sort out imports + first adjustments to Group Interface

src/AutGroup.jl

@@ -20,7 +20,7 @@ struct FlipAut
 end
 
 struct PermAut
-    perm::Generic.Perm{Int8}
+    perm::AbstractAlgebra.Generic.Perm{Int8}
 end
 
 struct Identity end
@@ -66,7 +66,7 @@ function flip(i::Integer, pow::Integer=1)
     return AutSymbol(id, 1, FlipAut(i))
 end
 
-function AutSymbol(p::Generic.Perm, pow::Integer=1)
+function AutSymbol(p::AbstractAlgebra.Generic.Perm, pow::Integer=1)
     if pow != 1
         p = p^pow
     end
@@ -81,7 +81,7 @@ end
 ϱ(i::Integer, j::Integer, pow::Integer=1) = transvection_R(i, j, pow)
 λ(i::Integer, j::Integer, pow::Integer=1) = transvection_L(i, j, pow)
 ε(i::Integer, pow::Integer=1) = flip(i, pow)
-σ(v::Generic.Perm, pow::Integer=1) = AutSymbol(v, pow)
+σ(v::AbstractAlgebra.Generic.Perm, pow::Integer=1) = AutSymbol(v, pow)
 
 function change_pow(s::AutSymbol, n::Integer)
     iszero(n) && id_autsymbol()
@@ -123,8 +123,8 @@ mutable struct Automorphism{N} <: GWord{AutSymbol}
     end
 end
 
-elem_type(::Type{AutGroup{N}}) where N = Automorphism{N}
+Base.eltype(::Type{AutGroup{N}}) where N = Automorphism{N}
-parent_type(::Type{Automorphism{N}}) where N = AutGroup{N}
+GroupsCore.parent_type(::Type{Automorphism{N}}) where N = AutGroup{N}
 
 function AutGroup(G::FreeGroup; special=false)
    S = AutSymbol[]
@@ -140,7 +140,7 @@ function AutGroup(G::FreeGroup; special=false)
 
    if !special
       flips = [ε(i) for i in 1:n]
-      syms = [σ(p) for p in SymmetricGroup(Int8(n))][2:end]
+      syms = [σ(p) for p in AbstractAlgebra.SymmetricGroup(Int8(n))][2:end]
 
       append!(S, [flips; syms])
    end
@@ -238,19 +238,19 @@ function compute_images(g::Automorphism)
     return images
 end
 
-function (==)(g::Automorphism{N}, h::Automorphism{N}) where N
+function Base.:(==)(g::Automorphism{N}, h::Automorphism{N}) where N
     syllables(g) == syllables(h) && return true
     img_computed, imh_computed = false, false
 
     if ismodified(g)
         img = compute_images(g) # sets modified bit
-        hash(g, images=img)
+        hash(g; images=img)
         img_computed = true
     end
 
     if ismodified(h)
         imh = compute_images(h) # sets modified bit
-        hash(h, images=imh)
+        hash(h; images=imh)
         imh_computed = true
     end
 
@@ -282,7 +282,7 @@ end
 #   String I/O
 #
 
-function show(io::IO, G::AutGroup)
+function Base.show(io::IO, G::AutGroup)
    print(io, "Automorphism Group of $(G.objectGroup)\n")
    print(io, "Generated by $(gens(G))")
 end

src/FPGroups.jl

@@ -29,8 +29,8 @@ export FPGroupElem, FPGroup
 #   Type and parent object methods
 #
 
-AbstractAlgebra.elem_type(::Type{FPGroup}) = FPGroupElem
+Base.eltype(::Type{FPGroup}) = FPGroupElem
-AbstractAlgebra.parent_type(::Type{FPGroupElem}) = FPGroup
+GroupsCore.parent_type(::Type{FPGroupElem}) = FPGroup
 
 ###############################################################################
 #
@@ -76,7 +76,7 @@ end
 #   String I/O
 #
 
-function show(io::IO, G::FPGroup)
+function Base.show(io::IO, G::FPGroup)
     print(io, "FPgroup on $(length(G.gens)) generators ")
     strrels = join(G.rels, ", ")
     if length(strrels) > 200

src/FreeGroup.jl

@@ -27,8 +27,8 @@ export FreeGroupElem, FreeGroup
 #   Type and parent object methods
 #
 
-AbstractAlgebra.elem_type(::Type{FreeGroup}) = FreeGroupElem
+Base.eltype(::Type{FreeGroup}) = FreeGroupElem
-AbstractAlgebra.parent_type(::Type{FreeGroupElem}) = FreeGroup
+GroupsCore.parent_type(::Type{FreeGroupElem}) = FreeGroup
 
