replace inv(A::Alphabet, ...) → inv(..., A)
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@ -96,7 +96,7 @@ function gersten_relations(::Type{W}, n::Integer; commutative) where {W<:Abstrac
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if i ≠ j
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push!(rels, _hexagonal_rule(W, A, ϱ(i, j), ϱ(j, i), λ(i, j), λ(j, i)))
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w = W([A[ϱ(i, j)], A[ϱ(j, i)^-1], A[λ(i, j)]])
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push!(rels, w^2 => inv(A, w)^2)
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push!(rels, w^2 => inv(w, A)^2)
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end
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end
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end
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@ -25,7 +25,7 @@ function Te_diagonal(λ::Groups.ΡΛ, ϱ::Groups.ΡΛ, i::Integer)
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if i == n
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τ = rotation_element(λ, ϱ)
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return inv(A, τ) * Te_diagonal(λ, ϱ, 1) * τ
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return inv(τ, A) * Te_diagonal(λ, ϱ, 1) * τ
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end
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@assert 1 <= i < n
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@ -37,32 +37,32 @@ function Te_diagonal(λ::Groups.ΡΛ, ϱ::Groups.ΡΛ, i::Integer)
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g = one(Word(Int[]))
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g *= λ[NJ, NI] # β ↦ α*β
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g *= λ[NI, I] * inv(A, ϱ[NI, J]) # α ↦ a*α*b^-1
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g *= inv(A, λ[NJ, NI]) # β ↦ b*α^-1*a^-1*α*β
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g *= λ[J, NI] * inv(A, λ[J, I]) # b ↦ α
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g *= inv(A, λ[J, NI]) # b ↦ b*α^-1*a^-1*α
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g *= inv(A, ϱ[J, NI]) * ϱ[J, I] # b ↦ b*α^-1*a^-1*α*b*α^-1
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g *= λ[NI, I] * inv(ϱ[NI, J], A) # α ↦ a*α*b^-1
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g *= inv(λ[NJ, NI], A) # β ↦ b*α^-1*a^-1*α*β
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g *= λ[J, NI] * inv(λ[J, I], A) # b ↦ α
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g *= inv(λ[J, NI], A) # b ↦ b*α^-1*a^-1*α
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g *= inv(ϱ[J, NI], A) * ϱ[J, I] # b ↦ b*α^-1*a^-1*α*b*α^-1
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g *= ϱ[J, NI] # b ↦ b*α^-1*a^-1*α*b*α^-1*a*α*b^-1
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return g
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end
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function Te_lantern(A::Alphabet, b₀::T, a₁::T, a₂::T, a₃::T, a₄::T, a₅::T) where {T}
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a₀ = (a₁ * a₂ * a₃)^4 * inv(A, b₀)
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a₀ = (a₁ * a₂ * a₃)^4 * inv(b₀, A)
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X = a₄ * a₅ * a₃ * a₄ # from Primer
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b₁ = inv(A, X) * a₀ * X # from Primer
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b₁ = inv(X, A) * a₀ * X # from Primer
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Y = a₂ * a₃ * a₁ * a₂
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return inv(A, Y) * b₁ * Y # b₂ from Primer
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return inv(Y, A) * b₁ * Y # b₂ from Primer
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end
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function Ta(λ::Groups.ΡΛ, i::Integer)
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@assert λ.id == :λ;
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return λ[mod1(λ.N-2i+1, λ.N), mod1(λ.N-2i+2, λ.N)]
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@assert λ.id == :λ
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return λ[mod1(λ.N - 2i + 1, λ.N), mod1(λ.N - 2i + 2, λ.N)]
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end
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function Tα(λ::Groups.ΡΛ, i::Integer)
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@assert λ.id == :λ;
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return inv(λ.A, λ[mod1(λ.N-2i+2, λ.N), mod1(λ.N-2i+1, λ.N)])
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@assert λ.id == :λ
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return inv(λ[mod1(λ.N - 2i + 2, λ.N), mod1(λ.N - 2i + 1, λ.N)], λ.A)
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end
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function Te(λ::ΡΛ, ϱ::ΡΛ, i, j)
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@ -85,16 +85,16 @@ function Te(λ::ΡΛ, ϱ::ΡΛ, i, j)
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if mod(j - (i + 1), genus) == 0
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return Te_diagonal(λ, ϱ, i)
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else
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return inv(A, Te_lantern(
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A,
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# Our notation: # Primer notation:
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inv(A, Ta(λ, i + 1)), # b₀
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inv(A, Ta(λ, i)), # a₁
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inv(A, Tα(λ, i)), # a₂
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inv(A, Te_diagonal(λ, ϱ, i)), # a₃
