)(41, 45, 44, 43, 42)(46, 50, 49, 48, 47)" ], [
[ 1, 1 ],
[ 3, 3, 3, 3, 3 ],
@@ -4314,9 +4314,9 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -2, -3, 2, 3 ],
[ 1, -3, 1, 3 ],
[ 2, 2, 2, 2, 2, -3 ]
-], [ (1, 1), (2, 1), (5, 4), (10, 4), (25, 20), (50, 20) ], [ (1, 1), (2, 1), (5, 1), (10, 1), (25, 1), (50, 1) ], true, true, true, true, 20), ([ perm"(1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7,
+], [ (1, 1), (2, 1), (5, 4), (10, 4), (25, 20), (50, 20) ], [ (1, 1), (2, 1), (5, 1), (10, 1), (25, 1), (50, 1) ], true, true, true, true, 20), ([ perm"(1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7,
32)(8, 33)(9, 34)(10, 35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50)", perm"(1, 21, 16, 11, 6)(2, 22, 17, 12, 7)(3, 23, 18,
-13, 8)(4, 24, 19, 14, 9)(5, 25, 20, 15, 10)(26, 46, 41, 36, 31)(27, 47, 42, 37, 32)(28, 48, 43, 38, 33)(29, 49, 44, 39, 34)(30, 50, 45, 40, 35)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13,
+13, 8)(4, 24, 19, 14, 9)(5, 25, 20, 15, 10)(26, 46, 41, 36, 31)(27, 47, 42, 37, 32)(28, 48, 43, 38, 33)(29, 49, 44, 39, 34)(30, 50, 45, 40, 35)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13,
12)(16, 20, 19, 18, 17)(21, 25, 24, 23, 22)(26, 27, 28, 29, 30)(31, 32, 33, 34, 35)(36, 37, 38, 39, 40)(41, 42, 43, 44, 45)(46, 47, 48, 49, 50)" ], [
[ 1, 1 ],
[ 2, 2, 2, 2, 2 ],
@@ -4328,7 +4328,7 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -2, 1, 2, 1 ],
[ -2, -3, 2, 3 ],
[ 1, -3, 1, -3 ]
-], [ (1, 1), (2, 5), (5, 24), (10, 20) ], [ (1, 1), (2, 5), (5, 6), (10, 6), (25, 1), (50, 1) ], false, false, true, false, 80), ([ perm"(1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9,
+], [ (1, 1), (2, 5), (5, 24), (10, 20) ], [ (1, 1), (2, 5), (5, 6), (10, 6), (25, 1), (50, 1) ], false, false, true, false, 80), ([ perm"(1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9,
34)(10, 35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50)", perm"(1, 21, 16, 11, 6)(2, 22, 17, 12, 7)(3, 23, 18, 13, 8)(4, 24,
19, 14, 9)(5, 25, 20, 15, 10)(26, 31, 36, 41, 46)(27, 32, 37, 42, 47)(28, 33, 38, 43, 48)(29, 34, 39, 44, 49)(30, 35, 40, 45, 50)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19,
18, 17)(21, 25, 24, 23, 22)(26, 27, 28, 29, 30)(31, 32, 33, 34, 35)(36, 37, 38, 39, 40)(41, 42, 43, 44, 45)(46, 47, 48, 49, 50)" ], [
@@ -4344,7 +4344,7 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ 1, -3, 1, -3 ]
], [ (1, 1), (2, 25), (5, 24) ], [ (1, 1), (2, 25), (5, 6), (10, 30), (25, 1), (50, 1) ], false, false, true, false, 12000), ([ perm"(1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9, 34)(10,
35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50)", perm"(1, 21, 16, 11, 6)(2, 22, 17, 12, 7)(3, 23, 18, 13, 8)(4, 24, 19, 14,
-9)(5, 25, 20, 15, 10)(26, 46, 41, 36, 31)(27, 47, 42, 37, 32)(28, 48, 43, 38, 33)(29, 49, 44, 39, 34)(30, 50, 45, 40, 35)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18,
+9)(5, 25, 20, 15, 10)(26, 46, 41, 36, 31)(27, 47, 42, 37, 32)(28, 48, 43, 38, 33)(29, 49, 44, 39, 34)(30, 50, 45, 40, 35)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18,
17)(21, 25, 24, 23, 22)(26, 30, 29, 28, 27)(31, 35, 34, 33, 32)(36, 40, 39, 38, 37)(41, 45, 44, 43, 42)(46, 50, 49, 48, 47)" ], [
[ 1, 1 ],
[ 2, 2, 2, 2, 2 ],
@@ -4356,7 +4356,7 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ -2, 1, 2, 1 ],
[ -2, -3, 2, 3 ],
[ 1, -3, 1, 3 ]
-], [ (1, 1), (2, 1), (5, 24), (10, 24) ], [ (1, 1), (2, 1), (5, 6), (10, 6), (25, 1), (50, 1) ], true, false, true, true, 480) ], [ ([ perm"(1, 35, 18)(2, 36, 19)(3, 37, 20)(4, 38, 21)(5, 39, 22)(6,
+], [ (1, 1), (2, 1), (5, 24), (10, 24) ], [ (1, 1), (2, 1), (5, 6), (10, 6), (25, 1), (50, 1) ], true, false, true, true, 480) ], [ ([ perm"(1, 35, 18)(2, 36, 19)(3, 37, 20)(4, 38, 21)(5, 39, 22)(6,
40, 23)(7, 41, 24)(8, 42, 25)(9, 43, 26)(10, 44, 27)(11, 45, 28)(12, 46, 29)(13, 47, 30)(14, 48, 31)(15, 49, 32)(16, 50, 33)(17, 51, 34)", perm"(1, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3,
2)(18, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19)(35, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36)" ], [
[ 1, 1, 1 ],
@@ -4365,8 +4365,8 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
], [
[ -1, -2, 1, 2 ]
], [ (1, 1), (3, 2), (17, 16), (51, 32) ], [ (1, 1), (3, 1), (17, 1), (51, 1) ], true, true, true, true, 32) ], [ ([ perm"(1, 40, 14, 27)(2, 41, 15, 28)(3, 42, 16, 29)(4, 43, 17, 30)(5, 44, 18, 31)(6,
-45, 19, 32)(7, 46, 20, 33)(8, 47, 21, 34)(9, 48, 22, 35)(10, 49, 23, 36)(11, 50, 24, 37)(12, 51, 25, 38)(13, 52, 26, 39)", perm"(1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7, 20)(8, 21)(9, 22)(10,
-23)(11, 24)(12, 25)(13, 26)(27, 40)(28, 41)(29, 42)(30, 43)(31, 44)(32, 45)(33, 46)(34, 47)(35, 48)(36, 49)(37, 50)(38, 51)(39, 52)", perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(14, 26, 25, 24,
+45, 19, 32)(7, 46, 20, 33)(8, 47, 21, 34)(9, 48, 22, 35)(10, 49, 23, 36)(11, 50, 24, 37)(12, 51, 25, 38)(13, 52, 26, 39)", perm"(1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7, 20)(8, 21)(9, 22)(10,
+23)(11, 24)(12, 25)(13, 26)(27, 40)(28, 41)(29, 42)(30, 43)(31, 44)(32, 45)(33, 46)(34, 47)(35, 48)(36, 49)(37, 50)(38, 51)(39, 52)", perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(14, 26, 25, 24,
23, 22, 21, 20, 19, 18, 17, 16, 15)(27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39)(40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -4376,8 +4376,8 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
], [
[ -1, -1, 2 ],
[ -1, -3, 1, -3 ]
-], [ (1, 1), (2, 1), (4, 26), (13, 12), (26, 12) ], [ (1, 1), (2, 1), (4, 13), (13, 1), (26, 1), (52, 1) ], false, false, true, false, 312), ([ perm"(1, 28, 2, 27)(3, 30, 4, 29)(5, 32, 6, 31)(7, 34,
-8, 33)(9, 36, 10, 35)(11, 38, 12, 37)(13, 40, 14, 39)(15, 42, 16, 41)(17, 44, 18, 43)(19, 46, 20, 45)(21, 48, 22, 47)(23, 50, 24, 49)(25, 52, 26, 51)", perm"(1, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7,
+], [ (1, 1), (2, 1), (4, 26), (13, 12), (26, 12) ], [ (1, 1), (2, 1), (4, 13), (13, 1), (26, 1), (52, 1) ], false, false, true, false, 312), ([ perm"(1, 28, 2, 27)(3, 30, 4, 29)(5, 32, 6, 31)(7, 34,
+8, 33)(9, 36, 10, 35)(11, 38, 12, 37)(13, 40, 14, 39)(15, 42, 16, 41)(17, 44, 18, 43)(19, 46, 20, 45)(21, 48, 22, 47)(23, 50, 24, 49)(25, 52, 26, 51)", perm"(1, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7,
5, 3)(2, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4)(27, 51, 49, 47, 45, 43, 41, 39, 37, 35, 33, 31, 29)(28, 52, 50, 48, 46, 44, 42, 40, 38, 36, 34, 32, 30)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11,
12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)(49, 50)(51, 52)" ], [
[ 1, 1, 1, 1 ],
@@ -4388,8 +4388,8 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
], [
[ -1, -1, 3 ],
[ -1, -2, 1, 2 ]
-], [ (1, 1), (2, 1), (4, 2), (13, 12), (26, 12), (52, 24) ], [ (1, 1), (2, 1), (4, 1), (13, 1), (26, 1), (52, 1) ], true, true, true, true, 24), ([ perm"(1, 40, 14, 27)(2, 41, 15, 28)(3, 42, 16,
-29)(4, 43, 17, 30)(5, 44, 18, 31)(6, 45, 19, 32)(7, 46, 20, 33)(8, 47, 21, 34)(9, 48, 22, 35)(10, 49, 23, 36)(11, 50, 24, 37)(12, 51, 25, 38)(13, 52, 26, 39)", perm"(1, 14)(2, 15)(3, 16)(4, 17)(5,
+], [ (1, 1), (2, 1), (4, 2), (13, 12), (26, 12), (52, 24) ], [ (1, 1), (2, 1), (4, 1), (13, 1), (26, 1), (52, 1) ], true, true, true, true, 24), ([ perm"(1, 40, 14, 27)(2, 41, 15, 28)(3, 42, 16,
+29)(4, 43, 17, 30)(5, 44, 18, 31)(6, 45, 19, 32)(7, 46, 20, 33)(8, 47, 21, 34)(9, 48, 22, 35)(10, 49, 23, 36)(11, 50, 24, 37)(12, 51, 25, 38)(13, 52, 26, 39)", perm"(1, 14)(2, 15)(3, 16)(4, 17)(5,
18)(6, 19)(7, 20)(8, 21)(9, 22)(10, 23)(11, 24)(12, 25)(13, 26)(27, 40)(28, 41)(29, 42)(30, 43)(31, 44)(32, 45)(33, 46)(34, 47)(35, 48)(36, 49)(37, 50)(38, 51)(39, 52)", perm"(1, 13, 12, 11, 10, 9, 8,
7, 6, 5, 4, 3, 2)(14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26)(27, 32, 37, 29, 34, 39, 31, 36, 28, 33, 38, 30, 35)(40, 48, 43, 51, 46, 41, 49, 44, 52, 47, 42, 50, 45)" ], [
[ 1, 1, 1, 1 ],
@@ -4402,8 +4402,8 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ 2, -3, 2, -3 ],
[ 1, -3, -3, -1, -3, -3, -3 ]
], [ (1, 1), (2, 13), (4, 26), (13, 12) ], [ (1, 1), (2, 13), (4, 13), (13, 1), (26, 1), (52, 1) ], false, false, true, false, 156), ([ perm"(1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9,
-35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)", perm"(1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7, 20)(8,
-21)(9, 22)(10, 23)(11, 24)(12, 25)(13, 26)(27, 40)(28, 41)(29, 42)(30, 43)(31, 44)(32, 45)(33, 46)(34, 47)(35, 48)(36, 49)(37, 50)(38, 51)(39, 52)", perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3,
+35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)", perm"(1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7, 20)(8,
+21)(9, 22)(10, 23)(11, 24)(12, 25)(13, 26)(27, 40)(28, 41)(29, 42)(30, 43)(31, 44)(32, 45)(33, 46)(34, 47)(35, 48)(36, 49)(37, 50)(38, 51)(39, 52)", perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3,
2)(14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15)(27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39)(40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -4415,9 +4415,9 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ 1, 2, 1, 2 ],
[ 1, -3, 1, -3 ],
[ 2, -3, 2, 3 ]
-], [ (1, 1), (2, 27), (13, 12), (26, 12) ], [ (1, 1), (2, 27), (4, 13), (13, 1), (26, 3), (52, 1) ], false, false, true, false, 312), ([ perm"(1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8,
-34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)", perm"(1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7,
-20)(8, 21)(9, 22)(10, 23)(11, 24)(12, 25)(13, 26)(27, 40)(28, 41)(29, 42)(30, 43)(31, 44)(32, 45)(33, 46)(34, 47)(35, 48)(36, 49)(37, 50)(38, 51)(39, 52)", perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4,
+], [ (1, 1), (2, 27), (13, 12), (26, 12) ], [ (1, 1), (2, 27), (4, 13), (13, 1), (26, 3), (52, 1) ], false, false, true, false, 312), ([ perm"(1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8,
+34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)", perm"(1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7,
+20)(8, 21)(9, 22)(10, 23)(11, 24)(12, 25)(13, 26)(27, 40)(28, 41)(29, 42)(30, 43)(31, 44)(32, 45)(33, 46)(34, 47)(35, 48)(36, 49)(37, 50)(38, 51)(39, 52)", perm"(1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4,
3, 2)(14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15)(27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28)(40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -4429,14 +4429,14 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ 1, 2, 1, 2 ],
[ 1, -3, 1, 3 ],
[ 2, -3, 2, 3 ]
-], [ (1, 1), (2, 3), (13, 12), (26, 36) ], [ (1, 1), (2, 3), (4, 1), (13, 1), (26, 3), (52, 1) ], true, false, true, true, 72) ], [ ([ perm"(1, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40,
+], [ (1, 1), (2, 3), (13, 12), (26, 36) ], [ (1, 1), (2, 3), (4, 1), (13, 1), (26, 3), (52, 1) ], true, false, true, true, 72) ], [ ([ perm"(1, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40,
39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)" ], [
-[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
+[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
-1, -1, -1, -1 ]
-], [], [ (1, 1), (53, 52) ], [ (1, 1), (53, 1) ], true, true, true, true, 52) ], [ ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15,
-42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 22, 13, 4, 25, 16, 7, 21, 12, 3, 24, 15, 6, 27, 18, 9, 20, 11, 2, 23, 14, 5, 26, 17, 8,
-19, 10)(28, 37, 46, 35, 44, 53, 32, 41, 50, 29, 38, 47, 36, 45, 54, 33, 42, 51, 30, 39, 48, 34, 43, 52, 31, 40, 49)", perm"(1, 8, 5, 2, 9, 6, 3, 7, 4)(10, 17, 14, 11, 18, 15, 12, 16, 13)(19, 26, 23,
-20, 27, 24, 21, 25, 22)(28, 31, 34, 30, 33, 36, 29, 32, 35)(37, 40, 43, 39, 42, 45, 38, 41, 44)(46, 49, 52, 48, 51, 54, 47, 50, 53)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18,
+], [], [ (1, 1), (53, 52) ], [ (1, 1), (53, 1) ], true, true, true, true, 52) ], [ ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15,
+42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 22, 13, 4, 25, 16, 7, 21, 12, 3, 24, 15, 6, 27, 18, 9, 20, 11, 2, 23, 14, 5, 26, 17, 8,
+19, 10)(28, 37, 46, 35, 44, 53, 32, 41, 50, 29, 38, 47, 36, 45, 54, 33, 42, 51, 30, 39, 48, 34, 43, 52, 31, 40, 49)", perm"(1, 8, 5, 2, 9, 6, 3, 7, 4)(10, 17, 14, 11, 18, 15, 12, 16, 13)(19, 26, 23,
+20, 27, 24, 21, 25, 22)(28, 31, 34, 30, 33, 36, 29, 32, 35)(37, 40, 43, 39, 42, 45, 38, 41, 44)(46, 49, 52, 48, 51, 54, 47, 50, 53)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18,
17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)(49, 50, 51)(52, 53, 54)" ], [
[ 1, 1 ],
[ 4, 4, 4 ],
@@ -4447,11 +4447,11 @@ perm"(1, 26, 2, 25)(3, 28, 4, 27)(5, 30, 6, 29)(7, 32, 8, 31)(9, 34, 10, 33)(11,
[ 2, 2, 2, 3 ],
[ -2, 1, -2, 1 ],
[ 3, 3, 3, 4 ]
-], [ (1, 1), (2, 27), (3, 2), (9, 6), (27, 18) ], [ (1, 1), (2, 27), (3, 1), (6, 9), (9, 1), (18, 3), (27, 1), (54, 1) ], false, false, true, false, 486), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5,
-32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 27, 18, 9,
-24, 15, 6, 21, 12, 3, 26, 17, 8, 23, 14, 5, 20, 11, 2, 25, 16, 7, 22, 13, 4, 19, 10)(28, 54, 45, 36, 51, 42, 33, 48, 39, 30, 53, 44, 35, 50, 41, 32, 47, 38, 29, 52, 43, 34, 49, 40, 31, 46, 37)",
+], [ (1, 1), (2, 27), (3, 2), (9, 6), (27, 18) ], [ (1, 1), (2, 27), (3, 1), (6, 9), (9, 1), (18, 3), (27, 1), (54, 1) ], false, false, true, false, 486), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5,
+32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 27, 18, 9,
+24, 15, 6, 21, 12, 3, 26, 17, 8, 23, 14, 5, 20, 11, 2, 25, 16, 7, 22, 13, 4, 19, 10)(28, 54, 45, 36, 51, 42, 33, 48, 39, 30, 53, 44, 35, 50, 41, 32, 47, 38, 29, 52, 43, 34, 49, 40, 31, 46, 37)",
perm"(1, 9, 6, 3, 8, 5, 2, 7, 4)(10, 18, 15, 12, 17, 14, 11, 16, 13)(19, 27, 24, 21, 26, 23, 20, 25, 22)(28, 36, 33, 30, 35, 32, 29, 34, 31)(37, 45, 42, 39, 44, 41, 38, 43, 40)(46, 54, 51, 48, 53, 50,
-47, 52, 49)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 33, 32)(34, 36, 35)(37, 39, 38)(40, 42, 41)(43, 45, 44)(46, 48,
+47, 52, 49)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 33, 32)(34, 36, 35)(37, 39, 38)(40, 42, 41)(43, 45, 44)(46, 48,
47)(49, 51, 50)(52, 54, 53)" ], [
[ 1, 1 ],
[ 4, 4, 4 ],
@@ -4462,11 +4462,11 @@ perm"(1, 9, 6, 3, 8, 5, 2, 7, 4)(10, 18, 15, 12, 17, 14, 11, 16, 13)(19, 27, 24,
[ 2, 2, 2, -3 ],
[ -2, 1, 2, 1 ],
[ 3, 3, 3, -4 ]
-], [ (1, 1), (2, 1), (3, 2), (6, 2), (9, 6), (18, 6), (27, 18), (54, 18) ], [ (1, 1), (2, 1), (3, 1), (6, 1), (9, 1), (18, 1), (27, 1), (54, 1) ], true, true, true, true, 18), ([ perm"(1, 28)(2,
-29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)",
-perm"(1, 19, 10)(2, 20, 11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9, 27, 18)(28, 46, 37)(29, 47, 38)(30, 48, 39)(31, 49, 40)(32, 50, 41)(33, 51, 42)(34, 52, 43)(35, 53,
-44)(36, 54, 45)", perm"(1, 8, 5, 2, 9, 6, 3, 7, 4)(10, 17, 14, 11, 18, 15, 12, 16, 13)(19, 26, 23, 20, 27, 24, 21, 25, 22)(28, 31, 34, 30, 33, 36, 29, 32, 35)(37, 40, 43, 39, 42, 45, 38, 41, 44)(46,
-49, 52, 48, 51, 54, 47, 50, 53)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41,
+], [ (1, 1), (2, 1), (3, 2), (6, 2), (9, 6), (18, 6), (27, 18), (54, 18) ], [ (1, 1), (2, 1), (3, 1), (6, 1), (9, 1), (18, 1), (27, 1), (54, 1) ], true, true, true, true, 18), ([ perm"(1, 28)(2,
+29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)",
+perm"(1, 19, 10)(2, 20, 11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9, 27, 18)(28, 46, 37)(29, 47, 38)(30, 48, 39)(31, 49, 40)(32, 50, 41)(33, 51, 42)(34, 52, 43)(35, 53,
+44)(36, 54, 45)", perm"(1, 8, 5, 2, 9, 6, 3, 7, 4)(10, 17, 14, 11, 18, 15, 12, 16, 13)(19, 26, 23, 20, 27, 24, 21, 25, 22)(28, 31, 34, 30, 33, 36, 29, 32, 35)(37, 40, 43, 39, 42, 45, 38, 41, 44)(46,
+49, 52, 48, 51, 54, 47, 50, 53)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41,
42)(43, 44, 45)(46, 47, 48)(49, 50, 51)(52, 53, 54)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -4481,10 +4481,10 @@ perm"(1, 19, 10)(2, 20, 11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 1
[ 1, -3, 1, -3 ],
[ 3, 3, 3, 4 ]
], [ (1, 1), (2, 9), (3, 8), (6, 18), (9, 18) ], [ (1, 1), (2, 9), (3, 4), (6, 12), (9, 4), (18, 4), (27, 1), (54, 1) ], false, false, true, false, 108), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6,
-33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 25, 16, 7, 22, 13,
-4, 19, 10)(2, 26, 17, 8, 23, 14, 5, 20, 11)(3, 27, 18, 9, 24, 15, 6, 21, 12)(28, 52, 43, 34, 49, 40, 31, 46, 37)(29, 53, 44, 35, 50, 41, 32, 47, 38)(30, 54, 45, 36, 51, 42, 33, 48, 39)", perm"(1, 7,
-4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 34, 31)(29, 35, 32)(30, 36, 33)(37, 43, 40)(38, 44, 41)(39, 45, 42)(46, 52, 49)(47, 53, 50)(48, 54,
-51)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)(49,
+33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 25, 16, 7, 22, 13,
+4, 19, 10)(2, 26, 17, 8, 23, 14, 5, 20, 11)(3, 27, 18, 9, 24, 15, 6, 21, 12)(28, 52, 43, 34, 49, 40, 31, 46, 37)(29, 53, 44, 35, 50, 41, 32, 47, 38)(30, 54, 45, 36, 51, 42, 33, 48, 39)", perm"(1, 7,
+4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 34, 31)(29, 35, 32)(30, 36, 33)(37, 43, 40)(38, 44, 41)(39, 45, 42)(46, 52, 49)(47, 53, 50)(48, 54,
+51)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)(49,
50, 51)(52, 53, 54)" ], [
[ 1, 1 ],
[ 3, 3, 3 ],
@@ -4499,10 +4499,10 @@ perm"(1, 19, 10)(2, 20, 11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 1
[ -2, -4, 2, 4 ],
[ 1, -4, 1, -4 ]
], [ (1, 1), (2, 3), (3, 8), (6, 6), (9, 18), (18, 18) ], [ (1, 1), (2, 3), (3, 4), (6, 4), (9, 4), (18, 4), (27, 1), (54, 1) ], false, false, true, false, 36), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5,
-32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 19, 10)(2,
-20, 11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9, 27, 18)(28, 46, 37)(29, 47, 38)(30, 48, 39)(31, 49, 40)(32, 50, 41)(33, 51, 42)(34, 52, 43)(35, 53, 44)(36, 54, 45)",
-perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 18, 14)(11, 16, 15)(12, 17, 13)(19, 26, 24)(20, 27, 22)(21, 25, 23)(28, 31, 34)(29, 32, 35)(30, 33, 36)(37, 41, 45)(38, 42, 43)(39, 40, 44)(46, 51, 53)(47, 49,
-54)(48, 50, 52)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46,
+32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 19, 10)(2,
+20, 11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9, 27, 18)(28, 46, 37)(29, 47, 38)(30, 48, 39)(31, 49, 40)(32, 50, 41)(33, 51, 42)(34, 52, 43)(35, 53, 44)(36, 54, 45)",
+perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 18, 14)(11, 16, 15)(12, 17, 13)(19, 26, 24)(20, 27, 22)(21, 25, 23)(28, 31, 34)(29, 32, 35)(30, 33, 36)(37, 41, 45)(38, 42, 43)(39, 40, 44)(46, 51, 53)(47, 49,
+54)(48, 50, 52)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46,
47, 48)(49, 50, 51)(52, 53, 54)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -4522,10 +4522,10 @@ perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 18, 14)(11, 16, 15)(12, 17, 13)(19, 26, 24)
[ -3, -4, 3, 4 ],
[ 2, -3, -2, 3, -4 ]
], [ (1, 1), (2, 9), (3, 26), (6, 18) ], [ (1, 1), (2, 9), (3, 13), (6, 21), (9, 4), (18, 4), (27, 1), (54, 1) ], false, false, true, false, 108), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7,
-34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 19, 10)(2, 20, 11)(3, 21,
+34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 19, 10)(2, 20, 11)(3, 21,
12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9, 27, 18)(28, 46, 37)(29, 47, 38)(30, 48, 39)(31, 49, 40)(32, 50, 41)(33, 51, 42)(34, 52, 43)(35, 53, 44)(36, 54, 45)", perm"(1, 8, 5, 2, 9,
-6, 3, 7, 4)(10, 16, 15, 11, 17, 13, 12, 18, 14)(19, 27, 22, 20, 25, 23, 21, 26, 24)(28, 31, 34, 30, 33, 36, 29, 32, 35)(37, 41, 45, 39, 40, 44, 38, 42, 43)(46, 51, 53, 48, 50, 52, 47, 49, 54)",
-perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)(49, 50,
+6, 3, 7, 4)(10, 16, 15, 11, 17, 13, 12, 18, 14)(19, 27, 22, 20, 25, 23, 21, 26, 24)(28, 31, 34, 30, 33, 36, 29, 32, 35)(37, 41, 45, 39, 40, 44, 38, 42, 43)(46, 51, 53, 48, 50, 52, 47, 49, 54)",
+perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)(49, 50,
51)(52, 53, 54)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -4541,11 +4541,11 @@ perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)
[ 3, 3, 3, 4 ],
[ -2, -4, 2, 4 ],
[ 2, -3, -2, 3, -4 ]
-], [ (1, 1), (2, 9), (3, 8), (6, 18), (9, 18) ], [ (1, 1), (2, 9), (3, 4), (6, 12), (9, 4), (18, 4), (27, 1), (54, 1) ], false, false, true, false, 54), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6,
-33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 20, 11, 2, 21, 12,
-3, 19, 10)(4, 23, 14, 5, 24, 15, 6, 22, 13)(7, 26, 17, 8, 27, 18, 9, 25, 16)(28, 37, 46, 30, 39, 48, 29, 38, 47)(31, 40, 49, 33, 42, 51, 32, 41, 50)(34, 43, 52, 36, 45, 54, 35, 44, 53)", perm"(1, 7,
-4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 31, 34)(29, 32, 35)(30, 33, 36)(37, 40, 43)(38, 41, 44)(39, 42, 45)(46, 49, 52)(47, 50, 53)(48, 51,
-54)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)(49,
+], [ (1, 1), (2, 9), (3, 8), (6, 18), (9, 18) ], [ (1, 1), (2, 9), (3, 4), (6, 12), (9, 4), (18, 4), (27, 1), (54, 1) ], false, false, true, false, 54), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6,
+33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 20, 11, 2, 21, 12,
+3, 19, 10)(4, 23, 14, 5, 24, 15, 6, 22, 13)(7, 26, 17, 8, 27, 18, 9, 25, 16)(28, 37, 46, 30, 39, 48, 29, 38, 47)(31, 40, 49, 33, 42, 51, 32, 41, 50)(34, 43, 52, 36, 45, 54, 35, 44, 53)", perm"(1, 7,
+4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 31, 34)(29, 32, 35)(30, 33, 36)(37, 40, 43)(38, 41, 44)(39, 42, 45)(46, 49, 52)(47, 50, 53)(48, 51,
+54)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)(49,
50, 51)(52, 53, 54)" ], [
[ 1, 1 ],
[ 3, 3, 3 ],
@@ -4559,11 +4559,11 @@ perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)
[ -2, 1, -2, 1 ],
[ -2, -3, 2, 3 ],
[ 1, -3, 1, -3 ]
-], [ (1, 1), (2, 27), (3, 8), (9, 18) ], [ (1, 1), (2, 27), (3, 4), (6, 36), (9, 4), (18, 12), (27, 1), (54, 1) ], false, false, true, false, 2916), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6,
-33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 19, 10)(2, 20,
-11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9, 27, 18)(28, 37, 46)(29, 38, 47)(30, 39, 48)(31, 40, 49)(32, 41, 50)(33, 42, 51)(34, 43, 52)(35, 44, 53)(36, 45, 54)", perm"(1,
-7, 4)(2, 8, 5)(3, 9, 6)(10, 18, 14)(11, 16, 15)(12, 17, 13)(19, 26, 24)(20, 27, 22)(21, 25, 23)(28, 31, 34)(29, 32, 35)(30, 33, 36)(37, 41, 45)(38, 42, 43)(39, 40, 44)(46, 51, 53)(47, 49, 54)(48, 50,
-52)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 33, 32)(34, 36, 35)(37, 39, 38)(40, 42, 41)(43, 45, 44)(46, 48, 47)(49,
+], [ (1, 1), (2, 27), (3, 8), (9, 18) ], [ (1, 1), (2, 27), (3, 4), (6, 36), (9, 4), (18, 12), (27, 1), (54, 1) ], false, false, true, false, 2916), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6,
+33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 19, 10)(2, 20,
+11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9, 27, 18)(28, 37, 46)(29, 38, 47)(30, 39, 48)(31, 40, 49)(32, 41, 50)(33, 42, 51)(34, 43, 52)(35, 44, 53)(36, 45, 54)", perm"(1,
+7, 4)(2, 8, 5)(3, 9, 6)(10, 18, 14)(11, 16, 15)(12, 17, 13)(19, 26, 24)(20, 27, 22)(21, 25, 23)(28, 31, 34)(29, 32, 35)(30, 33, 36)(37, 41, 45)(38, 42, 43)(39, 40, 44)(46, 51, 53)(47, 49, 54)(48, 50,
+52)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 33, 32)(34, 36, 35)(37, 39, 38)(40, 42, 41)(43, 45, 44)(46, 48, 47)(49,
51, 50)(52, 54, 53)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -4582,11 +4582,11 @@ perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)
[ 1, -4, 1, 4 ],
[ -3, -4, 3, 4 ],
[ 2, -3, -2, 3, -4 ]
-], [ (1, 1), (2, 9), (3, 26), (6, 18) ], [ (1, 1), (2, 9), (3, 13), (6, 21), (9, 4), (18, 12), (27, 1), (54, 1) ], false, false, true, false, 432), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6,
-33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 21, 12, 3, 20, 11,
-2, 19, 10)(4, 24, 15, 6, 23, 14, 5, 22, 13)(7, 27, 18, 9, 26, 17, 8, 25, 16)(28, 48, 39, 30, 47, 38, 29, 46, 37)(31, 51, 42, 33, 50, 41, 32, 49, 40)(34, 54, 45, 36, 53, 44, 35, 52, 43)", perm"(1, 7,
-4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 34, 31)(29, 35, 32)(30, 36, 33)(37, 43, 40)(38, 44, 41)(39, 45, 42)(46, 52, 49)(47, 53, 50)(48, 54,
-51)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 33, 32)(34, 36, 35)(37, 39, 38)(40, 42, 41)(43, 45, 44)(46, 48, 47)(49,
+], [ (1, 1), (2, 9), (3, 26), (6, 18) ], [ (1, 1), (2, 9), (3, 13), (6, 21), (9, 4), (18, 12), (27, 1), (54, 1) ], false, false, true, false, 432), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6,
+33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 21, 12, 3, 20, 11,
+2, 19, 10)(4, 24, 15, 6, 23, 14, 5, 22, 13)(7, 27, 18, 9, 26, 17, 8, 25, 16)(28, 48, 39, 30, 47, 38, 29, 46, 37)(31, 51, 42, 33, 50, 41, 32, 49, 40)(34, 54, 45, 36, 53, 44, 35, 52, 43)", perm"(1, 7,
+4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 34, 31)(29, 35, 32)(30, 36, 33)(37, 43, 40)(38, 44, 41)(39, 45, 42)(46, 52, 49)(47, 53, 50)(48, 54,
+51)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 33, 32)(34, 36, 35)(37, 39, 38)(40, 42, 41)(43, 45, 44)(46, 48, 47)(49,
51, 50)(52, 54, 53)" ], [
[ 1, 1 ],
[ 3, 3, 3 ],
@@ -4600,11 +4600,11 @@ perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)
[ -2, 1, 2, 1 ],
[ -2, -3, 2, 3 ],
[ 1, -3, 1, 3 ]
-], [ (1, 1), (2, 1), (3, 8), (6, 8), (9, 18), (18, 18) ], [ (1, 1), (2, 1), (3, 4), (6, 4), (9, 4), (18, 4), (27, 1), (54, 1) ], true, false, true, true, 108), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5,
-32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 19, 10)(2,
-20, 11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9, 27, 18)(28, 46, 37)(29, 47, 38)(30, 48, 39)(31, 49, 40)(32, 50, 41)(33, 51, 42)(34, 52, 43)(35, 53, 44)(36, 54, 45)",
-perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 18, 14)(11, 16, 15)(12, 17, 13)(19, 26, 24)(20, 27, 22)(21, 25, 23)(28, 34, 31)(29, 35, 32)(30, 36, 33)(37, 45, 41)(38, 43, 42)(39, 44, 40)(46, 53, 51)(47, 54,
-49)(48, 52, 50)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 33, 32)(34, 36, 35)(37, 39, 38)(40, 42, 41)(43, 45, 44)(46,
+], [ (1, 1), (2, 1), (3, 8), (6, 8), (9, 18), (18, 18) ], [ (1, 1), (2, 1), (3, 4), (6, 4), (9, 4), (18, 4), (27, 1), (54, 1) ], true, false, true, true, 108), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5,
+32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 19, 10)(2,
+20, 11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9, 27, 18)(28, 46, 37)(29, 47, 38)(30, 48, 39)(31, 49, 40)(32, 50, 41)(33, 51, 42)(34, 52, 43)(35, 53, 44)(36, 54, 45)",
+perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 18, 14)(11, 16, 15)(12, 17, 13)(19, 26, 24)(20, 27, 22)(21, 25, 23)(28, 34, 31)(29, 35, 32)(30, 36, 33)(37, 45, 41)(38, 43, 42)(39, 44, 40)(46, 53, 51)(47, 54,
+49)(48, 52, 50)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 33, 32)(34, 36, 35)(37, 39, 38)(40, 42, 41)(43, 45, 44)(46,
48, 47)(49, 51, 50)(52, 54, 53)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -4623,11 +4623,11 @@ perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 18, 14)(11, 16, 15)(12, 17, 13)(19, 26, 24)
[ 1, -4, 1, 4 ],
[ -3, -4, 3, 4 ],
[ 2, -3, -2, 3, -4 ]
-], [ (1, 1), (2, 1), (3, 26), (6, 26) ], [ (1, 1), (2, 1), (3, 13), (6, 13), (9, 4), (18, 4), (27, 1), (54, 1) ], false, false, true, true, 432), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7,
-34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 21, 12, 3, 20, 11, 2, 19,
+], [ (1, 1), (2, 1), (3, 26), (6, 26) ], [ (1, 1), (2, 1), (3, 13), (6, 13), (9, 4), (18, 4), (27, 1), (54, 1) ], false, false, true, true, 432), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7,
+34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 21, 12, 3, 20, 11, 2, 19,
10)(4, 24, 15, 6, 23, 14, 5, 22, 13)(7, 27, 18, 9, 26, 17, 8, 25, 16)(28, 48, 39, 30, 47, 38, 29, 46, 37)(31, 51, 42, 33, 50, 41, 32, 49, 40)(34, 54, 45, 36, 53, 44, 35, 52, 43)", perm"(1, 7, 4)(2, 8,
-5)(3, 9, 6)(10, 18, 14)(11, 16, 15)(12, 17, 13)(19, 26, 24)(20, 27, 22)(21, 25, 23)(28, 34, 31)(29, 35, 32)(30, 36, 33)(37, 45, 41)(38, 43, 42)(39, 44, 40)(46, 53, 51)(47, 54, 49)(48, 52, 50)",
-perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 33, 32)(34, 36, 35)(37, 39, 38)(40, 42, 41)(43, 45, 44)(46, 48, 47)(49, 51,
+5)(3, 9, 6)(10, 18, 14)(11, 16, 15)(12, 17, 13)(19, 26, 24)(20, 27, 22)(21, 25, 23)(28, 34, 31)(29, 35, 32)(30, 36, 33)(37, 45, 41)(38, 43, 42)(39, 44, 40)(46, 53, 51)(47, 54, 49)(48, 52, 50)",
+perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 33, 32)(34, 36, 35)(37, 39, 38)(40, 42, 41)(43, 45, 44)(46, 48, 47)(49, 51,
50)(52, 54, 53)" ], [
[ 1, 1 ],
[ 3, 3, 3 ],
@@ -4643,11 +4643,11 @@ perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)
[ 1, -3, 1, 3 ],
[ -3, -4, 3, 4 ],
[ 3, -2, -2, -3, -2 ]
-], [ (1, 1), (2, 1), (3, 8), (6, 8), (9, 18), (18, 18) ], [ (1, 1), (2, 1), (3, 4), (6, 4), (9, 4), (18, 4), (27, 1), (54, 1) ], false, false, true, true, 54), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5,
-32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 19, 10)(2,
-20, 11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9, 27, 18)(28, 46, 37)(29, 47, 38)(30, 48, 39)(31, 49, 40)(32, 50, 41)(33, 51, 42)(34, 52, 43)(35, 53, 44)(36, 54, 45)",
-perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 34, 31)(29, 35, 32)(30, 36, 33)(37, 43, 40)(38, 44, 41)(39, 45, 42)(46, 52, 49)(47, 53,
-50)(48, 54, 51)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46,
+], [ (1, 1), (2, 1), (3, 8), (6, 8), (9, 18), (18, 18) ], [ (1, 1), (2, 1), (3, 4), (6, 4), (9, 4), (18, 4), (27, 1), (54, 1) ], false, false, true, true, 54), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5,
+32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 19, 10)(2,
+20, 11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9, 27, 18)(28, 46, 37)(29, 47, 38)(30, 48, 39)(31, 49, 40)(32, 50, 41)(33, 51, 42)(34, 52, 43)(35, 53, 44)(36, 54, 45)",
+perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 34, 31)(29, 35, 32)(30, 36, 33)(37, 43, 40)(38, 44, 41)(39, 45, 42)(46, 52, 49)(47, 53,
+50)(48, 54, 51)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46,
47, 48)(49, 50, 51)(52, 53, 54)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -4666,11 +4666,11 @@ perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)
[ -2, -4, 2, 4 ],
[ 1, -4, 1, -4 ],
[ -3, -4, 3, 4 ]
-], [ (1, 1), (2, 3), (3, 26), (6, 24) ], [ (1, 1), (2, 3), (3, 13), (6, 13), (9, 13), (18, 7), (27, 1), (54, 1) ], false, false, true, false, 288), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6,
-33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 19, 10)(2, 20,
-11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9, 27, 18)(28, 46, 37)(29, 47, 38)(30, 48, 39)(31, 49, 40)(32, 50, 41)(33, 51, 42)(34, 52, 43)(35, 53, 44)(36, 54, 45)", perm"(1,
-7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 31, 34)(29, 32, 35)(30, 33, 36)(37, 40, 43)(38, 41, 44)(39, 42, 45)(46, 49, 52)(47, 50, 53)(48, 51,
-54)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)(49,
+], [ (1, 1), (2, 3), (3, 26), (6, 24) ], [ (1, 1), (2, 3), (3, 13), (6, 13), (9, 13), (18, 7), (27, 1), (54, 1) ], false, false, true, false, 288), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6,
+33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 19, 10)(2, 20,
+11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9, 27, 18)(28, 46, 37)(29, 47, 38)(30, 48, 39)(31, 49, 40)(32, 50, 41)(33, 51, 42)(34, 52, 43)(35, 53, 44)(36, 54, 45)", perm"(1,
+7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 31, 34)(29, 32, 35)(30, 33, 36)(37, 40, 43)(38, 41, 44)(39, 42, 45)(46, 49, 52)(47, 50, 53)(48, 51,
+54)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)(49,
50, 51)(52, 53, 54)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -4689,11 +4689,11 @@ perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)
[ -2, -4, 2, 4 ],
[ 1, -4, 1, -4 ],
[ -3, -4, 3, 4 ]
-], [ (1, 1), (2, 9), (3, 26), (6, 18) ], [ (1, 1), (2, 9), (3, 13), (6, 21), (9, 13), (18, 13), (27, 1), (54, 1) ], false, false, true, false, 864), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6,
-33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 19, 10)(2, 20,
-11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9, 27, 18)(28, 37, 46)(29, 38, 47)(30, 39, 48)(31, 40, 49)(32, 41, 50)(33, 42, 51)(34, 43, 52)(35, 44, 53)(36, 45, 54)", perm"(1,
-7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 31, 34)(29, 32, 35)(30, 33, 36)(37, 40, 43)(38, 41, 44)(39, 42, 45)(46, 49, 52)(47, 50, 53)(48, 51,
-54)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)(49,
+], [ (1, 1), (2, 9), (3, 26), (6, 18) ], [ (1, 1), (2, 9), (3, 13), (6, 21), (9, 13), (18, 13), (27, 1), (54, 1) ], false, false, true, false, 864), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6,
+33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 19, 10)(2, 20,
+11)(3, 21, 12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9, 27, 18)(28, 37, 46)(29, 38, 47)(30, 39, 48)(31, 40, 49)(32, 41, 50)(33, 42, 51)(34, 43, 52)(35, 44, 53)(36, 45, 54)", perm"(1,
+7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 31, 34)(29, 32, 35)(30, 33, 36)(37, 40, 43)(38, 41, 44)(39, 42, 45)(46, 49, 52)(47, 50, 53)(48, 51,
+54)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 29, 30)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)(49,
50, 51)(52, 53, 54)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -4712,11 +4712,11 @@ perm"(1, 7, 4)(2, 8, 5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)
[ -2, -4, 2, 4 ],
[ 1, -4, 1, -4 ],
[ -3, -4, 3, 4 ]
-], [ (1, 1), (2, 27), (3, 26) ], [ (1, 1), (2, 27), (3, 13), (6, 117), (9, 13), (18, 39), (27, 1), (54, 1) ], false, false, true, false, 303264), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7,
-34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 19, 10)(2, 20, 11)(3, 21,
+], [ (1, 1), (2, 27), (3, 26) ], [ (1, 1), (2, 27), (3, 13), (6, 117), (9, 13), (18, 39), (27, 1), (54, 1) ], false, false, true, false, 303264), ([ perm"(1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7,
+34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)", perm"(1, 19, 10)(2, 20, 11)(3, 21,
12)(4, 22, 13)(5, 23, 14)(6, 24, 15)(7, 25, 16)(8, 26, 17)(9, 27, 18)(28, 46, 37)(29, 47, 38)(30, 48, 39)(31, 49, 40)(32, 50, 41)(33, 51, 42)(34, 52, 43)(35, 53, 44)(36, 54, 45)", perm"(1, 7, 4)(2, 8,
-5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 34, 31)(29, 35, 32)(30, 36, 33)(37, 43, 40)(38, 44, 41)(39, 45, 42)(46, 52, 49)(47, 53, 50)(48, 54, 51)",
-perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 33, 32)(34, 36, 35)(37, 39, 38)(40, 42, 41)(43, 45, 44)(46, 48, 47)(49, 51,
+5)(3, 9, 6)(10, 16, 13)(11, 17, 14)(12, 18, 15)(19, 25, 22)(20, 26, 23)(21, 27, 24)(28, 34, 31)(29, 35, 32)(30, 36, 33)(37, 43, 40)(38, 44, 41)(39, 45, 42)(46, 52, 49)(47, 53, 50)(48, 54, 51)",
+perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 33, 32)(34, 36, 35)(37, 39, 38)(40, 42, 41)(43, 45, 44)(46, 48, 47)(49, 51,
50)(52, 54, 53)" ], [
[ 1, 1 ],
[ 2, 2, 2 ],
@@ -4735,8 +4735,8 @@ perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)
[ -2, -4, 2, 4 ],
[ 1, -4, 1, 4 ],
[ -3, -4, 3, 4 ]
-], [ (1, 1), (2, 1), (3, 26), (6, 26) ], [ (1, 1), (2, 1), (3, 13), (6, 13), (9, 13), (18, 13), (27, 1), (54, 1) ], true, false, true, true, 11232) ], [ ([ perm"(1, 45, 34, 23, 12)(2, 46, 35, 24,
-13)(3, 47, 36, 25, 14)(4, 48, 37, 26, 15)(5, 49, 38, 27, 16)(6, 50, 39, 28, 17)(7, 51, 40, 29, 18)(8, 52, 41, 30, 19)(9, 53, 42, 31, 20)(10, 54, 43, 32, 21)(11, 55, 44, 33, 22)", perm"(1, 11, 10, 9,
+], [ (1, 1), (2, 1), (3, 26), (6, 26) ], [ (1, 1), (2, 1), (3, 13), (6, 13), (9, 13), (18, 13), (27, 1), (54, 1) ], true, false, true, true, 11232) ], [ ([ perm"(1, 45, 34, 23, 12)(2, 46, 35, 24,
+13)(3, 47, 36, 25, 14)(4, 48, 37, 26, 15)(5, 49, 38, 27, 16)(6, 50, 39, 28, 17)(7, 51, 40, 29, 18)(8, 52, 41, 30, 19)(9, 53, 42, 31, 20)(10, 54, 43, 32, 21)(11, 55, 44, 33, 22)", perm"(1, 11, 10, 9,
8, 7, 6, 5, 4, 3, 2)(12, 19, 15, 22, 18, 14, 21, 17, 13, 20, 16)(23, 29, 24, 30, 25, 31, 26, 32, 27, 33, 28)(34, 36, 38, 40, 42, 44, 35, 37, 39, 41, 43)(45, 53, 50, 47, 55, 52, 49, 46, 54, 51, 48)" ],
[
[ 1, 1, 1, 1, 1 ],
@@ -4745,18 +4745,18 @@ perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)
], [
[ 2, 1, -2, -1, 2, 2 ],
[ 1, -2, -1, -1, 2, 1, -2 ]
-], [ (1, 1), (5, 44), (11, 10) ], [ (1, 1), (5, 11), (11, 1), (55, 1) ], false, false, true, false, 110), ([ perm"(1, 45, 34, 23, 12)(2, 46, 35, 24, 13)(3, 47, 36, 25, 14)(4, 48, 37, 26, 15)(5, 49,
-38, 27, 16)(6, 50, 39, 28, 17)(7, 51, 40, 29, 18)(8, 52, 41, 30, 19)(9, 53, 42, 31, 20)(10, 54, 43, 32, 21)(11, 55, 44, 33, 22)", perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17,
+], [ (1, 1), (5, 44), (11, 10) ], [ (1, 1), (5, 11), (11, 1), (55, 1) ], false, false, true, false, 110), ([ perm"(1, 45, 34, 23, 12)(2, 46, 35, 24, 13)(3, 47, 36, 25, 14)(4, 48, 37, 26, 15)(5, 49,
+38, 27, 16)(6, 50, 39, 28, 17)(7, 51, 40, 29, 18)(8, 52, 41, 30, 19)(9, 53, 42, 31, 20)(10, 54, 43, 32, 21)(11, 55, 44, 33, 22)", perm"(1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(12, 22, 21, 20, 19, 18, 17,
16, 15, 14, 13)(23, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24)(34, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35)(45, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46)" ], [
[ 1, 1, 1, 1, 1 ],
[ -1, -2, 1, 2 ],
[ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -1, -2, 1, 2 ]
-], [ (1, 1), (5, 4), (11, 10), (55, 40) ], [ (1, 1), (5, 1), (11, 1), (55, 1) ], true, true, true, true, 40) ], [ ([ perm"(1, 50, 22, 36, 8, 43, 15, 29)(2, 51, 23, 37, 9, 44, 16, 30)(3, 52, 24, 38,
-10, 45, 17, 31)(4, 53, 25, 39, 11, 46, 18, 32)(5, 54, 26, 40, 12, 47, 19, 33)(6, 55, 27, 41, 13, 48, 20, 34)(7, 56, 28, 42, 14, 49, 21, 35)", perm"(1, 22, 8, 15)(2, 23, 9, 16)(3, 24, 10, 17)(4, 25,
-11, 18)(5, 26, 12, 19)(6, 27, 13, 20)(7, 28, 14, 21)(29, 50, 36, 43)(30, 51, 37, 44)(31, 52, 38, 45)(32, 53, 39, 46)(33, 54, 40, 47)(34, 55, 41, 48)(35, 56, 42, 49)", perm"(1, 8)(2, 9)(3, 10)(4,
-11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)(29, 36)(30, 37)(31, 38)(32, 39)(33, 40)(34, 41)(35, 42)(43, 50)(44, 51)(45, 52)(46, 53)(47, 54)(48, 55)(49, 56)",
+], [ (1, 1), (5, 4), (11, 10), (55, 40) ], [ (1, 1), (5, 1), (11, 1), (55, 1) ], true, true, true, true, 40) ], [ ([ perm"(1, 50, 22, 36, 8, 43, 15, 29)(2, 51, 23, 37, 9, 44, 16, 30)(3, 52, 24, 38,
+10, 45, 17, 31)(4, 53, 25, 39, 11, 46, 18, 32)(5, 54, 26, 40, 12, 47, 19, 33)(6, 55, 27, 41, 13, 48, 20, 34)(7, 56, 28, 42, 14, 49, 21, 35)", perm"(1, 22, 8, 15)(2, 23, 9, 16)(3, 24, 10, 17)(4, 25,
+11, 18)(5, 26, 12, 19)(6, 27, 13, 20)(7, 28, 14, 21)(29, 50, 36, 43)(30, 51, 37, 44)(31, 52, 38, 45)(32, 53, 39, 46)(33, 54, 40, 47)(34, 55, 41, 48)(35, 56, 42, 49)", perm"(1, 8)(2, 9)(3, 10)(4,
+11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)(29, 36)(30, 37)(31, 38)(32, 39)(33, 40)(34, 41)(35, 42)(43, 50)(44, 51)(45, 52)(46, 53)(47, 54)(48, 55)(49, 56)",
perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)(29, 30, 31, 32, 33, 34, 35)(36, 37, 38, 39, 40, 41, 42)(43, 44, 45, 46, 47, 48, 49)(50, 51,
52, 53, 54, 55, 56)" ], [
[ 2, 2, 2, 2 ],
@@ -4770,10 +4770,10 @@ perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)
[ 2, 1, 1, 3 ],
[ -1, -4, 1, -4 ]
], [ (1, 1), (2, 1), (4, 2), (7, 6), (8, 28), (14, 6), (28, 12) ], [ (1, 1), (2, 1), (4, 1), (7, 1), (8, 7), (14, 1), (28, 1), (56, 1) ], false, false, true, false, 168), ([ perm"(1, 32, 4, 30, 2, 31,
-3, 29)(5, 36, 8, 34, 6, 35, 7, 33)(9, 40, 12, 38, 10, 39, 11, 37)(13, 44, 16, 42, 14, 43, 15, 41)(17, 48, 20, 46, 18, 47, 19, 45)(21, 52, 24, 50, 22, 51, 23, 49)(25, 56, 28, 54, 26, 55, 27, 53)",
+3, 29)(5, 36, 8, 34, 6, 35, 7, 33)(9, 40, 12, 38, 10, 39, 11, 37)(13, 44, 16, 42, 14, 43, 15, 41)(17, 48, 20, 46, 18, 47, 19, 45)(21, 52, 24, 50, 22, 51, 23, 49)(25, 56, 28, 54, 26, 55, 27, 53)",
perm"(1, 25, 21, 17, 13, 9, 5)(2, 26, 22, 18, 14, 10, 6)(3, 27, 23, 19, 15, 11, 7)(4, 28, 24, 20, 16, 12, 8)(29, 53, 49, 45, 41, 37, 33)(30, 54, 50, 46, 42, 38, 34)(31, 55, 51, 47, 43, 39, 35)(32, 56,
-52, 48, 44, 40, 36)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22, 23)(25, 28, 26, 27)(29, 32, 30, 31)(33, 36, 34, 35)(37, 40, 38, 39)(41, 44, 42, 43)(45,
-48, 46, 47)(49, 52, 50, 51)(53, 56, 54, 55)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39,
+52, 48, 44, 40, 36)", perm"(1, 4, 2, 3)(5, 8, 6, 7)(9, 12, 10, 11)(13, 16, 14, 15)(17, 20, 18, 19)(21, 24, 22, 23)(25, 28, 26, 27)(29, 32, 30, 31)(33, 36, 34, 35)(37, 40, 38, 39)(41, 44, 42, 43)(45,
+48, 46, 47)(49, 52, 50, 51)(53, 56, 54, 55)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39,
40)(41, 42)(43, 44)(45, 46)(47, 48)(49, 50)(51, 52)(53, 54)(55, 56)" ], [
[ 3, 3, 3, 3 ],
[ 4, 4 ],
@@ -4785,11 +4785,11 @@ perm"(1, 25, 21, 17, 13, 9, 5)(2, 26, 22, 18, 14, 10, 6)(3, 27, 23, 19, 15, 11,
[ -1, -1, 3 ],
[ 3, 1, 1, 4 ],
[ -1, -2, 1, 2 ]
-], [ (1, 1), (2, 1), (4, 2), (7, 6), (8, 4), (14, 6), (28, 12), (56, 24) ], [ (1, 1), (2, 1), (4, 1), (7, 1), (8, 1), (14, 1), (28, 1), (56, 1) ], true, true, true, true, 24), ([ perm"(1, 36, 8,
+], [ (1, 1), (2, 1), (4, 2), (7, 6), (8, 4), (14, 6), (28, 12), (56, 24) ], [ (1, 1), (2, 1), (4, 1), (7, 1), (8, 1), (14, 1), (28, 1), (56, 1) ], true, true, true, true, 24), ([ perm"(1, 36, 8,
29)(2, 37, 9, 30)(3, 38, 10, 31)(4, 39, 11, 32)(5, 40, 12, 33)(6, 41, 13, 34)(7, 42, 14, 35)(15, 50, 22, 43)(16, 51, 23, 44)(17, 52, 24, 45)(18, 53, 25, 46)(19, 54, 26, 47)(20, 55, 27, 48)(21, 56, 28,
-49)", perm"(1, 22, 8, 15)(2, 23, 9, 16)(3, 24, 10, 17)(4, 25, 11, 18)(5, 26, 12, 19)(6, 27, 13, 20)(7, 28, 14, 21)(29, 43, 36, 50)(30, 44, 37, 51)(31, 45, 38, 52)(32, 46, 39, 53)(33, 47, 40, 54)(34,
-48, 41, 55)(35, 49, 42, 56)", perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)(29, 36)(30, 37)(31, 38)(32, 39)(33, 40)(34, 41)(35, 42)(43,
-50)(44, 51)(45, 52)(46, 53)(47, 54)(48, 55)(49, 56)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)(29, 30, 31, 32, 33, 34, 35)(36, 37,
+49)", perm"(1, 22, 8, 15)(2, 23, 9, 16)(3, 24, 10, 17)(4, 25, 11, 18)(5, 26, 12, 19)(6, 27, 13, 20)(7, 28, 14, 21)(29, 43, 36, 50)(30, 44, 37, 51)(31, 45, 38, 52)(32, 46, 39, 53)(33, 47, 40, 54)(34,
+48, 41, 55)(35, 49, 42, 56)", perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)(29, 36)(30, 37)(31, 38)(32, 39)(33, 40)(34, 41)(35, 42)(43,
+50)(44, 51)(45, 52)(46, 53)(47, 54)(48, 55)(49, 56)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)(29, 30, 31, 32, 33, 34, 35)(36, 37,
38, 39, 40, 41, 42)(43, 44, 45, 46, 47, 48, 49)(50, 51, 52, 53, 54, 55, 56)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -4806,11 +4806,11 @@ perm"(1, 25, 21, 17, 13, 9, 5)(2, 26, 22, 18, 14, 10, 6)(3, 27, 23, 19, 15, 11,
[ -1, -2, 1, -2 ],
[ -1, -4, 1, -4 ],
[ -2, -4, 2, 4 ]
-], [ (1, 1), (2, 1), (4, 30), (7, 6), (14, 6), (28, 12) ], [ (1, 1), (2, 1), (4, 15), (7, 1), (8, 7), (14, 1), (28, 3), (56, 1) ], false, false, true, false, 336), ([ perm"(1, 29)(2, 30)(3, 31)(4,
-32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)",
+], [ (1, 1), (2, 1), (4, 30), (7, 6), (14, 6), (28, 12) ], [ (1, 1), (2, 1), (4, 15), (7, 1), (8, 7), (14, 1), (28, 3), (56, 1) ], false, false, true, false, 336), ([ perm"(1, 29)(2, 30)(3, 31)(4,
+32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)",
perm"(1, 22, 8, 15)(2, 23, 9, 16)(3, 24, 10, 17)(4, 25, 11, 18)(5, 26, 12, 19)(6, 27, 13, 20)(7, 28, 14, 21)(29, 50, 36, 43)(30, 51, 37, 44)(31, 52, 38, 45)(32, 53, 39, 46)(33, 54, 40, 47)(34, 55, 41,
-48)(35, 56, 42, 49)", perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)(29, 36)(30, 37)(31, 38)(32, 39)(33, 40)(34, 41)(35, 42)(43, 50)(44,
-51)(45, 52)(46, 53)(47, 54)(48, 55)(49, 56)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)(29, 30, 31, 32, 33, 34, 35)(36, 37, 38, 39,
+48)(35, 56, 42, 49)", perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)(29, 36)(30, 37)(31, 38)(32, 39)(33, 40)(34, 41)(35, 42)(43, 50)(44,
+51)(45, 52)(46, 53)(47, 54)(48, 55)(49, 56)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)(29, 30, 31, 32, 33, 34, 35)(36, 37, 38, 39,
40, 41, 42)(43, 44, 45, 46, 47, 48, 49)(50, 51, 52, 53, 54, 55, 56)" ], [
[ 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -4825,11 +4825,11 @@ perm"(1, 22, 8, 15)(2, 23, 9, 16)(3, 24, 10, 17)(4, 25, 11, 18)(5, 26, 12, 19)(6
[ -2, 1, 2, 1 ],
[ -2, -4, 2, 4 ],
[ 1, -4, 1, -4 ]
-], [ (1, 1), (2, 15), (4, 16), (7, 6), (14, 6), (28, 12) ], [ (1, 1), (2, 15), (4, 15), (7, 1), (8, 7), (14, 3), (28, 3), (56, 1) ], false, false, true, false, 168), ([ perm"(1, 29)(2, 30)(3, 31)(4,
-32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)",
+], [ (1, 1), (2, 15), (4, 16), (7, 6), (14, 6), (28, 12) ], [ (1, 1), (2, 15), (4, 15), (7, 1), (8, 7), (14, 3), (28, 3), (56, 1) ], false, false, true, false, 168), ([ perm"(1, 29)(2, 30)(3, 31)(4,
+32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)",
perm"(1, 22, 8, 15)(2, 23, 9, 16)(3, 24, 10, 17)(4, 25, 11, 18)(5, 26, 12, 19)(6, 27, 13, 20)(7, 28, 14, 21)(29, 43, 36, 50)(30, 44, 37, 51)(31, 45, 38, 52)(32, 46, 39, 53)(33, 47, 40, 54)(34, 48, 41,
-55)(35, 49, 42, 56)", perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)(29, 36)(30, 37)(31, 38)(32, 39)(33, 40)(34, 41)(35, 42)(43, 50)(44,
-51)(45, 52)(46, 53)(47, 54)(48, 55)(49, 56)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)(29, 30, 31, 32, 33, 34, 35)(36, 37, 38, 39,
+55)(35, 49, 42, 56)", perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)(29, 36)(30, 37)(31, 38)(32, 39)(33, 40)(34, 41)(35, 42)(43, 50)(44,
+51)(45, 52)(46, 53)(47, 54)(48, 55)(49, 56)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)(29, 30, 31, 32, 33, 34, 35)(36, 37, 38, 39,
40, 41, 42)(43, 44, 45, 46, 47, 48, 49)(50, 51, 52, 53, 54, 55, 56)" ], [
[ 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -4844,11 +4844,11 @@ perm"(1, 22, 8, 15)(2, 23, 9, 16)(3, 24, 10, 17)(4, 25, 11, 18)(5, 26, 12, 19)(6
[ -2, 1, -2, 1 ],
[ -2, -4, 2, 4 ],
[ 1, -4, 1, -4 ]
-], [ (1, 1), (2, 29), (4, 2), (7, 6), (14, 6), (28, 12) ], [ (1, 1), (2, 29), (4, 15), (7, 1), (8, 7), (14, 5), (28, 3), (56, 1) ], false, false, true, false, 336), ([ perm"(1, 36, 8, 29)(2, 37, 9,
-30)(3, 38, 10, 31)(4, 39, 11, 32)(5, 40, 12, 33)(6, 41, 13, 34)(7, 42, 14, 35)(15, 50, 22, 43)(16, 51, 23, 44)(17, 52, 24, 45)(18, 53, 25, 46)(19, 54, 26, 47)(20, 55, 27, 48)(21, 56, 28, 49)",
+], [ (1, 1), (2, 29), (4, 2), (7, 6), (14, 6), (28, 12) ], [ (1, 1), (2, 29), (4, 15), (7, 1), (8, 7), (14, 5), (28, 3), (56, 1) ], false, false, true, false, 336), ([ perm"(1, 36, 8, 29)(2, 37, 9,
+30)(3, 38, 10, 31)(4, 39, 11, 32)(5, 40, 12, 33)(6, 41, 13, 34)(7, 42, 14, 35)(15, 50, 22, 43)(16, 51, 23, 44)(17, 52, 24, 45)(18, 53, 25, 46)(19, 54, 26, 47)(20, 55, 27, 48)(21, 56, 28, 49)",
perm"(1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)(29, 43)(30, 44)(31, 45)(32, 46)(33, 47)(34, 48)(35, 49)(36, 50)(37, 51)(38, 52)(39, 53)(40,
-54)(41, 55)(42, 56)", perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)(29, 36)(30, 37)(31, 38)(32, 39)(33, 40)(34, 41)(35, 42)(43, 50)(44,
-51)(45, 52)(46, 53)(47, 54)(48, 55)(49, 56)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)(29, 30, 31, 32, 33, 34, 35)(36, 37, 38, 39,
+54)(41, 55)(42, 56)", perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)(29, 36)(30, 37)(31, 38)(32, 39)(33, 40)(34, 41)(35, 42)(43, 50)(44,
+51)(45, 52)(46, 53)(47, 54)(48, 55)(49, 56)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)(29, 30, 31, 32, 33, 34, 35)(36, 37, 38, 39,
40, 41, 42)(43, 44, 45, 46, 47, 48, 49)(50, 51, 52, 53, 54, 55, 56)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -4863,11 +4863,11 @@ perm"(1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11,
[ -1, 2, 1, 2 ],
[ -1, -4, 1, -4 ],
[ 2, -4, 2, 4 ]
-], [ (1, 1), (2, 3), (4, 28), (7, 6), (14, 18) ], [ (1, 1), (2, 3), (4, 15), (7, 1), (8, 7), (14, 3), (28, 3), (56, 1) ], false, false, true, false, 336), ([ perm"(1, 29)(2, 30)(3, 31)(4, 32)(5,
-33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)", perm"(1,
-15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)(29, 50)(30, 51)(31, 52)(32, 53)(33, 54)(34, 55)(35, 56)(36, 43)(37, 44)(38, 45)(39, 46)(40, 47)(41,
-48)(42, 49)", perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)(29, 36)(30, 37)(31, 38)(32, 39)(33, 40)(34, 41)(35, 42)(43, 50)(44, 51)(45,
-52)(46, 53)(47, 54)(48, 55)(49, 56)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)(29, 30, 31, 32, 33, 34, 35)(36, 37, 38, 39, 40, 41,
+], [ (1, 1), (2, 3), (4, 28), (7, 6), (14, 18) ], [ (1, 1), (2, 3), (4, 15), (7, 1), (8, 7), (14, 3), (28, 3), (56, 1) ], false, false, true, false, 336), ([ perm"(1, 29)(2, 30)(3, 31)(4, 32)(5,
+33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)", perm"(1,
+15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)(29, 50)(30, 51)(31, 52)(32, 53)(33, 54)(34, 55)(35, 56)(36, 43)(37, 44)(38, 45)(39, 46)(40, 47)(41,
+48)(42, 49)", perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)(29, 36)(30, 37)(31, 38)(32, 39)(33, 40)(34, 41)(35, 42)(43, 50)(44, 51)(45,
+52)(46, 53)(47, 54)(48, 55)(49, 56)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)(29, 30, 31, 32, 33, 34, 35)(36, 37, 38, 39, 40, 41,
42)(43, 44, 45, 46, 47, 48, 49)(50, 51, 52, 53, 54, 55, 56)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -4887,10 +4887,10 @@ perm"(1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11,
[ 3, -4, 3, 4 ],
[ 1, 2, 1, 2, 3 ]
], [ (1, 1), (2, 17), (4, 14), (7, 6), (14, 18) ], [ (1, 1), (2, 17), (4, 15), (7, 1), (8, 7), (14, 5), (28, 3), (56, 1) ], false, false, true, false, 168), ([ perm"(1, 30, 2, 29)(3, 32, 4, 31)(5, 34,
-6, 33)(7, 36, 8, 35)(9, 38, 10, 37)(11, 40, 12, 39)(13, 42, 14, 41)(15, 44, 16, 43)(17, 46, 18, 45)(19, 48, 20, 47)(21, 50, 22, 49)(23, 52, 24, 51)(25, 54, 26, 53)(27, 56, 28, 55)", perm"(1, 15)(2,
+6, 33)(7, 36, 8, 35)(9, 38, 10, 37)(11, 40, 12, 39)(13, 42, 14, 41)(15, 44, 16, 43)(17, 46, 18, 45)(19, 48, 20, 47)(21, 50, 22, 49)(23, 52, 24, 51)(25, 54, 26, 53)(27, 56, 28, 55)", perm"(1, 15)(2,
16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)(29, 43)(30, 44)(31, 45)(32, 46)(33, 47)(34, 48)(35, 49)(36, 50)(37, 51)(38, 52)(39, 53)(40, 54)(41, 55)(42,
-56)", perm"(1, 13, 11, 9, 7, 5, 3)(2, 14, 12, 10, 8, 6, 4)(15, 27, 25, 23, 21, 19, 17)(16, 28, 26, 24, 22, 20, 18)(29, 41, 39, 37, 35, 33, 31)(30, 42, 40, 38, 36, 34, 32)(43, 55, 53, 51, 49, 47,
-45)(44, 56, 54, 52, 50, 48, 46)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41,
+56)", perm"(1, 13, 11, 9, 7, 5, 3)(2, 14, 12, 10, 8, 6, 4)(15, 27, 25, 23, 21, 19, 17)(16, 28, 26, 24, 22, 20, 18)(29, 41, 39, 37, 35, 33, 31)(30, 42, 40, 38, 36, 34, 32)(43, 55, 53, 51, 49, 47,
+45)(44, 56, 54, 52, 50, 48, 46)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41,
42)(43, 44)(45, 46)(47, 48)(49, 50)(51, 52)(53, 54)(55, 56)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -4905,11 +4905,11 @@ perm"(1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11,
[ -1, 2, 1, 2 ],
[ -1, -3, 1, 3 ],
[ 2, -3, 2, 3 ]
-], [ (1, 1), (2, 3), (4, 4), (7, 6), (14, 18), (28, 24) ], [ (1, 1), (2, 3), (4, 3), (7, 1), (8, 1), (14, 3), (28, 3), (56, 1) ], true, false, true, true, 48), ([ perm"(1, 29)(2, 30)(3, 31)(4, 32)(5,
-33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)", perm"(1,
-15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)(29, 44)(30, 43)(31, 46)(32, 45)(33, 48)(34, 47)(35, 50)(36, 49)(37, 52)(38, 51)(39, 54)(40, 53)(41,