 ###############################################################################
 #
@@ -67,7 +67,7 @@ end
 #   String I/O
 #
 
-function show(io::IO, G::FreeGroup)
+function Base.show(io::IO, G::FreeGroup)
    print(io, "Free group on $(length(G.gens)) generators: ")
    join(io, G.gens, ", ")
 end

src/Groups.jl

@@ -1,19 +1,11 @@
 module Groups
 
-using AbstractAlgebra
-import AbstractAlgebra: Group, GroupElem, Ring
-import AbstractAlgebra: parent, parent_type, elem_type
-import AbstractAlgebra: order, gens, matrix_repr
-
-import Base: length, ==, hash, show, convert, eltype, iterate
-import Base: inv, reduce, *, ^, power_by_squaring
-import Base: findfirst, findnext, findlast, findprev, replace
-import Base: deepcopy_internal
-
 using GroupsCore
 using LinearAlgebra
 using ThreadsX
 
+import AbstractAlgebra
+
 export gens, FreeGroup, Aut, SAut
 
 include("types.jl")
@@ -23,7 +15,6 @@ include("FPGroups.jl")
 include("AutGroup.jl")
 
 include("symbols.jl")
-include("fallbacks.jl")
 include("words.jl")
 include("hashing.jl")
 include("freereduce.jl")
@@ -56,11 +47,7 @@ end
 #   Misc
 #
 
-"""
+GroupsCore.gens(G::AbstractFPGroup) = G.(G.gens)
-    gens(G::AbstractFPGroups)
-Return vector of generators of `G`, as its elements.
-"""
-AbstractAlgebra.gens(G::AbstractFPGroup) = G.(G.gens)
 
 """
     wlmetric_ball(S::AbstractVector{<:GroupElem}
@@ -74,7 +61,7 @@ function wlmetric_ball_serial(
     S::AbstractVector{T};
     radius = 2,
     op = *,
-) where {T<:Union{GroupElem,NCRingElem}}
+) where {T<:Union{GroupElement,AbstractAlgebra.NCRingElem}}
     old = unique!([one(first(S)), S...])
     sizes = [1, length(old)]
     for i = 2:radius
@@ -91,7 +78,7 @@ function wlmetric_ball_thr(
     S::AbstractVector{T};
     radius = 2,
     op = *,
-) where {T<:Union{GroupElem,NCRingElem}}
+) where {T<:Union{GroupElement,AbstractAlgebra.NCRingElem}}
     old = unique!([one(first(S)), S...])
     sizes = [1, length(old)]
     for r = 2:radius
@@ -114,7 +101,7 @@ function wlmetric_ball_serial(
     center::T;
     radius = 2,
     op = *,
-) where {T<:Union{GroupElem,NCRingElem}}
+) where {T<:Union{GroupElement,AbstractAlgebra.NCRingElem}}
     E, sizes = wlmetric_ball_serial(S, radius = radius, op = op)
     isone(center) && return E, sizes
     return c .* E, sizes
@@ -125,7 +112,7 @@ function wlmetric_ball_thr(
     center::T;
     radius = 2,
     op = *,
-) where {T<:Union{GroupElem,NCRingElem}}
+) where {T<:Union{GroupElement,AbstractAlgebra.NCRingElem}}
     E, sizes = wlmetric_ball_thr(S, radius = radius, op = op)
     isone(center) && return E, sizes
     return c .* E, sizes
@@ -137,7 +124,7 @@ function wlmetric_ball(
     radius = 2,
     op = *,
     threading = true,
-) where {T<:Union{GroupElem,NCRingElem}}
+) where {T<:Union{GroupElement,AbstractAlgebra.NCRingElem}}
     threading && return wlmetric_ball_thr(S, center, radius = radius, op = op)
     return return wlmetric_ball_serial(S, center, radius = radius, op = op)
 end

src/arithmetic.jl

@@ -55,15 +55,15 @@ lmul!(out::T, v::T) where T<:GWord = freereduce!(prepend!(out, v))
 
 lmul!(out::T, x::T, y::T) where T <: GWord = rmul!(out, y, x)
 
-AbstractAlgebra.mul!(out::T, x::T, y::T) where T <: GWord = rmul!(out, x, y)
+GroupsCore.mul!(out::T, x::T, y::T) where T <: GWord = rmul!(out, x, y)
 
