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@ -1,7 +1,7 @@
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function _abelianize(
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i::Integer,
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source::AutomorphismGroup{<:FreeGroup},
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target::MatrixGroups.SpecialLinearGroup{N, T}) where {N, T}
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target::MatrixGroups.SpecialLinearGroup{N,T}) where {N,T}
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n = ngens(object(source))
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@assert n == N
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aut = alphabet(source)[i]
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@ -10,10 +10,10 @@ function _abelianize(
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# Automorphisms act on the right which corresponds to action on
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# the columns in the matrix case
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eij = MatrixGroups.ElementaryMatrix{N}(
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aut.j,
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aut.i,
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ifelse(aut.inv, -one(T), one(T))
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)
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aut.j,
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aut.i,
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ifelse(aut.inv, -one(T), one(T))
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)
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k = alphabet(target)[eij]
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return word_type(target)([k])
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else
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@ -24,7 +24,7 @@ end
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function _abelianize(
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i::Integer,
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source::AutomorphismGroup{<:Groups.SurfaceGroup},
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target::MatrixGroups.SpecialLinearGroup{N, T}) where {N, T}
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target::MatrixGroups.SpecialLinearGroup{N,T}) where {N,T}
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n = ngens(Groups.object(source))
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@assert n == N
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g = alphabet(source)[i].autFn_word
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@ -39,8 +39,8 @@ end
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function Groups._abelianize(
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i::Integer,
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source::AutomorphismGroup{<:Groups.SurfaceGroup},
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target::MatrixGroups.SymplecticGroup{N, T}
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) where {N, T}
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target::MatrixGroups.SymplecticGroup{N,T}
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) where {N,T}
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@assert iseven(N)
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As = alphabet(source)
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At = alphabet(target)
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@ -53,7 +53,7 @@ function Groups._abelianize(
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ab = Groups.Homomorphism(Groups._abelianize, source, SlN, check=false)
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matrix_spn_map = let S = gens(target)
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Dict(MatrixGroups.matrix_repr(g)=> word(g) for g in union(S, inv.(S)))
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Dict(MatrixGroups.matrix_repr(g) => word(g) for g in union(S, inv.(S)))
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end
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# renumeration:
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@ -63,7 +63,7 @@ function Groups._abelianize(
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p = [reverse(2:2:N); reverse(1:2:N)]
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g = source([i])
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Mg = MatrixGroups.matrix_repr(ab(g))[p,p]
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Mg = MatrixGroups.matrix_repr(ab(g))[p, p]
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return matrix_spn_map[Mg]
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end
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@ -1,4 +1,4 @@
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function gersten_alphabet(n::Integer; commutative::Bool = true)
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function gersten_alphabet(n::Integer; commutative::Bool=true)
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indexing = [(i, j) for i in 1:n for j in 1:n if i ≠ j]
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S = [ϱ(i, j) for (i, j) in indexing]
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@ -6,7 +6,7 @@ function gersten_alphabet(n::Integer; commutative::Bool = true)
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append!(S, [λ(i, j) for (i, j) in indexing])
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end
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return Alphabet(S)
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return Alphabet(mapreduce(x -> [x, inv(x)], union, S))
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end
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function _commutation_rule(
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@ -41,12 +41,12 @@ function _hexagonal_rule(
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end
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gersten_relations(n::Integer; commutative) =
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gersten_relations(Word{UInt8}, n, commutative = commutative)
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gersten_relations(Word{UInt8}, n, commutative=commutative)
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function gersten_relations(::Type{W}, n::Integer; commutative) where {W<:AbstractWord}
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@assert n > 1 "Gersten relations are defined only for n>1, got n=$n"
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A = gersten_alphabet(n, commutative = commutative)
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@assert length(A) <= KnuthBendix._max_alphabet_length(W) "Type $W can not represent words over alphabet with $(length(A)) letters."
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A = gersten_alphabet(n, commutative=commutative)
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@assert length(A) <= typemax(eltype(W)) "Type $W can not represent words over alphabet with $(length(A)) letters."
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rels = Pair{W,W}[]
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@ -17,7 +17,7 @@ function Base.show(io::IO, S::SurfaceGroup)
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end
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end
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function SurfaceGroup(genus::Integer, boundaries::Integer)
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function SurfaceGroup(genus::Integer, boundaries::Integer, W=Word{Int16})
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@assert genus > 1
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# The (confluent) rewriting systems comes from
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@ -30,15 +30,15 @@ function SurfaceGroup(genus::Integer, boundaries::Integer)
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ltrs = String[]
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for i in 1:genus
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subscript = join('₀'+d for d in reverse(digits(i)))
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subscript = join('₀' + d for d in reverse(digits(i)))
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append!(ltrs, ["A" * subscript, "a" * subscript, "B" * subscript, "b" * subscript])
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end
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Al = Alphabet(reverse!(ltrs))
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for i in 1:genus
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subscript = join('₀'+d for d in reverse(digits(i)))
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KnuthBendix.set_inversion!(Al, "a" * subscript, "A" * subscript)
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KnuthBendix.set_inversion!(Al, "b" * subscript, "B" * subscript)
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subscript = join('₀' + d for d in reverse(digits(i)))
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KnuthBendix.setinverse!(Al, "a" * subscript, "A" * subscript)
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KnuthBendix.setinverse!(Al, "b" * subscript, "B" * subscript)
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end
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if boundaries == 0
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@ -46,10 +46,10 @@ function SurfaceGroup(genus::Integer, boundaries::Integer)
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for i in reverse(1:genus)
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x = 4 * i
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append!(word, [x, x-2, x-1, x-3])
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append!(word, [x, x - 2, x - 1, x - 3])
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end
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comms = Word(word)
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word_rels = [ comms => one(comms) ]
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comms = W(word)
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word_rels = [comms => one(comms)]
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rws = let R = KnuthBendix.RewritingSystem(word_rels, KnuthBendix.Recursive(Al))
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KnuthBendix.IndexAutomaton(KnuthBendix.knuthbendix(R))
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@ -60,11 +60,11 @@ function SurfaceGroup(genus::Integer, boundaries::Integer)
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KnuthBendix.IndexAutomaton(KnuthBendix.knuthbendix(R))
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end
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else
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throw("Not Implemented")
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throw("Not Implemented for MCG with $boundaryies boundary components")
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end
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F = FreeGroup(alphabet(rws))
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rels = [F(lhs)=>F(rhs) for (lhs,rhs) in word_rels]
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F = FreeGroup(Al)
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rels = [F(lhs) => F(rhs) for (lhs, rhs) in word_rels]
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return SurfaceGroup(genus, boundaries, [Al[i] for i in 2:2:length(Al)], rels, rws)
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end
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@ -77,13 +77,13 @@ function symplectic_twists(π₁Σ::SurfaceGroup)
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saut = SpecialAutomorphismGroup(FreeGroup(2g), max_rules=1000)
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Aij = [SymplecticMappingClass(saut, :A, i, j) for i in 1:g for j in 1:g if i≠j]
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Aij = [SymplecticMappingClass(saut, :A, i, j) for i in 1:g for j in 1:g if i ≠ j]
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Bij = [SymplecticMappingClass(saut, :B, i, j) for i in 1:g for j in 1:g if i≠j]
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Bij = [SymplecticMappingClass(saut, :B, i, j) for i in 1:g for j in 1:g if i ≠ j]
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mBij = [SymplecticMappingClass(saut, :B, i, j, minus=true) for i in 1:g for j in 1:g if i≠j]
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mBij = [SymplecticMappingClass(saut, :B, i, j, minus=true) for i in 1:g for j in 1:g if i ≠ j]
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Bii = [SymplecticMappingClass(saut, :B, i, i) for i in 1:g]
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Bii = [SymplecticMappingClass(saut, :B, i, i) for i in 1:g]
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mBii = [SymplecticMappingClass(saut, :B, i, i, minus=true) for i in 1:g]
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@ -99,6 +99,6 @@ function AutomorphismGroup(π₁Σ::SurfaceGroup; kwargs...)
