Update to MP renamings #31
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## master #31 +/- ##
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20 tasks
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@kalmarek |
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this thing came from AA previously; At the moment probably it's best to define julia> using PermutationGroups
[ Info: Precompiling PermutationGroups [8bc5a954-2dfc-11e9-10e6-cd969bffa420]
julia> symmetric_group(n) = PermGroup(Perm([2,1]), Perm([2:n;1]))
symmetric_group (generic function with 1 method)
julia> PermutationGroups.order(symmetric_group(4))
24
julia> collect(symmetric_group(3))
6-element Vector{Permutation{Perm{UInt16}, PermGroup{Perm{UInt16}, …}}}:
()
(2,3)
(1,2)
(1,2,3)
(1,3,2)
(1,3)
Do you think |
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@kalmarek I now get Is this a bug in CondensedMatterSOS ? It could be that my group is not satisfying the axioms of a group but we are checking that now |
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@blegat where is this group defined? |
* rewrite the definitions of groups in symmetry.jl * add Random
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Still the same error it seems. |
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hmm julia> G = Lattice1Group(2)
Lattice1Group(CondensedMatterSOS.CyclicGroup(2), CondensedMatterSOS.KleinPermGroup())
julia> SymbolicWedderburn.Characters.irreducible_characters(G)
ERROR: DomainError with 6:
6 is not a square modulo 13
Stacktrace:
[1] sqrtmod(n::Int64, q::Int64)
@ SymbolicWedderburn.Characters.FiniteFields ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/gf.jl:109
[2] sqrt
@ ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/gf.jl:103 [inlined]
[3] normalize!(chtbl::SymbolicWedderburn.Characters.CharacterTable{Lattice1Group, SymbolicWedderburn.Characters.FiniteFields.GF{13}, PermutationGroups.Orbit{CondensedMatterSOS.DirectSumElem{CondensedMatterSOS.CyclicElem, CondensedMatterSOS.KleinPermElement}}})
@ SymbolicWedderburn.Characters ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:141
[4] SymbolicWedderburn.Characters.CharacterTable(Fp::Type{SymbolicWedderburn.Characters.FiniteFields.GF{13}}, G::Lattice1Group, cclasses::Vector{PermutationGroups.Orbit{CondensedMatterSOS.DirectSumElem{CondensedMatterSOS.CyclicElem, CondensedMatterSOS.KleinPermElement}}})
@ SymbolicWedderburn.Characters ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:73
[5] SymbolicWedderburn.Characters.CharacterTable(R::Type{Rational{Int64}}, G::Lattice1Group, cclasses::Vector{PermutationGroups.Orbit{CondensedMatterSOS.DirectSumElem{CondensedMatterSOS.CyclicElem, CondensedMatterSOS.KleinPermElement}}})
@ SymbolicWedderburn.Characters ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:83
[6] irreducible_characters
@ ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:41 [inlined]
[7] irreducible_characters
@ ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:33 [inlined]
[8] irreducible_characters(G::Lattice1Group)
@ SymbolicWedderburn.Characters ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:33
[9] top-level scope
@ REPL[21]:1
julia> SymbolicWedderburn.Characters.irreducible_characters(G.K)
ERROR: DomainError with 6:
6 is not a square modulo 13
Stacktrace:
[1] sqrtmod(n::Int64, q::Int64)
@ SymbolicWedderburn.Characters.FiniteFields ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/gf.jl:109