-56)(42, 55)", perm"(1, 13, 11, 9, 7, 5, 3)(2, 14, 12, 10, 8, 6, 4)(15, 27, 25, 23, 21, 19, 17)(16, 28, 26, 24, 22, 20, 18)(29, 41, 39, 37, 35, 33, 31)(30, 42, 40, 38, 36, 34, 32)(43, 55, 53, 51, 49,
-47, 45)(44, 56, 54, 52, 50, 48, 46)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41,
+], [ (1, 1), (2, 3), (4, 4), (7, 6), (14, 18), (28, 24) ], [ (1, 1), (2, 3), (4, 3), (7, 1), (8, 1), (14, 3), (28, 3), (56, 1) ], true, false, true, true, 48), ([ perm"(1, 29)(2, 30)(3, 31)(4, 32)(5,
+33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)", perm"(1,
+15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)(29, 44)(30, 43)(31, 46)(32, 45)(33, 48)(34, 47)(35, 50)(36, 49)(37, 52)(38, 51)(39, 54)(40, 53)(41,
+56)(42, 55)", perm"(1, 13, 11, 9, 7, 5, 3)(2, 14, 12, 10, 8, 6, 4)(15, 27, 25, 23, 21, 19, 17)(16, 28, 26, 24, 22, 20, 18)(29, 41, 39, 37, 35, 33, 31)(30, 42, 40, 38, 36, 34, 32)(43, 55, 53, 51, 49,
+47, 45)(44, 56, 54, 52, 50, 48, 46)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41,
42)(43, 44)(45, 46)(47, 48)(49, 50)(51, 52)(53, 54)(55, 56)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -4929,10 +4929,10 @@ perm"(1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11,
[ -3, 4, 3, 4 ],
[ 1, 2, 1, 2, 4 ]
], [ (1, 1), (2, 5), (4, 2), (7, 6), (14, 30), (28, 12) ], [ (1, 1), (2, 5), (4, 3), (7, 1), (8, 1), (14, 5), (28, 3), (56, 1) ], false, false, true, true, 48), ([ perm"(1, 30, 2, 29)(3, 32, 4, 31)(5,
-34, 6, 33)(7, 36, 8, 35)(9, 38, 10, 37)(11, 40, 12, 39)(13, 42, 14, 41)(15, 44, 16, 43)(17, 46, 18, 45)(19, 48, 20, 47)(21, 50, 22, 49)(23, 52, 24, 51)(25, 54, 26, 53)(27, 56, 28, 55)", perm"(1, 16,
-2, 15)(3, 18, 4, 17)(5, 20, 6, 19)(7, 22, 8, 21)(9, 24, 10, 23)(11, 26, 12, 25)(13, 28, 14, 27)(29, 43, 30, 44)(31, 45, 32, 46)(33, 47, 34, 48)(35, 49, 36, 50)(37, 51, 38, 52)(39, 53, 40, 54)(41, 55,
-42, 56)", perm"(1, 13, 11, 9, 7, 5, 3)(2, 14, 12, 10, 8, 6, 4)(15, 27, 25, 23, 21, 19, 17)(16, 28, 26, 24, 22, 20, 18)(29, 41, 39, 37, 35, 33, 31)(30, 42, 40, 38, 36, 34, 32)(43, 55, 53, 51, 49, 47,
-45)(44, 56, 54, 52, 50, 48, 46)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41,
+34, 6, 33)(7, 36, 8, 35)(9, 38, 10, 37)(11, 40, 12, 39)(13, 42, 14, 41)(15, 44, 16, 43)(17, 46, 18, 45)(19, 48, 20, 47)(21, 50, 22, 49)(23, 52, 24, 51)(25, 54, 26, 53)(27, 56, 28, 55)", perm"(1, 16,
+2, 15)(3, 18, 4, 17)(5, 20, 6, 19)(7, 22, 8, 21)(9, 24, 10, 23)(11, 26, 12, 25)(13, 28, 14, 27)(29, 43, 30, 44)(31, 45, 32, 46)(33, 47, 34, 48)(35, 49, 36, 50)(37, 51, 38, 52)(39, 53, 40, 54)(41, 55,
+42, 56)", perm"(1, 13, 11, 9, 7, 5, 3)(2, 14, 12, 10, 8, 6, 4)(15, 27, 25, 23, 21, 19, 17)(16, 28, 26, 24, 22, 20, 18)(29, 41, 39, 37, 35, 33, 31)(30, 42, 40, 38, 36, 34, 32)(43, 55, 53, 51, 49, 47,
+45)(44, 56, 54, 52, 50, 48, 46)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41,
42)(43, 44)(45, 46)(47, 48)(49, 50)(51, 52)(53, 54)(55, 56)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2 ],
@@ -4949,11 +4949,11 @@ perm"(1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11,
[ -1, -2, 1, -2 ],
[ -1, -3, 1, 3 ],
[ -2, -3, 2, 3 ]
-], [ (1, 1), (2, 1), (4, 6), (7, 6), (14, 6), (28, 36) ], [ (1, 1), (2, 1), (4, 3), (7, 1), (8, 1), (14, 1), (28, 3), (56, 1) ], false, false, true, true, 144), ([ perm"(1, 49, 41, 33, 25, 17, 9)(2,
-50, 42, 34, 26, 18, 10)(3, 51, 43, 35, 27, 19, 11)(4, 52, 44, 36, 28, 20, 12)(5, 53, 45, 37, 29, 21, 13)(6, 54, 46, 38, 30, 22, 14)(7, 55, 47, 39, 31, 23, 15)(8, 56, 48, 40, 32, 24, 16)", perm"(1,
-5)(2, 6)(3, 7)(4, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 30)(26, 29)(27, 32)(28, 31)(33, 40)(34, 39)(35, 38)(36, 37)(41, 47)(42, 48)(43, 45)(44, 46)(49, 52)(50, 51)(53,
-56)(54, 55)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 22)(18, 21)(19, 24)(20, 23)(25, 32)(26, 31)(27, 30)(28, 29)(33, 39)(34, 40)(35, 37)(36, 38)(41, 44)(42, 43)(45, 48)(46,
-47)(49, 53)(50, 54)(51, 55)(52, 56)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 14)(10, 13)(11, 16)(12, 15)(17, 24)(18, 23)(19, 22)(20, 21)(25, 31)(26, 32)(27, 29)(28, 30)(33, 36)(34, 35)(37, 40)(38, 39)(41,
+], [ (1, 1), (2, 1), (4, 6), (7, 6), (14, 6), (28, 36) ], [ (1, 1), (2, 1), (4, 3), (7, 1), (8, 1), (14, 1), (28, 3), (56, 1) ], false, false, true, true, 144), ([ perm"(1, 49, 41, 33, 25, 17, 9)(2,
+50, 42, 34, 26, 18, 10)(3, 51, 43, 35, 27, 19, 11)(4, 52, 44, 36, 28, 20, 12)(5, 53, 45, 37, 29, 21, 13)(6, 54, 46, 38, 30, 22, 14)(7, 55, 47, 39, 31, 23, 15)(8, 56, 48, 40, 32, 24, 16)", perm"(1,
+5)(2, 6)(3, 7)(4, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 30)(26, 29)(27, 32)(28, 31)(33, 40)(34, 39)(35, 38)(36, 37)(41, 47)(42, 48)(43, 45)(44, 46)(49, 52)(50, 51)(53,
+56)(54, 55)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 22)(18, 21)(19, 24)(20, 23)(25, 32)(26, 31)(27, 30)(28, 29)(33, 39)(34, 40)(35, 37)(36, 38)(41, 44)(42, 43)(45, 48)(46,
+47)(49, 53)(50, 54)(51, 55)(52, 56)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 14)(10, 13)(11, 16)(12, 15)(17, 24)(18, 23)(19, 22)(20, 21)(25, 31)(26, 32)(27, 29)(28, 30)(33, 36)(34, 35)(37, 40)(38, 39)(41,
45)(42, 46)(43, 47)(44, 48)(49, 51)(50, 52)(53, 55)(54, 56)" ], [
[ 2, 2 ],
[ 3, 3 ],
@@ -4970,10 +4970,10 @@ perm"(1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11,
[ 2, 3, 2, 3 ],
[ 2, 4, 2, 4 ],
[ 1, 2, -1, 3, 4 ]
-], [ (1, 1), (2, 7), (7, 48) ], [ (1, 1), (2, 7), (4, 7), (7, 8), (8, 1), (56, 1) ], false, false, true, false, 168), ([ perm"(1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10,
+], [ (1, 1), (2, 7), (7, 48) ], [ (1, 1), (2, 7), (4, 7), (7, 8), (8, 1), (56, 1) ], false, false, true, false, 168), ([ perm"(1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10,
38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)", perm"(1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7,
-21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)(29, 43)(30, 44)(31, 45)(32, 46)(33, 47)(34, 48)(35, 49)(36, 50)(37, 51)(38, 52)(39, 53)(40, 54)(41, 55)(42, 56)", perm"(1, 8)(2, 9)(3, 10)(4,
-11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)(29, 36)(30, 37)(31, 38)(32, 39)(33, 40)(34, 41)(35, 42)(43, 50)(44, 51)(45, 52)(46, 53)(47, 54)(48, 55)(49, 56)",
+21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)(29, 43)(30, 44)(31, 45)(32, 46)(33, 47)(34, 48)(35, 49)(36, 50)(37, 51)(38, 52)(39, 53)(40, 54)(41, 55)(42, 56)", perm"(1, 8)(2, 9)(3, 10)(4,
+11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)(29, 36)(30, 37)(31, 38)(32, 39)(33, 40)(34, 41)(35, 42)(43, 50)(44, 51)(45, 52)(46, 53)(47, 54)(48, 55)(49, 56)",
perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)(29, 30, 31, 32, 33, 34, 35)(36, 37, 38, 39, 40, 41, 42)(43, 44, 45, 46, 47, 48, 49)(50, 51,
52, 53, 54, 55, 56)" ], [
[ 1, 1 ],
@@ -4993,11 +4993,11 @@ perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)
[ 1, -4, 1, -4 ],
[ 2, -4, 2, 4 ],
[ 3, -4, 3, 4 ]
-], [ (1, 1), (2, 31), (7, 6), (14, 18) ], [ (1, 1), (2, 31), (4, 43), (7, 1), (8, 7), (14, 7), (28, 7), (56, 1) ], false, false, true, false, 1008), ([ perm"(1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6,
-34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)", perm"(1, 15)(2,
+], [ (1, 1), (2, 31), (7, 6), (14, 18) ], [ (1, 1), (2, 31), (4, 43), (7, 1), (8, 7), (14, 7), (28, 7), (56, 1) ], false, false, true, false, 1008), ([ perm"(1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6,
+34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)", perm"(1, 15)(2,
16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)(29, 43)(30, 44)(31, 45)(32, 46)(33, 47)(34, 48)(35, 49)(36, 50)(37, 51)(38, 52)(39, 53)(40, 54)(41, 55)(42,
-56)", perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)(29, 36)(30, 37)(31, 38)(32, 39)(33, 40)(34, 41)(35, 42)(43, 50)(44, 51)(45, 52)(46,
-53)(47, 54)(48, 55)(49, 56)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)(29, 35, 34, 33, 32, 31, 30)(36, 42, 41, 40, 39, 38, 37)(43,
+56)", perm"(1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22)(16, 23)(17, 24)(18, 25)(19, 26)(20, 27)(21, 28)(29, 36)(30, 37)(31, 38)(32, 39)(33, 40)(34, 41)(35, 42)(43, 50)(44, 51)(45, 52)(46,
+53)(47, 54)(48, 55)(49, 56)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)(29, 35, 34, 33, 32, 31, 30)(36, 42, 41, 40, 39, 38, 37)(43,
49, 48, 47, 46, 45, 44)(50, 56, 55, 54, 53, 52, 51)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -5016,9 +5016,9 @@ perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)
[ 1, -4, 1, 4 ],
[ 2, -4, 2, 4 ],
[ 3, -4, 3, 4 ]
-], [ (1, 1), (2, 7), (7, 6), (14, 42) ], [ (1, 1), (2, 7), (4, 7), (7, 1), (8, 1), (14, 7), (28, 7), (56, 1) ], true, false, true, true, 1008) ], [ ([ perm"(1, 39, 20)(2, 40, 21)(3, 41, 22)(4, 42,
-23)(5, 43, 24)(6, 44, 25)(7, 45, 26)(8, 46, 27)(9, 47, 28)(10, 48, 29)(11, 49, 30)(12, 50, 31)(13, 51, 32)(14, 52, 33)(15, 53, 34)(16, 54, 35)(17, 55, 36)(18, 56, 37)(19, 57, 38)", perm"(1, 19, 18,
-17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(20, 32, 25, 37, 30, 23, 35, 28, 21, 33, 26, 38, 31, 24, 36, 29, 22, 34, 27)(39, 47, 55, 44, 52, 41, 49, 57, 46, 54, 43, 51, 40, 48, 56, 45, 53,
+], [ (1, 1), (2, 7), (7, 6), (14, 42) ], [ (1, 1), (2, 7), (4, 7), (7, 1), (8, 1), (14, 7), (28, 7), (56, 1) ], true, false, true, true, 1008) ], [ ([ perm"(1, 39, 20)(2, 40, 21)(3, 41, 22)(4, 42,
+23)(5, 43, 24)(6, 44, 25)(7, 45, 26)(8, 46, 27)(9, 47, 28)(10, 48, 29)(11, 49, 30)(12, 50, 31)(13, 51, 32)(14, 52, 33)(15, 53, 34)(16, 54, 35)(17, 55, 36)(18, 56, 37)(19, 57, 38)", perm"(1, 19, 18,
+17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(20, 32, 25, 37, 30, 23, 35, 28, 21, 33, 26, 38, 31, 24, 36, 29, 22, 34, 27)(39, 47, 55, 44, 52, 41, 49, 57, 46, 54, 43, 51, 40, 48, 56, 45, 53,
42, 50)" ], [
[ 1, 1, 1 ],
[ -2, -1, -2, -1, -2, -1 ],
@@ -5028,7 +5028,7 @@ perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)
[ -2, -1, -2, -1, -2, -1 ],
[ -2, 1, -2, 1, -2, 1 ],
[ 1, -2, -2, -1, 2, 2, 2 ]
-], [ (1, 1), (3, 38), (19, 18) ], [ (1, 1), (3, 19), (19, 1), (57, 1) ], false, false, true, false, 342), ([ perm"(1, 39, 20)(2, 40, 21)(3, 41, 22)(4, 42, 23)(5, 43, 24)(6, 44, 25)(7, 45, 26)(8, 46,
+], [ (1, 1), (3, 38), (19, 18) ], [ (1, 1), (3, 19), (19, 1), (57, 1) ], false, false, true, false, 342), ([ perm"(1, 39, 20)(2, 40, 21)(3, 41, 22)(4, 42, 23)(5, 43, 24)(6, 44, 25)(7, 45, 26)(8, 46,
27)(9, 47, 28)(10, 48, 29)(11, 49, 30)(12, 50, 31)(13, 51, 32)(14, 52, 33)(15, 53, 34)(16, 54, 35)(17, 55, 36)(18, 56, 37)(19, 57, 38)", perm"(1, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5,
4, 3, 2)(20, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21)(39, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40)" ], [
[ 1, 1, 1 ],
@@ -5036,31 +5036,31 @@ perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)
[ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -1, -2, 1, 2 ]
-], [ (1, 1), (3, 2), (19, 18), (57, 36) ], [ (1, 1), (3, 1), (19, 1), (57, 1) ], true, true, true, true, 36) ], [ ([ perm"(1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11,
-40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58)", perm"(1, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20,
+], [ (1, 1), (3, 2), (19, 18), (57, 36) ], [ (1, 1), (3, 1), (19, 1), (57, 1) ], true, true, true, true, 36) ], [ ([ perm"(1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11,
+40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58)", perm"(1, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20,
19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58)" ], [
[ 1, 1 ],
[ -2, 1, -2, 1 ],
[ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -2, 1, -2, 1 ]
-], [ (1, 1), (2, 29), (29, 28) ], [ (1, 1), (2, 29), (29, 1), (58, 1) ], false, false, true, false, 812), ([ perm"(1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12,
-41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58)", perm"(1, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18,
+], [ (1, 1), (2, 29), (29, 28) ], [ (1, 1), (2, 29), (29, 1), (58, 1) ], false, false, true, false, 812), ([ perm"(1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12,
+41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58)", perm"(1, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18,
17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(30, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31)" ], [
[ 1, 1 ],
[ -2, 1, 2, 1 ],
[ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -2, 1, 2, 1 ]
-], [ (1, 1), (2, 1), (29, 28), (58, 28) ], [ (1, 1), (2, 1), (29, 1), (58, 1) ], true, true, true, true, 28) ], [ ([ perm"(1, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42,
+], [ (1, 1), (2, 1), (29, 28), (58, 28) ], [ (1, 1), (2, 1), (29, 1), (58, 1) ], true, true, true, true, 28) ], [ ([ perm"(1, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42,
41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)" ], [
-[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
+[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1 ]
-], [], [ (1, 1), (59, 58) ], [ (1, 1), (59, 1) ], true, true, true, true, 58) ], [ ([ perm"(1, 34, 4, 31)(2, 35, 5, 32)(3, 36, 6, 33)(7, 40, 10, 37)(8, 41, 11, 38)(9, 42, 12, 39)(13, 46, 16, 43)(14,
+], [], [ (1, 1), (59, 58) ], [ (1, 1), (59, 1) ], true, true, true, true, 58) ], [ ([ perm"(1, 34, 4, 31)(2, 35, 5, 32)(3, 36, 6, 33)(7, 40, 10, 37)(8, 41, 11, 38)(9, 42, 12, 39)(13, 46, 16, 43)(14,
47, 17, 44)(15, 48, 18, 45)(19, 52, 22, 49)(20, 53, 23, 50)(21, 54, 24, 51)(25, 58, 28, 55)(26, 59, 29, 56)(27, 60, 30, 57)", perm"(1, 25, 19, 13, 7)(2, 26, 20, 14, 8)(3, 27, 21, 15, 9)(4, 28, 22, 16,
-10)(5, 29, 23, 17, 11)(6, 30, 24, 18, 12)(31, 55, 49, 43, 37)(32, 56, 50, 44, 38)(33, 57, 51, 45, 39)(34, 58, 52, 46, 40)(35, 59, 53, 47, 41)(36, 60, 54, 48, 42)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
-11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)(49, 52)(50, 53)(51, 54)(55, 58)(56, 59)(57,
-60)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)(49,
+10)(5, 29, 23, 17, 11)(6, 30, 24, 18, 12)(31, 55, 49, 43, 37)(32, 56, 50, 44, 38)(33, 57, 51, 45, 39)(34, 58, 52, 46, 40)(35, 59, 53, 47, 41)(36, 60, 54, 48, 42)", perm"(1, 4)(2, 5)(3, 6)(7, 10)(8,
+11)(9, 12)(13, 16)(14, 17)(15, 18)(19, 22)(20, 23)(21, 24)(25, 28)(26, 29)(27, 30)(31, 34)(32, 35)(33, 36)(37, 40)(38, 41)(39, 42)(43, 46)(44, 47)(45, 48)(49, 52)(50, 53)(51, 54)(55, 58)(56, 59)(57,
+60)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)(49,
50, 51)(52, 53, 54)(55, 56, 57)(58, 59, 60)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2, 2, 2 ],
@@ -5075,12 +5075,12 @@ perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)
[ -1, -2, 1, 2 ],
[ -1, -4, 1, -4 ],
[ -2, -4, 2, 4 ]
-], [ (1, 1), (2, 1), (3, 2), (4, 6), (5, 4), (6, 2), (10, 4), (15, 8), (20, 24), (30, 8) ], [ (1, 1), (2, 1), (3, 1), (4, 3), (5, 1), (6, 1), (10, 1), (12, 1), (15, 1), (20, 3), (30, 1), (60, 1) ],
-false, false, true, false, 48), ([ perm"(1, 36, 6, 31)(2, 37, 7, 32)(3, 38, 8, 33)(4, 39, 9, 34)(5, 40, 10, 35)(11, 46, 16, 41)(12, 47, 17, 42)(13, 48, 18, 43)(14, 49, 19, 44)(15, 50, 20, 45)(21, 56,
-26, 51)(22, 57, 27, 52)(23, 58, 28, 53)(24, 59, 29, 54)(25, 60, 30, 55)", perm"(1, 21, 11)(2, 22, 12)(3, 23, 13)(4, 24, 14)(5, 25, 15)(6, 26, 16)(7, 27, 17)(8, 28, 18)(9, 29, 19)(10, 30, 20)(31, 51,
-41)(32, 52, 42)(33, 53, 43)(34, 54, 44)(35, 55, 45)(36, 56, 46)(37, 57, 47)(38, 58, 48)(39, 59, 49)(40, 60, 50)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21,
-26)(22, 27)(23, 28)(24, 29)(25, 30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)(41, 46)(42, 47)(43, 48)(44, 49)(45, 50)(51, 56)(52, 57)(53, 58)(54, 59)(55, 60)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11,
-15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 25, 24, 23, 22)(26, 30, 29, 28, 27)(31, 32, 33, 34, 35)(36, 37, 38, 39, 40)(41, 42, 43, 44, 45)(46, 47, 48, 49, 50)(51, 52, 53, 54, 55)(56, 57, 58, 59, 60)" ],
+], [ (1, 1), (2, 1), (3, 2), (4, 6), (5, 4), (6, 2), (10, 4), (15, 8), (20, 24), (30, 8) ], [ (1, 1), (2, 1), (3, 1), (4, 3), (5, 1), (6, 1), (10, 1), (12, 1), (15, 1), (20, 3), (30, 1), (60, 1) ],
+false, false, true, false, 48), ([ perm"(1, 36, 6, 31)(2, 37, 7, 32)(3, 38, 8, 33)(4, 39, 9, 34)(5, 40, 10, 35)(11, 46, 16, 41)(12, 47, 17, 42)(13, 48, 18, 43)(14, 49, 19, 44)(15, 50, 20, 45)(21, 56,
+26, 51)(22, 57, 27, 52)(23, 58, 28, 53)(24, 59, 29, 54)(25, 60, 30, 55)", perm"(1, 21, 11)(2, 22, 12)(3, 23, 13)(4, 24, 14)(5, 25, 15)(6, 26, 16)(7, 27, 17)(8, 28, 18)(9, 29, 19)(10, 30, 20)(31, 51,
+41)(32, 52, 42)(33, 53, 43)(34, 54, 44)(35, 55, 45)(36, 56, 46)(37, 57, 47)(38, 58, 48)(39, 59, 49)(40, 60, 50)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21,
+26)(22, 27)(23, 28)(24, 29)(25, 30)(31, 36)(32, 37)(33, 38)(34, 39)(35, 40)(41, 46)(42, 47)(43, 48)(44, 49)(45, 50)(51, 56)(52, 57)(53, 58)(54, 59)(55, 60)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11,
+15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 25, 24, 23, 22)(26, 30, 29, 28, 27)(31, 32, 33, 34, 35)(36, 37, 38, 39, 40)(41, 42, 43, 44, 45)(46, 47, 48, 49, 50)(51, 52, 53, 54, 55)(56, 57, 58, 59, 60)" ],
[
[ 1, 1, 1, 1 ],
[ 2, 2, 2 ],
@@ -5095,12 +5095,12 @@ false, false, true, false, 48), ([ perm"(1, 36, 6, 31)(2, 37, 7, 32)(3, 38, 8, 3
[ -1, -2, 1, 2 ],
[ -1, -4, 1, -4 ],
[ -2, -4, 2, 4 ]
-], [ (1, 1), (2, 1), (3, 2), (4, 10), (5, 4), (6, 2), (10, 4), (12, 20), (15, 8), (30, 8) ], [ (1, 1), (2, 1), (3, 1), (4, 5), (5, 1), (6, 1), (10, 1), (12, 5), (15, 1), (20, 1), (30, 1), (60, 1) ],
-false, false, true, false, 80), ([ perm"(1, 46, 16, 31)(2, 47, 17, 32)(3, 48, 18, 33)(4, 49, 19, 34)(5, 50, 20, 35)(6, 51, 21, 36)(7, 52, 22, 37)(8, 53, 23, 38)(9, 54, 24, 39)(10, 55, 25, 40)(11, 56,
-26, 41)(12, 57, 27, 42)(13, 58, 28, 43)(14, 59, 29, 44)(15, 60, 30, 45)", perm"(1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)(31,
-46)(32, 47)(33, 48)(34, 49)(35, 50)(36, 51)(37, 52)(38, 53)(39, 54)(40, 55)(41, 56)(42, 57)(43, 58)(44, 59)(45, 60)", perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)(16, 26, 21)(17, 27,
-22)(18, 28, 23)(19, 29, 24)(20, 30, 25)(31, 36, 41)(32, 37, 42)(33, 38, 43)(34, 39, 44)(35, 40, 45)(46, 51, 56)(47, 52, 57)(48, 53, 58)(49, 54, 59)(50, 55, 60)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8,
-7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 25, 24, 23, 22)(26, 30, 29, 28, 27)(31, 32, 33, 34, 35)(36, 37, 38, 39, 40)(41, 42, 43, 44, 45)(46, 47, 48, 49, 50)(51, 52, 53, 54, 55)(56, 57, 58, 59,
+], [ (1, 1), (2, 1), (3, 2), (4, 10), (5, 4), (6, 2), (10, 4), (12, 20), (15, 8), (30, 8) ], [ (1, 1), (2, 1), (3, 1), (4, 5), (5, 1), (6, 1), (10, 1), (12, 5), (15, 1), (20, 1), (30, 1), (60, 1) ],
+false, false, true, false, 80), ([ perm"(1, 46, 16, 31)(2, 47, 17, 32)(3, 48, 18, 33)(4, 49, 19, 34)(5, 50, 20, 35)(6, 51, 21, 36)(7, 52, 22, 37)(8, 53, 23, 38)(9, 54, 24, 39)(10, 55, 25, 40)(11, 56,
+26, 41)(12, 57, 27, 42)(13, 58, 28, 43)(14, 59, 29, 44)(15, 60, 30, 45)", perm"(1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)(31,
+46)(32, 47)(33, 48)(34, 49)(35, 50)(36, 51)(37, 52)(38, 53)(39, 54)(40, 55)(41, 56)(42, 57)(43, 58)(44, 59)(45, 60)", perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)(16, 26, 21)(17, 27,
+22)(18, 28, 23)(19, 29, 24)(20, 30, 25)(31, 36, 41)(32, 37, 42)(33, 38, 43)(34, 39, 44)(35, 40, 45)(46, 51, 56)(47, 52, 57)(48, 53, 58)(49, 54, 59)(50, 55, 60)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8,
+7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 25, 24, 23, 22)(26, 30, 29, 28, 27)(31, 32, 33, 34, 35)(36, 37, 38, 39, 40)(41, 42, 43, 44, 45)(46, 47, 48, 49, 50)(51, 52, 53, 54, 55)(56, 57, 58, 59,
60)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -5115,12 +5115,12 @@ false, false, true, false, 80), ([ perm"(1, 46, 16, 31)(2, 47, 17, 32)(3, 48, 18
[ -1, -3, 1, -3 ],
[ -1, -4, 1, -4 ],
[ -3, -4, 3, 4 ]
-], [ (1, 1), (2, 1), (3, 2), (4, 30), (5, 4), (6, 2), (10, 4), (15, 8), (30, 8) ], [ (1, 1), (2, 1), (3, 1), (4, 15), (5, 1), (6, 1), (10, 1), (12, 5), (15, 1), (20, 3), (30, 1), (60, 1) ], false,
-false, true, false, 240), ([ perm"(1, 32, 2, 31)(3, 34, 4, 33)(5, 36, 6, 35)(7, 38, 8, 37)(9, 40, 10, 39)(11, 42, 12, 41)(13, 44, 14, 43)(15, 46, 16, 45)(17, 48, 18, 47)(19, 50, 20, 49)(21, 52, 22,
-51)(23, 54, 24, 53)(25, 56, 26, 55)(27, 58, 28, 57)(29, 60, 30, 59)", perm"(1, 21, 11)(2, 22, 12)(3, 23, 13)(4, 24, 14)(5, 25, 15)(6, 26, 16)(7, 27, 17)(8, 28, 18)(9, 29, 19)(10, 30, 20)(31, 51,
-41)(32, 52, 42)(33, 53, 43)(34, 54, 44)(35, 55, 45)(36, 56, 46)(37, 57, 47)(38, 58, 48)(39, 59, 49)(40, 60, 50)", perm"(1, 9, 7, 5, 3)(2, 10, 8, 6, 4)(11, 19, 17, 15, 13)(12, 20, 18, 16, 14)(21, 29,
-27, 25, 23)(22, 30, 28, 26, 24)(31, 39, 37, 35, 33)(32, 40, 38, 36, 34)(41, 49, 47, 45, 43)(42, 50, 48, 46, 44)(51, 59, 57, 55, 53)(52, 60, 58, 56, 54)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11,
-12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)(49, 50)(51, 52)(53, 54)(55, 56)(57, 58)(59, 60)" ],
+], [ (1, 1), (2, 1), (3, 2), (4, 30), (5, 4), (6, 2), (10, 4), (15, 8), (30, 8) ], [ (1, 1), (2, 1), (3, 1), (4, 15), (5, 1), (6, 1), (10, 1), (12, 5), (15, 1), (20, 3), (30, 1), (60, 1) ], false,
+false, true, false, 240), ([ perm"(1, 32, 2, 31)(3, 34, 4, 33)(5, 36, 6, 35)(7, 38, 8, 37)(9, 40, 10, 39)(11, 42, 12, 41)(13, 44, 14, 43)(15, 46, 16, 45)(17, 48, 18, 47)(19, 50, 20, 49)(21, 52, 22,
+51)(23, 54, 24, 53)(25, 56, 26, 55)(27, 58, 28, 57)(29, 60, 30, 59)", perm"(1, 21, 11)(2, 22, 12)(3, 23, 13)(4, 24, 14)(5, 25, 15)(6, 26, 16)(7, 27, 17)(8, 28, 18)(9, 29, 19)(10, 30, 20)(31, 51,
+41)(32, 52, 42)(33, 53, 43)(34, 54, 44)(35, 55, 45)(36, 56, 46)(37, 57, 47)(38, 58, 48)(39, 59, 49)(40, 60, 50)", perm"(1, 9, 7, 5, 3)(2, 10, 8, 6, 4)(11, 19, 17, 15, 13)(12, 20, 18, 16, 14)(21, 29,
+27, 25, 23)(22, 30, 28, 26, 24)(31, 39, 37, 35, 33)(32, 40, 38, 36, 34)(41, 49, 47, 45, 43)(42, 50, 48, 46, 44)(51, 59, 57, 55, 53)(52, 60, 58, 56, 54)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11,
+12)(13, 14)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 42)(43, 44)(45, 46)(47, 48)(49, 50)(51, 52)(53, 54)(55, 56)(57, 58)(59, 60)" ],
[
[ 1, 1, 1, 1 ],
[ 2, 2, 2 ],
@@ -5136,19 +5136,19 @@ false, true, false, 240), ([ perm"(1, 32, 2, 31)(3, 34, 4, 33)(5, 36, 6, 35)(7,
[ -1, -3, 1, 3 ],
[ -2, -3, 2, 3 ]
], [ (1, 1), (2, 1), (3, 2), (4, 2), (5, 4), (6, 2), (10, 4), (12, 4), (15, 8), (20, 8), (30, 8), (60, 16) ], [ (1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (10, 1), (12, 1), (15, 1), (20, 1), (30,
-1), (60, 1) ], true, true, true, true, 16), ([ perm"(1, 2, 4, 8, 15)(3, 6, 12, 22, 36)(5, 10, 19, 31, 46)(7, 14, 25, 9, 17)(11, 21, 34, 16, 28)(13, 23, 35, 48, 54)(18, 30, 40, 27, 41)(20, 32, 45, 55,
-59)(24, 29, 43, 37, 49)(26, 39, 44, 52, 58)(33, 42, 53, 47, 38)(50, 57, 60, 56, 51)", perm"(1, 3, 7)(2, 5, 11)(4, 9, 18)(6, 13, 24)(8, 16, 12)(10, 20, 33)(14, 26, 40)(15, 27, 19)(17, 29, 44)(21, 35,
+1), (60, 1) ], true, true, true, true, 16), ([ perm"(1, 2, 4, 8, 15)(3, 6, 12, 22, 36)(5, 10, 19, 31, 46)(7, 14, 25, 9, 17)(11, 21, 34, 16, 28)(13, 23, 35, 48, 54)(18, 30, 40, 27, 41)(20, 32, 45, 55,
+59)(24, 29, 43, 37, 49)(26, 39, 44, 52, 58)(33, 42, 53, 47, 38)(50, 57, 60, 56, 51)", perm"(1, 3, 7)(2, 5, 11)(4, 9, 18)(6, 13, 24)(8, 16, 12)(10, 20, 33)(14, 26, 40)(15, 27, 19)(17, 29, 44)(21, 35,
36)(22, 37, 25)(23, 38, 50)(28, 42, 54)(30, 45, 46)(31, 47, 34)(32, 39, 51)(41, 52, 59)(43, 48, 56)(49, 57, 58)(53, 55, 60)" ], [
[ 1, 1, 1, 1, 1 ],
[ 2, 2, 2 ],
[ 1, 2, 1, 1, 2, 1 ]
], [
[ 1, 2, 1, 1, 2, 1 ]
-], [ (1, 1), (2, 15), (3, 20), (5, 24) ], [ (1, 1), (2, 15), (3, 10), (4, 5), (5, 6), (6, 10), (10, 6), (12, 5), (60, 1) ], false, false, false, false, 120), ([ perm"(1, 36, 6, 31)(2, 37, 7, 32)(3,
-38, 8, 33)(4, 39, 9, 34)(5, 40, 10, 35)(11, 46, 16, 41)(12, 47, 17, 42)(13, 48, 18, 43)(14, 49, 19, 44)(15, 50, 20, 45)(21, 56, 26, 51)(22, 57, 27, 52)(23, 58, 28, 53)(24, 59, 29, 54)(25, 60, 30,
-55)", perm"(1, 21, 11)(2, 22, 12)(3, 23, 13)(4, 24, 14)(5, 25, 15)(6, 26, 16)(7, 27, 17)(8, 28, 18)(9, 29, 19)(10, 30, 20)(31, 51, 41)(32, 52, 42)(33, 53, 43)(34, 54, 44)(35, 55, 45)(36, 56, 46)(37,
-57, 47)(38, 58, 48)(39, 59, 49)(40, 60, 50)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24, 29)(25, 30)(31, 36)(32, 37)(33, 38)(34, 39)(35,
-40)(41, 46)(42, 47)(43, 48)(44, 49)(45, 50)(51, 56)(52, 57)(53, 58)(54, 59)(55, 60)", perm"(1, 5, 4, 3, 2)(6, 7, 8, 9, 10)(11, 15, 14, 13, 12)(16, 17, 18, 19, 20)(21, 25, 24, 23, 22)(26, 27, 28, 29,
+], [ (1, 1), (2, 15), (3, 20), (5, 24) ], [ (1, 1), (2, 15), (3, 10), (4, 5), (5, 6), (6, 10), (10, 6), (12, 5), (60, 1) ], false, false, false, false, 120), ([ perm"(1, 36, 6, 31)(2, 37, 7, 32)(3,
+38, 8, 33)(4, 39, 9, 34)(5, 40, 10, 35)(11, 46, 16, 41)(12, 47, 17, 42)(13, 48, 18, 43)(14, 49, 19, 44)(15, 50, 20, 45)(21, 56, 26, 51)(22, 57, 27, 52)(23, 58, 28, 53)(24, 59, 29, 54)(25, 60, 30,
+55)", perm"(1, 21, 11)(2, 22, 12)(3, 23, 13)(4, 24, 14)(5, 25, 15)(6, 26, 16)(7, 27, 17)(8, 28, 18)(9, 29, 19)(10, 30, 20)(31, 51, 41)(32, 52, 42)(33, 53, 43)(34, 54, 44)(35, 55, 45)(36, 56, 46)(37,
+57, 47)(38, 58, 48)(39, 59, 49)(40, 60, 50)", perm"(1, 6)(2, 7)(3, 8)(4, 9)(5, 10)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(21, 26)(22, 27)(23, 28)(24, 29)(25, 30)(31, 36)(32, 37)(33, 38)(34, 39)(35,
+40)(41, 46)(42, 47)(43, 48)(44, 49)(45, 50)(51, 56)(52, 57)(53, 58)(54, 59)(55, 60)", perm"(1, 5, 4, 3, 2)(6, 7, 8, 9, 10)(11, 15, 14, 13, 12)(16, 17, 18, 19, 20)(21, 25, 24, 23, 22)(26, 27, 28, 29,
30)(31, 34, 32, 35, 33)(36, 38, 40, 37, 39)(41, 44, 42, 45, 43)(46, 48, 50, 47, 49)(51, 54, 52, 55, 53)(56, 58, 60, 57, 59)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2, 2 ],
@@ -5165,11 +5165,11 @@ false, true, false, 240), ([ perm"(1, 32, 2, 31)(3, 34, 4, 33)(5, 36, 6, 35)(7,
[ -2, -4, 2, 4 ],
[ 3, -4, 3, -4 ],
[ 1, -4, -1, -4, -4 ]
-], [ (1, 1), (2, 5), (3, 2), (4, 10), (5, 4), (6, 10), (12, 20), (15, 8) ], [ (1, 1), (2, 5), (3, 1), (4, 5), (5, 1), (6, 5), (10, 1), (12, 5), (15, 1), (20, 1), (30, 1), (60, 1) ], false, false,
-true, false, 40), ([ perm"(1, 46, 16, 31)(2, 47, 17, 32)(3, 48, 18, 33)(4, 49, 19, 34)(5, 50, 20, 35)(6, 51, 21, 36)(7, 52, 22, 37)(8, 53, 23, 38)(9, 54, 24, 39)(10, 55, 25, 40)(11, 56, 26, 41)(12,
-57, 27, 42)(13, 58, 28, 43)(14, 59, 29, 44)(15, 60, 30, 45)", perm"(1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)(31, 46)(32, 47)(33,
-48)(34, 49)(35, 50)(36, 51)(37, 52)(38, 53)(39, 54)(40, 55)(41, 56)(42, 57)(43, 58)(44, 59)(45, 60)", perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)(16, 26, 21)(17, 27, 22)(18, 28, 23)(19,
-29, 24)(20, 30, 25)(31, 36, 41)(32, 37, 42)(33, 38, 43)(34, 39, 44)(35, 40, 45)(46, 51, 56)(47, 52, 57)(48, 53, 58)(49, 54, 59)(50, 55, 60)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13,
+], [ (1, 1), (2, 5), (3, 2), (4, 10), (5, 4), (6, 10), (12, 20), (15, 8) ], [ (1, 1), (2, 5), (3, 1), (4, 5), (5, 1), (6, 5), (10, 1), (12, 5), (15, 1), (20, 1), (30, 1), (60, 1) ], false, false,
+true, false, 40), ([ perm"(1, 46, 16, 31)(2, 47, 17, 32)(3, 48, 18, 33)(4, 49, 19, 34)(5, 50, 20, 35)(6, 51, 21, 36)(7, 52, 22, 37)(8, 53, 23, 38)(9, 54, 24, 39)(10, 55, 25, 40)(11, 56, 26, 41)(12,
+57, 27, 42)(13, 58, 28, 43)(14, 59, 29, 44)(15, 60, 30, 45)", perm"(1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)(31, 46)(32, 47)(33,
+48)(34, 49)(35, 50)(36, 51)(37, 52)(38, 53)(39, 54)(40, 55)(41, 56)(42, 57)(43, 58)(44, 59)(45, 60)", perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)(16, 26, 21)(17, 27, 22)(18, 28, 23)(19,
+29, 24)(20, 30, 25)(31, 36, 41)(32, 37, 42)(33, 38, 43)(34, 39, 44)(35, 40, 45)(46, 51, 56)(47, 52, 57)(48, 53, 58)(49, 54, 59)(50, 55, 60)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13,
12)(16, 17, 18, 19, 20)(21, 22, 23, 24, 25)(26, 27, 28, 29, 30)(31, 33, 35, 32, 34)(36, 38, 40, 37, 39)(41, 43, 45, 42, 44)(46, 49, 47, 50, 48)(51, 54, 52, 55, 53)(56, 59, 57, 60, 58)" ], [
[ 1, 1, 1, 1 ],
[ 2, 2 ],
@@ -5186,11 +5186,11 @@ true, false, 40), ([ perm"(1, 46, 16, 31)(2, 47, 17, 32)(3, 48, 18, 33)(4, 49, 1
[ 2, -4, 2, -4 ],
[ -3, -4, 3, 4 ],
[ 1, -4, -1, 4, 4 ]
-], [ (1, 1), (2, 5), (3, 2), (4, 30), (5, 4), (6, 10), (15, 8) ], [ (1, 1), (2, 5), (3, 1), (4, 15), (5, 1), (6, 5), (10, 1), (12, 5), (15, 1), (20, 3), (30, 1), (60, 1) ], false, false, true, false,
-120), ([ perm"(1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24,
-54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)", perm"(1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)(31, 46)(32, 47)(33, 48)(34,
-49)(35, 50)(36, 51)(37, 52)(38, 53)(39, 54)(40, 55)(41, 56)(42, 57)(43, 58)(44, 59)(45, 60)", perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)(16, 21, 26)(17, 22, 27)(18, 23, 28)(19, 24,
-29)(20, 25, 30)(31, 41, 36)(32, 42, 37)(33, 43, 38)(34, 44, 39)(35, 45, 40)(46, 51, 56)(47, 52, 57)(48, 53, 58)(49, 54, 59)(50, 55, 60)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16,
+], [ (1, 1), (2, 5), (3, 2), (4, 30), (5, 4), (6, 10), (15, 8) ], [ (1, 1), (2, 5), (3, 1), (4, 15), (5, 1), (6, 5), (10, 1), (12, 5), (15, 1), (20, 3), (30, 1), (60, 1) ], false, false, true, false,
+120), ([ perm"(1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24,
+54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)", perm"(1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)(31, 46)(32, 47)(33, 48)(34,
+49)(35, 50)(36, 51)(37, 52)(38, 53)(39, 54)(40, 55)(41, 56)(42, 57)(43, 58)(44, 59)(45, 60)", perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)(16, 21, 26)(17, 22, 27)(18, 23, 28)(19, 24,
+29)(20, 25, 30)(31, 41, 36)(32, 42, 37)(33, 43, 38)(34, 44, 39)(35, 45, 40)(46, 51, 56)(47, 52, 57)(48, 53, 58)(49, 54, 59)(50, 55, 60)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16,
20, 19, 18, 17)(21, 25, 24, 23, 22)(26, 30, 29, 28, 27)(31, 32, 33, 34, 35)(36, 37, 38, 39, 40)(41, 42, 43, 44, 45)(46, 47, 48, 49, 50)(51, 52, 53, 54, 55)(56, 57, 58, 59, 60)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -5209,11 +5209,11 @@ true, false, 40), ([ perm"(1, 46, 16, 31)(2, 47, 17, 32)(3, 48, 18, 33)(4, 49, 1
[ 1, -4, 1, -4 ],
[ 2, -4, 2, 4 ],
[ -3, -4, 3, 4 ]
-], [ (1, 1), (2, 23), (3, 2), (5, 4), (6, 10), (10, 12), (15, 8) ], [ (1, 1), (2, 23), (3, 1), (4, 15), (5, 1), (6, 11), (10, 7), (12, 5), (15, 1), (20, 3), (30, 3), (60, 1) ], false, false, true,
+], [ (1, 1), (2, 23), (3, 2), (5, 4), (6, 10), (10, 12), (15, 8) ], [ (1, 1), (2, 23), (3, 1), (4, 15), (5, 1), (6, 11), (10, 7), (12, 5), (15, 1), (20, 3), (30, 3), (60, 1) ], false, false, true,
false, 120), ([ perm"(1, 41, 21)(2, 42, 22)(3, 43, 23)(4, 44, 24)(5, 45, 25)(6, 46, 26)(7, 47, 27)(8, 48, 28)(9, 49, 29)(10, 50, 30)(11, 51, 31)(12, 52, 32)(13, 53, 33)(14, 54, 34)(15, 55, 35)(16, 56,
-36)(17, 57, 37)(18, 58, 38)(19, 59, 39)(20, 60, 40)", perm"(1, 17, 13, 9, 5)(2, 18, 14, 10, 6)(3, 19, 15, 11, 7)(4, 20, 16, 12, 8)(21, 37, 33, 29, 25)(22, 38, 34, 30, 26)(23, 39, 35, 31, 27)(24, 40,
-36, 32, 28)(41, 57, 53, 49, 45)(42, 58, 54, 50, 46)(43, 59, 55, 51, 47)(44, 60, 56, 52, 48)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 22)(23, 24)(25, 26)(27,
-28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 44)(42, 43)(45, 48)(46, 47)(49, 52)(50, 51)(53, 56)(54, 55)(57, 60)(58, 59)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17,
+36)(17, 57, 37)(18, 58, 38)(19, 59, 39)(20, 60, 40)", perm"(1, 17, 13, 9, 5)(2, 18, 14, 10, 6)(3, 19, 15, 11, 7)(4, 20, 16, 12, 8)(21, 37, 33, 29, 25)(22, 38, 34, 30, 26)(23, 39, 35, 31, 27)(24, 40,
+36, 32, 28)(41, 57, 53, 49, 45)(42, 58, 54, 50, 46)(43, 59, 55, 51, 47)(44, 60, 56, 52, 48)", perm"(1, 3)(2, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(17, 19)(18, 20)(21, 22)(23, 24)(25, 26)(27,
+28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)(41, 44)(42, 43)(45, 48)(46, 47)(49, 52)(50, 51)(53, 56)(54, 55)(57, 60)(58, 59)", perm"(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17,
18)(19, 20)(21, 24)(22, 23)(25, 28)(26, 27)(29, 32)(30, 31)(33, 36)(34, 35)(37, 40)(38, 39)(41, 43)(42, 44)(45, 47)(46, 48)(49, 51)(50, 52)(53, 55)(54, 56)(57, 59)(58, 60)" ], [
[ 1, 1, 1 ],
[ 2, 2, 2, 2, 2 ],
@@ -5230,11 +5230,11 @@ false, 120), ([ perm"(1, 41, 21)(2, 42, 22)(3, 43, 23)(4, 44, 24)(5, 45, 25)(6,
[ -2, 3, 2, 3 ],
[ 3, 4, 3, 4 ],
[ 1, 3, -1, 3, 4 ]
-], [ (1, 1), (2, 3), (3, 8), (5, 4), (10, 12), (15, 32) ], [ (1, 1), (2, 3), (3, 4), (4, 1), (5, 1), (10, 3), (12, 1), (15, 4), (20, 1), (60, 1) ], false, false, true, false, 96), ([ perm"(1, 31)(2,
+], [ (1, 1), (2, 3), (3, 8), (5, 4), (10, 12), (15, 32) ], [ (1, 1), (2, 3), (3, 4), (4, 1), (5, 1), (10, 3), (12, 1), (15, 4), (20, 1), (60, 1) ], false, false, true, false, 96), ([ perm"(1, 31)(2,
32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28,
-58)(29, 59)(30, 60)", perm"(1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)(31, 46)(32, 47)(33, 48)(34, 49)(35, 50)(36, 51)(37, 52)(38,
-53)(39, 54)(40, 55)(41, 56)(42, 57)(43, 58)(44, 59)(45, 60)", perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)(16, 26, 21)(17, 27, 22)(18, 28, 23)(19, 29, 24)(20, 30, 25)(31, 41, 36)(32, 42,
-37)(33, 43, 38)(34, 44, 39)(35, 45, 40)(46, 56, 51)(47, 57, 52)(48, 58, 53)(49, 59, 54)(50, 60, 55)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 25, 24, 23,
+58)(29, 59)(30, 60)", perm"(1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)(31, 46)(32, 47)(33, 48)(34, 49)(35, 50)(36, 51)(37, 52)(38,
+53)(39, 54)(40, 55)(41, 56)(42, 57)(43, 58)(44, 59)(45, 60)", perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)(16, 26, 21)(17, 27, 22)(18, 28, 23)(19, 29, 24)(20, 30, 25)(31, 41, 36)(32, 42,
+37)(33, 43, 38)(34, 44, 39)(35, 45, 40)(46, 56, 51)(47, 57, 52)(48, 58, 53)(49, 59, 54)(50, 60, 55)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16, 20, 19, 18, 17)(21, 25, 24, 23,
22)(26, 30, 29, 28, 27)(31, 32, 33, 34, 35)(36, 37, 38, 39, 40)(41, 42, 43, 44, 45)(46, 47, 48, 49, 50)(51, 52, 53, 54, 55)(56, 57, 58, 59, 60)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -5253,11 +5253,11 @@ false, 120), ([ perm"(1, 41, 21)(2, 42, 22)(3, 43, 23)(4, 44, 24)(5, 45, 25)(6,
[ 1, -4, 1, -4 ],
[ 2, -4, 2, 4 ],
[ -3, -4, 3, 4 ]
-], [ (1, 1), (2, 11), (3, 2), (5, 4), (6, 22), (10, 4), (15, 8), (30, 8) ], [ (1, 1), (2, 11), (3, 1), (4, 5), (5, 1), (6, 11), (10, 3), (12, 5), (15, 1), (20, 1), (30, 3), (60, 1) ], false, false,
-true, false, 80), ([ perm"(1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23,
-53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)", perm"(1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)(31, 46)(32, 47)(33,
-48)(34, 49)(35, 50)(36, 51)(37, 52)(38, 53)(39, 54)(40, 55)(41, 56)(42, 57)(43, 58)(44, 59)(45, 60)", perm"(1, 13, 10, 7, 4)(2, 14, 11, 8, 5)(3, 15, 12, 9, 6)(16, 28, 25, 22, 19)(17, 29, 26, 23,
-20)(18, 30, 27, 24, 21)(31, 43, 40, 37, 34)(32, 44, 41, 38, 35)(33, 45, 42, 39, 36)(46, 58, 55, 52, 49)(47, 59, 56, 53, 50)(48, 60, 57, 54, 51)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15,
+], [ (1, 1), (2, 11), (3, 2), (5, 4), (6, 22), (10, 4), (15, 8), (30, 8) ], [ (1, 1), (2, 11), (3, 1), (4, 5), (5, 1), (6, 11), (10, 3), (12, 5), (15, 1), (20, 1), (30, 3), (60, 1) ], false, false,
+true, false, 80), ([ perm"(1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23,
+53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)", perm"(1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)(31, 46)(32, 47)(33,
+48)(34, 49)(35, 50)(36, 51)(37, 52)(38, 53)(39, 54)(40, 55)(41, 56)(42, 57)(43, 58)(44, 59)(45, 60)", perm"(1, 13, 10, 7, 4)(2, 14, 11, 8, 5)(3, 15, 12, 9, 6)(16, 28, 25, 22, 19)(17, 29, 26, 23,
+20)(18, 30, 27, 24, 21)(31, 43, 40, 37, 34)(32, 44, 41, 38, 35)(33, 45, 42, 39, 36)(46, 58, 55, 52, 49)(47, 59, 56, 53, 50)(48, 60, 57, 54, 51)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15,
14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 32, 33)(34, 35, 36)(37, 38, 39)(40, 41, 42)(43, 44, 45)(46, 47, 48)(49, 50, 51)(52, 53, 54)(55, 56, 57)(58, 59, 60)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -5277,10 +5277,10 @@ true, false, 80), ([ perm"(1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 3
[ 2, -4, 2, 4 ],
[ -3, -4, 3, 4 ]
], [ (1, 1), (2, 7), (3, 2), (5, 4), (6, 2), (10, 28), (15, 8), (30, 8) ], [ (1, 1), (2, 7), (3, 1), (4, 3), (5, 1), (6, 3), (10, 7), (12, 1), (15, 1), (20, 3), (30, 3), (60, 1) ], false, false, true,
-false, 48), ([ perm"(1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24,
-54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)", perm"(1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)(31, 46)(32, 47)(33, 48)(34,
-49)(35, 50)(36, 51)(37, 52)(38, 53)(39, 54)(40, 55)(41, 56)(42, 57)(43, 58)(44, 59)(45, 60)", perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)(16, 26, 21)(17, 27, 22)(18, 28, 23)(19, 29,
-24)(20, 30, 25)(31, 36, 41)(32, 37, 42)(33, 38, 43)(34, 39, 44)(35, 40, 45)(46, 51, 56)(47, 52, 57)(48, 53, 58)(49, 54, 59)(50, 55, 60)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16,
+false, 48), ([ perm"(1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24,
+54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)", perm"(1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)(31, 46)(32, 47)(33, 48)(34,
+49)(35, 50)(36, 51)(37, 52)(38, 53)(39, 54)(40, 55)(41, 56)(42, 57)(43, 58)(44, 59)(45, 60)", perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)(16, 26, 21)(17, 27, 22)(18, 28, 23)(19, 29,
+24)(20, 30, 25)(31, 36, 41)(32, 37, 42)(33, 38, 43)(34, 39, 44)(35, 40, 45)(46, 51, 56)(47, 52, 57)(48, 53, 58)(49, 54, 59)(50, 55, 60)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13, 12)(16,
20, 19, 18, 17)(21, 25, 24, 23, 22)(26, 30, 29, 28, 27)(31, 32, 33, 34, 35)(36, 37, 38, 39, 40)(41, 42, 43, 44, 45)(46, 47, 48, 49, 50)(51, 52, 53, 54, 55)(56, 57, 58, 59, 60)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -5299,11 +5299,11 @@ false, 48), ([ perm"(1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9,
[ 1, -4, 1, -4 ],
[ 2, -4, 2, 4 ],
[ -3, -4, 3, 4 ]
-], [ (1, 1), (2, 31), (3, 2), (5, 4), (6, 2), (10, 4), (15, 8), (30, 8) ], [ (1, 1), (2, 31), (3, 1), (4, 15), (5, 1), (6, 11), (10, 7), (12, 5), (15, 1), (20, 3), (30, 3), (60, 1) ], false, false,
-true, false, 240), ([ perm"(1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23,
-53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)", perm"(1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)(31, 46)(32, 47)(33,
-48)(34, 49)(35, 50)(36, 51)(37, 52)(38, 53)(39, 54)(40, 55)(41, 56)(42, 57)(43, 58)(44, 59)(45, 60)", perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)(16, 26, 21)(17, 27, 22)(18, 28, 23)(19,
-29, 24)(20, 30, 25)(31, 41, 36)(32, 42, 37)(33, 43, 38)(34, 44, 39)(35, 45, 40)(46, 56, 51)(47, 57, 52)(48, 58, 53)(49, 59, 54)(50, 60, 55)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13,
+], [ (1, 1), (2, 31), (3, 2), (5, 4), (6, 2), (10, 4), (15, 8), (30, 8) ], [ (1, 1), (2, 31), (3, 1), (4, 15), (5, 1), (6, 11), (10, 7), (12, 5), (15, 1), (20, 3), (30, 3), (60, 1) ], false, false,
+true, false, 240), ([ perm"(1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23,
+53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)", perm"(1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)(31, 46)(32, 47)(33,
+48)(34, 49)(35, 50)(36, 51)(37, 52)(38, 53)(39, 54)(40, 55)(41, 56)(42, 57)(43, 58)(44, 59)(45, 60)", perm"(1, 11, 6)(2, 12, 7)(3, 13, 8)(4, 14, 9)(5, 15, 10)(16, 26, 21)(17, 27, 22)(18, 28, 23)(19,
+29, 24)(20, 30, 25)(31, 41, 36)(32, 42, 37)(33, 43, 38)(34, 44, 39)(35, 45, 40)(46, 56, 51)(47, 57, 52)(48, 58, 53)(49, 59, 54)(50, 60, 55)", perm"(1, 5, 4, 3, 2)(6, 10, 9, 8, 7)(11, 15, 14, 13,
12)(16, 20, 19, 18, 17)(21, 25, 24, 23, 22)(26, 30, 29, 28, 27)(31, 35, 34, 33, 32)(36, 40, 39, 38, 37)(41, 45, 44, 43, 42)(46, 50, 49, 48, 47)(51, 55, 54, 53, 52)(56, 60, 59, 58, 57)" ], [
[ 1, 1 ],
[ 2, 2 ],
@@ -5323,31 +5323,31 @@ true, false, 240), ([ perm"(1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8,
[ 2, -4, 2, 4 ],
[ -3, -4, 3, 4 ]
], [ (1, 1), (2, 3), (3, 2), (5, 4), (6, 6), (10, 12), (15, 8), (30, 24) ], [ (1, 1), (2, 3), (3, 1), (4, 1), (5, 1), (6, 3), (10, 3), (12, 1), (15, 1), (20, 1), (30, 3), (60, 1) ], true, false, true,
-true, 48) ], [ ([ perm"(1, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19,
+true, 48) ], [ ([ perm"(1, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19,
18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)" ], [
-[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
+[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 ]
-], [], [ (1, 1), (61, 60) ], [ (1, 1), (61, 1) ], true, true, true, true, 60) ], [ ([ perm"(1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15,
-46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62)", perm"(1, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18,
+], [], [ (1, 1), (61, 60) ], [ (1, 1), (61, 1) ], true, true, true, true, 60) ], [ ([ perm"(1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12, 43)(13, 44)(14, 45)(15,
+46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62)", perm"(1, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18,
17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62)" ], [
[ 1, 1 ],
[ -2, 1, -2, 1 ],
[ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -2, 1, -2, 1 ]
-], [ (1, 1), (2, 31), (31, 30) ], [ (1, 1), (2, 31), (31, 1), (62, 1) ], false, false, true, false, 930), ([ perm"(1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12,
-43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62)", perm"(1, 31, 30, 29, 28, 27, 26, 25, 24,
-23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(32, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34,
+], [ (1, 1), (2, 31), (31, 30) ], [ (1, 1), (2, 31), (31, 1), (62, 1) ], false, false, true, false, 930), ([ perm"(1, 32)(2, 33)(3, 34)(4, 35)(5, 36)(6, 37)(7, 38)(8, 39)(9, 40)(10, 41)(11, 42)(12,
+43)(13, 44)(14, 45)(15, 46)(16, 47)(17, 48)(18, 49)(19, 50)(20, 51)(21, 52)(22, 53)(23, 54)(24, 55)(25, 56)(26, 57)(27, 58)(28, 59)(29, 60)(30, 61)(31, 62)", perm"(1, 31, 30, 29, 28, 27, 26, 25, 24,
+23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2)(32, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34,
33)" ], [
[ 1, 1 ],
[ -2, 1, 2, 1 ],
[ -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2 ]
], [
[ -2, 1, 2, 1 ]
-], [ (1, 1), (2, 1), (31, 30), (62, 30) ], [ (1, 1), (2, 1), (31, 1), (62, 1) ], true, true, true, true, 30) ], [ ([ perm"(1, 57, 36, 15, 50, 29, 8, 43, 22)(2, 58, 37, 16, 51, 30, 9, 44, 23)(3, 59,
-38, 17, 52, 31, 10, 45, 24)(4, 60, 39, 18, 53, 32, 11, 46, 25)(5, 61, 40, 19, 54, 33, 12, 47, 26)(6, 62, 41, 20, 55, 34, 13, 48, 27)(7, 63, 42, 21, 56, 35, 14, 49, 28)", perm"(1, 15, 8)(2, 16, 9)(3,
-17, 10)(4, 18, 11)(5, 19, 12)(6, 20, 13)(7, 21, 14)(22, 36, 29)(23, 37, 30)(24, 38, 31)(25, 39, 32)(26, 40, 33)(27, 41, 34)(28, 42, 35)(43, 57, 50)(44, 58, 51)(45, 59, 52)(46, 60, 53)(47, 61, 54)(48,
-62, 55)(49, 63, 56)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 27, 25, 23, 28, 26, 24)(29, 34, 32, 30, 35, 33, 31)(36, 41, 39, 37, 42, 40, 38)(43, 46, 49,
+], [ (1, 1), (2, 1), (31, 30), (62, 30) ], [ (1, 1), (2, 1), (31, 1), (62, 1) ], true, true, true, true, 30) ], [ ([ perm"(1, 57, 36, 15, 50, 29, 8, 43, 22)(2, 58, 37, 16, 51, 30, 9, 44, 23)(3, 59,
+38, 17, 52, 31, 10, 45, 24)(4, 60, 39, 18, 53, 32, 11, 46, 25)(5, 61, 40, 19, 54, 33, 12, 47, 26)(6, 62, 41, 20, 55, 34, 13, 48, 27)(7, 63, 42, 21, 56, 35, 14, 49, 28)", perm"(1, 15, 8)(2, 16, 9)(3,
+17, 10)(4, 18, 11)(5, 19, 12)(6, 20, 13)(7, 21, 14)(22, 36, 29)(23, 37, 30)(24, 38, 31)(25, 39, 32)(26, 40, 33)(27, 41, 34)(28, 42, 35)(43, 57, 50)(44, 58, 51)(45, 59, 52)(46, 60, 53)(47, 61, 54)(48,
+62, 55)(49, 63, 56)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 27, 25, 23, 28, 26, 24)(29, 34, 32, 30, 35, 33, 31)(36, 41, 39, 37, 42, 40, 38)(43, 46, 49,
45, 48, 44, 47)(50, 53, 56, 52, 55, 51, 54)(57, 60, 63, 59, 62, 58, 61)" ], [
[ 2, 2, 2 ],
[ 1, 1, 1, -2 ],
@@ -5358,9 +5358,9 @@ true, 48) ], [ ([ perm"(1, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 4
[ -2, -3, 2, 3 ],
[ -3, -3, -1, 3, 1 ]
], [ (1, 1), (3, 2), (7, 6), (9, 42), (21, 12) ], [ (1, 1), (3, 1), (7, 1), (9, 7), (21, 1), (63, 1) ], false, false, true, false, 126), ([ perm"(1, 45, 24, 3, 44, 23, 2, 43, 22)(4, 48, 27, 6, 47, 26,
-5, 46, 25)(7, 51, 30, 9, 50, 29, 8, 49, 28)(10, 54, 33, 12, 53, 32, 11, 52, 31)(13, 57, 36, 15, 56, 35, 14, 55, 34)(16, 60, 39, 18, 59, 38, 17, 58, 37)(19, 63, 42, 21, 62, 41, 20, 61, 40)", perm"(1,
-19, 16, 13, 10, 7, 4)(2, 20, 17, 14, 11, 8, 5)(3, 21, 18, 15, 12, 9, 6)(22, 40, 37, 34, 31, 28, 25)(23, 41, 38, 35, 32, 29, 26)(24, 42, 39, 36, 33, 30, 27)(43, 61, 58, 55, 52, 49, 46)(44, 62, 59, 56,
-53, 50, 47)(45, 63, 60, 57, 54, 51, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 33, 32)(34, 36, 35)(37, 39, 38)(40,
+5, 46, 25)(7, 51, 30, 9, 50, 29, 8, 49, 28)(10, 54, 33, 12, 53, 32, 11, 52, 31)(13, 57, 36, 15, 56, 35, 14, 55, 34)(16, 60, 39, 18, 59, 38, 17, 58, 37)(19, 63, 42, 21, 62, 41, 20, 61, 40)", perm"(1,
+19, 16, 13, 10, 7, 4)(2, 20, 17, 14, 11, 8, 5)(3, 21, 18, 15, 12, 9, 6)(22, 40, 37, 34, 31, 28, 25)(23, 41, 38, 35, 32, 29, 26)(24, 42, 39, 36, 33, 30, 27)(43, 61, 58, 55, 52, 49, 46)(44, 62, 59, 56,
+53, 50, 47)(45, 63, 60, 57, 54, 51, 48)", perm"(1, 3, 2)(4, 6, 5)(7, 9, 8)(10, 12, 11)(13, 15, 14)(16, 18, 17)(19, 21, 20)(22, 24, 23)(25, 27, 26)(28, 30, 29)(31, 33, 32)(34, 36, 35)(37, 39, 38)(40,
42, 41)(43, 45, 44)(46, 48, 47)(49, 51, 50)(52, 54, 53)(55, 57, 56)(58, 60, 59)(61, 63, 62)" ], [
[ 3, 3, 3 ],
[ 1, 1, 1, -3 ],
@@ -5369,10 +5369,10 @@ true, 48) ], [ ([ perm"(1, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 4
], [
[ 1, 1, 1, -3 ],
[ -1, -2, 1, 2 ]
-], [ (1, 1), (3, 2), (7, 6), (9, 6), (21, 12), (63, 36) ], [ (1, 1), (3, 1), (7, 1), (9, 1), (21, 1), (63, 1) ], true, true, true, true, 36), ([ perm"(1, 43, 22)(2, 44, 23)(3, 45, 24)(4, 46, 25)(5,
-47, 26)(6, 48, 27)(7, 49, 28)(8, 50, 29)(9, 51, 30)(10, 52, 31)(11, 53, 32)(12, 54, 33)(13, 55, 34)(14, 56, 35)(15, 57, 36)(16, 58, 37)(17, 59, 38)(18, 60, 39)(19, 61, 40)(20, 62, 41)(21, 63, 42)",
-perm"(1, 15, 8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6, 20, 13)(7, 21, 14)(22, 36, 29)(23, 37, 30)(24, 38, 31)(25, 39, 32)(26, 40, 33)(27, 41, 34)(28, 42, 35)(43, 57, 50)(44, 58, 51)(45, 59,
-52)(46, 60, 53)(47, 61, 54)(48, 62, 55)(49, 63, 56)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 27, 25, 23, 28, 26, 24)(29, 34, 32, 30, 35, 33, 31)(36, 41,
+], [ (1, 1), (3, 2), (7, 6), (9, 6), (21, 12), (63, 36) ], [ (1, 1), (3, 1), (7, 1), (9, 1), (21, 1), (63, 1) ], true, true, true, true, 36), ([ perm"(1, 43, 22)(2, 44, 23)(3, 45, 24)(4, 46, 25)(5,
+47, 26)(6, 48, 27)(7, 49, 28)(8, 50, 29)(9, 51, 30)(10, 52, 31)(11, 53, 32)(12, 54, 33)(13, 55, 34)(14, 56, 35)(15, 57, 36)(16, 58, 37)(17, 59, 38)(18, 60, 39)(19, 61, 40)(20, 62, 41)(21, 63, 42)",
+perm"(1, 15, 8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6, 20, 13)(7, 21, 14)(22, 36, 29)(23, 37, 30)(24, 38, 31)(25, 39, 32)(26, 40, 33)(27, 41, 34)(28, 42, 35)(43, 57, 50)(44, 58, 51)(45, 59,
+52)(46, 60, 53)(47, 61, 54)(48, 62, 55)(49, 63, 56)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 27, 25, 23, 28, 26, 24)(29, 34, 32, 30, 35, 33, 31)(36, 41,
39, 37, 42, 40, 38)(43, 46, 49, 45, 48, 44, 47)(50, 53, 56, 52, 55, 51, 54)(57, 60, 63, 59, 62, 58, 61)" ], [
[ 1, 1, 1 ],
[ 2, 2, 2 ],
@@ -5384,9 +5384,9 @@ perm"(1, 15, 8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6, 20, 13)(7, 21, 14)
[ -2, -3, 2, 3 ],
[ -3, -3, -1, 3, 1 ]
], [ (1, 1), (3, 44), (7, 6), (21, 12) ], [ (1, 1), (3, 22), (7, 1), (9, 7), (21, 4), (63, 1) ], false, false, true, false, 252), ([ perm"(1, 43, 22)(2, 44, 23)(3, 45, 24)(4, 46, 25)(5, 47, 26)(6, 48,
-27)(7, 49, 28)(8, 50, 29)(9, 51, 30)(10, 52, 31)(11, 53, 32)(12, 54, 33)(13, 55, 34)(14, 56, 35)(15, 57, 36)(16, 58, 37)(17, 59, 38)(18, 60, 39)(19, 61, 40)(20, 62, 41)(21, 63, 42)", perm"(1, 15,
-8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6, 20, 13)(7, 21, 14)(22, 36, 29)(23, 37, 30)(24, 38, 31)(25, 39, 32)(26, 40, 33)(27, 41, 34)(28, 42, 35)(43, 57, 50)(44, 58, 51)(45, 59, 52)(46, 60,
-53)(47, 61, 54)(48, 62, 55)(49, 63, 56)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)(29, 35, 34, 33, 32, 31, 30)(36, 42, 41, 40, 39,
+27)(7, 49, 28)(8, 50, 29)(9, 51, 30)(10, 52, 31)(11, 53, 32)(12, 54, 33)(13, 55, 34)(14, 56, 35)(15, 57, 36)(16, 58, 37)(17, 59, 38)(18, 60, 39)(19, 61, 40)(20, 62, 41)(21, 63, 42)", perm"(1, 15,
+8)(2, 16, 9)(3, 17, 10)(4, 18, 11)(5, 19, 12)(6, 20, 13)(7, 21, 14)(22, 36, 29)(23, 37, 30)(24, 38, 31)(25, 39, 32)(26, 40, 33)(27, 41, 34)(28, 42, 35)(43, 57, 50)(44, 58, 51)(45, 59, 52)(46, 60,
+53)(47, 61, 54)(48, 62, 55)(49, 63, 56)", perm"(1, 7, 6, 5, 4, 3, 2)(8, 14, 13, 12, 11, 10, 9)(15, 21, 20, 19, 18, 17, 16)(22, 28, 27, 26, 25, 24, 23)(29, 35, 34, 33, 32, 31, 30)(36, 42, 41, 40, 39,
38, 37)(43, 49, 48, 47, 46, 45, 44)(50, 56, 55, 54, 53, 52, 51)(57, 63, 62, 61, 60, 59, 58)" ], [
[ 1, 1, 1 ],
[ 2, 2, 2 ],
diff --git a/src/GrpAb/ChainComplex.jl b/src/GrpAb/ChainComplex.jl
index 544016009b..41683dfe0b 100644
--- a/src/GrpAb/ChainComplex.jl
+++ b/src/GrpAb/ChainComplex.jl
@@ -11,7 +11,7 @@ export chain_complex, isexact, homology, free_resolution
V
F <- H
psi
- and Im(phi) subset Im(psi), then G -> H can be constructed
+ and Im(phi) subset Im(psi), then G -> H can be constructed
=#
@doc Markdown.doc"""
@@ -157,7 +157,7 @@ getindex(C::ChainComplex{T}, u::UnitRange) where {T} = ChainComplex(T, C.maps[u]
@doc Markdown.doc"""
isexact(C::ChainComplex) -> Bool
-Tests is the complex $A_i: G_i \to G_{i+1}$
+Tests is the complex $A_i: G_i \to G_{i+1}$
is exact, ie. if $\Im(A_i) = \Kern(A_{i+1})$.
"""
function isexact(C::ChainComplex)
@@ -166,7 +166,7 @@ end
@doc Markdown.doc"""
free_resolution(G::GrpAbFinGen) -> ChainComplex{GrpAbFinGen}
-A free resultion for $G$, ie. a chain complex terminating in
+A free resultion for $G$, ie. a chain complex terminating in
$G \to \{0\}$ that is exact.
"""
function free_resolution(G::GrpAbFinGen)
@@ -264,7 +264,7 @@ function hom(G::T, C::ChainComplex{T}) where {T}
g = elem_type(obj_type(C))[]
for h = gens(B)
phi = H[i][2](h) # G -> E
- psi = phi * C.maps[i]
+ psi = phi * C.maps[i]
push!(g, preimage(H[i+1][2], psi))
end
push!(R, hom(B, A, g))
@@ -274,7 +274,7 @@ end
@doc Markdown.doc"""
homology(C::ChainComplex{GrpAbFinGen}) -> Vector{GrpAbFinGen}
-Given a complex $A_i: G_i \to G_{i+1}$,
+Given a complex $A_i: G_i \to G_{i+1}$,
compute the homology, ie. the modules $H_i = \Kern A_{i+1}/\Im A_i$
"""
function homology(C::ChainComplex)
diff --git a/src/GrpAb/Dual.jl b/src/GrpAb/Dual.jl
index ece5a70fd7..8df1c5b604 100644
--- a/src/GrpAb/Dual.jl
+++ b/src/GrpAb/Dual.jl
@@ -147,7 +147,7 @@ lift(a::QmodnZElem) = a.elt
mutable struct GrpAbFinGenToQmodnZ <: Map{GrpAbFinGen, QmodnZ,
HeckeMap, GrpAbFinGenToQmodnZ}
header::MapHeader{GrpAbFinGen, QmodnZ}
-
+
function GrpAbFinGenToQmodnZ(G::GrpAbFinGen, QZ::QmodnZ, image)
z = new()
z.header = MapHeader(G, QZ, image)
@@ -195,7 +195,7 @@ function dual(G::GrpAbFinGen, u::QmodnZElem)
R::GrpAbFinGen
ex = MapFromFunc(x -> x[1]*u, y -> H(fmpz[numerator(y.elt) * div(o, denominator(y.elt))]), H, parent(u))
local mu
- let phi = phi, G = G, QZ = QZ, u = u
+ let phi = phi, G = G, QZ = QZ, u = u
function mu(r::GrpAbFinGenElem)
f = phi(r)
return GrpAbFinGenToQmodnZ(G, QZ, x -> f(x)[1]*u)
diff --git a/src/GrpAb/GrpAbFinGen.jl b/src/GrpAb/GrpAbFinGen.jl
index ad9d14e00e..c511b4d616 100644
--- a/src/GrpAb/GrpAbFinGen.jl
+++ b/src/GrpAb/GrpAbFinGen.jl
@@ -68,7 +68,7 @@ Creates the abelian group with relation matrix `M`. That is, the group will
have `ncols(M)` generators and each row of `M` describes one relation.