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# this is to fix the definitions of symplectic twists:
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# with i->gens(π₁Σ, i) the corresponding automorphisms return
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# reversed words
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domain = ntuple(i->inv(gens(π₁Σ, i)), 2genus(π₁Σ))
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domain = ntuple(i -> inv(gens(π₁Σ, i)), 2genus(π₁Σ))
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return AutomorphismGroup(π₁Σ, S, A, domain)
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end
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@ -1,7 +1,7 @@
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include("transvections.jl")
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include("gersten_relations.jl")
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function SpecialAutomorphismGroup(F::FreeGroup; ordering = KnuthBendix.LenLex, kwargs...)
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function SpecialAutomorphismGroup(F::FreeGroup; ordering=KnuthBendix.LenLex, kwargs...)
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n = length(alphabet(F)) ÷ 2
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A, rels = gersten_relations(n, commutative=false)
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@ -21,5 +21,5 @@ end
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function relations(G::AutomorphismGroup{<:FreeGroup})
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n = length(alphabet(object(G))) ÷ 2
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return last(gersten_relations(n, commutative = false))
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return last(gersten_relations(n, commutative=false))
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end
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@ -73,7 +73,7 @@ function Te(λ::ΡΛ, ϱ::ΡΛ, i, j)
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@assert λ.id == :λ && ϱ.id == :ϱ
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@assert iseven(λ.N)
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genus = λ.N÷2
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genus = λ.N ÷ 2
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i = mod1(i, genus)
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j = mod1(j, genus)
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@ -118,7 +118,7 @@ end
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function rotation_element(λ::ΡΛ, ϱ::ΡΛ)
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@assert iseven(λ.N)
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genus = λ.N÷2
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genus = λ.N ÷ 2
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A = λ.A
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halftwists = map(1:genus-1) do i
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@ -168,7 +168,7 @@ function mcg_twists(G::AutomorphismGroup{<:FreeGroup})
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return Tas, Tαs, Tes
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end
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struct SymplecticMappingClass{T, F} <: GSymbol
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struct SymplecticMappingClass{T,F} <: GSymbol
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id::Symbol # :A, :B
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i::UInt
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j::UInt
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@ -187,13 +187,13 @@ function SymplecticMappingClass(
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id::Symbol,
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i::Integer,
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j::Integer;
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minus = false,
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inverse = false,
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minus=false,
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inverse=false
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)
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@assert i > 0 && j > 0
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id === :A && @assert i ≠ j
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@assert iseven(ngens(object(sautFn)))
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genus = ngens(object(sautFn))÷2
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genus = ngens(object(sautFn)) ÷ 2
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A = alphabet(sautFn)
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λ = ΡΛ(:λ, A, 2genus)
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@ -241,7 +241,7 @@ end
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function Base.show(io::IO, smc::SymplecticMappingClass)
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smc.minus && print(io, 'm')
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if smc.i < 10 && smc.j < 10
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if smc.i < 10 && smc.j < 10
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print(io, smc.id, subscriptify(smc.i), subscriptify(smc.j))
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else
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print(io, smc.id, subscriptify(smc.i), ".", subscriptify(smc.j))
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@ -4,7 +4,7 @@ struct Transvection <: GSymbol
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j::UInt16
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inv::Bool
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function Transvection(id::Symbol, i::Integer, j::Integer, inv = false)
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function Transvection(id::Symbol, i::Integer, j::Integer, inv=false)
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@assert id in (:ϱ, :λ)
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return new(id, i, j, inv)
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end
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@ -33,7 +33,7 @@ Base.hash(t::Transvection, h::UInt) = hash(hash(t.id, hash(t.i)), hash(t.j, hash
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Base.@propagate_inbounds @inline function evaluate!(
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v::NTuple{T,N},
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t::Transvection,
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tmp = one(first(v)),
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tmp=one(first(v)),
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) where {T,N}
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i, j = t.i, t.j
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@assert 1 ≤ i ≤ length(v) && 1 ≤ j ≤ length(v)
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@ -92,4 +92,4 @@ Base.inv(p::PermRightAut) = PermRightAut(invperm(p.perm))
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Base.:(==)(p::PermRightAut, q::PermRightAut) = p.perm == q.perm
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Base.hash(p::PermRightAut, h::UInt) = hash(p.perm, hash(PermRightAut, h))
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evaluate!(v::NTuple{T,N}, p::PermRightAut, tmp = nothing) where {T,N} = v[p.perm]
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evaluate!(v::NTuple{T,N}, p::PermRightAut, tmp=nothing) where {T,N} = v[p.perm]
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@ -104,8 +104,8 @@ evaluate(f::AbstractFPGroupElement{<:AutomorphismGroup}) = evaluate!(domain(f),
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function evaluate!(
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t::NTuple{N,T},
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f::AbstractFPGroupElement{<:AutomorphismGroup{<:Group}},
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tmp = one(first(t)),
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) where {N, T<:FPGroupElement}
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tmp=one(first(t)),
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) where {N,T<:FPGroupElement}
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A = alphabet(f)
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for idx in word(f)
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t = @inbounds evaluate!(t, A[idx], tmp)::NTuple{N,T}
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@ -113,12 +113,12 @@ function evaluate!(
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return t
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end
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evaluate!(t::NTuple{N, T}, s::GSymbol, tmp=nothing) where {N, T} = throw("you need to implement `evaluate!(::$(typeof(t)), ::$(typeof(s)), ::Alphabet, tmp=one(first(t)))`")
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evaluate!(t::NTuple{N,T}, s::GSymbol, tmp=nothing) where {N,T} = throw("you need to implement `evaluate!(::$(typeof(t)), ::$(typeof(s)), ::Alphabet, tmp=one(first(t)))`")
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# forward evaluate by substitution
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struct LettersMap{T, A}
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indices_map::Dict{Int, T}
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struct LettersMap{T,A}
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indices_map::Dict{Int,T}
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A::A
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end
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@ -201,13 +201,14 @@ function generated_evaluate(a::FPGroupElement{<:AutomorphismGroup})
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throw("Letter $l doesn't seem to be mapped anywhere!")
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end
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end
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locals = Dict{Expr, Symbol}()
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locals = Dict{Expr,Symbol}()
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locals_counter = 0
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for (i,v) in enumerate(args)
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for (i, v) in enumerate(args)
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@assert length(v.args) >= 2
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if length(v.args) > 2
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for (j, a) in pairs(v.args)
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if a isa Expr && a.head == :call "$a"
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if a isa Expr && a.head == :call
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"$a"
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@assert a.args[1] == :inv
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if !(a in keys(locals))
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locals[a] = Symbol("var_#$locals_counter")
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@ -222,7 +223,7 @@ function generated_evaluate(a::FPGroupElement{<:AutomorphismGroup})
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end
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q = quote
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$([:(local $v = $k) for (k,v) in locals]...)
