Merge branch 'master' into enh/julia-v0.6
This commit is contained in:
commit
c18e2156b5
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@ -26,7 +26,7 @@ matrix:
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## uncomment the following lines to override the default test script
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script:
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- julia -e 'Pkg.clone("https://github.com/Nemocas/Nemo.jl"); Pkg.build("Nemo")'
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# - julia -e 'Pkg.clone("https://github.com/Nemocas/Nemo.jl"); Pkg.build("Nemo")'
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- julia -e 'Pkg.clone(pwd()); Pkg.build("Groups"); Pkg.test("Groups"; coverage=true)'
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after_success:
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134
src/AutGroup.jl
134
src/AutGroup.jl
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@ -7,8 +7,7 @@
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struct AutSymbol <: GSymbol
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str::String
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pow::Int
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ex::Expr
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func::Function
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typ::Union{RTransvect, LTransvect, FlipAut, PermAut, Identity}
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end
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AutGroupElem = GWord{AutSymbol}
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@ -36,21 +35,23 @@ parent_type(::AutGroupElem) = AutGroup
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#
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###############################################################################
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function ϱ(i,j, pow=1)
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# @assert i ≠ j
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return v -> [(k==i ? v[i]*v[j]^pow : v[k]) for k in eachindex(v)]
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function (ϱ::RTransvect)(v, pow=1::Int)
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return [(k==ϱ.i ? v[ϱ.i]*v[ϱ.j]^pow : v[k]) for k in eachindex(v)]
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end
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function λ(i,j, pow=1)
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# @assert i ≠ j
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return v -> [(k==i ? v[j]^pow*v[i] : v[k]) for k in eachindex(v)]
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function (λ::LTransvect)(v, pow=1::Int)
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return [(k==λ.i ? v[λ.j]^pow*v[λ.i] : v[k]) for k in eachindex(v)]
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end
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function σ(p::Generic.perm, pow=1)
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return v -> [v[(p^pow)[k]] for k in eachindex(v)]
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function (σ::PermAut)(v, pow=1::Int)
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return v[(σ.p^pow).d]
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end
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ɛ(i, pow=1) = v -> [(k==i ? v[k]^(-1*(2+pow%2)%2) : v[k]) for k in eachindex(v)]
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function (ɛ::FlipAut)(v, pow=1::Int)
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return [(k==ɛ.i ? v[k]^(-1^pow) : v[k]) for k in eachindex(v)]
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end
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(::Identity)(v, pow=1::Int) = v
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# taken from ValidatedNumerics, under under the MIT "Expat" License:
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# https://github.com/JuliaIntervals/ValidatedNumerics.jl/blob/master/LICENSE.md
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@ -60,32 +61,36 @@ function subscriptify(n::Int)
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end
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function id_autsymbol()
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return AutSymbol("(id)", 0, :(id()), identity)
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return AutSymbol("(id)", 0, Identity())
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end
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function rmul_autsymbol(i, j; pow::Int=1)
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str = "ϱ"*subscriptify(i)*subscriptify(j)
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return AutSymbol(str, pow, :(ϱ($i, $j, $pow)), ϱ(i, j, pow))
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return AutSymbol(str, pow, RTransvect(i, j))
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end
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function lmul_autsymbol(i, j; pow::Int=1)
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str = "λ"*subscriptify(i)*subscriptify(j)
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return AutSymbol(str, pow, :(λ($i, $j, $pow)), λ(i, j, pow))
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return AutSymbol(str, pow, LTransvect(i, j))
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end
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function flip_autsymbol(i; pow::Int=1)
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str = "ɛ"*subscriptify(i)
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pow = (2+pow%2)%2
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return AutSymbol(str, pow, :(ɛ($i, $pow)), ɛ(i, pow))
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if pow == 0
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return id_autsymbol()
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else
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str = "ɛ"*subscriptify(i)
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return AutSymbol(str, pow, FlipAut(i))
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end
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end
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function perm_autsymbol(p::Generic.perm; pow::Int=1)
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p = p^pow
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if p == parent(p)()
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return id_autsymbol()
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return id_autsymbol()
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else
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p = p^pow
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str = "σ"*join([subscriptify(i) for i in p.d])
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return AutSymbol(str, 1, :(σ($(p.d), 1)), σ(p, 1))
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str = "σ"*join([subscriptify(i) for i in p.d])
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return AutSymbol(str, 1, PermAut(p))
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end
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end
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@ -94,38 +99,30 @@ function perm_autsymbol(a::Vector{Int})
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return perm_autsymbol(G(a))
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end
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function getperm(s::AutSymbol)
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if s.ex.args[1] == :σ
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p = s.ex.args[2]
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return PermutationGroup(length(p))(p)
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else
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throw(ArgumentError("$s is not a permutation automorphism!"))
