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fix: change idel to idele and improve printing (#3859)
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@thofma
thofma authored Jun 18, 2024
1 parent a1cce05 commit 268c5f1
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20 changes: 10 additions & 10 deletions examples/Idel.jl → examples/Idele.jl
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Original file line number Diff line number Diff line change
@@ -1,8 +1,8 @@
module Idel
module Idele

using Oscar

mutable struct IdelParent
mutable struct IdeleParent
k::AbsSimpleNumField
mG::Map # AutGrp -> Automorohisms
S::Vector{AbsNumFieldOrderIdeal} # for each prime number ONE ideal above
Expand All @@ -20,35 +20,35 @@ mutable struct IdelParent
mU::Map #S-unit group map
M::FinGenAbGroup # the big module

function IdelParent()
function IdeleParent()
return new()
end
end

mutable struct Idel
parent::IdelParent
mutable struct Idele
parent::IdeleParent
m::FinGenAbGroupElem #in parent.M
end

function support(a::Idel)
function support(a::Idele)
#the full galois orbit of parent.S
end

function getindex(a::Idel, P::AbsNumFieldOrderIdeal)
function getindex(a::Idele, P::AbsNumFieldOrderIdeal)
#element at place P as an element in the completion
#needs to find the "correct" P in parent.S, the (index) of the coset
#and return the component of the induced module
end

function getindex(a::Idel, p) #real embedding
function getindex(a::Idele, p) #real embedding
# the unit representing this: find the correct component...
end

function getindex(a::Idel, p) #complex embedding
function getindex(a::Idele, p) #complex embedding
# the unit representing this + a vector with the lambda exponents
end

function disc_exp(a::Idel)
function disc_exp(a::Idele)
# a dict mapping primes/places to s.th. in the number field?
end

Expand Down
89 changes: 48 additions & 41 deletions experimental/GModule/src/GaloisCohomology.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -8,7 +8,7 @@ import Base: parent
import Oscar: direct_sum
import Oscar: pretty, Lowercase, Indent, Dedent, terse

export is_coboundary, idel_class_gmodule, relative_brauer_group
export is_coboundary, idele_class_gmodule, relative_brauer_group
export local_invariants, global_fundamental_class, shrink
export local_index, units_mod_ideal

Expand Down Expand Up @@ -610,9 +610,9 @@ Sort:
# - ???
# - a different type containing all this drivel? (probably)
# YES - need to have maps to and from local stuff
# use Klueners/ Acciaro to map arbitrary local into idel
# use Klueners/ Acciaro to map arbitrary local into idele
# use ... to project to ray class
# - a magic(?) function to get idel-approximations in and out?
# - a magic(?) function to get idele approximations in and out?

"""
M has to be a torsion free Z module with a C_2 action by sigma.
Expand All @@ -627,7 +627,7 @@ Two arrays are returned:
Follows Debeerst rather closely...
(Helper for the idel-class stuff)
(Helper for the idele class stuff)
"""
function debeerst(M::FinGenAbGroup, sigma::Map{FinGenAbGroup, FinGenAbGroup})
@assert domain(sigma) == codomain(sigma) == M
Expand Down Expand Up @@ -756,13 +756,13 @@ end


"""
IdelParent
IdeleParent
A container structure for computations around idel-class cohomology.
A container structure for computations around idele class cohomology.
Describes a gmodule that is cohomologically equivalent to the
idel-class group, following Chinberg/ Debeerst/ Aslam.
idele class group, following Chinberg/Debeerst/Aslam.
"""
mutable struct IdelParent
mutable struct IdeleParent
k::AbsSimpleNumField
mG::Map # AutGrp -> Automorphisms
S::Vector{AbsNumFieldOrderIdeal} # for each prime number ONE ideal above
Expand All @@ -785,29 +785,29 @@ mutable struct IdelParent

data

function IdelParent()
function IdeleParent()
return new()
end
end

"""
idel_class_gmodule(k::AbsSimpleNumField, s::Vector{Int} = Int[])
idele_class_gmodule(k::AbsSimpleNumField, s::Vector{Int} = Int[])
Following Debeerst:
Algorithms for Tamagawa Number Conjectures. Dissertation, University of Kassel, June 2011.
or Ali,
Find a gmodule C s.th. C is cohomology-equivalent to the cohomology
of the idel-class group. The primes in `s` will always be used.
of the idele class group. The primes in `s` will always be used.
"""
function idel_class_gmodule(k::AbsSimpleNumField, s::Vector{Int} = Int[]; redo::Bool=false)
function idele_class_gmodule(k::AbsSimpleNumField, s::Vector{Int} = Int[]; redo::Bool=false)
@vprint :GaloisCohomology 2 "Ideal class group cohomology for $k\n"
I = get_attribute(k, :IdelClassGmodule)
I = get_attribute(k, :IdeleClassGmodule)
if !redo && I !== nothing
return I
end