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$([:(local $v = $k) for (k, v) in locals]...)
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end
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# return args, locals
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@ -30,7 +30,7 @@ function Base.iterate(G::DirectPower)
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res = iterate(itr)
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@assert res !== nothing
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elt = DirectPowerElement(first(res), G)
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return elt, (iterator = itr, state = last(res))
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return elt, (iterator=itr, state=last(res))
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end
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function Base.iterate(G::DirectPower, state)
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@ -38,7 +38,7 @@ function Base.iterate(G::DirectPower, state)
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res = iterate(itr, st)
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res === nothing && return nothing
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elt = DirectPowerElement(first(res), G)
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return elt, (iterator = itr, state = last(res))
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return elt, (iterator=itr, state=last(res))
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end
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function Base.IteratorSize(::Type{<:DirectPower{Gr,N}}) where {Gr,N}
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@ -52,7 +52,7 @@ Base.size(G::DirectPower) = ntuple(_ -> length(G.group), _nfold(G))
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GroupsCore.order(::Type{I}, G::DirectPower) where {I<:Integer} =
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convert(I, order(I, G.group)^_nfold(G))
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GroupsCore.ngens(G::DirectPower) = _nfold(G)*ngens(G.group)
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GroupsCore.ngens(G::DirectPower) = _nfold(G) * ngens(G.group)
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function GroupsCore.gens(G::DirectPower, i::Integer)
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k = ngens(G.group)
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@ -66,7 +66,7 @@ end
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function GroupsCore.gens(G::DirectPower)
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N = _nfold(G)
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S = gens(G.group)
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tups = [ntuple(j->(i == j ? s : one(s)), N) for i in 1:N for s in S]
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tups = [ntuple(j -> (i == j ? s : one(s)), N) for i in 1:N for s in S]
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return [DirectPowerElement(elts, G) for elts in tups]
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end
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@ -99,7 +99,7 @@ function Base.:(*)(g::DirectPowerElement, h::DirectPowerElement)
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end
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GroupsCore.order(::Type{I}, g::DirectPowerElement) where {I<:Integer} =
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convert(I, reduce(lcm, (order(I, h) for h in g.elts), init = one(I)))
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convert(I, reduce(lcm, (order(I, h) for h in g.elts), init=one(I)))
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Base.isone(g::DirectPowerElement) = all(isone, g.elts)
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@ -25,7 +25,7 @@ function Base.iterate(G::DirectProduct)
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res = iterate(itr)
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@assert res !== nothing
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elt = DirectProductElement(first(res), G)
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return elt, (iterator = itr, state = last(res))
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return elt, (iterator=itr, state=last(res))
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end
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function Base.iterate(G::DirectProduct, state)
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@ -33,7 +33,7 @@ function Base.iterate(G::DirectProduct, state)
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res = iterate(itr, st)
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res === nothing && return nothing
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elt = DirectProductElement(first(res), G)
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return elt, (iterator = itr, state = last(res))
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return elt, (iterator=itr, state=last(res))
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end
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function Base.IteratorSize(::Type{<:DirectProduct{Gt,Ht}}) where {Gt,Ht}
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@ -52,7 +52,7 @@ function Base.iterate(G::WreathProduct)
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||||
res = iterate(itr)
|
||||
@assert res !== nothing
|
||||
elt = WreathProductElement(first(res)..., G)
|
||||
return elt, (iterator = itr, state = last(res))
|
||||
return elt, (iterator=itr, state=last(res))
|
||||
end
|
||||
|
||||
function Base.iterate(G::WreathProduct, state)
|
||||
@ -60,7 +60,7 @@ function Base.iterate(G::WreathProduct, state)
|
||||
res = iterate(itr, st)
|
||||
res === nothing && return nothing
|
||||
elt = WreathProductElement(first(res)..., G)
|
||||
return elt, (iterator = itr, state = last(res))
|
||||
return elt, (iterator=itr, state=last(res))
|
||||
end
|
||||
|
||||
function Base.IteratorSize(::Type{<:WreathProduct{DP,PGr}}) where {DP,PGr}
|
||||
|
||||
@ -58,8 +58,8 @@ true
|
||||
```
|
||||
|
||||
"""
|
||||
struct Homomorphism{Gr1, Gr2, I, W}