[2] sqrt
@ ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/gf.jl:103 [inlined]
[3] normalize!(chtbl::SymbolicWedderburn.Characters.CharacterTable{CondensedMatterSOS.KleinPermGroup, SymbolicWedderburn.Characters.FiniteFields.GF{13}, PermutationGroups.Orbit{CondensedMatterSOS.KleinPermElement}})
@ SymbolicWedderburn.Characters ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:141
[4] SymbolicWedderburn.Characters.CharacterTable(Fp::Type{SymbolicWedderburn.Characters.FiniteFields.GF{13}}, G::CondensedMatterSOS.KleinPermGroup, cclasses::Vector{PermutationGroups.Orbit{CondensedMatterSOS.KleinPermElement}})
@ SymbolicWedderburn.Characters ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:73
[5] SymbolicWedderburn.Characters.CharacterTable(R::Type{Rational{Int64}}, G::CondensedMatterSOS.KleinPermGroup, cclasses::Vector{PermutationGroups.Orbit{CondensedMatterSOS.KleinPermElement}})
@ SymbolicWedderburn.Characters ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:83
[6] irreducible_characters
@ ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:41 [inlined]
[7] irreducible_characters
@ ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:33 [inlined]
[8] irreducible_characters(G::CondensedMatterSOS.KleinPermGroup)
@ SymbolicWedderburn.Characters ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:33
[9] top-level scope
@ REPL[22]:1
julia> order(G.K)
24Since all groups of order up to 30 are tested here: |
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TLDR: bug was in There are also two fixes for botched Longer version if you wish...julia> K = KleinPermGroup()
KleinPermGroup()
julia> Characters.CharacterTable(Rational{Int}, K)
ERROR: DomainError with 6:
6 is not a square modulo 13
Stacktrace:
[1] sqrtmod(n::Int64, q::Int64)
@ SymbolicWedderburn.Characters.FiniteFields ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/gf.jl:109
[2] sqrt
@ ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/gf.jl:103 [inlined]
[3] normalize!(chtbl::CharacterTable{KleinPermGroup, SymbolicWedderburn.Characters.FiniteFields.GF{13}, Orbit{KleinPermElement}})
@ SymbolicWedderburn.Characters ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:141
[4] CharacterTable(Fp::Type{SymbolicWedderburn.Characters.FiniteFields.GF{13}}, G::KleinPermGroup, cclasses::Vector{Orbit{KleinPermElement}})
@ SymbolicWedderburn.Characters ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:73
[5] CharacterTable(R::Type{Rational{Int64}}, G::KleinPermGroup, cclasses::Vector{Orbit{KleinPermElement}})
@ SymbolicWedderburn.Characters ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:83
[6] CharacterTable(R::Type{Rational{Int64}}, G::KleinPermGroup)
@ SymbolicWedderburn.Characters ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:82
[7] top-level scope
@ REPL[4]:1the error that we've seen. julia> p = Characters.dixon_prime(K)
13
julia> Characters.CharacterTable(Characters.FiniteFields.GF{p}, K)
ERROR: DomainError with 6:
6 is not a square modulo 13
Stacktrace:
[1] sqrtmod(n::Int64, q::Int64)
@ SymbolicWedderburn.Characters.FiniteFields ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/gf.jl:109
[2] sqrt
@ ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/gf.jl:103 [inlined]
[3] normalize!(chtbl::CharacterTable{KleinPermGroup, SymbolicWedderburn.Characters.FiniteFields.GF{13}, Orbit{KleinPermElement}})