"""
function abelian_group(M::fmpz_mat; name::String = "")
- if issnf(M) && nrows(M) > 0 && ncols(M) > 0 && !isone(M[1, 1])
+ if issnf(M) && nrows(M) > 0 && ncols(M) > 0 && !isone(M[1, 1])
N = fmpz[M[i, i] for i = 1:min(nrows(M), ncols(M))]
if ncols(M) > nrows(M)
N = vcat(N, fmpz[0 for i = 1:ncols(M)-nrows(M)])
@@ -116,7 +116,7 @@ function _issnf(N::Vector{T}) where T <: Union{Integer, fmpz}
return false
end
for i = 1:length(N)-1
- if isone(abs(N[i]))
+ if isone(abs(N[i]))
return false
end
if iszero(N[i])
@@ -395,7 +395,7 @@ function snf(G::GrpAbFinGen)
else
S, _, T = snf_with_transform(G.rels, false, true)
end
-
+
m = min(nrows(S), ncols(S))
if m > 0 && nrows(S) >= ncols(S)
e = S[m, m]
@@ -530,7 +530,7 @@ order_gen(A::GrpAbFinGen) = order(snf(A)[1])
Returns the exponent of $A$. It is assumed that $A$ is finite.
"""
function exponent(A::GrpAbFinGen)
- if issnf(A)
+ if issnf(A)
res = exponent_snf(A)
if !iszero(res)
A.exponent = res
@@ -1007,7 +1007,7 @@ end
function _sub_integer_snf(G::GrpAbFinGen, n::fmpz, add_to_lattice::Bool = true, L::GrpAbLattice = GroupLattice)
ind = 1
- while ind <= ngens(G) && gcd(n, G.snf[ind]) == G.snf[ind]
+ while ind <= ngens(G) && gcd(n, G.snf[ind]) == G.snf[ind]
ind += 1
end
if ind == ngens(G) && gcd(n, G.snf[ind]) == G.snf[ind]
@@ -1035,7 +1035,7 @@ function _sub_integer_snf(G::GrpAbFinGen, n::fmpz, add_to_lattice::Bool = true,
end
if isdefined(G, :exponent)
Gnew.exponent = G.exponent
- end
+ end
mp = hom(Gnew, G, mat_map)
if add_to_lattice
append!(L, mp)
@@ -1142,7 +1142,7 @@ function quo(G::GrpAbFinGen, M::fmpz_mat,
Q = abelian_group(m)
if isdefined(G, :exponent)
Q.exponent = G.exponent
- end
+ end
I = identity_matrix(FlintZZ, ngens(G))
m = hom(G, Q, I, I, check = false)
if add_to_lattice
@@ -1181,7 +1181,7 @@ function quo_snf(G::GrpAbFinGen, n::Union{fmpz, Integer},
Q.exponent = gcd(G.exponent, n)
else
Q.exponent = n
- end
+ end
m = hom(G, Q, I, I, check = false)
if add_to_lattice
append!(L, m)
@@ -1321,7 +1321,7 @@ function issubgroup(G::GrpAbFinGen, H::GrpAbFinGen, L::GrpAbLattice = GroupLatti
end
end
-#checks if the image of mG contains the image of mH
+#checks if the image of mG contains the image of mH
#cannot define == as this produces problems elsewhere... need some thought
@@ -1892,8 +1892,8 @@ id(G::GrpAbFinGen) = G(zeros(fmpz, ngens(G)))
################################################################################
-#Given a subgroup H of a group G, I want to find generators $g_1, dots, g_s$ of
-#G such that H = \sum H \cap and the relation matrix of $G$ is diagonal.
+#Given a subgroup H of a group G, I want to find generators $g_1, dots, g_s$ of
+#G such that H = \sum H \cap and the relation matrix of $G$ is diagonal.
function isdiagonalisable(mH::GrpAbFinGenMap)
H = domain(mH)
diff --git a/src/GrpAb/Lattice.jl b/src/GrpAb/Lattice.jl
index c9455f6800..98be436b82 100644
--- a/src/GrpAb/Lattice.jl
+++ b/src/GrpAb/Lattice.jl
@@ -89,7 +89,7 @@ function Base.append!(G::Graph{T, M}, e::Tuple{T, T}, data::M) where {T, M}
else
G.new_low_degrees[e[1]] = nothing
end
-
+
if G.degrees[e[2]] > 1
delete!(G.new_low_degrees, e[2])
else
@@ -273,7 +273,7 @@ function find_common(G::Graph{T, M}, root1::T, root2::T) where {T, M}
end
end
end
-
+
while length(Q2) > 0 && found == false
current = pop!(Q2)
if current in S1
@@ -291,7 +291,7 @@ function find_common(G::Graph{T, M}, root1::T, root2::T) where {T, M}
if found
target = current
-
+
path1 = [ target ]
while current != root1
@@ -303,7 +303,7 @@ function find_common(G::Graph{T, M}, root1::T, root2::T) where {T, M}
end
end
end
-
+
path2 = [ target ]
current = target
@@ -339,7 +339,7 @@ end
# Here is the most important rule:
#
# A vertex in the lattice of groups is allowed to be removed only if
-# the degree is < 2.
+# the degree is < 2.
#
# We achieve this by keeping an additional dictionary L.block_gc, which
# contains the groups which must not be gc'ed.
@@ -450,7 +450,7 @@ function update!(L::RelLattice)
#end
delete_from_lattice!(L, L.to_delete)
#L.to_delete = UInt[]
-
+
for k in keys(L.graph.new_low_degrees)
@assert haskey(L.graph.degrees, k)
# TODO: Why does it crash without the following?
@@ -512,7 +512,7 @@ function can_map_into_overstructure(L::RelLattice{T, D}, G::T, H::T) where {T, D
@assert pG[1] == pH[1]
M = L.weak_vertices_rev[pG[1]].value::T
@assert M != nothing
-
+
mG = eval_path(L, M, pG)
mH = eval_path(L, M, pH)
diff --git a/src/GrpAb/Map.jl b/src/GrpAb/Map.jl
index ec73266089..0a03a243c4 100644
--- a/src/GrpAb/Map.jl
+++ b/src/GrpAb/Map.jl
@@ -147,7 +147,7 @@ function hom(A::Vector{GrpAbFinGenElem}, B::Vector{GrpAbFinGenElem}; check::Bool
if ngens(GB) == 0
return hom(GA, GB, matrix(FlintZZ, ngens(GA), 0, fmpz[]), check = check)
end
-
+
M = vcat([hcat(A[i].coeff, B[i].coeff) for i = 1:length(A)])
RA = rels(GA)
M = vcat(M, hcat(RA, zero_matrix(FlintZZ, nrows(RA), ncols(B[1].coeff))))
diff --git a/src/GrpAb/SubgroupEnum.jl b/src/GrpAb/SubgroupEnum.jl
index 5741902cf4..a1b5e17bd2 100644
--- a/src/GrpAb/SubgroupEnum.jl
+++ b/src/GrpAb/SubgroupEnum.jl
@@ -115,7 +115,7 @@ function index_to_group(s::IndexPSubgroups, i::UInt)
end
function Base.iterate(s::IndexPSubgroups, i::UInt = UInt(0))
- if i + 1 > s.n
+ if i + 1 > s.n
return nothing
end
@@ -186,14 +186,14 @@ function Base.iterate(F::yIterator, i::Vector{Int})
for j in 1:length(i)
if i[j] != F.x[j]
- done = false
+ done = false
end
end
if done
return nothing
end
-
+
if i[1] < F.x[1]
i[1] = i[1] + 1
else # the first one is as large as possible
@@ -216,7 +216,7 @@ function Base.iterate(F::yIterator, i::Vector{Int})
return copy(F.res), i
end
-function Base.iterate(F::yIterator)
+function Base.iterate(F::yIterator)
i = ones(Int, F.t)
if F.t == 0
@@ -226,7 +226,7 @@ function Base.iterate(F::yIterator)
@inbounds if F.t > 0
i[1] = 0
end
-
+
@inbounds if i[1] < F.x[1]
i[1] = i[1] + 1
else # the first one is as large as possible
@@ -430,7 +430,7 @@ function _subgroup_type_iterator(x, y, p)
t = something(findlast(!iszero, y), 0)
# have to treat the empty y separately
-
+
if any(y[i] > x[i] for i in 1:length(x))
return (x for x in 1:-1)
@@ -686,7 +686,7 @@ function pSubgroupIterator(G::GrpAbFinGen, p::Union{fmpz, Integer};
it = _psubgroups(G, p; subtype = subtype, quotype = quotype,
fun = fun, index = index, order = order)
end
-
+
E = Core.Compiler.return_type(fun, (GrpAbFinGen, Vector{GrpAbFinGenElem}))
z = pSubgroupIterator{typeof(fun), typeof(it), E}(G, fmpz(p), subtype, [-1],
diff --git a/src/GrpAb/stable_sub.jl b/src/GrpAb/stable_sub.jl
index bdab4a0af5..8f22bfdef8 100644
--- a/src/GrpAb/stable_sub.jl
+++ b/src/GrpAb/stable_sub.jl
@@ -164,7 +164,7 @@ function dual_module(M::ZpnGModule)
end
-function _dualize(M::nmod_mat, V::GrpAbFinGen, v::Vector{fmpz})
+function _dualize(M::nmod_mat, V::GrpAbFinGen, v::Vector{fmpz})
# First, compute the kernel of the corresponding homomorphisms
K = abelian_group(fmpz[V.snf[end] for j=1:nrows(M)])
A = lift(transpose(M))
@@ -610,7 +610,7 @@ function _submodules_with_struct_main(M::ZpnGModule, typesub::Vector{Int})
diag = typesub - new_typesub1
Gtest = snf(abelian_group(Int[p^x for x in diag]))[1]
order_test = order(Gtest)
- for x in list
+ for x in list
L, _ = quo(M, x)
newlist = _submodules_with_struct(L, new_typesub)
@vprint :StabSub 1 "Candidates to be added at this step: $(length(newlist)) \n"
@@ -920,7 +920,7 @@ function _stable_subgroup_snf(R::GrpAbFinGen, act::Vector{GrpAbFinGenMap}; quoty
G, mG = psylow_subgroup(R, p, false)
S, mS = snf(G)
comp = mS*mG
-
+
#We need to distinguish between FqGModule and ZpnGModule (in the first case the algorithm is more efficient)
if x1 == 1
@@ -1018,7 +1018,7 @@ function _lift_and_construct(A::Zmodn_mat, mp::GrpAbFinGenMap)
y = view(A, i:i, 1:ncols(A))
el = GrpAbFinGenElem(G, lift(y))
push!(newsub, mp(el))
- end
+ end
end
return newsub
end
diff --git a/src/Hecke.jl b/src/Hecke.jl
index 4a6224d12b..4591719551 100644
--- a/src/Hecke.jl
+++ b/src/Hecke.jl
@@ -358,7 +358,7 @@ function conjugate_data_arb_roots(K::AnticNumberField, p::Int)
rcomplex = Vector{acb}(undef, div(degree(K), 2))
while true
R = ArbField(pstart, cached = false)
- # We need to pair them
+ # We need to pair them
_rall = Tuple{arb, arb}[ sincospi(fmpq(2*k, f), R) for k in 1:f if gcd(f, k) == 1]
if all(x -> radiuslttwopower(x[1], -p) && radiuslttwopower(x[2], -p), _rall)
CC = AcbField(pstart, cached = false)
@@ -464,7 +464,7 @@ if VERSION >= v"1.4"
global VERSION_NUMBER = "building"
end
else
- ver = Pkg.API.__installed(PKGMODE_MANIFEST)["Hecke"]
+ ver = Pkg.API.__installed(PKGMODE_MANIFEST)["Hecke"]
dir = dirname(@__DIR__)
if occursin("/dev/", dir)
global VERSION_NUMBER = VersionNumber("$(ver)-dev")
@@ -499,7 +499,7 @@ end
abstract type HeckeMap <: SetMap end #needed here for the hasspecial stuff
#maybe move to Maps?
-import AbstractAlgebra: get_special, set_special, @show_name, @show_special,
+import AbstractAlgebra: get_special, set_special, @show_name, @show_special,
@show_special_elem, @declare_other, extra_name, set_name!, find_name
function hasspecial(G::T) where T <: Map{<:Any, <:Any, HeckeMap, <:Any}
diff --git a/src/LargeField/FB.jl b/src/LargeField/FB.jl
index b654ff8c6f..1a60418737 100644
--- a/src/LargeField/FB.jl
+++ b/src/LargeField/FB.jl
@@ -31,10 +31,10 @@ end
@doc Markdown.doc"""
induce_action(primes::Vector{NfOrdIdl}, A::Map) -> Perm{Int}
-Given a set of prime ideals invariant under the action of $A$, this function
+Given a set of prime ideals invariant under the action of $A$, this function
returns the corresponding permutation induced by $A$.
"""
-function induce_action(primes::Vector{NfOrdIdl}, A::Map)
+function induce_action(primes::Vector{NfOrdIdl}, A::Map)
K = domain(A)
f = A(gen(K)) # essentially a polynomial in the primitive element
@@ -54,7 +54,7 @@ function induce_action(primes::Vector{NfOrdIdl}, A::Map)
for (i, j) in prm_p
push!(prm, (indices[i], indices[j]))
end
- end
+ end
sort!(prm, by = a -> a[1])
return G([x[2] for x = prm])
end
@@ -82,7 +82,7 @@ function _induce_action_p(lp::Vector{NfOrdIdl}, A::Map)
break
end
end
- @assert !iszero(id)
+ @assert !iszero(id)
push!(prm, (i, id))
end
else
@@ -94,7 +94,7 @@ function _induce_action_p(lp::Vector{NfOrdIdl}, A::Map)
# an irreducible factor of gpx (Kummer/ Dedekind)
# an ideal is divisible by P iff the canonical 2nd generator of the prime ideal
# divides the 2nd generator of the target (CRT)
- # so
+ # so
lpols = gfp_poly[gcd(px(K(P.gen_two)), gpx) for P in lp]
# this makes lp canonical (should be doing nothing actually)
@@ -105,7 +105,7 @@ function _induce_action_p(lp::Vector{NfOrdIdl}, A::Map)
else
im = compose_mod(hp, fpx, gpx)
# the image, directly mod p...
- end
+ end
im = Hecke.gcd!(im, gpx, im)
# canonical
push!(prm, (i, findfirst(isequal(im), lpols)))
@@ -117,7 +117,7 @@ end
-function induce(FB::Hecke.NfFactorBase, A::Map)
+function induce(FB::Hecke.NfFactorBase, A::Map)
K = domain(A)
f = A(gen(K)) # essentially a polynomial in the primitive element
@@ -145,7 +145,7 @@ end
Algo 4: Dimino
Tested for cyclic groups - unfortunately only.
I still need to generate other input
-=#
+=#
#function orbit_in_FB(op::Vector{Tuple{Map, Generic.Perm}}, a::nf_elem, s::SRow)
function orbit_in_FB(op::Array, a::nf_elem, s::SRow)
function op_smat(n::SRow, p::Generic.Perm)
@@ -166,7 +166,7 @@ function orbit_in_FB(op::Array, a::nf_elem, s::SRow)
b = op[1][1](b)
end
- for i=2:length(op)
+ for i=2:length(op)
bb = op[i][1](a)
if haskey(Ss, bb)
continue
@@ -207,7 +207,7 @@ function generated_subgroup(op::Array) #pairs: permutations and Map
push!(elt, c_g)
# g = (x->op[1][1](c_g[1](x)), op[1][2]*c_g[2])
g = (x->op[1][1](c_g[1](x)), c_g[2]*op[1][2])
- end
+ end
end
ord = length(elt)
@@ -233,7 +233,7 @@ function generated_subgroup(op::Array) #pairs: permutations and Map
if g[2] in [x[2] for x=elt]
continue
end
- end
+ end
let c_g = g
push!(elt, c_g)
for j = 2:pord
@@ -241,11 +241,11 @@ function generated_subgroup(op::Array) #pairs: permutations and Map
# push!(elt, (x->elt[c_j][1](c_g[1](x)), elt[c_j][2]*c_g[2]))
push!(elt, (x->elt[c_j][1](c_g[1](x)), c_g[2]*elt[c_j][2]))
end
- end
+ end
ord = length(elt)
end
rpos += pord
- if rpos > length(elt)
+ if rpos > length(elt)
break
end
end
diff --git a/src/LargeField/basis.jl b/src/LargeField/basis.jl
index 42a2c51086..9b471aeca3 100644
--- a/src/LargeField/basis.jl
+++ b/src/LargeField/basis.jl
@@ -32,11 +32,11 @@ end
# return q
#end
-function bkz_basis(A::NfOrdIdl, bs::Int;
+function bkz_basis(A::NfOrdIdl, bs::Int;
v::fmpz_mat = zero_matrix(FlintZZ, 1, 1),
prec::Int = 100)
-
+
K = nf(order(A))
c = minkowski_matrix(K, prec)
@@ -65,10 +65,10 @@ function bkz_basis(A::NfOrdIdl, bs::Int;
return q
end
-function fplll_basis(rt_c::Hecke.roots_ctx, A::NfOrdIdl, bs::Int;
+function fplll_basis(rt_c::Hecke.roots_ctx, A::NfOrdIdl, bs::Int;
v::fmpz_mat = zero_matrix(FlintZZ, 1,1),
prec::Int = 100)
-
+
K = nf(order(A))
c = minkowski_matrix(rt_c, K, prec)
@@ -141,15 +141,15 @@ function auto_simplify(A::Map, K::AnticNumberField)
return hom(K, K, b, check = false)
end
-function auto_power(A::Map, n::Int)
- if n==1
+function auto_power(A::Map, n::Int)
+ if n==1
return A
end;
B = x->A(A(x));
C = auto_power(B, div(n, 2))
if n%2==0
return C
- else
+ else
return x-> A(C(x))
end
end
diff --git a/src/LargeField/misc2.jl b/src/LargeField/misc2.jl
index d0b9a99924..f664ee04bc 100644
--- a/src/LargeField/misc2.jl
+++ b/src/LargeField/misc2.jl
@@ -17,7 +17,7 @@ function basis_rels(b::Vector{nf_elem}, c; bd::fmpz = fmpz(10^35), no_b::Int = 2
end
iszero(a) && continue
n = norm_div(a, one, no_b)
- if cmpabs(numerator(n), bd) <= 0
+ if cmpabs(numerator(n), bd) <= 0
if no_id != 0
g = gcd(no_id, numerator(n))
if g==1 || gcd(div(numerator(n), g), g) == 1
@@ -29,7 +29,7 @@ function basis_rels(b::Vector{nf_elem}, c; bd::fmpz = fmpz(10^35), no_b::Int = 2
if class_group_add_relation(c, a, n, one)
a = b[1].parent()
end
- end
+ end
end
end
end
@@ -67,7 +67,7 @@ function basis_rels_2(b::Vector{nf_elem}, bd::fmpz = fmpz(10^35), no_b::Int = 25
if smooth != 0
!issmooth(smooth, numerator(n))[1] && continue
end
- if cmpabs(numerator(n), bd) <= 0
+ if cmpabs(numerator(n), bd) <= 0
if no_id != 0
g = gcd(no_id, numerator(n))
if g==1 || gcd(div(numerator(n), g), g) == 1
@@ -79,7 +79,7 @@ function basis_rels_2(b::Vector{nf_elem}, bd::fmpz = fmpz(10^35), no_b::Int = 25
rels[i] = deepcopy(a)
i = i + 1
println(i)
- end
+ end
end
end
return rels
@@ -201,7 +201,7 @@ function basis_rels_4(b::Vector{nf_elem}, no_b::Int = 250, no_rel::Int = 10000,
end
nb = length(b)
-
+
rels = Dict{fmpz, Vector{Int}}()
i = 1
ll = 0
@@ -231,8 +231,8 @@ function basis_rels_4(b::Vector{nf_elem}, no_b::Int = 250, no_rel::Int = 10000,
# println(local_norm(sum(b[lc]), lpx[j]))
# @assert local_norm(sum(b[lc]), lpx[j]) == np[j]
end
-
-
+
+
no = Hecke.crt_signed(np, crt_env)
sum_nb += nbits(no)
# println("testing $no")
@@ -321,7 +321,7 @@ function basis_rels_5(b::Vector{nf_elem}, no_b::Int = 250, no_rel::Int = 10000,
end
nb = length(b)
-
+
rels = Dict{fmpz, Vector{Int}}()
i = 1
ll = 0
@@ -358,8 +358,8 @@ function basis_rels_5(b::Vector{nf_elem}, no_b::Int = 250, no_rel::Int = 10000,
end
if zero continue; end
-
-
+
+
no = crt_signed(np, crt_env)
# @assert no == norm(sum(b[lc]))
sum_nb += nbits(no)
@@ -431,7 +431,7 @@ function rels_stat(b::Vector{Hecke.nf_elem}; no_b = 250, no_rel::Int = 10000, no
one = fmpz(1)
stat = Dict{Int, Int}()
- if fixed != 0
+ if fixed != 0
stat[-1] = 0
end
if smooth != 0
@@ -464,7 +464,7 @@ function rels_stat(b::Vector{Hecke.nf_elem}; no_b = 250, no_rel::Int = 10000, no
stat[-2] += 1
push!(all_g, a)
a = a = b[1].parent()
- end
+ end
end
return stat, all_g
end
@@ -491,7 +491,7 @@ function int_fb_max_real(f::Int, B::Int)
else
pp *= p
end
- end
+ end
end
p = next_prime(p)
end
@@ -535,7 +535,7 @@ end
# If M is upper-triangular with more columns then rows,
# this function returns the non-pivot column indices.
function _find_missing_pivot(M::SMat)
- return setdiff(Set(1:ncols(M)), Set([y.pos[1] for y = M.rows ]))
+ return setdiff(Set(1:ncols(M)), Set([y.pos[1] for y = M.rows ]))
end
function res_degree_in_max_real(p::Int, n::Int)
diff --git a/src/LinearAlgebra/FakeFmpqMat.jl b/src/LinearAlgebra/FakeFmpqMat.jl
index 0f014aaa9f..1569c8d68c 100644
--- a/src/LinearAlgebra/FakeFmpqMat.jl
+++ b/src/LinearAlgebra/FakeFmpqMat.jl
@@ -31,7 +31,7 @@ ncols(x::FakeFmpqMat) = ncols(x.num)
function simplify_content!(x::FakeFmpqMat)
c = content(x.num)
gcd!(c, c, x.den)
- if !isone(c)
+ if !isone(c)
divexact!(x.num, x.num, c)
divexact!(x.den, x.den, c)
end
@@ -83,10 +83,10 @@ function -(x::FakeFmpqMat)
return FakeFmpqMat(-x.num, x.den, true)
end
-#TODO: may be possible to simplify more efficiently.
+#TODO: may be possible to simplify more efficiently.
#The content of the numerator of the inverse may be non trivial!
function inv(x::FakeFmpqMat)
- i, d_i = pseudo_inv(x.num)
+ i, d_i = pseudo_inv(x.num)
g = gcd(d_i, x.den)
if isone(g)
return FakeFmpqMat(i * x.den, d_i)
@@ -327,7 +327,7 @@ end
function det(x::FakeFmpqMat)
nrows(x) != ncols(x) && error("Matrix must be square")
-
+
return det(x.num)//(x.den)^nrows(x)
end
diff --git a/src/LinearAlgebra/Howell.jl b/src/LinearAlgebra/Howell.jl
index 22ad3c6fe3..0eff43ab87 100644
--- a/src/LinearAlgebra/Howell.jl
+++ b/src/LinearAlgebra/Howell.jl
@@ -26,8 +26,8 @@ if Nemo.version() > v"0.15.1"
#
# for the in-place function, the number of rows must be at least equal to the number of columns
#
- function howell_form!(A::Generic.Mat{Nemo.fmpz_mod})
-
+ function howell_form!(A::Generic.Mat{Nemo.fmpz_mod})
+
R = base_ring(A)
A1 = lift(A)
ccall((:fmpz_mat_howell_form_mod, libflint), Nothing,
@@ -45,9 +45,9 @@ if Nemo.version() > v"0.15.1"
n=R.modulus
#
- # Get an upper triangular matrix
+ # Get an upper triangular matrix
#
-
+
for j=1:ncols(A)
for i=j+1:ncols(A)
g,s,t,u,v = _xxgcd(A[j,j].data,A[i,j].data,n)
@@ -82,7 +82,7 @@ else
#
# for the in-place function, the number of rows must be at least equal to the number of columns
#
- function howell_form!(A::Generic.Mat{Nemo.Generic.Res{Nemo.fmpz}})
+ function howell_form!(A::Generic.Mat{Nemo.Generic.Res{Nemo.fmpz}})
R = base_ring(A)
A1 = lift(A)
@@ -101,7 +101,7 @@ else
n=R.modulus
#
- # Get an upper triangular matrix
+ # Get an upper triangular matrix
#
for j=1:ncols(A)
diff --git a/src/LinearAlgebra/LatEnum.jl b/src/LinearAlgebra/LatEnum.jl
index abb56638f0..f186af69b0 100644
--- a/src/LinearAlgebra/LatEnum.jl
+++ b/src/LinearAlgebra/LatEnum.jl
@@ -52,11 +52,11 @@ function show(io::IO, E::enum_ctx)
println(io, "EnumCtx")
if isdefined(E, :c)
println(io, "curr. length ", E.c, " elt ", E.x, "(", (typeof(E.x), typeof(E.C), typeof(E.U)), ")")
- end
+ end
end
#need to only compute the top l x l submatrix when using limited enum
-function pseudo_cholesky(G::fmpz_mat, den=1;
+function pseudo_cholesky(G::fmpz_mat, den=1;
TC::Type=Rational{BigInt}, limit = nrows(G))
n = ncols(G)
@hassert :LatEnum 1 nrows(G) == n
@@ -69,7 +69,7 @@ function pseudo_cholesky(G::fmpz_mat, den=1;
C[i,j] = TC(t//den)
end
end
- for i = 1:limit-1
+ for i = 1:limit-1
for j = i+1:limit
C[j,i] = C[i,j]
C[i,j] = C[i,j]/C[i,i]
@@ -101,8 +101,8 @@ end
function enum_ctx_from_gram(G::FakeFmpqMat; Tx = BigInt, TC = Rational{BigInt}, TU = Rational{BigInt}, limit = nrows(G))
return enum_ctx_from_gram(numerator(G), denominator(G), Tx=Tx, TC=TC, TU=TU, limit = limit)
-end
-
+end
+
function enum_ctx_from_basis(B::fmpz_mat, den::fmpz = fmpz(1); Tx::Type = BigInt, TC::Type = Rational{BigInt}, TU::Type = Rational{BigInt}, limit = nrows(B))
G = gram(B)
return enum_ctx_from_gram(G, den*den, Tx=Tx, TC=TC, TU=TU, limit = limit)
@@ -112,7 +112,7 @@ function enum_ctx_from_gram(G::fmpz_mat, den = 1; Tx = BigInt, TC = Rational{Big
E = enum_ctx{Tx, TC, TU}()
E.G = G
n = nrows(G)
- E.n = n
+ E.n = n
limit = min(limit, n)
E.limit = limit
E.d = den
@@ -138,7 +138,7 @@ function enum_ctx_local_bound(a::Rational{T}, b::Rational{T}) where T
L = Base.ceil(a-(i+1)//d)
U = Base.floor(a+(i+1)//d)
# @show L, U, Base.ceil(BigFloat(a) - sqrt(BigFloat(b))), Base.floor(BigFloat(a) + sqrt(BigFloat(b)))
- if (a-L)^2 >b
+ if (a-L)^2 >b
L +=1
end
if (a-U)^2>b
@@ -187,7 +187,7 @@ function enum_ctx_start(E::enum_ctx{A,B,C}, x::fmpz_mat; eps::Float64=1.0) where
E.x = x
for i=E.limit-1:-1:1
E.tail[i] = sum(E.C[i, j]*C(E.x[1,j]) for j=i+1:E.limit)
- end
+ end
b = sum(E.C[i,i]*(C(E.x[1,i]) + E.tail[i])^2 for i=1:E.limit) #curr. length
#@show b, C((x*E.G*x')[1,1])
#@assert b == C((x*E.G*x')[1,1])
@@ -216,7 +216,7 @@ end
#@inline function fmpz_mat_entry(a::fmpz_mat, r::Int, c::Int)
#return unsafe_load(reinterpret(Ptr{Ptr{fmpz}}, a.rows), r)+(c-1)*sizeof(Ptr)
end
-
+
@inline function fmpz_mat_entry_incref!(a::fmpz_mat, r::Int, c::Int)
z = ccall((:fmpz_mat_entry, libflint), Ptr{fmpz},
(Ref{fmpz_mat}, Int, Int), a, r - 1, c - 1)
@@ -265,7 +265,7 @@ function enum_ctx_next(E::enum_ctx{A,B,C}) where {A,B,C}
n = E.limit
i=1
t = fmpz()
- while true
+ while true
enum_ctx_advance_level(E, i)
getindex!(t, E.x, 1, i)
if E.L[i] <= A(t) <= E.U[i] #coordinate is valid
@@ -306,12 +306,12 @@ function enum_ctx_next(E::enum_ctx{A,B,C}) where {A,B,C}
# @hassert :LatEnum 1 typeof(L) == C
E.L[i] = L
E.U[i] = U
-
+
x = A(Base.ceil((E.L[i] +E.U[i])/2))
E.x[1, i] = x
if -E.L[i] == E.U[i] && E.last_non_zero == i+1
E.last_non_zero = i
-# @hassert :LatEnum 1 x == 0
+# @hassert :LatEnum 1 x == 0
end
if x <= E.U[i] # coordinate is valid
i -= 1 # go further up
@@ -364,7 +364,7 @@ end
function pseudo_cholesky(G::arb_mat)
n = ncols(G)
C = deepcopy(G)
- for i = 1:n-1
+ for i = 1:n-1
for j = i+1:n
C[j,i] = C[i,j]
C[i,j] = C[i,j]//C[i,i]
@@ -450,7 +450,7 @@ function _enumerate(E::EnumCtxArb, c::arb, i::Int, x::fmpz_mat)
ub = -CC + C
tr_ptr = ccall((:arb_rad_ptr, libarb), Ptr{Nemo.mag_struct}, (Ref{arb}, ), lb)
-
+
tm_ptr = ccall((:arb_mid_ptr, libarb), Ptr{arf_struct}, (Ref{arb}, ), lb)
u = arf_struct(0, 0, 0, 0)
ccall((:arf_init, libarb), Nothing, (Ref{arf_struct}, ), u)
@@ -499,7 +499,7 @@ function _enumerate(E::EnumCtxArb, c::arb, i::Int, x::fmpz_mat)
x[1,i] = j
l = _enumerate(E, t, i - 1, x)
for k in 1:length(l)
- if n == length(l[k]) + 1 && iszero(j) && all(iszero, l[k])
+ if n == length(l[k]) + 1 && iszero(j) && all(iszero, l[k])
continue
end
push!(A, push!(l[k], fmpz(j)))
diff --git a/src/LocalField/Completions.jl b/src/LocalField/Completions.jl
index c33cc3e697..98b6ca3dfd 100644
--- a/src/LocalField/Completions.jl
+++ b/src/LocalField/Completions.jl
@@ -137,7 +137,7 @@ function generic_completion(K::AnticNumberField, P::NfOrdIdl, precision::Int = 6
for j = 1:f
push!(els, el*pows_gq[j])
end
- mul!(el, el, u)
+ mul!(el, el, u)
end
append!(els, map(elem_in_nf, basis(P^precision, copy = false)))
MK = basis_matrix(els, FakeFmpqMat)
@@ -213,7 +213,7 @@ function setprecision!(f::CompletionMap{LocalField{qadic, EisensteinLocalField},
for j = 1:f
push!(els, mod(el*pows_gq[j], modulo))
end
- mul!(el, el, u)
+ mul!(el, el, u)
end
MK = basis_matrix(els)
bK = basis_matrix(nf_elem[_powermod(u, e, modulo), gen(K)])
@@ -254,7 +254,7 @@ end
@doc Markdown.doc"""
totally_ramified_completion(K::AnticNumberField, P::NfOrdIdl, precision::Int) -> LocalField, CompletionMap
-The completion of $K$ wrt to the topology induced by the valuation at a totally ramified prime ideal $P$,
+The completion of $K$ wrt to the topology induced by the valuation at a totally ramified prime ideal $P$,
presented as a Eisenstein extension of $Q_p$.
The map giving the embedding of $K$ into the completion, admits a pointwise pre-image to obtain a lift.
Note, that the map is not well defined by this data: $K$ will have $\deg P$ many embeddings.
@@ -264,7 +264,7 @@ function totally_ramified_completion(K::AnticNumberField, P::NfOrdIdl, precision
OK = order(P)
@assert isprime(P)
@assert nf(OK) == K
- @assert isone(degree(P))
+ @assert isone(degree(P))
e = ramification_index(P)
Qp = PadicField(minimum(P), precision)
Zp = maximal_order(Qp)
@@ -320,7 +320,7 @@ function setprecision!(f::CompletionMap{LocalField{padic, EisensteinLocalField},
u = f.inv_img[2]
Kp = codomain(f)
ex, r = divrem(new_prec, ramification_index(P))
- if r > 0
+ if r > 0
ex += 1
end
Qp = PadicField(prime(Kp), div(new_prec, e)+1)
@@ -363,7 +363,7 @@ end
@doc Markdown.doc"""
unramified_completion(K::AnticNumberField, P::NfOrdIdl, precision::Int) -> QadicField, CompletionMap
-The completion of $K$ wrt to the topology induced by the valuation at an unramified prime ideal $P$, presented
+The completion of $K$ wrt to the topology induced by the valuation at an unramified prime ideal $P$, presented
as a QadicField.
The map giving the embedding of $K$ into the completion, admits a pointwise pre-image to obtain a lift.
Note, that the map is not well defined by this data: $K$ will have $\deg P$ many embeddings.
diff --git a/src/LocalField/Elem.jl b/src/LocalField/Elem.jl
index d257f271ed..dc4088eb0a 100644
--- a/src/LocalField/Elem.jl
+++ b/src/LocalField/Elem.jl
@@ -119,12 +119,12 @@ function O(K::LocalField, prec::T) where T <: Union{Integer, fmpz}
return K(O(base_field(K), d))
end
-function zero(K::LocalField)
+function zero(K::LocalField)
a = zero(parent(defining_polynomial(K)))
return setprecision(K(a), precision(K))
end
-(K::LocalField)() = zero(K)
+(K::LocalField)() = zero(K)
function one(K::LocalField)
a = one(parent(defining_polynomial(K)))
@@ -153,25 +153,25 @@ end
#
################################################################################
-function (K::LocalField{S, T})(a::Integer) where {S <: FieldElem, T <: LocalFieldParameter}
+function (K::LocalField{S, T})(a::Integer) where {S <: FieldElem, T <: LocalFieldParameter}
el = K(parent(defining_polynomial(K))(a))
return setprecision!(el, precision(K))
end
-function (K::LocalField{S, T})(a::Union{fmpz, fmpq}) where {S <: FieldElem, T <: LocalFieldParameter}
+function (K::LocalField{S, T})(a::Union{fmpz, fmpq}) where {S <: FieldElem, T <: LocalFieldParameter}
el = K(parent(defining_polynomial(K))(a))
return setprecision!(el, precision(K))
end
function (K::LocalField{S, T})(a::U) where {U <: Union{padic, qadic}, S <: FieldElem, T <: LocalFieldParameter}
- return K(parent(defining_polynomial(K))(a))
+ return K(parent(defining_polynomial(K))(a))
end
-function (K::LocalField{S, T})(a::LocalFieldElem{S, T}) where {S <: FieldElem, T <: LocalFieldParameter}
+function (K::LocalField{S, T})(a::LocalFieldElem{S, T}) where {S <: FieldElem, T <: LocalFieldParameter}
return a
end
-function (K::LocalField{S, T})(a::LocalFieldElem{U, V}) where {S <: FieldElem, U <: FieldElem, T <: LocalFieldParameter, V <: LocalFieldParameter}
+function (K::LocalField{S, T})(a::LocalFieldElem{U, V}) where {S <: FieldElem, U <: FieldElem, T <: LocalFieldParameter, V <: LocalFieldParameter}
if parent(a) === K
return a
elseif base_field(K) === parent(a)
@@ -182,7 +182,7 @@ function (K::LocalField{S, T})(a::LocalFieldElem{U, V}) where {S <: FieldElem, U
end
end
-function (K::LocalField{S, T})(p::Generic.Poly{S}) where {S <: FieldElem, T <: LocalFieldParameter}
+function (K::LocalField{S, T})(p::Generic.Poly{S}) where {S <: FieldElem, T <: LocalFieldParameter}
if degree(p) >= degree(K)
p = mod(p, defining_polynomial(K))
end
@@ -251,7 +251,7 @@ function valuation(a::LocalFieldElem{S, UnramifiedLocalField}) where S <: FieldE
end
v = valuation(c)
for j = i+1:degree(K)
- c = coeff(a, j)
+ c = coeff(a, j)
vc = valuation(c)
if vc < v
v = vc
@@ -539,7 +539,7 @@ function exp(a::LocalFieldElem)
res = one(K)
res = setprecision(res, N)
el = one(K)
- res = res
+ res = res
den = setprecision!(one(Qp), N)
max_i = fmpq(N)//(valuation(a) - fmpq(1, p-1)) + 1
bound = Int(floor(fmpz, max_i))
@@ -565,7 +565,7 @@ extended so that $log(p) = 0$.
function log(a::LocalFieldElem)
K = parent(a)
va = valuation(a)
- if iszero(va) && valuation(a-1) > 0
+ if iszero(va) && valuation(a-1) > 0
return _log_one_units(a)
end
e = absolute_ramification_index(K)
@@ -622,7 +622,7 @@ function _log_one_units(a::LocalFieldElem)
else
num = el
den = d
- end
+ end
end
return _log_one_units_fast(num)//den
end
@@ -640,7 +640,7 @@ function _log_one_units_fast(a::LocalFieldElem)
res = setprecision!(res, N)
e = absolute_ramification_index(K)
bound1 = div(N, numerator(vb*e))
-
+
l = 1
left = p*vb*e
right = N + e
diff --git a/src/LocalField/LocalField.jl b/src/LocalField/LocalField.jl
index ed74bf1ed4..f06c63fdf5 100644
--- a/src/LocalField/LocalField.jl
+++ b/src/LocalField/LocalField.jl
@@ -59,7 +59,7 @@ isinfinite(K::LocalField) = isinfinite(base_field(K))
################################################################################
#
-# Generating polynomials properties
+# Generating polynomials properties
#
################################################################################
@@ -295,7 +295,7 @@ end
function unramified_extension(L::LocalField, n::Int, prec::Int, s::String = "z")
K, mK = ResidueField(L)
f = find_irreducible_polynomial(K, n)
- coeffs =
+ coeffs =
return local
end
=#
diff --git a/src/LocalField/Poly.jl b/src/LocalField/Poly.jl
index b6610a3388..07e01fe1b8 100644
--- a/src/LocalField/Poly.jl
+++ b/src/LocalField/Poly.jl
@@ -177,7 +177,7 @@ function fun_factor(f::Generic.Poly{S}) where S <: Union{qadic, LocalFieldElem}
ind -= 1
end
g = setprecision_fixed_precision(Kt(S[coeff(f, i) for i = ind:degree(f)]), 1)
- h = setprecision_fixed_precision(Kt(S[divexact(coeff(f, i), coeff(f, ind)) for i = 0:ind]), 1)
+ h = setprecision_fixed_precision(Kt(S[divexact(coeff(f, i), coeff(f, ind)) for i = 0:ind]), 1)
s = setprecision_fixed_precision(Kt(inv(coeff(g, 0))), 2)
t = setprecision_fixed_precision(zero(Kt), 2)
ch = Int[v]
@@ -930,17 +930,17 @@ function _factor(f::Generic.Poly{T}) where T <: Union{padic, qadic, LocalFieldEl
if degree(facts[1]) > 1
#Extend the base field
F, gF = unramified_extension(K, degree(facts[1]), precision(K))
- fF = map_coefficients(F, f)
+ fF = map_coefficients(F, f)
lf = Hensel_factorization(fF)
fnew = first(values(lf))
lfF = _factor()
end
end
-
+
end
-
-
+
+
end
diff --git a/src/LocalField/Ring.jl b/src/LocalField/Ring.jl
index e1a264cb2f..2c57db456e 100644
--- a/src/LocalField/Ring.jl
+++ b/src/LocalField/Ring.jl
@@ -1,7 +1,7 @@
################################################################################
#
# (q/p)adic integers
-#
+#
# complete enough to support hnf
################################################################################
# CHECK precision!!!
@@ -15,7 +15,7 @@ mutable struct QadicRing{S, T} <: Generic.Ring
z.Q = x
return z
end
-
+
end
function Base.show(io::IO, Q::QadicRing)
@@ -46,7 +46,7 @@ end
function Base.show(io::IO, a::QadicRingElem)
print(io, a.x)
end
-
+
*(a::QadicRingElem, b::QadicRingElem) = QadicRingElem(a.P, a.x*b.x)
+(a::QadicRingElem, b::QadicRingElem) = QadicRingElem(a.P, a.x+b.x)
-(a::QadicRingElem, b::QadicRingElem) = QadicRingElem(a.P, a.x-b.x)
@@ -54,12 +54,12 @@ end
^(a::QadicRingElem, b::QadicRingElem) = QadicRingElem(a.P, a.x^b.x)
^(a::T, b::QadicRingElem{S, T}) where {S, T} = a^b.x
-function inv(a::QadicRingElem)
+function inv(a::QadicRingElem)
valuation(a.x) == 0 || error("The element is not invertible!")
return QadicRingElem(a.P, inv(a.x))
end
-==(a::QadicRingElem, b::QadicRingElem) = a.x == b.x
+==(a::QadicRingElem, b::QadicRingElem) = a.x == b.x
function divexact(a::QadicRingElem, b::QadicRingElem)
@assert !iszero(b.x)
@@ -70,7 +70,7 @@ end
function Base.divrem(a::QadicRingElem, b::QadicRingElem)
if valuation(a.x) < valuation(b.x)
- return setprecision(a.P(0), precision(a)), a
+ return setprecision(a.P(0), precision(a)), a
end
q = divexact(a, b)
return q, a-q*b
@@ -96,7 +96,7 @@ one(Q::QadicRing) = QadicRingElem(Q, Q.Q(1))
(Q::QadicRing)(a::Integer) = QadicRingElem(Q, Q.Q(a))
(Q::QadicRing)(a::fmpz) = QadicRingElem(Q, Q.Q(a))
-function (Q::QadicRing)(a::fmpq)
+function (Q::QadicRing)(a::fmpq)
p = prime(Q.Q)
if iszero(mod(denominator(a), p))
error("The element is not in the ring!")
@@ -182,7 +182,7 @@ Base.isone(a::QadicRingElem) = isone(a.x)
Base.precision(Q::QadicRing) = precision(Q.Q)
Base.precision(a::QadicRingElem) = precision(a.x)
-function setprecision!(Q::QadicRing, n::Int)
+function setprecision!(Q::QadicRing, n::Int)
setprecision!(Q.Q, n)
end
diff --git a/src/LocalField/Types.jl b/src/LocalField/Types.jl
index 0ebea63cb5..e10c73158a 100644
--- a/src/LocalField/Types.jl
+++ b/src/LocalField/Types.jl
@@ -37,8 +37,8 @@ mutable struct CompletionMap{S, T} <: Map{AnticNumberField, S, HeckeMap, Complet
inv_img::Tuple{nf_elem, nf_elem}
precision::Int
- function CompletionMap(K::AnticNumberField, L::LocalField{qadic, EisensteinLocalField},
- img::LocalFieldElem{qadic, EisensteinLocalField},
+ function CompletionMap(K::AnticNumberField, L::LocalField{qadic, EisensteinLocalField},
+ img::LocalFieldElem{qadic, EisensteinLocalField},
inv_img::Tuple{nf_elem, nf_elem}, precision::Int)
z = new{LocalField{qadic, EisensteinLocalField}, LocalFieldElem{qadic, EisensteinLocalField}}()
z.header = MapHeader(K, L)
@@ -48,8 +48,8 @@ mutable struct CompletionMap{S, T} <: Map{AnticNumberField, S, HeckeMap, Complet
return z
end
- function CompletionMap(K::AnticNumberField, L::LocalField{padic, EisensteinLocalField},
- img::LocalFieldElem{padic, EisensteinLocalField},
+ function CompletionMap(K::AnticNumberField, L::LocalField{padic, EisensteinLocalField},
+ img::LocalFieldElem{padic, EisensteinLocalField},
inv_img::nf_elem, precision::Int)
z = new{LocalField{padic, EisensteinLocalField}, LocalFieldElem{padic, EisensteinLocalField}}()
z.header = MapHeader(K, L)
@@ -59,8 +59,8 @@ mutable struct CompletionMap{S, T} <: Map{AnticNumberField, S, HeckeMap, Complet
return z
end
- function CompletionMap(K::AnticNumberField, L::FlintQadicField,
- img::qadic,
+ function CompletionMap(K::AnticNumberField, L::FlintQadicField,
+ img::qadic,
inv_img::nf_elem, precision::Int)
z = new{FlintQadicField, qadic}()
z.header = MapHeader(K, L)
diff --git a/src/LocalField/qAdic.jl b/src/LocalField/qAdic.jl
index 5f85646d62..c9e8cceb54 100644
--- a/src/LocalField/qAdic.jl
+++ b/src/LocalField/qAdic.jl
@@ -71,7 +71,7 @@ function norm(r::qadic)
end
function setcoeff!(x::fq_nmod, n::Int, u::UInt)
- ccall((:nmod_poly_set_coeff_ui, libflint), Nothing,
+ ccall((:nmod_poly_set_coeff_ui, libflint), Nothing,
(Ref{fq_nmod}, Int, UInt), x, n, u)
end
@@ -82,7 +82,7 @@ function (Rx::Generic.PolyRing{padic})(a::qadic)
coeffs = Vector{padic}(undef, degree(Qq))
for i = 1:length(coeffs)
c = R()
- ccall((:padic_poly_get_coeff_padic, libflint), Nothing,
+ ccall((:padic_poly_get_coeff_padic, libflint), Nothing,
(Ref{padic}, Ref{qadic}, Int, Ref{FlintQadicField}), c, a, i-1, parent(a))
coeffs[i] = c
end
@@ -93,20 +93,20 @@ end
function coeff(x::qadic, i::Int)
R = FlintPadicField(prime(parent(x)), parent(x).prec_max)
c = R()
- ccall((:padic_poly_get_coeff_padic, libflint), Nothing,
+ ccall((:padic_poly_get_coeff_padic, libflint), Nothing,
(Ref{padic}, Ref{qadic}, Int, Ref{FlintQadicField}), c, x, i, parent(x))
- return c
+ return c
end
function setcoeff!(x::qadic, i::Int, y::padic)
- ccall((:padic_poly_set_coeff_padic, libflint), Nothing,
+ ccall((:padic_poly_set_coeff_padic, libflint), Nothing,
(Ref{qadic}, Int, Ref{padic}, Ref{FlintQadicField}), x, i, y, parent(x))
end
function setcoeff!(x::qadic, i::Int, y::UInt)
R = FlintPadicField(prime(parent(x)), parent(x).prec_max)
Y = R(fmpz(y))
- ccall((:padic_poly_set_coeff_padic, libflint), Nothing,
+ ccall((:padic_poly_set_coeff_padic, libflint), Nothing,
(Ref{qadic}, Int, Ref{padic}, Ref{FlintQadicField}), x, i, Y, parent(x))
end
@@ -175,7 +175,7 @@ function lift_reco(::FlintRationalField, a::padic; reco::Bool = false)
R = parent(a)
fl, c, d = rational_reconstruction(u, prime(R, N-v))
!fl && return nothing
-
+
x = FlintQQ(c, d)
if v < 0
return x//prime(R, -v)
diff --git a/src/Map/FiniteField.jl b/src/Map/FiniteField.jl
index 8433fff411..e5f437a7fc 100644
--- a/src/Map/FiniteField.jl
+++ b/src/Map/FiniteField.jl
@@ -36,7 +36,7 @@ function hom(F::FinField, K::FinField, a::FinFieldElem; check::Bool = true)
M[i, j] = coeff(el, j-1)
end
end
-
+
aux = zero_matrix(Kp, 1, degree(F))
aux1 = zero_matrix(Kp, 1, degree(K))
function img(x::FinFieldElem)
@@ -47,7 +47,7 @@ function hom(F::FinField, K::FinField, a::FinFieldElem; check::Bool = true)
mul!(aux1, aux, M)
pol = Kpx(elem_type(Kp)[aux1[1, j] for j = 1:degree(K)])
return K(pol)
- end
+ end
function preimg(x::FinFieldElem)
diff --git a/src/Map/GrpAb.jl b/src/Map/GrpAb.jl
index a9ef995b49..1d38339b46 100644
--- a/src/Map/GrpAb.jl
+++ b/src/Map/GrpAb.jl
@@ -206,7 +206,7 @@ mutable struct GrpAbFinGenToAbsOrdMap{S, T} <: Map{GrpAbFinGen, S, HeckeMap, Grp
generators::Vector{T}
discrete_logarithm::Function
modulus # this can be anything, for which powermod(::T, ::fmpz, modulus) is defined
-
+
disc_log::GrpAbFinGenElem #Needed in the conductor computation
function GrpAbFinGenToAbsOrdMap{S, T}(G::GrpAbFinGen, O::S, generators::Vector{T}, disc_log::Function, modulus...) where {S, T}
@@ -293,7 +293,7 @@ mutable struct GrpAbFinGenToAbsOrdQuoRingMultMap{S, T, U} <: Map{GrpAbFinGen, Ab
# Multiplicative group, wild part
wild::Dict{T, GrpAbFinGenToAbsOrdMap{S, U}}
-
+
function GrpAbFinGenToAbsOrdQuoRingMultMap{S, T, U}(G::GrpAbFinGen, Q::AbsOrdQuoRing{S, T}, generators::Vector{AbsOrdQuoRingElem{S, T, U}}, disc_log::Function) where {S, T, U}
@assert ngens(G) == length(generators)
diff --git a/src/Map/Map.jl b/src/Map/Map.jl
index 7887f19ba0..f062e6dd1d 100644
--- a/src/Map/Map.jl
+++ b/src/Map/Map.jl
@@ -105,7 +105,7 @@ function _allow_cache!(M::Map, lim::Int, ::Type{D}, ::Type{C}, ::Type{De}, ::Typ
M.header.cache.old_pr = M.header.preimage
M.header.cache.old_im = M.header.image
end
-
+
if length(methods(M.header.image)) > 1
println("Cannot do image cache, too many types")
else
diff --git a/src/Map/MapType.jl b/src/Map/MapType.jl
index d367753da7..7f5adff28e 100644
--- a/src/Map/MapType.jl
+++ b/src/Map/MapType.jl
@@ -1,5 +1,5 @@
###########################################################
-##
+##
## MAPS
##
## maps between residue rings of polynomials and in general
@@ -38,7 +38,7 @@ mutable struct MapCache{D, C, De, Ce}
im::Dict{De, Ce}
imStat::Dict{De, Int}
- pr::Dict{Ce, De}
+ pr::Dict{Ce, De}
prStat::Dict{Ce, Int}
old_im::Function
@@ -210,7 +210,7 @@ function Base.show(io::IO, M::MapFromFunc)
io = IOContext(io, :compact => true)
# println(io, "Map from the $(M.f) julia-function")
println(io, "Map from")
- show(io, domain(M))
+ show(io, domain(M))
print(io, " to ")
show(io, codomain(M))
print(io, " defined by a julia-function")
diff --git a/src/Map/NfOrd.jl b/src/Map/NfOrd.jl
index 2cd491e01f..f2ae3e33b9 100644
--- a/src/Map/NfOrd.jl
+++ b/src/Map/NfOrd.jl
@@ -10,7 +10,7 @@ mutable struct NfOrdToFqNmodMor <: Map{NfOrd, FqNmodFiniteField, HeckeMap, NfOrd
poly_of_the_field::gfp_poly
P::NfOrdIdl
powers::Vector{nf_elem}
-
+
function NfOrdToFqNmodMor()
r = new()
r.header = MapHeader{NfOrd, FqNmodFiniteField}()
@@ -64,7 +64,7 @@ mutable struct NfOrdToFqNmodMor <: Map{NfOrd, FqNmodFiniteField, HeckeMap, NfOrd
z.header = MapHeader{NfOrd, FqNmodFiniteField}(O, F, _image, _preimage)
return z
end
-
+
function NfOrdToFqNmodMor(O::NfOrd, P::NfOrdIdl)
z = NfOrdToFqNmodMor()
z.P = P
@@ -80,7 +80,7 @@ mutable struct NfOrdToFqNmodMor <: Map{NfOrd, FqNmodFiniteField, HeckeMap, NfOrd
powers = Vector{nf_elem}(undef, d)
c = Rx()
for i in 1:n
- ib = F()
+ ib = F()
@assert d == ncols(b[i])
for j in 1:d
setcoeff!(c, j - 1, b[i][1, j])
@@ -316,7 +316,7 @@ function NfOrdToFqMor(O::NfOrd, P::NfOrdIdl)#, g::fmpz_poly, a::NfOrdElem, b::Ve
c = Rx()
for i in 1:n
- ib = F()
+ ib = F()
@assert d == ncols(b[i])
for j in 1:d
setcoeff!(c, j - 1, b[i][1, j])
@@ -410,7 +410,7 @@ mutable struct NfOrdToGFMor <: Map{NfOrd, GaloisField, HeckeMap, NfOrdToFqNmodMo
header::MapHeader{NfOrd, GaloisField}
poly_of_the_field::gfp_poly
P::NfOrdIdl
-
+
function NfOrdToGFMor()
r = new()
r.header = MapHeader{NfOrd, GaloisField}()
@@ -438,7 +438,7 @@ mutable struct NfOrdToGFMor <: Map{NfOrd, GaloisField, HeckeMap, NfOrdToFqNmodMo
z.header = MapHeader{NfOrd, GaloisField}(O, F, _image)
return z
end
-
+
function NfOrdToGFMor(O::NfOrd, P::NfOrdIdl)
z = NfOrdToGFMor()
z.P = P
@@ -481,7 +481,7 @@ mutable struct NfOrdToGFFmpzMor <: Map{NfOrd, Nemo.GaloisFmpzField, HeckeMap, Nf
header::MapHeader{NfOrd, Nemo.GaloisFmpzField}
poly_of_the_field::gfp_fmpz_poly
P::NfOrdIdl
-
+
function NfOrdToGFFmpzMor()
r = new()
return r
@@ -506,7 +506,7 @@ mutable struct NfOrdToGFFmpzMor <: Map{NfOrd, Nemo.GaloisFmpzField, HeckeMap, Nf
z.header = MapHeader{NfOrd, Nemo.GaloisFmpzField}(O, F, _image)
return z
end
-
+
function NfOrdToGFFmpzMor(O::NfOrd, P::NfOrdIdl)
z = NfOrdToGFFmpzMor()
z.P = P
@@ -550,7 +550,7 @@ Mor(O::NfOrd, F::Nemo.GaloisFmpzField, h::gfp_fmpz_poly) = NfOrdToGFFmpzMor(O, F
#
################################################################################
-mutable struct NfToFinFldMor{T} <: Map{AnticNumberField, T, HeckeMap, NfToFinFldMor{T}}
+mutable struct NfToFinFldMor{T} <: Map{AnticNumberField, T, HeckeMap, NfToFinFldMor{T}}
header::MapHeader{AnticNumberField, T}
function NfToFinFldMor{T}() where T
@@ -613,7 +613,7 @@ evaluated using `image(map, elem)`.
The resulting map can be applied to
* `nf_elem`
* `FacElem{nf_elem}`
-Will throw a `BadPrime` exception if applied to an element in the
+Will throw a `BadPrime` exception if applied to an element in the
field with a $p$ in the denominator. In the case of `FacElem`, zero
is also not permitted (and will produce a `BadPrime` error).
"""
@@ -659,7 +659,7 @@ function image(mF::NfToFqMor_easy, a::FacElem{nf_elem, AnticNumberField}, quo::I
for (k, v) = a.fac
vv = v
if quo != 0
- vv = v % quo
+ vv = v % quo
if vv < 0
vv += quo
end
@@ -726,7 +726,7 @@ function image(mF::NfToFqNmodMor_easy, a::FacElem{nf_elem, AnticNumberField}, qu
for (k, v) = a.fac
# I want to map k^v to F. I can reduce mod q (reduction modulo q - 1 is
# done by the power function itself.
-
+
inver = false
if v < 0
@@ -782,7 +782,7 @@ function image(mF::NfToFqNmodMor_easy, a::FacElem{nf_elem, AnticNumberField}, D:
for (k, v) in a.fac
i += 1
-
+
inver = false
if v < 0
@@ -847,7 +847,7 @@ function image(mF::NfToFqNmodMor_easy, a::FacElem{nf_elem, AnticNumberField}, D:
if iszero(s)
throw(BadPrime(1))
end
-
+
if inver
ccall((:fq_nmod_inv, libflint), Nothing, (Ref{fq_nmod}, Ref{fq_nmod}, Ref{FqNmodFiniteField}), s, s, Fq)
end
@@ -916,7 +916,7 @@ function image(mF::NfToGFMor_easy, a::FacElem{nf_elem, AnticNumberField}, quo::I
for (k, v) = a.fac
vv = v
if quo != 0
- vv = v %quo
+ vv = v %quo
if vv < 0
vv += quo
end
@@ -1027,7 +1027,7 @@ function image(mF::NfToGFMor_easy, a::nf_elem, D::Vector, cached::Bool, n_quo::I
Fq = mF.Fq
p = mF.defining_pol
t = mF.t
-
+
@assert ismonic(p)
evaluateat = -coeff(p, 0)
@@ -1075,7 +1075,7 @@ function image(mF::NfToGFFmpzMor_easy, a::FacElem{nf_elem, AnticNumberField}, qu
for (k, v) = a.fac
vv = v
if quo != 0
- vv = v %quo
+ vv = v %quo
if vv < 0
vv += quo
end
diff --git a/src/Map/NumField.jl b/src/Map/NumField.jl
index 606a3a9edf..076fbefd48 100644
--- a/src/Map/NumField.jl
+++ b/src/Map/NumField.jl
@@ -88,13 +88,13 @@
# hom(::NfRelNS{nf_elem}, AnticNumberField, nf_elem, Vector{nf_elem}))
# - a homorphism base_field(K) -> base_field(L)
# hom(K, L, ::Vector{elem_type(L)})
-# - this assumes that the base_field of K embeds naturally into L
+# - this assumes that the base_field of K embeds naturally into L
#
# We also get a nice syntax to create inverses for free:
#
# hom(K, L, ..., inverse = (x))
#
-# where x is such that hom(L, K, x) works.
+# where x is such that hom(L, K, x) works.
#
export restrict
@@ -124,7 +124,7 @@ mutable struct NumFieldMor{S, T, U, V, W} <: Map{S, T, HeckeMap, NumFieldMor}
z.header = MapHeader(K, L)
return z
end
-
+
function NumFieldMor{S, T, U, V}(h::MapHeader{S, T}, i::U, p::V) where {S, T, U, V}
z = new{S, T, U, V, elem_type(S)}(h, i, p)
return z
@@ -151,7 +151,7 @@ function hom(K::S, L::T, x...; inverse = nothing,
# This goes through _validata_data, since we don't want to split the
# argument if for example the argument is a Vector
inverse_data = _map_data(L, K, inverse, check = check)
-
+
z = NumFieldMor{S, T, typeof(image_data),
typeof(inverse_data)}(header, image_data, inverse_data)
@@ -231,7 +231,7 @@ mutable struct MapDataFromAnticNumberField{T}
z.isid = true
return z
end
-
+
function MapDataFromAnticNumberField{T}(x::T) where T
z = new{T}(x, false)
return z
@@ -271,7 +271,7 @@ function map_data(K::AnticNumberField, L, x::NumFieldElem; check = true)
xx = x
else
xx = L(x)::elem_type(L)
- end
+ end
if check
if !iszero(evaluate(defining_polynomial(K), xx))
@@ -301,7 +301,7 @@ mutable struct MapDataFromNfRel{T, S}
z = new{T, S}(x, y, false)
return z
end
-
+
function MapDataFromNfRel{T, S}(x::Bool) where {T, S}
@assert x
z = new{T, S}()
@@ -374,7 +374,7 @@ function map_data(K::NfRel, L, x...; check = true)
@assert typeof(yy) == elem_type(L)
@assert typeof(z) == map_data_type(base_field(K), L)
-
+
return MapDataFromNfRel{typeof(yy), typeof(z)}(yy, z)
end
@@ -387,7 +387,7 @@ mutable struct MapDataFromNfAbsNS{T}
z = new{T}(x, false)
return z
end
-
+
function MapDataFromNfAbsNS{T}(x::Bool) where {T}
@assert x
z = new{T}()
@@ -406,7 +406,7 @@ function _isequal(K, L, u::MapDataFromNfAbsNS{T}, v::MapDataFromNfAbsNS{T}) wher
return true
end
- return v.images == u.images
+ return v.images == u.images
end
function image(f::MapDataFromNfAbsNS, L, y)
@@ -442,12 +442,12 @@ function map_data(K::NfAbsNS, L, x::Vector; check = true)
error("Data does not define a morphism")
end
end
- end
+ end
@assert typeof(xx) == Vector{elem_type(L)}
return MapDataFromNfAbsNS{typeof(xx)}(xx)
-end
+end
# From NfRelNS into something
mutable struct MapDataFromNfRelNS{T, S}
@@ -459,7 +459,7 @@ mutable struct MapDataFromNfRelNS{T, S}
z = new{T, S}(x, y, false)
return z
end
-
+
function MapDataFromNfRelNS{T, S}(x::Bool) where {T, S}
@assert x
z = new{T, S}()
diff --git a/src/Map/NumberField.jl b/src/Map/NumberField.jl
index 6f6fa6f3a7..d0d0806573 100644
--- a/src/Map/NumberField.jl
+++ b/src/Map/NumberField.jl
@@ -109,9 +109,9 @@ Base.copy(f::NfToNfMor) = f
isnormal(K::AnticNumberField) -> Bool
Returns true if $K$ is a normal extension of $\mathbb Q$, false otherwise.
-"""
+"""
function isnormal(K::AnticNumberField)
- #Before computing the automorphisms, I split a few primes and check if the
+ #Before computing the automorphisms, I split a few primes and check if the
#splitting behaviour is fine
c = get_special(K, :isnormal)
if c isa Bool
@@ -177,7 +177,7 @@ function iscm_field(K::NumField)
end
if isodd(degree(K)) || !istotally_complex(K)
return false, id_hom(K)
- end
+ end
if isautomorphisms_known(K)
auts = automorphisms(K, copy = false)
return _find_complex_conj(auts)
@@ -246,7 +246,7 @@ function iscm_field_easy(K::AnticNumberField)
if !fl
return false
end
- j += 1
+ j += 1
end
i += 1
end
@@ -297,7 +297,7 @@ function induce_image(f::NfToNfMor, x::NfOrdIdl)
OK = order(x)
K = nf(OK)
- if has_2_elem(x) && ismaximal_known(OK) && ismaximal(OK)
+ if has_2_elem(x) && ismaximal_known(OK) && ismaximal(OK)
int_in_ideal = x.gen_one
if has_minimum(x)
int_in_ideal = minimum(x, copy = false)
diff --git a/src/Map/Old.jl b/src/Map/Old.jl
index 4773444ca2..fbea621f87 100644
--- a/src/Map/Old.jl
+++ b/src/Map/Old.jl
@@ -16,7 +16,7 @@ mutable struct ResidueRingPolyMap{D, C, T} <: Map{D, C, HeckeMap, ResidueRingPol
end
return I::elem_type(C)
end
-
+
# I need to call preimage in _preimage
_preimage = function(a::Generic.Res)
R = codomain
@@ -37,7 +37,7 @@ mutable struct ResidueRingPolyMap{D, C, T} <: Map{D, C, HeckeMap, ResidueRingPol
## over rings than fields?
s = s[1] * inv(s[2]) # all rings here (type) are actually fields (math)
end
-
+
s = sum([preimage(z.coeff_map, s[i,1])*g[i] for i=1:length(g)])
@assert parent(s) == domain
return s::elem_type(domain)
diff --git a/src/Map/automorphisms.jl b/src/Map/automorphisms.jl
index b31a39ddce..b2dd37dce3 100644
--- a/src/Map/automorphisms.jl
+++ b/src/Map/automorphisms.jl
@@ -128,7 +128,7 @@ end
automorphism_type(::AnticNumberField) = NfToNfMor
automorphism_type(::NfAbsNS) = NfAbsNSToNfAbsNS
-
+
function automorphisms(K::NumField{fmpq}; copy::Bool = true, isabelian::Bool = false)
T = automorphism_type(K)
if isautomorphisms_known(K)
@@ -155,7 +155,7 @@ function automorphisms(K::NumField{fmpq}; copy::Bool = true, isabelian::Bool = f
return auts
end
end
-
+
function isautomorphisms_known(K::AnticNumberField)
return _get_automorphisms_nf(K, false) != nothing
end
@@ -193,7 +193,7 @@ end
automorphism_group(K::AnticNumberField) -> GenGrp, GrpGenToNfMorSet
Given a number field $K$, this function returns a group $G$ and a map from $G$ to the automorphisms of $K$.
-"""
+"""
function automorphism_group(K::AnticNumberField)
if Nemo.iscyclo_type(K)
return _automorphism_group_cyclo(K)
@@ -381,7 +381,7 @@ function _automorphisms_abelian(K::AnticNumberField)
Fx = PolynomialRing(F, cached = false)[1]
fF = Fx(K.pol)
if degree(fF) != degree(K) || iszero(discriminant(fF))
- continue
+ continue
end
@vprint :Automorphisms 1 "Trying $p \n"
@vtime :Automorphisms 1 isnew, h = _frobenius_at(K, p, auts)
@@ -425,7 +425,7 @@ function lift_root(K::AnticNumberField, b, bound::Int)
mul!(r, r, dF)
mod_sym!(r, modu)
i = 0
- while i < bound && r != r_old && !check_root(K, test, r)
+ while i < bound && r != r_old && !check_root(K, test, r)
i += 1
modu = modu^2
R = ResidueRing(FlintZZ, modu, cached = false)
@@ -473,7 +473,7 @@ function _frobenius_at(K::AnticNumberField, p::Int, auts::Vector{NfToNfMor} = Nf
return true, hom(K, K, rt, check = false)
else
return false, id_hom(K)
- end
+ end
end
@@ -492,7 +492,7 @@ function _coefficients_bound(K::AnticNumberField)
E = EquationOrder(K)
c1, c2 = norm_change_const(E)
- #First, t2 norm
+ #First, t2 norm
R = parent(bound_root[1])
bd = zero(R)
for i in 1:r1
@@ -550,7 +550,7 @@ function _automorphisms_center(K::AnticNumberField)
Fx = PolynomialRing(F, cached = false)[1]
fF = Fx(K.pol)
if degree(fF) != degree(K) || iszero(discriminant(fF))
- continue
+ continue
end
lf = factor_distinct_deg(fF)
if length(lf) != 1
@@ -589,7 +589,7 @@ function isabelian2(K::AnticNumberField)
Fx, gFx = PolynomialRing(F, cached = false)
fF = Fx(K.pol)
if degree(fF) != degree(K) || iszero(discriminant(fF))
- continue
+ continue
end
lf = factor_distinct_deg(fF)
if length(lf) != 1
diff --git a/src/Misc/FactoredElem.jl b/src/Misc/FactoredElem.jl
index 672e115b2f..f06e188de8 100644
--- a/src/Misc/FactoredElem.jl
+++ b/src/Misc/FactoredElem.jl
@@ -22,7 +22,7 @@ function add_to_key!(D::Dict{S, T}, k::S, v::T; remove_zero::Bool = true) where
if w != v && iszero(cmpabs(w, v))
Base._delete!(D, hash_k)
else
- @inbounds D.vals[hash_k] = w + v
+ @inbounds D.vals[hash_k] = w + v
end
else
@inbounds D.vals[hash_k] = w + v
@@ -312,7 +312,7 @@ function *(x::FacElem{B, S}, y::FacElem{B, S}) where {B, S}
for (a, v) in y
add_to_key!(z.fac, a, v, remove_zero = true)
end
-
+
return z
end
diff --git a/src/Misc/FactoredElemIntegers.jl b/src/Misc/FactoredElemIntegers.jl
index 4584cbf969..649376146a 100644
--- a/src/Misc/FactoredElemIntegers.jl
+++ b/src/Misc/FactoredElemIntegers.jl
@@ -5,7 +5,7 @@ const FacElemQ = Union{FacElem{fmpq, FlintRationalField}, FacElem{fmpz, FlintInt
evaluate(x::FacElem{fmpz}) -> fmpz
Expands or evaluates the factored element, i.e. actually computes the
-the element.
+the element.
Works by first obtaining a simplified version of the power product
into coprime base elements.
