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Macro for entering permutations in cycle notation #1307

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135 changes: 135 additions & 0 deletions src/Groups/perm.jl
Original file line number Diff line number Diff line change
Expand Up @@ -387,3 +387,138 @@ function cycle_structure(g::PermGroupElem)
# TODO: use SortedDict from DataStructures.jl ?
return Pair{Int,Int}[ i+1 => c[i] for i in 1:length(c) if GAP.Globals.ISB_LIST(c, i) ]
end


# The following code implements a new way to input permutations in Julia. For example
# it is possible to create a permutation as follow
# pi = Oscar.Permutations.@perm (1,2,3)(4,5)(6,7,8)
# > (1,2,3)(4,5)(6,7,8)
# For this we use macros to modify the syntax tree of (1,2,3)(4,5)(6,7,8) such that
# Julia can deal with the expression.


################################################################################
#
# perm
#
@doc Markdown.doc"""
@perm(ex)
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Macro to input a permutation as
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pi = @perm (1,2,3)(4,5)(6,7,8) to obtain
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(1,2,3)(4,5)(6,7,8)
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# Examples (jldoctest)
```
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julia> @perm (1,2,3)(4,5)(6,7,8)
(1,2,3)(4,5)(6,7,8)
```
"""
macro perm(ex)
res = []

while (ex).head == :call
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pushfirst!(res, Expr(:vect, (ex).args[2:end]...))
ex = (ex).args[1]
end

if (ex).head != :tuple
error("Input is not a permutation.")
end

pushfirst!(res, Expr(:vect,(ex).args...))

return esc(:(Oscar.cperm($(res...))))
end


################################################################################
#
# perm(n,gens)
#
@doc Markdown.doc"""
@perm(n,gens)
Macro to input a list of permutation which are generated as elements of
the symmetric_group(n)
# Examples (jldoctest)
```
julia> gens = Oscar.Permutations.@perm 14 [
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(1,10)
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(2,11)
(3,12)
(4,13)
(5,14)
(6,8)
(7,9)
(1,2,3,4,5,6,7)(8,9,10,11,12,13,14)
(1,2)(10,11)
]
9-element Vector{PermGroupElem}:
(1,10)
(2,11)
(3,12)
(4,13)
(5,14)
(6,8)
(7,9)
(1,2,3,4,5,6,7)(8,9,10,11,12,13,14)
(1,2)(10,11)
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julia> gens[1].parent
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Sym( [ 1 .. 14 ] )
```
"""
macro perm(n,gens)

s = symmetric_group(n)
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ores = Vector{Expr}(undef,length(gens.args))
i = 1
for ex in gens.args
res = []

while (ex).head == :call
pushfirst!(res, Expr(:vect, (ex).args[2:end]...))
ex = (ex).args[1]
end

if (ex).head != :tuple
error("Input is not a permutation.")
end

pushfirst!(res, Expr(:vect,(ex).args...))

ores[i] = esc(:(Oscar.cperm(symmetric_group($n),$(res...))))
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This calls symmetric_group again and again, which isn't great, as we create a new group object each time. This could be improved by using let block; but I don't want to complicate things even further, so I suggest we first iron out everything else and get this merged, then we can worry about fine tuning.

Just for the record, here is what I'd do: I'd only collect the res values here:

Suggested change
ores[i] = esc(:(Oscar.cperm(symmetric_group($n),$(res...))))
ores[i] = esc(:( [$(res...)] ))

Then, the final return of this macro could look something like this:

return quote
   let g = symmetric_group($n)
       [ cperm(g, pi) for pi in [$(ores...)] ]
   end
end

