fix FPGroups and add basic tests

src/FPGroups.jl

@@ -42,6 +42,7 @@ elem_type(::FPGroup) = FPGroupElem
 
 FPSymbol(s::Symbol) = FPSymbol(s, 1)
 FPSymbol(s::String) = FPSymbol(Symbol(s))
+FPSymbol(s::GSymbol) = FPSymbol(s.id, s.pow)
 
 convert(::Type{FPSymbol}, s::FreeSymbol) = FPSymbol(s.id, s.pow)
 
@@ -70,7 +71,7 @@ function (G::FPGroup)(w::GWord)
    end
 
    if eltype(w.symbols) == FreeSymbol
-      w = FPGroupElem(w.symbols)
+      w = FPGroupElem(FPSymbol.(w.symbols))
    end
 
    if eltype(w.symbols) == FPSymbol
@@ -169,8 +170,8 @@ function add_rels!(G::FPGroup, newrels::Dict{FPGroupElem,FPGroupElem})
    end
 end
 
-function /(G::FPGroup, newrels::Vector{FPGroupElem})
-   for r in rels
+function Base.:/(G::FPGroup, newrels::Vector{FPGroupElem})
+   for r in newrels
       parent(r) == G || throw(DomainError(
       "Can not form quotient group: $r is not an element of $G"))
    end
@@ -180,12 +181,12 @@ function /(G::FPGroup, newrels::Vector{FPGroupElem})
    return H
 end
 
-function /(G::FreeGroup, rels::Vector{FreeGroupElem})
+function Base.:/(G::FreeGroup, rels::Vector{FreeGroupElem})
    for r in rels
       parent(r) == G || throw(DomainError(
          "Can not form quotient group: $r is not an element of $G"))
    end
-   H = FPGroup(G)
+   H = FPGroup(deepcopy(G))
    H.rels = Dict(H(rel) => one(H) for rel in unique(rels))
    return H
 end

test/FPGroup-tests.jl

@@ -0,0 +1,15 @@
+@testset "FPGroups definitions" begin
+    F = FreeGroup(["a", "b", "c"])
+    a,b,c = gens(F)
+    R = [a^2, a*b*a, c*b*a]
+    @test F/R isa FPGroup
+    @test F isa FreeGroup
+    G = F/R
+    A,B,C = gens(G)
+
+    @test A^2 == one(G)
+    @test A*B*A*A == A
+    @test A*A*B*A == B*A
+
+    @test G/[B^2, C*B*C] isa FPGroup
+end

test/runtests.jl

@@ -21,4 +21,5 @@ using LinearAlgebra
    include("AutGroup-tests.jl")
    include("DirectPower-tests.jl")
    include("WreathProd-tests.jl")
+   include("FPGroup-tests.jl")
 end