"""
@@ -102,7 +102,7 @@ function simplify!(x::FacElem{fmpz})
for (b, vb) in x
v += valuation(b, abs(p))*vb
end
- if v < 0
+ if v < 0
throw(DomainError(v, "Negative valuation in simplify!"))
end
if v != 0
diff --git a/src/Misc/Fields.jl b/src/Misc/Fields.jl
index 9bb88c2b39..7d3fafffca 100644
--- a/src/Misc/Fields.jl
+++ b/src/Misc/Fields.jl
@@ -86,7 +86,7 @@ mutable struct FldToVecMor{R, S, T, U, V}
z.isone = isone(M)
return z
end
-
+
function FldToVecMor(L, Q)
K = Q
L = L
diff --git a/src/Misc/FiniteField.jl b/src/Misc/FiniteField.jl
index 9d50e9fdb6..f69f14426e 100644
--- a/src/Misc/FiniteField.jl
+++ b/src/Misc/FiniteField.jl
@@ -74,9 +74,9 @@ function Base.iterate(F::FqNmodFiniteField, st::Vector{UInt})
st[j + 1] = st[j + 1] + 1
end
end
-
+
d = F()
- ccall((:fq_nmod_init2, libflint), Nothing,
+ ccall((:fq_nmod_init2, libflint), Nothing,
(Ref{fq_nmod}, Ref{FqNmodFiniteField}), d, F)
for j in 1:length(st)
ccall((:nmod_poly_set_coeff_ui, libflint), Nothing,
@@ -119,7 +119,7 @@ function Base.iterate(F::FqFiniteField, st::Vector{fmpz})
end
d = F()
- ccall((:fq_init2, libflint), Nothing,
+ ccall((:fq_init2, libflint), Nothing,
(Ref{fq}, Ref{FqFiniteField}), d, F)
g = Hecke.Globals.Zx()
for j in 1:length(st)
@@ -197,7 +197,7 @@ function _nf_to_fq!(a::fq_nmod, b::nf_elem, K::FqNmodFiniteField, a_tmp::nmod_po
a, a_tmp, K)
_reduce(a)
end
-
+
function _nf_to_fq!(a::fq_nmod, b::nf_elem, K::FqNmodFiniteField, a_tmp::gfp_poly)
nf_elem_to_gfp_poly!(a_tmp, b)
ccall((:fq_nmod_set, libflint), Nothing,
@@ -256,7 +256,7 @@ function has_primitive_root_1(K::Nemo.FqNmodFiniteField, m::Int)
continue
end
return true, g^div(size(K)-1, m)
- end
+ end
end
@@ -386,7 +386,7 @@ function unit_group(F::T; n_quo::Int = -1) where T <: FinField
else
return G([mod(inv*disc_log_bs_gs(g, y, npart), k)])
end
- end
+ end
mG = FiniteFieldMultGrpMap{T, elem_type(F)}(G, F, g, disc_log)
return G, mG
end
@@ -502,7 +502,7 @@ struct FrobeniusCtx
fb::VeryBad
K::FqNmodFiniteField
i::Int
-
+
function FrobeniusCtx(K::FqNmodFiniteField, i::Int = 1)
m = frobenius_matrix(K, i)
return new(m, VeryBad(m.n, m.ninv, m.norm), VeryBad(m.n, m.ninv, m.norm), K, i)
diff --git a/src/Misc/IJulia.jl b/src/Misc/IJulia.jl
index 7e55e9f6e1..b5ae816605 100644
--- a/src/Misc/IJulia.jl
+++ b/src/Misc/IJulia.jl
@@ -151,7 +151,7 @@ function math_html(io::IO, a::nf_elem)
t = Symbol("\\zeta_{$c}")
end
end
- if s in [:_a, Symbol("_\$")]
+ if s in [:_a, Symbol("_\$")]
t = Symbol("\\alpha")
end
parent(a).S = t
@@ -264,7 +264,7 @@ end
math_html(io::IO, a::Rational) = math_html(io, fmpq(a))
-#function Base.show(io::IO, ::MIME"text/html", a::Rational)
+#function Base.show(io::IO, ::MIME"text/html", a::Rational)
# print(io, "\$")
# math_html(io, a)
# print(io, "\$")
@@ -294,7 +294,7 @@ end
#= infinite recursion through generic math_html, so don't
-function Base.show(io::IO, ::MIME"text/html", a)
+function Base.show(io::IO, ::MIME"text/html", a)
print(io, "\$")
math_html(io, a)
print(io, "\$")
@@ -359,7 +359,7 @@ function math_html(io::IO, O::NfAbsOrd{AnticNumberField, nf_elem})
return
end
n = find_name(nf(O))
- if n === nothing
+ if n === nothing
print(io, "\\text{$n }")
math_html(io, nf(O))
else
@@ -437,7 +437,7 @@ function math_html(io::IO, G::GrpAbFinGen)
n = find_name(G)
if !(n === nothing) && get(io, :compact, false)
print(io, string(n))
- return
+ return
end
s = get_special(G, :show)
if s !== nothing
@@ -465,7 +465,7 @@ function math_html(io::IO, R::PolyRing)
n = find_name(R)
if !(n === nothing) && get(io, :compact, false)
print(io, string(n))
- return
+ return
end
print(io, "\\text{Polynomial ring over }")
print(IOContext(io, :compact => true), base_ring(R))
@@ -481,7 +481,7 @@ function math_html(io::IO, K::NfRel)
n = find_name(K)
if !(n === nothing) && get(io, :compact, false)
print(io, string(n))
- return
+ return
end
print(io, "\\text{Relative number field over }")
math_html(IOContext(io, :compact => true), base_field(K))
diff --git a/src/Misc/Integer.jl b/src/Misc/Integer.jl
index 8890e326be..6752e8a9a3 100644
--- a/src/Misc/Integer.jl
+++ b/src/Misc/Integer.jl
@@ -126,7 +126,7 @@ iscommutative(::FlintIntegerRing) = true
# end
# return fmpz(0)
# end
-#
+#
# if a == 1
# return fmpz(1)
# end
@@ -147,7 +147,7 @@ function ^(a::fmpq, k::fmpz)
end
return fmpq(0)
end
-
+
if a == 1
return fmpq(1)
end
@@ -1559,7 +1559,7 @@ end
Returns a vector containing all the squarefree numbers up to $n$.
"""
function squarefree_up_to(n::Int; coprime_to::Vector{fmpz} = fmpz[], prime_base::Vector{fmpz} = fmpz[])
-
+
@assert isempty(coprime_to) || isempty(prime_base)
if !isempty(prime_base)
listi = Int[1]
diff --git a/src/Misc/MPoly.jl b/src/Misc/MPoly.jl
index 7ea086fd16..bf2487528e 100644
--- a/src/Misc/MPoly.jl
+++ b/src/Misc/MPoly.jl
@@ -53,7 +53,7 @@ end
#
#Tests if $f$ involves only one variable. If so, return a corresponding univariate polynomial.
#"""
-#function isunivariate(f::Generic.MPoly{T}) where T
+#function isunivariate(f::Generic.MPoly{T}) where T
# kx, x = PolynomialRing(base_ring(f), "x", cached = false)
# if ngens(parent(f)) == 1
# f1 = kx()
@@ -108,7 +108,7 @@ end
#not used here
"""
-`content` as a polynomial in the variable `i`, i.e. the gcd of all the
+`content` as a polynomial in the variable `i`, i.e. the gcd of all the
coefficients when viewed as univariate polynomial in `i`.
"""
function Hecke.content(f::MPolyElem, i::Int)
diff --git a/src/Misc/MPolyFactor.jl b/src/Misc/MPolyFactor.jl
index 9114d24f01..1ef8a06d37 100644
--- a/src/Misc/MPolyFactor.jl
+++ b/src/Misc/MPolyFactor.jl
@@ -828,7 +828,7 @@ end
(false, junk, junk) if the ufacs don't lift straight to bivariate ones
TODO: allow this function to do a bit of zassenhaus and add a parameter to
- limit the size of the subsets.
+ limit the size of the subsets.
=#
function hlift_bivar_combine(
a::E,
@@ -1026,7 +1026,7 @@ end
#=
Try to determine divisors of the leading coefficients of the factors of A.
This is accomplished by looking at the bivariate factoration of A when
- all but one of the minor variables are evaluated away. The resulting
+ all but one of the minor variables are evaluated away. The resulting
univariate leading coefficients are lifted against the supplied
leading_coefficient(A) factorization. return is Tuple{::Boole, ::Vector{E}}
If the bool is true, then the method can be considered to have fully found
@@ -1131,7 +1131,7 @@ function mfactor_irred_mvar_char_zero(
# make sure univar is squarefree. TODO also zassenhaus pruning here
ok, fac = mfactor_irred_univar(evals[1], mainvar)
if !ok
- @goto next_alpha
+ @goto next_alpha
end
r = length(fac)
@@ -1216,7 +1216,7 @@ function mfactor_irred_char_zero(a::E) where E
if !isone(lc)
res.unit = lc
a *= inv(lc)
- end
+ end
degs = degrees(a)
vars = Int[] # variables that actually appear
@@ -1326,7 +1326,7 @@ function factor(a::MPolyElem)
return mfactor_char_zero(a)
else
error("factor not implemented for the ring $R")
- end
+ end
end
function factor_squarefree(a::MPolyElem)
@@ -1336,6 +1336,6 @@ function factor_squarefree(a::MPolyElem)
return mfactor_squarefree_char_zero(a)
else
error("factor_squarefree not implemented for the ring $R")
- end
+ end
end
diff --git a/src/Misc/MSet.jl b/src/Misc/MSet.jl
index 34a08769f5..78e29db3ed 100644
--- a/src/Misc/MSet.jl
+++ b/src/Misc/MSet.jl
@@ -27,9 +27,9 @@ function Base.show(io::IO, ::MIME"text/plain", s::MSet)
first || print(io, ", ")
first = false
if v > 1
- print(io, "$k : $v")
+ print(io, "$k : $v")
else
- print(io, "$k")
+ print(io, "$k")
end
end
print(io,")")
@@ -50,7 +50,7 @@ function Base.push!(s::MSet, x, mult::Int = 1)
#end
end
-function Base.pop!(s::MSet, x)
+function Base.pop!(s::MSet, x)
s.dict[x] -= 1
if s.dict[x] == 0
delete!(s.dict, x)
@@ -238,7 +238,7 @@ function subsets(s::Set{T}, k::Int) where T
end
end
push!(C, B)
- k -=1
+ k -=1
end
return SubSetSizeItr{T}(b, length(C), C, m)
diff --git a/src/Misc/Matrix.jl b/src/Misc/Matrix.jl
index e6b26427d7..a3dc0a49f0 100644
--- a/src/Misc/Matrix.jl
+++ b/src/Misc/Matrix.jl
@@ -138,7 +138,7 @@ function saturate(A::fmpz_mat)
Hi, d = pseudo_inv(H)
S = Hi*A
divexact!(S, S, d)
- end
+ end
# @hassert :HNF 1 d*Sd == S
return S
end
@@ -378,7 +378,7 @@ function ishnf(x::fmpz_mat, shape::Symbol)
end
j = ncols(x)
- while j >= 0 && iszero_entry(x, i, j)
+ while j >= 0 && iszero_entry(x, i, j)
j = j - 1
end
if j == -1
@@ -1325,8 +1325,8 @@ end
function snf_for_groups(A::fmpz_mat, mod::fmpz)
R = identity_matrix(FlintZZ, ncols(A))
S = deepcopy(A)
-
-
+
+
if !isdiagonal(S)
T = zero_matrix(FlintZZ, ncols(A), ncols(A))
GC.@preserve S R T begin
@@ -1504,7 +1504,7 @@ end
function isdiagonal(A::fmpz_mat)
for i = 1:ncols(A)
for j = 1:nrows(A)
- if i != j
+ if i != j
t = ccall((:fmpz_mat_entry, libflint), Ptr{fmpz}, (Ref{fmpz_mat}, Int, Int), A, j - 1, i - 1)
fl = ccall((:fmpz_is_zero, libflint), Bool, (Ref{fmpz},), t)
if !fl
diff --git a/src/Misc/Plesken.jl b/src/Misc/Plesken.jl
index 2b662c4649..81e5e12956 100644
--- a/src/Misc/Plesken.jl
+++ b/src/Misc/Plesken.jl
@@ -55,13 +55,13 @@ end
################################################################################
#
-# Presentation for extensions of prime power degree
+# Presentation for extensions of prime power degree
#
################################################################################
@doc Markdown.doc"""
presentation(p, r, n) -> FinField
-Computes a presentation for the finite field of order p^(r^n) as defined
+Computes a presentation for the finite field of order p^(r^n) as defined
by Plesken.
"""
function presentation(p::T, r::T, n::Int) where T <: Union{fmpz, Int}
@@ -94,7 +94,7 @@ function _presentation_artin_schreier(F, n)
end
function smallest_pkth_root(F, r)
- #First, I find a rk-th root of unity
+ #First, I find a rk-th root of unity
#by taking random elements
p = order(F)
nit, cop = ppio(p-1, fmpz(r))
@@ -104,7 +104,7 @@ function smallest_pkth_root(F, r)
x = rand(F)^cop
end
k = valuation(p-1, r)
- #Now, iteratively, I search for
+ #Now, iteratively, I search for
#the smallest r-th root
pow_ind = 1
for i = 1:k
@@ -131,7 +131,7 @@ function _presentation_kummer(F, r::T, n::Int) where T <: Union{fmpz, Int}
def_pol1 = Fx()
setcoeff!(def_pol1, 0, -pr_root)
- setcoeff!(def_pol1, r^n, one(F))
+ setcoeff!(def_pol1, r^n, one(F))
F1, gF1 = FiniteField(def_pol1, "a1", cached = false, check = false)
return F1
end
diff --git a/src/Misc/Poly.jl b/src/Misc/Poly.jl
index a363b574c2..ac509ce302 100644
--- a/src/Misc/Poly.jl
+++ b/src/Misc/Poly.jl
@@ -80,7 +80,7 @@ Apply `rational_reconstruction` to each coefficient of $a$, resulting
in either a fail (return (false, s.th.)) or (true, g) for some rational
polynomial $g$ s.th. $g \equiv a \bmod M$.
"""
-function induce_rational_reconstruction(a::fmpz_poly, M::fmpz; parent=PolynomialRing(FlintQQ, parent(a).S, cached = false)[1])
+function induce_rational_reconstruction(a::fmpz_poly, M::fmpz; parent=PolynomialRing(FlintQQ, parent(a).S, cached = false)[1])
b = parent()
for i=0:degree(a)
fl, x,y = rational_reconstruction(coeff(a, i), M)
@@ -162,12 +162,12 @@ function my_compose_mod(x::fmpz_mod_poly, y::fmpz_mod_poly, z::fmpz_mod_poly)
end
function my_compose_mod_precomp(x::fmpz_mod_poly, A::fmpz_mat, z::fmpz_mod_poly, zinv::fmpz_mod_poly)
-
+
if degree(x) < degree(z)
res1 = compose_mod_precomp(x, A, z, zinv)
return res1
end
-
+
#First, I compute x^degree(z) mod z
#The rows of A contain the powers up to sqrt(degree(z))...
Rx = parent(x)
@@ -180,7 +180,7 @@ function my_compose_mod_precomp(x::fmpz_mod_poly, A::fmpz_mat, z::fmpz_mod_poly,
yind = mulmod(yind, ydiff, z)
end
x1 = shift_right(x, degree(z))
- res = mulmod(compose_mod_precomp(x1, A, z, zinv), yind, z)
+ res = mulmod(compose_mod_precomp(x1, A, z, zinv), yind, z)
x2 = truncate(x, degree(z))
add!(res, res, compose_mod_precomp(x2, A, z, zinv))
return res
@@ -832,7 +832,7 @@ function factor_equal_deg(x::gfp_fmpz_poly, d::Int)
end
return res
end
-
+
################################################################################
#
# Squarefree factorization for fmpq_poly
@@ -1146,7 +1146,7 @@ function mod(f::AbstractAlgebra.PolyElem{T}, g::AbstractAlgebra.PolyElem{T}) whe
c = base_ring(f)()
while length(f) >= length(g)
l = -leading_coefficient(f)
- for i = 1:length(g)
+ for i = 1:length(g)
c = mul!(c, coeff(g, i - 1), l)
u = coeff(f, i + length(f) - length(g) - 1)
u = addeq!(u, c)
@@ -1177,7 +1177,7 @@ function Base.divrem(f::AbstractAlgebra.PolyElem{T}, g::AbstractAlgebra.PolyElem
q1 = leading_coefficient(f)
l = -q1
q = setcoeff!(q, length(f) - length(g), q1*binv)
- for i = 1:length(g)
+ for i = 1:length(g)
c = mul!(c, coeff(g, i - 1), l)
u = coeff(f, i + length(f) - length(g) - 1)
u = addeq!(u, c)
@@ -1192,7 +1192,7 @@ end
@doc Markdown.doc"""
fmpz_poly_read!(a::fmpz_poly, b::String) -> fmpz_poly
-Use flint's native read function to obtain the polynomial in the file with name `b`.
+Use flint's native read function to obtain the polynomial in the file with name `b`.
"""
function fmpz_poly_read!(a::fmpz_poly, b::String)
f = ccall((:fopen, :libc), Ptr{Nothing}, (Cstring, Cstring), b, "r")
@@ -1203,7 +1203,7 @@ end
@doc Markdown.doc"""
mahler_measure_bound(f::fmpz_poly) -> fmpz
-
+
A upper bound on the Mahler measure of `f`.
The Mahler measure is the product over the roots of absolute value at least `1`.
"""
@@ -1243,7 +1243,7 @@ function prod1(a::Vector{T}; inplace::Bool = false) where T <: PolyElem
else
anew[end] = a[end]*a[end-1]
end
- end
+ end
return prod1(anew, inplace = true)
end
diff --git a/src/Misc/Primes.jl b/src/Misc/Primes.jl
index 34f923b08c..a734b9621c 100644
--- a/src/Misc/Primes.jl
+++ b/src/Misc/Primes.jl
@@ -65,7 +65,7 @@ struct PrimesSet{T}
end
if !isone(gcd(mod, val))
error("Modulus and value need to be coprime.")
- end
+ end
r = new{T}(f, t, false, false, mod, val, sv)
return r
end
@@ -77,20 +77,20 @@ end
Returns an iterable object $S$ representing the prime numbers $p$
for $f \le p \le t$. If $t=-1$, then the upper bound is infinite.
-"""
+"""
function PrimesSet(f::T, t::T) where T
return PrimesSet{T}(f, t)
end
@doc Markdown.doc"""
- PrimesSet(f::Integer, t::Integer, mod::Integer, val::Integer)
- PrimesSet(f::fmpz, t::fmpz, mod::fmpz, val::fmpz)
+ PrimesSet(f::Integer, t::Integer, mod::Integer, val::Integer)
+ PrimesSet(f::fmpz, t::fmpz, mod::fmpz, val::fmpz)
Returns an iterable object $S$ representing the prime numbers $p$
for $f \le p \le t$ and $p\equiv val \bmod mod$ (primes in arithmetic
-progression).
+progression).
If $t=-1$, then the upper bound is infinite.
-"""
+"""
function PrimesSet(f::T, t::T, mod::T, val::T) where {T}
return PrimesSet{T}(f, t, mod, val)
end
@@ -118,7 +118,7 @@ function Base.iterate(A::PrimesSet{T}) where {T <: Integer}
end
end
- curr = A.from
+ curr = A.from
c = curr % A.mod
if A.mod > 1 && c != A.a
curr += (- c + A.a) % A.mod
@@ -165,7 +165,7 @@ function Base.iterate(A::PrimesSet{fmpz})
end
end
- curr = A.from
+ curr = A.from
c = curr % A.mod
if A.mod > 1 && c != A.a
curr += (-c + A.a) % A.mod
@@ -182,7 +182,7 @@ function Base.iterate(A::PrimesSet{fmpz})
break
end
end
-
+
if A.to != -1 && curr > A.to
return nothing
else
@@ -248,7 +248,7 @@ end
# return p
# end
#
-# curr = A.from
+# curr = A.from
# c = curr % A.mod
# if A.mod > 1 && c != A.a
# curr += (- c + A.a) % A.mod
@@ -274,7 +274,7 @@ end
# return p
# end
#
-# curr = A.from
+# curr = A.from
# c = curr % A.mod
# if A.mod > 1 && c != A.a
# curr += (-c + A.a) % A.mod
diff --git a/src/Misc/PseudoPolynomial.jl b/src/Misc/PseudoPolynomial.jl
index c6d5bff143..f25603f83f 100644
--- a/src/Misc/PseudoPolynomial.jl
+++ b/src/Misc/PseudoPolynomial.jl
@@ -1,7 +1,7 @@
mutable struct PseudoPoly{S, T}
poly::S
coeff::T
-
+
function PseudoPoly{S, T}(f::S, A::T) where {S, T}
return new{S, T}(f, A)
end
@@ -209,7 +209,7 @@ function gb(G::Vector{S}, mmod) where {S}
r = reduce(r, GG)
-
+
if iszero(polynomial(r))
continue
end
diff --git a/src/Misc/RatRecon.jl b/src/Misc/RatRecon.jl
index 92ea3ecf23..43ba9ed7b2 100644
--- a/src/Misc/RatRecon.jl
+++ b/src/Misc/RatRecon.jl
@@ -199,7 +199,7 @@ function rational_reconstruction_subres(g::PolyElem{T}, f::PolyElem{T}, bnd::Int
elseif !isone(g)
return false, l_rt[1], l_rt[2]
else
- return true, l_rt[1], l_rt[2]
+ return true, l_rt[1], l_rt[2]
end
else
g = gcd(r_m, t_m)
@@ -233,8 +233,8 @@ function rational_reconstruction_mod(g::fmpq_poly, f::fmpq_poly, bnd::Int = -1;
rethrow(e)
end
end
- # bound n and a starting p
- kp = 10
+ # bound n and a starting p
+ kp = 10
L =[]
pp = FlintZZ(1)
j = 0
@@ -279,7 +279,7 @@ function _modp_results(g::fmpq_poly,f::fmpq_poly, p::fmpz, M::Int, n::Int, Error
gp = Rp(g)
fp = Rp(f)
fl, nu_p, de_p = rational_reconstruction_subres(gp, fp, -1, ErrorTolerant = ErrorTolerant)
- if fl
+ if fl
ut = Rp(inv(leading_coefficient(de_p)))
push!(l1, ut*nu_p)
push!(l2, ut*de_p)
diff --git a/src/Misc/RelFiniteField.jl b/src/Misc/RelFiniteField.jl
index a83c4f4bc8..9d75b8ff57 100644
--- a/src/Misc/RelFiniteField.jl
+++ b/src/Misc/RelFiniteField.jl
@@ -52,7 +52,7 @@ var(F::RelFinField) = F.var
prime_field(F::RelFinField; cached::Bool = true) = prime_field(base_field(F), cached = cached)
-function defining_polynomial(F::RelFinField{T}) where T
+function defining_polynomial(F::RelFinField{T}) where T
return F.defining_polynomial::dense_poly_type(T)
end
@@ -79,7 +79,7 @@ absolute_degree(F::FinField) = degree(F)
#
################################################################################
-function Base.deepcopy_internal(x::RelFinFieldElem{S, T}, id::IdDict) where {S, T}
+function Base.deepcopy_internal(x::RelFinFieldElem{S, T}, id::IdDict) where {S, T}
return RelFinFieldElem{S, T}(x.parent, Base.deepcopy_internal(x.data, id))
end
@@ -93,7 +93,7 @@ AbstractAlgebra.promote_rule(::Type{RelFinFieldElem{S, T}}, ::Type{fmpz}) where
AbstractAlgebra.promote_rule(::Type{fmpz}, ::Type{RelFinFieldElem{S, T}}) where {S, T} = RelFinFieldElem{S, T}
-function AbstractAlgebra.promote_rule(::Type{RelFinFieldElem{RelFinField{S}, T}}, ::Type{V}) where {S, T, V <: Union{fq_nmod, fq, gfp_elem, gfp_fmpz_elem}}
+function AbstractAlgebra.promote_rule(::Type{RelFinFieldElem{RelFinField{S}, T}}, ::Type{V}) where {S, T, V <: Union{fq_nmod, fq, gfp_elem, gfp_fmpz_elem}}
U = AbstractAlgebra.promote_rule(S, fq_nmod)
if U === S
return RelFinFieldElem{RelFinField{S}, T}
@@ -102,7 +102,7 @@ function AbstractAlgebra.promote_rule(::Type{RelFinFieldElem{RelFinField{S}, T}}
end
end
-function AbstractAlgebra.promote_rule(::Type{V}, ::Type{RelFinFieldElem{RelFinField{S}, T}}) where {S, T, V <: Union{fq_nmod, fq, gfp_elem, gfp_fmpz_elem}}
+function AbstractAlgebra.promote_rule(::Type{V}, ::Type{RelFinFieldElem{RelFinField{S}, T}}) where {S, T, V <: Union{fq_nmod, fq, gfp_elem, gfp_fmpz_elem}}
U = AbstractAlgebra.promote_rule(S, fq_nmod)
if U === S
return RelFinFieldElem{RelFinField{S}, T}
@@ -115,7 +115,7 @@ function AbstractAlgebra.promote_rule(::Type{RelFinFieldElem{RelFinField{S}, T}}
NT = AbstractAlgebra.promote_rule(S, U)
if NT === S
return RelFinFieldElem{RelFinField{S}, T}
- elseif NT === U
+ elseif NT === U
return RelFinFieldElem{RelFinField{U}, V}
else
return Union{}
@@ -139,7 +139,7 @@ iszero(x::RelFinFieldElem) = iszero(x.data)
isone(x::RelFinFieldElem) = isone(x.data)
isunit(x::RelFinFieldElem) = !iszero(x)
-==(x::RelFinFieldElem{S, T}, y::RelFinFieldElem{S, T}) where {S, T} = x.data == y.data
+==(x::RelFinFieldElem{S, T}, y::RelFinFieldElem{S, T}) where {S, T} = x.data == y.data
coeff(a::RelFinFieldElem, i::Int) = coeff(a.data, i)
@@ -175,7 +175,7 @@ function (F::RelFinField{T})(x::S) where {S <: Union{Integer, fmpz}, T}
return F(parent(defining_polynomial(F))(x))
end
-function (F::RelFinField{T})(x::PolyElem{T}) where T
+function (F::RelFinField{T})(x::PolyElem{T}) where T
r = mod(x, defining_polynomial(F))
return RelFinFieldElem{typeof(F), typeof(r)}(F, r)
end
@@ -211,7 +211,7 @@ function (F::RelFinField{T})(x::gfp_fmpz_elem) where T
return F(parent(defining_polynomial(F))(y))
end
-function (F::RelFinField{T})(x::S) where {S, T}
+function (F::RelFinField{T})(x::S) where {S, T}
U = AbstractAlgebra.promote_rule(elem_type(F), S)
if U == S
#I an trying to coerce x to the subfield F!
@@ -229,28 +229,28 @@ end
function (F::GaloisField)(a::RelFinFieldElem)
for i = 1:degree(parent(a))-1
- @assert iszero(coeff(a, i))
+ @assert iszero(coeff(a, i))
end
return F(coeff(a, 0))
end
function (F::GaloisField)(a::fq_nmod)
for i = 1:degree(parent(a))-1
- @assert iszero(coeff(a, i))
+ @assert iszero(coeff(a, i))
end
return F(coeff(a, 0))
end
function (F::GaloisFmpzField)(a::RelFinFieldElem)
for i = 1:degree(parent(a))-1
- @assert iszero(coeff(a, i))
+ @assert iszero(coeff(a, i))
end
return F(coeff(a, 0))
end
function (F::GaloisFmpzField)(a::fq)
for i = 1:degree(parent(a))-1
- @assert iszero(coeff(a, i))
+ @assert iszero(coeff(a, i))
end
return F(coeff(a, 0))
end
@@ -341,7 +341,7 @@ function Base.:(^)(a::RelFinFieldElem, b::Int)
b = mul!(b, b, a)
return b
end
-end
+end
################################################################################
#
@@ -361,7 +361,7 @@ function assure_traces(F::RelFinField{T}) where T
res = T[base_field(F)(degree(F))]
append!(res, polynomial_to_power_sums(defining_polynomial(F), degree(F)-1))
F.basis_tr = res
- return nothing
+ return nothing
end
function tr(x::RelFinFieldElem)
@@ -397,7 +397,7 @@ function minpoly(a::T, Rx::PolyRing = PolynomialRing(base_field(parent(a)), "x",
end
end
Fx, x = PolynomialRing(F, "x", cached = false)
- minp = prod([x - Fx(y) for y in conjs])
+ minp = prod([x - Fx(y) for y in conjs])
Fp = base_ring(Rx)
coeffs = Vector{elem_type(Fp)}(undef, degree(minp)+1)
@@ -450,8 +450,8 @@ function absolute_minpoly(a::T, Rx::PolyRing = PolynomialRing(prime_field(parent
end
end
Fx, x = PolynomialRing(F, "x", cached = false)
- minp = prod(typeof(x)[x - Fx(y) for y in conjs])
-
+ minp = prod(typeof(x)[x - Fx(y) for y in conjs])
+
#Now, I need to coerce the polynomial down to a gfp_poly/gfp_fmpz_poly
Fp = base_ring(Rx)
coeffs = Vector{elem_type(Fp)}(undef, degree(minp)+1)
@@ -514,7 +514,7 @@ function absolute_coordinates(x::FinFieldElem)
end
for i = 1:length(v)
v[i] = Fp(coeff(x, i-1))
- end
+ end
return v
end
@@ -610,7 +610,7 @@ function hom(F::FinField, K::RelFinField, a::RelFinFieldElem; check::Bool = true
M[i, j] = Kp(v[j])
end
end
-
+
aux = zero_matrix(Kp, 1, absolute_degree(F))
aux1 = zero_matrix(Kp, 1, absolute_degree(K))
bF = absolute_basis(F)
@@ -624,7 +624,7 @@ function hom(F::FinField, K::RelFinField, a::RelFinFieldElem; check::Bool = true
mul!(aux1, aux, M)
pol = sum(aux1[1, i]*bK[i] for i = 1:absolute_degree(K))
return pol
- end
+ end
function preimg(x::FinFieldElem)
@assert parent(x) == K
diff --git a/src/Misc/ResidueRingPoly.jl b/src/Misc/ResidueRingPoly.jl
index 395a2fdcd1..55441a7d17 100644
--- a/src/Misc/ResidueRingPoly.jl
+++ b/src/Misc/ResidueRingPoly.jl
@@ -1,7 +1,7 @@
import Nemo.characteristic, Nemo.gen, Nemo.size
export gen, characteristic, size, elem_to_mat_row!, rand
-function gen(R::Union{Generic.ResRing{T},Generic.ResField{T}}) where T<:PolyElem
+function gen(R::Union{Generic.ResRing{T},Generic.ResField{T}}) where T<:PolyElem
return R(gen(base_ring(R)))
end
@@ -9,8 +9,8 @@ function gen(R::Union{Generic.ResRing{fq_nmod_poly},Generic.ResField{fq_nmod_pol
return R(gen(base_ring(R))) ## and I don't know why
end
-function gen(R::Union{Generic.ResRing{nmod_poly},Generic.ResField{nmod_poly}})
- return R(gen(base_ring(R)))
+function gen(R::Union{Generic.ResRing{nmod_poly},Generic.ResField{nmod_poly}})
+ return R(gen(base_ring(R)))
end
function characteristic(R::Union{Generic.ResRing{Nemo.fmpz},Generic.ResField{Nemo.fmpz}})
@@ -68,7 +68,7 @@ end
#################################################
# in triplicate.... and probably cases missing...
-function elem_to_mat_row!(M::MatElem, i::Int, a::ResElem{T}) where T <: PolyElem
+function elem_to_mat_row!(M::MatElem, i::Int, a::ResElem{T}) where T <: PolyElem
z = zero(parent(M[1,1]))
for j=0:degree(a.data)
M[i,j+1] = coeff(a.data, j)
@@ -77,7 +77,7 @@ function elem_to_mat_row!(M::MatElem, i::Int, a::ResElem{T}) where T <: PolyElem
M[i,j] = z
end
end
-function elem_to_mat_row!(M::MatElem, i::Int, a::ResElem{fq_poly})
+function elem_to_mat_row!(M::MatElem, i::Int, a::ResElem{fq_poly})
z = zero(parent(M[1,1]))
for j=0:degree(a.data)
M[i,j+1] = coeff(a.data, j)
@@ -86,7 +86,7 @@ function elem_to_mat_row!(M::MatElem, i::Int, a::ResElem{fq_poly})
M[i,j] = z
end
end
-function elem_to_mat_row!(M::MatElem, i::Int, a::ResElem{fq_nmod_poly})
+function elem_to_mat_row!(M::MatElem, i::Int, a::ResElem{fq_nmod_poly})
z = zero(parent(M[1,1]))
for j=0:degree(a.data)
M[i,j+1] = coeff(a.data, j)
@@ -162,7 +162,7 @@ function gens(R::Union{Generic.ResRing{T},Generic.ResField{T}}) where T<:PolyEle
return r
end
-function gens(R::Union{Generic.ResRing{nmod_poly},Generic.ResField{nmod_poly}})
+function gens(R::Union{Generic.ResRing{nmod_poly},Generic.ResField{nmod_poly}})
g = gen(R)
r = Vector{typeof(g)}()
push!(r, one(R))
diff --git a/src/Misc/Series.jl b/src/Misc/Series.jl
index 1b32890f6b..6bddd2c362 100644
--- a/src/Misc/Series.jl
+++ b/src/Misc/Series.jl
@@ -18,15 +18,15 @@ function Nemo.integral(f::RelSeriesElem{T}) where T
setcoeff!(g, i, divexact(c, i+v+1))
end
end
- Nemo.renormalize!(g)
+ Nemo.renormalize!(g)
return g
end
-function *(f::PolyElem{<:SeriesElem{qadic}}, g::PolyElem{<:SeriesElem{qadic}})
+function *(f::PolyElem{<:SeriesElem{qadic}}, g::PolyElem{<:SeriesElem{qadic}})
if degree(f) > 2 && degree(g) > 2
fg = mymul_ks(f, g)
# @hassert :AbsFact 2 fg == Nemo.mul_classical(f, g)
-# This cannot be asserted unfortunately: mymul_ks works in the
+# This cannot be asserted unfortunately: mymul_ks works in the
# capped abs. prec world, while mul_classical does not:
# f = t*((p+O(p^2) + O(s))), then in the classical world
# f^2 = t^2*p^2+O(p^3), while in the capped world we get 0
@@ -38,12 +38,12 @@ function *(f::PolyElem{<:SeriesElem{qadic}}, g::PolyElem{<:SeriesElem{qadic}})
end
#=
-function *(f::RelSeriesElem{qadic}, g::RelSeriesElem{qadic})
+function *(f::RelSeriesElem{qadic}, g::RelSeriesElem{qadic})
return mymul_ks(f, g)
if pol_length(f) > 2 && pol_length(g) > 2
fg = mymul_ks(f, g)
# @hassert :AbsFact 2 fg == Nemo.mul_classical(f, g)
-# This cannot be asserted unfortunately: mymul_ks works in the
+# This cannot be asserted unfortunately: mymul_ks works in the
# capped abs. prec world, while mul_classical does not:
# f = t*((p+O(p^2) + O(s))), then in the classical world
# f^2 = t^2*p^2+O(p^3), while in the capped world we get 0
@@ -120,7 +120,7 @@ function mymul_ks(f::SeriesElem{qadic}, g::SeriesElem{qadic})
end
end
end
-
+
G = Hecke.Globals.Zx()
fit!(G, 1+rg*(2*h-1))
for j=0:rg-1
@@ -248,7 +248,7 @@ function mymul_ks(f::PolyElem{<:SeriesElem{qadic}}, g::PolyElem{<:SeriesElem{qad
end
-function Nemo.canonical_unit(a::SeriesElem)
+function Nemo.canonical_unit(a::SeriesElem)
iszero(a) && return one(parent(a))
v = valuation(a)
v == 0 && return a
diff --git a/src/Misc/UnitsModM.jl b/src/Misc/UnitsModM.jl
index 97e4122ad9..c8e38b7910 100644
--- a/src/Misc/UnitsModM.jl
+++ b/src/Misc/UnitsModM.jl
@@ -666,10 +666,10 @@ function _unit_grp_residue_field_mod_n(p::Int, n::Int)
else
return mod(inv*disc_log_bs_gs(w, y, npart), k)
end
- end
- end
+ end
+ end
return Int(g.data), k, disc_log
-
+
end
unit_group(A::Nemo.FmpzModRing) = UnitGroup(A)
@@ -700,7 +700,7 @@ function Base.iterate(R::GaloisField, st::UInt)
if st == R.n - 1
return nothing
end
-
+
return R(st + 1), st + 1
end
diff --git a/src/Misc/acb_root_ctx.jl b/src/Misc/acb_root_ctx.jl
index 98dc4ff1f3..f4f68bc2c6 100644
--- a/src/Misc/acb_root_ctx.jl
+++ b/src/Misc/acb_root_ctx.jl
@@ -102,8 +102,8 @@ function refine(x::acb_root_ctx, target_prec::Int = 2*precision(x))
end
@assert j == s
nothing
-end
-
+end
+
function _evaluate(x::fmpq_poly, y::acb)
z = parent(y)(0)
for i in 0:degree(x)
@@ -123,7 +123,7 @@ end
# are smaller then 2^(-abs_tol).
function _validate_size_of_zeros(roots::Ptr{acb_struct}, deg::Int, abs_tol::Int)
ok = true
- if abs_tol < 0
+ if abs_tol < 0
return true
end
@@ -142,7 +142,7 @@ function _validate_size_of_zeros(roots::Ptr{acb_struct}, deg::Int, abs_tol::Int)
break
end
end
- if !ok
+ if !ok
return false
end
return true
@@ -174,7 +174,7 @@ function _refine_roots!(x::Union{fmpq_poly, fmpz_poly}, roots::Ptr{acb_struct},
return res
end
-# This is the workhorse.
+# This is the workhorse.
# It computes the roots of x with with radii <= 2^(-abs_tol)
# The result will be stored in roots
# If have_approx = true, it is assumed that roots contains approximations
@@ -193,7 +193,7 @@ function _roots!(roots::Ptr{acb_struct}, x::Union{fmpq_poly, fmpz_poly},
while true
in_roots = roots
step_max_iter = (max_iter >= 1) ? max_iter : min(max(deg, div(wp, 4)), wp)
- y = acb_poly(x, wp)
+ y = acb_poly(x, wp)
if have_approx
isolated = ccall((:acb_poly_find_roots, libarb), Int,
@@ -210,13 +210,13 @@ function _roots!(roots::Ptr{acb_struct}, x::Union{fmpq_poly, fmpz_poly},
continue
end
have_approx = true
-
+
if isolated == deg
have_approx = true
ok = _validate_size_of_zeros(roots, deg, abs_tol)
real_ok = ccall((:acb_poly_validate_real_roots, libarb),
Bool, (Ptr{acb_struct}, Ref{acb_poly}, Int), roots, y, wp)
-
+
if !real_ok
ok = false
else
diff --git a/src/Misc/arf.jl b/src/Misc/arf.jl
index 27a60bf69b..2ba9726016 100644
--- a/src/Misc/arf.jl
+++ b/src/Misc/arf.jl
@@ -52,7 +52,7 @@ const ArfFieldID = IdDict()
mutable struct ArfField <: Field
prec::Int
rndmode::Cint
-
+
function ArfField(p::Int = 256, r::Cint = Cint(4))
try
return ArfFieldID[p,r]::ArfField
@@ -77,7 +77,7 @@ mutable struct arf
finalizer(z, _arf_clear_fn)
return z
end
-
+
function arf(i::Int)
z = new()
ccall((:arf_init, libarb), Nothing, (Ref{arf}, ), z)
@@ -449,7 +449,7 @@ function -(x::arf, y::fmpz)
end
-(x::fmpz, y::arf) = -(y - x)
-
+
function /(x::arf, y::arf)
check_parent(x,y)
z = parent(x)()
diff --git a/src/Misc/fmpr.jl b/src/Misc/fmpr.jl
index 83e924c645..2aa48cc1af 100644
--- a/src/Misc/fmpr.jl
+++ b/src/Misc/fmpr.jl
@@ -30,7 +30,7 @@ end
function _fmpr_clear_fn(x::fmpr)
ccall((:fmpr_clear, libarb), Nothing, (Ref{fmpr}, ), x)
end
-
+
function fmpq(x::fmpr)
z = fmpq()
ccall((:fmpr_get_fmpq, libarb), Nothing, (Ref{fmpq}, Ref{fmpr}), z, x)
@@ -64,7 +64,7 @@ function show(io::IO, x::cfrac)
end
print(io, "]")
end
-
+
# THIS LEAKS MEMORY
function cfrac(x::fmpq, y::Int)
diff --git a/src/Misc/nmod_poly.jl b/src/Misc/nmod_poly.jl
index 8990d4fda4..f0934a5f5b 100644
--- a/src/Misc/nmod_poly.jl
+++ b/src/Misc/nmod_poly.jl
@@ -20,7 +20,7 @@ function resultant_ideal(f::PolyElem{T}, g::PolyElem{T}) where T <: ResElem{S} w
Rt = parent(f)
R = base_ring(Rt)
m = fmpz(modulus(R))
-
+
#easy = isprime_power(m)
#if easy
# return resultant_ideal_pp(f,g)
@@ -749,7 +749,7 @@ function _rresx_sircana(f::PolyElem{T}, g::PolyElem{T}) where T <: ResElem{S} wh
end
# f = U*f_in + V*g_in
# g = u*f_in + v*g_in
- # r = u_ * f + v_ * g
+ # r = u_ * f + v_ * g
return res, (u_*U + v_*u), (u_*V + v_*v)
end
q, f = divrem(f, g)
@@ -1345,7 +1345,7 @@ end
@doc Markdown.doc"""
compose_mod(x::nmod_poly, y::nmod_poly, z::nmod_poly) -> nmod_poly
-
+
Compute $x(y)$ mod $z$.
"""
function compose_mod(x::nmod_poly, y::nmod_poly, z::nmod_poly)
@@ -1369,7 +1369,7 @@ end
@doc Markdown.doc"""
taylor_shift(x::nmod_poly, c::UInt) -> nmod_poly
-
+
Compute $x(t-c)$.
"""
function taylor_shift(x::nmod_poly, c::UInt)
@@ -1426,7 +1426,7 @@ function isprimitive(f::nmod_poly)
for i = 1:degree(f)
n = gcd(n, coeff(f, i))
if isone(n)
- return true, R(n)
+ return true, R(n)
end
end
return isone(n), R(n)
@@ -1504,7 +1504,7 @@ function _coprimality_test(f::T, g::T, h::T) where T <: Union{nmod_poly, fmpz_mo
if isunit(c)
for i = degree(f):-1:0
cfi = coeff(f, i)
- if isnilpotent(cfi)
+ if isnilpotent(cfi)
continue
end
if isunit(cfi)
@@ -1531,7 +1531,7 @@ function _coprimality_test(f::T, g::T, h::T) where T <: Union{nmod_poly, fmpz_mo
if !must_split && isunit(c1)
for i = degree(g):-1:0
cgi = coeff(g, i)
- if isnilpotent(cgi)
+ if isnilpotent(cgi)
continue
end
if isunit(cgi)
@@ -1588,7 +1588,7 @@ function _coprimality_test(f::T, g::T, h::T) where T <: Union{nmod_poly, fmpz_mo
h1 = Rx(lift(Zx, h))
if !_coprimality_test(f1, g1, h1)
return false
- end
+ end
end
return true
end
diff --git a/src/Misc/toHecke.jl b/src/Misc/toHecke.jl
index 4af8150969..220bea27e7 100644
--- a/src/Misc/toHecke.jl
+++ b/src/Misc/toHecke.jl
@@ -14,7 +14,7 @@ function to_hecke(f::IOStream, a::Dict{T, S}; name::String="R") where {T, S}
end
-function to_hecke(s::String, a::Dict; name::String="R", mode::String ="w")
+function to_hecke(s::String, a::Dict; name::String="R", mode::String ="w")
f = open(s, mode)
to_hecke(f, a, name = name)
close(f)
diff --git a/src/Misc/toMagma.jl b/src/Misc/toMagma.jl
index edadd4f3a9..5a13dc4cb6 100644
--- a/src/Misc/toMagma.jl
+++ b/src/Misc/toMagma.jl
@@ -30,14 +30,14 @@ function to_magma(f::IOStream, t::Tuple)
print(f, ">\n")
end
end
-end
+end
function to_magma(s::String, a::Vector{T}; name::String="R", mode::String ="w") where T
f = open(s, mode)
to_magma(f, a, name = name)
close(f)
end
-
+
################################################################################
# fmpz_mat -> magma file
@@ -73,7 +73,7 @@ end
function to_magma(io::IOStream, A::SMat; name = "A")
println(io, name, " := SparseMatrix(Integers(), ", nrows(A), ", ", ncols(A), ", [")
for i = 1:nrows(A)
- for xx = 1:length(A.rows[i].pos)
+ for xx = 1:length(A.rows[i].pos)
print(io, "<", i, ", ", A.rows[i].pos[xx], ", ", A.rows[i].values[xx], ">")
if xx < length(A.rows[i].pos) || i nffactor(k, f);
#=
-from
+from
https://www.math.u-bordeaux.fr/~kbelabas/research/vanhoeij.pdf
p 26, polys h_1, ..., h_10 (so far)
diff --git a/src/ModAlgAss/MeatAxe.jl b/src/ModAlgAss/MeatAxe.jl
index e4988d3443..90b8d3521f 100644
--- a/src/ModAlgAss/MeatAxe.jl
+++ b/src/ModAlgAss/MeatAxe.jl
@@ -57,7 +57,7 @@ function cleanvect!(M::T, v::T) where T
if !iszero(c)
w[1,k] -= mult * c
end
- end
+ end
end
return v
end
@@ -130,13 +130,13 @@ function closure(C::T, G::Vector{T}) where {T}
res = cleanvect!(C, w*G[j]) # cleanvect(C, w*G[j]) but we
# can do it inplace since w*G[j] is fresh
if !iszero(res)
- C = vcat(C, res)
+ C = vcat(C, res)
if nrows(C) == nc
i = ncols(C)+1
break
end
- end
- end
+ end
+ end
i+=1
end
@@ -160,7 +160,7 @@ function closure(C::T, G::Vector{T}) where {T}
else
r = rref!(C)
end
-
+
if r != nrows(C)
C = sub(C, 1:r, 1:ncols(C))
end
@@ -187,15 +187,15 @@ function clean_and_quotient(M::T, N::T, pivotindex::Set{Int}) where {T}
N[i,s]-=coeff[i,j]*M[j,s]
end
end
- end
+ end
vec= zero_matrix(base_ring(M), nrows(N), ncols(M)-length(pivotindex))
- for i=1:nrows(N)
+ for i=1:nrows(N)
pos=0
for s=1:ncols(M)
if !(s in pivotindex)
pos+=1
vec[i,pos]=N[i,s]
- end
+ end
end
end
return coeff, vec
@@ -217,9 +217,9 @@ function clean_and_quotient_quo(M::T, N::T, pivotindex::Set{Int}) where {T}
N[i,s] -= r*M[j,s]
end
end
- end
+ end
vec = zero_matrix(base_ring(M), nrows(N), ncols(M)-length(pivotindex))
- for i=1:nrows(N)
+ for i=1:nrows(N)
pos=0
for s=1:ncols(M)
if !(s in pivotindex)
@@ -678,7 +678,7 @@ function eigenspace_as_matrix(M::MatElem{T}, lambda::T) where T <: FieldElem
return view(res, 1:d, 1:ncols(res))
end
-
+
function _relations_dim_1(M::ModAlgAss{S, T, V}, N::ModAlgAss{S, T, V}) where {S, T, V}
@assert M.isirreducible == 1
@assert dimension(M) == 1
@@ -780,7 +780,7 @@ function irreducible_submodules(N::ModAlgAss{S, T, V}, M::ModAlgAss{S, T, V}) wh
if a == 1
return T[closure(kern, N.action)]
end
- end
+ end
vects = T[sub(kern, i:i, 1:N.dimension) for i=1:a]
if dimension(M) == 1
return _submodules_direct_sum_dim_1(vects, N)
@@ -821,7 +821,7 @@ function _all_combinations(M::MatElem{T}) where T
end
res[ind] = m * M
ind += 1
- end
+ end
return res
end
@@ -961,13 +961,13 @@ end
@doc Markdown.doc"""
minimal_submodules(M::ModAlgAss)
-
+
Given a Fq[G]-module $M$, it returns all the minimal submodules of $M$.
"""
function minimal_submodules(M::ModAlgAss{S, T, V}, dim::Int=M.dimension+1, lf = Tuple{ModAlgAss{S, T, V}, Int}[]) where {S, T, V}
return T[x[1] for x in _minimal_submodules(M, dim, lf)]
end
-
+
@doc Markdown.doc"""
maximal_submodules(M::ModAlgAss)
diff --git a/src/ModAlgAss/ModAlgAss.jl b/src/ModAlgAss/ModAlgAss.jl
index ea694a4ea4..cb3d7bfe9e 100644
--- a/src/ModAlgAss/ModAlgAss.jl
+++ b/src/ModAlgAss/ModAlgAss.jl
@@ -10,7 +10,7 @@ mutable struct ModAlgAss{S, T, V}
algebra::AlgAss{V}
action_of_gens::Vector{T}
action_of_basis::Vector{T}
-
+
function ModAlgAss{S, T}(action::Vector{T}) where {S, T}
z = new{S, T, elem_type(S)}()
z.action = action
@@ -19,7 +19,7 @@ mutable struct ModAlgAss{S, T, V}
if z.dimension == 1
z.isirreducible = 1
z.dimension_splitting_field = 1
- else
+ else
z.isirreducible = 0
z.dimension_splitting_field = 0
end
diff --git a/src/NumField/Field.jl b/src/NumField/Field.jl
index facb171b07..f40e147408 100644
--- a/src/NumField/Field.jl
+++ b/src/NumField/Field.jl
@@ -330,8 +330,8 @@ end
@doc doc"""
absolute_basis(K::NumField) -> Vector{NumFieldElem}
-Returns an array of elements that form a basis of $K$ (as a vector space)
-over the rationals.
+Returns an array of elements that form a basis of $K$ (as a vector space)
+over the rationals.
"""
absolute_basis(::NumField)
diff --git a/src/NumField/NfAbs.jl b/src/NumField/NfAbs.jl
index c1981a7a18..f335c89b86 100644
--- a/src/NumField/NfAbs.jl
+++ b/src/NumField/NfAbs.jl
@@ -1,13 +1,13 @@
-import Nemo.sub!, Base.gcd
+import Nemo.sub!, Base.gcd
export induce_rational_reconstruction, induce_crt, root, roots,
ismonic, radical_extension, isradical_extension,
- iskummer_extension, cyclotomic_field, wildanger_field,
+ iskummer_extension, cyclotomic_field, wildanger_field,
compositum
-add_verbose_scope(:PolyFactor)
-add_assert_scope(:PolyFactor)
-add_verbose_scope(:CompactPresentation)
-add_assert_scope(:CompactPresentation)
+add_verbose_scope(:PolyFactor)
+add_assert_scope(:PolyFactor)
+add_verbose_scope(:CompactPresentation)
+add_assert_scope(:CompactPresentation)
if Int==Int32
global const p_start = next_prime(2^30)
diff --git a/src/NumField/NfAbs/CompactRepresentation.jl b/src/NumField/NfAbs/CompactRepresentation.jl
index 9092f21691..a1f79d7c9c 100644
--- a/src/NumField/NfAbs/CompactRepresentation.jl
+++ b/src/NumField/NfAbs/CompactRepresentation.jl
@@ -14,7 +14,7 @@ function compact_presentation(a::FacElem{nf_elem, AnticNumberField}, nn::Int = 2
if isempty(a.fac)
return a
end
-
+
if typeof(decom) == Bool
ZK = lll(maximal_order(K))
de::Dict{NfOrdIdl, fmpz} = factor_coprime(a, IdealSet(ZK), refine = true)
@@ -60,7 +60,7 @@ function compact_presentation(a::FacElem{nf_elem, AnticNumberField}, nn::Int = 2
if haskey(cached_red, p)
Dp = cached_red[p]
if haskey(Dp, e_p)
- Ap, ap = Dp[e_p]
+ Ap, ap = Dp[e_p]
else
Ap, ap = power_reduce(p, fmpz(e_p))
Dp[e_p] = (Ap, ap)
@@ -292,7 +292,7 @@ function evaluate_mod(a::FacElem{nf_elem, AnticNumberField}, B::NfOrdFracIdl)
ZK = order(B)
dB = denominator(B)#*denominator(basis_matrix(ZK, copy = false))
-
+
@hassert :CompactPresentation 1 factored_norm(B) == abs(factored_norm(a))
@hassert :CompactPresentation 2 B == ideal(order(B), a)
@@ -438,7 +438,7 @@ function _ispower(a::FacElem{nf_elem, AnticNumberField}, n::Int; with_roots_unit
end
df = FacElem(d)
@hassert :CompactPresentation 2 evaluate(df^n*b *inv(a))== 1
-
+
den = denominator(b, ZK)
fl, den1 = ispower(den, n)
if fl
diff --git a/src/NumField/NfAbs/ConjugatesNS.jl b/src/NumField/NfAbs/ConjugatesNS.jl
index cfb679ccfe..2617e6ecbd 100644
--- a/src/NumField/NfAbs/ConjugatesNS.jl
+++ b/src/NumField/NfAbs/ConjugatesNS.jl
@@ -165,7 +165,7 @@ function _is_complex_conj(v::Vector, w::Vector, pos::Vector, roots::Vector)
elseif v[i] != w[i]
return false
end
- i += 1
+ i += 1
end
return true
end
@@ -215,7 +215,7 @@ function _evaluate(f::fmpq_mpoly, vals::Vector{acb})
end
mul!(t, t, powers[j][exp])
#t = t*powers[j][exp]
- end
+ end
push!(r, c*t)
j = i = i + 1
while iseven(j) && length(r) > 1
diff --git a/src/NumField/NfAbs/Elem.jl b/src/NumField/NfAbs/Elem.jl
index a7d8020287..4a5f5b37e4 100644
--- a/src/NumField/NfAbs/Elem.jl
+++ b/src/NumField/NfAbs/Elem.jl
@@ -501,14 +501,14 @@ function factor_trager(f::PolyElem{nf_elem})
end
@vprint :PolyFactor 2 "need to shift by $k, now the norm\n"
- if any(x -> denominator(x) > 1, coefficients(g)) ||
+ if any(x -> denominator(x) > 1, coefficients(g)) ||
!isdefining_polynomial_nice(K)
@vtime :PolyFactor 2 N = Hecke.Globals.Qx(norm(g))
else
@vtime :PolyFactor 2 N = norm_mod(g, Zx)
@hassert :PolyFactor 1 N == Zx(norm(g))
end
-
+
while isconstant(N) || !issquarefree(N)
error("should not happen")
k = k + 1
diff --git a/src/NumField/NfAbs/MPolyAbsFact.jl b/src/NumField/NfAbs/MPolyAbsFact.jl
index ff937fe199..f94b497afc 100644
--- a/src/NumField/NfAbs/MPolyAbsFact.jl
+++ b/src/NumField/NfAbs/MPolyAbsFact.jl
@@ -51,7 +51,7 @@ end
in F_p[[t]][x]
a RootCtx for poly in F_p[[t]][x] to find roots in F_q[[t]]
Done.
-
+
See what Dan did in this case.
=#
@@ -183,11 +183,11 @@ end
function lift(C::HenselCtxFqRelSeries{<:SeriesElem})
St = parent(C.lf[1])
S = base_ring(C.lf[1])
-
+
C.lf[1]
pr = precision(coeff(C.lf[1], 0))
N2 = 2*pr
-
+
S.prec_max = N2+1
i = length(C.lf)
@@ -207,7 +207,7 @@ function lift(C::HenselCtxFqRelSeries{<:SeriesElem})
@assert ismonic(C.lf[i])
end
@assert ismonic(f)
-
+
#formulae and names from the Flint doc
h = C.lf[j]
g = C.lf[j-1]
@@ -219,12 +219,12 @@ function lift(C::HenselCtxFqRelSeries{<:SeriesElem})
set_precision!(b, N2)
fgh = shift_coeff_right(f-g*h, pr)
-
+
G = shift_coeff_left(rem(fgh*b, g), pr)+g
H = shift_coeff_left(rem(fgh*a, h), pr)+h
-
+
t = shift_coeff_right(1-a*G-b*H, pr)
-
+
B = shift_coeff_left(rem(t*b, g), pr)+b
A = shift_coeff_left(rem(t*a, h), pr)+a
if i < length(C.lf)
@@ -258,7 +258,7 @@ function _set_precision!(f::PolyElem{<:SeriesElem{qadic}}, n::Int)
end
return f
end
-# TODO: bad names...
+# TODO: bad names...
function _shift_coeff_left(f::PolyElem{<:SeriesElem{qadic}}, n::Int)
g = parent(f)()
for i = 0:length(f)
@@ -282,7 +282,7 @@ end
function _shift_coeff_right(f::PolyElem{<:SeriesElem{qadic}}, n::Int)
g = parent(f)()
for i = 0:length(f)
- @assert all(y -> valuation(polcoeff(coeff(f, i), y)) >= n, 0:pol_length(coeff(f, i)))
+ @assert all(y -> valuation(polcoeff(coeff(f, i), y)) >= n, 0:pol_length(coeff(f, i)))
setcoeff!(g, i, map_coefficients(x -> shift_right(x, n), coeff(f, i), parent = base_ring(f)))
end
return g
@@ -309,7 +309,7 @@ function lift(P::Preinv)
P.fi = truncate(P.fi*truncate((parent(f)(2)-f*P.fi), 2*P.n), 2*P.n)
P.n *= 2
end
-# von zur Gathen: Modern Computer Algebra, p 243:
+# von zur Gathen: Modern Computer Algebra, p 243:
# 9.1. Division with remainder using Newton iteration
function Base.rem(g::PolyElem, P::Preinv)
if degree(g) < degree(P.f)
@@ -341,10 +341,10 @@ function lift_q(C::HenselCtxFqRelSeries{<:SeriesElem{qadic}})
St = parent(C.lf[1])
S = base_ring(C.lf[1])
Q = base_ring(S)
-
+
pr = precision(coeff(coeff(C.lf[1], 0), 0))
N2 = 2*pr
-
+
setprecision!(Q, N2)
i = length(C.lf)
@@ -373,7 +373,7 @@ function lift_q(C::HenselCtxFqRelSeries{<:SeriesElem{qadic}})
b = _set_precision(b, N2)
fgh = _shift_coeff_right(f-g*h, pr)
-
+
@assert ismonic(g)
@assert !iszero(constant_coefficient(g))
@assert ismonic(h)
@@ -387,7 +387,7 @@ function lift_q(C::HenselCtxFqRelSeries{<:SeriesElem{qadic}})
@assert ismonic(H)
t = _shift_coeff_right(1-a*G-b*H, pr)
-
+
B = _shift_coeff_left(rem(t*b, gi), pr)+b
A = _shift_coeff_left(rem(t*a, hi), pr)+a
@@ -566,7 +566,7 @@ function root(R::RootCtx, i::Int, j::Int)
o = one(parent(R.all_R[1]))
R.RP = [[set_precision(o, precision(R.all_R[1])) for x = R.all_R], copy(R.all_R)]
end
- if length(R.RP) > j
+ if length(R.RP) > j
return (R.RP[j+1][i])
end
while length(R.RP) <= j+1
@@ -598,7 +598,7 @@ function roots(f::fmpq_mpoly, p_max::Int=2^15; pr::Int = 2)
#f needs to be irreducible over Q and g square-free
g = evaluate(ff, [gen(Zx), Zx(0)])
@assert degree(g) == degree(f, 1)
-
+
d = typemax(Int)
best_p = p_max
pc = 0
@@ -618,7 +618,7 @@ function roots(f::fmpq_mpoly, p_max::Int=2^15; pr::Int = 2)
else
pc += 1
end
-
+
if e == 1 || pc > 1.5 * degree(g)
p = best_p
@vprint :AbsFact 1 "using $best_p of degree $d\n"
@@ -665,8 +665,8 @@ function combination(RC::RootCtx)
n = precision(R[1])
@assert all(x->precision(x) == n, R)
- #ps = [[div(x^i % tn, td^i) for i = 1:n] for x = R]
-
+ #ps = [[div(x^i % tn, td^i) for i = 1:n] for x = R]
+
F = base_ring(Ft)
k = degree(F)
@@ -681,7 +681,7 @@ function combination(RC::RootCtx)
#also: it would make the lifting above trivial (precision 2)
#deal: if monic in x of degree n and deg_y(coeff of x^(n-1)) = r,
# then for the 1st power sum we get r as a degree bound. In the paper
- # r == 1...
+ # r == 1...
# reasoning: sum of second highest terms of factor == second highest
# of poly => bound
# similar would be for other power sums - if I'd compute them.
@@ -730,9 +730,9 @@ function combination(RC::RootCtx)
ld = evaluate(map_coefficients(x->F(ZZ(x)), lc), [set_precision(Ft(0), n), set_precision(gen(Ft), n)])
R = R .* ld
@assert precision(R[1]) >= n
-
+
mn = matrix([[Fp(coeff(coeff(x^pow, pow*d+j), lk)) for lk = 0:k-1] for x = R])
-
+
if false && iszero(mn)
@vprint :AbsFact 2 "found zero column, disgarding\n"
bad += 1
@@ -752,7 +752,7 @@ function combination(RC::RootCtx)
ke = kernel(nn)
@vprint :AbsFact 2 "current kernel dimension: $(ke[1])\n"
- if last_rank == ke[1]
+ if last_rank == ke[1]
bad += 1
if bad > max(2, div(length(R), 2))
pow += 1
@@ -807,14 +807,14 @@ function block_system(a::Vector{T}) where {T}
d[a[i]] = [i]
end
end
- return sort(collect(values(d)), lt = (a,b) -> isless(a[1], b[1]))
+ return sort(collect(values(d)), lt = (a,b) -> isless(a[1], b[1]))
end
#= bounds:
f in Z[x,y], g, h in C[x,y]
H(f) = max abs value coeff of f
gh = f
- then
+ then
H(g) H(h) <= 2^(deg_x(f) + deg_y(g) - 2) ((deg_x(f)+1)(deg_y(f)+1))^(1/2) H(f)
=#
"""
@@ -826,7 +826,7 @@ function field(RC::RootCtx, m::MatElem)
bnd = numerator(maximum(abs(x) for x = coefficients(RC.f))) * fmpz(2)^(degree(RC.f, 1) + degree(RC.f, 2)-2) * Hecke.root(fmpz((degree(RC.f, 1)+1)*(degree(RC.f, 2)+1)), 2)
- #all coeffs should be bounded by bnd...
+ #all coeffs should be bounded by bnd...
#we have roots, we need to combine roots for each row in m where the entry is pm 1
#the coeffs then live is a number field, meaning that the elem sym functions or
@@ -879,7 +879,7 @@ function field(RC::RootCtx, m::MatElem)
Qq = QadicField(characteristic(F), k, 1, cached = false)[1]
Qqt = PolynomialRing(Qq, cached = false)[1]
k, mk = ResidueField(Qq)
-
+
phi = find_morphism(k, F) #avoids embed - which stores the info
kt, t = PolynomialRing(k, cached = false)
@@ -933,7 +933,7 @@ function field(RC::RootCtx, m::MatElem)
llc = coeff(P, 1)
P *= inv(llc)
-
+
_lc = evaluate(leading_coefficient(P, 1), [zero(Hecke.Globals.Qx), gen(Hecke.Globals.Qx)])
_lc = Hecke.squarefree_part(_lc)
local H, fa
@@ -1022,16 +1022,16 @@ function field(RC::RootCtx, m::MatElem)
mc(f) = # PolyElem{SeriesElem{Fq}} -> PolyElem{SeriesElem{Qq}}
map_coefficients(x->map_coefficients(y->setprecision(preimage(mk, y), 1), x, parent = SQq), f, parent = SQqt)
-
+
HQ = HenselCtxFqRelSeries(HH.f, map(mc, HH.lf), map(mc, HH.cf), HH.n)
QqXY, (X, Y) = PolynomialRing(Qq, 2, cached = false)
- pr = 1
+ pr = 1
while true
pr *= 2
- if pr > 800
+ if pr > 800
error("too bas")
end
@vprint :AbsFact 1 "using p-adic precision of $pr\n"
@@ -1125,7 +1125,7 @@ end
Given an irreducible bivariate polynomial over `Q` compute the
absolute factorisation.
-Returns two polynomials:
+Returns two polynomials:
- the (absolutely) irreducible factor over the smallest number field
- the co-factor
@@ -1138,7 +1138,7 @@ function absolute_bivariate_factorisation(f::fmpq_mpoly)
x, y = gens(R)
lf = factor(f)
- if length(lf.fac) > 1 || any(x->x>1, values(lf.fac))
+ if length(lf.fac) > 1 || any(x->x>1, values(lf.fac))
error("poly must be irreducible over Q")
end
@@ -1169,7 +1169,7 @@ function absolute_bivariate_factorisation(f::fmpq_mpoly)
return b, divexact(map_coefficients(k, f, parent = kXY), b)
end
- s =-1
+ s =-1
while true
s += 1
@vprint :AbsFact 1 "substitution to $s\n"
@@ -1195,7 +1195,7 @@ function absolute_bivariate_factorisation(f::fmpq_mpoly)
if nrows(z) == 1
return f, one(parent(f))
end
-
+
@vtime :AbsFact 1 aa = field(r, z)
aa !== nothing && break
end
@@ -1526,7 +1526,7 @@ export factor_absolute
#application (for free)
-function factor(f::Union{fmpq_mpoly, fmpz_mpoly}, C::AcbField)
+function factor(f::Union{fmpq_mpoly, fmpz_mpoly}, C::AcbField)
fa = factor_absolute(f)
D = Dict{Generic.MPoly{acb}, Int}()
Cx, x = PolynomialRing(C, map(String, symbols(parent(f))), cached = false)
@@ -1550,7 +1550,7 @@ function factor(f::Union{fmpq_mpoly, fmpz_mpoly}, C::AcbField)
return Fac(map_coefficients(C, fa[1], parent = Cx), D)
end
-function factor(f::Union{fmpq_mpoly, fmpz_mpoly}, R::ArbField)
+function factor(f::Union{fmpq_mpoly, fmpz_mpoly}, R::ArbField)
fa = factor_absolute(f)
D = Dict{Generic.MPoly{arb}, Int}()
Rx, x = PolynomialRing(R, map(String, symbols(parent(f))), cached = false)
@@ -1600,7 +1600,7 @@ end
example:
Qxy, (y, x) = PolynomialRing(QQ, ["y", "x"])
-include("/home/fieker/Downloads/n60s3.m");
+include("/home/fieker/Downloads/n60s3.m");
#from https://www.math.univ-toulouse.fr/~cheze/n60s3.m
r = absolute_bivariate_factorisation(P)
diff --git a/src/NumField/NfAbs/MPolyGcd.jl b/src/NumField/NfAbs/MPolyGcd.jl
index b06eea7fa3..2c4afebeb0 100644
--- a/src/NumField/NfAbs/MPolyGcd.jl
+++ b/src/NumField/NfAbs/MPolyGcd.jl
@@ -116,7 +116,7 @@ end
function data_assure(R::RecoCtx)
R.new_data || return
-
+
R.L = lll(basis_matrix(R.p1, R.f, R.k))
if isdefined(R, :LI) #to keep stucture consistent
R.LI, R.d = pseudo_inv(R.L)
@@ -201,7 +201,7 @@ function Hecke.rational_reconstruction(a::nf_elem, R::RecoCtx; integral::Bool =
K = parent(a)
d = Nemo.elem_from_mat_row(K, sub(L, 1:1, 1:n), 1, fmpz(1))
n = Nemo.elem_from_mat_row(K, sub(L, 1:1, n+1:2*n), 1, fmpz(1))
- if split
+ if split
return true, n, d
else
return true, n//d
@@ -282,7 +282,7 @@ function _gcd(f::Hecke.Generic.MPoly{nf_elem}, g::Hecke.Generic.MPoly{nf_elem},
if isempty(me)
continue
end
-
+
@vtime :MPolyGcd 3 fp = Hecke.modular_proj(f, me)
@vtime :MPolyGcd 3 gp = Hecke.modular_proj(g, me)
glp = Hecke.modular_proj(gl, me)
@@ -328,7 +328,7 @@ function _gcd(f::Hecke.Generic.MPoly{nf_elem}, g::Hecke.Generic.MPoly{nf_elem},
d *= p
stable -= 1
end
- if fl && stable <= 0
+ if fl && stable <= 0
if divides(f, gd)[1] && divides(g, gd)[1]
# @show "gcd stop", nbits(d), length(gd), gd
gd*=inv(gl)
@@ -411,7 +411,7 @@ function Hecke.induce_crt(a::Hecke.Generic.MPoly{nf_elem}, p::fmpz, b::Hecke.Gen
end
end
return finish(c), pq
-end
+end
function Hecke.induce_crt(a::fmpz_mat, p::fmpz, b::fmpz_mat, q::fmpz, signed::Bool = false)
pi = invmod(p, q)
@@ -431,7 +431,7 @@ function Hecke.induce_crt(a::fmpz_mat, p::fmpz, b::fmpz_mat, q::fmpz, signed::Bo
end
end
return c, pq
-end
+end
function Hecke.modular_proj(f::Generic.MPoly{nf_elem}, me::Hecke.modular_env)
if !isdefined(me, :Kxy)
diff --git a/src/NumField/NfAbs/NfAbs.jl b/src/NumField/NfAbs/NfAbs.jl
index 116a759b79..d7afabbfc6 100644
--- a/src/NumField/NfAbs/NfAbs.jl
+++ b/src/NumField/NfAbs/NfAbs.jl
@@ -416,7 +416,7 @@ function normal_basis(K::AnticNumberField)
break
end
end
-
+
return _normal_basis_generator(K, p)
end
@@ -975,7 +975,7 @@ function islinearly_disjoint(K1::AnticNumberField, K2::AnticNumberField)
f = change_base_ring(K2, K1.pol)
return isirreducible(f)
end
-
+
################################################################################
#
# more general coercion, field lattice
@@ -1116,7 +1116,7 @@ end
@doc Markdown.doc"""
embed(f::Map{<:NumField, <:NumField})
-
+
Registers `f` as a canonical embedding from the domain into the co-domain.
Once this embedding is registered, it cannot be changed.
"""
@@ -1161,7 +1161,7 @@ end
@doc Markdown.doc"""
hasembedding(F::NumField, G::NumField) -> Bool
-
+
Checks if an embedding from $F$ into $G$ is already known.
"""
function hasembedding(F::NumField, G::NumField)
@@ -1213,7 +1213,7 @@ function find_all_super(A::NumField, filter::Function = x->true)
return all_s
end
-#finds a common super field for A and B, using the weak-refs
+#finds a common super field for A and B, using the weak-refs
# in special -> :sub_of
function common_super(A::NumField, B::NumField)
A === B && return A
@@ -1263,8 +1263,8 @@ end
@doc Markdown.doc"""
embedding(k::NumField, K::NumField) -> Map
-
-Assuming $k$ is known to be a subfield of $K$, return the embedding map.
+
+Assuming $k$ is known to be a subfield of $K$, return the embedding map.
"""
function embedding(k::NumField, K::NumField)
if issimple(k)
@@ -1278,7 +1278,7 @@ function force_coerce_cyclo(a::AnticNumberField, b::nf_elem, throw_error::Type{V
# Base.show_backtrace(stdout, backtrace())
fa = get_special(a, :cyclo)
fb = get_special(parent(b), :cyclo)
-
+
if fa % fb == 0 #coerce up, includes fa == fb
#so a = p(z) for p in Q(x) and z = gen(parent(b))
q = divexact(fa, fb)
@@ -1323,7 +1323,7 @@ function force_coerce_cyclo(a::AnticNumberField, b::nf_elem, throw_error::Type{V
q = divexact(fb, fa)
cb = [i for i=1:fb if gcd(i, fb) == 1] # the "conjugates" in the large field
- ca = [[i for i = cb if i % fa == j] for j=1:fa if gcd(j, fa) == 1] #broken into blocks
+ ca = [[i for i = cb if i % fa == j] for j=1:fa if gcd(j, fa) == 1] #broken into blocks
#in general one could test first if the evaluation is constant on a block
#equivalently, if the element is Galois invariant under the fix group of a.
diff --git a/src/NumField/NfAbs/NonSimple.jl b/src/NumField/NfAbs/NonSimple.jl
index db062e318a..9a81b81070 100644
--- a/src/NumField/NfAbs/NonSimple.jl
+++ b/src/NumField/NfAbs/NonSimple.jl
@@ -761,7 +761,7 @@ end
#end
# TODO: - Preallocate the exps array
-# - Do we still need this?