I = IdelParent()
I = IdeleParent()
I.k = k
G, mG = automorphism_group(PermGroup, k)
I.mG = mG
Expand Down Expand Up @@ -1012,17 +1012,17 @@ function idel_class_gmodule(k::AbsSimpleNumField, s::Vector{Int} = Int[]; redo::
@hassert :GaloisCohomology 1 is_consistent(q)
I.mq = mq
I.data = (q, F[1])
set_attribute!(k, :IdelClassGmodule=>I)
set_attribute!(k, :IdeleClassGmodule=>I)
return I
end

"""
returns a `Dict` containing the prime ideals where the idel
returns a `Dict` containing the prime ideals where the idele
represented by `a` as an element of `I` can be non-trivial,
ie. at the places in `I`.
The values are elements in the corresponding completion.
"""
function idel_finite(I::IdelParent, a::FinGenAbGroupElem)
function idele_finite(I::IdeleParent, a::FinGenAbGroupElem)
a = preimage(I.mq, a)
#a lives in a direct product
# 1st the units - induced, thus a direct product
Expand Down Expand Up @@ -1055,10 +1055,10 @@ function _local_norm(m0::AbsSimpleNumFieldOrderIdeal, a::AbsNumFieldOrderElem, p
end


#maybe we need Idel's as independent objects?
#maybe we need Idele's as independent objects?
#realizes C -> Cl (or the coprime version into a ray class group:
#for the idel `a` in `I` find an "equivalent" ideal.
function Oscar.ideal(I::IdelParent, a::FinGenAbGroupElem; coprime::Union{AbsSimpleNumFieldOrderIdeal, Nothing})
#for the idele `a` in `I` find an "equivalent" ideal.
function Oscar.ideal(I::IdeleParent, a::FinGenAbGroupElem; coprime::Union{AbsSimpleNumFieldOrderIdeal, Nothing})
a = preimage(I.mq, a)
zk = maximal_order(I.k)
o_zk = zk
Expand Down Expand Up @@ -1092,7 +1092,7 @@ function Oscar.galois_group(A::ClassField)
end

