Constructing a quotient ring of multivatiate polynomial ring in GAP

Question

I need to construct the following ring in GAP:

$$F_2(u_1,u_2) / \langle u_1^2=u_2^2=0,u_1u_2=u_2u_1 \rangle $$.

This is what I tried and it didn't work:

gap> R:=PolynomialRing(GF(2),["u1","u2"]);AssignGeneratorVariables(R);
GF(2)[u1,u2]
#I  Assigned the global variables [ u1, u2 ]
gap> I:=Ideal(R,[(u1)^2,(u2)^2,u1*u2-u2*u1]);
<two-sided ideal in GF(2)[u1,u2], (3 generators)>
gap> A:=R/I;
Error, List Element: <list>[1] must have an assigned value in
return i[LeadingMonomialPosExtRep( fam, i, orderext )]; called from
func( C[i] ) called from
List( baslte, function ( i )
  return i[LeadingMonomialPosExtRep( fam, i, orderext )];
end ) called from
GBASIS.GroebnerBasis( elms, order ) called from
ReducedGroebnerBasis( GeneratorsOfIdeal( I ), order ) called from
GroebnerBasis( I, ord ) called from
...  at line 9 of *stdin*
you can 'return;' after assigning a value
brk>

Does anyone know how to construct this ring in GAP?

Thanking you in advance!

Answer 1

There is a minor quirk in the code in that ideal generators $0$ are not processed properly. Remove u1*u2-u2*u1(which holds anyhow) and everything will work fine.