|
||||
gens_images::Dict{I, W}
|
||||
struct Homomorphism{Gr1,Gr2,I,W}
|
||||
gens_images::Dict{I,W}
|
||||
source::Gr1
|
||||
target::Gr2
|
||||
|
||||
@ -70,11 +70,11 @@ struct Homomorphism{Gr1, Gr2, I, W}
|
||||
check=true
|
||||
)
|
||||
A = alphabet(source)
|
||||
dct = Dict(i=>convert(word_type(target), f(i, source, target))
|
||||
for i in 1:length(A))
|
||||
dct = Dict(i => convert(word_type(target), f(i, source, target))
|
||||
for i in 1:length(A))
|
||||
I = eltype(word_type(source))
|
||||
W = word_type(target)
|
||||
hom = new{typeof(source), typeof(target), I, W}(dct, source, target)
|
||||
hom = new{typeof(source),typeof(target),I,W}(dct, source, target)
|
||||
|
||||
if check
|
||||
@assert hom(one(source)) == one(target)
|
||||
@ -83,8 +83,8 @@ struct Homomorphism{Gr1, Gr2, I, W}
|
||||
@assert hom(x^-1) == hom(x)^-1
|
||||
|
||||
for y in gens(source)
|
||||
@assert hom(x*y) == hom(x)*hom(y)
|
||||
@assert hom(x*y)^-1 == hom(y^-1)*hom(x^-1)
|
||||
@assert hom(x * y) == hom(x) * hom(y)
|
||||
@assert hom(x * y)^-1 == hom(y^-1) * hom(x^-1)
|
||||
end
|
||||
end
|
||||
for (lhs, rhs) in relations(source)
|
||||
|
||||
@ -1,4 +1,4 @@
|
||||
mutable struct FPGroupIter{S, T, GEl}
|
||||
mutable struct FPGroupIter{S,T,GEl}
|
||||
seen::S
|
||||
seen_iter_state::T
|
||||
current::GEl
|
||||
|
||||
@ -1,12 +1,12 @@
|
||||
include("eltary_matrices.jl")
|
||||
|
||||
struct SpecialLinearGroup{N, T, R, A, S} <: MatrixGroup{N,T}
|
||||
struct SpecialLinearGroup{N,T,R,A,S} <: MatrixGroup{N,T}
|
||||
base_ring::R
|
||||
alphabet::A
|
||||
gens::S
|
||||
|
||||
function SpecialLinearGroup{N}(base_ring) where N
|
||||
S = [ElementaryMatrix{N}(i,j, one(base_ring)) for i in 1:N for j in 1:N if i≠j]
|
||||
function SpecialLinearGroup{N}(base_ring) where {N}
|
||||
S = [ElementaryMatrix{N}(i, j, one(base_ring)) for i in 1:N for j in 1:N if i ≠ j]
|
||||
alphabet = Alphabet(S)
|
||||
|
||||
return new{
|
||||
@ -19,16 +19,16 @@ struct SpecialLinearGroup{N, T, R, A, S} <: MatrixGroup{N,T}
|
||||
end
|
||||
end
|
||||
|
||||
GroupsCore.ngens(SL::SpecialLinearGroup{N}) where N = N^2 - N
|
||||
GroupsCore.ngens(SL::SpecialLinearGroup{N}) where {N} = N^2 - N
|
||||
|
||||
Base.show(io::IO, SL::SpecialLinearGroup{N, T}) where {N, T} =
|
||||
Base.show(io::IO, SL::SpecialLinearGroup{N,T}) where {N,T} =
|
||||
print(io, "special linear group of $N×$N matrices over $T")
|
||||
|
||||
function Base.show(
|
||||
io::IO,
|
||||
::MIME"text/plain",
|
||||
sl::Groups.AbstractFPGroupElement{<:SpecialLinearGroup{N}}
|
||||
) where N
|
||||
) where {N}
|
||||
|
||||
Groups.normalform!(sl)
|
||||
|
||||
|
||||
@ -1,11 +1,11 @@
|
||||
include("eltary_symplectic.jl")
|
||||
|
||||
struct SymplecticGroup{N, T, R, A, S} <: MatrixGroup{N,T}
|
||||
struct SymplecticGroup{N,T,R,A,S} <: MatrixGroup{N,T}
|
||||
base_ring::R
|
||||
alphabet::A
|
||||
gens::S
|
||||
|
||||
function SymplecticGroup{N}(base_ring) where N
|
||||
function SymplecticGroup{N}(base_ring) where {N}
|
||||
S = symplectic_gens(N, eltype(base_ring))
|
||||
alphabet = Alphabet(S)
|
||||
|
||||
@ -21,7 +21,7 @@ end
|
||||
|
||||
GroupsCore.ngens(Sp::SymplecticGroup) = length(Sp.gens)
|
||||
|
||||
Base.show(io::IO, ::SymplecticGroup{N}) where N = print(io, "group of $N×$N symplectic matrices")
|
||||
Base.show(io::IO, ::SymplecticGroup{N}) where {N} = print(io, "group of $N×$N symplectic matrices")
|
||||
|
||||
function Base.show(
|
||||
io::IO,
|
||||
@ -35,15 +35,15 @@ function Base.show(
|
||||
Base.print_array(io, matrix_repr(sp))
|
||||
end
|
||||
|
||||
_offdiag_idcs(n) = ((i,j) for i in 1:n for j in 1:n if i ≠ j)
|
||||
_offdiag_idcs(n) = ((i, j) for i in 1:n for j in 1:n if i ≠ j)
|
||||
|
||||
function symplectic_gens(N, T=Int8)
|
||||
iseven(N) || throw(ArgumentError("N needs to be even!"))
|
||||
n = N÷2
|
||||
n = N ÷ 2
|
||||
|
||||
a_ijs = [ElementarySymplectic{N}(:A, i,j, one(T)) for (i,j) in _offdiag_idcs(n)]
|
||||
b_is = [ElementarySymplectic{N}(:B, n+i,i, one(T)) for i in 1:n]
|
||||
c_ijs = [ElementarySymplectic{N}(:B, n+i,j, one(T)) for (i,j) in _offdiag_idcs(n)]
|
||||
a_ijs = [ElementarySymplectic{N}(:A, i, j, one(T)) for (i, j) in _offdiag_idcs(n)]
|
||||
b_is = [ElementarySymplectic{N}(:B, n + i, i, one(T)) for i in 1:n]
|
||||
c_ijs = [ElementarySymplectic{N}(:B, n + i, j, one(T)) for (i, j) in _offdiag_idcs(n)]
|
||||
|
||||
S = [a_ijs; b_is; c_ijs]
|
||||
|
||||
@ -53,18 +53,18 @@ function symplectic_gens(N, T=Int8)
|
||||
end
|
||||
|
||||
function _std_symplectic_form(m::AbstractMatrix)
|
||||
r,c = size(m)
|
||||
r, c = size(m)
|
||||
r == c || return false
|
||||
iseven(r) || return false
|
||||
|
||||
n = r÷2
|
||||
n = r ÷ 2
|
||||
𝕆 = zeros(eltype(m), n, n)
|
||||
𝕀 = one(eltype(m))*LinearAlgebra.I
|
||||
𝕀 = one(eltype(m)) * LinearAlgebra.I
|
||||
Ω = [𝕆 -𝕀
|
||||
𝕀 𝕆]
|
||||
𝕀 𝕆]
|
||||
return Ω
|
||||
end
|
||||
|
||||
function issymplectic(mat::M, Ω = _std_symplectic_form(mat)) where M <: AbstractMatrix
|
||||
function issymplectic(mat::M, Ω=_std_symplectic_form(mat)) where {M<:AbstractMatrix}
|
||||
return Ω == transpose(mat) * Ω * mat
|
||||
end
|
||||
|
||||
@ -1,17 +1,17 @@
|
||||
abstract type MatrixGroup{N, T} <: Groups.AbstractFPGroup end
|
||||
const MatrixGroupElement{N, T} = Groups.AbstractFPGroupElement{<:MatrixGroup{N, T}}
|
||||
abstract type MatrixGroup{N,T} <: Groups.AbstractFPGroup end
|
||||
const MatrixGroupElement{N,T} = Groups.AbstractFPGroupElement{<:MatrixGroup{N,T}}
|
||||
|
||||
Base.isone(g::MatrixGroupElement{N, T}) where {N, T} =
|
||||
Base.isone(g::MatrixGroupElement{N,T}) where {N,T} =
|
||||
isone(word(g)) || matrix_repr(g) == LinearAlgebra.I
|
||||
|
||||
function Base.:(==)(m1::M1, m2::M2) where {M1<:MatrixGroupElement, M2<:MatrixGroupElement}
|
||||
function Base.:(==)(m1::M1, m2::M2) where {M1<:MatrixGroupElement,M2<:MatrixGroupElement}
|
||||
parent(m1) === parent(m2) || return false
|
||||
word(m1) == word(m2) && return true
|
||||
return matrix_repr(m1) == matrix_repr(m2)
|
||||
end
|
||||
|
||||
Base.size(m::MatrixGroupElement{N}) where N = (N, N)
|
||||
Base.eltype(m::MatrixGroupElement{N, T}) where {N, T} = T
|
||||
Base.size(m::MatrixGroupElement{N}) where {N} = (N, N)
|
||||