Note: normally we'd have to worry that g and pi could clash with symbols defined by the programmer in the surrounding code, and referenced in the permutation expression. This is where the esc function comes into play: we applied it to the expressions we got from the user, but not to the outer expression above. This leads to the Julia macro hygiene functionality kicking in, which determines that g and pi (unlike symmetric_group and cperm) are not known variables, and replaces them by special generated names. You can check the effect of this via macroexpand:

julia> g = 7  # introduce a variable g and use it in the macro expression:
7

julia> macroexpand(Main, :( Oscar.@perm 14 [
                     (g,9)
                     (1,2)(10,11)
                    ]))
quote
    let var"#332#g" = Oscar.symmetric_group(14)
        [Oscar.cperm(var"#332#g", var"#333#pi"...) for var"#333#pi" = [[[g, 9]], [[1, 2], [10, 11]]]]
    end
end

i = i + 1
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You could just let ores start out as an empty vector and then do push!(ores, ...), then you don't need i.

end

return Expr(:vect,ores...)
end


################################################################################
#
# permgroup(n::Int64,gens::Vector{PermGroupElem})
#
@doc Markdown.doc"""
permgroup(n::Int64,gens::Vector{PermGroupElem})
Generates a PermGroup with generators gens as a subgroup of symmetric_group(n)
# Examples (jldoctest)
```
julia> gens = Oscar.Permutations.@perm 14 [
(1,10)
(2,11)
(3,12)
(4,13)
(5,14)
(6,8)
(7,9)
(1,2,3,4,5,6,7)(8,9,10,11,12,13,14)
(1,2)(10,11)
];
julia> G = Oscar.Permutations.permgroup(14,gens)
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<permutation group with 9 generators>
```
"""
function permgroup(n::Int64,gens::Vector{PermGroupElem})

return PermGroup(GAP.Globals.Subgroup(GAP.Globals.SymmetricGroup(GAP.Obj(n)),GAP.Obj([GAP.Obj(x) for x in gens ])))
end

export @perm,permgroup,size
44 changes: 44 additions & 0 deletions test/Groups/Permutations.jl
Original file line number Diff line number Diff line change
@@ -0,0 +1,44 @@
@testset "Examples.Permutations" begin
p = @perm (1,2)(3,4)(5,6)
@test p == cperm([1,2],[3,4],[5,6])
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p = @perm (1,2)(3,4,5)(7,8,9)
@test p == cperm([1,2],[3,4,5],[7,8,9])

a=1;b=2;f=x->3*x + 2;
p = @perm (a,f(a),b)(a+1,b*2)
@test p == cperm([1,5,4,2])

@test_throws ErrorException @perm (-1, 1)
@test_throws LoadError @perm "bla"
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@test_throws LoadError @perm 1 + 1

gens = @perm 14 [
(1,10)
(2,11)
(3,12)
(4,13)
(5,14)
(6,8)
(7,9)
(1,2,3,4,5,6,7)(8,9,10,11,12,13,14)
(1,2)(10,11)
]
p = Vector{PermGroupElem}(undef,9)
p[1] = cperm(symmetric_group(14),[1,10])
p[2] = cperm(symmetric_group(14),[2,11])
p[3] = cperm(symmetric_group(14),[3,12])
p[4] = cperm(symmetric_group(14),[4,13])
p[5] = cperm(symmetric_group(14),[5,14])
p[6] = cperm(symmetric_group(14),[6,8])
p[7] = cperm(symmetric_group(14),[7,9])
p[8] = cperm(symmetric_group(14),[1,2,3,4,5,6,7],[8,9,10,11,12,13,14])
p[9] = cperm(symmetric_group(14),[1,2],[10,11])
@test gens == p

@test_throws ArgumentError @perm 10 [(1,11)]

G = permgroup(14,gens)
@test order(G) == 645120
end


1 change: 1 addition & 0 deletions test/runtests.jl
Original file line number Diff line number Diff line change
Expand Up @@ -31,6 +31,7 @@ include("Groups/runtests.jl")
include("Rings/NumberField.jl")
include("Rings/FunctionField-test.jl")
include("Rings/AbelianClosure.jl")
include("Groups/Permutations.jl")
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include("Rings/MPolyAnyMap/MPolyRing.jl")
include("Rings/MPolyAnyMap/MPolyQuo.jl")
Expand Down