+# - Do we still need this?
function msubst(f::fmpq_mpoly, v::Vector{T}) where {T}
n = length(v)
@assert n == nvars(parent(f))
diff --git a/src/NumField/NfAbs/NormRelation/Clgp.jl b/src/NumField/NfAbs/NormRelation/Clgp.jl
index 35e2d6659b..c87e034898 100644
--- a/src/NumField/NfAbs/NormRelation/Clgp.jl
+++ b/src/NumField/NfAbs/NormRelation/Clgp.jl
@@ -15,7 +15,7 @@ function get_sunits_from_subfield_data!(c::Hecke.ClassGrpCtx, UZK::Hecke.UnitGrp
@vprint :NormRelation 1 "Using the compact presentation\n"
_add_sunits_from_brauer_relation!(c, UZK, N, compact = onlyp)
end
-end
+end
function class_group_via_brauer(O::NfOrd, N::NormRelation; compact::Bool = true)
K = N.K
diff --git a/src/NumField/NfAbs/NormRelation/SUnits.jl b/src/NumField/NfAbs/NormRelation/SUnits.jl
index 19ebc7e462..800f16636c 100644
--- a/src/NumField/NfAbs/NormRelation/SUnits.jl
+++ b/src/NumField/NfAbs/NormRelation/SUnits.jl
@@ -222,7 +222,7 @@ function _add_sunits_from_brauer_relation!(c, UZK, N; invariant::Bool = false, c
end
end
=#
- has_full_rk = Hecke.has_full_rank(UZK)
+ has_full_rk = Hecke.has_full_rank(UZK)
@vtime :NormRelation 4 ff = Hecke.add_unit!(UZK, img_u)
if !has_full_rk && !ff
push!(add_unit_later, img_u)
@@ -463,7 +463,7 @@ function __sunit_group_fac_elem_quo_via_brauer(N::NormRelation, S::Vector{NfOrdI
UZK.finished = true
end
- if saturate_units && !UZK.finished
+ if saturate_units && !UZK.finished
for (p, e) in factor(index(N))
@vprint :NormRelation 1 "Saturating at $p \n"
b = Hecke.saturate!(UZK, Int(p), 3.5, easy_root = true, use_LLL = true)
@@ -551,11 +551,11 @@ function __sunit_group_fac_elem_quo_via_brauer(N::NormRelation, S::Vector{NfOrdI
function exp(a::GrpAbFinGenElem)
@assert parent(a) == res_group
z = prod(units[i]^a[i] for i = 1:length(units))
- if !isempty(sunitsmodunits)
+ if !isempty(sunitsmodunits)
zz = prod(sunitsmodunits[i]^a[length(units) + i] for i in 1:length(sunitsmodunits))
mul!(z, z, zz)
end
-
+
for (k, v) in z.fac
if iszero(v)
delete!(z.fac, k)
@@ -569,7 +569,7 @@ function __sunit_group_fac_elem_quo_via_brauer(N::NormRelation, S::Vector{NfOrdI
disclog = function(a)
throw(NotImplemented())
end
-
+
r = Hecke.MapSUnitGrpFacElem()
r.valuations = Vector{SRow{fmpz}}(undef, ngens(res_group))
for i = 1:length(units)
diff --git a/src/NumField/NfAbs/NormRelation/Setup.jl b/src/NumField/NfAbs/NormRelation/Setup.jl
index 9fd3f30ab9..14fe3db548 100644
--- a/src/NumField/NfAbs/NormRelation/Setup.jl
+++ b/src/NumField/NfAbs/NormRelation/Setup.jl
@@ -5,12 +5,12 @@
################################################################################
# Example
-#
+#
# julia> f = x^8+8*x^6+64*x^4-192*x^2+576
# x^8+8*x^6+64*x^4-192*x^2+576
-#
+#
# julia> K, a = number_field(f);
-#
+#
# julia> N = Hecke._norm_relation_setup(K)
# Norm relation of
# Number field over Rational Field with defining polynomial x^8+8*x^6+64*x^4-192*x^2+576
@@ -22,7 +22,7 @@
# Number field over Rational Field with defining polynomial x^2+6
# Number field over Rational Field with defining polynomial x^2-3
# Number field over Rational Field with defining polynomial x^2-x+1
-
+
mutable struct NormRelation{T}
K::AnticNumberField
subfields::Vector{Tuple{AnticNumberField, NfToNfMor}}
@@ -136,7 +136,7 @@ function _norm_relation_for_sunits(K::AnticNumberField; small_degree::Bool = tru
nonredundant = trues(length(ls))
for i in 1:length(ls)
- if !nonredundant[i]
+ if !nonredundant[i]
continue
end
for j = i+1:length(ls)
@@ -215,7 +215,7 @@ function _norm_relation_setup_generic(K::AnticNumberField; small_degree::Bool =
nonredundant[i] = true
end
end
-
+
z = NormRelation{Int}()
z.K = K
z.isnormal = falses(n)
@@ -348,7 +348,7 @@ function induce_action_from_subfield(N::NormRelation, i, s, FB, cache)
mk = embedding(N, i)
zk = order(s[1])
-
+
if length(cache) == 0
cache = resize!(cache, length(s))
cached = false
@@ -362,7 +362,7 @@ function induce_action_from_subfield(N::NormRelation, i, s, FB, cache)
if haskey(N.induced, auto)
p = N.induced[auto]
else
- p = induce(FB, auto)
+ p = induce(FB, auto)
N.induced[auto] = p
end
end
@@ -560,7 +560,7 @@ function Hecke.simplify(c::Hecke.ClassGrpCtx)
Hecke._add_unit(U, c.R_rel[i])
end
end
- for i=1:length(U.units)
+ for i=1:length(U.units)
Hecke.class_group_add_relation(d, U.units[i], SRow(FlintZZ))
end
return d, U
@@ -655,7 +655,7 @@ function _has_norm_relation_abstract(G::GrpGen, H::Vector{Tuple{GrpGen, GrpGenTo
if large_index
reverse!(H)
end
-
+
QG = AlgGrp(FlintQQ, G)
norms_rev = Dict{elem_type(QG), Int}()
norms = Vector{elem_type(QG)}(undef, length(H))
@@ -1111,7 +1111,7 @@ function has_coprime_norm_relation(K::AnticNumberField, m::fmpz)
for i in 1:n
z.embed_cache_triv[i] = Dict{nf_elem, nf_elem}()
end
-
+
for i in 1:n
F, mF = Hecke.fixed_field1(K, NfToNfMor[mG(f) for f in ls[i][1]])
S, mS = simplify(F, cached = false)
diff --git a/src/NumField/NfAbs/PolyFact.jl b/src/NumField/NfAbs/PolyFact.jl
index f4528eeee9..f558f565e0 100644
--- a/src/NumField/NfAbs/PolyFact.jl
+++ b/src/NumField/NfAbs/PolyFact.jl
@@ -173,7 +173,7 @@ end
@doc Markdown.doc"""
round(::fmpz, a::fmpz, b::fmpz, bi::fmpz) -> fmpz
-Computes `round(a//b)` using the pre-inverse of `2b`.
+Computes `round(a//b)` using the pre-inverse of `2b`.
"""
function Base.round(::Type{fmpz}, a::fmpz, b::fmpz, bi::fmpz_preinvn_struct)
s = sign(a)
@@ -232,7 +232,7 @@ function isprime_nice(K::AnticNumberField, p::Int)
end
F = GF(p)
f = map_coefficients(F, d*K.pol)
- if degree(f) < degree(K)
+ if degree(f) < degree(K)
return false
end
if iszero(discriminant(f))
@@ -646,9 +646,9 @@ function van_hoeij(f::PolyElem{nf_elem}, P::NfOrdIdl; prec_scale = 1)
if degree(P) == 1
mD = MapFromFunc(x->coeff(mC(x),0), y->K(lift(y)), K, base_ring(vH.H.f))
- @vtime :PolyFactor 1 C = cld_data(vH.H, up_to, from, mD, vH.pM[1], den*leading_coefficient(f))
+ @vtime :PolyFactor 1 C = cld_data(vH.H, up_to, from, mD, vH.pM[1], den*leading_coefficient(f))
else
- @vtime :PolyFactor 1 C = cld_data(vH.H, up_to, from, mC, vH.pM[1], den*leading_coefficient(f))
+ @vtime :PolyFactor 1 C = cld_data(vH.H, up_to, from, mC, vH.pM[1], den*leading_coefficient(f))
end
# In the end, p-adic precision needs to be large enough to
@@ -782,7 +782,7 @@ function van_hoeij(f::PolyElem{nf_elem}, P::NfOrdIdl; prec_scale = 1)
for v = values(d)
#trivial test:
if isone(den) && ismonic(f) #don't know what to do for non-monics
- a = prod(map(constant_coefficient, factor(vH.H)[v]))
+ a = prod(map(constant_coefficient, factor(vH.H)[v]))
if degree(P) == 1
A = K(reco(order(P)(lift(a)), vH.Ml, vH.pMr))
else
diff --git a/src/NumField/NfAbs/Simplify.jl b/src/NumField/NfAbs/Simplify.jl
index a1b0f15b2b..17572260f7 100644
--- a/src/NumField/NfAbs/Simplify.jl
+++ b/src/NumField/NfAbs/Simplify.jl
@@ -99,7 +99,7 @@ end
function _simplify(O::NfAbsOrd)
K = nf(O)
-
+
B = basis(O, K, copy = false)
nrep = min(3, degree(K))
Bnew = elem_type(K)[]
@@ -112,7 +112,7 @@ function _simplify(O::NfAbsOrd)
end
#First, we search for elements that are primitive using block systems in the simple case.
B1 = _sieve_primitive_elements(Bnew)
-
+
#Now, we select the one of smallest T2 norm
a = primitive_element(K)
d = denominator(a, O)
@@ -164,7 +164,7 @@ function _sieve_primitive_elements(B::Vector{NfAbsNSElem})
end
if _is_primitive_via_block(B[i], rt_all, Fpt)
push!(indices, i)
- end
+ end
end
return B[indices]
end
diff --git a/src/NumField/NfRel/Conjugates.jl b/src/NumField/NfRel/Conjugates.jl
index 0c310af631..ddd89d0776 100644
--- a/src/NumField/NfRel/Conjugates.jl
+++ b/src/NumField/NfRel/Conjugates.jl
@@ -112,7 +112,7 @@ function infinite_places(L::NfRel{T}) where {T}
r_cnt = 1
c_cnt = 1
for (P, rts, r_rts, c_rts) in data
- if isreal(P)
+ if isreal(P)
for i in 1:length(r_rts)
plcs[r_cnt] = InfPlcNfRel{S, typeof(L)}(L, P, true, i, rts[i], r_cnt)
r_cnt += 1
@@ -120,7 +120,7 @@ function infinite_places(L::NfRel{T}) where {T}
rr = length(r_rts)
for i in 1:length(c_rts)
plcs[r + c_cnt] = InfPlcNfRel{S, typeof(L)}(L, P, false, rr + i, rts[rr + i], r + c_cnt)
- c_cnt +=1
+ c_cnt +=1
end
else
for i in 1:length(rts)
@@ -257,7 +257,7 @@ function conjugates_arb(a::NfRelElem, prec::Int = 64)
CC = AcbField(wprec, cached = false)
CCy, y = PolynomialRing(CC, cached = false)
-
+
r, s = signature(parent(a))
_r, _s = signature(K)
real_cnt = 1
diff --git a/src/NumField/NfRel/NEQ.jl b/src/NumField/NfRel/NEQ.jl
index 336fd81464..fba24f7fc4 100644
--- a/src/NumField/NfRel/NEQ.jl
+++ b/src/NumField/NfRel/NEQ.jl
@@ -23,7 +23,7 @@ function isnorm_fac_elem(K::NfRel{nf_elem}, a::nf_elem)
q, mmq = quo(q, [mq(preimage(mC, FB[i]))], false)
mq = mq*mmq
end
-
+
s = Set(ideal_type(order_type(AnticNumberField))[minimum(mkK, I) for I = S])
#make S relative Galois closed:
PS = IdealSet(ZKa)
diff --git a/src/NumField/NfRel/NfRel.jl b/src/NumField/NfRel/NfRel.jl
index 59ba60d072..f9e3421d71 100644
--- a/src/NumField/NfRel/NfRel.jl
+++ b/src/NumField/NfRel/NfRel.jl
@@ -754,7 +754,7 @@ rand(rng::AbstractRNG, L::NfRel, B::UnitRange{Int}) = rand(rng, make(L, B))
@doc Markdown.doc"""
kummer_generator(K::NfRel{nf_elem}) -> nf_elem
-Given an extension $K/k$ which is a cyclic Kummer extension of degree $n$, returns an element $a\in k$
+Given an extension $K/k$ which is a cyclic Kummer extension of degree $n$, returns an element $a\in k$
such that $K = k(\sqrt[n]{a})$. Throws an error if the extension is not a cyclic Kummer extension.
"""
function kummer_generator(K::NfRel{nf_elem})
diff --git a/src/NumField/NfRel/NfRelNS.jl b/src/NumField/NfRel/NfRelNS.jl
index 6b45fe9c65..155387855b 100644
--- a/src/NumField/NfRel/NfRelNS.jl
+++ b/src/NumField/NfRel/NfRelNS.jl
@@ -130,7 +130,7 @@ function reduce!(a::NfRelNSElem)
q, a.data = divrem(a.data, parent(a).pol)
return a
end
-
+
################################################################################
#
# String I/O
@@ -260,7 +260,7 @@ Nemo.divexact(a::NfRelNSElem, b::NfRelNSElem; check::Bool = true) = div(a, b)
################################################################################
#via julia
-function Base.:(^)(a::NfRelNSElem{T}, b::Integer) where T
+function Base.:(^)(a::NfRelNSElem{T}, b::Integer) where T
if b < 0
return inv(a)^(-b)
elseif b == 0
@@ -271,7 +271,7 @@ function Base.:(^)(a::NfRelNSElem{T}, b::Integer) where T
c = a^(div(b, 2))
mul!(c, c, c)
return c
- else
+ else
c = a^(b - 1)
mul!(c, c, a)
return c
@@ -289,7 +289,7 @@ function Base.:(^)(a::NfRelNSElem{T}, b::fmpz) where T
c = a^(div(b, 2))
mul!(c, c, c)
return c
- else
+ else
c = a^(b - 1)
mul!(c, c, a)
return c
@@ -366,7 +366,7 @@ function (R::Generic.PolyRing{nf_elem})(f::Generic.MPoly)
if f.exps[j, 1] != 0
if c==0
c = j
- else
+ else
error("poly is not univariate")
end
end
@@ -467,11 +467,11 @@ function SRow(a::NfRelElem)
if !iszero(c)
push!(sr.pos, i+1)
push!(sr.values, c)
- end
+ end
end
return sr
end
-
+
function minpoly_dense(a::NfRelNSElem)
K = parent(a)
n = degree(K)
@@ -503,7 +503,7 @@ function Base.Matrix(a::SMat)
end
end
return A
-end
+end
function minpoly_sparse(a::NfRelNSElem)
K = parent(a)
@@ -536,7 +536,7 @@ function minpoly_sparse(a::NfRelNSElem)
end
return f
end
- end
+ end
push!(sz.values, k(1))
push!(sz.pos, n+i+1)
push!(M, sz)
@@ -779,7 +779,7 @@ function basis(K::NfRel)
push!(b, b[end]*a)
end
return b
-end
+end
function (K::NfRelNS)(a::Vector)
return dot(a, basis(K))
diff --git a/src/NumField/NfRel/NfRelNSMor.jl b/src/NumField/NfRel/NfRelNSMor.jl
index bf8be2d471..69948a444d 100644
--- a/src/NumField/NfRel/NfRelNSMor.jl
+++ b/src/NumField/NfRel/NfRelNSMor.jl
@@ -189,8 +189,8 @@ end
Evaluate the polynomial by substituting in the supplied values in the array `vals` for
the corresponding variables with indices given by the array `vars`. The evaluation will
succeed if multiplication is defined between elements of the coefficient ring of $a$ and
-elements of `vals`. The result will be reduced modulo "mod". If "mod" is a Groebner basis for the ideal
-the elements generate.
+elements of `vals`. The result will be reduced modulo "mod". If "mod" is a Groebner basis for the ideal
+the elements generate.
"""
function compose_mod(a::S, vars::Vector{Int}, vals::Vector{S}, mod::Vector{S}) where S <:MPolyElem{T} where T <: RingElem
unique(vars) != vars && error("Variables not unique")
diff --git a/src/NumField/NfRel/Simplify.jl b/src/NumField/NfRel/Simplify.jl
index 4231081354..2f22d134dc 100644
--- a/src/NumField/NfRel/Simplify.jl
+++ b/src/NumField/NfRel/Simplify.jl
@@ -127,7 +127,7 @@ function _find_prime(L::NfRel{nf_elem})
i += 1
end
end
-
+
res = candidates[1]
for j = 2:n_attempts
if candidates[j][2] < res[2]
diff --git a/src/NumField/NfRel/absolute_field.jl b/src/NumField/NfRel/absolute_field.jl
index 2eb5d71380..2831b3d37e 100644
--- a/src/NumField/NfRel/absolute_field.jl
+++ b/src/NumField/NfRel/absolute_field.jl
@@ -26,7 +26,7 @@ function absolute_primitive_element(K::NfRelNS)
end
return a
end
-
+
function absolute_primitive_element(K::NfRel)
k = base_field(K)
gk = absolute_primitive_element(k)
@@ -99,11 +99,11 @@ absolute_simple_field(::NumField)
function absolute_simple_field(K::AnticNumberField)
return K, id_hom(K)
end
-
+
function absolute_simple_field(K::NfAbsNS; cached::Bool = true, simplify::Bool = false)
return simple_extension(K, cached = cached, simplified = simplify)
end
-
+
function absolute_simple_field(K::NumField; cached::Bool = false, simplify::Bool = false)
if simplify
return simplified_absolute_field(K, cached = cached)
@@ -128,8 +128,8 @@ function absolute_simple_field(K::NfRel{nf_elem}; cached::Bool = false, simplify
embed(MapFromFunc(x->preimage(h1, x), K, Ka))
return Ka, h1
end
-
-
+
+
#Trager: p4, Algebraic Factoring and Rational Function Integration
function _absolute_field(K::NfRel; cached::Bool = false)
f = K.pol
@@ -152,15 +152,15 @@ function _absolute_field(K::NfRel; cached::Bool = false)
g = compose(f, gen(kx) - l*gen(k))
N = norm(g)
end
-
+
Ka, gKa = NumberField(N, "x", cached = cached, check = false)
KaT, T = PolynomialRing(Ka, "T", cached = false)
-
+
# map Ka -> K: gen(Ka) -> gen(K)+ k gen(k)
-
+
# gen(k) -> Root(gcd(g, poly(k))) #gcd should be linear:
# g in kx = (Q[a])[x]. Want to map x -> gen(Ka), a -> T
-
+
gg = zero(KaT)
for i=degree(g):-1:0
auxp = change_base_ring(Ka, Qx(coeff(g, i)), parent = KaT)
@@ -168,7 +168,7 @@ function _absolute_field(K::NfRel; cached::Bool = false)
add!(gg, gg, auxp)
#gg = gg*gKa + auxp
end
-
+
q = gcd(gg, change_base_ring(Ka, k.pol, parent = KaT))
@assert degree(q) == 1
al = -constant_coefficient(q)//leading_coefficient(q)
diff --git a/src/NumField/NfRel/relative_extension.jl b/src/NumField/NfRel/relative_extension.jl
index 59d679712e..1fdf201b13 100644
--- a/src/NumField/NfRel/relative_extension.jl
+++ b/src/NumField/NfRel/relative_extension.jl
@@ -9,7 +9,7 @@ export relative_simple_extension, isprimitive, isprimitive_over
@doc Markdown.doc"""
relative_simple_extension(K::NumField, k::NumField) -> NfRel
-Given two fields $K\supset k$, it returns $K$ as a simple relative
+Given two fields $K\supset k$, it returns $K$ as a simple relative
extension $L$ of $k$ and an isomorphism $L \to K$.
"""
function relative_simple_extension(K::NumField, k::NumField)
@@ -102,7 +102,7 @@ end
################################################################################
#
-# Relative primitive element
+# Relative primitive element
#
################################################################################
diff --git a/src/NumField/NonSimpleNumField/Conjugates.jl b/src/NumField/NonSimpleNumField/Conjugates.jl
index 74d7379699..1623d067ff 100644
--- a/src/NumField/NonSimpleNumField/Conjugates.jl
+++ b/src/NumField/NonSimpleNumField/Conjugates.jl
@@ -4,7 +4,7 @@ mutable struct InfPlcNonSimple{S, U}
data::Vector{acb}
absolute_index::Int
isreal::Bool
-
+
function InfPlcNonSimple{S, U}(field::S, base_field_place::U, data::Vector{acb}, absolute_index::Int, isreal::Bool) where {S, U}
z = new{S, U}(field, base_field_place, data, absolute_index, isreal)
@@ -58,7 +58,7 @@ function infinite_places(L::NfRelNS{T}) where {T}
data = _conjugates_data(L, 32)
ind = 1
res = Vector{place_type(L)}(undef, r + s)
- for (p, rts) in data
+ for (p, rts) in data
res[ind] = S(L, p, rts, ind, ind <= r)
ind += 1
end
@@ -161,17 +161,17 @@ function __conjugates_data(L::NfRelNS{T}, p::Int) where T
ind_real, ind_complex = enumerate_conj_prim_rel(datas)
for y in ind_real
r_cnt += 1
- res[r_cnt] = (P, acb[datas[j][2][y[j]] for j = 1:length(y)])
+ res[r_cnt] = (P, acb[datas[j][2][y[j]] for j = 1:length(y)])
end
for y in ind_complex
c_cnt += 1
- res[r + c_cnt] = (P, acb[datas[j][2][y[j]] for j = 1:length(y)])
+ res[r + c_cnt] = (P, acb[datas[j][2][y[j]] for j = 1:length(y)])
end
else
it = cartesian_product_iterator([1:length(x[2]) for x in datas], inplace = true)
for y in it
c_cnt += 1
- res[r + c_cnt] = (P, acb[datas[j][2][y[j]] for j = 1:length(y)])
+ res[r + c_cnt] = (P, acb[datas[j][2][y[j]] for j = 1:length(y)])
end
end
end
@@ -246,7 +246,7 @@ function _is_complex_conj_rel(v::Vector{Int}, w::Vector{Int}, pos::Vector, roots
elseif v[i] != w[i]
return false
end
- i += 1
+ i += 1
end
return true
end
diff --git a/src/NumField/NonSimpleNumField/Field.jl b/src/NumField/NonSimpleNumField/Field.jl
index 6d5f30662c..9bbad9dab3 100644
--- a/src/NumField/NonSimpleNumField/Field.jl
+++ b/src/NumField/NonSimpleNumField/Field.jl
@@ -122,7 +122,7 @@ function _check_consistency(K::NonSimpleNumField)
end
if !isirreducible(f)
return false
- end
+ end
end
return true
end
@@ -136,7 +136,7 @@ end
@doc Markdown.doc"""
component(L::NonSimpleNumField, i::Int) -> SimpleNumField, Map
-Given a non-simple extension $L/K$, this function returns the simple number field
+Given a non-simple extension $L/K$, this function returns the simple number field
corresponding to the $i$-th component of $L$ together with its embedding.
"""
function component(K::NonSimpleNumField, i::Int)
@@ -266,7 +266,7 @@ end
@doc Markdown.doc"""
simplified_simple_extension(L::NonSimpleNumField) -> SimpleNumField, Map
-Given a non-simple extension $L/K$, this function returns an isomorphic simple number field
+Given a non-simple extension $L/K$, this function returns an isomorphic simple number field
with a "small" defining equation together with the isomorphism.
"""
function simplified_simple_extension(L::NonSimpleNumField; cached::Bool = true, isabelian::Bool = false)
diff --git a/src/NumField/QQ.jl b/src/NumField/QQ.jl
index 699c02e001..d47ec44b6a 100644
--- a/src/NumField/QQ.jl
+++ b/src/NumField/QQ.jl
@@ -103,7 +103,7 @@ gcd(I::ZZIdl, J::ZZIdl) = ZZIdl(gcd(I.gen, J.gen))
gcd(I::ZZIdl, n::T) where T <: Union{fmpz, Int} = ZZIdl(gcd(I.gen, n))
gcd(n::T, I::ZZIdl) where T <: Union{fmpz, Int} = ZZIdl(gcd(I.gen, n))
-isone(I::ZZIdl) = isone(I.gen)
+isone(I::ZZIdl) = isone(I.gen)
maximal_order(::FlintRationalField) = ZZ
diff --git a/src/NumField/SimpleNumField/Subfields.jl b/src/NumField/SimpleNumField/Subfields.jl
index ce44dd81b1..c309cfa66a 100644
--- a/src/NumField/SimpleNumField/Subfields.jl
+++ b/src/NumField/SimpleNumField/Subfields.jl
@@ -313,7 +313,7 @@ function subfields(K::SimpleNumField; degree::Int = -1)
if isprime(n)
res = Tuple{T, morphism_type(T)}[]
- if degree == n
+ if degree == n
push!(res, (K, id_hom(K)))
elseif degree == 1
kt, t = PolynomialRing(k, "t", cached = false)
diff --git a/src/NumField/Subfields.jl b/src/NumField/Subfields.jl
index 96bceb5fae..d7ddbb8d93 100644
--- a/src/NumField/Subfields.jl
+++ b/src/NumField/Subfields.jl
@@ -295,7 +295,7 @@ function fixed_field(K::AnticNumberField, A::Vector{NfToNfMor}; simplify::Bool =
return K, id_hom(K)
end
- if ismaximal_order_known(K)
+ if ismaximal_order_known(K)
OK = maximal_order(K)
if isdefined(OK, :lllO)
k, mk = fixed_field1(K, A)
@@ -332,7 +332,7 @@ function fixed_field(K::AnticNumberField, A::Vector{NfToNfMor}; simplify::Bool =
m[j, j] = m[j, j] - bm.den # This is autos[i] - identity
end
-
+
push!(ar_mat, m)
end
@@ -370,7 +370,7 @@ function fixed_field(K::NfRel, A::Vector{T}; simplify::Bool = true) where {T <:
if length(autos) == 0
return K, id_hom(K)
end
-
+
F = base_field(K)
a = gen(K)
n = degree(K)
diff --git a/src/NumFieldOrd/NfOrd/Clgp.jl b/src/NumFieldOrd/NfOrd/Clgp.jl
index 9890fc411c..874fcfd7d4 100644
--- a/src/NumFieldOrd/NfOrd/Clgp.jl
+++ b/src/NumFieldOrd/NfOrd/Clgp.jl
@@ -271,7 +271,7 @@ function _class_unit_group(O::NfOrd; saturate_at_2::Bool = true, bound::Int = -1
@v_do :UnitGroup 1 popindent()
# r == 1 means full rank
if isone(r) # use saturation!!!!
- idx, reg_expected = _validate_class_unit_group(c, U)
+ idx, reg_expected = _validate_class_unit_group(c, U)
if isone(idx)
break
end
@@ -310,7 +310,7 @@ function _class_unit_group(O::NfOrd; saturate_at_2::Bool = true, bound::Int = -1
end
@assert fl # so I can switch assertions off...
c.sat_done = 2*Int(idx)
- n_idx, reg_expected = _validate_class_unit_group(c, U)
+ n_idx, reg_expected = _validate_class_unit_group(c, U)
@vprint :ClassGroup 1 "index estimate down to $n_idx from $idx\n"
@assert idx != n_idx
idx = n_idx
@@ -331,7 +331,7 @@ function _class_unit_group(O::NfOrd; saturate_at_2::Bool = true, bound::Int = -1
do_units = true
if length(c.M.rel_gens) < unit_group_rank(O)
do_units = false
- end
+ end
else
add += 2
do_units = false
@@ -419,8 +419,8 @@ function class_group(O::NfOrd; bound::Int = -1, method::Int = 3,
if do_lll
OK = maximal_order(nf(O))
@assert OK.ismaximal == 1
- L = lll(OK)
- @assert L.ismaximal == 1
+ L = lll(OK)
+ @assert L.ismaximal == 1
else
L = O
end
diff --git a/src/NumFieldOrd/NfOrd/Clgp/Ctx.jl b/src/NumFieldOrd/NfOrd/Clgp/Ctx.jl
index 191837bec4..4869b4279b 100644
--- a/src/NumFieldOrd/NfOrd/Clgp/Ctx.jl
+++ b/src/NumFieldOrd/NfOrd/Clgp/Ctx.jl
@@ -43,7 +43,7 @@ function class_group_init(FB::NfFactorBase, T::DataType = SMat{fmpz}; add_rels::
class_group_add_relation(clg, b, abs(bn), fmpz(1), orbit = false)
end
end
-
+
l = zero_matrix(FlintZZ, n, 1+clg.c.r2)
for i = 1:n
l[i,1] = 1
@@ -67,7 +67,7 @@ function class_group_init(FB::NfFactorBase, T::DataType = SMat{fmpz}; add_rels::
if use_aut
au = automorphisms(nf(O), copy = false)
clg.aut_grp = class_group_add_auto(clg, au)
- clg.normCtx = NormCtx(O, div(nbits(discriminant(O)), 2) + 20,
+ clg.normCtx = NormCtx(O, div(nbits(discriminant(O)), 2) + 20,
length(au) == degree(O))
else
clg.normCtx = NormCtx(O, div(nbits(discriminant(O)), 2) + 20, false)
@@ -76,7 +76,7 @@ function class_group_init(FB::NfFactorBase, T::DataType = SMat{fmpz}; add_rels::
return clg
end
-function class_group_init(O::NfOrd, B::Int; min_size::Int = 20, add_rels::Bool = true,
+function class_group_init(O::NfOrd, B::Int; min_size::Int = 20, add_rels::Bool = true,
use_aut::Bool = false,
complete::Bool = true, degree_limit::Int = 0, T::DataType = SMat{fmpz})
@vprint :ClassGroup 2 "Computing factor base ...\n"
diff --git a/src/NumFieldOrd/NfOrd/Clgp/FacBase_Euc.jl b/src/NumFieldOrd/NfOrd/Clgp/FacBase_Euc.jl
index 6429c93bce..406d73b114 100644
--- a/src/NumFieldOrd/NfOrd/Clgp/FacBase_Euc.jl
+++ b/src/NumFieldOrd/NfOrd/Clgp/FacBase_Euc.jl
@@ -46,7 +46,7 @@ end
function issmooth(c::FactorBase{T}, a::T) where T
@assert a != 0
g = gcd(c.prod, a)
- while g != 1
+ while g != 1
a = div(a, g)
g = gcd(g, a)
end
@@ -60,7 +60,7 @@ function issmooth!(c::FactorBase{fmpz}, a::fmpz)
return a==1 || a==-1, a
end
b = copy(a)
- while g != 1
+ while g != 1
divexact!(b, b, g)
gcd!(g, g, b)
end
@@ -88,7 +88,7 @@ function _split(c::node{T}, a::T) where T
end
if isdefined(c, :right)
r = gcd(a, c.right.content)
- if r != 1
+ if r != 1
rs = _split(c.right, r)
else
rs = Vector{T}()
@@ -118,7 +118,7 @@ function factor(c::FactorBase{T}, a::T, do_error::Bool = true) where T
return f
end
-function factor(c::FactorBase{fmpz}, a::fmpq)
+function factor(c::FactorBase{fmpz}, a::fmpq)
@assert a != 0
a = deepcopy(a)
f = Dict{fmpz, Int}()
diff --git a/src/NumFieldOrd/NfOrd/Clgp/FacBase_Idl.jl b/src/NumFieldOrd/NfOrd/Clgp/FacBase_Idl.jl
index 6c7023b87d..bcb3d1f2dc 100644
--- a/src/NumFieldOrd/NfOrd/Clgp/FacBase_Idl.jl
+++ b/src/NumFieldOrd/NfOrd/Clgp/FacBase_Idl.jl
@@ -1,6 +1,6 @@
################################################################################
#
-# NfFactorBase : Factor bases for number fields
+# NfFactorBase : Factor bases for number fields
# A factor basis is mostly a collection of prime ideals, designed,
# if possible, to allow for rapid testing if elements are smooth.
#
@@ -26,7 +26,7 @@ function NfFactorBase(O::NfOrd, B::Int;
lp = prime_ideals_up_to(O, B, complete = complete, degree_limit = degree_limit)
@vprint :ClassGroup 2 " done \n"
return NfFactorBase(O, lp)
-end
+end
function NfFactorBase(O::NfOrd, lp::Vector{NfOrdIdl})
lp = sort(lp, lt = function(a,b) return norm(a) > norm(b); end)
@@ -88,7 +88,7 @@ end
function _factor!(FB::NfFactorBase, a::nf_elem,
error::Bool = true, n::fmpq = abs(norm(a)), integral::Bool = true)
T = fmpz
- O = order(FB.ideals[1])
+ O = order(FB.ideals[1])
n = deepcopy(n)
if integral
@@ -128,7 +128,7 @@ function _factor!(FB::NfFactorBase, a::nf_elem,
end
@hassert :ClassGroup 1 length(r) > 0
return ret, SRow{T}(r)
- else
+ else
# factor failed or I have a unit.
# sparse rel mat must not have zero-rows.
return false, SRow{T}()
@@ -141,7 +141,7 @@ end
function _factor!(FB::Hecke.NfFactorBase, A::Hecke.NfOrdIdl,
error::Bool = true)
- T = fmpz
+ T = fmpz
O = order(A)
n = norm(A)
@@ -152,9 +152,9 @@ function _factor!(FB::Hecke.NfFactorBase, A::Hecke.NfOrdIdl,
return true, SRow{T}()
end
- d = factor(FB.fb_int, n) # as above: fails - even if error is false -
+ d = factor(FB.fb_int, n) # as above: fails - even if error is false -
# if the norm is not smooth
-
+
rw = FB.rw
r = Vector{Tuple{Int, Int}}()
for p in keys(d)
@@ -188,7 +188,7 @@ function _factor!(FB::Hecke.NfFactorBase, A::Hecke.NfOrdIdl,
@hassert :ClassGroup 9000 A == prod([FB.ideals[i]^j for (i, j) in r])
@hassert :ClassGroup 1 length(r) > 0
return true, res
- else
+ else
# factor failed or I have a unit.
# sparse rel mat must not have zero-rows.
return false, SRow{T}()
diff --git a/src/NumFieldOrd/NfOrd/Clgp/Main_LLL.jl b/src/NumFieldOrd/NfOrd/Clgp/Main_LLL.jl
index fc4b5dbfe0..5327eeb418 100644
--- a/src/NumFieldOrd/NfOrd/Clgp/Main_LLL.jl
+++ b/src/NumFieldOrd/NfOrd/Clgp/Main_LLL.jl
@@ -36,7 +36,7 @@ function single_env(c::ClassGrpCtx{T}, I::Hecke.SmallLLLRelationsCtx, rat::Float
@vprint :ClassGroup 2 "not enough progress $(I.cnt) $(c.expect) $good\n"
break
end
- if fl
+ if fl
good += length(c.M.bas_gens) #= + length(c.M.rel_gens) =# - bef
end
if fl && max_good > -1
@@ -105,7 +105,7 @@ function class_group_new_relations_via_lll(c::ClassGrpCtx{T}, rat::Float64 = 0.2
end
@vprint :ClassGroup 1 "piv was empty, supplemented it to\n"
@vprint :ClassGroup 1 "$(piv)\n"
- end
+ end
start = max(1, max(div(length(c.FB.ideals), 2)+1, length(c.FB.ideals)-10*(1+div(rand_exp, 3))))
@@ -177,13 +177,13 @@ function class_group_new_relations_via_lll(c::ClassGrpCtx{T}, rat::Float64 = 0.2
end
end
end
- end
+ end
@vprint :ClassGroup 1 "eval info\n"
@vtime :ClassGroup 1 h, piv_new = class_group_get_pivot_info(c)
@vprint :ClassGroup 1 "length(piv) = $(length(piv_new)) and h = $h\n"
@vprint :ClassGroup 1 "$(piv_new)\n"
-
+
if piv_new == piv
if h > 0
extra = 2
@@ -198,14 +198,14 @@ function class_group_new_relations_via_lll(c::ClassGrpCtx{T}, rat::Float64 = 0.2
while gcd(rand_exp, h) > 1
rand_exp += 1
end
- end
+ end
if rand_exp % 3 == 0
start = max(start -10, 1)
end
end
piv = piv_new
- if h == 1
+ if h == 1
return nothing
end
end
diff --git a/src/NumFieldOrd/NfOrd/Clgp/Main_enum.jl b/src/NumFieldOrd/NfOrd/Clgp/Main_enum.jl
index a9aad0a9d2..7da983a21c 100644
--- a/src/NumFieldOrd/NfOrd/Clgp/Main_enum.jl
+++ b/src/NumFieldOrd/NfOrd/Clgp/Main_enum.jl
@@ -10,13 +10,13 @@ function class_group_random_ideal_relation(clg::ClassGrpCtx, r::Int,
if r < 2
r = 2
end
- for i = 1:r
+ for i = 1:r
I = I*rand(clg.FB.ideals)
I, g = reduce_ideal_class(I)
s *= g
end
return s;
-end
+end
# Do better: re-use partial hnf, check rank mod p, ...
@@ -157,7 +157,7 @@ function class_group_find_relations(clg::ClassGrpCtx; val = 0, prec::Int = 100,
end
e = class_group_small_real_elements_relation_next(E)
n = abs(norm_div(e, norm(E.A), np))
-
+
if nbits(numerator(n)) > np-10
bad_norm += 1
if bad_norm /(E.cnt + E.bad + 1) > 0.1
@@ -204,12 +204,12 @@ function class_group_find_relations(clg::ClassGrpCtx; val = 0, prec::Int = 100,
println("current h=$h from $(clg.M)")
if h != 0
- if h==1
+ if h==1
return h, piv
end
@v_do :ClassGroup 1 println("full rank: current h = ", h,
" want ", want_extra, " more")
- if h == last_h
+ if h == last_h
want_extra -= 1
else
want_extra = 15
@@ -227,7 +227,7 @@ function class_group_find_relations(clg::ClassGrpCtx; val = 0, prec::Int = 100,
clg.time[:hnf_time]/1e9, " sec for hnf in ", clg.hnf_call, " calls");
@v_do :ClassGroup 1 println("added ", clg.rel_cnt, " good relations and ",
clg.bad_rel, " bad ones, ratio ", clg.bad_rel/clg.rel_cnt)
-
+
class_group_process_relmatrix(clg)
h, piv = class_group_get_pivot_info(clg)
@@ -258,7 +258,7 @@ function class_group_find_relations2(clg::ClassGrpCtx; val = 0, prec = 100,
for i in nI:-1:1
I = Idl[i]
too_slow = false
- f = class_group_small_real_elements_relation_start(clg, I,
+ f = class_group_small_real_elements_relation_start(clg, I,
limit = limit, prec = prec, val = val)
f.vl = val
@@ -279,7 +279,7 @@ function class_group_find_relations2(clg::ClassGrpCtx; val = 0, prec = 100,
a = rank(clg.M)
if (a-old_r) < 0.5
@v_do :ClassGroup 2 println("rank too slow $a ($old_r) and $(clg.rel_mat_full_rank)")
- too_slow = true
+ too_slow = true
break
end
old_r = a
@@ -292,7 +292,7 @@ function class_group_find_relations2(clg::ClassGrpCtx; val = 0, prec = 100,
@v_do :ClassGroup 2 println("too slow in getting s.th. for ", i,
"\ngood: ", f.cnt, " bad: ", f.bad,
" ratio: ", (clg.bad_rel/clg.rel_cnt))
- too_slow = true
+ too_slow = true
break
end
end
@@ -347,7 +347,7 @@ function class_group_find_relations2(clg::ClassGrpCtx; val = 0, prec = 100,
# println(n, " should be ", sqrt_disc)
# println("offending element is ", e)
# println("prec now ", prec)
-# end
+# end
A = Idl[i]
j = 0
# TH: without added no_rand_local < nI it crashes sometimes
@@ -403,13 +403,13 @@ function class_group_find_relations2(clg::ClassGrpCtx; val = 0, prec = 100,
end
a_old = a
if h != 0
- if h==1
+ if h==1
return h, piv
end
@vprint :ClassGroup 1 "Now have $(clg.M)"
@v_do :ClassGroup 1 println("full rank: current h = ", h,
" want ", want_extra, " more")
- if h == last_h
+ if h == last_h
want_extra -= 1
else
want_extra = 15
@@ -437,7 +437,7 @@ function class_group_find_new_relation(clg::ClassGrpCtx; val = 0, prec = 100,
limit = 10, extra = 1)
if !isdefined(clg, :randomClsEnv)
clg.randomClsEnv = random_init(clg.FB.ideals)
- end
+ end
O = parent(clg.FB.ideals[1]).order
sqrt_disc = isqrt(abs(discriminant(O)))
@@ -461,7 +461,7 @@ function class_group_find_new_relation(clg::ClassGrpCtx; val = 0, prec = 100,
if class_group_add_relation(clg, e, n, norm(E.A))
E.cnt += 1
extra -= 1
- if extra <= 0
+ if extra <= 0
return
end
else
@@ -471,8 +471,8 @@ function class_group_find_new_relation(clg::ClassGrpCtx; val = 0, prec = 100,
end
end
end
- end
+ end
class_group_process_relmatrix(clg)
-end
+end
diff --git a/src/NumFieldOrd/NfOrd/Clgp/Map.jl b/src/NumFieldOrd/NfOrd/Clgp/Map.jl
index deab8498ee..9938a47166 100644
--- a/src/NumFieldOrd/NfOrd/Clgp/Map.jl
+++ b/src/NumFieldOrd/NfOrd/Clgp/Map.jl
@@ -142,7 +142,7 @@ function class_group_ideal_relation(I::NfOrdIdl, c::ClassGrpCtx)
end
#really annoying, but at least we have a small(ish) ideal now
#println("have to work")
-
+
E = class_group_small_lll_elements_relation_start(c, I)
iI = inv(I)
if isdefined(c, :randomClsEnv)
@@ -162,7 +162,7 @@ function class_group_ideal_relation(I::NfOrdIdl, c::ClassGrpCtx)
@vprint :ClassGroup 1 "New random \n"
last_j = random_get(J, reduce = false)
@vprint :ClassGroup 1 "Using $last_j \n"
- E = class_group_small_lll_elements_relation_start(c, I*last_j)
+ E = class_group_small_lll_elements_relation_start(c, I*last_j)
iI = inv(E.A)
end
@@ -176,7 +176,7 @@ function class_group_ideal_relation(I::NfOrdIdl, c::ClassGrpCtx)
@vprint :ClassGroup 1 "New random \n"
last_j = random_get(J, reduce = false)
@vprint :ClassGroup 1 "Using $last_j \n"
- E = class_group_small_lll_elements_relation_start(c, I*last_j)
+ E = class_group_small_lll_elements_relation_start(c, I*last_j)
iI = inv(E.A)
continue
end
@@ -204,7 +204,7 @@ function class_group_ideal_relation(I::NfOrdIdl, c::ClassGrpCtx)
fl, s = _factor!(c.FB, last_j)
@assert fl
res2 = r-s
-
+
else
res2 = r
end
diff --git a/src/NumFieldOrd/NfOrd/Clgp/Proof.jl b/src/NumFieldOrd/NfOrd/Clgp/Proof.jl
index 98a2b10156..4929129cd2 100644
--- a/src/NumFieldOrd/NfOrd/Clgp/Proof.jl
+++ b/src/NumFieldOrd/NfOrd/Clgp/Proof.jl
@@ -47,7 +47,7 @@ function showprogress(io::IO, p::MiniProgressBar, info)
print(io, info)
print(io, "\r")
end
-
+
function class_group_proof(clg::ClassGrpCtx, lb::fmpz, ub::fmpz; extra :: fmpz=fmpz(0), prec::Int = 100, do_it=1:ub)
PB = MiniProgressBar(header = "Class group proof")
@@ -84,7 +84,7 @@ function class_group_proof(clg::ClassGrpCtx, lb::fmpz, ub::fmpz; extra :: fmpz=f
while p < do_it.stop
no_primes += 1
-
+
@v_do :ClassGroupProof if no_primes % interval == 0
#println("did $no_primes prime numbers so far, now $p, need to reach $ub (~$(no_primes/_no_of_primes))")
last_time = PB.time_shown
@@ -92,7 +92,7 @@ function class_group_proof(clg::ClassGrpCtx, lb::fmpz, ub::fmpz; extra :: fmpz=f
prev = PB.prev
PB.current = no_primes/_no_of_primes
# from PB.current to prev it took cur_time - last_time seconds
-
+
if rate == 0.0
rate = ((PB.current - PB.prev)/(cur_time - last_time))
else
@@ -121,7 +121,7 @@ function class_group_proof(clg::ClassGrpCtx, lb::fmpz, ub::fmpz; extra :: fmpz=f
fac = prime_decomposition(O, Int(p), deg_lim, low_lim)
for _k in fac
k = _k[1]
- if norm(k) <= lb
+ if norm(k) <= lb
continue
end
no_ideals += 1
@@ -141,13 +141,13 @@ function class_group_proof(clg::ClassGrpCtx, lb::fmpz, ub::fmpz; extra :: fmpz=f
sucess = false
a = class_group_small_real_elements_relation_next(E)
n = norm_div(a, norm(k), np)
- if gcd(numerator(n), p) > extra
+ if gcd(numerator(n), p) > extra
# println("a: $a, $(norm(a)), $(norm(k)), $n")
# println("contains too many conjugates, bad")
continue
end
f, r = issmooth!(clg.FB.fb_int, numerator(n))
- if f
+ if f
M = SMat{Int}()
fl = _factor!(clg.FB, a, false, n)[1]
if fl
diff --git a/src/NumFieldOrd/NfOrd/Clgp/Rel_LLL.jl b/src/NumFieldOrd/NfOrd/Clgp/Rel_LLL.jl
index 8d45acaee0..283e330e79 100644
--- a/src/NumFieldOrd/NfOrd/Clgp/Rel_LLL.jl
+++ b/src/NumFieldOrd/NfOrd/Clgp/Rel_LLL.jl
@@ -78,7 +78,7 @@ function class_group_small_lll_elements_relation_start(clg::ClassGrpCtx{T},
if m < 2
m = n
end
- while length(f) < m
+ while length(f) < m
f = Int[i for i = 1:n if compare_index(L.num, i, i, bd) < 0]
bd *= 2
end
diff --git a/src/NumFieldOrd/NfOrd/Clgp/Rel_Schmettow.jl b/src/NumFieldOrd/NfOrd/Clgp/Rel_Schmettow.jl
index 2cab2c7348..715eb02477 100644
--- a/src/NumFieldOrd/NfOrd/Clgp/Rel_Schmettow.jl
+++ b/src/NumFieldOrd/NfOrd/Clgp/Rel_Schmettow.jl
@@ -8,9 +8,9 @@ function one_step(b::NfOrdFracIdl, p::NfOrdIdl; prec::Int = 100)
b = p*b
simplify(b)
g1 = short_elem(b, prec = prec)
- b = g1*inv(b)
+ b = g1*inv(b)
simplify(b)
- g2 = short_elem(b, prec = prec)
+ g2 = short_elem(b, prec = prec)
return simplify(g2*inv(b)), g1, g2
end
diff --git a/src/NumFieldOrd/NfOrd/Clgp/Rel_add.jl b/src/NumFieldOrd/NfOrd/Clgp/Rel_add.jl
index a64b8c929d..552eb9eb16 100644
--- a/src/NumFieldOrd/NfOrd/Clgp/Rel_add.jl
+++ b/src/NumFieldOrd/NfOrd/Clgp/Rel_add.jl
@@ -16,7 +16,7 @@ function special_prime_ideal(p::fmpz, a::nf_elem)
R = parent(f)
Zx = PolynomialRing(FlintZZ)[1]
Zpx = PolynomialRing(GF(UInt(p), cached=false), "\$x_p", cached=false)[1]
- g = Zpx(a)
+ g = Zpx(a)
ff = Zpx(f)
gcd!(g, g, ff)
return lift(Zx, g)
@@ -28,7 +28,7 @@ function push_normStat!(clg::ClassGrpCtx, n::fmpz, b::Bool)
clg.normStat[nb] = (0,0)
end
t = clg.normStat[nb]
- if b
+ if b
clg.normStat[nb] = (t[1], t[2] + 1)
else
clg.normStat[nb] = (t[1] + 1, t[2])
@@ -45,20 +45,20 @@ function class_group_add_relation(clg::ClassGrpCtx{T}, a::nf_elem, n::fmpq, nI::
if iszero(a) || isone(a)
return false
end
- if hash(a) in clg.RS
+ if hash(a) in clg.RS
return false
end
- O = order(clg.FB.ideals[1])
+ O = order(clg.FB.ideals[1])
easy = isdefining_polynomial_nice(parent(a))
@vprint :ClassGroup 3 "trying relation of length $(Float64(length(a))) and norm $(Float64(n*nI)), effective $(Float64(n))\n"
if integral #element is known to be integral
fl, r = issmooth!(clg.FB.fb_int, numerator(n*nI))
push_normStat!(clg, numerator(n), fl)
- else
+ else
fl, r = issmooth!(clg.FB.fb_int, numerator(n*nI)*denominator(a, O))
push_normStat!(clg, numerator(n)*denominator(a), fl)
- end
+ end
@assert issmooth!(clg.FB.fb_int, nI)[1]
@@ -66,7 +66,7 @@ function class_group_add_relation(clg::ClassGrpCtx{T}, a::nf_elem, n::fmpq, nI::
@vprint :ClassGroup 3 "not int-smooth\n"
# println("not int-smooth");
# try for large prime?
- if easy && abs(r) < clg.B2 && isprime(r) && !isindex_divisor(O, r)
+ if easy && abs(r) < clg.B2 && isprime(r) && !isindex_divisor(O, r)
@vprint :ClassGroup 3 "gives potential large prime\n"
i = special_prime_ideal(r, a)
#TODO: check Galois orbit of special ideal
@@ -76,7 +76,7 @@ function class_group_add_relation(clg::ClassGrpCtx{T}, a::nf_elem, n::fmpq, nI::
fl, r2 = _factor!(clg.FB, lp[1], false, norm(lp[1]))
b = FacElem(Dict([(a,1), (lp[1],-1)]))
fl = class_group_add_relation(clg, b, r1 - r2)
- if fl
+ if fl
clg.largePrime_success += 1
else
clg.largePrime_no_success += 1
@@ -113,11 +113,11 @@ function class_group_add_relation(clg::ClassGrpCtx{T}, a::nf_elem, n::fmpq, nI::
clg.rel_cnt += 1
end
end
-
+
if new_gen && orbit && isdefined(clg, :aut_grp)
n = res
o = _get_autos_from_ctx(clg)
-
+
@v_do :ClassGroup 1 println(" adding orbit with $(length(o)) elements")
for (b, m) in o
nn = Hecke.permute_row(n, m)
@@ -133,9 +133,9 @@ function class_group_add_relation(clg::ClassGrpCtx{T}, a::nf_elem, n::fmpq, nI::
end
end
end
- end
+ end
+
-
# @assert clg.rel_cnt < 2*ncols(clg.M)
@v_do :ClassGroup 1 println(" -> OK, rate currently ",
clg.bad_rel/clg.rel_cnt, " this ", clg.bad_rel - clg.last,
@@ -164,13 +164,13 @@ function class_group_add_relation(clg::ClassGrpCtx{SMat{fmpz}}, a::FacElem{nf_el
return class_group_add_relation(clg, a, R)
end
-function class_group_add_relation(clg::ClassGrpCtx{SMat{fmpz}}, a::FacElem{nf_elem, AnticNumberField}, R::SRow{fmpz}; always::Bool = true, add_orbit = true)
-
- if hash(a) in clg.RS
+function class_group_add_relation(clg::ClassGrpCtx{SMat{fmpz}}, a::FacElem{nf_elem, AnticNumberField}, R::SRow{fmpz}; always::Bool = true, add_orbit = true)
+
+ if hash(a) in clg.RS
return false
end
- O = order(clg.FB.ideals[1])
+ O = order(clg.FB.ideals[1])
@vprint :ClassGroup 3 "adding $R\n"
@@ -208,7 +208,7 @@ function class_group_add_relation(clg::ClassGrpCtx{SMat{fmpz}}, a::FacElem{nf_el
end
end
end
- end
+ end
clg.last = clg.bad_rel
return true
diff --git a/src/NumFieldOrd/NfOrd/Clgp/Rel_enum.jl b/src/NumFieldOrd/NfOrd/Clgp/Rel_enum.jl
index b8c2eceb88..44d3aa0e12 100644
--- a/src/NumFieldOrd/NfOrd/Clgp/Rel_enum.jl
+++ b/src/NumFieldOrd/NfOrd/Clgp/Rel_enum.jl
@@ -27,7 +27,7 @@ function enum_ctx_from_ideal(A::NfOrdIdl,
E.t = t*b
E.t_den = b_den
## we want to find x sth. norm(x) <= sqrt(|disc|)*norm(A)
- ## |N(x)^2|^(1/n) <= T_2(x)/n
+ ## |N(x)^2|^(1/n) <= T_2(x)/n
## so if T_2(x) <= n * D^(1/n)
## then |N(x)| <= D^(1/2)
#d = abs(discriminant(order(A))) * norm(A)^2
diff --git a/src/NumFieldOrd/NfOrd/Clgp/Saturate.jl b/src/NumFieldOrd/NfOrd/Clgp/Saturate.jl
index f67585ed8b..034620e44d 100644
--- a/src/NumFieldOrd/NfOrd/Clgp/Saturate.jl
+++ b/src/NumFieldOrd/NfOrd/Clgp/Saturate.jl
@@ -34,7 +34,7 @@ function mod_p(R::Vector{FacElem{nf_elem, AnticNumberField}}, Q::NfOrdIdl, p::In
for i = 1:pp-1
dl[y] = i
y *= x
- end
+ end
return matrix(T, 1, length(R), Int[dl[image(mF1, R[i], D[i], cached, pp)^e] % p for i in 1:length(R)])
end
@@ -131,14 +131,14 @@ function compute_candidates_for_saturate(v::Vector{FacElem{nf_elem, AnticNumberF
T = GF(p, cached = false)
cA = length(v1)
A = identity_matrix(T, cA)
-
+
S = Hecke.PrimesSet(Hecke.p_start, -1, p, 1)
D = Vector{Vector{gfp_poly}}(undef, length(v1))
for i in 1:length(v1)
D[i] = Vector{gfp_poly}(undef, length(v1[i].fac))
end
- dK = discriminant(OK)
+ dK = discriminant(OK)
threshold = stable*ncols(A)
i = 1
@@ -170,7 +170,7 @@ function compute_candidates_for_saturate(v::Vector{FacElem{nf_elem, AnticNumberF
return zero_matrix(FlintZZ, 0, length(v1))
end
A = A*sub(z, 1:nrows(z), 1:rrz)
- if cA == ncols(A)
+ if cA == ncols(A)
i += 1
else
i = 0
@@ -209,10 +209,10 @@ function compute_candidates_for_saturate1(c::Hecke.ClassGrpCtx, p::Int, stable::
T = GF(p, cached = false)
cA = length(R)
A = identity_matrix(T, cA)
-
+
S = Hecke.PrimesSet(Hecke.p_start, -1, p, 1)
- dK = discriminant(ZK)
+ dK = discriminant(ZK)
threshold = stable*ncols(A)
f = K.pol
@@ -309,7 +309,7 @@ function compute_candidates_for_saturate1(c::Hecke.ClassGrpCtx, p::Int, stable::
for i = 1:pp-1
disc_log[y] = T(i)
y *= elF
- end
+ end
#The disc log dictionary is ready. Now we need the subspace.
for i = 1:lfacts
z = matrix(T, 1, length(R), Hecke.gfp_elem[disc_log[evals[j][i]^e] for j = 1:length(R)])
@@ -319,7 +319,7 @@ function compute_candidates_for_saturate1(c::Hecke.ClassGrpCtx, p::Int, stable::
return zero_matrix(FlintZZ, 0, length(R))
end
A = A*sub(z, 1:nrows(z), 1:rrz)
- if cA == ncols(A)
+ if cA == ncols(A)
att += 1
else
att = 0
@@ -399,7 +399,7 @@ function saturate!(U::Hecke.UnitGrpCtx, n::Int, stable::Float64 = 3.5; use_orbit
if restart
restart = false
continue
- elseif wasted
+ elseif wasted
stable *= 2
else
@vprint :Saturate 1 "sat success at $(stable)\n"
@@ -443,7 +443,7 @@ function saturate!(d::Hecke.ClassGrpCtx, U::Hecke.UnitGrpCtx, n::Int, stable::Fl
continue
end
end
-
+
decom = Dict{NfOrdIdl, fmpz}((c.FB.ideals[k], v) for (k, v) = fac_a)
@vprint :Saturate 1 "Testing if element is an n-th power\n"
@vtime :Saturate 1 fl, x = ispower(a, n, decom = decom, easy = easy_root)
@@ -451,13 +451,13 @@ function saturate!(d::Hecke.ClassGrpCtx, U::Hecke.UnitGrpCtx, n::Int, stable::Fl
@vprint :Saturate 1 "The element is an n-th power\n"
success = true
fac_a = divexact(fac_a, n)
- if iszero(fac_a)
+ if iszero(fac_a)
#In this case, the element we have found is a unit and
#we want to make sure it is used
#find units can be randomised...
#maybe that should also be addressed elsewhere
@vprint :Saturate 1 "The new element is a unit\n"
-
+
if use_orbit
auts_action = Hecke._get_autos_from_ctx(d)
for s = 1:length(auts_action)
@@ -491,7 +491,7 @@ function saturate!(d::Hecke.ClassGrpCtx, U::Hecke.UnitGrpCtx, n::Int, stable::Fl
if restart
restart = false
continue
- elseif wasted
+ elseif wasted
stable *= 2
else
@vprint :Saturate 1 "sat success at $(stable)\n"
@@ -512,7 +512,7 @@ function simplify(c::Hecke.ClassGrpCtx, U::Hecke.UnitGrpCtx, cp::Int = 0; use_LL
vals_new_rels = Vector{SRow{fmpz}}()
@vprint :Saturate 1 "Computing rels...\n"
for i=1:length(c.FB.ideals)
- if cp != 0 && isone(c.M.basis.rows[i].values[1])
+ if cp != 0 && isone(c.M.basis.rows[i].values[1])
continue
end
@assert all(x -> x > 0, c.M.basis.rows[i].values)
@@ -551,7 +551,7 @@ function simplify(c::Hecke.ClassGrpCtx, U::Hecke.UnitGrpCtx, cp::Int = 0; use_LL
@assert fl
end
end
- for i=1:length(U.units)
+ for i=1:length(U.units)
Hecke.class_group_add_relation(d, U.units[i], SRow(FlintZZ))
end
return d
diff --git a/src/NumFieldOrd/NfOrd/Clgp/Sunits.jl b/src/NumFieldOrd/NfOrd/Clgp/Sunits.jl
index bd6341ec39..811970e109 100644
--- a/src/NumFieldOrd/NfOrd/Clgp/Sunits.jl
+++ b/src/NumFieldOrd/NfOrd/Clgp/Sunits.jl
@@ -4,7 +4,7 @@ function show(io::IO, mC::MapSUnitModUnitGrpFacElem)
@show_name(io, mC)
io = IOContext(io, :compact => true)
println(io, "SUnits (in factored form) mod Units map of ")
- show(io, codomain(mC))
+ show(io, codomain(mC))
println(io, "for $(mC.idl)")
end
@@ -52,7 +52,7 @@ function sunit_mod_units_group_fac_elem(I::Vector{NfOrdIdl})
@vtime :ClassGroup 1 for (i, A) = enumerate(I)
@vprint :ClassGroup 2 "doin' $(i)/$(length(I)):\n$A\n"
@vtime :ClassGroup 2 x, r = class_group_ideal_relation(A, c)
-# TODO: write == for Idl and FracIdl
+# TODO: write == for Idl and FracIdl
# @assert prod([c.FB.ideals[p]^Int(v) for (p,v) = r]) == x*A
push!(X, x)
push!(rr, r)
@@ -64,7 +64,7 @@ function sunit_mod_units_group_fac_elem(I::Vector{NfOrdIdl})
end
@vprint :ClassGroup 1 "... done\n"
-
+
@vprint :ClassGroup 1 "solving...\n"
@vtime :ClassGroup 1 R, d = solve_ut(H, rr)
Rd = hcat(d*identity_matrix(SMat, FlintZZ, nrows(R)), fmpz(-1)*R)
@@ -74,7 +74,7 @@ function sunit_mod_units_group_fac_elem(I::Vector{NfOrdIdl})
S1 = sub(S, 1:nrows(S), 1:nrows(S))
S2 = sub(S, 1:nrows(S), (nrows(S) + 1):ncols(S))
@assert nrows(S1) == nrows(S2) && nrows(S1) == nrows(S)
-
+
g = vcat(c.R_gen, c.R_rel)
valuations = SRow{fmpz}[]
@@ -118,8 +118,8 @@ function sunit_mod_units_group_fac_elem(I::Vector{NfOrdIdl})
C = abelian_group(fmpz[0 for i=U])
r = MapSUnitModUnitGrpFacElem()
r.idl = I_in
-
- local exp
+
+ local exp
let U = U
function exp(a::GrpAbFinGenElem)
b = U[1]^a.coeff[1, 1]
@@ -208,7 +208,7 @@ function sunit_group_fac_elem(I::Vector{NfOrdIdl})
end
local log
- let mS = mS, mU = mU, G = G
+ let mS = mS, mU = mU, G = G
function log(a::FacElem{nf_elem, AnticNumberField})
a1 = preimage(mS, a)
a2 = a*inv(image(mS, a1))
diff --git a/src/NumFieldOrd/NfOrd/Clgp/Types.jl b/src/NumFieldOrd/NfOrd/Clgp/Types.jl
index d3cb159b65..717b795aa2 100644
--- a/src/NumFieldOrd/NfOrd/Clgp/Types.jl
+++ b/src/NumFieldOrd/NfOrd/Clgp/Types.jl
@@ -1,6 +1,6 @@
mutable struct MapClassGrp <: Map{GrpAbFinGen, NfOrdIdlSet, HeckeMap, MapClassGrp}
header::MapHeader{GrpAbFinGen, NfOrdIdlSet}
-
+
quo::Int
princ_gens::Vector{Tuple{FacElem{NfOrdIdl,NfOrdIdlSet}, FacElem{nf_elem, AnticNumberField}}}
small_gens::Vector{NfOrdIdl}
diff --git a/src/NumFieldOrd/NfOrd/Clgp/cm_field.jl b/src/NumFieldOrd/NfOrd/Clgp/cm_field.jl
index 4ebdcd0c8c..ed30f32db4 100644
--- a/src/NumFieldOrd/NfOrd/Clgp/cm_field.jl
+++ b/src/NumFieldOrd/NfOrd/Clgp/cm_field.jl
@@ -107,13 +107,13 @@ function create_ctx(OK::NfOrd; bound::Int = -1, method::Int = 3, large::Int = 10
return c::ClassGrpCtx{SMat{fmpz}}
end
end
-
+
if bound == -1
bound = Int(ceil(log(abs(discriminant(OK)))^2*0.3))
(bound == 0) && (bound = 1)
end
-
+
c = class_group_init(OK, bound, complete = false, use_aut = use_aut)::ClassGrpCtx{SMat{fmpz}}
@assert order(c) === OK
- return c
+ return c
end
\ No newline at end of file
diff --git a/src/NumFieldOrd/NfOrd/FacElem.jl b/src/NumFieldOrd/NfOrd/FacElem.jl
index 6033175fe8..bd852cae7c 100644
--- a/src/NumFieldOrd/NfOrd/FacElem.jl
+++ b/src/NumFieldOrd/NfOrd/FacElem.jl
@@ -420,7 +420,7 @@ function factor_coprime(a::FacElem{nf_elem, AnticNumberField}, I::NfOrdIdlSet; r
if iszero(e)
continue
end
- if divisible(norm(b, copy = false), P)
+ if divisible(norm(b, copy = false), P)
v += valuation(b, p)*e
end
end
diff --git a/src/NumFieldOrd/NfOrd/FactorBaseBound.jl b/src/NumFieldOrd/NfOrd/FactorBaseBound.jl
index 5156d8ba75..86a943f8b8 100644
--- a/src/NumFieldOrd/NfOrd/FactorBaseBound.jl
+++ b/src/NumFieldOrd/NfOrd/FactorBaseBound.jl
@@ -52,9 +52,9 @@ ideals of norm bounded by $B$.
function factor_base_bound_bdf(O::NfOrd)
return _factor_base_bound_bdf(O, 100.0, 100.0)
end
-
+
function _factorbase_bound_bdf_right_side(O::NfOrd, x0::Float64, D::Dict{Int, Vector{Tuple{Int, Int}}})
- K = nf(O)
+ K = nf(O)
d = degree(K)
r, s = signature(O)
@@ -74,14 +74,14 @@ function _factorbase_bound_bdf_right_side(O::NfOrd, x0::Float64, D::Dict{Int, Ve
pm2 = R(p)^(R(FlintZZ(m)//FlintZZ(2)))
secondterm = R(1) - m*logp//logcurval
-
+
return logp//pm2 * secondterm
end
function comp_summand(p::Int, m::Int)
return comp_summand(fmpz(p), m)
end
-
+
p = 2
while p < curval
@@ -96,7 +96,7 @@ function _factorbase_bound_bdf_right_side(O::NfOrd, x0::Float64, D::Dict{Int, Ve
Pnorm = fmpz(p)^P[1]
if Pnorm < curval
max_exp = _max_power_in(Pnorm, curval)
-
+
for m in 1:max_exp
summand = comp_summand(Pnorm, m)
summ = summ + summand
@@ -105,13 +105,13 @@ function _factorbase_bound_bdf_right_side(O::NfOrd, x0::Float64, D::Dict{Int, Ve
end
p = next_prime(p)
end
-
+
y = 2*summ - (R(d)*(const_pi(R)^2//R(2)) + r*4*const_catalan(R))//logcurval
return y::arb
end
function _factor_base_bound_bdf(O::NfOrd, x0::Float64 = 50.0, ste::Float64 = 20.0)
- K = nf(O)
+ K = nf(O)
d = degree(K)
r, s = signature(O)
@@ -135,18 +135,18 @@ function _factor_base_bound_bdf(O::NfOrd, x0::Float64 = 50.0, ste::Float64 = 20.
x1 = 2*x0
y = _factorbase_bound_bdf_right_side(O, x1, dec_cache)
end
-
+
dista = abs(x0-x1)
while !( y > D && dista < ste)
- if y < D
+ if y < D
x1 = x0 + 3*dista/2
else
x1 = x0 - dista/2
end
dista = abs(x1-x0)
-
+
x0 = x1
y = _factorbase_bound_bdf_right_side(O, x0, dec_cache)
end
diff --git a/src/NumFieldOrd/NfOrd/Hensel.jl b/src/NumFieldOrd/NfOrd/Hensel.jl
index 46e734fd35..ead99ab146 100644
--- a/src/NumFieldOrd/NfOrd/Hensel.jl
+++ b/src/NumFieldOrd/NfOrd/Hensel.jl
@@ -72,7 +72,7 @@ function lift(R::NmodPolyRing, a::fq_nmod)
return f
end
-function (Zx::FmpzPolyRing)(a::nf_elem)
+function (Zx::FmpzPolyRing)(a::nf_elem)
b = Zx()
@assert denominator(a) == 1
if degree(parent(a)) == 1
@@ -120,7 +120,7 @@ function _roots_hensel(f::Generic.Poly{nf_elem};
n = degree(K)
deg = degree(f)
- # First we find a prime ideal such that f is squarefree modulo P
+ # First we find a prime ideal such that f is squarefree modulo P
# (The discriminant of f has only finitely many divisors).
p = degree(f)+1
@@ -160,7 +160,7 @@ function _roots_hensel(f::Generic.Poly{nf_elem};
if any(x->iszero(denominator(x) % p), coefficients(K.pol))
continue
end
-
+
Rp = Nemo.GF(p, cached=false)
Rpt, t = PolynomialRing(Rp, "t", cached=false)
gp = Rpt(K.pol)
@@ -184,7 +184,7 @@ function _roots_hensel(f::Generic.Poly{nf_elem};
red_coeff1 = Vector{fq_nmod}(undef, length(f))
red_coeff1[length(f)] = S(1)
for i = 2:length(f)-1
- red_coeff1[i] = zero(S)
+ red_coeff1[i] = zero(S)
end
red_coeff1[1] = S(Rpt(coeff(f, 0)))
fp = ST(red_coeff1)
@@ -233,7 +233,7 @@ function _roots_hensel(f::Generic.Poly{nf_elem};
#TODO: we need norm_change_const wrt. any basis to apply it to an
# equation order even if it is no order.
# probably needs an entire trail of other stuff
- r1, r2 = signature(K)
+ r1, r2 = signature(K)
gsa = derivative(K.pol)(gen(K))
if !isdefining_polynomial_nice(K)
@@ -414,12 +414,12 @@ function _hensel(f::Generic.Poly{nf_elem},
#assumes f squarefree
#assumes constant_coefficient(f) != 0
-
+
ZX, X = PolynomialRing(FlintZZ, "X", cached = false)
#to avoid embarrasment...