-(*)(W::GW, Z::GW) where GW <: GWord = rmul!(deepcopy(W), W, Z)
+Base.:(*)(W::GW, Z::GW) where GW <: GWord = rmul!(deepcopy(W), W, Z)
-(*)(W::GWord, s::GSymbol) = freereduce!(push!(deepcopy(W), s))
+Base.:(*)(W::GWord, s::GSymbol) = freereduce!(push!(deepcopy(W), s))
-(*)(s::GSymbol, W::GWord) = freereduce!(pushfirst!(deepcopy(W), s))
+Base.:(*)(s::GSymbol, W::GWord) = freereduce!(pushfirst!(deepcopy(W), s))
 
-function power_by_squaring(W::GWord, p::Integer)
+function Base.power_by_squaring(W::GWord, p::Integer)
     if p < 0
-        return power_by_squaring(inv(W), -p)
+        return Base.power_by_squaring(inv(W), -p)
     elseif p == 0
         return one(W)
     elseif p == 1
@@ -90,4 +90,4 @@ function power_by_squaring(W::GWord, p::Integer)
     return freereduce!(Z)
 end
 
-(^)(x::GWord, n::Integer) = power_by_squaring(x,n)
+Base.:(^)(x::GWord, n::Integer) = Base.power_by_squaring(x,n)

src/fallbacks.jl

@@ -1,16 +0,0 @@
-# workarounds
-Base.one(G::Generic.SymmetricGroup) = Generic.Perm(G.n)
-
-# fallback definitions
-# note: the user should implement those on type, when possible
-Base.eltype(w::GW) where GW<:GWord = eltype(GW)
-AbstractAlgebra.elem_type(G::Gr) where Gr <:AbstractFPGroup = elem_type(Gr)
-
-AbstractAlgebra.parent_type(g::Gw) where Gw <:GWord = parent_type(parent(Gr))
-
-function Base.one(G::Gr) where Gr <: AbstractFPGroup
-    El = elem_type(G)
-    id = El(eltype(El)[])
-    id.parent = G
-    return id
-end

src/findreplace.jl

@@ -28,10 +28,11 @@ function issubword(z::GWord, w::GWord, sindex::Integer)
     return true
 end
 
-"""doc
+"""
+
 Find the first syllable index k>=i such that Z < syllables(W)[k:k+syllablelength(Z)-1]
 """
-function findnext(subword::GWord, word::GWord, start::Integer)
+function Base.findnext(subword::GWord, word::GWord, start::Integer)
     @boundscheck 1 ≤ start ≤ syllablelength(word) || throw(BoundsError(word, start))
     isempty(subword) && return start
     stop = syllablelength(word) - syllablelength(subword) +1
@@ -42,7 +43,7 @@ function findnext(subword::GWord, word::GWord, start::Integer)
     return nothing
 end
 
-function findnext(s::FreeSymbol, word::GWord, start::Integer)
+function Base.findnext(s::FreeSymbol, word::GWord, start::Integer)
     @boundscheck 1 ≤ start ≤ syllablelength(word) || throw(BoundsError(word, start))
     isone(s) && return start
     stop = syllablelength(word)
@@ -53,7 +54,7 @@ function findnext(s::FreeSymbol, word::GWord, start::Integer)
     return nothing
 end
 
-function findprev(subword::GWord, word::GWord, start::Integer)
+function Base.findprev(subword::GWord, word::GWord, start::Integer)
     @boundscheck 1 ≤ start ≤ syllablelength(word) || throw(BoundsError(word, start))
     isempty(subword) && return start
     stop = 1
@@ -64,7 +65,7 @@ function findprev(subword::GWord, word::GWord, start::Integer)
     return nothing
 end
 
-function findprev(s::FreeSymbol, word::GWord, start::Integer)
+function Base.findprev(s::FreeSymbol, word::GWord, start::Integer)
     @boundscheck 1 ≤ start ≤ syllablelength(word) || throw(BoundsError(word, start))
     isone(s) && return start
     stop = 1
@@ -75,11 +76,11 @@ function findprev(s::FreeSymbol, word::GWord, start::Integer)
     return nothing
 end
 
-findfirst(subword::GWord, word::GWord) = findnext(subword, word, 1)
+Base.findfirst(subword::GWord, word::GWord) = findnext(subword, word, 1)
-findlast(subword::GWord, word::GWord) =
+Base.findlast(subword::GWord, word::GWord) =
     findprev(subword, word, syllablelength(word)-syllablelength(subword)+1)
 
