unify the two definitions of generate_balls; rename to metric_ball

src/Groups.jl

@@ -75,45 +75,31 @@ end
 #
 #   Misc
 #
-###############################################################################
 
-function generate_balls(S::AbstractVector{T}, Id::T=one(parent(first(S)));
-        radius=2, op=*) where T<:GroupElem
+@doc doc"""
+    gens(G::AbstractFPGroups)
+> returns vector of generators of `G`, as its elements.
+"""
+AbstractAlgebra.gens(G::AbstractFPGroup) = G.(G.gens)
+
+@doc doc"""
+    metric_ball(S::Vector{GroupElem}, center=Id; radius=2, op=*)
+Compute metric ball as a list of elements of non-decreasing length, given the
+word-length metric on 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 generate_balls(S::AbstractVector{T}, center::T=one(first(S));
+        radius=2, op=*) where T<:Union{GroupElem, NCRingElem}
     sizes = Int[]
-    B = [Id]
+    B = [one(first(S))]
     for i in 1:radius
         BB = [op(i,j) for (i,j) in Base.product(B,S)]
         B = unique([B; vec(BB)])
         push!(sizes, length(B))
     end
-    return B, sizes
+    isone(center) && return B, sizes
+    return c.*B, sizes
 end
 
-function generate_balls(S::AbstractVector{T}, Id::T=one(parent(first(S)));
-        radius=2, op=*) where {T<:NCRingElem}
-    sizes = Int[]
-    B = [Id]
-    for i in 1:radius
-        BB = [op(i,j) for (i,j) in Base.product(B,S)]
-        B = unique([B; vec(BB)])
-        push!(sizes, length(B))
-    end
-    return B, sizes
-end
-
-########### iteration for GFField
-
-
-length(F::AbstractAlgebra.GFField) = order(F)
-
-function iterate(F::AbstractAlgebra.GFField, s=0)
-   if s >= order(F)
-      return nothing
-   else
-      return F(s), s+1
-   end
-end
-
-eltype(::Type{AbstractAlgebra.GFField{I}}) where I = AbstractAlgebra.gfelem{I}
-
 end # of module Groups