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inv(A, Tα(λ, i + 1)), # a₄
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inv(A, Te(λ, ϱ, i + 1, j)), # a₅
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))
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return inv(Te_lantern(
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A,
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# Our notation: # Primer notation:
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inv(Ta(λ, i + 1), A), # b₀
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inv(Ta(λ, i), A), # a₁
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inv(Tα(λ, i), A), # a₂
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inv(Te_diagonal(λ, ϱ, i), A), # a₃
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inv(Tα(λ, i + 1), A), # a₄
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inv(Te(λ, ϱ, i + 1, j), A), # a₅
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), A)
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end
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end
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@ -123,24 +123,24 @@ function rotation_element(λ::ΡΛ, ϱ::ΡΛ)
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halftwists = map(1:genus-1) do i
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j = i + 1
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x = Ta(λ, j) * inv(A, Ta(λ, i)) * Tα(λ, j) * Te_diagonal(λ, ϱ, i)
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δ = x * Tα(λ, i) * inv(A, x)
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x = Ta(λ, j) * inv(Ta(λ, i), A) * Tα(λ, j) * Te_diagonal(λ, ϱ, i)
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δ = x * Tα(λ, i) * inv(x, A)
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c =
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inv(A, Ta(λ, j)) *
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inv(Ta(λ, j), A) *
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Te(λ, ϱ, i, j) *
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Tα(λ, i)^2 *
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inv(A, δ) *
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inv(A, Ta(λ, j)) *
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inv(δ, A) *
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inv(Ta(λ, j), A) *
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Ta(λ, i) *
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δ
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z =
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Te_diagonal(λ, ϱ, i) *
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inv(A, Ta(λ, i)) *
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inv(Ta(λ, i), A) *
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Tα(λ, i) *
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Ta(λ, i) *
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inv(A, Te_diagonal(λ, ϱ, i))
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inv(Te_diagonal(λ, ϱ, i), A)
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Ta(λ, i) * inv(A, Ta(λ, j) * Tα(λ, j))^6 * (Ta(λ, j) * Tα(λ, j) * z)^4 * c
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Ta(λ, i) * inv(Ta(λ, j) * Tα(λ, j), A)^6 * (Ta(λ, j) * Tα(λ, j) * z)^4 * c
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end
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τ = (Ta(λ, 1) * Tα(λ, 1))^6 * prod(halftwists)
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@ -201,24 +201,24 @@ function SymplecticMappingClass(
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w = if id === :A
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Te(λ, ϱ, i, j) *
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inv(A, Ta(λ, i)) *
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inv(Ta(λ, i), A) *
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Tα(λ, i) *
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Ta(λ, i) *
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inv(A, Te(λ, ϱ, i, j)) *
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inv(A, Tα(λ, i)) *
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inv(A, Ta(λ, j))
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inv(Te(λ, ϱ, i, j), A) *
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inv(Tα(λ, i), A) *
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inv(Ta(λ, j), A)
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elseif id === :B
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if !minus
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if i ≠ j
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x = Ta(λ, j) * inv(A, Ta(λ, i)) * Tα(λ, j) * Te(λ, ϱ, i, j)
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δ = x * Tα(λ, i) * inv(A, x)
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Tα(λ, i) * Tα(λ, j) * inv(A, δ)
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x = Ta(λ, j) * inv(Ta(λ, i), A) * Tα(λ, j) * Te(λ, ϱ, i, j)
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δ = x * Tα(λ, i) * inv(x, A)
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Tα(λ, i) * Tα(λ, j) * inv(δ, A)
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else
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inv(A, Tα(λ, i))
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inv(Tα(λ, i), A)
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end
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else
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if i ≠ j
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Ta(λ, i) * Ta(λ, j) * inv(A, Te(λ, ϱ, i, j))
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Ta(λ, i) * Ta(λ, j) * inv(Te(λ, ϱ, i, j), A)