Base.eltype(m::MatrixGroupElement{N,T}) where {N,T} = T
|
||||
|
||||
# three structural assumptions about matrix groups
|
||||
Groups.word(sl::MatrixGroupElement) = sl.word
|
||||
@ -22,9 +22,9 @@ Groups.rewriting(M::MatrixGroup) = alphabet(M)
|
||||
Base.hash(sl::MatrixGroupElement, h::UInt) =
|
||||
hash(matrix_repr(sl), hash(parent(sl), h))
|
||||
|
||||
function matrix_repr(m::MatrixGroupElement{N, T}) where {N, T}
|
||||
function matrix_repr(m::MatrixGroupElement{N,T}) where {N,T}
|
||||
if isone(word(m))
|
||||
return StaticArrays.SMatrix{N, N, T}(LinearAlgebra.I)
|
||||
return StaticArrays.SMatrix{N,N,T}(LinearAlgebra.I)
|
||||
end
|
||||
A = alphabet(parent(m))
|
||||
return prod(matrix_repr(A[l]) for l in word(m))
|
||||
@ -33,7 +33,7 @@ end
|
||||
function Base.rand(
|
||||
rng::Random.AbstractRNG,
|
||||
rs::Random.SamplerTrivial{<:MatrixGroup},
|
||||
)
|
||||
)
|
||||
Mgroup = rs[]
|
||||
S = gens(Mgroup)
|
||||
return prod(g -> rand(Bool) ? g : inv(g), rand(S, rand(1:30)))
|
||||
|
||||
@ -1,9 +1,9 @@
|
||||
struct ElementaryMatrix{N, T} <: Groups.GSymbol
|
||||
struct ElementaryMatrix{N,T} <: Groups.GSymbol
|
||||
i::Int
|
||||
j::Int
|
||||
val::T
|
||||
ElementaryMatrix{N}(i, j, val=1) where N =
|
||||
(@assert i≠j; new{N, typeof(val)}(i, j, val))
|
||||
ElementaryMatrix{N}(i, j, val=1) where {N} =
|
||||
(@assert i ≠ j; new{N,typeof(val)}(i, j, val))
|
||||
end
|
||||
|
||||
function Base.show(io::IO, e::ElementaryMatrix)
|
||||
@ -11,18 +11,18 @@ function Base.show(io::IO, e::ElementaryMatrix)
|
||||
!isone(e.val) && print(io, "^$(e.val)")
|
||||
end
|
||||
|
||||
Base.:(==)(e::ElementaryMatrix{N}, f::ElementaryMatrix{N}) where N =
|
||||
Base.:(==)(e::ElementaryMatrix{N}, f::ElementaryMatrix{N}) where {N} =
|
||||
e.i == f.i && e.j == f.j && e.val == f.val
|
||||
|
||||
Base.hash(e::ElementaryMatrix, h::UInt) =
|
||||
hash(typeof(e), hash((e.i, e.j, e.val), h))
|
||||
|
||||
Base.inv(e::ElementaryMatrix{N}) where N =
|
||||
Base.inv(e::ElementaryMatrix{N}) where {N} =
|
||||
ElementaryMatrix{N}(e.i, e.j, -e.val)
|
||||
|
||||
function matrix_repr(e::ElementaryMatrix{N, T}) where {N, T}
|
||||
m = StaticArrays.MMatrix{N, N, T}(LinearAlgebra.I)
|
||||
function matrix_repr(e::ElementaryMatrix{N,T}) where {N,T}
|
||||
m = StaticArrays.MMatrix{N,N,T}(LinearAlgebra.I)
|
||||
m[e.i, e.j] = e.val
|
||||
x = StaticArrays.SMatrix{N, N}(m)
|
||||
x = StaticArrays.SMatrix{N,N}(m)
|
||||
return x
|
||||
end
|
||||
|
||||
@ -1,18 +1,18 @@
|
||||
struct ElementarySymplectic{N, T} <: Groups.GSymbol
|
||||
struct ElementarySymplectic{N,T} <: Groups.GSymbol
|
||||
symbol::Symbol
|
||||
i::Int
|
||||
j::Int
|
||||
val::T
|
||||
function ElementarySymplectic{N}(s::Symbol, i::Integer, j::Integer, val=1) where N
|
||||
function ElementarySymplectic{N}(s::Symbol, i::Integer, j::Integer, val=1) where {N}
|
||||
@assert s ∈ (:A, :B)
|
||||
@assert iseven(N)
|
||||
n = N÷2
|
||||
n = N ÷ 2
|
||||
if s === :A
|
||||
@assert 1 ≤ i ≤ n && 1 ≤ j ≤ n && i ≠ j
|
||||
elseif s === :B
|
||||
@assert xor(1 ≤ i ≤ n, 1 ≤ j ≤ n) && xor(n < i ≤ N, n < j ≤ N)
|
||||
end
|
||||
return new{N, typeof(val)}(s, i, j, val)
|
||||
return new{N,typeof(val)}(s, i, j, val)
|
||||
end
|
||||
end
|
||||
|
||||
@ -22,12 +22,12 @@ function Base.show(io::IO, s::ElementarySymplectic)
|
||||
!isone(s.val) && print(io, "^$(s.val)")
|
||||
end
|
||||
|
||||
_ind(s::ElementarySymplectic{N}) where N = (s.i, s.j)
|
||||
_local_ind(N_half::Integer, i::Integer) = ifelse(i<=N_half, i, i-N_half)
|
||||
function _dual_ind(s::ElementarySymplectic{N}) where N
|
||||
_ind(s::ElementarySymplectic{N}) where {N} = (s.i, s.j)
|
||||
_local_ind(N_half::Integer, i::Integer) = ifelse(i <= N_half, i, i - N_half)
|
||||
function _dual_ind(s::ElementarySymplectic{N}) where {N}
|
||||
if s.symbol === :A && return _ind(s)
|
||||
else#if s.symbol === :B
|
||||
return _dual_ind(N÷2, s.i, s.j)
|
||||
return _dual_ind(N ÷ 2, s.i, s.j)
|
||||
end
|
||||
end
|
||||
|
||||
@ -41,7 +41,7 @@ function _dual_ind(N_half, i, j)
|
||||
return i, j
|
||||
end
|
||||
|
||||
function Base.:(==)(s::ElementarySymplectic{N}, t::ElementarySymplectic{M}) where {N, M}
|
||||
function Base.:(==)(s::ElementarySymplectic{N}, t::ElementarySymplectic{M}) where {N,M}
|
||||
N == M || return false
|
||||
s.symbol == t.symbol || return false
|
||||
s.val == t.val || return false
|
||||
@ -51,18 +51,18 @@ end
|
||||
Base.hash(s::ElementarySymplectic, h::UInt) =
|
||||
hash(Set([_ind(s); _dual_ind(s)]), hash(s.symbol, hash(s.val, h)))
|
||||
|
||||
LinearAlgebra.transpose(s::ElementarySymplectic{N}) where N =
|
||||
LinearAlgebra.transpose(s::ElementarySymplectic{N}) where {N} =
|
||||
ElementarySymplectic{N}(s.symbol, s.j, s.i, s.val)
|
||||
|
||||
Base.inv(s::ElementarySymplectic{N}) where N =
|
||||
Base.inv(s::ElementarySymplectic{N}) where {N} =
|
||||
ElementarySymplectic{N}(s.symbol, s.i, s.j, -s.val)
|
||||
|
||||
function matrix_repr(s::ElementarySymplectic{N, T}) where {N, T}
|
||||
function matrix_repr(s::ElementarySymplectic{N,T}) where {N,T}
|
||||
@assert iseven(N)
|
||||
n = div(N, 2)
|
||||
m = StaticArrays.MMatrix{N, N, T}(LinearAlgebra.I)
|
||||
i,j = _ind(s)
|
||||
m[i,j] = s.val
|
||||
m = StaticArrays.MMatrix{N,N,T}(LinearAlgebra.I)
|
||||
i, j = _ind(s)
|
||||
m[i, j] = s.val
|
||||
if s.symbol === :A
|
||||
m[n+j, n+i] = -s.val
|
||||
else#if s.symbol === :B
|
||||
@ -72,5 +72,5 @@ function matrix_repr(s::ElementarySymplectic{N, T}) where {N, T}
|
||||
m[j-n, i+n] = s.val
|
||||
end
|
||||
end
|
||||
return StaticArrays.SMatrix{N, N}(m)
|
||||
return StaticArrays.SMatrix{N,N}(m)
|
||||
end
|
||||
|
||||
@ -96,7 +96,7 @@ mutable struct FPGroupElement{Gr<:AbstractFPGroup,W<:AbstractWord} <:
|
||||
FPGroupElement(
|
||||
word::W,
|
||||
G::AbstractFPGroup,
|
||||
hash::UInt = UInt(0),
|
||||
hash::UInt=UInt(0),
|
||||
) where {W<:AbstractWord} = new{typeof(G),W}(word, hash, G)
|
||||
|
||||
FPGroupElement{Gr,W}(word::AbstractWord, G::Gr) where {Gr,W} =
|
||||
@ -222,8 +222,8 @@ rewriting(G::FPGroup) = G.rw
|
||||
function FPGroup(
|
||||
G::AbstractFPGroup,
|
||||
rels::AbstractVector{<:Pair{GEl,GEl}};
|
||||
ordering = KnuthBendix.ordering(G),
|
||||
kwargs...,
|
||||
ordering=KnuthBendix.ordering(G),
|
||||
kwargs...