"""
galois_group(A::ClassField, ::QQField; idel_parent::IdelParent = idel_class_gmodule(base_field(A)))
galois_group(A::ClassField, ::QQField; idele_parent::IdeleParent = idele_class_gmodule(base_field(A)))
Determines the Galois group (over `QQ`) of the extension parametrized by `A`.
`A` needs to be normal over `QQ`.
Expand All @@ -1107,9 +1107,9 @@ julia> a = ray_class_field(8*3*maximal_order(k), n_quo = 2);
julia> a = filter(is_normal, subfields(a, degree = 2));
julia> I = idel_class_gmodule(k);
julia> I = idele_class_gmodule(k);
julia> b = [galois_group(x, QQ, idel_parent = I) for x = a];
julia> b = [galois_group(x, QQ, idele_parent = I) for x = a];
julia> [describe(x[1]) for x = b]
3-element Vector{String}:
Expand All @@ -1119,7 +1119,7 @@ julia> [describe(x[1]) for x = b]
```
"""
function Oscar.galois_group(A::ClassField, ::QQField; idel_parent::Union{IdelParent,Nothing} = nothing)
function Oscar.galois_group(A::ClassField, ::QQField; idele_parent::Union{IdeleParent,Nothing} = nothing)

m0, m_inf = defining_modulus(A)
@assert length(m_inf) == 0
Expand All @@ -1134,20 +1134,20 @@ function Oscar.galois_group(A::ClassField, ::QQField; idel_parent::Union{IdelPar
s, ms = split_extension(gmodule(A))
return permutation_group(s), ms
end
if idel_parent === nothing
idel_parent = idel_class_gmodule(base_field(A))
if idele_parent === nothing
idele_parent = idele_class_gmodule(base_field(A))
end

qI = cohomology_group(idel_parent, 2)
qI = cohomology_group(idele_parent, 2)
q, mq = snf(qI[1])
a = qI[2](image(mq, q[1])) # should be a 2-cycle in q
@assert Oscar.GrpCoh.istwo_cocycle(a)
gA = gmodule(A, idel_parent.mG)
gA = gmodule(A, idele_parent.mG)
qA = cohomology_group(gA, 2)
n = degree(Hecke.nf(zk))
aa = map_entries(a, parent = gA) do x
x = parent(x)(Hecke.mod_sym(x.coeff, gcd(n, degree(A))))
J = ideal(idel_parent, x, coprime = m0)
J = ideal(idele_parent, x, coprime = m0)
mQ(preimage(mR, numerator(J)) - preimage(mR, denominator(J)*zk))
end
@assert Oscar.GrpCoh.istwo_cocycle(aa)
Expand All @@ -1158,7 +1158,7 @@ function Oscar.components(A::FinGenAbGroup)
return get_attribute(A, :direct_product)
end

function Oscar.completion(I::IdelParent, P::AbsNumFieldOrderIdeal)
function Oscar.completion(I::IdeleParent, P::AbsNumFieldOrderIdeal)
s = [minimum(x) for x = I.S]
p = findfirst(isequal(minimum(P)), s)
@assert p !== nothing
Expand Down Expand Up @@ -1843,7 +1843,7 @@ function Hecke.StructureConstantAlgebra(CC::GrpCoh.CoChain{2, PermGroupElem, Grp
return Hecke.StructureConstantAlgebra(base_field(k), M)
end

function serre(A::IdelParent, P::AbsNumFieldOrderIdeal)
function serre(A::IdeleParent, P::AbsNumFieldOrderIdeal)
C = A.data[1]
Kp, mKp, mGp, mUp, pro, inj = completion(A, P)
mp = decomposition_group(A.k, mKp, A.mG, mGp)
Expand All @@ -1860,7 +1860,7 @@ function serre(A::IdelParent, P::AbsNumFieldOrderIdeal)
return c
end

function serre(A::IdelParent, P::Union{Integer, ZZRingElem})
function serre(A::IdeleParent, P::Union{Integer, ZZRingElem})
C = A.data[1]
t = findfirst(isequal(ZZ(P)), [minimum(x) for x = A.S])
Inj = canonical_injection(A.M, t+1)
Expand All @@ -1885,10 +1885,10 @@ function serre(A::IdelParent, P::Union{Integer, ZZRingElem})
#g is the (non-canonical) generator of H^2 of the induced module
hg = map_entries(Inj*A.mq, g, parent = C)
#hg is the (non-canonical) generator of H^2 of the induced module
#in the global idel-class cohomology
#in the global idele class cohomology
#
#Z[G_p] K_p <-> Ind_G_p^G K_p = Z[G] prod K_p over all conjugate primes
# -> Z[G] C the idel-class group
# -> Z[G] C the idele class group
#the image should be the restriction I think
gg = map_entries(pro, g, parent = tt.C)
#gg is the non-canomical generator in Z[G_p] K_p
Expand All @@ -1906,16 +1906,16 @@ function serre(A::IdelParent, P::Union{Integer, ZZRingElem})
end

"""
global_fundamental_class(A::IdelParent)
global_fundamental_class(A::IdeleParent)
Tries to find the canonical generator of `H^2(C)` the 2nd
cohomology group of the idel-class group.
cohomology group of the idele class group.
Currently only works if this can be inferred from the local data in
the field, ie. if the `lcm` of the degrees of the completions is the
full field degree.
"""
function global_fundamental_class(A::IdelParent)
function global_fundamental_class(A::IdeleParent)
C = A.data[1]
d = lcm([ramification_index(P) * inertia_degree(P) for P = A.S])
G = C.G
Expand Down Expand Up @@ -1963,7 +1963,7 @@ function global_fundamental_class(A::IdelParent)
return p[1]
end

function Oscar.cohomology_group(A::IdelParent, i::Int)
function Oscar.cohomology_group(A::IdeleParent, i::Int)
return Oscar.cohomology_group(A.data[1], i)
end

Expand Down Expand Up @@ -2024,12 +2024,19 @@ end

#deliberately at the end as it messes up the syntax-highlighting for me
#confusion about " and ()...
function Base.show(io::IO, I::IdelParent)
print(io, "Idel-group for $(I.k) using $(sort(collect(Set(minimum(x) for x = I.S)))) as places")
function Base.show(io::IO, I::IdeleParent)
io = pretty(io)
#print(io, "Relative Brauer group for ", Lowercase(), B.K, " over ", Lowercase(), B.k)
println(io, "Idele group of")
print(io, Indent())
println(io, Lowercase(), I.k)
plcs = sort(collect(Set(minimum(x) for x = I.S)))
print(io, "using prime ideals over [", join(plcs, ", "), "] as places")
print(io, Dedent())
end

end # module GrpCoh

using .GaloisCohomology_Mod
export is_coboundary, idel_class_gmodule, relative_brauer_group, units_mod_ideal
export is_coboundary, idele_class_gmodule, relative_brauer_group, units_mod_ideal

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