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fix ccmatrix tests
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@kalmarek
kalmarek committed Jul 28, 2020
1 parent 3ac225a commit 1cec08b
Showing 1 changed file with 112 additions and 50 deletions.
162 changes: 112 additions & 50 deletions test/ccmatrix.jl
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Original file line number Diff line number Diff line change
@@ -1,4 +1,8 @@
function _ccmatrix(C)
using Pkg
Pkg.add(PackageSpec(url="https://github.com/kalmarek/PermutationGroups.jl"))
using PermutationGroups

function generic_tests_ccmatrix(C)
r = length(C)
for i = 1:r
ccm = SymbolicWedderburn.CCMatrix(C, i)
Expand All @@ -10,60 +14,118 @@ function _ccmatrix(C)
end

@testset "ConjClassMatrix" begin
@testset "example" begin
# S_4
@testset "example: Symmetric group (4)" begin
G = SymbolicWedderburn.AbstractAlgebra.SymmetricGroup(4)
C = SymbolicWedderburn.PermutationGroups.conjugacy_classes(G)
_ccmatrix(C)
@test Matrix(SymbolicWedderburn.CCMatrix(C, 2)) == [0 1 0 0 0;
6 0 3 0 2;
0 4 0 4 0;
0 0 3 0 4;
0 1 0 2 0]
@test Matrix(SymbolicWedderburn.CCMatrix(C, 3)) == [0 0 1 0 0;
0 4 0 4 0;
8 0 4 0 8;
0 4 0 4 0;
0 0 3 0 0]
@test Matrix(SymbolicWedderburn.CCMatrix(C, 4)) == [0 0 0 1 0;
0 0 3 0 4;
0 4 0 4 0;
6 0 3 0 2;
0 2 0 1 0]
@test Matrix(SymbolicWedderburn.CCMatrix(C, 5)) == [0 0 0 0 1;
0 1 0 2 0;
0 0 3 0 0;
0 2 0 1 0;
3 0 0 0 2]

# Alt(4)
a = SymbolicWedderburn.PermutationGroups.perm"(1,2,3)"
b = SymbolicWedderburn.PermutationGroups.perm"(1,2,4)"
G = SymbolicWedderburn.PermutationGroups.PermGroup([a,b])
C = SymbolicWedderburn.PermutationGroups.conjugacy_classes(G)
_ccmatrix(C)
@test_broken Matrix(SymbolicWedderburn.CCMatrix(C, 2)) == [0 1 0 0;
3 2 0 0;
0 0 3 0;
0 0 0 3]
@test_broken Matrix(SymbolicWedderburn.CCMatrix(C, 3)) == [0 0 1 0;
0 0 3 0;
0 0 0 4;
4 4 0 0]
@test_broken Matrix(SymbolicWedderburn.CCMatrix(C, 4)) == [0 0 0 1;
0 0 0 3;
4 4 0 0;
0 0 4 0]
C = conjugacy_classes(G)
generic_tests_ccmatrix(C)
@test SymbolicWedderburn.CCMatrix(C, 2) == [0 1 0 0 0;
6 0 3 0 2;
0 4 0 4 0;
0 0 3 0 4;
0 1 0 2 0]
@test SymbolicWedderburn.CCMatrix(C, 3) == [0 0 1 0 0;
0 4 0 4 0;
8 0 4 0 8;
0 4 0 4 0;
0 0 3 0 0]
@test SymbolicWedderburn.CCMatrix(C, 4) == [0 0 0 1 0;
0 0 3 0 4;
0 4 0 4 0;
6 0 3 0 2;
0 2 0 1 0]
@test SymbolicWedderburn.CCMatrix(C, 5) == [0 0 0 0 1;
0 1 0 2 0;
0 0 3 0 0;
0 2 0 1 0;
3 0 0 0 2]
end
@testset "example: Alternating group (4)" begin
a = PermutationGroups.perm"(1,2,3)(4)"
b = PermutationGroups.perm"(1,2,4)"
G = PermutationGroups.PermGroup([a,b])
C = [
Orbit([a,b], one(G)),
Orbit([a,b], PermutationGroups.perm"(1,2)(3,4)"),
Orbit([a,b], PermutationGroups.perm"(1,2,3)(4)"),
Orbit([a,b], PermutationGroups.perm"(1,3,2)(4)"),
]

generic_tests_ccmatrix(C)
@test SymbolicWedderburn.CCMatrix(C, 1) == [1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1]
@test SymbolicWedderburn.CCMatrix(C, 2) == [0 1 0 0
3 2 0 0
0 0 3 0
0 0 0 3]
@test SymbolicWedderburn.CCMatrix(C, 3) == [0 0 1 0
0 0 3 0
0 0 0 4
4 4 0 0]
@test SymbolicWedderburn.CCMatrix(C, 4) == [0 0 0 1
0 0 0 3
4 4 0 0
0 0 4 0]
end

@testset "example: C₅ ⋊ C₄" begin
S = [PermutationGroups.perm"(1,2,4,5,3)", PermutationGroups.perm"(2,5,3,4)"]
G = PermGroup(S);

# I'd like to reproduce the example on p. 259.

ccG = [
Orbit(S, one(G)),
Orbit(S, PermutationGroups.perm"(2,3)(4,5)"),
Orbit(S, PermutationGroups.perm"(2,4,3,5)"),
Orbit(S, PermutationGroups.perm"(2,5,3,4)"),
Orbit(S, PermutationGroups.perm"(1,2,4,5,3)"),
]
# the order of cclasses is taken from GAP

@assert sum(length, ccG) == PermutationGroups.order(G)

@test SymbolicWedderburn.CCMatrix(ccG, 1) ==
[ 1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1 ]
@test SymbolicWedderburn.CCMatrix(ccG, 2) ==
[ 0 1 0 0 0
5 0 0 0 5
0 0 0 5 0
0 0 5 0 0
0 4 0 0 0 ]
@test SymbolicWedderburn.CCMatrix(ccG, 3) ==
[ 0 0 1 0 0
0 0 0 5 0
0 5 0 0 0
5 0 0 0 5
0 0 4 0 0 ]
@test SymbolicWedderburn.CCMatrix(ccG, 4) ==
[ 0 0 0 1 0
0 0 5 0 0
5 0 0 0 5
0 5 0 0 0
0 0 0 4 0 ]
@test SymbolicWedderburn.CCMatrix(ccG, 5) ==
[ 0 0 0 0 1
0 4 0 0 0
0 0 4 0 0
0 0 0 4 0
4 0 0 0 3 ]

generic_tests_ccmatrix(ccG)
generic_tests_ccmatrix(conjugacy_classes(G)) # might be in different order
end
@testset "random" begin

@testset "random subgroups of SymetricGroup(N)" begin
for i in 2:6
G = SymbolicWedderburn.AbstractAlgebra.SymmetricGroup(i)
_ccmatrix(SymbolicWedderburn.PermutationGroups.conjugacy_classes(G))
for _ in 1:5
PG = PermutationGroups.PermGroup(rand(G, 2))
generic_tests_ccmatrix(SymbolicWedderburn.conjugacy_classes(PG))
end
end
end
end
@warn "Should actually be tested on subgroups of S_n"

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