|
||||
) where {GEl<:FPGroupElement}
|
||||
for (lhs, rhs) in rels
|
||||
@assert parent(lhs) === parent(rhs) === G
|
||||
|
||||
@ -1,20 +1,31 @@
|
||||
"""
|
||||
wlmetric_ball(S::AbstractVector{<:GroupElem}
|
||||
[, center=one(first(S)); radius=2, op=*])
|
||||
[, center=one(first(S)); radius=2, op=*, threading=true])
|
||||
Compute metric ball as a list of elements of non-decreasing length, given the
|
||||
word-length metric on the group generated by `S`. The ball is centered at `center`
|
||||
(by default: the identity element). `radius` and `op` keywords specify the
|
||||
radius and multiplication operation to be used.
|
||||
"""
|
||||
function wlmetric_ball_serial(S::AbstractVector{T}, center::T=one(first(S)); radius = 2, op = *) where {T}
|
||||
function wlmetric_ball(
|
||||
S::AbstractVector{T},
|
||||
center::T=one(first(S));
|
||||
radius=2,
|
||||
op=*,
|
||||
threading=true
|
||||
) where {T}
|
||||
threading && return wlmetric_ball_thr(S, center, radius=radius, op=op)
|
||||
return wlmetric_ball_serial(S, center, radius=radius, op=op)
|
||||
end
|
||||
|
||||
function wlmetric_ball_serial(S::AbstractVector{T}, center::T=one(first(S)); radius=2, op=*) where {T}
|
||||
@assert radius >= 1
|
||||
old = union!([center], [center*s for s in S])
|
||||
old = union!([center], [center * s for s in S])
|
||||
return _wlmetric_ball(S, old, radius, op, collect, unique!)
|
||||
end
|
||||
|
||||
function wlmetric_ball_thr(S::AbstractVector{T}, center::T=one(first(S)); radius = 2, op = *) where {T}
|
||||
function wlmetric_ball_thr(S::AbstractVector{T}, center::T=one(first(S)); radius=2, op=*) where {T}
|
||||
@assert radius >= 1
|
||||
old = union!([center], [center*s for s in S])
|
||||
old = union!([center], [center * s for s in S])
|
||||
return _wlmetric_ball(S, old, radius, op, Folds.collect, Folds.unique)
|
||||
end
|
||||
|
||||
@ -26,6 +37,7 @@ function _wlmetric_ball(S, old, radius, op, collect, unique)
|
||||
(g = op(o, s); hash(g); g)
|
||||
for o in @view(old[sizes[end-1]:end]) for s in S
|
||||
)
|
||||
|
||||
append!(old, new)
|
||||
unique(old)
|
||||
end
|
||||
@ -34,13 +46,3 @@ function _wlmetric_ball(S, old, radius, op, collect, unique)
|
||||
return old, sizes[2:end]
|
||||
end
|
||||
|
||||
function wlmetric_ball(
|
||||
S::AbstractVector{T},
|
||||
center::T = one(first(S));
|
||||
radius = 2,
|
||||
op = *,
|
||||
threading = true,
|
||||
) where {T}
|
||||
threading && return wlmetric_ball_thr(S, center, radius = radius, op = op)
|
||||
return wlmetric_ball_serial(S, center, radius = radius, op = op)
|
||||
end
|
||||
|
||||
102
test/AutFn.jl
102
test/AutFn.jl
@ -29,54 +29,54 @@
|
||||
end
|
||||
|
||||
A4 = Alphabet(
|
||||
[:a,:A,:b,:B,:c,:C,:d,:D],
|
||||
[ 2, 1, 4, 3, 6, 5, 8, 7]
|
||||
[:a, :A, :b, :B, :c, :C, :d, :D],
|
||||
[2, 1, 4, 3, 6, 5, 8, 7]
|
||||
)
|
||||
|
||||
A5 = Alphabet(
|
||||
[:a,:A,:b,:B,:c,:C,:d,:D,:e,:E],
|
||||
[ 2, 1, 4, 3, 6, 5, 8, 7,10, 9]
|
||||
[:a, :A, :b, :B, :c, :C, :d, :D, :e, :E],
|
||||
[2, 1, 4, 3, 6, 5, 8, 7, 10, 9]
|
||||
)
|
||||
|
||||
F4 = FreeGroup([:a, :b, :c, :d], A4)
|
||||
a,b,c,d = gens(F4)
|
||||
D = ntuple(i->gens(F4, i), 4)
|
||||
a, b, c, d = gens(F4)
|
||||
D = ntuple(i -> gens(F4, i), 4)
|
||||
|
||||
@testset "Transvection action correctness" begin
|
||||
i,j = 1,2
|
||||
r = Groups.Transvection(:ϱ,i,j)
|
||||
l = Groups.Transvection(:λ,i,j)
|
||||
i, j = 1, 2
|
||||
r = Groups.Transvection(:ϱ, i, j)
|
||||
l = Groups.Transvection(:λ, i, j)
|
||||
|
||||
(t::Groups.Transvection)(v::Tuple) = Groups.evaluate!(v, t)
|
||||
|
||||
@test r(deepcopy(D)) == (a*b, b, c, d)
|
||||
@test inv(r)(deepcopy(D)) == (a*b^-1,b, c, d)
|
||||
@test l(deepcopy(D)) == (b*a, b, c, d)
|
||||
@test inv(l)(deepcopy(D)) == (b^-1*a,b, c, d)
|
||||
@test r(deepcopy(D)) == (a * b, b, c, d)
|
||||
@test inv(r)(deepcopy(D)) == (a * b^-1, b, c, d)
|
||||
@test l(deepcopy(D)) == (b * a, b, c, d)
|
||||
@test inv(l)(deepcopy(D)) == (b^-1 * a, b, c, d)
|
||||
|
||||
i,j = 3,1
|
||||
r = Groups.Transvection(:ϱ,i,j)
|
||||
l = Groups.Transvection(:λ,i,j)
|
||||
@test r(deepcopy(D)) == (a, b, c*a, d)
|
||||
@test inv(r)(deepcopy(D)) == (a, b, c*a^-1,d)
|
||||
@test l(deepcopy(D)) == (a, b, a*c, d)
|
||||
@test inv(l)(deepcopy(D)) == (a, b, a^-1*c,d)
|
||||
i, j = 3, 1
|
||||
r = Groups.Transvection(:ϱ, i, j)
|
||||
l = Groups.Transvection(:λ, i, j)
|
||||
@test r(deepcopy(D)) == (a, b, c * a, d)
|
||||
@test inv(r)(deepcopy(D)) == (a, b, c * a^-1, d)
|
||||
@test l(deepcopy(D)) == (a, b, a * c, d)
|
||||
@test inv(l)(deepcopy(D)) == (a, b, a^-1 * c, d)
|
||||
|
||||