@ SymbolicWedderburn.Characters ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:141
[4] CharacterTable(Fp::Type{SymbolicWedderburn.Characters.FiniteFields.GF{13}}, G::KleinPermGroup, cclasses::Vector{Orbit{KleinPermElement}})
@ SymbolicWedderburn.Characters ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:73
[5] CharacterTable(Fp::Type{SymbolicWedderburn.Characters.FiniteFields.GF{13}}, G::KleinPermGroup)
@ SymbolicWedderburn.Characters ~/.julia/packages/SymbolicWedderburn/hBhTJ/src/Characters/character_tables.jl:61
[6] top-level scope
@ REPL[6]:1actually happens when computing over the finite field. Let's investigate further. julia> SWpath = joinpath(dirname(dirname(pathof(SymbolicWedderburn))),)
"/home/kalmar/.julia/packages/SymbolicWedderburn/hBhTJ/test"
julia> include(joinpath(SWpath, "test", "smallgroups.jl"));
julia> length(SmallPermGroups[24])
15one of them should be isomorphic to our julia> K_ords = sort!(vec(map(g->order(Int, g), K))))
24-element Vector{Int64}:
1
2
2
2
2
2
2
2
⋮
3
4
4
4
4
4
4
julia> candidates = [i for (i, G) in pairs(SmallPermGroups[24]) if
sort!(map(g->order(Int, g), G)) == K_ords]
1-element Vector{Int64}:
12
julia> K_perm = SmallPermGroups[24][first(candidates)]
Permutation group on 4 generators of order 24 generated by
(1,2)(3,13)(4,8)(5,7)(6,9)(10,21)(11,20)(12,16)(14,18)(15,17)(19,24)(22,23)
(1,3,9)(2,6,13)(4,11,23)(5,19,17)(7,15,24)(8,22,20)(10,18,12)(14,21,16)
(1,4)(2,7)(3,10)(5,12)(6,14)(8,16)(9,17)(11,19)(13,20)(15,22)(18,23)(21,24)
(1,5)(2,8)(3,11)(4,12)(6,15)(7,16)(9,18)(10,19)(13,21)(14,22)(17,23)(20,24)
Clearly isomorphism should preserve orders, and there's only one group with the same set of orders as Ok, since we get a strange error while normalizing "characters" my guess is that something is wrong with conjugacy classes of julia> [order.(Int, c) for c in Characters.conjugacy_classes(K)]
7-element Vector{Vector{Int64}}:
[1]
[2, 2, 2]
[3, 3]
[2, 2, 2]
[2, 2, 2]
[4, 4, 4, 4, 4, 4]
[3, 3, 3, 3, 3, 3]
julia> [order.(Int, c) for c in Characters.conjugacy_classes(K_perm)]
5-element Vector{Vector{Int64}}:
[1]
[2, 2, 2, 2, 2, 2]
[3, 3, 3, 3, 3, 3, 3, 3]
[2, 2, 2]
[4, 4, 4, 4, 4, 4]yes they are, but it seems that some elements which should be conjugated are not? Lets take a permutation representation of julia> S = let elts = collect(K)
idict = Dict(e=>i for (i,e) in pairs(vec(elts)))
map(gens(K)) do g
Perm([idict[h*g] for h in vec(elts)])
end
end;
julia> PermGroup(S)
Permutation group on 2 generators generated by
(1,3)(2,4)(5,6)(7,15)(8,16)(9,13)(10,14)(11,18)(12,17)(19,21)(20,22)(23,24)
(1,4,5)(2,3,6)(7,16,23)(8,15,24)(9,18,20)(10,17,19)(11,13,22)(12,14,21)
julia> order(Int, ans)
6only two generators and order 6! we have a solution: julia> gens(K)
2-element Vector{KleinPermElement}:
KleinPermElement((1,2), KleinElement(0))
KleinPermElement((1,2,3), KleinElement(0))these surely don't generate With function GroupsCore.gens(::KleinPermGroup)
Kid = one(KleinGroup())
elts = [KleinPermElement(g, Kid) for g in __symmetric_grp_gens(3)]
Pid = one(first(__symmetric_grp_gens(3)))
append!(elts, KleinPermElement(Pid, k) for k in gens(KleinGroup()))
return elts
endI get julia> Characters.CharacterTable(Rational{Int}, K)
Character table of KleinPermGroup() over Cyclotomics.Cyclotomic{Rational{Int64}, SparseArrays.SparseVector{Rational{Int64}, Int64}}
1 2 3 4 5
───┬─────────────────────────────
χ₁ │ 2//1 0//1 -1//1 2//1 0//1