-function replace!(out::GW, W::GW, lhs_rhs::Pair{GS, T}; count::Integer=typemax(Int)) where
+function Base.replace!(out::GW, W::GW, lhs_rhs::Pair{GS, T}; count::Integer=typemax(Int)) where
         {GS<:GSymbol, T<:GWord, GW<:GWord}
     (count == 0 || isempty(W)) && return W
     count < 0 && throw(DomainError(count, "`count` must be non-negative."))
@@ -117,7 +118,7 @@ function replace!(out::GW, W::GW, lhs_rhs::Pair{GS, T}; count::Integer=typemax(I
     return freereduce!(out)
 end
 
-function replace!(out::GW, W::GW, lhs_rhs::Pair{T, T}; count::Integer=typemax(Int)) where
+function Base.replace!(out::GW, W::GW, lhs_rhs::Pair{T, T}; count::Integer=typemax(Int)) where
     {GW<:GWord, T <: GWord}
     (count == 0 || isempty(W)) && return W
     count < 0 && throw(DomainError(count, "`count` must be non-negative."))
@@ -164,12 +165,12 @@ function replace!(out::GW, W::GW, lhs_rhs::Pair{T, T}; count::Integer=typemax(In
     return freereduce!(out)
 end
 
-function replace(W::GW, lhs_rhs::Pair{T, T}; count::Integer=typemax(Int)) where
+function Base.replace(W::GW, lhs_rhs::Pair{T, T}; count::Integer=typemax(Int)) where
     {GW<:GWord, T <: GWord}
     return replace!(one(W), W, lhs_rhs; count=count)
 end
 
-function replace(W::GW, subst_dict::Dict{T,T}) where {GW<:GWord, T<:GWord}
+function Base.replace(W::GW, subst_dict::Dict{T,T}) where {GW<:GWord, T<:GWord}
     out = W
     for toreplace in reverse!(sort!(collect(keys(subst_dict)), by=length))
         replacement = subst_dict[toreplace]

src/freereduce.jl

@@ -46,4 +46,4 @@ performs reduction/simplification of a group element (word in generators).
 The default reduction is the reduction in the free group reduction.
 More specific procedures should be dispatched on `GWord`s type parameter.
 """
-reduce(w::GWord) = reduce!(deepcopy(w))
+Base.reduce(w::GWord) = reduce!(deepcopy(w))

src/hashing.jl

@@ -9,7 +9,7 @@ function hash_internal(W::GWord)
     return hash(syllables(W), hash(typeof(W), h))
 end
 
-function hash(W::GWord, h::UInt=UInt(0); kwargs...)
+function Base.hash(W::GWord, h::UInt=UInt(0); kwargs...)
     if ismodified(W)
         savehash!(W, hash_internal(W; kwargs...))
         unsetmodified!(W)
@@ -25,7 +25,7 @@ function Base.deepcopy_internal(W::T, dict::IdDict) where T<:GWord
     return g
 end
 
-function (==)(W::T, Z::T) where T <: GWord
+function Base.:(==)(W::T, Z::T) where T <: GWord
     hash(W) != hash(Z) && return false # distinguishes parent and parentless words
     if hasparent(W) && hasparent(Z)
         parent(W) != parent(Z) && return false

src/symbols.jl

@@ -12,7 +12,7 @@ Base.isone(s::GSymbol) = iszero(s.pow)
 Base.inv(s::GSymbol) = change_pow(s, -s.pow)
 Base.hash(s::S, h::UInt) where S<:GSymbol = hash(s.id, hash(s.pow, hash(S, h)))
 
-function (==)(s::GSymbol, t::GSymbol)
+function Base.:(==)(s::GSymbol, t::GSymbol)
     isone(s) && isone(t) && return true
     s.pow == t.pow && s.id == t.id && return true
     return false

src/types.jl

@@ -1,7 +1,14 @@
-abstract type AbstractFPGroup <: Group end
+abstract type AbstractFPGroup <: GroupsCore.Group end
+
+function Base.one(G::Gr) where Gr <: AbstractFPGroup
+    El = eltype(G)
+    id = El(eltype(El)[])
+    id.parent = G
+    return id
+end
 
 """
-    ::GSymbol
+    GSymbol
 Represents a syllable. Abstract type which all group symbols of
 `AbstractFPGroups` should subtype. Each concrete subtype should implement fields:
  * `id` which is the `Symbol` representation/identification of a symbol
@@ -9,7 +16,7 @@ Represents a syllable. Abstract type which all group symbols of
 """
 abstract type GSymbol end
 