- #find the prime ideal - as I don't want to use orders, this is
+ #find the prime ideal - as I don't want to use orders, this is
#fun (computing a max order just for this is wasteful)
#fun fact: if g = prod g_i mod p^k, then P_i^k =
#so instead of powering, and simplify and such, lets write it down
@@ -430,7 +430,7 @@ function _hensel(f::Generic.Poly{nf_elem},
ff = ZX(d_pol*K.pol)
gg = hensel_lift(ff, g1, fmpz(p), k)
else
- gg = ZX(d_pol * K.pol)
+ gg = ZX(d_pol * K.pol)
pk = fmpz(p)^k
gg *= invmod(leading_coefficient(gg), pk)
mod_sym!(gg, pk)
@@ -450,8 +450,8 @@ function _hensel(f::Generic.Poly{nf_elem},
end
# Now if we are in the normal case and want max_roots, we only have
- # to lift max_roots
-
+ # to lift max_roots
+
if isnormal
rt = eltype(rt)[1:max(max_roots, degree(f))]
end
@@ -510,7 +510,7 @@ function _hensel(f::Generic.Poly{nf_elem},
M = zero_matrix(FlintZZ, n, n)
local Mi::fmpz_mat
local d::fmpz
-
+
@vprint :Saturate 1 "Maximum number of steps: $(length(pr))\n"
for i=2:length(pr)
@vprint :Saturate 1 "Step number $i\n"
@@ -597,7 +597,7 @@ function _hensel(f::Generic.Poly{nf_elem},
_cache_lll[pr[i]] = (M, Mi, d)
end
end
-
+
if ispure
ap = Qt((-coeff(f, 0)))
@@ -702,7 +702,7 @@ function _hensel(f::Generic.Poly{nf_elem}, p::Int, k::Int; max_roots::Int = degr
break
end
end
-
+
S = FqNmodFiniteField(lpfac, :z, false)
ST, T = PolynomialRing(S,"T", cached=false)
fp = ST([S(Rpt(coeff(f, i))) for i=0:degree(f)])
@@ -745,7 +745,7 @@ function _lifting_expo(p::Int, deg_p::Int, K::AnticNumberField, bnd::Vector{arb}
@assert denominator(t) == 1
tt = numerator(t)
tt *= tt'
- if degree(K) == 1
+ if degree(K) == 1
c3 = BigFloat(tt[1,1])
else
#see norm_change_const for an explanation
diff --git a/src/NumFieldOrd/NfOrd/Ideal/Arithmetic.jl b/src/NumFieldOrd/NfOrd/Ideal/Arithmetic.jl
index 18354b1f59..b1205ba711 100644
--- a/src/NumFieldOrd/NfOrd/Ideal/Arithmetic.jl
+++ b/src/NumFieldOrd/NfOrd/Ideal/Arithmetic.jl
@@ -79,7 +79,7 @@ function sum_princ_gen_special(x::NfAbsOrdIdl, y::NfAbsOrdIdl)
else
M1 = _hnf_modular_eldiv(basis_matrix(y, copy = false), genx, :lowerleft)
res = ideal(OK, M1, false, true)
- end
+ end
@hassert :NfOrd 1 res == sum_via_basis_matrix(x, y)
return res
end
@@ -135,10 +135,10 @@ function +(x::NfAbsOrdIdl, y::NfAbsOrdIdl)
if isdefined(x, :norm) && isdefined(y, :norm) && isone(gcd(x.norm, y.norm))
return ideal(OK, 1)
end
- if has_princ_gen_special(x)
+ if has_princ_gen_special(x)
return sum_princ_gen_special(x, y)
end
- if has_princ_gen_special(y)
+ if has_princ_gen_special(y)
return sum_princ_gen_special(y, x)
end
g = gcd(minimum(x, copy = false), minimum(y, copy = false))
diff --git a/src/NumFieldOrd/NfOrd/Ideal/Enum.jl b/src/NumFieldOrd/NfOrd/Ideal/Enum.jl
index 3c7e66dc89..deef4915d6 100644
--- a/src/NumFieldOrd/NfOrd/Ideal/Enum.jl
+++ b/src/NumFieldOrd/NfOrd/Ideal/Enum.jl
@@ -17,7 +17,7 @@ mutable struct FactoredIdeal
end
end
-function ==(a::FactoredIdeal, b::FactoredIdeal)
+function ==(a::FactoredIdeal, b::FactoredIdeal)
return a.exp == b.exp
end
diff --git a/src/NumFieldOrd/NfOrd/Ideal/FacElem.jl b/src/NumFieldOrd/NfOrd/Ideal/FacElem.jl
index fb417e4be9..3ad77e9eeb 100644
--- a/src/NumFieldOrd/NfOrd/Ideal/FacElem.jl
+++ b/src/NumFieldOrd/NfOrd/Ideal/FacElem.jl
@@ -239,7 +239,7 @@ function factor_over_coprime_base(x::FacElem{NfOrdIdl, NfOrdIdlSet}, coprime_bas
if iszero(e)
continue
end
- if divisible(norm(b, copy = false), P)
+ if divisible(norm(b, copy = false), P)
v += valuation(b, p)*e
end
end
@@ -252,9 +252,9 @@ function factor_over_coprime_base(x::FacElem{NfOrdIdl, NfOrdIdlSet}, coprime_bas
end
function simplify!(x::FacElem{NfOrdIdl, NfOrdIdlSet}; refine::Bool = false)
- if length(x.fac) <= 1
+ if length(x.fac) <= 1
return nothing
- elseif all(x -> iszero(x), values(x.fac))
+ elseif all(x -> iszero(x), values(x.fac))
x.fac = Dict{NfOrdIdl, fmpz}()
return nothing
end
@@ -263,7 +263,7 @@ function simplify!(x::FacElem{NfOrdIdl, NfOrdIdlSet}; refine::Bool = false)
ev = factor_over_coprime_base(x, cp)
x.fac = ev
return nothing
-end
+end
function simplify(x::FacElem{NfOrdFracIdl, NfOrdFracIdlSet})
z = deepcopy(x)
diff --git a/src/NumFieldOrd/NfOrd/Ideal/Ideal.jl b/src/NumFieldOrd/NfOrd/Ideal/Ideal.jl
index e3f781da15..0415bd7aea 100644
--- a/src/NumFieldOrd/NfOrd/Ideal/Ideal.jl
+++ b/src/NumFieldOrd/NfOrd/Ideal/Ideal.jl
@@ -616,7 +616,7 @@ function assure_has_minimum(A::NfAbsOrdIdl)
if has_minimum(A)
return nothing
end
-
+
if degree(order(A)) == 1
if has_2_elem(A)
A.minimum = gcd(A.gen_one, numerator(coeff(A.gen_two.elem_in_nf, 0)))
@@ -1187,7 +1187,7 @@ function _minmod_comp(a::fmpz, b::NfOrdElem)
# ub + vf = r
# so u/r is the inverse and r is the den in the field
# we want gcd(r, a). so we use rres
- #at this point, min() SHOULD be
+ #at this point, min() SHOULD be
end
function _invmod(a::fmpz, b::NfAbsOrdElem)
@@ -1213,7 +1213,7 @@ function __invmod(a::fmpz, b::NfOrdElem)
k = nf(Zk)
d = denominator(b.elem_in_nf)
d, _ = ppio(d, a)
- e, _ = ppio(basis_matrix(Zk, copy = false).den, a)
+ e, _ = ppio(basis_matrix(Zk, copy = false).den, a)
mod_r = a^2*d*e
if fits(Int, mod_r)
S1 = ResidueRing(FlintZZ, Int(mod_r), cached=false)
@@ -1236,7 +1236,7 @@ function __invmod(a::fmpz, b::NfOrdElem)
St = PolynomialRing(S, cached=false)[1]
B = St(d*b.elem_in_nf)
F = St(k.pol)
-
+
m, u, v = rresx(B, F) # u*B + v*F = m mod modulus(S)
if iszero(m)
m = mod_r
@@ -2243,8 +2243,8 @@ function iscoprime(I::NfAbsOrdIdl, J::NfAbsOrdIdl)
if isprime_known(J) && isprime(J)
return iszero(valuation(I, J))
end
- #Lemma: Let R be a (commutative) artinian ring, let I be an ideal of R and
- #let x be a nilpotent element. Then I = 1 if and only if I + x = 1
+ #Lemma: Let R be a (commutative) artinian ring, let I be an ideal of R and
+ #let x be a nilpotent element. Then I = 1 if and only if I + x = 1
m = gcd(minimum(I, copy = false), minimum(J, copy = false))
m = ispower(m)[2]
if has_2_elem(I) && has_2_elem(J)
@@ -2270,7 +2270,7 @@ function iscoprime(I::NfAbsOrdIdl, J::NfAbsOrdIdl)
end
end
return isone(gcd(I, m)+J)
-end
+end
function iscoprime(I::NfAbsOrdIdl, a::fmpz)
return iscoprime(minimum(I, copy = false), a)
diff --git a/src/NumFieldOrd/NfOrd/Ideal/Prime.jl b/src/NumFieldOrd/NfOrd/Ideal/Prime.jl
index 6d3bd4000a..62d3ac6e5a 100644
--- a/src/NumFieldOrd/NfOrd/Ideal/Prime.jl
+++ b/src/NumFieldOrd/NfOrd/Ideal/Prime.jl
@@ -717,7 +717,7 @@ function coprime_base(A::Vector{NfOrdIdl}, p::fmpz)
return coprime_base_steel(Ap)
end
-
+
function _get_integer_in_ideal(I::NfOrdIdl)
if has_minimum(I)
return minimum(I)
@@ -730,7 +730,7 @@ function _get_integer_in_ideal(I::NfOrdIdl)
end
return minimum(I)
end
-
+
@doc Markdown.doc"""
coprime_base(A::Vector{NfOrdIdl}) -> Vector{NfOrdIdl}
coprime_base(A::Vector{NfOrdElem}) -> Vector{NfOrdIdl}
@@ -1608,7 +1608,7 @@ end
# Decomposition Group of a prime ideal
#
################################################################################
-
+
@doc Markdown.doc"""
decomposition_group(P::NfOrdIdl; G::Vector{NfToNfMor}) -> Vector{NfToNfMor}
@@ -1616,7 +1616,7 @@ Given a prime ideal $P$ in a normal number field $G$, it returns a vector of the
such that $\sigma_i(P) = P$ for all $i = 1,\dots, s$.
If a subgroup $G$ of automorphisms is given, the output is the intersection of the decomposition group with that subgroup.
"""
-
+
function decomposition_group(P::NfOrdIdl; G::Vector{NfToNfMor} = NfToNfMor[],
orderG::Int = degree(P)*ramification_index(P))
@assert isprime(P)
@@ -1697,9 +1697,9 @@ end
@doc Markdown.doc"""
decomposition_group(K::AnticNumberField, P::NfOrdIdl, m::Map)
-> Grp, GrpToGrp
-
+
Given a prime ideal $P$ of a number field $K$ and a map `m` return from
-`automorphism_group(K)`, return the decompositon group of $P$ as a subgroup of
+`automorphism_group(K)`, return the decompositon group of $P$ as a subgroup of
the domain of `m`.
"""
function decomposition_group(K::AnticNumberField, P::NfOrdIdl, mG::Map)
@@ -1712,7 +1712,7 @@ end
# Inertia subgroup of a prime ideal
#
################################################################################
-
+
@doc Markdown.doc"""
inertia_subgroup(P::NfOrdIdl; G::Vector{NfToNfMor}) -> Vector{NfToNfMor}
@@ -1720,7 +1720,7 @@ Given a prime ideal $P$ in a normal number field, it returns a vector of the aut
such that $\sigma_i(P) = P$ for all $i = 1,\dots, s$ and induce the identity on the residue field.
If a subgroup $G$ of automorphisms is given, the output is the intersection of the inertia group with $G$.
"""
-
+
function inertia_subgroup(P::NfOrdIdl; G::Vector{NfToNfMor} = NfToNfMor[])
@assert isprime(P)
O = order(P)
@@ -1803,7 +1803,7 @@ end
@doc Markdown.doc"""
inertia_subgroup(K::AnticNumberField, P::NfOrdIdl, m::Map) -> Grp, GrpToGrp
-
+
Given a prime ideal $P$ of a number field $K$ and a map `m` return from
`automorphism_group(K)`, return the intertia subgroup of $P$ as a subgroup of
the domain of `m`.
@@ -1838,9 +1838,9 @@ end
@doc Markdown.doc"""
ramification_group(K::AnticNumberField, P::NfOrdIdl, m::Map) -> Grp, GrpToGrp
-
+
Given a prime ideal $P$ of a number field $K$ and a map `m` return from
-`automorphism_group(K)`, return the ramification group of $P$ as a subgroup of
+`automorphism_group(K)`, return the ramification group of $P$ as a subgroup of
the domain of `m`.
"""
function ramification_group(K::AnticNumberField, P::NfOrdIdl, i::Int, mG::Map)
diff --git a/src/NumFieldOrd/NfOrd/Ideal/Relative.jl b/src/NumFieldOrd/NfOrd/Ideal/Relative.jl
index cf5ba92f68..beafa28203 100644
--- a/src/NumFieldOrd/NfOrd/Ideal/Relative.jl
+++ b/src/NumFieldOrd/NfOrd/Ideal/Relative.jl
@@ -248,7 +248,7 @@ function prime_decomposition_type_nonindex(f::Map, p::NfOrdIdl, ZK = maximal_ord
Gp = factor_shape(gcd(Fp(f(K(p.gen_two))), Fp(G)))
else
Fpp = PolynomialRing(GF(minimum(p), cached = false), cached = false)[1]
- Gp = factor_shape(gcd(Fpp(f(K(p.gen_two))), Fpp(G)))
+ Gp = factor_shape(gcd(Fpp(f(K(p.gen_two))), Fpp(G)))
end
res = Vector{Tuple{Int, Int}}(undef, sum(values(Gp)))
ind = 1
diff --git a/src/NumFieldOrd/NfOrd/Ideal/TwoElement.jl b/src/NumFieldOrd/NfOrd/Ideal/TwoElement.jl
index bf26ee382d..b0aaa08b2f 100644
--- a/src/NumFieldOrd/NfOrd/Ideal/TwoElement.jl
+++ b/src/NumFieldOrd/NfOrd/Ideal/TwoElement.jl
@@ -30,7 +30,7 @@ Returns whether $A$ has normal two element generators.
"""
function has_2_elem_normal(A::NfAbsOrdIdl)
#the one ideal <1, ?> is automatomatically normal>
- if isdefined(A, :gens_normal)
+ if isdefined(A, :gens_normal)
return isone(A.gen_one) || A.gens_normal > 1
end
if has_2_elem(A) && defines_2_normal(A)
@@ -51,7 +51,7 @@ function isconsistent(A::NfAbsOrdIdl)
if has_2_elem_normal(A) && !iszero(A.gen_two)
if !defines_2_normal(A)
@show "Not 2 normal"
- vshow(A)
+ vshow(A)
return false
end
end
@@ -284,7 +284,7 @@ function assure_2_normal_difficult(A::NfAbsOrdIdl)
else
d = Int[2, 3, 5, 7]
end
-
+
I = ideal(ZK, 1)
for i = 1:length(d)
m1, m = ppio(m, fmpz(d[i]))
@@ -295,7 +295,7 @@ function assure_2_normal_difficult(A::NfAbsOrdIdl)
lp = prime_decomposition(ZK, d[i])
v = Int[valuation_of_ideal_difficult(A1, p[1]) for p = lp]
for i = 1:length(v)
- if v[i] > 0
+ if v[i] > 0
I *= lp[i][1]^v[i]
end
end
@@ -341,7 +341,7 @@ function assure_2_normal(A::NfAbsOrdIdl)
A.gens_normal = fmpz(1)
return nothing
end
-
+
if norm(A) == 0
A.gen_one = fmpz(0)
A.gen_two = zero(O)
@@ -389,7 +389,7 @@ function assure_2_normal(A::NfAbsOrdIdl)
mg = _minmod(m^2, gen)
g = gcd(m, mg)
-
+
if gcd(m, div(mg, g)) == 1
if gcd(m^n, _normmod(m^n, gen)) != norm(A)
@vprint :NfOrd 2 "\n\noffending ideal $A \ngen is $gen\nWrong ideal\n"
@@ -441,7 +441,7 @@ function assure_2_normal(A::NfAbsOrdIdl)
if cnt > 100 && is2_normal_difficult(A)
assure_2_normal_difficult(A)
@hassert :NfOrd 1 isconsistent(A)
- return
+ return
end
if cnt > 1000
error("Having a hard time making generators normal for $A")
diff --git a/src/NumFieldOrd/NfOrd/Ideal/Valuation.jl b/src/NumFieldOrd/NfOrd/Ideal/Valuation.jl
index edc81fb26f..f3d6473836 100644
--- a/src/NumFieldOrd/NfOrd/Ideal/Valuation.jl
+++ b/src/NumFieldOrd/NfOrd/Ideal/Valuation.jl
@@ -98,8 +98,8 @@ function val_func_index(p::NfOrdIdl)
P = p.gen_one
pi_2 = mod(pi.num.gen_two.elem_in_nf, P^2)
M = representation_matrix(O(pi_2, false))
-
-
+
+
local val
let P = P, O = O, M = M, p = p
function val(x::nf_elem, no::fmpq = fmpq(0))
@@ -151,12 +151,12 @@ function val_fun_generic_small(p::NfOrdIdl)
mul!(x, x, e)
while x in O && v < 10
v += 1
- if !iszero(no)
+ if !iszero(no)
nn = divexact(nn, norm(p))
if !divisible(nn, norm(p))
break
end
- end
+ end
x = mod(x, p_mod)
mul!(x, x, e)
end
@@ -191,13 +191,13 @@ function val_func_generic(p::NfOrdIdl)
x = x*e
while x in O
v += 1
- if !iszero(no)
+ if !iszero(no)
nn = divexact(nn, norm(p))
if !divisible(nn, norm(p))
break
end
x = mod(x, p_mod)
- end
+ end
mul!(x, x, e)
end
return v-valuation(d, P)*p.splitting_type[1]
@@ -225,7 +225,7 @@ function _isindex_divisor(O::NfOrd, P::NfOrdIdl)
@assert isprime_known(P) && isprime(P)
if !isone(denominator(P.gen_two.elem_in_nf))
return true
- end
+ end
R = GF(Int(minimum(P)), cached = false)
Rt, t = PolynomialRing(R, "x", cached = false)
f = Rt(nf(P).pol)
@@ -242,7 +242,7 @@ end
function assure_valuation_function(p::NfOrdIdl)
if isdefined(p, :valuation)
return nothing
- end
+ end
O = order(p)
K = nf(O)
# for generic ideals
@@ -265,7 +265,7 @@ function assure_valuation_function(p::NfOrdIdl)
return nothing
end
P = minimum(p)
- if degree(O) < 40 && p.splitting_type[1]*p.splitting_type[2] == degree(O)
+ if degree(O) < 40 && p.splitting_type[1]*p.splitting_type[2] == degree(O)
local val3
let P = P, p = p
function val3(s::nf_elem, no::fmpq = fmpq(0))
@@ -375,7 +375,7 @@ function valuation(a::nf_elem, p::NfOrdIdl, no::fmpq = fmpq(0))
end
@hassert :NfOrd 0 !iszero(a)
assure_valuation_function(p)
- if p.is_prime != 1
+ if p.is_prime != 1
return Int(p.valuation(a, no))::Int
end
#First, check the content of a as a polynomial.
@@ -457,7 +457,7 @@ function valuation_naive(x::NfAbsOrdElem, B::NfAbsOrdIdl)
return i
end
-function valuation_naive(x::T, B::NfAbsOrdIdl) where T <: Union{nf_elem, NfAbsNSElem}
+function valuation_naive(x::T, B::NfAbsOrdIdl) where T <: Union{nf_elem, NfAbsNSElem}
@assert !isone(B)
i = 0
C = B
diff --git a/src/NumFieldOrd/NfOrd/LLL.jl b/src/NumFieldOrd/NfOrd/LLL.jl
index 0c4852c201..57c1c436be 100644
--- a/src/NumFieldOrd/NfOrd/LLL.jl
+++ b/src/NumFieldOrd/NfOrd/LLL.jl
@@ -51,7 +51,7 @@ function lll(A::NfOrdIdl, v::fmpz_mat = zero_matrix(FlintZZ, 1, 1); prec::Int =
K = nf(order(A))
- if iszero(v)
+ if iszero(v)
if istotally_real(K)
#in this case the gram-matrix of the minkowski lattice is the trace-matrix
#which is exact.
@@ -161,16 +161,16 @@ function _lll(A::NfOrdIdl, v::fmpz_mat = zero_matrix(FlintZZ, 1, 1); prec::Int =
end
## lattice has lattice disc = order_disc * norm^2
## lll needs to yield a basis sth
- ## l[1,1] = |b_i|^2 <= 2^((n-1)/2) disc^(1/n)
+ ## l[1,1] = |b_i|^2 <= 2^((n-1)/2) disc^(1/n)
## and prod(l[i,i]) <= 2^(n(n-1)/2) disc
n = nrows(l)
disc = abs(discriminant(order(A)))*norm(A)^2 * den^(2*n) * fmpz(2)^(2*sv)
di = root(disc, n)+1
di *= fmpz(2)^(div(n+1,2)) * fmpz(2)^prec
- if compare_index(l, 1, 1, di) > 0
+ if compare_index(l, 1, 1, di) > 0
@v_do :ClassGroup 2 printstyled("LLL basis too large\n", color = :red);
- @v_do :ClassGroup 3 println("bound is ", di, " value at ", 1, " is ", l[1,1]);
+ @v_do :ClassGroup 3 println("bound is ", di, " value at ", 1, " is ", l[1,1]);
throw(LowPrecisionLLL())
end
pr = prod_diagonal(l)
@@ -196,7 +196,7 @@ end
The same order, but with the basis now being LLL reduced wrt. the Minkowski metric.
"""
function lll(M::NfAbsOrd; prec::Int = 100)
-
+
if isdefined(M, :lllO)
return M.lllO::typeof(M)
end
@@ -207,7 +207,7 @@ function lll(M::NfAbsOrd; prec::Int = 100)
M.lllO = On
return On::typeof(M)
end
-
+
if degree(K) == 2
On = _lll_quad(M)
M.lllO = On
@@ -222,7 +222,7 @@ function lll(M::NfAbsOrd; prec::Int = 100)
return On::typeof(M)
end
end
-
+
return _lll(M, prec)
end
@@ -375,7 +375,7 @@ function _lll(M::NfAbsOrd, prec::Int)
M1 = _ordering_by_T2(M)
prec = max(prec, 10*n)
prec = max(prec, 100 + 25*div(degree(M), 3) + Int(round(log(abs(discriminant(M))))))
-
+
if n > 10
if n > 100
prec, M1 = lll_precomputation(M1, prec)
@@ -389,7 +389,7 @@ function _lll(M::NfAbsOrd, prec::Int)
end
function _ordering_by_T2(M::NfAbsOrd, prec::Int = 32)
-
+
K = nf(M)
B = basis(M, K)
ints = fmpz[lower_bound(t2(x, prec), fmpz) for x in B]
@@ -526,7 +526,7 @@ function _lll_sublattice(M::NfAbsOrd, u::Vector{Int}; prec = 100)
@vprint :LLL 3 "Block of dimension $(l)\n"
prec = max(prec, 10*n)
local g::fmpz_mat
-
+
bas = basis(M, K)[u]
profile_sub = nbits(prod(Hecke.upper_bound(t2(x), fmpz) for x in bas))
@vprint :LLL 3 "Starting with profile $(profile_sub)\n"
@@ -587,10 +587,10 @@ function _lll_with_parameters(M::NfAbsOrd, parameters::Tuple{Float64, Float64},
dM = sum(nbits(Hecke.upper_bound(t2(x), fmpz)) for x in basis(M, K))
@vprint :LLL 1 "Input profile: $(dM)\n"
@vprint :LLL 1 "Target profile: $(nbits(disc^2)+divexact(n*(n-1), 2)) \n"
- att = 0
+ att = 0
while steps == -1 || att < steps
att += 1
- if att > 3
+ if att > 3
@vprint :LLL "Having a hard time computing a LLL basis"
end
@vprint :LLL 3 "Attempt number : $(att)\n"
@@ -606,7 +606,7 @@ function _lll_with_parameters(M::NfAbsOrd, parameters::Tuple{Float64, Float64},
@vprint :LLL 3 "Minkowski matrix computed\n"
diag_d = prod_diagonal(d)
g = identity_matrix(FlintZZ, n)
-
+
prec = div(prec, 2)
shift!(d, -prec) #TODO: remove?
@@ -614,7 +614,7 @@ function _lll_with_parameters(M::NfAbsOrd, parameters::Tuple{Float64, Float64},
fmpz_mat_entry_add_ui!(d, i, i, UInt(nrows(d)))
end
@vtime :LLL 3 ccall((:fmpz_lll, libflint), Nothing, (Ref{fmpz_mat}, Ref{fmpz_mat}, Ref{Nemo.lll_ctx}), d, g, ctx)
-
+
if nbits(maximum(abs, g)) <= div(prec, 2)
fl = true
disc = abs(discriminant(M))
@@ -624,7 +624,7 @@ function _lll_with_parameters(M::NfAbsOrd, parameters::Tuple{Float64, Float64},
fl = false
else
pr = prod_diagonal(d)
- if pr > fmpz(2)^(div(n*(n-1), 2)+(n*prec)) * disc
+ if pr > fmpz(2)^(div(n*(n-1), 2)+(n*prec)) * disc
fl = false
end
end
@@ -815,7 +815,7 @@ function reduce_ideal(I::FacElem{NfOrdIdl, NfOrdIdlSet})
@hassert :PID_Test 1 A*evaluate(a) == evaluate(I)
return A, a
end
-
+
# The bound should be sqrt(disc) (something from LLL)
@doc Markdown.doc"""
@@ -955,7 +955,7 @@ function _new_power_reduce(A::NfOrdIdl, e::fmpz, Ainv::NfOrdIdl, d::fmpz)
C2inv = IJ
C2d = dCinv*dCinv
end
-
+
if isodd(e)
if norm(A)*norm(C2) > bdisc
a = divexact(short_elem_product(C2inv, Ainv), C2d*d)
@@ -998,9 +998,9 @@ end
#
################################################################################
-# Claus and Tommy:
+# Claus and Tommy:
# We express the basis of IJ in terms of the basis of I (I contains IJ)
-# Then we compute the lll of the matrix of the coordinates. This way we get a
+# Then we compute the lll of the matrix of the coordinates. This way we get a
# better basis to start the computation of LLL
#We compute the hnf to have a guaranteed bound on the entries
function _lll_product_basis(I::NfOrdIdl, J::NfOrdIdl)
@@ -1013,7 +1013,7 @@ function _lll_product_basis(I::NfOrdIdl, J::NfOrdIdl)
divexact!(iA, iA, de)
hnf_modular_eldiv!(iA, minimum(J))
@vtime :LLL 3 lll!(iA, lll_ctx(0.3, 0.51))
- @vtime :LLL 3 lll!(iA)
+ @vtime :LLL 3 lll!(iA)
mul!(iA, iA, A)
return iA
end
diff --git a/src/NumFieldOrd/NfOrd/LLLctx.jl b/src/NumFieldOrd/NfOrd/LLLctx.jl
index 2d6432be7c..57687c2c34 100644
--- a/src/NumFieldOrd/NfOrd/LLLctx.jl
+++ b/src/NumFieldOrd/NfOrd/LLLctx.jl
@@ -94,7 +94,7 @@ function weighted_minkowski_gram_scaled(L::NfLattice, v::fmpz_mat, prec::Int)
for i=1:n
fmpz_mat_entry_add_ui!(g, i, i, UInt(nrows(d)))
end
- return g
+ return g
end
function lll(L::NfLattice, weights::fmpz_mat = zero_matrix(FlintZZ, 1, 1); starting_prec::Int = 100 + 25*div(dim(L), 3) + Int(round(log(abs(discriminant(L))))))
@@ -168,7 +168,7 @@ function _lll(L::NfLattice, weights::fmpz_mat, prec::Int)
disc = discriminant(L) * fmpz(2)^(2*sv)
di = root(disc, n) + 1
di *= fmpz(2)^(div(n+1,2)) * fmpz(2)^prec
- if compare_index(d, 1, 1, di) > 0
+ if compare_index(d, 1, 1, di) > 0
fl = false
end
pr = prod_diagonal(d)
diff --git a/src/NumFieldOrd/NfOrd/LinearAlgebra.jl b/src/NumFieldOrd/NfOrd/LinearAlgebra.jl
index cedf299f32..a85fc9087d 100644
--- a/src/NumFieldOrd/NfOrd/LinearAlgebra.jl
+++ b/src/NumFieldOrd/NfOrd/LinearAlgebra.jl
@@ -249,7 +249,7 @@ end
@doc Markdown.doc"""
coefficient_ideals(M::PMat)
-Returns the vector of coefficient ideals.
+Returns the vector of coefficient ideals.
"""
coefficient_ideals(M::PMat) = M.coeffs
diff --git a/src/NumFieldOrd/NfOrd/MaxOrd/DedekindCriterion.jl b/src/NumFieldOrd/NfOrd/MaxOrd/DedekindCriterion.jl
index 49012cb153..4de8cb83b2 100644
--- a/src/NumFieldOrd/NfOrd/MaxOrd/DedekindCriterion.jl
+++ b/src/NumFieldOrd/NfOrd/MaxOrd/DedekindCriterion.jl
@@ -50,8 +50,8 @@ function dedekind_test(O::NfOrd, p::fmpz, compute_order::Type{Val{S}} = Val{true
Zyf = Zy(f)
- fmodp = Kx(Zyf)
-
+ fmodp = Kx(Zyf)
+
fac = factor_squarefree(fmodp)
g = prod(x for x in keys(fac.fac))
@@ -68,10 +68,10 @@ function dedekind_test(O::NfOrd, p::fmpz, compute_order::Type{Val{S}} = Val{true
@assert r == 0
setcoeff!(g1,i,q)
end
-
+
g1modp = Kx(g1)
U = gcd(gcd(g, h), g1modp)
-
+
if compute_order == Val{false}
if isone(U)
return true
@@ -80,7 +80,7 @@ function dedekind_test(O::NfOrd, p::fmpz, compute_order::Type{Val{S}} = Val{true
end
else
- pmaximal = (isone(U))
+ pmaximal = (isone(U))
if pmaximal
return true, O
@@ -132,26 +132,26 @@ dedekind_poverorder(O::NfOrd, p::Integer) = dedekind_poverorder(O, FlintZZ(p))
function dedekind_test_composite(O::NfOrd, p::fmpz)
@assert isequation_order(O)
-
+
Zy = PolynomialRing(FlintZZ, "y")[1]
R = ResidueRing(FlintZZ, p, cached = false)
Rx = PolynomialRing(R, "x", cached=false)[1]
f = Zy(nf(O).pol)
- fmodp = Rx(f)
-
+ fmodp = Rx(f)
+
# Now, I would like to have the squarefree factorization of fmodp
# I go for the f/gcd(f,f')
-
+
divs, gcdfderf = _gcd_with_failure(fmodp, derivative(fmodp))
-
+
if !isone(divs)
return gcd(divs, p), O
end
-
+
sqff = divexact(fmodp, gcdfderf)
-
+
# first build 1/p ( f - g*h)
gZ = lift(Zy,sqff)
@@ -159,14 +159,14 @@ function dedekind_test_composite(O::NfOrd, p::fmpz)
g1 = f - gZ*hZ
g1 = divexact(g1, p)
-
+
g1modp = Rx(g1)
- divs, par1 = _gcd_with_failure(gcdfderf, sqff)
+ divs, par1 = _gcd_with_failure(gcdfderf, sqff)
if !isone(divs)
return gcd(divs, p), O
end
- divs, U = _gcd_with_failure(par1, g1modp)
+ divs, U = _gcd_with_failure(par1, g1modp)
if !isone(divs)
return gcd(divs, p), O
end
diff --git a/src/NumFieldOrd/NfOrd/MaxOrd/MaxOrd.jl b/src/NumFieldOrd/NfOrd/MaxOrd/MaxOrd.jl
index d5ece9f58a..ff983f8e7c 100644
--- a/src/NumFieldOrd/NfOrd/MaxOrd/MaxOrd.jl
+++ b/src/NumFieldOrd/NfOrd/MaxOrd/MaxOrd.jl
@@ -301,7 +301,7 @@ function _TameOverorderBL(O::NfOrd, lp::Vector{fmpz})
end
else
if isdefining_polynomial_nice(nf(O)) && iscoprime(index(OO), q)
- q1, OOq = dedekind_test_composite(EquationOrder(K), q)
+ q1, OOq = dedekind_test_composite(EquationOrder(K), q)
if !isone(q1)
push!(M, q1)
push!(M, divexact(q, q1))
diff --git a/src/NumFieldOrd/NfOrd/MaxOrd/MaxOrdNS.jl b/src/NumFieldOrd/NfOrd/MaxOrd/MaxOrdNS.jl
index 43f05ac6c8..53d9cce3f6 100644
--- a/src/NumFieldOrd/NfOrd/MaxOrd/MaxOrdNS.jl
+++ b/src/NumFieldOrd/NfOrd/MaxOrd/MaxOrdNS.jl
@@ -53,7 +53,7 @@ function _maximal_order_round_four(O::NfAbsOrd{<:NumField{fmpq}, <:NumFieldElem{
O1 = pmaximal_overorder(O, p)
if valuation(discriminant(O1), p) < valuation(discriminant(OO),p)
OO += O1
- end
+ end
@vprint :NfOrd 1 "done\n"
end
end
@@ -177,7 +177,7 @@ function _maximal_order_of_components(L::NfAbsNS) where {S, T}
end
end
return B, lp, d
-end
+end
function pradical_trace1(O::NfAbsOrd{NfAbsNS, NfAbsNSElem}, p::Union{Int, fmpz})
return pradical_trace(O, p)
diff --git a/src/NumFieldOrd/NfOrd/MaxOrd/Polygons.jl b/src/NumFieldOrd/NfOrd/MaxOrd/Polygons.jl
index e21526c6c3..c0945fc1a3 100644
--- a/src/NumFieldOrd/NfOrd/MaxOrd/Polygons.jl
+++ b/src/NumFieldOrd/NfOrd/MaxOrd/Polygons.jl
@@ -497,7 +497,7 @@ function _order_for_polygon_overorder(K::S, elt::Vector{T}, dold::fmpq = fmpq(0)
break
end
- B = basis_matrix(prods, FakeFmpqMat)
+ B = basis_matrix(prods, FakeFmpqMat)
hnf_modular_eldiv!(B.num, B.den, :lowerleft)
dd = B.num[nrows(B) - degree(K) + 1, 1]
@@ -605,11 +605,11 @@ function _decomposition(O::NfAbsOrd, I::NfAbsOrdIdl, Ip::NfAbsOrdIdl, T::NfAbsOr
end
k = (1-1/BigInt(p))^degree(O) < 0.1
-
+
if !k
#The probability of finding a random generator is high
for j in 1:length(ideals)
-
+
P = ideals[j][1]
f = P.splitting_type[2]
#@vprint :NfOrd 1 "Chances for finding second generator: ~$((1-1/BigInt(p)))\n"
@@ -688,7 +688,7 @@ function _decomposition(O::NfAbsOrd, I::NfAbsOrdIdl, Ip::NfAbsOrdIdl, T::NfAbsOr
if issimple(nf(O)) && isdefining_polynomial_nice(nf(O))
u = O(mod(u.elem_in_nf, p))
end
-
+
@hassert :NfOrd 1 containment_by_matrices(u, P)
modulo = norm(P)*p
if iszero(mod(norm(u), modulo))
diff --git a/src/NumFieldOrd/NfOrd/NarrowPicardGroup.jl b/src/NumFieldOrd/NfOrd/NarrowPicardGroup.jl
index 691e5a9c7e..a2ba2bda7f 100644
--- a/src/NumFieldOrd/NfOrd/NarrowPicardGroup.jl
+++ b/src/NumFieldOrd/NfOrd/NarrowPicardGroup.jl
@@ -55,7 +55,7 @@ function narrow_picard_group(O::NfOrd)
I0 = mC(C[i])
I = I0^(order(C[i]))
push!(idealgens, I0)
- # I is principal
+ # I is principal
fl, a = isprincipal(I)
@assert fl
q = elem_to_Q(elem_in_nf(a))
@@ -106,7 +106,7 @@ function narrow_picard_group(O::NfOrd)
end
# A test
-
+
_Q, = units_modulo_totally_positive_units(O)
r, s = signature(nf(O))
@assert order(BS) == divexact(order(C) * 2^r, order(_Q))
diff --git a/src/NumFieldOrd/NfOrd/NfOrd.jl b/src/NumFieldOrd/NfOrd/NfOrd.jl
index f986ff7f7c..bd714bea50 100644
--- a/src/NumFieldOrd/NfOrd/NfOrd.jl
+++ b/src/NumFieldOrd/NfOrd/NfOrd.jl
@@ -344,7 +344,7 @@ function index(O::NfAbsOrd; copy::Bool = true)
!isone(denominator(i)) && error("Order does not contain the equation order")
O.index = abs(numerator(i))
end
- if copy
+ if copy
return deepcopy(O.index)
else
return O.index
@@ -529,7 +529,7 @@ Checks whether $a$ lies in $\mathcal O$.
"""
function in(a::nf_elem, O::NfOrd)
@assert parent(a) == nf(O)
- if isdefining_polynomial_nice(nf(O)) && contains_equation_order(O)
+ if isdefining_polynomial_nice(nf(O)) && contains_equation_order(O)
d = denominator!(O.tcontain_fmpz, a)
if isone(d)
return true
@@ -652,7 +652,7 @@ function norm_change_const(O::NfOrd; cached::Bool = true)
if cached && isdefined(O, :norm_change_const)
return O.norm_change_const::Tuple{BigFloat, BigFloat}
end
-
+
z = _norm_change_const(O.basis_nf)
O.norm_change_const = z
return z::Tuple{BigFloat, BigFloat}
@@ -827,7 +827,7 @@ end
any_order(K::NumberField)
Return some order in $K$. In case the defining polynomial for $K$
-is monic and integral, this just returns the equation order.
+is monic and integral, this just returns the equation order.
In the other case $\mathbb Z[\alpha]\cap \mathbb Z[1/\alpha]$
is returned.
"""
@@ -1300,7 +1300,7 @@ function different(R::NfAbsOrd; proof::Bool = true)
end
if norm(D) == nD
nt += 1
- if nt > 20
+ if nt > 20
if proof
if !isgorenstein(R)
error("function only works for Gorenstein")
diff --git a/src/NumFieldOrd/NfOrd/Overorders.jl b/src/NumFieldOrd/NfOrd/Overorders.jl
index fe6a964d72..54e2efae0f 100644
--- a/src/NumFieldOrd/NfOrd/Overorders.jl
+++ b/src/NumFieldOrd/NfOrd/Overorders.jl
@@ -24,7 +24,7 @@ function defines_minimal_overorder(B::Vector, l::Vector)
m[1, i] = numerator(x.coeffs[i])
end
fl = iszero_mod_hnf!(m, M.num)
- return fl, M
+ return fl, M
end
function defines_minimal_overorder(B::Vector{nf_elem}, l::Vector{nf_elem})
@@ -39,7 +39,7 @@ function defines_minimal_overorder(B::Vector{nf_elem}, l::Vector{nf_elem})
m[1, i] = numerator(coeff(x, i - 1))
end
fl = iszero_mod_hnf!(m, M.num)
- return fl, M
+ return fl, M
end
################################################################################
@@ -250,7 +250,7 @@ function _minimal_overorders_nonrecursive_meataxe(O, M)
end
B = mA.bottom_snf_basis
-
+
autos = GrpAbFinGenMap[]
for i in 1:degree(O)
@@ -331,7 +331,7 @@ function _minimal_poverorders_in_ring_of_multipliers(O, P, excess = Int[0], use_
d = degree(O)
K = _algebra(O)
#@assert isone(B[1])
-
+
autos = GrpAbFinGenMap[]
for i in 1:degree(O)
@@ -359,13 +359,13 @@ function _minimal_poverorders_in_ring_of_multipliers(O, P, excess = Int[0], use_
else
subs = stable_subgroups(A, autos, minimal = true, op = (G, z) -> sub(G, z, false))
end
-
+
for i in 1:mA.offset
potential_basis[i] = mA.bottom_snf_basis[i]
end
offset = mA.offset
-
+
#The degree of the extension divides the degree of a prime of M lying over P
lQ = prime_ideals_over(M, P)
rel_fs = fmpz[divexact(valuation(norm(Q), p), f) for Q in lQ]
@@ -403,11 +403,11 @@ function _minimal_poverorders_in_ring_of_multipliers(O, P, excess = Int[0], use_
end
end
end
-
+
if !(2 in fac) && length(lQ) == 1 && norm(P)^rel_fs[1] == order(A)
return orders
end
-
+
for s in subs
T = image(s[2], false)
G = domain(T[2])
@@ -431,8 +431,8 @@ function _minimal_poverorders_in_ring_of_multipliers(O, P, excess = Int[0], use_
L = Order(K, hnf!(bL, :lowerleft), check = false, cached = false)
push!(orders, L)
end
-
-
+
+
return orders
end
@@ -452,9 +452,9 @@ function _minimal_poverorders_at_2(O, P, excess = Int[])
push!(orders, O1)
return orders
end
-
+
f = valuation(norm(P), 2)
-
+
autos = GrpAbFinGenMap[]
for i in 1:degree(O)
@@ -471,7 +471,7 @@ function _minimal_poverorders_at_2(O, P, excess = Int[])
push!(autos, induce(mA, x -> x^2))
filter!(x -> !iszero(x.map), autos)
-
+
potential_basis = Vector{elem_type(K)}(undef, d)
offset = mA.offset
@@ -531,11 +531,11 @@ function _minimal_poverorders_at_2(O, P, excess = Int[])
end
end
end
-
+
if !(2 in fac) && length(lQ) == 1 && norm(P)^rel_fs[1] == order(A)
return orders
end
-
+
for s in subs
T = image(s[2], false)
G = domain(T[2])
@@ -555,8 +555,8 @@ function _minimal_poverorders_at_2(O, P, excess = Int[])
L = Order(K, bL, check = false, cached = false)
push!(orders, L)
end
-
-
+
+
return orders
end
@@ -771,7 +771,7 @@ function poverorders_one_step_generic(O, p::fmpz)
end
offset = mA.offset
-
+
excess = 0
subs = stable_subgroups(A, autos, op = (G, z) -> sub(G, z, false))
@@ -792,7 +792,7 @@ function poverorders_one_step_generic(O, p::fmpz)
end
b, bmat = defines_order(K, deepcopy(potential_basis))
bmat = hnf!(bmat)
- if b
+ if b
push!(orders, Order(K, bmat))
else
excess += 1
@@ -900,7 +900,7 @@ function poverorders_nonrecursive_meataxe(O, N, p::fmpz)
end
offset = mA.offset
-
+
excess = 0
subs = stable_subgroups(A, autos, op = (G, z) -> sub(G, z, false))
@@ -921,7 +921,7 @@ function poverorders_nonrecursive_meataxe(O, N, p::fmpz)
end
b, bmat = defines_order(K, deepcopy(potential_basis))
bmat = hnf!(bmat)
- if b
+ if b
push!(orders, Order(K, bmat))
else
excess += 1
@@ -985,9 +985,9 @@ function pprimary_overorders_bass(O, P)
push!(res1, O2n)
O3 = O2
P = prime_ideals_over(O2, primes[1])[1]
- O2 = ring_of_multipliers(P)
+ O2 = ring_of_multipliers(P)
end
-
+
res2 = typeof(O)[]
O3 = O1
O2 = ring_of_multipliers(primes[2])
@@ -996,7 +996,7 @@ function pprimary_overorders_bass(O, P)
push!(res2, O2)
O3 = O2
P = prime_ideals_over(O2, primes[2])[1]
- O2 = ring_of_multipliers(P)
+ O2 = ring_of_multipliers(P)
end
append!(res, res1)
append!(res, res2)
@@ -1006,7 +1006,7 @@ function pprimary_overorders_bass(O, P)
end
end
return res
-
+
end
################################################################################
diff --git a/src/NumFieldOrd/NfOrd/RayClassGrp.jl b/src/NumFieldOrd/NfOrd/RayClassGrp.jl
index eb07e34201..dc757b25d6 100644
--- a/src/NumFieldOrd/NfOrd/RayClassGrp.jl
+++ b/src/NumFieldOrd/NfOrd/RayClassGrp.jl
@@ -15,7 +15,7 @@ mutable struct MapRayClassGrp <: Map{GrpAbFinGen, FacElemMon{Hecke.NfOrdIdlSet},
fact_mod::Dict{NfOrdIdl, Int} #The factorization of the finite part of the defining modulus
gens::Tuple{Vector{NfOrdIdl}, Vector{GrpAbFinGenElem}}
-
+
#Dictionaries to cache preimages. Used in the action on the ray class group
prime_ideal_preimage_cache::Dict{NfOrdIdl, GrpAbFinGenElem}
prime_ideal_cache::Vector{NfOrdIdl}
@@ -111,7 +111,7 @@ function __assure_princ_gen(c::Hecke.ClassGrpCtx{SMat{fmpz}}, nquo::Int)
return res
end
-function _assure_princ_gen(mC::MapClassGrp)
+function _assure_princ_gen(mC::MapClassGrp)
if isdefined(mC, :princ_gens)
return nothing
end
@@ -190,7 +190,7 @@ function class_as_ray_class(C::GrpAbFinGen, mC::MapClassGrp, exp_class::Function
function disclog1(J::NfOrdIdl)
return mQ(mC\(J))
end
-
+
function disclog1(J::FacElem{NfOrdIdl, NfOrdIdlSet})
a = X[0]
for (f, k) in J.fac
@@ -214,9 +214,9 @@ function class_as_ray_class(C::GrpAbFinGen, mC::MapClassGrp, exp_class::Function
mp1.clgrpmap = mC
return Q, mp1
end
-
+
local disclog
- let X = X, mC = mC
+ let X = X, mC = mC
function disclog(J::NfOrdIdl)
return X((mC\J).coeff)
end
@@ -241,21 +241,21 @@ end
function empty_ray_class(m::NfOrdIdl)
O = order(parent(m))
X = abelian_group(Int[])
-
+
local exp
let O = O
function exp(a::GrpAbFinGenElem)
return FacElem(Dict(ideal(O,1) => fmpz(1)))
end
end
-
+
local disclog
let X = X
function disclog(J::Union{NfOrdIdl, FacElem{NfOrdIdl}})
return id(X)
end
end
-
+
mp = Hecke.MapRayClassGrp()
mp.header = Hecke.MapHeader(X, FacElemMon(parent(m)) , exp, disclog)
mp.defining_modulus = (m, InfPlc[])
@@ -620,7 +620,7 @@ end
#
@doc Markdown.doc"""
ray_class_group(m::NfOrdIdl, inf_plc::Vector{InfPlc}; n_quo::Int, lp::Dict{NfOrdIdl, Int}) -> GrpAbFinGen, MapRayClassGrp
-
+
Given an ideal $m$ and a set of infinite places of $K$,
this function returns the corresponding ray class group as an abstract group $\mathcal {Cl}_m$ and a map going
from the group into the group of ideals of $K$ that are coprime to $m$.
@@ -777,13 +777,13 @@ function ray_class_group(m::NfOrdIdl, inf_plc::Vector{InfPlc} = Vector{InfPlc}()
R[j, ngens(C)+ind-1+s] = -a[1, s]
end
end
- end
-
+ end
+
X = abelian_group(R)
if n_quo != -1
X.exponent = n_quo
end
-
+
local disclog
let X = X, mC = mC, C = C, exp_class = exp_class, powers = powers, groups_and_maps = groups_and_maps, quo_rings = quo_rings, lH = lH, diffC = diffC, n_quo = n_quo, m = m, expon = expon
invd = invmod(fmpz(diffC), expon)
@@ -976,7 +976,7 @@ function ray_class_groupQQ(O::NfOrd, modulus::Int, inf_plc::Bool, n_quo::Int)
R=ResidueRing(FlintZZ, modulus, cached=false)
U, mU = unit_group_mod(R, n_quo)
U.exponent = n_quo
- if inf_plc
+ if inf_plc
function disc_log1(I::NfOrdIdl)
@assert gcd(minimum(I),modulus)==1
i = Int(mod(I.minimum, modulus))
@@ -1068,7 +1068,7 @@ function find_gens(mR::MapRayClassGrp; coprime_to::fmpz = fmpz(-1))
if coprime_to != -1
mm = lcm(mm, coprime_to)
end
- mm = lcm(mm, discriminant(EquationOrder(nf(O))))
+ mm = lcm(mm, discriminant(EquationOrder(nf(O))))
if isdefined(mR, :gens)
if coprime_to == -1
return mR.gens[1], mR.gens[2]
@@ -1123,7 +1123,7 @@ function find_gens(mR::MapRayClassGrp; coprime_to::fmpz = fmpz(-1))
push!(lp, ideal(O, gens_m[i][1]))
q, mq = quo(R, sR, false)
s, ms = snf(q)
- if order(s) == 1
+ if order(s) == 1
if !isdefined(mR, :gens)
mR.gens = (lp, sR)
end
@@ -1135,7 +1135,7 @@ function find_gens(mR::MapRayClassGrp; coprime_to::fmpz = fmpz(-1))
push!(lp, ideal(O, gens_m[i][1]))
q, mq = quo(R, sR, false)
s, ms = snf(q)
- if order(s) == 1
+ if order(s) == 1
if !isdefined(mR, :gens)
mR.gens = (lp, sR)
end
diff --git a/src/NumFieldOrd/NfOrd/ResidueRing.jl b/src/NumFieldOrd/NfOrd/ResidueRing.jl
index 93d0c54e46..7ca43936f0 100644
--- a/src/NumFieldOrd/NfOrd/ResidueRing.jl
+++ b/src/NumFieldOrd/NfOrd/ResidueRing.jl
@@ -402,7 +402,7 @@ function ==(x::AbsOrdQuoRing, y::AbsOrdQuoRing)
return base_ring(x) === base_ring(y) && ideal(x) == ideal(y)
end
-function ==(x::AbsOrdQuoRingElem, y::AbsOrdQuoRingElem)
+function ==(x::AbsOrdQuoRingElem, y::AbsOrdQuoRingElem)
mod!(x.elem, parent(x))
mod!(y.elem, parent(x))
return x.elem == y.elem
diff --git a/src/NumFieldOrd/NfOrd/ResidueRingMultGrp.jl b/src/NumFieldOrd/NfOrd/ResidueRingMultGrp.jl
index e35fe2ab80..a2b919f043 100644
--- a/src/NumFieldOrd/NfOrd/ResidueRingMultGrp.jl
+++ b/src/NumFieldOrd/NfOrd/ResidueRingMultGrp.jl
@@ -92,7 +92,7 @@ function _multgrp(Q::NfOrdQuoRing, save_tame_wild::Bool = false; method = nothin
G, GtoQ = _direct_product(groups, maps, prime_powers, Q, save_tame_wild)
S, StoG, StoQ = snf(G, GtoQ)
-
+
if save_tame_wild
for s = 1:length(tame_ind)
StoQ.tame[tame_ind[s][1]].disc_log = StoG\(G[tame_ind[s][2]]) #Relies on the ordering tame\wild in the construction!
@@ -135,7 +135,7 @@ function _multgrp_mod_pv(p::NfOrdIdl, v::Int, pv::NfOrdIdl; method=nothing)
@assert issnf(G2)
wild_part[p] = G2toO
gen1 = G1toO(G1[1])
-
+
rel1 = exponent(G1)
# G2.snf[end] is the order of the biggest cyclic subgroup of G2
gen1_obcs = powermod(gen1, G2.snf[end], pnumv)
@@ -147,7 +147,7 @@ function _multgrp_mod_pv(p::NfOrdIdl, v::Int, pv::NfOrdIdl; method=nothing)
G1toO.disc_log = G[1]
tame_part[p] = G1toO
-
+
obcs_inv = gcdx(G2.snf[end], rel1)[2]
function disc_log2(x::NfOrdQuoRingElem)
y = OtoQ\x
@@ -196,7 +196,7 @@ function _multgrp_mod_p(p::NfOrdIdl, pnumv::fmpz = fmpz(0))
res += 1
end
return fmpz[res]
- else
+ else
return fmpz[pohlig_hellman(gen_quo,n,y;factor_n=factor_n, big_step_cache = big_step_cache)]
end
end
@@ -235,7 +235,7 @@ end
function _1_plus_p_mod_1_plus_pv(p::NfOrdIdl, v::Int, pv::NfOrdIdl, pnumv::fmpz = fmpz(0); method=nothing)
@hassert :NfOrdQuoRing 2 isprime(p)
@assert v >= 1
-
+
if method == :quadratic
gens, rels, disc_log = _iterative_method(p,v;base_method=:quadratic,use_p_adic=false)
elseif method == :artin_hasse
@@ -325,7 +325,7 @@ end
#
-# Given generators and relations for groups of two consecutives steps, this function computes
+# Given generators and relations for groups of two consecutives steps, this function computes
# generators and relations for the product
#
function _expand(g::Vector{NfOrdElem}, M::fmpz_mat, h::Vector{NfOrdElem}, N::Vector{fmpz}, disc_log::Function, pl::NfOrdIdl)
@@ -333,7 +333,7 @@ function _expand(g::Vector{NfOrdElem}, M::fmpz_mat, h::Vector{NfOrdElem}, N::Vec
M1 = zero_matrix(FlintZZ, length(N), length(N))
for i = 1:length(N)
M1[i, i] = N[i]
- end
+ end
return h, M1
end
isempty(h) && return g,M
@@ -361,7 +361,7 @@ function _expand(g::Vector{NfOrdElem}, M::fmpz_mat, h::Vector{NfOrdElem}, N::Vec
end
end
append!(g,h)
-
+
return g, Z
end
@@ -378,7 +378,7 @@ function _pu_mod_pv(pu::NfOrdIdl, pv::NfOrdIdl)
@assert isone(N.den)
G = abelian_group(N.num)
S, mS=snf(G)
-
+
#Generators
gens=Vector{NfOrdElem}(undef, ngens(S))
for i=1:ngens(S)
@@ -388,8 +388,8 @@ function _pu_mod_pv(pu::NfOrdIdl, pv::NfOrdIdl)
add!(gens[i], gens[i], mod(x[j], S.snf[end])*b[j])
end
end
-
- #Disclog
+
+ #Disclog
M = basis_mat_inv(pu, copy = false)*mS.imap
x_fakemat2 = FakeFmpqMat(zero_matrix(FlintZZ, 1, ncols(M)), fmpz(1))
local disclog
@@ -407,7 +407,7 @@ function _pu_mod_pv(pu::NfOrdIdl, pv::NfOrdIdl)
end
end
return gens, S.snf, disclog
-
+
end
# Let p be a prime ideal above a prime number pnum. Let e = v_p(pnum) be
@@ -470,7 +470,7 @@ function _artin_hasse_method(p::NfOrdIdl, u::Int, v::Int; pu::NfOrdIdl=p^u, pv::
local discrete_logarithm
let Q = Q, pnum = pnum, dlog = dlog
function discrete_logarithm(x::NfOrdElem)
- res = dlog(artin_hasse_log(Q(x), pnum))
+ res = dlog(artin_hasse_log(Q(x), pnum))
for i = 1:length(res)
res[i] = mod(res[i], M[end])
end
@@ -516,7 +516,7 @@ function artin_hasse_log(y::NfOrdQuoRingElem, pnum::fmpz)
invi = invmod(fmpz(i), m)
if iseven(i)
sub!(s, s, invi*t)
- else
+ else
add!(s, s, invi*t)
end
end
@@ -551,7 +551,7 @@ function _p_adic_method(p::NfOrdIdl, u::Int, v::Int; pu::NfOrdIdl=p^u, pv::NfOrd
powers = Dict{Int, nf_elem}()
local discrete_logarithm
let Q = Q, p = p, v = v, dlog = dlog, powers = powers
- function discrete_logarithm(b::NfOrdElem)
+ function discrete_logarithm(b::NfOrdElem)
res = dlog(p_adic_log(Q, p, v, b, powers))
for i = 1:length(res)
res[i] = mod(res[i], M[end])
@@ -608,7 +608,7 @@ function p_adic_exp(Q::NfOrdQuoRing, p::NfOrdIdl, v::Int, x::NfOrdElem)
end
add!(s, s, Q(inc.elem))
i_old = i
- end
+ end
return s.elem
end
@@ -644,9 +644,9 @@ function p_adic_log(Q::NfOrdQuoRing, p::NfOrdIdl, v::Int, y::NfOrdElem, powers::
val_p_xi += val_p_x
val_p_xi - val_p_i >= v && continue
mul!(xi, xi, x^(i-i_old))
- if iszero(val_pnum_i)
+ if iszero(val_pnum_i)
inc = _divexact(Q(xi), fmpz(i))
- else
+ else
if haskey(powers, val_p_i)
el = powers[val_p_i]
else
@@ -657,7 +657,7 @@ function p_adic_log(Q::NfOrdQuoRing, p::NfOrdIdl, v::Int, y::NfOrdElem, powers::
denom = O(i*el, false)
inc = divexact(Q(numer),Q(denom))
end
- if isodd(i)
+ if isodd(i)
add!(s, s, inc)
else
sub!(s, s, inc)
@@ -670,9 +670,9 @@ function p_adic_log(Q::NfOrdQuoRing, p::NfOrdIdl, v::Int, y::NfOrdElem, powers::
val_p_xi += val_p_x
val_p_xi - val_p_i >= v && continue
mul!(xi, xi, x^(i-i_old))
- if iszero(val_pnum_i)
+ if iszero(val_pnum_i)
inc = _divexact(Q(xi), fmpz(i))
- else
+ else
if haskey(powers, val_p_i)
el = powers[val_p_i]
else
@@ -683,7 +683,7 @@ function p_adic_log(Q::NfOrdQuoRing, p::NfOrdIdl, v::Int, y::NfOrdElem, powers::
denom = O(i*el, false)
inc = divexact(Q(numer),Q(denom))
end
- if isodd(i)
+ if isodd(i)
add!(s, s, inc)
else
sub!(s, s, inc)
@@ -796,26 +796,26 @@ function _prime_part_multgrp_mod_p(p::NfOrdIdl, prime::Int)
@hassert :NfOrdQuoRing 2 isprime(p)
O = order(p)
Q, mQ = ResidueField(O,p)
-
+
n = norm(p) - 1
s=valuation(n,prime)
powerp=prime^s
m=divexact(n,powerp)
-
+
powm=divexact(powerp,prime)
found=false
g=Q(1)
while found==false
g = rand(Q)
- if g != Q(0)
+ if g != Q(0)
g=g^m
- if g^powm != Q(1)
+ if g^powm != Q(1)
found=true
end
end
end
inv=gcdx(m,fmpz(powerp))[2]
-
+
function disclog(x::NfOrdElem)
t=mQ(x)^m
if powerp<10
@@ -923,10 +923,10 @@ function _find_gen(Q::FqFiniteField, powm::Vector{fmpz}, m::fmpz)
g = g^m
found = true
for i=1:length(powm)
- if isone(g^powm[i])
+ if isone(g^powm[i])
found = false
break
- end
+ end
end
end
return g
@@ -944,7 +944,7 @@ function _n_part_multgrp_mod_p(p::NfOrdIdl, n::Int)
k = gcd(npart, fmpz(n))
fac = factor(k)
powm = fmpz[divexact(npart, x) for x in keys(fac.fac)]
-
+
#
# We search for a random element with the right order
#
@@ -971,8 +971,8 @@ function _n_part_multgrp_mod_p(p::NfOrdIdl, n::Int)
mul!(el, el, w)
end
return fmpz[mod(fmpz(s)*inv, k)]
- else
- return fmpz[pohlig_hellman(w, k, t)*inv]
+ else
+ return fmpz[pohlig_hellman(w, k, t)*inv]
end
end
end
@@ -1041,16 +1041,16 @@ function _mult_grp_mod_n(Q::NfOrdQuoRing, y1::Dict{NfOrdIdl, Int}, y2::Dict{NfOr
end
tame_part[q].generators[1] = powermod(tame_part[q].generators[1], e1, minimum(idQ, copy = false))
end
-
+
i += ngens(G2)
nq = norm(q) - 1
@assert issnf(G2)
obcs = G2.snf[end] # order of the biggest cyclic subgroup
obcs_inv = gcdx(nq, obcs)[2]
-
+
local disc_log2
- let Q = Q, nq = nq, G2toO = G2toO
+ let Q = Q, nq = nq, G2toO = G2toO
function disc_log2(x::NfOrdElem)
y = Q(x)^nq
z = G2toO.discrete_logarithm(y.elem)
@@ -1059,8 +1059,8 @@ function _mult_grp_mod_n(Q::NfOrdQuoRing, y1::Dict{NfOrdIdl, Int}, y2::Dict{NfOr
end
return z
end
- end
-
+ end
+
G2toO2 = GrpAbFinGenToNfAbsOrdMap(G2, O, G2toO.generators, disc_log2)::GrpAbFinGenToAbsOrdMap{NfOrd, NfOrdElem}
push!(maps, G2toO2)
wild_part[q] = G2toO2
@@ -1338,7 +1338,7 @@ function _direct_product(groups::Vector{GrpAbFinGen}, maps::Vector{U}, ideals::V
end
gens = map(Q, [ g.elem for g in maps[1].generators ])
-
+
local disc_log1
let maps = maps
function disc_log1(x::AbsOrdQuoRingElem)
@@ -1416,8 +1416,8 @@ function _direct_product(groups::Vector{GrpAbFinGen}, maps::Vector{U}, ideals::V
return result
end
end
-
-
+
+
m = GrpAbFinGenToAbsOrdQuoRingMultMap(G, Q, generators, disc_log)
if tame_wild
m.tame = tame
diff --git a/src/NumFieldOrd/NfOrd/StrongEchelonForm.jl b/src/NumFieldOrd/NfOrd/StrongEchelonForm.jl
index f3d5a3de6d..4e6f8fae8c 100644
--- a/src/NumFieldOrd/NfOrd/StrongEchelonForm.jl
+++ b/src/NumFieldOrd/NfOrd/StrongEchelonForm.jl
@@ -166,8 +166,8 @@ function strong_echelon_form_naive!(A::Generic.Mat{NfOrdQuoRingElem})
end
end
- for i in j+1:m
-
+ for i in j+1:m
+
if iszero(T[1, i])
continue
end
@@ -303,7 +303,7 @@ function z_split(I::NfOrdIdl)
else
nz = prod(b[i, i] for i in 2:n)
end
-
+
A = NfOrdIdl[]
B = NfOrdIdl[]
@@ -388,7 +388,7 @@ function _strong_echelon_form_split(M::MatElem{NfOrdQuoRingElem}, ideals1)
m = ncols(M)
M_cur = zero_matrix(Q, n, m)
-
+
if length(ideals) == 1
return _strong_echelon_form_nonsplit(M)
end
@@ -439,7 +439,7 @@ function _strong_echelon_form_split(M::MatElem{NfOrdQuoRingElem}, ideals1)
end
end
-
+
_assure_weakly_normal_presentation(I)
gI = gcd(Q(I.gen_one), Q(I.gen_two))
@@ -478,7 +478,7 @@ end
function mul!(a::MatElem{NfOrdQuoRingElem}, b::MatElem{NfOrdQuoRingElem}, c::NfOrdQuoRingElem)
for i = 1:nrows(b)
for j = 1:ncols(b)
- mul!(a[i, j], b[i, j], c)
+ mul!(a[i, j], b[i, j], c)
end
end
return a
@@ -487,7 +487,7 @@ end
function mul_special!(a::MatElem{NfOrdQuoRingElem}, b::NfOrdQuoRingElem)
for i = 1:min(nrows(a), ncols(a))
for j = i:ncols(a)
- mul!(a[i, j], a[i, j], b)
+ mul!(a[i, j], a[i, j], b)
end
end
return a
@@ -496,7 +496,7 @@ end
function add_special!(a::MatElem{NfOrdQuoRingElem}, b::MatElem{NfOrdQuoRingElem})
for i = 1:min(nrows(b), ncols(b))
for j = i:ncols(b)
- add!(a[i, j], a[i, j], b[i, j])
+ add!(a[i, j], a[i, j], b[i, j])
end
end
return a
@@ -505,7 +505,7 @@ end
function add!(a::MatElem{NfOrdQuoRingElem}, b::MatElem{NfOrdQuoRingElem}, c::MatElem{NfOrdQuoRingElem})
for i = 1:nrows(b)
for j = 1:ncols(b)
- add!(a[i, j], b[i, j], c[i, j])
+ add!(a[i, j], b[i, j], c[i, j])
end
end
return a
@@ -526,7 +526,7 @@ end
# a *:= l;
# b *:= gi;
# assert g eq 1;
-# end if;
+# end if;
# assert 1 eq a+b;
# r := r*b+m*a;
# l *:= gi;
@@ -572,7 +572,7 @@ function _strong_echelon_form_nonsplit!(M)
ccall((:fmpz_mat_strong_echelon_form_mod, libflint), Nothing, (Ref{fmpz_mat}, Ref{fmpz}), forflint, modulus(RmodIZ))
for i in 1:min(n, m)
for j = 1:i-1
- zero!(M[i, j])
+ zero!(M[i, j])
end
for j in i:m
M[i, j] = Q(forflint[i, j])
@@ -669,7 +669,7 @@ function test_pseudohnf()
end
@show length(ideals)
-
+
gc()
@time pseudo_hnf_mod(pm, d, strategy = :split)
gc()
diff --git a/src/NumFieldOrd/NfOrd/TorsionUnits.jl b/src/NumFieldOrd/NfOrd/TorsionUnits.jl
index 149c11d1c9..34b97d2acc 100644
--- a/src/NumFieldOrd/NfOrd/TorsionUnits.jl
+++ b/src/NumFieldOrd/NfOrd/TorsionUnits.jl
@@ -1,6 +1,6 @@
################################################################################
#
-# NfOrd/TorsionUnits.jl : Torsion units in generic number field orders
+# NfOrd/TorsionUnits.jl : Torsion units in generic number field orders
#
# This file is part of Hecke.
#
@@ -160,7 +160,7 @@ function torsion_units_gen_order(O::T) where T <: Union{NfAbsOrd, NfRelOrd}
u = g^divexact(ord, ord_p)
while !(u in O)
u = u^p_int
- ord_p = divexact(ord_p, p_int)
+ ord_p = divexact(ord_p, p_int)
end
ord_O *= ord_p
end
@@ -203,17 +203,17 @@ function _torsion_units_lattice_enum(O::NfOrd)
local i
v = minkowski_map(x, p)
w = minkowski_map(y, p)
-
+
t = zero(parent(v[1]))
-
+
for i in 1:r1
t = t + v[i]*w[i]
end
-
+
for i in (r1 + 1):(r1 + 2*r2)
t = t + v[i]*w[i]
end
-
+
return t
end
@@ -225,7 +225,7 @@ function _torsion_units_lattice_enum(O::NfOrd)
A = ArbField(p, false)
M = ArbMatSpace(A, n, n,false)()
-
+
while true
A = ArbField(p, false)
M = ArbMatSpace(A, n, n, false)()
@@ -394,7 +394,7 @@ function _torsion_group_order_divisor(K::NumField)
while true
p = next_prime(p)
if divides(numerator(d1), fmpz(p))[1] || divides(denominator(d1), fmpz(p))[1]
-
+
end
lP = prime_decomposition(OK, p)
@@ -466,7 +466,7 @@ function _torsion_units_gen(K::AnticNumberField)
ord *= Int(p)^(i)
break
end
- end
+ end
end
_set_nf_torsion_units(K, (ord, gen))
return ord, gen
@@ -502,7 +502,7 @@ function _torsion_units_gen(K::NumField)
ord *= Int(p)^(i)
break
end
- end
+ end
end
set_special(K, :torsion_units => (ord, gen))
return ord, gen
diff --git a/src/NumFieldOrd/NfOrd/Unit.jl b/src/NumFieldOrd/NfOrd/Unit.jl
index 599b4e5a89..70d718b44d 100644
--- a/src/NumFieldOrd/NfOrd/Unit.jl
+++ b/src/NumFieldOrd/NfOrd/Unit.jl
@@ -1,6 +1,6 @@
################################################################################
#
-# NfOrd/Units.jl : Units in generic number field orders
+# NfOrd/Units.jl : Units in generic number field orders
#
# This file is part of Hecke.
#
diff --git a/src/NumFieldOrd/NfOrd/Unit/FindUnits.jl b/src/NumFieldOrd/NfOrd/Unit/FindUnits.jl
index 9f5e682cb8..f03b5dfaba 100644
--- a/src/NumFieldOrd/NfOrd/Unit/FindUnits.jl
+++ b/src/NumFieldOrd/NfOrd/Unit/FindUnits.jl
@@ -28,7 +28,7 @@ function find_candidates(x::ClassGrpCtx, u::UnitGrpCtx, add::Int = 0)
end
push!(u.relations_used, xj)
else
- if xj in add_units
+ if xj in add_units
continue
end
end
@@ -43,7 +43,7 @@ function find_candidates(x::ClassGrpCtx, u::UnitGrpCtx, add::Int = 0)
end
push!(u.relations_used, xj)
else
- if xj in add_units
+ if xj in add_units
continue
end
end
@@ -126,7 +126,7 @@ function _unit_group_find_units(u::UnitGrpCtx, x::ClassGrpCtx; add_orbit::Bool =
end
end
new_add = 0
- while not_larger < not_larger_bound
+ while not_larger < not_larger_bound
add += new_add
new_add = 2
k, add_units, s1 = find_candidates(x, u, add)
@@ -185,11 +185,11 @@ function _unit_group_find_units(u::UnitGrpCtx, x::ClassGrpCtx; add_orbit::Bool =
@v_do :UnitGroup 2 pushindent()
m = add_unit!(u, y)
- if m
+ if m
new_add = 0
done[i] = true
- not_larger = 0
- if has_full_rank(u)
+ not_larger = 0
+ if has_full_rank(u)
@vprint :UnitGroup 1 "improved reg, reg is $(tentative_regulator(u))\n"
if first
idx, expected_reg = _validate_class_unit_group(x, u)
@@ -224,7 +224,7 @@ function _unit_group_find_units(u::UnitGrpCtx, x::ClassGrpCtx; add_orbit::Bool =
@v_do :UnitGroup 2 popindent()
end
-
+
if has_full_rank(u)
add_done = false
for i = 1:length(elements)
@@ -239,7 +239,7 @@ function _unit_group_find_units(u::UnitGrpCtx, x::ClassGrpCtx; add_orbit::Bool =
done[i] = true
continue
end
- add_done = add_unit!(u, elements[i]) || add_done
+ add_done = add_unit!(u, elements[i]) || add_done
if expected_reg > divexact(abs(tentative_regulator(u)), 2)
done = trues(length(elements))
not_larger = not_larger_bound + 1
@@ -263,14 +263,14 @@ function _unit_group_find_units(u::UnitGrpCtx, x::ClassGrpCtx; add_orbit::Bool =
@vprint :UnitGroup 1 "Regulator of current unit group is $(u.tentative_regulator)\n"
else
@vprint :UnitGroup 1 "current rank is $(length(u.units)), need $r\n"
- end
+ end
@vprint :UnitGroup 1 "-"^80 * "\n"
@vprint :UnitGroup 1 "Independent unit time: $time_indep\n"
@vprint :UnitGroup 1 "Adding dependent unit time: $time_add_dep_unit\n"
@vprint :UnitGroup 1 "Torsion test time: $time_torsion\n"
-
-
+
+
if starting_full_rank
return 1, div(starting_idx, _validate_class_unit_group(x, u)[1])
elseif has_full_rank(u)
diff --git a/src/NumFieldOrd/NfOrd/Unit/IsUnit.jl b/src/NumFieldOrd/NfOrd/Unit/IsUnit.jl
index 63736cb31b..1761586f56 100644
--- a/src/NumFieldOrd/NfOrd/Unit/IsUnit.jl
+++ b/src/NumFieldOrd/NfOrd/Unit/IsUnit.jl
@@ -10,7 +10,7 @@
Returns whether $x$ is invertible or not.
