Add ideals and quotients of free associative algebras

[fingolfin]

We already have groebner_basis and normal_form so this shouldn't be too hard.

Of course this won't work in many examples, but there are definitely some where it would be nice. E.g. for Clifford algebras and variants:

julia> n = 3; R, x = free_associative_algebra(QQ, :x => 1:n)
(Free associative algebra on 3 indeterminates over QQ, AbstractAlgebra.Generic.FreeAssociativeAlgebraElem{QQFieldElem}[x[1], x[2], x[3]])

julia> rels = [x[i]^2-1 for i in 1:n];

julia> append!(rels, [x[i]*x[j]-x[j]*x[i] for i in 1:n for j in i+1:n]);

julia> I = ideal(R, rels)
Ideal of Free associative algebra on 3 indeterminates over QQ with 6 generators

julia> gb = groebner_basis(I)
Ideal generating system with elements
  1: x[1]^2 - 1
  2: x[2]^2 - 1
  3: x[3]^2 - 1
  4: x[1]*x[2] - x[2]*x[1]
  5: x[1]*x[3] - x[3]*x[1]
  6: x[2]*x[3] - x[3]*x[2]

julia> normal_form(x[1]^3 + x[2]*x[1]*x[3] - 5 * x[2]*x[1]*x[2], gb)
x[3]*x[2]*x[1] - 4*x[1]

This works but it'd be nice if one could just work in the corresponding quotient algebra.

[lgoettgens]

For the ideal part, we already have FreeAssociativeAlgebraIdeal in Oscar.

[fingolfin]

I see. But then we still should have a quotient ring implementation there.