i,j = 4,3
|
||||
r = Groups.Transvection(:ϱ,i,j)
|
||||
l = Groups.Transvection(:λ,i,j)
|
||||
@test r(deepcopy(D)) == (a, b, c, d*c)
|
||||
@test inv(r)(deepcopy(D)) == (a, b, c, d*c^-1)
|
||||
@test l(deepcopy(D)) == (a, b, c, c*d)
|
||||
@test inv(l)(deepcopy(D)) == (a, b, c, c^-1*d)
|
||||
i, j = 4, 3
|
||||
r = Groups.Transvection(:ϱ, i, j)
|
||||
l = Groups.Transvection(:λ, i, j)
|
||||
@test r(deepcopy(D)) == (a, b, c, d * c)
|
||||
@test inv(r)(deepcopy(D)) == (a, b, c, d * c^-1)
|
||||
@test l(deepcopy(D)) == (a, b, c, c * d)
|
||||
@test inv(l)(deepcopy(D)) == (a, b, c, c^-1 * d)
|
||||
|
||||
i,j = 2,4
|
||||
r = Groups.Transvection(:ϱ,i,j)
|
||||
l = Groups.Transvection(:λ,i,j)
|
||||
@test r(deepcopy(D)) == (a, b*d, c, d)
|
||||
@test inv(r)(deepcopy(D)) == (a, b*d^-1,c, d)
|
||||
@test l(deepcopy(D)) == (a, d*b, c, d)
|
||||
@test inv(l)(deepcopy(D)) == (a, d^-1*b,c, d)
|
||||
i, j = 2, 4
|
||||
r = Groups.Transvection(:ϱ, i, j)
|
||||
l = Groups.Transvection(:λ, i, j)
|
||||
@test r(deepcopy(D)) == (a, b * d, c, d)
|
||||
@test inv(r)(deepcopy(D)) == (a, b * d^-1, c, d)
|
||||
@test l(deepcopy(D)) == (a, d * b, c, d)
|
||||
@test inv(l)(deepcopy(D)) == (a, d^-1 * b, c, d)
|
||||
end
|
||||
|
||||
A = SpecialAutomorphismGroup(F4, max_rules=1000)
|
||||
@ -91,33 +91,33 @@
|
||||
|
||||
@testset "Automorphisms: hash and evaluate" begin
|
||||
@test Groups.domain(gens(A, 1)) == D
|
||||
g, h = gens(A, 1), gens(A, 8)
|
||||
g, h = gens(A, 1), gens(A, 8) # (ϱ₁.₂, ϱ₃.₂)
|
||||
|
||||
@test evaluate(g*h) == evaluate(h*g)
|
||||
@test (g*h).savedhash == zero(UInt)
|
||||
@test evaluate(g * h) == evaluate(h * g)
|
||||
@test (g * h).savedhash == zero(UInt)
|
||||
|
||||
@test sprint(show, typeof(g)) == "Automorphism{FreeGroup{Symbol, KnuthBendix.LenLex{Symbol}}, …}"
|
||||
@test contains(sprint(show, typeof(g)), "Automorphism{FreeGroup{Symbol")
|
||||
|
||||
a = g*h
|
||||
b = h*g
|
||||
a = g * h
|
||||
b = h * g
|
||||
@test hash(a) != zero(UInt)
|
||||
@test hash(a) == hash(b)
|
||||
@test a.savedhash == b.savedhash
|
||||
|
||||
@test length(unique([a,b])) == 1
|
||||
@test length(unique([g*h, h*g])) == 1
|
||||
@test length(unique([a, b])) == 1
|
||||
@test length(unique([g * h, h * g])) == 1
|
||||
|
||||
# Not so simple arithmetic: applying starting on the left:
|
||||
# ϱ₁₂*ϱ₂₁⁻¹*λ₁₂*ε₂ == σ₂₁₃₄
|
||||
|
||||
g = gens(A, 1)
|
||||
x1, x2, x3, x4 = Groups.domain(g)
|
||||
@test evaluate(g) == (x1*x2, x2, x3, x4)
|
||||
@test evaluate(g) == (x1 * x2, x2, x3, x4)
|
||||
|
||||
g = g*inv(gens(A, 4)) # ϱ₂₁
|
||||
@test evaluate(g) == (x1*x2, x1^-1, x3, x4)
|
||||
g = g * inv(gens(A, 4)) # ϱ₂₁
|
||||
@test evaluate(g) == (x1 * x2, x1^-1, x3, x4)
|
||||
|
||||
g = g*gens(A, 13)
|
||||
g = g * gens(A, 13)
|
||||
@test evaluate(g) == (x2, x1^-1, x3, x4)
|
||||
end
|
||||
|
||||
@ -128,7 +128,7 @@
|
||||
S = gens(G)
|
||||
@test S isa Vector{<:FPGroupElement{<:AutomorphismGroup{<:FreeGroup}}}
|
||||
|
||||
@test length(S) == 2*N*(N-1)
|
||||
@test length(S) == 2 * N * (N - 1)
|
||||
@test length(unique(S)) == length(S)
|
||||
|
||||
S_sym = [S; inv.(S)]
|
||||
@ -136,12 +136,12 @@
|
||||
|
||||
pushfirst!(S_sym, one(G))
|
||||
|
||||
B_2 = [i*j for (i,j) in Base.product(S_sym, S_sym)]
|
||||
B_2 = [i * j for (i, j) in Base.product(S_sym, S_sym)]
|
||||
@test length(B_2) == 2401
|
||||
@test length(unique(B_2)) == 1777
|
||||
|
||||
@test all(g->isone(inv(g)*g), B_2)
|
||||
@test all(g->isone(g*inv(g)), B_2)
|
||||
@test all(g -> isone(inv(g) * g), B_2)
|
||||
@test all(g -> isone(g * inv(g)), B_2)
|
||||
end
|
||||
|
||||
@testset "Forward evaluate" begin
|
||||
@ -153,7 +153,7 @@
|
||||
|
||||
f = gens(F)
|
||||
|
||||
@test a(f[1]) == f[1]*f[2]
|
||||
@test a(f[1]) == f[1] * f[2]
|
||||
@test all(a(f[i]) == f[i] for i in 2:length(f))
|
||||
|
||||
S = let s = gens(G)
|
||||
|
||||
@ -3,6 +3,8 @@
|
||||
|
||||
π₁Σ = Groups.SurfaceGroup(genus, 0)
|
||||
|
||||
@test contains(sprint(print, π₁Σ), "surface")
|
||||
|
||||
Groups.PermRightAut(p::Perm) = Groups.PermRightAut(p.d)
|
||||
# Groups.PermLeftAut(p::Perm) = Groups.PermLeftAut(p.d)
|
||||
autπ₁Σ = let autπ₁Σ = AutomorphismGroup(π₁Σ)
|
||||
@ -18,7 +20,7 @@
|
||||
π₁Σ,
|
||||
autπ₁Σ.gens,
|
||||
A,
|
||||
ntuple(i->inv(gens(π₁Σ, i)), 2Groups.genus(π₁Σ))
|
||||
ntuple(i -> inv(gens(π₁Σ, i)), 2Groups.genus(π₁Σ))
|
||||
)
|
||||
|
||||
autG
|
||||
@ -36,7 +38,7 @@
|
||||
λ = Groups.ΡΛ(:λ, A, 2genus)
|
||||
ϱ = Groups.ΡΛ(:ϱ, A, 2genus)
|
||||
@test sautFn(Groups.Te_diagonal(λ, ϱ, 1)) ==
|
||||
conj(sautFn(Groups.Te_diagonal(λ, ϱ, 2)), τ)
|
||||