χ₂ │ 3//1 1//1 0//1 -1//1 -1//1
χ₃ │ 1//1 1//1 1//1 1//1 1//1
χ₄ │ 1//1 -1//1 1//1 1//1 -1//1
χ₅ │ 3//1 -1//1 0//1 -1//1 1//1
julia> Characters.CharacterTable(Rational{Int}, K_perm)
Character table of PermGroup( (1,2)(3,13)(4,8)(5,7)(6,9)(10,21)(11,20)(12,16)(14,18)(15,17)(19,24)(22,23), (1,3,9)(2,6,13)(4,11,23)(5,19,17)(7,15,24)(8,22,20)(10,18,12)(14,21,16), (1,4)(2,7)(3,10)(5,12)(6,14)(8,16)(9,17)(11,19)(13,20)(15,22)(18,23)(21,24), (1,5)(2,8)(3,11)(4,12)(6,15)(7,16)(9,18)(10,19)(13,21)(14,22)(17,23)(20,24) ) over Cyclotomics.Cyclotomic{Rational{Int64}, SparseArrays.SparseVector{Rational{Int64}, Int64}}
1 2 3 4 5
───┬─────────────────────────────
χ₁ │ 2//1 0//1 -1//1 2//1 0//1
χ₂ │ 3//1 1//1 0//1 -1//1 -1//1
χ₃ │ 1//1 1//1 1//1 1//1 1//1
χ₄ │ 1//1 -1//1 1//1 1//1 -1//1
χ₅ │ 3//1 -1//1 0//1 -1//1 1//1 |
kalmarek
reviewed
Sep 15, 2023
src/symmetry.jl
Outdated
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98
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| symmetric_group(n) = PermutationGroups.PermGroup(PermutationGroups.Perm([2,1]), PermutationGroups.Perm([2:n;1])) | ||
| function PermutationGroups.gens(::KleinPermGroup) | ||
| els = [KleinPermElement(Perm(3), KleinElement(1))] | ||
| for g in gens(symmetric_group(3)) | ||
| function PermutationGroups.gens(g::KleinPermGroup) | ||
| els = [one(g)] | ||
| for g in gens(G3) |
There was a problem hiding this comment.
@blegat this is where the bug was introduced;
The old version generated KleinPermGroup, since Sym(3) acts transively on non-trivial KleinElements, the new one doesn't since KleinElement(0) is fixed under Sym(3).
I just updated the function without thinking ;)
kalmarek
reviewed
Sep 15, 2023
kalmarek
reviewed
Sep 15, 2023
src/symmetry.jl
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| function Base.deepcopy_internal(g::KleinPermElement, dict::IdDict) | ||
| p = if haskey(dict, objectid(g.p)) | ||
| dict[objectid(g.p)] | ||
| else | ||
| el, st = el_st | ||
| return KleinPermElement(P3[el[1]], KleinElement(el[2])), st | ||
| Base.deepcopy_internal(g.p, dict) | ||
| end | ||
| return KleinPermElement(p, g.k) | ||
| end |
There was a problem hiding this comment.
I think I've botched both deepcopy_internals. Here's the corrected version:
function Base.deepcopy_internal(g::KleinPermElement, dict::IdDict)
haskey(dict, g) && return dict[g]
h = KleinPermElement(Base.deepcopy_internal(g.p, dict), g.k)
dict[g] = h
return h
end
kalmarek
reviewed
Sep 15, 2023
src/symmetry.jl
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| function Base.deepcopy_internal(g::DirectSumElem, dict::IdDict) | ||
| h = if isbits(g.h) | ||
| g.h | ||
| elseif haskey(dict, objectid(g.h)) | ||
| dict[objectid(g.h)] | ||
| else | ||
| Base.deepcopy_internal(g.h, dict) | ||
| end |
There was a problem hiding this comment.
and again:
function Base.deepcopy_internal(g::DirectSumElem, dict::IdDict)
haskey(dict, g) && return g
h = if isbits(g.h)
g.h
elseif haskey(dict, g.h)
dict[g.h]
else
Base.deepcopy_internal(g.h, dict)
end
k = if isbits(g.k)
g.k
elseif haskey(dict, g.k)
dict[g.k]
else
Base.deepcopy_internal(g.k, dict)
end
new_g = DirectSumElem(h, k)
dict[g] = new_g
return new_g
endCo-authored-by: Marek Kaluba <marek.kaluba@kit.edu>
* sort out deepcopy_internal stuff * move imports/exports away from symmetry.jl * update action.jl to the rewrite of symmetry.jl
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