[GAP Forum] Extending Orderings

[rcone]

GAP Forum,

Is there a way to treat terms (w/o coefficients) from noncommutative 
polynomials as associative words on generators?  This is with the mind of 
formulating a treatment of monomial orderings on noncommutative polynomials 
based on the ordering system built into GAP4.

Here is what I've come up with so far, but I'm hoping there's a more direct 
way:

gap> A := FreeAssociativeAlgebraWithOne(Rationals,"a","b");
<algebra-with-one over Rationals, with 2 generators>
gap> B := FreeGroup("x","y");
<free group on the generators [ x, y ]>
gap> a := A.a;; b := A.b;; x := B.x;; y := B.y;;
gap> f := a^3*b;
(1)*a^3*b
gap> fe := ExtRepOfObj(f);
[ 0, [ [ 1, 3, 2, 1 ], 1 ] ]
gap> g := ObjByExtRep(FamilyObj(x),fe[2][1]);
x^3*y
gap> g in A;
false
gap> g in B;
true
gap> B;

Cheers, and thanks,
Randy Cone