conj(sautFn(Groups.Te_diagonal(λ, ϱ, 2)), τ)
|
||||
|
||||
@test sautFn(Groups.Te_diagonal(λ, ϱ, 3)) == sautFn(Groups.Te(λ, ϱ, 3, 1))
|
||||
end
|
||||
|
||||
@ -1,5 +1,5 @@
|
||||
@testset "FPGroups" begin
|
||||
A = Alphabet([:a, :A, :b, :B, :c, :C], [2,1,4,3,6,5])
|
||||
A = Alphabet([:a, :A, :b, :B, :c, :C], [2, 1, 4, 3, 6, 5])
|
||||
|
||||
@test FreeGroup(A) isa FreeGroup
|
||||
@test sprint(show, FreeGroup(A)) == "free group on 3 generators"
|
||||
@ -7,26 +7,26 @@
|
||||
F = FreeGroup([:a, :b, :c], A)
|
||||
@test sprint(show, F) == "free group on 3 generators"
|
||||
|
||||
a,b,c = gens(F)
|
||||
@test c*b*a isa FPGroupElement
|
||||
a, b, c = gens(F)
|
||||
@test c * b * a isa FPGroupElement
|
||||
|
||||
# quotient of F:
|
||||
G = FPGroup(F, [a*b=>b*a, a*c=>c*a, b*c=>c*b])
|
||||
G = FPGroup(F, [a * b => b * a, a * c => c * a, b * c => c * b])
|
||||
|
||||
@test G isa FPGroup
|
||||
@test sprint(show, G) == "⟨ a b c | \n\t a*b => b*a a*c => c*a b*c => c*b ⟩"
|
||||
@test rand(G) isa FPGroupElement
|
||||
|
||||
f = a*c*b
|
||||
f = a * c * b
|
||||
@test word(f) isa Word{UInt8}
|
||||
|
||||
aG,bG,cG = gens(G)
|
||||
aG, bG, cG = gens(G)
|
||||
|
||||
@test aG isa FPGroupElement
|
||||
@test_throws AssertionError aG == a
|
||||
@test word(aG) == word(a)
|
||||
|
||||
g = aG*cG*bG
|
||||
g = aG * cG * bG
|
||||
|
||||
@test_throws AssertionError f == g
|
||||
@test word(f) == word(g)
|
||||
@ -34,7 +34,7 @@
|
||||
Groups.normalform!(g)
|
||||
@test word(g) == [1, 3, 5]
|
||||
|
||||
let g = aG*cG*bG
|
||||
let g = aG * cG * bG
|
||||
# test that we normalize g before printing
|
||||
@test sprint(show, g) == "a*b*c"
|
||||
end
|
||||
@ -46,7 +46,7 @@
|
||||
|
||||
@test h isa FPGroupElement
|
||||
@test_throws AssertionError h == g
|
||||
@test_throws MethodError h*g
|
||||
@test_throws MethodError h * g
|
||||
|
||||
H′ = FPGroup(G, [aG^2 => cG, bG * cG => aG], max_rules=200)
|
||||
@test_throws AssertionError one(H) == one(H′)
|
||||
|
||||
@ -4,23 +4,25 @@ using Groups.MatrixGroups
|
||||
@testset "SL(n, ℤ)" begin
|
||||
SL3Z = SpecialLinearGroup{3}(Int8)
|
||||
|
||||
S = gens(SL3Z); union!(S, inv.(S))
|
||||
S = gens(SL3Z)
|
||||
union!(S, inv.(S))
|
||||
|
||||
E, sizes = Groups.wlmetric_ball(S, radius=4)
|
||||
_, sizes = Groups.wlmetric_ball(S, radius=4)
|
||||
|
||||
@test sizes == [13, 121, 883, 5455]
|
||||
|
||||
E(i,j) = SL3Z([A[MatrixGroups.ElementaryMatrix{3}(i,j, Int8(1))]])
|
||||
E(i, j) = SL3Z([A[MatrixGroups.ElementaryMatrix{3}(i, j, Int8(1))]])
|
||||
|
||||
A = alphabet(SL3Z)
|
||||
w = E(1,2)
|
||||
r = E(2,3)^-3
|
||||
s = E(1,3)^2*E(3,2)^-1
|
||||
w = E(1, 2)
|
||||
r = E(2, 3)^-3
|
||||
s = E(1, 3)^2 * E(3, 2)^-1
|
||||
|
||||
S = [w,r,s]; S = unique([S; inv.(S)]);
|
||||
_, sizes = Groups.wlmetric_ball(S, radius=4);
|
||||
S = [w, r, s]
|
||||
S = unique([S; inv.(S)])
|
||||
_, sizes = Groups.wlmetric_ball(S, radius=4)
|
||||
@test sizes == [7, 33, 141, 561]
|
||||
_, sizes = Groups.wlmetric_ball_serial(S, radius=4);
|
||||
_, sizes = Groups.wlmetric_ball_serial(S, radius=4)
|
||||
@test sizes == [7, 33, 141, 561]
|
||||
|
||||
Logging.with_logger(Logging.NullLogger()) do
|
||||
@ -34,10 +36,10 @@ using Groups.MatrixGroups
|
||||
end
|
||||
|
||||
|
||||
x = w*inv(w)*r
|
||||
x = w * inv(w) * r
|
||||
|
||||
@test length(word(x)) == 5
|
||||
@test size(x) == (3,3)
|
||||
@test size(x) == (3, 3)
|
||||
@test eltype(x) == Int8
|
||||
|
||||
@test contains(sprint(print, SL3Z), "special linear group of 3×3")
|
||||
@ -50,12 +52,14 @@ using Groups.MatrixGroups
|
||||
@testset "Sp(6, ℤ)" begin
|
||||
Sp6 = MatrixGroups.SymplecticGroup{6}(Int8)
|
||||
|
||||
@testset "GroupsCore conformance" begin
|
||||
test_Group_interface(Sp6)
|
||||
g = Sp6(rand(1:length(alphabet(Sp6)), 10))
|
||||
h = Sp6(rand(1:length(alphabet(Sp6)), 10))
|
||||
Logging.with_logger(Logging.NullLogger()) do
|
||||
@testset "GroupsCore conformance" begin
|
||||
test_Group_interface(Sp6)
|
||||
g = Sp6(rand(1:length(alphabet(Sp6)), 10))
|
||||
h = Sp6(rand(1:length(alphabet(Sp6)), 10))
|
||||
|
||||
test_GroupElement_interface(g, h)
|
||||
test_GroupElement_interface(g, h)
|
||||
end
|
||||
end
|
||||
|
||||
@test contains(sprint(print, Sp6), "group of 6×6 symplectic matrices")
|
||||
@ -64,7 +68,7 @@ using Groups.MatrixGroups
|
||||
x *= inv(x) * gens(Sp6, 2)
|
||||
|
||||
@test length(word(x)) == 3
|
||||
@test size(x) == (6,6)
|
||||
@test size(x) == (6, 6)
|
||||
@test eltype(x) == Int8
|
||||
|
||||
@test contains(sprint(show, MIME"text/plain"(), x), "6×6 symplectic matrix:")
|
||||
|
||||
Loading…
Reference in New Issue
Block a user