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end
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end
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###############################################################################
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#
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# AutGroup / AutGroupElem constructors
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#
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###############################################################################
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function AutGroup(G::FreeGroup; outer=false, special=false)
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function AutGroup(G::FreeGroup; special=false)
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n = length(G.gens)
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n == 0 && return AutGroup(G, AutSymbol[])
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S = AutSymbol[]
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indexing = [[i,j] for i in 1:n for j in 1:n if i≠j]
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rmuls = [rmul_autsymbol(i,j) for (i,j) in indexing]
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append!(S, rmuls)
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lmuls = [lmul_autsymbol(i,j) for (i,j) in indexing]
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append!(S, lmuls)
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append!(S, [rmuls; lmuls])
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if !special
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flips = [flip_autsymbol(i) for i in 1:n]
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append!(S, flips)
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end
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if !outer
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perms = collect(elements(PermutationGroup(n)))
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perms = [perm_autsymbol(p) for p in perms[2:end]] # leave the identity
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append!(S, perms)
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syms = [perm_autsymbol(p) for p in elements(PermutationGroup(n))][2:end]
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append!(S, [flips; syms])
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end
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return AutGroup(G, S)
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end
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@ -160,10 +157,12 @@ end
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###############################################################################
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function (f::AutSymbol){T}(v::Vector{GWord{T}})
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if f.pow == 0
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return v
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end
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return f.func(v)
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if f.pow == 0
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nothing
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else
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v = f.typ(v, f.pow)
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end
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return v
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end
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function (F::AutGroupElem)(v::Vector)
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@ -182,30 +181,31 @@ end
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hash(s::AutSymbol, h::UInt) = hash(s.str, hash(s.pow, hash(:AutSymbol, h)))
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function hash(g::AutGroupElem, h::UInt)
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gs = gens(parent(g).objectGroup)
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return hash(g(gs), hash(typeof(g), hash(parent(g), h)))
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if g.modified
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g.savedhash = hash(g(gens(parent(g).objectGroup)), hash(typeof(g), hash(parent(g), h)))
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g.modified = false
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end
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return g.savedhash
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end
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function change_pow(s::AutSymbol, n::Int)
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if n == 0
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return id_autsymbol()
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end
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symbol = s.ex.args[1]
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if symbol == :ɛ
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return flip_autsymbol(s.ex.args[2], pow=n)
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elseif symbol == :σ
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G = PermutationGroup(length(s.ex.args[2]))
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return perm_autsymbol(G(s.ex.args[2]), pow=n)
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elseif symbol == :ϱ
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s.ex.args[2:end-1]
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return rmul_autsymbol(s.ex.args[2:end-1]..., pow=n)
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elseif symbol == :λ
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return lmul_autsymbol(s.ex.args[2:end-1]..., pow=n)
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elseif symbol == :id
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symbol = s.typ
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if isa(symbol, FlipAut)
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return flip_autsymbol(symbol.i, pow=n)
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elseif isa(symbol, PermAut)
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return perm_autsymbol(symbol.p, pow=n)
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elseif isa(symbol, RTransvect)
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return rmul_autsymbol(symbol.i, symbol.j, pow=n)
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elseif isa(symbol, LTransvect)
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return lmul_autsymbol(symbol.i, symbol.j, pow=n)
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elseif isa(symbol, Identity)
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return s
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else
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warn("Changing power of an unknown type of symbol! $s")
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return AutSymbol(s.str, n, s.ex, s.func)
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return AutSymbol(s.str, n, s.typ)
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end
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end
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@ -257,18 +257,22 @@ inv(f::AutSymbol) = change_pow(f, -f.pow)
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#
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###############################################################################
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ispermauto(s::AutSymbol) = s.ex.args[1] == :σ
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function getperm(s::AutSymbol)
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isa(s.typ, PermAut) || throw("$s is not a permutation automorphism")
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return s.typ.p
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end
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function simplify_perms!(W::AutGroupElem)
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reduced = true
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for i in 1:length(W.symbols) - 1
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current = W.symbols[i]
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if ispermauto(current)
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if current.pow != 1
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current = perm_autsymbol(perm(current), pow=current.pow)
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end
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if isa(current.typ, PermAut)