-abstract type GWord{T<:GSymbol} <: GroupElem end
+abstract type GWord{T<:GSymbol} <: GroupsCore.GroupElement end
 
 """
     W::GroupWord{T} <: GWord{T<:GSymbol} <:GroupElem

src/words.jl

@@ -5,7 +5,7 @@ setmodified!(w::GWord) = (w.modified = true; w)
 unsetmodified!(w::GWord) = (w.modified = false; w)
 savehash!(w::GWord, h::UInt) = (w.savedhash = h; w)
 savedhash(w::GWord) = w.savedhash
-parent(w::GWord) = w.parent
+Base.parent(w::GWord) = w.parent
 hasparent(w::GWord) = isdefined(w, :parent)
 setparent!(w::GWord, G::AbstractFPGroup) = (w.parent = G; w)
 

test/AutGroup-tests.jl

@@ -1,6 +1,8 @@
+import AbstractAlgebra.@perm_str
+
 @testset "Automorphisms" begin
 
-   G = SymmetricGroup(Int8(4))
+   G = AbstractAlgebra.SymmetricGroup(Int8(4))
 
    @testset "AutSymbol" begin
       @test_throws MethodError Groups.AutSymbol(:a)
@@ -91,7 +93,7 @@
       f = Groups.AutSymbol(:a, 1, Groups.FlipAut(1))
       @test isa(Automorphism{3}(f), Groups.GWord)
       @test isa(Automorphism{3}(f), Automorphism)
-      @test isa(AutGroup(FreeGroup(3)), AbstractAlgebra.Group)
+      @test isa(AutGroup(FreeGroup(3)), GroupsCore.Group)
       @test isa(AutGroup(FreeGroup(1)), Groups.AbstractFPGroup)
 
       A = AutGroup(FreeGroup(1))

test/FreeGroup-tests.jl

@@ -42,7 +42,7 @@ end
 end
 
 @testset "FreeGroup" begin
-   @test isa(FreeGroup(["s", "t"]), AbstractAlgebra.Group)
+   @test isa(FreeGroup(["s", "t"]), GroupsCore.Group)
    G = FreeGroup(["s", "t"])
    s, t = gens(G)
 
@@ -87,7 +87,7 @@ end
       w = deepcopy(t)
       @test length(Groups.rmul!(w, t)) == 2
       @test length(Groups.lmul!(w, inv(t))) == 1
-      w = AbstractAlgebra.mul!(w, w, s)
+      w = GroupsCore.mul!(w, w, s)
       @test length(w) == 2
       @test length(Groups.lmul!(w, inv(s))) == 3
 

test/runtests.jl

@@ -1,13 +1,14 @@
 using Test
-using AbstractAlgebra
+import AbstractAlgebra
 using Groups
 
+include("symmetric.jl")
 using LinearAlgebra
 
 @testset "Groups" begin
 
    @testset "wlmetric_ball" begin
-      M = MatrixAlgebra(zz, 3)
+      M = AbstractAlgebra.MatrixAlgebra(AbstractAlgebra.zz, 3)
       w = one(M); w[1,2] = 1;
       r = one(M); r[2,3] = -3;
       s = one(M); s[1,3] = 2; s[3,2] = -1;

test/symmetric.jl

@@ -0,0 +1,31 @@
+import AbstractAlgebra
+using GroupsCore
+
+# disambiguation
+GroupsCore.order(
+    ::Type{I},
+    G::AbstractAlgebra.Generic.SymmetricGroup,
+) where {I<:Integer} = I(factorial(G.n))
+
+# disambiguation
+GroupsCore.order(
+    ::Type{I},
+    g::AbstractAlgebra.Generic.Perm,
+) where {I<:Integer} =
+    I(foldl(lcm, length(c) for c in AbstractAlgebra.cycles(g)))
+
+# correct the AA length:
+Base.length(G::AbstractAlgebra.Generic.SymmetricGroup) = order(Int, G)
+
+# genuinely new methods:
+Base.IteratorSize(::Type{<:AbstractAlgebra.AbstractPermutationGroup}) = Base.HasLength()
+
+function GroupsCore.gens(G::AbstractAlgebra.Generic.SymmetricGroup{I}) where {I}
+    a, b = one(G), one(G)
+    circshift!(a.d, b.d, -1)
+    b.d[1], b.d[2] = 2, 1
+    return [a, b]
+end
+
+Base.deepcopy_internal(g::AbstractAlgebra.Generic.Perm, ::IdDict) =
+    AbstractAlgebra.Generic.Perm(deepcopy(g.d), false)