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else
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Ta(λ, i)
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end
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@ -45,9 +45,9 @@ Base.@propagate_inbounds @inline function evaluate!(
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if !t.inv
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append!(word(v[i]), word(v[j]))
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else
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# append!(word(v[i]), inv(A, word(v[j])))
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# append!(word(v[i]), inv(word(v[j]), A))
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for l in Iterators.reverse(word(v[j]))
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push!(word(v[i]), inv(A, l))
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push!(word(v[i]), inv(l, A))
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end
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end
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else # if t.id === :λ
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@ -57,9 +57,9 @@ Base.@propagate_inbounds @inline function evaluate!(
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pushfirst!(word(v[i]), l)
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end
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else
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# prepend!(word(v[i]), inv(A, word(v[j])))
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# prepend!(word(v[i]), inv(word(v[j]), A))
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for l in word(v[j])
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pushfirst!(word(v[i]), inv(A, l))
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pushfirst!(word(v[i]), inv(l, A))
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end
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end
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end
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@ -147,8 +147,8 @@ function Base.getindex(lm::LettersMap, i::Integer)
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@boundscheck 1 ≤ i ≤ length(lm.A)
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if !haskey(lm.indices_map, i)
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img = if haskey(lm.indices_map, inv(lm.A, i))
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inv(lm.A, lm.indices_map[inv(lm.A, i)])
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img = if haskey(lm.indices_map, inv(i, lm.A))
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inv(lm.indices_map[inv(i, lm.A)], lm.A)
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else
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@warn "LetterMap: neither $i nor its inverse has assigned value"
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one(valtype(lm.indices_map))
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@ -193,7 +193,7 @@ function generated_evaluate(a::FPGroupElement{<:AutomorphismGroup})
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push!(args[idx].args, :(d[$k]))
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continue
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end
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k = findfirst(==(inv(A, l)), first_ltrs)
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k = findfirst(==(inv(l, A)), first_ltrs)
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if k !== nothing
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push!(args[idx].args, :(inv(d[$k])))
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continue
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@ -88,7 +88,7 @@ struct Homomorphism{Gr1, Gr2, I, W}
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end
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end
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for (lhs, rhs) in relations(source)
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relator = lhs*inv(alphabet(source), rhs)
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relator = lhs * inv(rhs, alphabet(source))
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im_r = hom.target(hom(relator))
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@assert isone(im_r) "Map does not define a homomorphism: h($relator) = $(im_r) ≠ $(one(target))."
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end
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@ -128,7 +128,7 @@ end
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function Base.inv(g::GEl) where {GEl<:AbstractFPGroupElement}
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G = parent(g)
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return GEl(inv(alphabet(G), word(g)), G)
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return GEl(inv(word(g), alphabet(G)), G)
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end
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function Base.:(*)(g::GEl, h::GEl) where {GEl<:AbstractFPGroupElement}
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@ -169,7 +169,7 @@ function FreeGroup(A::Alphabet)
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for l in A
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l ∈ invs && continue
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push!(gens, l)
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push!(invs, inv(A, l))
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push!(invs, inv(l, A))
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end
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return FreeGroup(gens, A)
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