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next_s = W.symbols[i+1]
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if ispermauto(next_s)
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if isa(next_s.typ, PermAut)
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if current.pow != 1
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current = perm_autsymbol(perm(current), pow=current.pow)
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end
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reduced = false
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if next_s.pow != 1
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next_s = perm_autsymbol(perm(next_s), pow=next_s.pow)
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@ -295,7 +299,7 @@ function reduce!(W::AutGroupElem)
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end
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end
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W.modified = false
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W.savedhash = hash(W.symbols,hash(typeof(W)))
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W.modified = true
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return W
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end
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@ -1,3 +1,4 @@
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__precompile__()
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module Groups
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using Nemo
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@ -376,30 +377,23 @@ end
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#
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###############################################################################
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function products(X::AbstractVector{T}, Y::AbstractVector{T}, op=*) where {T<:GroupElem}
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result = Vector{T}()
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seen = Set{T}()
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for x in X
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for y in Y
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z = op(x,y)
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if !in(z, seen)
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push!(seen, z)
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push!(result, z)
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end
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end
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end
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return result
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end
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function generate_balls(S::Vector{T}, Id::T; radius=2, op=*) where {T<:GroupElem}
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sizes = Vector{Int}()
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S = deepcopy(S)
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S = unshift!(S, Id)
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function generate_balls{T<:GroupElem}(S::Vector{T}, Id::T=parent(first(S))(); radius=2, op=*)
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sizes = Int[]
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B = [Id]
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for i in 1:radius
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B = products(B, S, op);
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BB = [op(i,j) for (i,j) in Base.product(B,S)]
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B = unique([B; vec(BB)])
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push!(sizes, length(B))
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end
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return B, sizes
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end
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function generate_balls{T<:RingElem}(S::Vector{T}, Id::T=one(parent(first(S))); radius=2, op=*)
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sizes = Int[]
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B = [Id]
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for i in 1:radius
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BB = [op(i,j) for (i,j) in Base.product(B,S)]
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B = unique([B; vec(BB)])
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push!(sizes, length(B))
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end
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return B, sizes
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@ -5,7 +5,7 @@
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@testset "AutSymbol" begin
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@test_throws MethodError Groups.AutSymbol("a")
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@test_throws MethodError Groups.AutSymbol("a", 1)
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f = Groups.AutSymbol("a", 1, :(a()), v -> v)
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f = Groups.AutSymbol("a", 1, Groups.FlipAut(2))
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@test isa(f, Groups.GSymbol)
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@test isa(f, Groups.AutSymbol)
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@test isa(Groups.perm_autsymbol(G([1,2,3,4])), Groups.AutSymbol)
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@ -83,7 +83,7 @@
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end
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@testset "AutGroup/AutGroupElem constructors" begin
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f = Groups.AutSymbol("a", 1, :(a()), v -> v)
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f = Groups.AutSymbol("a", 1, Groups.FlipAut(1))
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@test isa(AutGroupElem(f), Groups.GWord)
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@test isa(AutGroupElem(f), AutGroupElem)
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@test isa(AutGroup(FreeGroup(3)), Nemo.Group)
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@ -129,7 +129,6 @@
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@test (Groups.change_pow(f, -2)).pow == 1
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@test (inv(f)).pow == 1
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f = Groups.perm_autsymbol(G([2,1,4,3]))
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@test isa(inv(f), Groups.AutSymbol)
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@ -150,6 +149,16 @@
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b = Groups.flip_autsymbol(2)*A(inv(Groups.rmul_autsymbol(1,2)))
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@test a*b == b*a
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@test a^3 * b^3 == A()
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g,h = Nemo.gens(A)[[1,8]]
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domain = Nemo.gens(A.objectGroup)
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@test (g*h)(domain) == (h*g)(domain)
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@test (g*h).savedhash != (h*g).savedhash
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a = g*h
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b = h*g
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@test hash(a) == hash(b)
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@test a.savedhash == b.savedhash
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@test length(unique([a,b])) == 1
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@test length(unique([g*h, h*g])) == 1
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end
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@testset "specific Aut(F4) tests" begin
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@ -164,7 +173,7 @@
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S_inv = [S..., [inv(s) for s in S]...]
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@test length(unique(S_inv)) == 75
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G = AutGroup(FreeGroup(N), special=true, outer=true)
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G = AutGroup(FreeGroup(N), special=true)
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S = Nemo.gens(G)
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S_inv = [G(), S..., [inv(s) for s in S]...]
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S_inv = unique(S_inv)
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