Groups.jl/src/wl_ball.jl

"""
    wlmetric_ball(S::AbstractVector{<:GroupElem}
        [, center=one(first(S)); radius=2, op=*])
Compute metric ball as a list of elements of non-decreasing length, given the
word-length metric on the 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 wlmetric_ball(
    S::AbstractVector{T},
    center::T = one(first(S));
    radius = 2,
    op = *,
) where {T}
    ball = [center]
    sizes = [1]
    if radius ≤ 0
        return ball, sizes[2:end]
    else
        ball = union!(ball, [center * s for s in S])
        push!(sizes, length(ball))
        if radius == 1
            return ball, sizes[2:end]
        else
            for _ in 2:radius
                new = collect(
                    op(o, s) for o in @view(ball[sizes[end-1]:end]) for s in S
                )
                ball = union!(ball, new)
                push!(sizes, length(ball))
            end
        end
        return ball, sizes[2:end]
    end
    # return wlmetric_ball_serial(S, center; radius = radius, op = op)
end