"""
function isunit(x::NfOrdElem)
- return abs(norm(x)) == 1
+ return abs(norm(x)) == 1
end
_isunit(x::NfOrdElem) = isunit(x)
diff --git a/src/NumFieldOrd/NfOrd/Unit/Map.jl b/src/NumFieldOrd/NfOrd/Unit/Map.jl
index e170deeadd..880214409d 100644
--- a/src/NumFieldOrd/NfOrd/Unit/Map.jl
+++ b/src/NumFieldOrd/NfOrd/Unit/Map.jl
@@ -57,7 +57,7 @@ function unit_group_disc_log(x::FacElem{nf_elem, AnticNumberField} , U::UnitGrpC
push!(res, r[i])
end
return G(res)
-end
+end
function unit_group_fac_elem(c::ClassGrpCtx; redo::Bool = false)
u = unit_group_ctx(c, redo = redo)
diff --git a/src/NumFieldOrd/NfOrd/Unit/Reduction.jl b/src/NumFieldOrd/NfOrd/Unit/Reduction.jl
index 580a209f87..750e23d9fe 100644
--- a/src/NumFieldOrd/NfOrd/Unit/Reduction.jl
+++ b/src/NumFieldOrd/NfOrd/Unit/Reduction.jl
@@ -109,6 +109,6 @@ function reduce(u::Vector{T}, prec::Int = 32) where T
return u
end
@vprint :UnitGroup 1 "trying to reduce further...\n"
- end
+ end
end
diff --git a/src/NumFieldOrd/NfOrd/Unit/Relation.jl b/src/NumFieldOrd/NfOrd/Unit/Relation.jl
index a9938ea1f4..74fe17134c 100644
--- a/src/NumFieldOrd/NfOrd/Unit/Relation.jl
+++ b/src/NumFieldOrd/NfOrd/Unit/Relation.jl
@@ -1,12 +1,12 @@
# Checks whether x[1]^z[1] * ... x[n]^z[n]*y^[n+1] is a torsion unit
# This can be improved
-function _check_relation_mod_torsion(x::Vector{FacElem{nf_elem, AnticNumberField}}, y::FacElem{nf_elem, AnticNumberField}, z::Vector{fmpz}, p::Int = 16)
+function _check_relation_mod_torsion(x::Vector{FacElem{nf_elem, AnticNumberField}}, y::FacElem{nf_elem, AnticNumberField}, z::Vector{fmpz}, p::Int = 16)
(length(x) + 1 != length(z)) && error("Lengths of arrays does not fit")
r = x[1]^z[1]
for i in 2:length(x)
r = r*x[i]^z[i]
- end
+ end
w = r*y^z[length(z)]
@@ -77,7 +77,7 @@ function _find_rational_relation!(rel::Vector{fmpz}, v::arb_mat, bound::fmpz)
for i in 1:r
rel[i] = numerator(z[i]*dlcm)
- end
+ end
rel[r + 1] = -dlcm
diff --git a/src/NumFieldOrd/NfOrd/Unit/UnitGrpCtx.jl b/src/NumFieldOrd/NfOrd/Unit/UnitGrpCtx.jl
index 15fc47c01b..4fc932049b 100644
--- a/src/NumFieldOrd/NfOrd/Unit/UnitGrpCtx.jl
+++ b/src/NumFieldOrd/NfOrd/Unit/UnitGrpCtx.jl
@@ -19,7 +19,7 @@ end
################################################################################
#
-# Initialization
+# Initialization
#
################################################################################
@@ -31,7 +31,7 @@ end
function _search_rational_relation(U::UnitGrpCtx{S}, y::S, bound::fmpz) where S
p = _rel_add_precision(U)
r = rank(U)
-
+
@v_do :UnitGroup 1 pushindent()
p, B = _conj_log_mat_cutoff_inv(U, p)
@@ -83,10 +83,10 @@ function _add_dependent_unit!(U::UnitGrpCtx{S}, y::S, rel_only::Type{Val{T}} = V
@assert has_full_rank(U)
K = nf(order(U))
-
+
deg = degree(K)
r = rank(U)
-
+
rreg = tentative_regulator(U)
bound = _denominator_bound_in_relation(rreg, K)
@vprint :UnitGroup 1 "Adding dependent unit ... \n"
@@ -302,10 +302,10 @@ function tentative_regulator(U::UnitGrpCtx)
if isdefined(U, :tentative_regulator)
rreg = U.tentative_regulator
else
- @vprint :UnitGroup 1 "Computing regulator of independent units with 64 bits ... \n"
+ @vprint :UnitGroup 1 "Computing regulator of independent units with 64 bits ... \n"
rreg = regulator(U.units, 64)
U.tentative_regulator = rreg
- @vprint :UnitGroup 1 "done \n"
+ @vprint :UnitGroup 1 "done \n"
end
return rreg
end
diff --git a/src/NumFieldOrd/NfOrd/Zeta.jl b/src/NumFieldOrd/NfOrd/Zeta.jl
index 7c8bc94623..d300aaf896 100644
--- a/src/NumFieldOrd/NfOrd/Zeta.jl
+++ b/src/NumFieldOrd/NfOrd/Zeta.jl
@@ -36,7 +36,7 @@ export zeta_log_residue
################################################################################
#
-# Macros to make floating point life (hopefully) easier
+# Macros to make floating point life (hopefully) easier
#
################################################################################
@@ -94,7 +94,7 @@ function _approx_error_bf(disc::fmpz, degree::Int, Tc = BigFloat)
logd_up = Tc(0)::Tc
logd_down = Tc(0)::Tc
sqrt_logd_up = Tc(0)::Tc
-
+
setrounding(Tc,RoundDown) do
logd_down = log(Tc(abs(disc)))
end
@@ -108,9 +108,9 @@ function _approx_error_bf(disc::fmpz, degree::Int, Tc = BigFloat)
C1 = @with_round_down(Tc(FlintQQ(2324)//FlintQQ(1000)),Tc)
C2 = @with_round_down(Tc(FlintQQ(388)//FlintQQ(100)),Tc)
- C3 = Tc(2)
+ C3 = Tc(2)
C4 = @with_round_down(Tc(FlintQQ(426)//FlintQQ(100)),Tc)
-
+
function F(X)#(X::Tc)
A1 = @with_round_down(C1*logd_down/(@with_round_up(sqrt(X)*log(3*X),Tc)),Tc)
A2 = @with_round_down(1 + C2/@with_round_up(log(X/9),Tc),Tc)
@@ -136,18 +136,18 @@ function _find_threshold(f, C, ste, decreasing::Bool, Tc = BigFloat)
x1 = 2*x0
y = f(x1)
end
-
+
dista = abs(x0-x1)
while !( y < C && dista < ste)
- if y > C
+ if y > C
x1 = x0 + 3*dista/2
else
x1 = x0 - dista/2
end
dista = abs(x1-x0)
-
+
x0 = x1
y = f(x0)
end
@@ -167,11 +167,11 @@ end
pro2 = logp*pm2
pro2 = pro2*m
-
+
# Now the inverse
inv2 = inv(pro2)
- # Now sqrt(x)log(X)/p^(m/2)*m*p
+ # Now sqrt(x)log(X)/p^(m/2)*m*p
pro3 = aa*inv2
pro3 = pro3 - 1
@@ -181,7 +181,7 @@ end
function _comp_summand(R, p::Int, m::Int, aa::arb)
return _comp_summand(R, fmpz(p), m, aa)
end
-
+
# Computing the g_K(X) term of Belabas-Friedmann
function _term_bf(O::NfOrd, B::Int, R::ArbField)
@@ -211,7 +211,7 @@ function _term_bf(O::NfOrd, B::Int, R::ArbField)
prodx9 = logxx09 * sqrtxx09
# small helper function (is this fast?)
-
+
while p < xx0
max_exp = _max_power_in(p, xx0)
@@ -222,14 +222,14 @@ function _term_bf(O::NfOrd, B::Int, R::ArbField)
summ = summ - summand
end
- #x += @elapsed
+ #x += @elapsed
lP = prime_decomposition_type(O, p)
for P in lP
Pnorm = fmpz(p)^P[1]
if Pnorm < xx0
max_exp = _max_power_in(Pnorm, xx0)
-
+
for m in 1:max_exp
summand = _comp_summand(R, Pnorm, m, prodx)
summ = summ + summand
@@ -238,7 +238,7 @@ function _term_bf(O::NfOrd, B::Int, R::ArbField)
end
if p < xx09
-
+
max_exp = _max_power_in(p, xx09)
for m in 1:max_exp
@@ -250,7 +250,7 @@ function _term_bf(O::NfOrd, B::Int, R::ArbField)
Pnorm = fmpz(p)^P[1]
if (Pnorm < xx09)
max_exp = _max_power_in(Pnorm, xx09)
-
+
for m in 1:max_exp
summand = _comp_summand(R, Pnorm, m, prodx9)
summ = summ - summand
@@ -280,7 +280,7 @@ function _residue_approx_bf(O::NfOrd, error::Float64)
der = Int(20)
- @assert error > 0.5^der
+ @assert error > 0.5^der
error_prime = @with_round_down(error - 0.5^der, BigFloat)
@@ -297,7 +297,7 @@ function _residue_approx_bf(O::NfOrd, error::Float64)
x0 = Int(ceil(_find_threshold(F, error_prime, Float64(10), true, Float64)))
x0 = x0 + 1
- prec = 64
+ prec = 64
val = _term_bf(O, x0, ArbField(prec, cached = false))
diff --git a/src/NumFieldOrd/NfOrd/norm_eqn.jl b/src/NumFieldOrd/NfOrd/norm_eqn.jl
index 5dd8fdd0fb..9e188a2f91 100644
--- a/src/NumFieldOrd/NfOrd/norm_eqn.jl
+++ b/src/NumFieldOrd/NfOrd/norm_eqn.jl
@@ -8,15 +8,15 @@ function norm_1_generators(A::Vector{NfOrdIdl})
f = matrix(FlintZZ, 1, length(A), [degree(x) for x = A])
k = nullspace(f)[2]
-
+
id = [FacElem(A, [k[i,j] for i=1:length(A)]) for j=1:ncols(k)]
- return id
+ return id
end
@doc Markdown.doc"""
norm_equation(K::AnticNumerField, a) -> nf_elem
-For $a$ an integer or rational, try to find $T \in K$ s.th.
+For $a$ an integer or rational, try to find $T \in K$ s.th.
$N(T) = a$. Raises an error if unsuccessful.
"""
function norm_equation(K::AnticNumberField, a)
@@ -52,15 +52,15 @@ For a fmpz $a$, try to find $T \in K$ s.th. $N(T) = a$
holds. If successful, return true and $T$, otherwise false and some element.
In \testtt{extra} one can pass in additional prime numbers that
are allowed to occur in the solution. This will then be supplemented.
-The element will be returned in factored form.
+The element will be returned in factored form.
"""
function isnorm(K::AnticNumberField, a::fmpz; extra::Vector{fmpz}=fmpz[])
L = lll(maximal_order(K))
- C, mC = narrow_class_group(L)
+ C, mC = narrow_class_group(L)
# println("narrow group is : $C")
S = union(Set(keys(factor(a).fac)), Set(keys(factor(discriminant(L)).fac)))
S = union(S, Set(extra))
-
+
g = Set(elem_type(C)[])
for p = S
P = prime_ideals_over(L, typeof(p)[p])
diff --git a/src/NumFieldOrd/NumFieldOrdElem.jl b/src/NumFieldOrd/NumFieldOrdElem.jl
index b7ca93e1c6..207a636915 100644
--- a/src/NumFieldOrd/NumFieldOrdElem.jl
+++ b/src/NumFieldOrd/NumFieldOrdElem.jl
@@ -312,7 +312,7 @@ end
@doc Markdown.doc"""
absolute_tr(a::NumFieldOrdElem) -> fmpz
-Return the absolute trace as an integer.
+Return the absolute trace as an integer.
"""
absolute_tr(a::NfAbsOrdElem) = tr(a)
absolute_tr(a::NfRelOrdElem) = absolute_tr(tr(a))
@@ -324,7 +324,7 @@ absolute_tr(a::NfRelOrdElem) = absolute_tr(tr(a))
################################################################################
@doc Markdown.doc"""
- norm(a::NumFieldOrdElem)
+ norm(a::NumFieldOrdElem)
Returns the norm of $a$ as an element in the base ring.
"""
@@ -336,7 +336,7 @@ end
@doc Markdown.doc"""
absolute_norm(a::NumFieldOrdElem) -> fmpz
-Return the absolute norm as an integer.
+Return the absolute norm as an integer.
"""
absolute_norm(a::NfAbsOrdElem) = norm(a)
absolute_norm(a::NfRelOrdElem) = absolute_norm(norm(a))
diff --git a/src/NumFieldOrd/NumFieldOrdIdl.jl b/src/NumFieldOrd/NumFieldOrdIdl.jl
index 22a83e7eb0..26c3baf8db 100644
--- a/src/NumFieldOrd/NumFieldOrdIdl.jl
+++ b/src/NumFieldOrd/NumFieldOrdIdl.jl
@@ -162,7 +162,7 @@ function uniformizer(P::NfAbsOrdIdl)
if isdefined(P, :gens_normal) && P.gens_normal == p
return P.gen_two
elseif isone(ramification_index(P))
- return order(P)(p)
+ return order(P)(p)
else
if p > 250
r = 500 # should still have enough elements...
@@ -358,7 +358,7 @@ function isintegral(I::NfOrdFracIdl)
return denominator(I) == 1
end
-function isintegral(a::NfRelOrdFracIdl)
+function isintegral(a::NfRelOrdFracIdl)
@assert ismaximal(order(a))
return defines_ideal(order(a), basis_pmatrix(a, copy = false))
end
diff --git a/src/QuadForm/Enumeration.jl b/src/QuadForm/Enumeration.jl
index 33ca70e15c..bcffb76029 100644
--- a/src/QuadForm/Enumeration.jl
+++ b/src/QuadForm/Enumeration.jl
@@ -47,7 +47,7 @@ function __pseudo_cholesky!(C::fmpq_mat, G)
C[i, j] = G[i, j]
end
end
- for i = 1:limit-1
+ for i = 1:limit-1
for j = i+1:limit
C[j, i] = deepcopy(C[i, j])
C[i, j] = divexact(C[i, j], C[i, i])
@@ -82,7 +82,7 @@ function __pseudo_cholesky!(C::Matrix{fmpq}, G)
C[i, j] = G[i, j]
end
end
- for i = 1:limit-1
+ for i = 1:limit-1
for j = i+1:limit
C[j, i] = _deepcopy_cheap(C[i, j])
#C[i, j] = divexact(C[i, j], C[i, i])
@@ -144,7 +144,7 @@ function __enumerate_gram(G::fmpz_mat, l::Union{Nothing, Int}, c::Int)
@hassert :Lattice 1 length(__enumerate_gram(G, l, c, Rational{Int128})) == length(res)
else
@vprint :Lattice 1 "Enumerating using fmpq\n"
- res = __enumerate_cholesky(Q, c)
+ res = __enumerate_cholesky(Q, c)
end
@hassert :Lattice 1 length(__enumerate_gram(G, l, c, fmpq)) == length(res)
return res
@@ -208,7 +208,7 @@ function __enumerate_cholesky(Q::Matrix{fmpq}, l::Union{Int, fmpz, Nothing}, c::
#_t = isqrt(FlintZZ(floor(divexact(T[i], Q[i, i]))))
#_new_upp = Int(FlintZZ(ceil(_t + 2 - U[i])))
#_new_low = Int(FlintZZ(floor(-(_t + 2) - U[i]))) - 1
-
+
@inbounds _new_upp, _new_low = _compute_bounds(T[i], Qd[i], U[i], t1, t2, t3, t4, t5)
@inbounds x[i] = _new_low
@@ -231,7 +231,7 @@ function __enumerate_cholesky(Q::Matrix{fmpq}, l::Union{Int, fmpz, Nothing}, c::
i = i - 1
#U[i] = sum(Q[i, j] * x[j] for j in (i + 1):n)
update_U!(U, Q, i, n, x, t1, t2)
- @goto compute_bounds
+ @goto compute_bounds
end
end
@@ -323,14 +323,14 @@ function __enumerate_cholesky(Q::Matrix{S}, l::Union{Int, Nothing}, c::Int) wher
#_t = isqrt(FlintZZ(floor(divexact(T[i], Q[i, i]))))
#_new_upp = Int(FlintZZ(ceil(_t + 2 - U[i])))
#_new_low = Int(FlintZZ(floor(-(_t + 2) - U[i]))) - 1
-
+
_new_upp, _new_low = @inbounds _compute_bounds(T[i], Qd[i], U[i])
@inbounds x[i] = _new_low
@inbounds L[i] = _new_upp
@label main_loop
-
+
@inbounds x[i] = x[i] + 1
@inbounds if x[i] > L[i]
@@ -347,7 +347,7 @@ function __enumerate_cholesky(Q::Matrix{S}, l::Union{Int, Nothing}, c::Int) wher
#U[i] = sum(Q[i, j] * x[j] for j in (i + 1):n)
update_U!(U, Q, i, n, x)
- @goto compute_bounds
+ @goto compute_bounds
end
end
diff --git a/src/QuadForm/Herm/Genus.jl b/src/QuadForm/Herm/Genus.jl
index 5d45f2a2df..c5adebe027 100644
--- a/src/QuadForm/Herm/Genus.jl
+++ b/src/QuadForm/Herm/Genus.jl
@@ -1500,7 +1500,7 @@ function genus_generators(L::HermLat)
E = nf(R)
D = different(R)
b, P0, bad = smallest_neighbour_prime(L)
-
+
local bad_prod::ideal_type(base_ring(R))
if isempty(bad)
diff --git a/src/QuadForm/Herm/GenusRep.jl b/src/QuadForm/Herm/GenusRep.jl
index ebb3e61fbe..5d02a5144d 100644
--- a/src/QuadForm/Herm/GenusRep.jl
+++ b/src/QuadForm/Herm/GenusRep.jl
@@ -98,7 +98,7 @@ function genus_representatives(L::HermLat; max = inf, use_auto::Bool = true,
missing_mass = Ref(mass)
local result::Vector{typeof(L)}
-
+
if definite
result = typeof(L)[]
for L in LL
@@ -291,7 +291,7 @@ function neighbour(L, B, xG, x, h, P, CC, split)
local C::ideal_type(R)
- if CC isa Int
+ if CC isa Int
C = split ? involution(L)(P) : P
else
C = CC
@@ -353,7 +353,7 @@ function iterated_neighbours(L::HermLat, P; use_auto = false, max = inf,
#require IsModular(L, P) : "The lattice must be locally modular";
#require Rank(L) ge 2: "The rank of the lattice must be at least 2";
#require IsIsotropic(L, P): "The lattice must be locally isotropic";
-
+
if callback == false && isdefinite(L)
_callback = stdcallback
else
@@ -377,7 +377,7 @@ function iterated_neighbours(L::HermLat, P; use_auto = false, max = inf,
no_lattices = length(result) - oldlength
oldlength = length(result)
if use_mass && no_lattices > 0
- _mass = _mass - sum(fmpq[1//automorphism_group_order(result[i]) for i in (length(result) - no_lattices + 1):length(result)])
+ _mass = _mass - sum(fmpq[1//automorphism_group_order(result[i]) for i in (length(result) - no_lattices + 1):length(result)])
if iszero(_mass)
break
end
diff --git a/src/QuadForm/Herm/LocallyIsometricSublattice.jl b/src/QuadForm/Herm/LocallyIsometricSublattice.jl
index efc7fab0a0..0e9d8a4e4d 100644
--- a/src/QuadForm/Herm/LocallyIsometricSublattice.jl
+++ b/src/QuadForm/Herm/LocallyIsometricSublattice.jl
@@ -261,7 +261,7 @@ function _locally_isometric_sublattice_even_ramified(M, L, p, P, absolute_map)
KM = map_entries(x -> E(h\x), _KM)
_new_pmat = _sum_modules(pseudo_matrix(KM * BBM), pM)
LL = lattice(ambient_space(M), _new_pmat)
-
+
if islocally_isometric(X, LL, p)
break
end
@@ -287,7 +287,7 @@ function locally_isometric_sublattice(M::HermLat, L::HermLat, p)
absolute_map = absolute_simple_field(ambient_space(M))[2]
P = D[1][1]
-
+
if length(D) == 2 # split case
LL = _locally_isometric_sublattice_split(M, L, p, P, absolute_map)
elseif length(D) == 1 && D[1][2] == 1 # inert case
diff --git a/src/QuadForm/Herm/Mass.jl b/src/QuadForm/Herm/Mass.jl
index dd3968ccfc..c066fcea57 100644
--- a/src/QuadForm/Herm/Mass.jl
+++ b/src/QuadForm/Herm/Mass.jl
@@ -62,7 +62,7 @@ function _local_factor_dyadic(L::HermLat, p)
t = iseven(e) ? k1 : k0
return (q^t + 1) * lf
end
-
+
if !b
if iseven(e)
return q^(m * (f2 - l) - k1) * (q^m1 - 1) * lf
@@ -221,7 +221,7 @@ function local_factor(L::HermLat, p)
if length(s) == 1 && !ram
return fmpq(1)
end
-
+
m = rank(L)
local f::fmpq
if ram
@@ -279,7 +279,7 @@ function _standard_mass(L::HermLat, prec::Int = 10)
RR = ArbField(wprec, cached = false)
_stdmass = RR(stdmass)
-
+
local relzeta::arb
while true
diff --git a/src/QuadForm/Lattices.jl b/src/QuadForm/Lattices.jl
index e542a5d184..9018cc68e3 100644
--- a/src/QuadForm/Lattices.jl
+++ b/src/QuadForm/Lattices.jl
@@ -877,7 +877,7 @@ function assert_has_automorphisms(L::AbsLat{<: NumField}; redo::Bool = false)
end
# Create the automorphism context and compute generators as well as orders
-
+
C = ZLatAutoCtx(ZgramL)
fl, Csmall = try_init_small(C)
if fl
@@ -962,7 +962,7 @@ end
@doc Markdown.doc"""
automorphism_group_generators(L::AbsLat; ambient_representation = true)
-Given a definite lattice $L$ returns generators for the automorphism group of $L$.
+Given a definite lattice $L$ returns generators for the automorphism group of $L$.
If `ambient_representation` is `true` (the default), the transformations are represented
with respect to the ambient space of $L$. Otherwise, the transformations are represented
with respect to the (pseudo-)basis of $L$.
@@ -1092,7 +1092,7 @@ function isisometric(L::AbsLat{<: NumField}, M::AbsLat{<: NumField};
fl, s1 = can_solve_with_solution(BabsmatL, basis_matrix_of_rational_span(L), side = :left)
fl, s2 = can_solve_with_solution(basis_matrix_of_rational_span(M), BabsmatM, side = :left)
T = s1 * change_base_ring(E, T) * s2
- @hassert :Lattice 1 T * gram_matrix(rational_span(M)) *
+ @hassert :Lattice 1 T * gram_matrix(rational_span(M)) *
_map(transpose(T), involution(L)) ==
gram_matrix(rational_span(L))
if !ambient_representation
@@ -1120,7 +1120,7 @@ end
function maximal_sublattices(L::AbsLat, p; use_auto::Bool = false,
callback = false, max = inf)
@req base_ring(L) == order(p) "asdsd"
-
+
B = local_basis_matrix(L, p, type = :submodule)
n = nrows(B)
R = base_ring(L)
diff --git a/src/QuadForm/LineOrbits.jl b/src/QuadForm/LineOrbits.jl
index cf7db5ee2e..e7f9a3ba6b 100644
--- a/src/QuadForm/LineOrbits.jl
+++ b/src/QuadForm/LineOrbits.jl
@@ -337,7 +337,7 @@ function _line_orbits(G::Vector)
end
res = Tuple{eltype(P), Int}[]
-
+
visited = trues(l)
sofar = zero(BigInt)
newline = zero_matrix(K, 1, n)
@@ -346,7 +346,7 @@ function _line_orbits(G::Vector)
# temporary variables in some cases
while sofar < l
pt = findfirst(visited)
- @assert pt !== nothing
+ @assert pt !== nothing
visited[pt] = false
norb = 1
cnd = 1
@@ -407,13 +407,13 @@ function _normalize!(x::gfp_mat)
el = x[1, j]
if !iszero(el)
piv = j
- ell = inv(el)
+ ell = inv(el)
break
end
end
@assert piv != 0
-
+
for j in (piv+1):ncols(x)
el = x[j] * ell
Nemo.setindex_raw!(x, el.data, 1, j)
@@ -465,13 +465,13 @@ function _normalize!(x::MatElem{gfp_fmpz_elem})
el = x[1, j]
if !iszero(el)
piv = j
- ell = inv(el)
+ ell = inv(el)
break
end
end
@assert piv != 0
-
+
for j in (piv+1):ncols(x)
t = x[1, j]
mul!(t, t, ell)
@@ -560,7 +560,7 @@ function _normalize!(x::fq_nmod_mat)
end
@assert piv != 0
-
+
for j in (piv+1):ncols(x)
el = ccall((:fq_nmod_mat_entry, libflint), Ptr{fq_nmod},
(Ref{fq_nmod_mat}, Int, Int), x, 0, j - 1)
@@ -692,7 +692,7 @@ function _normalize!(x::fq_mat)
end
@assert piv != 0
-
+
for j in (piv+1):ncols(x)
el = ccall((:fq_mat_entry, libflint), Ptr{fq},
(Ref{fq_mat}, Int, Int), x, 0, j - 1)
diff --git a/src/QuadForm/Misc.jl b/src/QuadForm/Misc.jl
index c49321c645..e62fb34172 100644
--- a/src/QuadForm/Misc.jl
+++ b/src/QuadForm/Misc.jl
@@ -133,7 +133,7 @@ function _find_special_class(u, p)
K = nf(R)
@assert valuation(u, p) == 0
k, _h = ResidueField(R, p)
- h = extend(_h, K)
+ h = extend(_h, K)
fl, s = issquare_with_sqrt(h(u))
@assert fl
u = divexact(u, (h\s)^2)
@@ -141,16 +141,16 @@ function _find_special_class(u, p)
e = valuation(2, p)
pi = elem_in_nf(uniformizer(p))
val = isone(u) ? inf : valuation(u - 1, p)
- while val < 2 * e
+ while val < 2 * e
if isodd(val)
return u
end
fl, s = issquare_with_sqrt(h((u - 1)//pi^val))
- @assert fl
+ @assert fl
# TODO:FIXME the div is wrong for negative valuations I think
@assert val >= 0
u = divexact(u, (1 + (h\s) * pi^(div(val, 2)))^2)
- val = valuation(u - 1, p)
+ val = valuation(u - 1, p)
end
kt, t = PolynomialRing(k, "t", cached = false)
return val == 2 * e && isirreducible(kt([h(divexact(u - 1, 4)), one(k), one(k)])) ? u : one(K)
@@ -320,7 +320,7 @@ function _idempotents(x::Vector)
#println("V:\n", sprint(show, "text/plain", V))
m = lcm(fmpz[minimum(x[i], copy = false) for i in 1:length(x)])
-
+
H = hnf_modular_eldiv!(V, m) # upper right
for i in 2:(1 + d)
@@ -676,7 +676,7 @@ end
################################################################################
#
-# Treat FlintQQ as a number field
+# Treat FlintQQ as a number field
#
################################################################################
diff --git a/src/QuadForm/Morphism.jl b/src/QuadForm/Morphism.jl
index d7c24c4722..b6faee383f 100644
--- a/src/QuadForm/Morphism.jl
+++ b/src/QuadForm/Morphism.jl
@@ -198,7 +198,7 @@ mutable struct ZLatAutoCtx{S, T, V}
for i in 1:length(z.G)
z.issymmetric[i] = issymmetric(z.G[i])
end
-
+
return z
end
@@ -228,7 +228,7 @@ function init(C::ZLatAutoCtx, auto::Bool = true, bound::fmpz = fmpz(-1), use_dic
# Compute the necessary short vectors
r = length(C.G)
-
+
n = nrows(C.G[1])
if bound == -1
@@ -240,7 +240,7 @@ function init(C::ZLatAutoCtx, auto::Bool = true, bound::fmpz = fmpz(-1), use_dic
@vprint :Lattice 1 "Computing short vectors of length $bound\n"
- @vtime :Lattice 1 V = _short_vectors_gram_integral(C.G[1], bound)
+ @vtime :Lattice 1 V = _short_vectors_gram_integral(C.G[1], bound)
vectors = Vector{fmpz_mat}(undef, length(V))
@@ -257,7 +257,7 @@ function init(C::ZLatAutoCtx, auto::Bool = true, bound::fmpz = fmpz(-1), use_dic
k += 1
end
if v[k] < 0
- v .*= -1
+ v .*= -1
end
vfmpz = matrix(FlintZZ, 1, n, v)
@@ -296,12 +296,12 @@ function init(C::ZLatAutoCtx, auto::Bool = true, bound::fmpz = fmpz(-1), use_dic
for i in 1:dim(C)
z[1, C.per[i]] = 1
k = find_point(z, C.V)
- C.std_basis[i] = k
+ C.std_basis[i] = k
z[1, C.per[i]] = 0
end
end
- #
+ #
C.v = Vector{fmpz_mat}(undef, length(C.G))
@@ -338,7 +338,7 @@ function init(C::ZLatAutoCtx, auto::Bool = true, bound::fmpz = fmpz(-1), use_dic
C.ng[1] = 1
# Calculate orbit lengths
-
+
nH = 0
for i in 1:dim(C)
@@ -385,7 +385,7 @@ function try_init_small(C::ZLatAutoCtx, auto::Bool = true, bound::fmpz = fmpz(-1
end
@assert bound > 0
- @vtime :Lattice 1 V = _short_vectors_gram_integral(C.G[1], bound)
+ @vtime :Lattice 1 V = _short_vectors_gram_integral(C.G[1], bound)
vectors = Vector{Vector{Int}}(undef, length(V))
@@ -426,7 +426,7 @@ function try_init_small(C::ZLatAutoCtx, auto::Bool = true, bound::fmpz = fmpz(-1
end
if v[k] < 0
- v .*= -1
+ v .*= -1
end
if vectors_nbits > abs_maxbits_vectors
@@ -454,7 +454,7 @@ function try_init_small(C::ZLatAutoCtx, auto::Bool = true, bound::fmpz = fmpz(-1
end
V = VectorList(vectors, lengths, use_dict)
-
+
Csmall.V = V
@@ -482,12 +482,12 @@ function try_init_small(C::ZLatAutoCtx, auto::Bool = true, bound::fmpz = fmpz(-1
for i in 1:dim(Csmall)
z[Csmall.per[i]] = 1
k = find_point(z, V)
- Csmall.std_basis[i] = k
+ Csmall.std_basis[i] = k
z[Csmall.per[i]] = 0
end
end
- #
+ #
Csmall.v = Vector{Matrix{Int}}(undef, length(C.G))
@@ -529,7 +529,7 @@ function try_init_small(C::ZLatAutoCtx, auto::Bool = true, bound::fmpz = fmpz(-1
Csmall.ng[1] = 1
# Calculate orbit lengths
-
+
nH = 0
for i in 1:dim(Csmall)
@@ -576,7 +576,7 @@ end
# vector sums */
# scpvecs(&comb[i].list, &sumveclist, i, fp.e, flags.DEPTH, V, F);
#/* compute a basis for the lattice that is generated by the vector sums and
-# a transformation matrix that expresses the basis in terms of the
+# a transformation matrix that expresses the basis in terms of the
# vector sums */
# base(&comb[i], &sumvecbase, sumveclist, F.A[0], dim);
# if (flags.PRINT == 1)
@@ -683,11 +683,11 @@ function compute_short_vectors(C::ZLatAutoCtx, max::fmpz = fmpz(-1))
for k in 2:length(C.G)
z[k] = (m * C.G[k] * mt)[1, 1]
end
- C.V[i] = m
+ C.V[i] = m
C.V_length[i] = z
end
#@show length(C.V)
- C.max = max
+ C.max = max
return C
end
@@ -762,7 +762,7 @@ function possible(V, W, F, Ftr, _issymmetric, n, f, per, I, J)
end
# length is correct
-
+
good_scalar = true
@inbounds for k in 1:f
@@ -810,10 +810,10 @@ end
# for j from per[i] to per[dim-1] the
# value f[i][j] in the fingerprint f is
# the number of vectors, which have the
-# same scalar product with the
-# basis-vectors per[0]...per[i-1] as the
-# basis-vector j and the same length as
-# this vector with respect to all
+# same scalar product with the
+# basis-vectors per[0]...per[i-1] as the
+# basis-vector j and the same length as
+# this vector with respect to all
# invariant forms
function fingerprint(C::ZLatAutoCtx)
@@ -856,7 +856,7 @@ function fingerprint(C::ZLatAutoCtx)
per[mini], per[i] = per[i], per[mini]
- # Set entries below the minimal entry to zero
+ # Set entries below the minimal entry to zero
for j in (i + 1):n
fp[j, per[i]] = 0
end
@@ -931,7 +931,7 @@ Base.replace!(::typeof(-), m::fmpz_mat) = -m
function _operate(point, A, V, tmp)
# V.v is a sorted list of length V.n of vectors
# of dimension V.dim, the number of V.v[nr]*A in
-# the list is returned, where a negative number
+# the list is returned, where a negative number
# indicates the negative of a vector
tmp = _vec_times_matrix!(tmp, V[point], A)
#w = V[abs(point)] * A
@@ -1012,7 +1012,7 @@ function _orbitlen_naive(point::Int, orblen::Int, G::Vector{fmpz_mat}, nG::Int,
while !isempty(working_list)
current_point = pop!(working_list)
for i in 1:nG
- if current_point < 0
+ if current_point < 0
new_point_coord = -V[abs(current_point)] * G[i]
else
new_point_coord = V[current_point] * G[i]
@@ -1152,7 +1152,7 @@ function auto(C::ZLatAutoCtx{S, T, U}) where {S, T, U}
end
end
if step == sta
- # test, whether on step flags.STAB some generators may be omitted
+ # test, whether on step flags.STAB some generators may be omitted
tries = C.nsg[step]
while tries <= C.ng[step]
#for tries in C.nsg[step]:C.ng[step]
@@ -1193,7 +1193,7 @@ end
function _get_generators(C::ZLatAutoCtx{S, T, U}) where {S, T, U}
# Extract generators
-
+
gens = T[]
orde = prod(fmpz.(C.orders))
@@ -1289,13 +1289,13 @@ function cand(candidates, I, x, C::ZLatAutoCtx{S, T, U}, comb) where {S, T, U}
#@show C.V[j]
for i in 1:length(C.G)
_issym = C.issymmetric[i]
- CAiI = C.G[i][C.per[I]]
+ CAiI = C.G[i][C.per[I]]
Cvi = C.v[i]
#@show Cvi
-
+
# vec is the vector of scalar products of V.v[j] with the first I base vectors
- # x[1]...x[I]
-
+ # x[1]...x[I]
+
for k in 1:(I - 1)
#@show x[k]
xk = x[k]
@@ -1515,17 +1515,17 @@ end
function stab(I, C::ZLatAutoCtx{SS, T, U}) where {SS, T, U}
V = C.V
-# computes the orbit of fp.e[I] under the
-# generators in G->g[I]...G->g[n-1] and elements
+# computes the orbit of fp.e[I] under the
+# generators in G->g[I]...G->g[n-1] and elements
# stabilizing fp.e[I],
# has some heuristic break conditions,
-# the generators in G->g[i] stabilize
-# fp.e[0]...fp.e[i-1] but not fp.e[i],
+# the generators in G->g[i] stabilize
+# fp.e[0]...fp.e[i-1] but not fp.e[i],
# G->ng[i] is the number of generators in G->g[i],
# the first G->nsg[i] of which are elements which
-# are obtained as stabilizer elements in
+# are obtained as stabilizer elements in
# g[0],...,G->g[i-1]>, G->ord[i] is the orbit
-# length of fp.e[i] under
+# length of fp.e[i] under
# g[i],...,G->g[n-1]> *****/
#group *G;
#fpstruct fp;
@@ -1538,8 +1538,8 @@ function stab(I, C::ZLatAutoCtx{SS, T, U}) where {SS, T, U}
#
#/* some heuristic break conditions for the computation of stabilizer elements:
# it would be too expensive to calculate all the stabilizer generators, which
-# are obtained from the orbit, since this is highly redundant,
-# on the other hand every new generator which enlarges the group is much
+# are obtained from the orbit, since this is highly redundant,
+# on the other hand every new generator which enlarges the group is much
# cheaper than one obtained from the backtrack,
# after Maxfail subsequent stabilizer elements, that do not enlarge the group,
# Rest more elements are calculated even if they leave the group unchanged,
@@ -1563,7 +1563,7 @@ function stab(I, C::ZLatAutoCtx{SS, T, U}) where {SS, T, U}
Maxfail += 1
end
end
-
+
nH = 0
for i in I:dim
nH += C.ng[i]
@@ -1609,7 +1609,7 @@ function stab(I, C::ZLatAutoCtx{SS, T, U}) where {SS, T, U}
if fail >= Maxfail
#/* there have already been Maxfail successive failures, now a random generator
- # is applied to a random point of the orbit to get Rest more stabilizer
+ # is applied to a random point of the orbit to get Rest more stabilizer
# elements */
cnd = rand(1:len)
i = rand(1:nH)
@@ -1673,7 +1673,7 @@ function stab(I, C::ZLatAutoCtx{SS, T, U}) where {SS, T, U}
end
resize!(Hj, nH + 1)
#/* the new generator is appended to H */
-#/* the number of failures is reset to 0 */
+#/* the number of failures is reset to 0 */
else
#/* the new stabilizer element S does not enlarge the orbit of e[j] */
fail += 1
@@ -1709,7 +1709,7 @@ function stabil(x1, x2, per, G, V, C)
XG = matgen(x, dim, per, V)
X2 = matgen(x2, dim, per, V)
-
+
b, S = can_solve_with_solution(X2, XG, side = :left)
return S
end
@@ -1729,7 +1729,7 @@ function stabil(x1, x2, per, G::Matrix{Int}, V, C)
SS = zeros(Int, dim, dim)
_psolve(SS, X2, XG, dim, C.prime)
@hassert :Lattice 1 SS * X22 == XGG
-
+
return SS
end
@@ -1739,7 +1739,7 @@ zero_matrix(Int, r, c) = zeros(Int, r, c)
base_ring(::Vector{Int}) = Int
-function _one(::Type{Matrix{Int}}, n::Int)
+function _one(::Type{Matrix{Int}}, n::Int)
z = zeros(Int, n, n)
for i in 1:n
z[i, i] = 1
@@ -1755,7 +1755,7 @@ _zero(::Type{fmpz_mat}, n::Int, m::Int) = zero_matrix(FlintZZ, n, m)
function matgen(x, dim, per, v)
#/***** generates the matrix X which has as row
-# per[i] the vector nr. x[i] from the
+# per[i] the vector nr. x[i] from the
# list v *****
X = zero_matrix(base_ring(v[1]), dim, dim)
#@show x
@@ -1884,15 +1884,15 @@ function iso(step, x, C, Ci, Co, G)
end
function isostab(pt, G, C::ZLatAutoCtx{S, T, U}, Maxfail) where {S, T, U}
-# computes the orbit of V.v[pt]
-# under the generators
+# computes the orbit of V.v[pt]
+# under the generators
# G[0],...,G[nG-1] and elements
-# stabilizing V.v[pt], which are
+# stabilizing V.v[pt], which are
# stored in H, returns the number
# of generators in H
# a heuristic break condition for the computation of stabilizer elements:
# it would be too expensive to calculate all the stabilizer generators, which
-# are obtained from the orbit, since this is highly redundant,
+# are obtained from the orbit, since this is highly redundant,
# on the other hand every new generator which enlarges the group reduces the
# number of orbits and hence the number of candidates to be tested,
# after Maxfail subsequent stabilizer elements, that do not enlarge the group,
@@ -2019,7 +2019,7 @@ function isocand(CI, I, x, Ci::ZLatAutoCtx{S, T, U}, Co) where {S, T, U}
end
good = true
for k in 1:(I - 1)
- if vec[k] != Ci.G[i][Ci.per[I], Ci.per[k]] || vec2[k] != Ci.G[i][Ci.per[k], Ci.per[I]]
+ if vec[k] != Ci.G[i][Ci.per[I], Ci.per[k]] || vec2[k] != Ci.G[i][Ci.per[k], Ci.per[I]]
good = false
break
end
@@ -2029,7 +2029,7 @@ function isocand(CI, I, x, Ci::ZLatAutoCtx{S, T, U}, Co) where {S, T, U}
end
good = true
for k in 1:(I - 1)
- if vec[k] != -Ci.G[i][Ci.per[I], Ci.per[k]] || vec2[k] != -Ci.G[i][Ci.per[k], Ci.per[I]]
+ if vec[k] != -Ci.G[i][Ci.per[I], Ci.per[k]] || vec2[k] != -Ci.G[i][Ci.per[k], Ci.per[I]]
good = false
break
diff --git a/src/QuadForm/Quad/Lattices.jl b/src/QuadForm/Quad/Lattices.jl
index 91a1595b11..4d2580ef6a 100644
--- a/src/QuadForm/Quad/Lattices.jl
+++ b/src/QuadForm/Quad/Lattices.jl
@@ -475,7 +475,7 @@ function ismaximal_integral(L::QuadLat, p)
for x in PP
@assert !iszero(x)
xV = matrix(k, 1, length(x), x) * V
- e = elem_type(K)[ hext\(xV[1, i]) for i in 1:ncols(xV) ]
+ e = elem_type(K)[ hext\(xV[1, i]) for i in 1:ncols(xV) ]
v = matrix(K, 1, length(e), e)
_z = (v * G * transpose(v))[1, 1]
# Test if valv >= val2 + 2
@@ -575,7 +575,7 @@ function maximal_integral_lattice(V::QuadSpace)
n = norm(L)
@assert isintegral(n)
end
-
+
return maximal_integral_lattice(L)
end
diff --git a/src/QuadForm/Quad/NormalForm.jl b/src/QuadForm/Quad/NormalForm.jl
index 9526845069..87fadcbacd 100644
--- a/src/QuadForm/Quad/NormalForm.jl
+++ b/src/QuadForm/Quad/NormalForm.jl
@@ -138,7 +138,7 @@ end
Return the normal `D` and the transformation `T` to the `p`-adic normal form of
the symmetric matrix `G`, such that `d * D = d * B * G * B'` holds modulo `p^prec`.
-If `prec == -1`,
+If `prec == -1`,
Let `p` be odd and `u` be the smallest non-square modulo `p`. The normal form
is a block diagonal matrix with blocks `p^k G_k` such that `G_k` is either the
@@ -1087,7 +1087,7 @@ function _normalize_twobytwo(G, p)
D = B * G * B'
end
@assert _val(D[2, 2], p) == 1
-
+
if mod(lift(det(D)), 8) == 3
# # in this case we can transform D to
# # 2 1
diff --git a/src/QuadForm/Quad/Spaces.jl b/src/QuadForm/Quad/Spaces.jl
index 06f9df68cf..eaf01cf127 100644
--- a/src/QuadForm/Quad/Spaces.jl
+++ b/src/QuadForm/Quad/Spaces.jl
@@ -1449,7 +1449,7 @@ function _isisotropic_with_vector(F::MatrixElem)
if _isisotropic(D[3:5], p)
continue
end
-
+
local x::elem_type(K)
local y::elem_type(K)
diff --git a/src/QuadForm/QuadBin.jl b/src/QuadForm/QuadBin.jl
index 7fbc272ebe..1c22b39ed6 100644
--- a/src/QuadForm/QuadBin.jl
+++ b/src/QuadForm/QuadBin.jl
@@ -465,7 +465,7 @@ function isequivalent(f::QuadBin{fmpz}, g::QuadBin{fmpz}; proper::Bool = true)
if proper || is_prop
return is_prop
end
-
+
# note that our definition of improper equivalence
# differs from that of Buchmann and Vollmer
# their action is det f * q(f(x,y))
@@ -495,7 +495,7 @@ function isequivalent(f::QuadBin{fmpz}, g::QuadBin{fmpz}; proper::Bool = true)
f1 = reduction(binary_quadratic_form(f[3], f[2], f[1]))
return f1 == gred
end
-
+
return false
end
end
@@ -505,7 +505,7 @@ function _isequivalent_reducible(f::QuadBin{fmpz}, g::QuadBin{fmpz}; proper = tr
return false
end
- c = content(f)
+ c = content(f)
if content(g) != c
return false
end
diff --git a/src/QuadForm/Spaces.jl b/src/QuadForm/Spaces.jl
index 259c51602d..2b3f72a25a 100644
--- a/src/QuadForm/Spaces.jl
+++ b/src/QuadForm/Spaces.jl
@@ -487,7 +487,7 @@ end
#
################################################################################
-# TODO: Use absolute_coordinates
+# TODO: Use absolute_coordinates
function restrict_scalars(V::AbsSpace, K::FlintRationalField,
alpha = one(base_ring(V)))
E = base_ring(V)
diff --git a/src/QuadForm/Torsion.jl b/src/QuadForm/Torsion.jl
index 817461aa29..c7fcb6cbc1 100644
--- a/src/QuadForm/Torsion.jl
+++ b/src/QuadForm/Torsion.jl
@@ -728,8 +728,8 @@ EXAMPLES::
julia> brown_invariant(T)
4
"""
-function brown_invariant(T::TorQuadMod)
- @req T.modulus_qf == 2 "the torsion quadratic form must have values in Q/2Z"
+function brown_invariant(T::TorQuadMod)
+ @req T.modulus_qf == 2 "the torsion quadratic form must have values in Q/2Z"
brown = ResidueRing(ZZ, 8)(0)
for p in prime_divisors(exponent(T))
q = normal_form(primary_part(T, p)[1])[1]
@@ -744,7 +744,7 @@ end
@doc Markdown.doc"""
genus(T::TorQuadMod, signature_pair::Tuple{Int, Int}) -> ZGenus
-
+
Return the genus defined by a TorQuadMod T and the ``signature_pair``.
If no such genus exists, raise a ``ErrorException``.
diff --git a/src/RCF/Types.jl b/src/RCF/Types.jl
index 4558ef8a10..1f757ed8ff 100644
--- a/src/RCF/Types.jl
+++ b/src/RCF/Types.jl
@@ -95,7 +95,7 @@ mutable struct RCFCharacter{S, T}
mrcond::Union{MapClassGrp, MapRayClassGrp}
mp_cond::GrpAbFinGenMap
charcond::Map #Character directly on the rcf given by the conductor
-
+
function RCFCharacter(C::ClassField{S, T}, x::GrpAbFinGenElem, mGhat::Map) where {S, T}
z = new{S, T}()
z.C = C
diff --git a/src/RCF/autos.jl b/src/RCF/autos.jl
index 53e1ec484a..b5a34fefde 100644
--- a/src/RCF/autos.jl
+++ b/src/RCF/autos.jl
@@ -182,25 +182,25 @@ Given a cyclotomic extension $C$ of a number field $K$ and an automorphism $\tau
computes an extension of $\tau$ to $C$.
"""
-function extend_to_cyclotomic(C::CyclotomicExt, tau::NfToNfMor)
- K = domain(tau)
+function extend_to_cyclotomic(C::CyclotomicExt, tau::NfToNfMor)
+ K = domain(tau)
@assert K == base_field(C.Kr)
gKr = gen(C.Kr)
if euler_phi(C.n) == degree(C.Kr)
#The extension with the roots of unity is disjoint from K
#Therefore, the minimal polynomial has coefficient over QQ.
return hom(C.Kr, C.Kr, tau, gKr)
- end
- g = C.Kr.pol
- tau_g = parent(g)([tau(coeff(g, i)) for i=0:degree(g)])
- i = 1
- z = deepcopy(gKr)
- while gcd(i, C.n) != 1 || !iszero(tau_g(z))
- i += 1
- mul!(z, z, gKr)
- end
- return hom(C.Kr, C.Kr, tau, z)
-
+ end
+ g = C.Kr.pol
+ tau_g = parent(g)([tau(coeff(g, i)) for i=0:degree(g)])
+ i = 1
+ z = deepcopy(gKr)
+ while gcd(i, C.n) != 1 || !iszero(tau_g(z))
+ i += 1
+ mul!(z, z, gKr)
+ end
+ return hom(C.Kr, C.Kr, tau, z)
+
end
function new_extend_aut(A::ClassField, auto::T) where T <: Map
@@ -473,11 +473,11 @@ function extend_aut_pp(A::ClassField, autos::Vector{NfToNfMor}, p::fmpz)
if d == 2
return extend_aut2(A, autos)
end
-
+
m = minimum(defining_modulus(A)[1])
ind_image = 1
if !isone(gcd(d, m)) && d != minimum(degree(x) for x in Cp)
- #Difficult case. First, we check that the extension and
+ #Difficult case. First, we check that the extension and
#the cyclotomic extension are disjoint
ind_image = check_disjoint_cyclotomic(A, p)
if !isone(ind_image)
@@ -591,7 +591,7 @@ end
#This function restricts the automorphisms in autos to the number field generated by the class fields in Cp
# incs are the inclusions of the class fields in K
function restriction(K::NfRelNS{nf_elem}, Cp::Vector{ClassField_pp{S, T}}, autos::Vector{NfRelNSToNfRelNSMor_nf_elem}, incs::Vector{NfRelToNfRelNSMor_nf_elem}) where {S, T}
-
+
C = cyclotomic_extension(base_field(Cp[1]), maximum(degree(x) for x in Cp))
#First, I compute the images in K of the generators of the class fields
# and their images under the automorphisms
@@ -1032,7 +1032,7 @@ function extend_autos_hard_case(A::ClassField, autos::Vector{NfToNfMor}, p::fmpz
gens_real_KK = Vector{FacElem{nf_elem, AnticNumberField}}(undef, ngens(S))
for i = 1:ngens(S)
imgSi = mS(S[i])
- gens_real_KK[i] = prod(KK.gens[j]^imgSi[j] for j = 1:ngens(KK))
+ gens_real_KK[i] = prod(KK.gens[j]^imgSi[j] for j = 1:ngens(KK))
end
KK_real = kummer_extension(gens_real_KK, S.snf)
new_act_on_gens = Vector{Vector{FacElem{nf_elem, AnticNumberField}}}(undef, length(KK.gen))
@@ -1046,7 +1046,7 @@ function extend_autos_hard_case(A::ClassField, autos::Vector{NfToNfMor}, p::fmpz
act_on_gen_i[j] = FacElem(D1)
end
new_act_on_gens[i] = act_on_gen_i
- end
+ end
@show find_frob = find_gens(KK_real, new_act_on_gens, minimum(defining_modulus(A)[1]))
error("stop")
AA, gAA = number_field(KK_real)
diff --git a/src/RCF/class_fields.jl b/src/RCF/class_fields.jl
index 682c649286..67f1aa816e 100644
--- a/src/RCF/class_fields.jl
+++ b/src/RCF/class_fields.jl
@@ -320,7 +320,7 @@ end
@doc Markdown.doc"""
prime_decomposition_type(C::ClassField, p::NfAbsOrdIdl) -> (Int, Int, Int)
-For a prime $p$ in the base ring of $r$, determine the splitting type of $p$
+For a prime $p$ in the base ring of $r$, determine the splitting type of $p$
in $r$. ie. the tuple $(e, f, g)$ giving the ramification degree, the inertia
and the number of primes above $p$.
"""
@@ -357,7 +357,7 @@ end
ray_class_field(m::MapRayClassGrp) -> ClassField
Creates the (formal) abelian extension defined by the map $m: A \to I$
-where $I$ is the set of ideals coprime to the modulus defining $m$ and $A$
+where $I$ is the set of ideals coprime to the modulus defining $m$ and $A$
is a quotient of the ray class group (or class group). The map $m$
must be the map returned from a call to {class_group} or {ray_class_group}.
"""
@@ -369,7 +369,7 @@ end
ray_class_field(m::Union{MapClassGrp, MapRayClassGrp}, quomap::GrpAbFinGenMap) -> ClassField
For $m$ a map computed by either {ray_class_group} or {class_group} and
-$q$ a canonical projection (quotient map) as returned by {quo} for q
+$q$ a canonical projection (quotient map) as returned by {quo} for q
quotient of the domain of $m$ and a subgroup of $m$, create the
(formal) abelian extension where the (relative) automorphism group
is canonically isomorphic to the codomain of $q$.
diff --git a/src/RCF/conductor.jl b/src/RCF/conductor.jl
index f0a045dfd0..97c39752d5 100644
--- a/src/RCF/conductor.jl
+++ b/src/RCF/conductor.jl
@@ -473,7 +473,7 @@ function discriminant(C::ClassField)
end
end
-
+
@assert typeof(m) == NfOrdIdl
mR = C.rayclassgroupmap
@@ -652,7 +652,7 @@ function norm_group(f::Nemo.PolyElem, mR::T, isabelian::Bool = true; of_closure:
end
function norm_group(l_pols::Vector{T}, mR::U, isabelian::Bool = true; of_closure::Bool = false, cached::Bool = true, check::Bool = false) where {T <: PolyElem{nf_elem}, U <: Union{MapClassGrp, MapRayClassGrp}}
-
+
R = domain(mR)
O = order(codomain(mR))
K = nf(O)
@@ -666,19 +666,19 @@ function norm_group(l_pols::Vector{T}, mR::U, isabelian::Bool = true; of_closure
#Thus I will check for every prime if the projection has discriminant 0
n = lcm(Int[degree(x) for x = l_pols])
- if of_closure
+ if of_closure
#we cannot work in the quotient, it "could" be lcm(factorial(degree(x)) for x = f)
Q, mQ = quo(R, GrpAbFinGenElem[])
else
Q, mQ = quo(R, n, false)
end
-
+
p = maximum(degree(x)+1 for x = l_pols)
-
- listprimes = GrpAbFinGenElem[]
+
+ listprimes = GrpAbFinGenElem[]
# Adding small primes until it stabilizes
- B = prod(Int[degree(x) for x in l_pols])
+ B = prod(Int[degree(x) for x in l_pols])
max_stable = 50*n
stable = max_stable
denom = lcm([denominator(coeff(x, i)) for x in l_pols for i = 0:degree(x)])
@@ -697,7 +697,7 @@ function norm_group(l_pols::Vector{T}, mR::U, isabelian::Bool = true; of_closure
continue
end
if divides(indexO, fmpz(p))[1]
- continue
+ continue
end
found = false
L = prime_decomposition(O, p, 1)
@@ -707,9 +707,9 @@ function norm_group(l_pols::Vector{T}, mR::U, isabelian::Bool = true; of_closure
continue
end
F, mF = ResidueFieldSmallDegree1(O, L[i][1])
- mFp = extend_easy(mF, K)
+ mFp = extend_easy(mF, K)
all_deg = Vector{Int}[]
- #=
+ #=
the idea, taking 2 polys:
f splits in d_i
g splits in e_i
@@ -747,7 +747,7 @@ function norm_group(l_pols::Vector{T}, mR::U, isabelian::Bool = true; of_closure
Q, mQ = quo(R, listprimes, false)
found = true
stable = max_stable
- end
+ end
end
if !found
stable -= 1
@@ -831,8 +831,8 @@ function norm_group(KK::KummerExt, mp::NfToNfMor, mR::Union{MapRayClassGrp, MapC
zk = order(codomain(mR))
# disc(ZK/Q) = N(disc(ZK/zk)) * disc(zk)^deg
# we need the disc ZK/k, well a conductor.
-
-
+
+
n = degree(KK)
els = GrpAbFinGenElem[]
stable = 0
@@ -990,7 +990,7 @@ end
function factored_modulus(A::ClassField_pp{MapClassGrp, T}) where T
return Dict{NfOrdIdl, Int}()
end
-
+
function maximal_abelian_subfield(A::ClassField, mp::NfToNfMor)
k = domain(mp)
K = codomain(mp)
@@ -1387,7 +1387,7 @@ function Base.intersect(I::NfAbsOrdIdl, R::NfAbsOrd)
@assert fl
return minimum(m, I)
end
-
+
Base.intersect(R::NfAbsOrd, I::NfAbsOrdIdl) = intersect(I, R)
function Base.intersect(I::NfOrdFracIdl, R::NfAbsOrd)
diff --git a/src/RCF/cyclo.jl b/src/RCF/cyclo.jl
index df9b235513..3b8b3b62e2 100644
--- a/src/RCF/cyclo.jl
+++ b/src/RCF/cyclo.jl
@@ -50,7 +50,7 @@ function simplify!(C::CyclotomicExt)
return nothing
end
Ka, mKa = simplified_absolute_field(C.Kr, cached = false)
- Ks, mKs = simplify(Ka, cached = false)
+ Ks, mKs = simplify(Ka, cached = false)
abs2rel = mKs*mKa
imKa = inv(abs2rel)
small2abs = hom(base_field(C.Kr), Ks, imKa(C.Kr(gen(base_field(C.Kr)))))
@@ -194,7 +194,7 @@ function cyclotomic_extension(k::AnticNumberField, n::Int; cached::Bool = true,
Kr, Kr_gen = number_field(fk, "z_$n", cached = false, check = false)
if degree(fk) != 1
Ka, abs2rel, small2abs = collapse_top_layer(Kr, cached = false)
-
+
if compute_maximal_order && !simplified
# An equation order defined from a factor of a
# cyclotomic polynomial is always maximal by Dedekind
diff --git a/src/RCF/kummer_extensions.jl b/src/RCF/kummer_extensions.jl
index 4ae2609f38..158aa2320b 100644
--- a/src/RCF/kummer_extensions.jl
+++ b/src/RCF/kummer_extensions.jl
@@ -289,7 +289,7 @@ end
#
################################################################################
-# In this context, we are computing the Frobenius for conjugate prime ideals
+# In this context, we are computing the Frobenius for conjugate prime ideals
# We save the projection of the factor base, we can reuse them
#Computes a set of prime ideals of the base field of K such that the corresponding Frobenius
#automorphisms generate the automorphism group
@@ -299,10 +299,10 @@ function find_gens(K::KummerExt, S::PrimesSet, cp::fmpz=fmpz(1))
end
k = base_field(K)
ZK = maximal_order(k)
- R = K.AutG
+ R = K.AutG
sR = Vector{GrpAbFinGenElem}(undef, length(K.gen))
lp = Vector{NfOrdIdl}(undef, length(K.gen))
-
+
indZK = index(ZK)
q, mq = quo(R, GrpAbFinGenElem[], false)
s, ms = snf(q)
@@ -326,7 +326,7 @@ function find_gens(K::KummerExt, S::PrimesSet, cp::fmpz=fmpz(1))
for i = 1:length(D)
D[i] = Vector{gfp_poly}(undef, length(K.gen[i].fac))
end
-
+
first = false
for P in LP
try
@@ -342,7 +342,7 @@ function find_gens(K::KummerExt, S::PrimesSet, cp::fmpz=fmpz(1))
if iszero(mq(f))
continue
end
- #At least one of the coefficient of the element
+ #At least one of the coefficient of the element
#must be invertible in the snf form.
el = ms\f
to_be = false
@@ -361,7 +361,7 @@ function find_gens(K::KummerExt, S::PrimesSet, cp::fmpz=fmpz(1))
q, mq = quo(R, sR[1:ind-1], false)
s, ms = snf(q)
end
- if order(s) == 1
+ if order(s) == 1
break
end
@vprint :ClassField 3 "Index: $(exponent(s))^($(valuation(order(s), exponent(s))))\n"
@@ -396,7 +396,7 @@ end
function _compute_frob(K, mF, p, cached, D)
z_p = image(mF, K.zeta)^(K.n-1)
-
+
# K = k(sqrt[n_i](gen[i]) for i=1:length(gen)), an automorphism will be
# K[i] -> zeta^divexact(n, n_i) * ? K[i]
# Frob(sqrt[n](a), p) = sqrt[n](a)^N(p) (mod p) = zeta^r sqrt[n](a)
@@ -545,13 +545,13 @@ function reduce_mod_powers(a::FacElem{nf_elem, AnticNumberField}, n::Int, decom:
d = d1^(div(k, n) + 1)
end
b1 *= d^n #non-optimal, but integral...
- return FacElem(b1)
+ return FacElem(b1)
end
function reduce_mod_powers(a::FacElem{nf_elem, AnticNumberField}, n::Int, primes::Vector{NfOrdIdl})
vals = fmpz[valuation(a, p) for p in primes]
lp = Dict{NfOrdIdl, fmpz}(primes[i] => vals[i] for i = 1:length(primes) if !iszero(vals[i]))
- return reduce_mod_powers(a, n, lp)
+ return reduce_mod_powers(a, n, lp)
end
function reduce_mod_powers(a::FacElem{nf_elem, AnticNumberField}, n::Int)
diff --git a/src/RCF/rcf.jl b/src/RCF/rcf.jl
index 42beefd202..f61ea55174 100644
--- a/src/RCF/rcf.jl
+++ b/src/RCF/rcf.jl
@@ -200,7 +200,7 @@ function _s_unit_for_kummer_using_Brauer(C::CyclotomicExt, f::fmpz)
if isdefined(ZK, :lllO)
ZK = ZK.lllO::NfOrd
end
-
+
lP = Hecke.NfOrdIdl[]
for p = keys(lf.fac)
@@ -298,7 +298,7 @@ end
function find_gens_descent(mR::Map, A::ClassField_pp, cp::fmpz)
ZK = order(domain(mR))
C = cyclotomic_extension(nf(ZK), degree(A))
- R = codomain(mR)
+ R = codomain(mR)
Zk = order(codomain(A.rayclassgroupmap))
sR = GrpAbFinGenElem[]
lp = elem_type(domain(mR))[]
@@ -439,7 +439,7 @@ function find_gens_descent(mR::Map, A::ClassField_pp, cp::fmpz)
q, mq = quo(R, sR, false)
s, ms = snf(q)
end
- if order(q) == 1
+ if order(q) == 1
break
end
end
@@ -631,7 +631,7 @@ function _rcf_find_kummer(CF::ClassField_pp{S, T}) where {S, T}
CF.a = FacElem(one(C.Ka))
return nothing
end
- k, mk = kernel(h, false)
+ k, mk = kernel(h, false)
G = domain(h)
# Now, we find the kummer generator by considering the action
@@ -688,7 +688,7 @@ end
#roots of unit over the base field and the action of the automorphisms on it.
#The Kummer generator is always primitive! (Carlo and Claus)
function _find_prim_elem(CF::ClassField_pp, AutA)
-
+
AutA_gen = CF.AutG
A = domain(AutA_gen[1])
pe = gen(A)
@@ -700,7 +700,7 @@ function _find_prim_elem(CF::ClassField_pp, AutA)
Auto = Dict{GrpAbFinGenElem, NfRelElem{nf_elem}}(find_orbit(AutA_gen, AutA, pe))
end
end
- @vprint :ClassField 2 "have action on the primitive element!!!\n"
+ @vprint :ClassField 2 "have action on the primitive element!!!\n"
return pe, Auto
end
@@ -711,13 +711,13 @@ function find_orbit(auts, AutG, x)
order = 1
elements = Tuple{GrpAbFinGenElem, NfRelElem{nf_elem}}[(id(AutG), x)]
g = S[1]
-
+
while !iszero(g)
order = order +1
push!(elements, (g, auts[1](elements[end][2])))
g = g + S[1]
end
-
+
for i in 2:t
previous_order = order
for j = 1:previous_order
@@ -827,7 +827,7 @@ function _aut_A_over_k(C::CyclotomicExt, CF::ClassField_pp)
CF.AutR = AutA_rel
auts_in_snf!(CF)
return nothing
-
+
end
function auts_in_snf!(CF::ClassField_pp)
@@ -943,7 +943,7 @@ function _rcf_descent(CF::ClassField_pp)
else
@vprint :ClassField 2 "Computing automorphisms of the extension and orbit of primitive element\n"
pe, Auto = _find_prim_elem(CF, AutA)
-
+
@vprint :ClassField 2 ".. interesting...\n"
# want: hom: AutA = Gal(A/k) -> Gal(K/k) = domain(mq)
# K is the target field.
@@ -1022,8 +1022,8 @@ function _rcf_descent(CF::ClassField_pp)
end
end
genssq = NfRelToNfRelMor_nf_elem_nf_elem[gsq]
-
-
+
+
@assert Int(order(q)) == degree(CF)
#now, hopefully either norm or trace will be primitive for the target
@@ -1041,11 +1041,11 @@ function _rcf_descent(CF::ClassField_pp)
end
res = power_sums_to_polynomial(tr_in_K)
return res
- end
+ end
end
-
-
+
+
@vprint :ClassField 2 "trying relative trace\n"
@assert length(os) > 0
t = os[1]
diff --git a/src/RCF/rcf_stark.jl b/src/RCF/rcf_stark.jl
index bb065c4182..75937c9216 100644
--- a/src/RCF/rcf_stark.jl
+++ b/src/RCF/rcf_stark.jl
@@ -11,7 +11,7 @@ end
#
################################################################################
-function Base.show(io::IO, C::RCFCharacter)
+function Base.show(io::IO, C::RCFCharacter)
println(IOContext(io, :compact => true), "Character of $(C.C)")
end
@@ -272,7 +272,7 @@ function _find_coeffs(K, pol, v)
c = coeff(pol, i-1)
bn = 3*nbits(Hecke.upper_bound(c, fmpz))
fl, comb = _approximate(c, bconjs, bn)
- if !fl
+ if !fl
add = 10
while !fl && add < 100
fl, comb = _approximate(c, bconjs, bn)
@@ -328,7 +328,7 @@ function _find_suitable_quadratic_extension(C::T) where T <: ClassField_pp
ctx = rayclassgrp_ctx(OK, Int(exponent(C))*2)
allow_cache!(ctx.class_group_map)
lc = ideals_up_to(OK, bound, conductor(C)[1])
- cnt = 0
+ cnt = 0
while true
@vprint :ClassField 1 "Batch of ideals with $(length(lc)) elements \n"
for I in lc
@@ -828,7 +828,7 @@ function _C(chi::RCFCharacter, prec::Int)
OK = order(c)
nc = norm(c)
p = const_pi(RR)^degree(OK)
- d = sqrt(RR(abs(discriminant(OK))))*sqrt(RR(nc))
+ d = sqrt(RR(abs(discriminant(OK))))*sqrt(RR(nc))
return d//sqrt(p)
end
@@ -977,11 +977,11 @@ function _compute_A_coeffs(n::Int, nterms::Int, prec::Int)
res = Vector{arb}(undef, n+1)
q = divexact(i-1, 2)
r0 = spi*_coeff_0_odd(n, q)
- vg = coeffs_exp_odd[q+1]
+ vg = coeffs_exp_odd[q+1]
res[n+1] = zero(RR)
for j = 1:n
mul!(vg[n-j+1], vg[n-j+1], r0)
- res[j] = vg[n-j+1]
+ res[j] = vg[n-j+1]
end
end
res_final[i+1] = res
diff --git a/src/RCF/rcf_subfield.jl b/src/RCF/rcf_subfield.jl
index 913061cade..1ddb7fa394 100644
--- a/src/RCF/rcf_subfield.jl
+++ b/src/RCF/rcf_subfield.jl
@@ -45,7 +45,7 @@ function translate_extension(mL::NfToNfMor, C::ClassField_pp)
for (p, v) in fM0
p1 = Hecke.intersect_prime(mL, p)
if !haskey(fm0, p1)
- if iscoprime(minimum(p1, copy = false), n)
+ if iscoprime(minimum(p1, copy = false), n)
fm0[p1] = 1
else
fm0[p1] = v
@@ -57,14 +57,14 @@ function translate_extension(mL::NfToNfMor, C::ClassField_pp)
#Now, I have problems, so I need to add the ramification of the other extension.
for (p, v) in f
if !haskey(fm0, p)
- if isone(gcd(minimum(p), n))
+ if isone(gcd(minimum(p), n))
fm0[p] = 1
else
fm0[p] = v
end
else
- if !isone(gcd(minimum(p), n))
- fm0[p] = max(v, fm0[p])
+ if !isone(gcd(minimum(p), n))
+ fm0[p] = max(v, fm0[p])
end
end
lPP = prime_decomposition(mL, p)
@@ -77,7 +77,7 @@ function translate_extension(mL::NfToNfMor, C::ClassField_pp)
end
end
infplc = InfPlc[]
- if iszero(mod(n, 2))
+ if iszero(mod(n, 2))
infplc = real_places(L)
end
@vprint :ClassField 3 "Checking if I can compute the field over a subfield\n"
@@ -87,7 +87,7 @@ function translate_extension(mL::NfToNfMor, C::ClassField_pp)
end
#Now, the norm group of K over L
@vtime :ClassField 3 ngL, mngL = Hecke.norm_group(mL, mr)
- @hassert :ClassField 1 divisible(divexact(fmpz(degree(codomain(mL))), degree(domain(mL))), divexact(order(r), order(ngL)))
+ @hassert :ClassField 1 divisible(divexact(fmpz(degree(codomain(mL))), degree(domain(mL))), divexact(order(r), order(ngL)))
if !divisible(order(ngL), degree(C)) || !divisible(exponent(C), n)
return false, C
end
@@ -101,7 +101,7 @@ function translate_extension(mL::NfToNfMor, C::ClassField_pp)
fM0[p] = max(v, fM0[p])
else
fM0[p] = v
- end
+ end
end
end
inf_plc2 = InfPlc[]
@@ -127,7 +127,7 @@ function translate_extension(mL::NfToNfMor, C::ClassField_pp)
@hassert :ClassField 1 isisomorphic(cokernel(mk, false)[1], codomain(C.quotientmap))
mp = mk*proj
ck, mck = cokernel(mp, false)
- #If everything could work, then ck should be the direct product of the abelian extension I am searching for and
+ #If everything could work, then ck should be the direct product of the abelian extension I am searching for and
#the maximal abelian subextension of K/L
G1 = snf(cokernel(mngL, false)[1])[1]
G2 = snf(codomain(C.quotientmap))[1]
@@ -138,7 +138,7 @@ function translate_extension(mL::NfToNfMor, C::ClassField_pp)
fl, ms1 = has_complement(ms)
@assert fl
mq1 = cokernel(ms1, false)[2]
- mqq = mck * mq1
+ mqq = mck * mq1
@hassert :ClassField 1 domain(mqq) == r
C1 = ClassField_pp{MapRayClassGrp, GrpAbFinGenMap}()
C1.quotientmap = mqq
@@ -161,7 +161,7 @@ function translate_up(mL::NfToNfMor, C::ClassField_pp, C1::ClassField_pp)
mul!(img, img, gen(CEK.Kr))
end
end
- mrel = hom(CEL.Kr, CEK.Kr, mL, img)
+ mrel = hom(CEL.Kr, CEK.Kr, mL, img)
#@hassert :Fields 1 isconsistent(mrel)
g = mrel(CEL.mp[1](gen(CEL.Ka)))
mp = hom(CEL.Ka, CEK.Ka, CEK.mp[1]\(g), check = false)
@@ -183,7 +183,7 @@ function translate_up(mL::NfToNfMor, C::ClassField_pp, C1::ClassField_pp)
C.A = number_field(fdef, cached = false, check = false)[1]
#Now, the primitive element of the target extension seen in Cpp.K
mrel2 = hom(C1.K, C.K, mp, gen(C.K))
- C.pe = mrel2(C1.pe)
+ C.pe = mrel2(C1.pe)
CEKK = cyclotomic_extension(K, d)
@hassert :ClassField 1 iszero(map_coefficients(CEKK.mp[2], fdef, cached = false)(C.pe))
C.o = d1
diff --git a/src/Sparse/Matrix.jl b/src/Sparse/Matrix.jl
index bcd9c5b728..7c47e3a0a6 100644
--- a/src/Sparse/Matrix.jl
+++ b/src/Sparse/Matrix.jl
@@ -901,7 +901,7 @@ end
#
################################################################################
@doc Markdown.doc"""
- push!(A::SMat{T}, B::SRow{T}) where T
+ push!(A::SMat{T}, B::SRow{T}) where T
Appends the sparse row ```B``` to ```A```.
"""
diff --git a/src/Sparse/Module.jl b/src/Sparse/Module.jl
index 6c9917a31f..05f1145ebd 100644
--- a/src/Sparse/Module.jl
+++ b/src/Sparse/Module.jl
@@ -4,7 +4,7 @@
# Hecke.lift, Hecke.rational_reconstruction, Hecke.elementary_divisors,
# Hecke.rank, Hecke.det
-export det_mc, id, isupper_triangular, norm2, hadamard_bound2,
+export det_mc, id, isupper_triangular, norm2, hadamard_bound2,
hnf, hnf!, echelon_with_transform
add_verbose_scope(:HNF)
@@ -45,7 +45,7 @@ function add_gen!(M::ModuleCtxNmod, g::SRow{nmod})
push!(M.gens, g)
return true
end
- return false
+ return false
end
function add_gen!(M::ModuleCtx_fmpz, g::SRow{fmpz}, always::Bool = true)
@@ -57,7 +57,7 @@ function add_gen!(M::ModuleCtx_fmpz, g::SRow{fmpz}, always::Bool = true)
else
always && push!(M.rel_gens, g)
end
- return false
+ return false
end
function check_index(M::ModuleCtx_fmpz)
@@ -171,7 +171,7 @@ end
function non_trivial_pivot(M::ModuleCtx_fmpz)
h = check_index(M)
- if h == 0
+ if h == 0
return missing_pivot(M)
end
C = M.basis
diff --git a/src/Sparse/Row.jl b/src/Sparse/Row.jl
index e2c26b7058..a9953f937f 100644
--- a/src/Sparse/Row.jl
+++ b/src/Sparse/Row.jl
@@ -421,7 +421,7 @@ end
function +(A::SRow{T}, B::SRow{T}) where T
if length(A.values) == 0
- return B
+ return B
elseif length(B.values) == 0
return A
end
@@ -435,7 +435,7 @@ function -(A::SRow{T}, B::SRow{T}) where T
else
return add_scaled_row(B, A, base_ring(B)(-1))
end
- end
+ end
return add_scaled_row(B, A, base_ring(A)(-1))
end
@@ -486,7 +486,7 @@ function div(A::SRow{T}, b::T) where T
if !iszero(nv)
push!(B.pos, p)
push!(B.values, nv)
- end
+ end
end
return B
end
@@ -650,7 +650,7 @@ function add_scaled_row!(Ai::SRow{fmpz}, Aj::SRow{fmpz}, c::fmpz)
n = add!(n, n, Aj.values[pj])
# n = c*Ai.values[pi] + Aj.values[pj]
- if !iszero(n)
+ if !iszero(n)
nb = max(nb, nbits(n))
push!(sr.pos, Ai.pos[pi])
push!(sr.values, n)
diff --git a/src/Sparse/Solve.jl b/src/Sparse/Solve.jl
index 548557bb76..957b8d4eb3 100644
--- a/src/Sparse/Solve.jl
+++ b/src/Sparse/Solve.jl
@@ -372,8 +372,8 @@ function echelon!(S::SMat{T}; complete::Bool = false) where T <: FieldElem
j += 1
end
end
- i += 1
- end
+ i += 1
+ end
if complete
for i = nrows(S):-1:2
p = S[i].pos[1]
diff --git a/src/analytic.jl b/src/analytic.jl
index bc794f8455..a79f425872 100644
--- a/src/analytic.jl
+++ b/src/analytic.jl
@@ -323,7 +323,7 @@ function class_group_expected(d::fmpz, deg::Int, B::Int, samples::Int = 100)
else
Int(c)
end
-end
+end
#= D is supposed to be the disccriminant
n the dimension
diff --git a/src/conjugates.jl b/src/conjugates.jl
index ac4fd360df..9a4aebcfa0 100644
--- a/src/conjugates.jl
+++ b/src/conjugates.jl
@@ -1,5 +1,5 @@
-export conjugates_init, isconstant, issquarefree, conjugates, angle, cos,
+export conjugates_init, isconstant, issquarefree, conjugates, angle, cos,
sin, abs, abs2, sqrt
function isconstant(f::PolyElem)
@@ -20,7 +20,7 @@ function conjugates_init(f_in::Union{fmpz_poly, fmpq_poly})
end
g = PolynomialRing(FlintZZ, string(var(parent(f_in))), cached = false)[1](gz)
f = g
- else
+ else
f = f_in
end
isconstant(gcd(f, derivative(f))) || error("poly should be square-free")
@@ -36,7 +36,7 @@ function conjugates_init(f_in::Union{fmpz_poly, fmpq_poly})
push!(r_d, rr)
continue
end
- if imag(rr) > 0
+ if imag(rr) > 0
push!(c_d, rr)
continue
end
@@ -167,7 +167,7 @@ end
function minkowski_matrix(K::AnticNumberField, p::Int = 50)
c = roots_ctx(K)
- if isdefined(c, :minkowski_matrix)
+ if isdefined(c, :minkowski_matrix)
if c.minkowski_mat_p == p
return c.minkowski_matrix
elseif c.minkowski_mat_p >= p
diff --git a/src/helper.jl b/src/helper.jl
index c306b14976..ea378e3ebd 100644
--- a/src/helper.jl
+++ b/src/helper.jl
@@ -70,7 +70,7 @@ function check_return_type(f::DataType, M::Module, print_only_bad::Bool = false)
print("--------------------------------------------------------------------------------\n")
end
end
-end
+end
function check_bad_return_type(M::Module)
for x in names(M)
diff --git a/system/Build.jl b/system/Build.jl
index 7c67ffd0e6..8f3a30cc9e 100644
--- a/system/Build.jl
+++ b/system/Build.jl
@@ -11,7 +11,7 @@ println(f, "using Pkg")
println(f, "Hecke.system(\"precompile.jl\")")
close(f)
-PackageCompiler.create_sysimage([:Hecke], sysimage_path="/tmp/Hecke.$(Libdl.dlext)", precompile_execution_file="/tmp/CompileHecke.jl")
+PackageCompiler.create_sysimage([:Hecke], sysimage_path="/tmp/Hecke.$(Libdl.dlext)", precompile_execution_file="/tmp/CompileHecke.jl")
println("(re)start julia as")
println("\tjulia -J /tmp/Hecke.$(Libdl.dlext)")
\ No newline at end of file
diff --git a/system/HeckeProfile.jl b/system/HeckeProfile.jl
index 1c6b171357..0e577e5bf6 100644
--- a/system/HeckeProfile.jl
+++ b/system/HeckeProfile.jl
@@ -94,7 +94,7 @@ end
iz = find(bt .== 0)
then bt[1:iz[1]-1] is a complete trace
bt[iz[1]+1:iz[2]-1] the next, ...
-=#
+=#
function callers_frame(fname::Symbol, bt::Vector, lidict::Profile.LineInfoDict)
counts = []
@@ -127,7 +127,7 @@ function callers_frame(fname::Symbol, bt::Vector, lidict::Profile.LineInfoDict)
break
end
end
- end
+ end
return counts
end
@@ -146,7 +146,7 @@ function leafs(bt::Vector, lidict::Profile.LineInfoDict, skipC::Bool = false)
push!(M, fr.func)
skip = true
break
- end
+ end
else
skip = f!=0
end
@@ -161,14 +161,14 @@ function counts(bt::Vector, lidict::Profile.LineInfoDict, skipC::Bool = false)
continue
end
for fr = lidict[f]
- if skipC
+ if skipC
if !fr.from_c
push!(M, fr.func)
end
else
push!(M, fr.func)
end
- end
+ end
end
return M
end
@@ -198,8 +198,8 @@ function prune(fname::Symbol, bt::Vector, lidict::Profile.LineInfoDict)
push!(last, g)
break
end
- end
- end
+ end
+ end
if bingo
append!(rt, reverse(last))
push!(rt, UInt(0))
@@ -265,7 +265,7 @@ function graph(bt::Vector, lidict::Profile.LineInfoDict, skipC::Bool = true, ski
e[t] = 1
end
last = fn
- end
+ end
end
return g
end
@@ -278,7 +278,7 @@ end
function parents_with_count(g::Graph{T}, c::T) where {T}
return [(a, d) for ((a,b), d) = g.e if b==c]
-end
+end
function children(g::Graph{T}, c::T) where {T}
return [b for (a,b) = keys(g.e) if a==c]
@@ -296,6 +296,6 @@ end
HeckeProfile.children(G, :+)
...
-=#
+=#
end
diff --git a/test/AlgAss/AlgMat.jl b/test/AlgAss/AlgMat.jl
index c7bfb10e26..dfa56b215d 100644
--- a/test/AlgAss/AlgMat.jl
+++ b/test/AlgAss/AlgMat.jl
@@ -15,7 +15,7 @@
end
@testset "Radical" begin
-
+
mats = [[0 0 0 0 0 0 0 0 0 0;
1 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0;
diff --git a/test/AlgAssAbsOrd/Conjugacy/Conjugacy.jl b/test/AlgAssAbsOrd/Conjugacy/Conjugacy.jl
index 88141f7609..a4c112f166 100644
--- a/test/AlgAssAbsOrd/Conjugacy/Conjugacy.jl
+++ b/test/AlgAssAbsOrd/Conjugacy/Conjugacy.jl
@@ -4,7 +4,7 @@
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, -9604, -7056, -12076, -2392, -2253, 952, 46, -16, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -4900, -140]
-
+
b = fmpz[-4645900, -49391, -3848404, -16744, -15771, 6664, 17066, 470484,
33488, 3779643, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1,
0, -2, 0, -26, 0, -8, 0, 1, 0, 0, 1, 0, 9, -55750240, -592692,
diff --git a/test/EllCrv/EllCrv.jl b/test/EllCrv/EllCrv.jl
index 5214cb71aa..27d63bdea6 100644
--- a/test/EllCrv/EllCrv.jl
+++ b/test/EllCrv/EllCrv.jl
@@ -96,7 +96,7 @@
@test @inferred isfinite(P)
@test @inferred !isinfinite(P)
-# the error is/was from doing QQ(K(0)) - which is possible now
+# the error is/was from doing QQ(K(0)) - which is possible now
# @test_throws MethodError E43_a1([gen(K), gen(K)])
@test_throws ErrorException E43_a1([2, 2])
diff --git a/test/Examples/MultiQuad.jl b/test/Examples/MultiQuad.jl
index a4a873f6bf..01a3659008 100644
--- a/test/Examples/MultiQuad.jl
+++ b/test/Examples/MultiQuad.jl
@@ -10,6 +10,6 @@
# f = MultiQuad.saturate(e, 2)
# @test MultiQuad.Hecke.class_group_get_pivot_info(f) == (1, BitSet([]))
-end
+end
diff --git a/test/FieldFactory/FieldFactory.jl b/test/FieldFactory/FieldFactory.jl
index 6e2f9f19e6..c7c357e52b 100644
--- a/test/FieldFactory/FieldFactory.jl
+++ b/test/FieldFactory/FieldFactory.jl
@@ -5,7 +5,7 @@
@testset "Quadratic Fields" begin
lq = fields(2, 1, fmpz(10)^4)
@test length(lq) == 6086
-
+
lqreal = fields(2, 1, fmpz(10)^4, only_real = true)
@test length(lqreal) == 3043
@@ -17,17 +17,17 @@
end
@test ind == 3043
end
- end
+ end
println("Biquadratic Fields")
@time begin
@testset "Biquadratic Fields" begin
l = fields(4, 2, fmpz(10)^6)
@test length(l) == 1014
-
+
l1 = fields(4, 2, fmpz(10)^6, only_real = true)
@test length(l1) == 196
-
+
ind = 0
for x in l
if istotally_real(x.field)
@@ -43,7 +43,7 @@
@testset "Abelian fields" begin
l = fields(6, 2, fmpz(10)^6)
@test length(l) == 10
-
+
l1 = fields(9, 2, fmpz(10)^13)
@test length(l1) == 4
end
@@ -55,11 +55,11 @@
@testset "Direct product decomposition" begin
@time l_direct_product = fields(12, 4, fmpz(10)^13)
@test length(l_direct_product) == 25
-
+
@time l_without = fields(12, 4, fmpz(10)^13, using_direct_product = false)
@test length(l_without) == 25
- d1 = length(fields(24, 13, fmpz(10)^24))
+ d1 = length(fields(24, 13, fmpz(10)^24))
d2 = length(fields(24, 13, fmpz(10)^24, using_direct_product = false))
@test d1 == d2
@@ -96,14 +96,14 @@
l = fields(4, 2, fmpz(10)^6)
forQ8 = Hecke.check_obstruction(l, L, 2, [2])
@test length(forQ8) == 53
-
-
+
+
lQ8 = fields(8, 4, fmpz(10)^12)
@test length(lQ8) == 2
-
+
lQ8_2 = fields(8, 4, forQ8, fmpz(10)^12)
@test length(lQ8_2) == 2
-
+
lQ8real = fields(8, 4, forQ8, fmpz(10)^12, only_real = true)
@test length(lQ8real) == 1
end
@@ -124,7 +124,7 @@
@test length(lsieved) == 24
end
end
-
+
println("Obstructions: prime power case")
@time begin
@testset "Obstructions: prime_power_case" begin
@@ -153,7 +153,7 @@
end
end
-
+
println("Some examples")
@time begin
@testset "Some examples" begin
diff --git a/test/FunField/DegreeLocalization.jl b/test/FunField/DegreeLocalization.jl
index 5826f85878..9eee1c2534 100644
--- a/test/FunField/DegreeLocalization.jl
+++ b/test/FunField/DegreeLocalization.jl
@@ -72,7 +72,7 @@ L = Localization(R, degree)
@test divides(L(1//x), L(1//x)) == (true, L(1))
@test_throws DivideError divexact(L(1//(x + 1)), L())
-
+
for i in 1:300
a = rand(L, 0:10, -10:10)
b = rand(L, 0:10, -10:10)
diff --git a/test/GrpAb/Elem.jl b/test/GrpAb/Elem.jl
index 4715af4480..3fe32e380d 100644
--- a/test/GrpAb/Elem.jl
+++ b/test/GrpAb/Elem.jl
@@ -75,11 +75,11 @@
aa = @inferred(2 * a)
@test aa == G([2, 0, 0])
-
+
aa = @inferred(a * 2)
@test aa == G([2, 0, 0])
-
+
aa = @inferred(fmpz(2) * a)
@test aa == G([2, 0, 0])
end
@@ -87,7 +87,7 @@
@testset "Neutral element" begin
G = abelian_group([3, 3, 3])
a = G[1]
-
+
aa = @inferred(a * fmpz(2))
@test aa == G([2, 0, 0])
@@ -180,7 +180,7 @@
@test length(collect(G)) == 3*9*27
end
-
+
@testset "Helper" begin
@testset "Reduce mod Hermite normal form" begin
a = FlintZZ[21 32 43]
@@ -198,7 +198,7 @@
Hecke.reduce_mod_hnf_ur!(a, H)
@test a == FlintZZ[0 0 1]
end
-
+
@testset "Smith normal form with transform" begin
M = MatrixSpace(FlintZZ,1,1)([0])
S = MatrixSpace(FlintZZ,1,1)([0])
diff --git a/test/GrpAb/GrpAbFinGen.jl b/test/GrpAb/GrpAbFinGen.jl
index 3c6bf2a98d..a948303584 100644
--- a/test/GrpAb/GrpAbFinGen.jl
+++ b/test/GrpAb/GrpAbFinGen.jl
@@ -220,7 +220,7 @@
H, mH = @inferred sub(G, fmpz(2))
@test isisomorphic(H, abelian_group([3, 3, 6, 5]))
-
+
G = abelian_group([2, 2, 6, 6])
H, mH = @inferred sub(G, 2)
@test isisomorphic(H, abelian_group([3, 3]))
@@ -316,10 +316,10 @@
A = abelian_group([3 1; 0 3])
B = abelian_group([9 2 1; 0 12 1; 0 0 25])
C = abelian_group([3, 4, 0])
- @test isisomorphic(hom(tensor_product(A, B, task = :none), C)[1],
+ @test isisomorphic(hom(tensor_product(A, B, task = :none), C)[1],
hom(A, hom(B, C)[1])[1])
end
-
+
@testset "Complement" begin
d = rand(2:1000)
d1 = rand(2:1000)
diff --git a/test/GrpAb/Lattice.jl b/test/GrpAb/Lattice.jl
index ab7d7d8c4b..43ec173f35 100644
--- a/test/GrpAb/Lattice.jl
+++ b/test/GrpAb/Lattice.jl
@@ -118,7 +118,7 @@
b, M = @inferred Hecke.can_map_into(L, Q, H)
@test !b
-
+
HH, mHH = sub(G, [G[2]], true, L)
b, GG, MH, MHH = @inferred Hecke.can_map_into_overstructure(L, H, HH)
@test b
diff --git a/test/GrpAb/Map.jl b/test/GrpAb/Map.jl
index 235c22fcc0..f319edd04b 100644
--- a/test/GrpAb/Map.jl
+++ b/test/GrpAb/Map.jl
@@ -77,7 +77,7 @@
b = @inferred issurjective(h)
@test b
end
-
+
@testset "Bijectivity" begin
G = abelian_group([4, 4, 4])
H = abelian_group([4, 4, 4])
diff --git a/test/GrpAb/SubgroupEnum.jl b/test/GrpAb/SubgroupEnum.jl
index 223e99925c..0268dd7f77 100644
--- a/test/GrpAb/SubgroupEnum.jl
+++ b/test/GrpAb/SubgroupEnum.jl
@@ -11,7 +11,7 @@
end
@testset "Given subgroup type" begin
-
+
T = psubgroups(G, 3, subtype = [3])
@test 0 == length(collect(T))
@@ -25,7 +25,7 @@
T = psubgroups(G, 3, subtype = [2])
@test 9 == length(collect(T))
@test all([snf(t[1])[1].snf == fmpz[9] for t in T])
-
+
T = psubgroups(G, 3, subtype = [1, 1])
@test 13 == length(collect(T))
@test all([snf(t[1])[1].snf == fmpz[3, 3] for t in T])
@@ -51,7 +51,7 @@
TH = psubgroups(G, 3, subtype = [2])
@test 9 == length(collect(TH))
@test all([snf(t[1])[1].snf == fmpz[9] for t in TH])
-
+
TH = psubgroups(G, 3, subtype = [1, 1])
@test 13 == length(collect(TH))
@test all([snf(t[1])[1].snf == fmpz[3, 3] for t in TH])
@@ -73,7 +73,7 @@
T = psubgroups(G, 3, quotype = [1, 1], fun = quo)
@test 13 == length(collect(T))
@test all([snf(t[1])[1].snf == fmpz[3, 3] for t in T])
-
+
T = psubgroups(G, 3, quotype = [2, 1, 1], fun = quo)
@test 1 == length(collect(T))
@test all([snf(t[1])[1].snf == fmpz[3, 3, 9] for t in T])
@@ -81,7 +81,7 @@
T = psubgroups(G, 3, quotype = Int[], fun = quo)
@test 1 == length(collect(T))
@test all([order(t[1]) == 1 for t in T])
-
+
TH = psubgroups(G, 3, quotype = [2], fun = quo)
@test 9 == length(collect(TH))
@test all([snf(t[1])[1].snf == fmpz[9] for t in TH])
@@ -89,7 +89,7 @@
TH = psubgroups(G, 3, quotype = [1, 1], fun = quo)
@test 13 == length(collect(TH))
@test all([snf(t[1])[1].snf == fmpz[3, 3] for t in TH])
-
+
TH = psubgroups(G, 3, quotype = [2, 1, 1], fun = quo)
@test 1 == length(collect(TH))
@test all([snf(t[1])[1].snf == fmpz[3, 3, 9] for t in TH])
@@ -98,7 +98,7 @@
@test 1 == length(collect(TH))
@test all([order(t[1]) == 1 for t in TH])
end
-
+
@testset "Given order" begin
T = psubgroups(G, 3, order = 1)
@@ -112,11 +112,11 @@
T = psubgroups(G, 3, order = 9)
@test 22 == length(collect(T))
@test all([order(t[1]) == 9 for t in T])
-
+
T = psubgroups(G, 3, order = 81)
@test 1 == length(collect(T))
@test all([order(t[1]) == 81 for t in T])
-
+
TH = psubgroups(G, 3, order = 1)
@test 1 == length(collect(TH))
@test all([order(t[1]) == 1 for t in TH])
@@ -128,7 +128,7 @@
TH = psubgroups(G, 3, order = 9)
@test 22 == length(collect(TH))
@test all([order(t[1]) == 9 for t in TH])
-
+
TH = psubgroups(G, 3, order = 81)
@test 1 == length(collect(TH))
@test all([order(t[1]) == 81 for t in TH])
@@ -147,11 +147,11 @@
T = psubgroups(G, 3, index = 9, fun = quo)
@test 22 == length(collect(T))
@test all([order(t[1]) == 9 for t in T])
-
+
T = psubgroups(G, 3, index = 81, fun = quo)
@test 1 == length(collect(T))
@test all([order(t[1]) == 81 for t in T])
-
+
TH = psubgroups(G, 3, index = 1, fun = quo)
@test 1 == length(collect(TH))
@test all([order(t[1]) == 1 for t in TH])
@@ -163,7 +163,7 @@
TH = psubgroups(G, 3, index = 9, fun = quo)
@test 22 == length(collect(TH))
@test all([order(t[1]) == 9 for t in TH])
-
+
TH = psubgroups(G, 3, index = 81, fun = quo)
@test 1 == length(collect(TH))
@test all([order(t[1]) == 81 for t in TH])
@@ -192,7 +192,7 @@
T = subgroups(G, subtype = [5, 5, 9, 3])
@test 1 == length(collect(T))
@test all([snf(t[1])[1].snf == fmpz[15, 45] for t in T])
-
+
T = subgroups(G, subtype = [3, 5, 9, 5])
@test 1 == length(collect(T))
@test all([snf(t[1])[1].snf == fmpz[15, 45] for t in T])
@@ -202,12 +202,12 @@
@testset "Given quotype" begin
T = subgroups(G, quotype = [25, 27], fun = quo)
@test 0 == length(collect(T))
-
+
T = subgroups(G, quotype = [5, 7], fun = quo)
@test 6 == length(collect(T))
@test all([snf(t[1])[1].snf == fmpz[35] for t in T])
end
-
+
@testset "Given order" begin
T = subgroups(G, order = 5*7*3)
@test 24 == length(collect(T))
diff --git a/test/LocalField/Conjugates.jl b/test/LocalField/Conjugates.jl
index b97a4ec93c..98ceb27c6c 100644
--- a/test/LocalField/Conjugates.jl
+++ b/test/LocalField/Conjugates.jl
@@ -16,7 +16,7 @@
end
@testset "Completion" begin
-
+
if VERSION < v"1.6.0-DEV.1332"
L1, mL1 = completion(k, 37, 1)
L2, mL2 = completion(k, 37, 3)
@@ -42,5 +42,5 @@
end
end
end
-
+
diff --git a/test/LocalField/LocalField.jl b/test/LocalField/LocalField.jl
index 23d9a82375..fbd2b6c704 100644
--- a/test/LocalField/LocalField.jl
+++ b/test/LocalField/LocalField.jl
@@ -1,5 +1,5 @@
@testset "LocalField" begin
-
+
@testset "Creation" begin
Qx, x = FlintQQ["x"]
f = x^2-2*x+2
@@ -16,7 +16,7 @@
@test degree(L) == 2
@test absolute_degree(L) == 4
@test prime(L) == 2
-
+
Q2 = PadicField(2, 10)
Q2s, s = PolynomialRing(Q2, "s")
f = s^2+s+1
@@ -42,9 +42,9 @@
K = QadicField(3, 4, 10)[1]
Kx, x = PolynomialRing(K, "x")
L = eisenstein_extension(x^20+3)[1]
- b = @inferred basis(L)
+ b = @inferred basis(L)
for i = 1:10
- r = 1+2*uniformizer(L)^i * sum([rand(1:10)*b[i] for i in 1:5])
+ r = 1+2*uniformizer(L)^i * sum([rand(1:10)*b[i] for i in 1:5])
M = @inferred representation_matrix(r)
n = @inferred norm(r)
@test n == det(M)
@@ -129,12 +129,12 @@
Kx, x = PolynomialRing(K, "x", cached = false)
L, b = Hecke.eisenstein_extension(x^7+2, "a")
pi = uniformizer(L)
- @test iszero(log(pi))
+ @test iszero(log(pi))
B = basis(L)
for i = 15:20
el = sum([rand(FlintZZ, 0:10)*B[j] for j = 1:7])*pi^i
explog = exp(log(1+el))
- logexp = log(exp(el))
+ logexp = log(exp(el))
@test iszero(setprecision(explog, precision(explog)-35) - 1 - el)
@test iszero(setprecision(logexp, precision(logexp)-35)-el)
end
diff --git a/test/LocalField/Poly.jl b/test/LocalField/Poly.jl
index 65bb60b5cd..4d89c36539 100644
--- a/test/LocalField/Poly.jl
+++ b/test/LocalField/Poly.jl
@@ -3,8 +3,8 @@
K = PadicField(2, 100)
Kx, x = PolynomialRing(K, "x")
L, gL = eisenstein_extension(x^2+2, "a")
-
- @testset "Fun Factor" for F in [K, L]
+
+ @testset "Fun Factor" for F in [K, L]
Fx, x = PolynomialRing(F, "x")
f = x^5
for i = 0:4
@@ -16,29 +16,29 @@
c = K(rand(FlintZZ, 1:100))
u += 2*c*x^i
end
-
+
g = f*u
u1, f1 = @inferred Hecke.fun_factor(g)
@test u == u1
@test f1 == f
end
-
+
@testset "Gcd" for F in [K, L]
Fx, x = PolynomialRing(F, "x")
f = (2*x+1)*(x+1)
g = x^3+1
gg = @inferred gcd(f, g)
- @test gg == x+1
-
+ @test gg == x+1
+
f = (2*x+1)*(x+1)
g = (2*x+1)*(x+2)
@test gcd(f, g) == 2*x+1
-
+
f = (x + 1//K(2)) * (2*x^2+x+1)
g = 2*x+1
@test gcd(f, g) == g
end
-
+
@testset "Gcdx" for F in [K, L]
Fx, x = PolynomialRing(F, "x")
f = (2*x+1)*(x+1)
@@ -46,24 +46,24 @@
d, u, v = gcdx(f, g)
@test d == gcd(f, g)
@test u*f + v*g == d
-
+
f = (2*x+1)*(x+1)
g = (2*x+1)*(x+2)
d, u, v = @inferred gcdx(f, g)
@test gcd(f, g) == d
@test d == u*f + v*g
-
+
f = (x + 1//K(2)) * (2*x^2+x+1)
g = 2*x+1
d, u, v = gcdx(f, g)
@test g == d
@test u*f + v*g == d
- end
-
+ end
+
@testset "Hensel" for F in [K, L]
Fx, x = PolynomialRing(F, "x")
- f = (x+1)^3
- g = (x^2+x+1)
+ f = (x+1)^3
+ g = (x^2+x+1)
h = x^2 +2*x + 8
ff = f*g*h
lf = @inferred Hecke.Hensel_factorization(ff)
@@ -84,5 +84,5 @@
b = derivative(a)
rab = @inferred resultant(a, b)
@test rab == det(sylvester_matrix(a, b))
- end
+ end
end
diff --git a/test/Map/NumField.jl b/test/Map/NumField.jl
index df6e7cfe40..48fb0a1d23 100644
--- a/test/Map/NumField.jl
+++ b/test/Map/NumField.jl
@@ -52,7 +52,7 @@
end
# AnticNumberField -> NfRel{nf_elem}
-
+
QQQ, q = NumberField(x - 1, "q")
QQQt, t = QQQ["t"]
K, a = NumberField(x^2 - 2, "a")
@@ -190,7 +190,7 @@
@test f(L(a)) == LL(-a)
# NfRel to NfRelNfRel
-
+
Qx, x = QQ["x"]
_K, a = NumberField(x^2 - 2, "a")
_Ky, y = _K["y"]
@@ -201,7 +201,7 @@
f = hom(Ka, K, c, inverse = (-_b^2 - _b + 5, _b))
# NfAbsNS
-
+
K, a = NumberField([x^2 - 2])
f = @inferred id_hom(K)
for i in 1:10
diff --git a/test/Map/NumberField.jl b/test/Map/NumberField.jl
index 623c0bed31..b76a25cb0d 100644
--- a/test/Map/NumberField.jl
+++ b/test/Map/NumberField.jl
@@ -20,12 +20,12 @@ end
for i = 1:length(lP)
I_new = A[2](lP1[1])
id = findfirst(isequal(I_new), lP1)
- @test id != nothing
+ @test id != nothing
end
f = hom(K, K, a^4//12+a//2)
E = EquationOrder(K)
I = ideal(E, E(a))
- @test_throws ErrorException Hecke.induce_image(f, I)
+ @test_throws ErrorException Hecke.induce_image(f, I)
end
diff --git a/test/Misc/NumberField.jl b/test/Misc/NumberField.jl
index 4f213149ee..e36da2e06a 100644
--- a/test/Misc/NumberField.jl
+++ b/test/Misc/NumberField.jl
@@ -7,11 +7,11 @@
c, KtoL = Hecke.issubfield(K, L)
@test c == true
@test parent(KtoL(a)) == L
-
+
c, KtoL = Hecke.issubfield_normal(K, L)
@test c == true
@test parent(KtoL(a)) == L
-
+
OK = maximal_order(K)
OL = maximal_order(L)
c, KtoL = Hecke.issubfield(K, L)
diff --git a/test/Misc/Places.jl b/test/Misc/Places.jl
index ed717dd3a6..ae54509d4f 100644
--- a/test/Misc/Places.jl
+++ b/test/Misc/Places.jl
@@ -33,7 +33,7 @@
@test S[1] != S[2]
string(S[1]); # Just check that it does not error
-
+
S = infinite_places(K2)
@test length(S) == 5
@@ -47,7 +47,7 @@
r = conjugates_arb(a2)
@test overlaps(r[1], SR[1].r)
- @test overlaps(r[2], SC[1].r) && overlaps(r[3], SC[2].r) && overlaps(r[4], SC[3].r) && overlaps(r[5], SC[4].r)
+ @test overlaps(r[2], SC[1].r) && overlaps(r[3], SC[2].r) && overlaps(r[4], SC[3].r) && overlaps(r[5], SC[4].r)
P = infinite_place(K2, 1)
@test P == S[1]
@@ -82,7 +82,7 @@
@test !ispositive(b, infinite_places(K1))
@test ispositive(b, [C])
@test !istotally_positive(b)
-
+
c = b^10*b^2
sc = signs(c)
@test sc == Dict(P => 1)
@@ -120,7 +120,7 @@
@test !ispositive(b, [P, C])
@test !ispositive(b, infinite_places(K3))
@test !istotally_positive(b)
-
+
c = b^10*b^2
@test signs(c) == Dict(P => 1, P2 => 1)
@test sign(c, P) == 1
diff --git a/test/Misc/Poly.jl b/test/Misc/Poly.jl
index 3ca191e6d5..3528928eaf 100644
--- a/test/Misc/Poly.jl
+++ b/test/Misc/Poly.jl
@@ -55,7 +55,7 @@
end
function random_symmetric_matrix(x::Int)
- M = zero_matrix(FlintZZ, x, x)
+ M = zero_matrix(FlintZZ, x, x)
for i = 1:x
for j= i:x
a = rand(1:5)
@@ -69,6 +69,6 @@
for i = 1:20
@test _test_sturm()
end
-
-
+
+
end
diff --git a/test/Misc/Primes.jl b/test/Misc/Primes.jl
index 120d6e41d0..d358b46313 100644
--- a/test/Misc/Primes.jl
+++ b/test/Misc/Primes.jl
@@ -42,7 +42,7 @@
@test length(PP) == 35
@test PP[1] == T(101)
@test PP[end] == T(991)
- @test all(isprime(p) && iszero(mod(p - T(1), T(5))) for p in P)
+ @test all(isprime(p) && iszero(mod(p - T(1), T(5))) for p in P)
P = @inferred PrimesSet(T(100), T(1000))
PP = collect(P)
@@ -58,7 +58,7 @@
a = rand(0:modd)
end
P = @inferred PrimesSet(T(B), 2 * T(B), T(modd), T(a))
- @test all(isprime(p) && iszero(mod(p - T(a), T(modd))) for p in P)
+ @test all(isprime(p) && iszero(mod(p - T(a), T(modd))) for p in P)
end
end
diff --git a/test/Misc/RelFinField.jl b/test/Misc/RelFinField.jl
index 057d0e1bb9..bcbb06ef88 100644
--- a/test/Misc/RelFinField.jl
+++ b/test/Misc/RelFinField.jl
@@ -10,7 +10,7 @@
bK = @inferred base_field(K)
@test bK == F
o = @inferred order(K)
- @test o == 27^2
+ @test o == 27^2
@test absolute_degree(K) == 6
end
@@ -45,7 +45,7 @@
@test gL^3 == gL*gL*gL
@test gL^5 == 2*(gL^4+gL^2+1)
@test isone(-gL^5-gL^4-gL^2)
- end
+ end
@testset "Norm, Trace, Minpoly" begin
F, gF = FiniteField(3, 3, cached = false)
@@ -62,12 +62,12 @@
f = @inferred Hecke.absolute_minpoly(gL)
Fx = parent(f)
x = gen(Fx)
- @test f == x^5+x^4+x^2+1
+ @test f == x^5+x^4+x^2+1
g = @inferred minpoly(gL+1)
@test iszero(g(gL+1))
Rx = parent(g)
y = gen(Rx)
- @test g(y+1) == y^5+y^4+y^2+1
+ @test g(y+1) == y^5+y^4+y^2+1
end
@testset "Absolute basis and coordinates" begin
diff --git a/test/Misc/jordan_test.jl b/test/Misc/jordan_test.jl
index 4c191f5e16..44ec1b2d41 100644
--- a/test/Misc/jordan_test.jl
+++ b/test/Misc/jordan_test.jl
@@ -27,7 +27,7 @@
@test S*M*inv(S) == J
for i = 1:6
for j = 1:i-1
- @test iszero(J[i, j])
+ @test iszero(J[i, j])
end
end
for i = 1:5
@@ -50,5 +50,5 @@
CF, TM = rational_canonical_form(C)
@test CF == C
@test TM * C * inv(TM) == CF
-
+
end
diff --git a/test/Misc/meataxe.jl b/test/Misc/meataxe.jl
index 72c78f342c..d8d3a4a6cd 100644
--- a/test/Misc/meataxe.jl
+++ b/test/Misc/meataxe.jl
@@ -7,9 +7,9 @@
@test iszero(Hecke.cleanvect(M,v))
v[1,3]=1
@test !iszero(Hecke.cleanvect(M,v))
-
+
end
-
+
@testset "closure and spinning" begin
G=[MatrixSpace(F,4,4)([1,2,0,0,1,1,0,0,0,0,1,2,0,0,1,1])]
M=Hecke.ModAlgAss(G)
@@ -21,7 +21,7 @@
@test nrows(Hecke.closure(v,M.action))==4
end
-
+
@testset "meataxe" begin
G=[MatrixSpace(F,4,4)([1,2,0,0,1,1,0,0,0,0,1,2,0,0,1,1])]
M=Hecke.ModAlgAss(G)
@@ -29,19 +29,19 @@
@test !bool
@test nrows(B)==2
#@test nrows(Hecke.closure(B, M.action))==2
-
+
N=Hecke._actsub(B,G)
bool,B=meataxe(N)
@test bool
-
+
G=[MatrixSpace(F,3,3)([1,0,0,0,0,1,0,1,0]), MatrixSpace(F,3,3)([0,0,1,1,0,0,0,1,0])]
M=Hecke.ModAlgAss(G)
bool,B=meataxe(M)
@test !bool
#@test nrows(Hecke.closure(B, M.action))==nrows(B)
-
+
end
-
+
@testset "composition factors and series" begin
G=[MatrixSpace(F,4,4)([1,2,0,0,1,1,0,0,0,0,1,2,0,0,1,1])]
M=Hecke.ModAlgAss(G)
@@ -58,27 +58,27 @@
N=Hecke.ModAlgAss([matrix(F,2,2,[0,2,1,0])])
M.isirreducible= 1
@test Hecke.isisomorphic(M,N)
-
-
+
+
M1=matrix(F,2,2,[1,0,1,1])
M2=matrix(F,2,2,[1,1,0,1])
M=Hecke.ModAlgAss([M1,M2])
M.isirreducible= 1
-
+
N1=matrix(F,2,2,[2,2,1,0])
N2=matrix(F,2,2,[1,1,0,1])
N=Hecke.ModAlgAss([N1,N2])
-
+
@test Hecke.isisomorphic(M,N)
-
+
end
-
+
@testset "Submodules" begin
A=MatrixSpace(F,3,3)(1)
M=Hecke.ModAlgAss([A])
ls=minimal_submodules(M)
@test length(ls)==13
-
+
F = f(2) #FiniteField(2, 1, "a")
A=MatrixSpace(F,6,6)(1)
A[5,6]=1
diff --git a/test/Misc/stable_subgroups.jl b/test/Misc/stable_subgroups.jl
index 908be7b3c7..396650ee6e 100644
--- a/test/Misc/stable_subgroups.jl
+++ b/test/Misc/stable_subgroups.jl
@@ -1,23 +1,23 @@
@testset "ZpnGModules" begin
@testset "Minimal Submodules" begin
-
+
F, a = FiniteField(3,1,"a")
R = ResidueRing(FlintZZ,9)
-
+
V=abelian_group([3,3,9,9])
-
+
l=[1,1,3,0,2,1,3,3,1,1,1,1,0,0,0,1]
l1=[1,1,1,0,2,1,1,1,0,0,1,1,0,0,0,1]
A=MatrixSpace(R,4,4)(l)
A1=MatrixSpace(F,4,4)(l1)
-
+
M = ZpnGModule(V,[A])
M1 = Hecke.ModAlgAss([A1])
-
+
ls = minimal_submodules(M)
ls1 = minimal_submodules(M1)
-
+
@test length(ls) == length(ls1)
for y in ls
@test Hecke.issubmodule(M,y)
@@ -26,7 +26,7 @@
@testset "Dual Module" begin
-
+
R=ResidueRing(FlintZZ,9)
V=abelian_group([3,3,9,9])
V.issnf=true
@@ -40,12 +40,12 @@
for y in ls
@test Hecke.issubmodule(M,Hecke._dualize(y,V,v))
end
-
+
end
-
-
+
+
@testset "submodules with given structure" begin
-
+
R=ResidueRing(FlintZZ,8)
V=abelian_group([2,4,8,8])
V.issnf=true
@@ -59,12 +59,12 @@
M=ZpnGModule(V,[A,B,C])
ls=submodules(M,typesub=[2,3])
y=subgroups(V,quotype=[4,8])
-
+
mp1=Hecke.GrpAbFinGenMap(V,V,lift(A))
mp2=Hecke.GrpAbFinGenMap(V,V,lift(B))
mp3=Hecke.GrpAbFinGenMap(V,V,lift(C))
act=[mp1,mp2,mp3]
-
+
i=0
for el in y
if Hecke.isstable(act,el[2])
@@ -72,7 +72,7 @@
end
end
@test i==length(ls)
-
+
ls=submodules(M,typesub=[3])
y=subgroups(V,quotype=[8])
i=0
@@ -82,11 +82,11 @@
end
end
@test i==length(ls)
-
+
end
-
+
@testset "submodules" begin
-
+
R=ResidueRing(FlintZZ,4)
V=abelian_group([2,2,4])
V.issnf=true
@@ -96,7 +96,7 @@
ls=submodules(M)
lsub=subgroups(V)
@test length(collect(ls))==length(collect(lsub))
-
+
end
diff --git a/test/NfAbs/Elem.jl b/test/NfAbs/Elem.jl
index ab39b10748..f8abf31874 100644
--- a/test/NfAbs/Elem.jl
+++ b/test/NfAbs/Elem.jl
@@ -99,7 +99,7 @@ end
@test length(factor(t^10)) == 1
end
- K, a = NumberField(x - 1, "a")
+ K, a = NumberField(x - 1, "a")
Kt, t = K["t"]
f = t^5 -3 * t^4 - 104 * t^3 + 312 * t^2 + 400*t -1200
@test length(factor(f)) == 5
@@ -108,13 +108,13 @@ end
for i in 1:10
n = rand(1:10)
d = rand(1:10)
- K, a = NumberField(n//d * change_base_ring(FlintQQ, x - 1), "a")
+ K, a = NumberField(n//d * change_base_ring(FlintQQ, x - 1), "a")
Kt, t = K["t"]
f = t^5 -3 * t^4 - 104 * t^3 + 312 * t^2 + 400*t -1200
@test length(factor(f)) == 5
@test length(factor(f*t)) == 6
-
- K, a = NumberField(change_base_ring(FlintQQ, x) - n//d, "a")
+
+ K, a = NumberField(change_base_ring(FlintQQ, x) - n//d, "a")
Kt, t = K["t"]
f = t^5 -3 * t^4 - 104 * t^3 + 312 * t^2 + 400*t -1200
@test length(factor(f)) == 5
@@ -123,7 +123,7 @@ end
#Tommys
K, a = number_field(x^2 - x - 4)
- Ky, y = K["y"]
+ Ky, y = K["y"]
f = y^16+(39)*y^14+(449)*y^12+(1794)*y^10+(2830)*y^8+(1794)*y^6+(449)*y^4+(39)*y^2+(1)
@test length(factor(f)) == 2
diff --git a/test/NfOrd/Clgp.jl b/test/NfOrd/Clgp.jl
index 58dbf83411..f5492cdcec 100644
--- a/test/NfOrd/Clgp.jl
+++ b/test/NfOrd/Clgp.jl
@@ -22,7 +22,7 @@ using Random
Cl, mCl = Hecke.class_group(O, redo = true)
U, mU = Hecke.unit_group(O)
@test order(Cl) == h
-
+
Cl, mCl = Hecke.class_group(O, redo = true, do_lll = false)
U, mU = Hecke.unit_group(O)
@test order(Cl) == h
@@ -46,7 +46,7 @@ using Random
Cl, mCl = Hecke.class_group(O, redo = true, do_lll = false)
U, mU = Hecke.unit_group(O)
@test order(Cl) == 1
-
+
O = Order(K, shuffle(basis(O)), isbasis = true)
O.ismaximal = 1
Cl, mCl = Hecke.class_group(O, redo = true, do_lll = false)
@@ -60,7 +60,7 @@ using Random
O = maximal_order(K)
Cl, mCl = Hecke.class_group(O)
@test order(Cl) == 8
-
+
O = Order(K, shuffle(basis(O)), isbasis = true)
O.ismaximal = 1
Cl, mCl = Hecke.class_group(O, redo = true, do_lll = false)
@@ -95,7 +95,7 @@ end
@testset "K = Q" begin
K, a = NumberField(x, "a", cached = false)
O = maximal_order(K)
-
+
Cl, mCl = Hecke.class_group(O, redo = true)
U, mU = Hecke.unit_group(O)
@test order(Cl) == 1
@@ -117,7 +117,7 @@ end
@test U.torsion_units_order == 2
@test contains(AF(0.88137358701),U.tentative_regulator)
@test order(Cl) == 1
-
+
O = Order(K, shuffle(basis(O)), isbasis = true)
O.ismaximal = 1
Cl, mCl = Hecke.class_group(O, redo = true, do_lll = false)
@@ -158,7 +158,7 @@ end
@test U.torsion_units_order == 2
@test contains(AF(2027.9289425180057),U.tentative_regulator)
@test order(Cl) == 5
-
+
O = Order(K, shuffle(basis(O)), isbasis = true)
O.ismaximal = 1
Cl, mCl = Hecke.class_group(O, redo = true, do_lll = false)
@@ -174,7 +174,7 @@ end
@test contains(AF(2027.9289425180057),U.tentative_regulator)
@test order(Cl) == 5
end
-
+
@testset "Cyclotomic Field 13" begin
K, a = cyclotomic_field(13, cached = false)
O = maximal_order(K)
@@ -188,7 +188,7 @@ end
@test order(U) == O
@test U.torsion_units_order == 26
@test order(Cl) == 1
-
+
O = Order(K, shuffle(basis(O)), isbasis = true, cached = false)
O.ismaximal = 1
Cl, mCl = Hecke.class_group(O, redo = true, do_lll = false)
@@ -202,7 +202,7 @@ end
@test U.torsion_units_order == 26
@test order(Cl) == 1
end
-
+
@testset "f = Q[x]/(f), f = x^18 + 18*x^16 + 135*x^14 + 192*x^12 - 2961*x^10 - 17334*x^8+ 20361*x^6 + 315108*x^4 + 514944*x^2 + 123904" begin
K, a = NumberField(x^18 + 18*x^16 + 135*x^14 + 192*x^12 - 2961*x^10 - 17334*x^8+ 20361*x^6 + 315108*x^4 + 514944*x^2 + 123904, "a")
O = maximal_order(K)
@@ -211,7 +211,7 @@ end
UU, mU = Hecke.unit_group(O)
@test order(Cl)== 36
-
+
O = Order(K, shuffle(basis(O)), isbasis = true)
O.ismaximal = 1
@@ -220,7 +220,7 @@ end
@test order(Cl)== 36
end
-
+
@testset "S3 field" begin
Qx, x = PolynomialRing(FlintQQ, "x")
f = x^6-24*x^4+157*x^2-162
diff --git a/test/NfOrd/Elem.jl b/test/NfOrd/Elem.jl
index b2370db28a..6b740649ca 100644
--- a/test/NfOrd/Elem.jl
+++ b/test/NfOrd/Elem.jl
@@ -66,7 +66,7 @@
b = O1(a1//2, false)
@test_throws ErrorException coordinates(b)
-
+
b = O1(a1)
c = @inferred K1(b)
@test c == a1
@@ -132,7 +132,7 @@
c = @inferred divexact(O1(a1^2), O1(a1))
@test c == O1(a1)
-
+
c = @inferred divexact(O1(a1^2), O1(a1), true)
@test c == O1(a1)
@@ -190,7 +190,7 @@
@test_throws ErrorException divexact(b, O1(4*a1))
end
-
+
@testset "Exponentiation" begin
b = O1(a1)
c = @inferred b^3
@@ -238,7 +238,7 @@
b = O1(a1)
c = @inferred tr(b)
@test c == 0
- end
+ end
@testset "Norm" begin
b = O1(a1)
@@ -319,7 +319,7 @@
fac = @inferred factor(b)
@test isunit(unit(fac)) == 1
@test b == unit(fac) * prod(p^e for (p, e) in fac)
-
+
K, a = NumberField(x^3 - 2, "a")
OK = maximal_order(K)
b = rand(OK, -10:10)
diff --git a/test/NfOrd/FracIdl.jl b/test/NfOrd/FracIdl.jl
index 58c6179880..e8477ed95c 100644
--- a/test/NfOrd/FracIdl.jl
+++ b/test/NfOrd/FracIdl.jl
@@ -1,7 +1,7 @@
Qx, x = PolynomialRing(FlintQQ, "x")
K2, a2 = NumberField(x^3 - 2, "a1")
K3, (a3,) = NumberField([x^3 - 2], "a2")
-@testset "Fractional ideals for $K1" for (K1, a1) in [(K2, a2), (K3, a3)]
+@testset "Fractional ideals for $K1" for (K1, a1) in [(K2, a2), (K3, a3)]
O1 = Order(K1, Hecke.FakeFmpqMat(FlintZZ[1 0 0; 0 2 0; 0 0 4], one(FlintZZ)))
i = ideal(O1, O1(2*a1))
diff --git a/test/NfOrd/Ideal.jl b/test/NfOrd/Ideal.jl
index 26b0db3cd9..fe6a361e66 100644
--- a/test/NfOrd/Ideal.jl
+++ b/test/NfOrd/Ideal.jl
@@ -32,7 +32,7 @@
@test I == J && J == K && K == M && M == L && L == I
I2 = @inferred ideal(O2, O2(1 + a2))
-
+
Ib = basis(I2)
II = ideal(O2, Ib)
@test I2 == II
@@ -190,7 +190,7 @@
I = @inferred pradical(O1, 2)
@test I == ideal(O1, FlintZZ[2 0 0; 0 1 0; 0 0 1])
end
-
+
@testset "Prime Decomposition" begin
L = NumberField(x^30-x^29+x^28-x^27+x^26+743*x^25-1363*x^24-3597*x^23-22009*x^22+458737*x^21+2608403*x^20+6374653*x^19-1890565*x^18-112632611*x^17-467834081*x^16-1365580319*x^15-1188283908*x^14+3831279180*x^13+28661663584*x^12+89106335984*x^11+226912479680*x^10+443487548480*x^9+719797891328*x^8+946994403328*x^7+1015828094976*x^6+878645952512*x^5+555353440256*x^4+124983967744*x^3+67515711488*x^2-5234491392*x+400505700352)[1]
OL = maximal_order(L)
@@ -212,7 +212,7 @@
lp = prime_decomposition(OK, 7)
P = lp[1][1]
@test Hecke.frobenius_automorphism(P) != id_hom(K)
- end
+ end
@testset "Minimum" begin
k, = number_field(x^2 - 2);
diff --git a/test/NfOrd/Ideal/Prime.jl b/test/NfOrd/Ideal/Prime.jl
index 0bcd9db32c..2b8030bcf5 100644
--- a/test/NfOrd/Ideal/Prime.jl
+++ b/test/NfOrd/Ideal/Prime.jl
@@ -19,13 +19,13 @@
S = @inferred PrimeIdealsSet(O, fmpz(2), fmpz(100), indexdivisors = false, ramified = false)
@test @inferred length(collect(S)) == 33
S = @inferred PrimeIdealsSet(O, fmpz(2), fmpz(100), indexdivisors = false, ramified = false, degreebound = 1)
- @test @inferred length(collect(S)) == 20
+ @test @inferred length(collect(S)) == 20
K, a = NumberField(x^5 - x + 1, "a")
O = maximal_order(K)
S = @inferred PrimeIdealsSet(O, fmpz(2), fmpz(100))
- @test @inferred length(collect(S)) == 51
+ @test @inferred length(collect(S)) == 51
S = @inferred PrimeIdealsSet(O, fmpz(2), fmpz(100), degreebound = 1)
@test @inferred length(collect(S)) == 18
@@ -45,19 +45,19 @@
P = prime_decomposition(O, 2)[1][1]
S = @inferred PrimeIdealsSet(O, fmpz(2), fmpz(100), coprimeto = P)
- @test @inferred length(collect(S)) == 50
-
+ @test @inferred length(collect(S)) == 50
+
el = Hecke.find_elem_of_valuation_1(P, P^2)
@test valuation(el, P) == 1
-
+
S = @inferred PrimeIdealsSet(O, fmpz(2), fmpz(100), coprimeto = 2)
@test @inferred length(collect(S)) == 49
S = @inferred PrimeIdealsSet(O, fmpz(2), fmpz(100), coprimeto = fmpz(6))
- @test @inferred length(collect(S)) == 48
+ @test @inferred length(collect(S)) == 48
S = @inferred PrimeIdealsSet(O, fmpz(2), fmpz(100), coprimeto = O(30))
- @test @inferred length(collect(S)) == 47
+ @test @inferred length(collect(S)) == 47
@test_throws ErrorException PrimeIdealsSet(O, fmpz(-1), fmpz(1))
@test_throws ErrorException PrimeIdealsSet(O, fmpz(1), -2)
diff --git a/test/NfOrd/LinearAlgebra.jl b/test/NfOrd/LinearAlgebra.jl
index c7a33f855f..5a50ce7b78 100644
--- a/test/NfOrd/LinearAlgebra.jl
+++ b/test/NfOrd/LinearAlgebra.jl
@@ -61,8 +61,8 @@
# Construct random pseudo-matrices over different fields and check if the
# pseudo hermite normal form span the same module
-
- @testset "Q[x]/x^$i - 10)" for i in 2:5
+
+ @testset "Q[x]/x^$i - 10)" for i in 2:5
K, a = NumberField(x^i - 10, "a")
O = maximal_order(K)
#println(" Testing over field $(x^i - 10)")
diff --git a/test/NfOrd/NfOrd.jl b/test/NfOrd/NfOrd.jl
index a709782a1b..03c6774006 100644
--- a/test/NfOrd/NfOrd.jl
+++ b/test/NfOrd/NfOrd.jl
@@ -63,7 +63,7 @@
#@test O7 == O77
#@test !(O7 === O77)
-
+
O8 = Order(K6, [a1])
@test O8 == EquationOrder(K1)
@@ -392,7 +392,7 @@
7222691559*x^80 + 31283828160*x^79 + 525642325551*x^78 +
1906118141542*x^77 + 24142920697938*x^76 + 79592960305643*x^75 +
838232263382574*x^74 + 2605205454422475*x^73 + 24565284675046150*x^72 +
- 70981918657774030*x^71 + 641054201228592185*x^70 +
+ 70981918657774030*x^71 + 641054201228592185*x^70 +
1734903783394973997*x^69 + 15495356543087563190*x^68 +
39815058831494401595*x^67 + 351972255697672269132*x^66 +
866446351271000834294*x^65 + 7284533695483449887998*x^64 +
@@ -450,9 +450,9 @@
132835684951238038126841006782845727573364179*x^7 +
101387674327323669504054265029073554782913385*x^6 -
12293053226599581249247685498068796993543192*x^5 +
- 1490584272544043051357580914905419718739398*x^4 -
+ 1490584272544043051357580914905419718739398*x^4 -
180650443636285117226206582673575773019341*x^3 +
- 21986977593862597199128608447146928784347*x^2 -
+ 21986977593862597199128608447146928784347*x^2 -
2582145971030886336723659422476783673912*x +
373314295307719514165340295548734564161
K, a = NumberField(f)
diff --git a/test/NfOrd/RayClassGroup.jl b/test/NfOrd/RayClassGroup.jl
index 095be804ed..f0d798dd93 100644
--- a/test/NfOrd/RayClassGroup.jl
+++ b/test/NfOrd/RayClassGroup.jl
@@ -11,12 +11,12 @@
end
@testset "quadratic fields" begin
-
+
Qx,x=PolynomialRing(FlintQQ,"x")
K,a=NumberField(x^2+199,"a")
O=maximal_order(K)
C,mC=class_group(O)
-
+
for i=9:13
R1,mR1=ray_class_group(ideal(O,i), n_quo=3)
for r in R1
@@ -26,12 +26,12 @@
q,mq=quo(R,3)
@test Hecke.isisomorphic(R1,q)
end
-
+
K,a=NumberField(x^2-5,"a")
O=maximal_order(K)
C,mC=class_group(O, redo = true)
inf_plc=real_places(K)
-
+
for i=9:13
R1,mR1=ray_class_group(ideal(O,i),inf_plc)
for r in R1
@@ -45,9 +45,9 @@
@test Hecke.isisomorphic(q1,R2)
end
end
-
+
@testset "infinite places" begin
-
+
Qx, x = PolynomialRing(FlintQQ, "x");
K, a = NumberField(x^4-4*x^3-11*x^2+30*x+20, cached = false)
O = maximal_order(K)
@@ -57,9 +57,9 @@
@test el == mr\(mr(el))
end
end
-
+
@testset "stable subgroups" begin
-
+
Qx,x=PolynomialRing(FlintQQ,"x");
f=x^2+1;
K,a=NumberField(f,"a");
@@ -78,7 +78,7 @@
end
end
@test length(x)==i
-
+
x=Hecke.stable_subgroups(r, act, op = quo, quotype = [2,4]);
y=subgroups(r, quotype=[2,4])
i=0
@@ -88,7 +88,7 @@
end
end
@test length(x)==i
-
+
r,mr=ray_class_group(ideal(O,9*19*29), n_quo=9);
act=Hecke.induce_action(mr, auts);
x=Hecke.stable_subgroups(r, act, op = quo, quotype = [9]);
@@ -100,7 +100,7 @@
end
end
@test length(x)==i
-
+
x=Hecke.stable_subgroups(r, act, op = quo, quotype = [3,9]);
y=subgroups(r, quotype=[3,9])
i=0
@@ -111,5 +111,5 @@
end
@test length(x)==i
end
-
+
end
diff --git a/test/NfOrd/ResidueField.jl b/test/NfOrd/ResidueField.jl
index 884101bc08..090364d197 100644
--- a/test/NfOrd/ResidueField.jl
+++ b/test/NfOrd/ResidueField.jl
@@ -15,7 +15,7 @@
@test order(F1) == order(F2)
@test order(F1) == order(F3)
@test order(F1) == order(F)
-
+
for b in B
a1 = mF(b)
a2 = mF1(b)
@@ -27,7 +27,7 @@
@test (mF3\(a4) - b) in P
end
end
-
+
lp = prime_decomposition(OK, 47)
for i = 1:length(lp)
P = lp[i][1]
@@ -38,7 +38,7 @@
@test order(F1) == order(F2)
@test order(F1) == order(F3)
@test order(F1) == order(F)
-
+
for b in B
a1 = mF(b)
a2 = mF1(b)
diff --git a/test/NumField/Elem.jl b/test/NumField/Elem.jl
index 9d813a8a9e..352400eba2 100644
--- a/test/NumField/Elem.jl
+++ b/test/NumField/Elem.jl
@@ -152,7 +152,7 @@
f = x^2 + 12x - 92
K, a = NumberField(f, "a")
Ky, y = K["y"]
- L, b = NumberField(y^2 + y + 1, "b")
+ L, b = NumberField(y^2 + y + 1, "b")
Lt, t = PolynomialRing(L)
L1, gL1 = number_field([t^3-2])
L1rel, mL1rel = relative_simple_extension(L1, K)
@@ -215,7 +215,7 @@ end
@test isone(mA(A[1])^6)
@test !isone(mA(A[1])^3)
@test !isone(mA(A[1])^2)
-
+
Kt, t = PolynomialRing(K, cached = false)
Ls, gLs = number_field(t^2+1)
G, mG = torsion_unit_group(Ls)
@@ -227,7 +227,7 @@ end
@test isone(g^12)
@test !isone(g^4)
@test !isone(g^3)
-
+
Lns, gLns = number_field([t^2+1, t^2+2])
G, mG = torsion_unit_group(Lns)
@test ngens(G) == 1
diff --git a/test/NumField/Hilbert.jl b/test/NumField/Hilbert.jl
index 4479ed92f2..d02c01a1d6 100644
--- a/test/NumField/Hilbert.jl
+++ b/test/NumField/Hilbert.jl
@@ -31,7 +31,7 @@
for P in prime_ideals_up_to(OK, 200)
@test hilbert_symbol(b, -3, P) == 1
end
-
+
# Test where Magma div(x, y) differs from julia div(x, y) (internally)
K, a = CyclotomicRealSubfield(8, "a") # x^2 - 2
z = 9278908160780559301//4*a+6561375391013480455//2
diff --git a/test/NumField/NfAbs/MPolyAbsFact.jl b/test/NumField/NfAbs/MPolyAbsFact.jl
index 138fcca4ca..01ed7e7d33 100644
--- a/test/NumField/NfAbs/MPolyAbsFact.jl
+++ b/test/NumField/NfAbs/MPolyAbsFact.jl
@@ -3,7 +3,7 @@
f = Hecke.MPolyFact.example(wildanger_field(3, 13)[1], 3, 5)
@test length(factor_absolute(f)) >= 2
- f = Hecke.MPolyFact.example(cyclotomic_field(4)[1], 3, 5)
+ f = Hecke.MPolyFact.example(cyclotomic_field(4)[1], 3, 5)
@test length(factor_absolute(f)) >= 2
@test length(factor(f, ComplexField(40)).fac) >= 2
diff --git a/test/QuadForm/Genus.jl b/test/QuadForm/Genus.jl
index f17a471953..22d8169ea9 100644
--- a/test/QuadForm/Genus.jl
+++ b/test/QuadForm/Genus.jl
@@ -13,7 +13,7 @@
GG = G[1]
u = @inferred uniformizer(GG)
@assert parent(u) == K
-
+
p = prime_decomposition(maximal_order(K), 17)[1][1]
G = @inferred local_genera_hermitian(L, p, 5, 5, 5)
@test length(G) == 7
@@ -21,7 +21,7 @@
@test rank(G[i]) == 5
@test (@inferred representative(G[i])) in G[i]
end
-
+
K, a = CyclotomicRealSubfield(8, "a")
Kt, t = K["t"]
L, b = number_field(t^2 - gen(K) * t + 1)
@@ -62,7 +62,7 @@
end
# Representatives
-
+
Qx, x = FlintQQ["x"]
K, a = NumberField(x - 1, "a")
Kt, t = K["t"]
@@ -108,7 +108,7 @@
@test length(Hecke.local_genera_quadratic(K, p, rank = 2, det_val = 1)) == 8
# Addition of genera
-
+
K, a = CyclotomicRealSubfield(8, "a")
Kt, t = PolynomialRing(K, "t")
L, b = number_field(t^2 - gen(K) * t + 1)
diff --git a/test/QuadForm/Lattices.jl b/test/QuadForm/Lattices.jl
index 924f43518a..5d9b22af75 100644
--- a/test/QuadForm/Lattices.jl
+++ b/test/QuadForm/Lattices.jl
@@ -56,7 +56,7 @@
V = hermitian_space(L, L(a) * identity_matrix(L, 3))
M = @inferred Hecke.maximal_integral_lattice(V)
@test Hecke.genus(M, p) == genus(HermLat, L, p, [(-2, 2, 1, 0), (0, 1, -1, 0)])
-
+
V = hermitian_space(L, L(10) * identity_matrix(L, 3))
M = @inferred Hecke.maximal_integral_lattice(V)
@test Hecke.genus(M, p) == genus(HermLat, L, p, [(-2, 2, 1, 0), (0, 1, 1, 0)])
diff --git a/test/QuadForm/Quad/GenusRep.jl b/test/QuadForm/Quad/GenusRep.jl
index b0646f9074..0e9d070a38 100644
--- a/test/QuadForm/Quad/GenusRep.jl
+++ b/test/QuadForm/Quad/GenusRep.jl
@@ -71,7 +71,7 @@
# Rank 2 case
# This is the Zlattice with basis [1 2; 3 4]
-
+
Qx, x = PolynomialRing(FlintQQ, "x", cached = false)
f = x - 1;
K, a = number_field(f)
diff --git a/test/QuadForm/Quad/NormalForm.jl b/test/QuadForm/Quad/NormalForm.jl
index 093c5384b3..43de81f0d4 100644
--- a/test/QuadForm/Quad/NormalForm.jl
+++ b/test/QuadForm/Quad/NormalForm.jl
@@ -22,25 +22,25 @@ end
for R in [ZZ, GF(3)]
W = R[1;]
V = R[0 1; 1 0]
-
+
L = diagonal_matrix([W, V])
@test (@inferred diagonal_matrix(Hecke.collect_small_blocks(L))) == L
-
+
L = diagonal_matrix([W, W])
@test diagonal_matrix(Hecke.collect_small_blocks(L)) == L
-
+
L = diagonal_matrix([W, V, W])
@test diagonal_matrix(Hecke.collect_small_blocks(L)) == L
-
+
L = diagonal_matrix([W])
@test diagonal_matrix(Hecke.collect_small_blocks(L)) == L
-
+
L = diagonal_matrix([V])
@test diagonal_matrix(Hecke.collect_small_blocks(L)) == L
-
+
L = diagonal_matrix([V, W, W, V, V, W, W])
@test diagonal_matrix(Hecke.collect_small_blocks(L)) == L
-
+
L = zero_matrix(ZZ, 0, 0)
@test Hecke.collect_small_blocks(L) == typeof(L)[]
end
diff --git a/test/QuadForm/Quad/ZGenus.jl b/test/QuadForm/Quad/ZGenus.jl
index 85daee7278..93b97febbb 100644
--- a/test/QuadForm/Quad/ZGenus.jl
+++ b/test/QuadForm/Quad/ZGenus.jl
@@ -247,7 +247,7 @@
G2 = genus(L2)
@test G==G2
end
-
+
for d in 1:(long_test ? 400 : 10)
for sig in [(2,0), (1,1), (0,3),(1,2), (4,0), (2,2)]
for G in genera(sig, d)
diff --git a/test/QuadForm/Torsion.jl b/test/QuadForm/Torsion.jl
index 182dfb645c..924556f7d3 100644
--- a/test/QuadForm/Torsion.jl
+++ b/test/QuadForm/Torsion.jl
@@ -74,7 +74,7 @@
@test Hecke.gram_matrix_quadratic(Hecke.rescale(t, 3)) == matrix(QQ, 2, 2, [1,0,0,1//3])
#The next form is defined modulo `4`
@test Hecke.gram_matrix_quadratic(Hecke.rescale(t, 4)) == matrix(QQ, 2, 2, [4//3,0,0,4//9])
-
+
#test for normal form
L1 = Zlattice(gram=matrix(ZZ, [[-2,0,0],[0,1,0],[0,0,4]]))
@@ -98,13 +98,13 @@
L3 = Zlattice(gram=matrix(ZZ, [[2,0,0,-1],[0,2,0,-1],[0,0,2,-1],[-1,-1,-1,2]]))
T=torsion_quadratic_module((1//6)*dual(L3), L3)
n3 = normal_form(T)[1]
- g3 = QQ[1//6 1//12 0 0 0 0 0 0;
- 1//12 1//6 0 0 0 0 0 0;
- 0 0 1//12 1//24 0 0 0 0;
- 0 0 1//24 1//12 0 0 0 0;
- 0 0 0 0 1//9 0 0 0;
- 0 0 0 0 0 1//9 0 0;
- 0 0 0 0 0 0 1//9 0;
+ g3 = QQ[1//6 1//12 0 0 0 0 0 0;
+ 1//12 1//6 0 0 0 0 0 0;
+ 0 0 1//12 1//24 0 0 0 0;
+ 0 0 1//24 1//12 0 0 0 0;
+ 0 0 0 0 1//9 0 0 0;
+ 0 0 0 0 0 1//9 0 0;
+ 0 0 0 0 0 0 1//9 0;
0 0 0 0 0 0 0 1//9]
@test Hecke.gram_matrix_quadratic(n3) == g3
T2 = torsion_quadratic_module((1//6)*dual(L3), L3, modulus=fmpq(1//36))
@@ -121,7 +121,7 @@
#test for brown invariant
L1 = Zlattice(gram=matrix(ZZ, [[2,-1,0,0],[-1,2,-1,-1],[0,-1,2,0],[0,-1,0,2]]))
- T1 = discriminant_group(L1)
+ T1 = discriminant_group(L1)
@test Hecke.brown_invariant(T1) == 4
L2 = Zlattice(matrix(ZZ, 2,2,[4,2,2,4]))
T2 = Hecke.discriminant_group(L2)
@@ -143,7 +143,7 @@
D = discriminant_group(L)
@test_throws ErrorException isgenus(D, (4,0))
L1 = Zlattice(gram=matrix(ZZ, [[2, -1, 0, 0, 0, 0],[-1, 2, -1, -1, 0, 0],[0, -1, 2, 0, 0, 0],[0, -1, 0, 2, 0, 0],[0, 0, 0, 0, 6, 3],[0, 0, 0, 0, 3, 6]]))
- T1 = discriminant_group(L1)
+ T1 = discriminant_group(L1)
@test isgenus(T1, (6,0)) == true
@test isgenus(T1, (4,2)) == false
@test isgenus(T1, (16,2)) == true
diff --git a/test/RCF/conductor_sieve.jl b/test/RCF/conductor_sieve.jl
index 2992217c7f..be9a34f38d 100644
--- a/test/RCF/conductor_sieve.jl
+++ b/test/RCF/conductor_sieve.jl
@@ -1,7 +1,7 @@
@testset "RCF" begin
@testset "abelian extensions && related examples" begin
-
+
Qx, x = PolynomialRing(FlintQQ, "x")
K, a = NumberField(x - 1, "a")
l = Hecke.abelian_normal_extensions(K, Int[2,2], fmpz(10)^4)
@@ -9,7 +9,7 @@
l1 = collect(Hecke.C22_extensions(10^4))
@test length(l1)==47
@test length(abelian_fields(FlintQQ, [3], fmpz(10)^3)) == 5
-
+
K, a = number_field(x^2+1, "a")
auts = small_generating_set(automorphisms(K, copy = false))
l = Hecke.abelian_normal_extensions(K, Int[2], fmpz(10)^5)
diff --git a/test/RCF/rcf.jl b/test/RCF/rcf.jl
index 3ead4c4ef3..d586e41608 100644
--- a/test/RCF/rcf.jl
+++ b/test/RCF/rcf.jl
@@ -42,13 +42,13 @@
L2 = number_field(H, using_stark_units = true, redo = true)
@test isisomorphic(Hecke.simplified_absolute_field(L1)[1], Hecke.simplified_absolute_field(L2)[1])[1]
@test length(closure(Hecke.absolute_automorphism_group(H), *)) == 10
-
+
r, mr = Hecke.ray_class_groupQQ(Z, 32, true, 8);
q, mq = quo(r, [r[1]])
C = ray_class_field(mr, mq)
KC = number_field(C)
auts = Hecke.rel_auto(C)
- @test length(closure(auts, *)) == 8
+ @test length(closure(auts, *)) == 8
k, a = wildanger_field(3, 13)
zk = maximal_order(k)
@@ -56,7 +56,7 @@
@test degree(r0) == 9
r1 = ray_class_field(4*zk, n_quo = 2)
r2 = ray_class_field(5*zk, n_quo = 2)
- @test isone(conductor(intersect(r1, r2))[1])
+ @test isone(conductor(intersect(r1, r2))[1])
@test conductor(r1 * r2)[1] == 20*zk
@test Hecke.issubfield(r1, r1*r2)
@test !Hecke.issubfield(r0, r1*r2)
@@ -88,7 +88,7 @@
K, _ = compositum(k, wildanger_field(3, 13)[1])
A = maximal_abelian_subfield(ClassField, K)
@test degree(A) == 2
- @test degree(intersect(A, cyclotomic_field(ClassField, 10))) == 1
+ @test degree(intersect(A, cyclotomic_field(ClassField, 10))) == 1
end
@testset "Some abelian extensions" begin
diff --git a/test/Sparse/Matrix.jl b/test/Sparse/Matrix.jl
index 5e7d28dd12..da6e4c2574 100644
--- a/test/Sparse/Matrix.jl
+++ b/test/Sparse/Matrix.jl
@@ -5,7 +5,7 @@ using SparseArrays
M = SMatSpace(R, 3, 3)
@test R == @inferred base_ring(M)
-
+
A = identity_matrix(FlintZZ, 3)
Asparse = sparse_matrix(A)
@@ -145,7 +145,7 @@ using SparseArrays
v = fmpz[1 1 1; 1 2 3; 0 0 4; 0 0 0]
w = @inferred mul(D, view(v, 2:4, :))
@test w == fmpz[1 2 23; 0 0 0; 0 0 4]
-
+
v = matrix(FlintZZ, fmpz[1 2 3; 0 0 4; 0 0 0])
w = @inferred mul(D, v)
@test w == matrix(FlintZZ, fmpz[1 2 23; 0 0 0; 0 0 4])