GBNP bugs

[erich-9]

There seem to be some bugs in the GBNP package. I reported them about four month ago, but didn't get any response so far. Below you can find two QPA examples that use the following path algebra:

Q := Quiver(1, [ [1,1,"a"], [1,1,"b"] ]);
KQ := PathAlgebra(Rationals, Q);
AssignGeneratorVariables(KQ);

This first example raises an error because of an out-of-range index:

# set of generators for the ideal < a^3, a^2*b, b*a^2, b*a*b, b*a+b^2, a*b*a-a^2 >
rels := [
 a^3, a^2*b, a*b^2+a^2, b*a^2, a^3+b^2+b*a, a*b^2+a*b*a, b*a*b+b*a^2, b^2*a+b*a^2,
 b^3+b*a^2, a^2*b*a, a*b*a^2, b*a^2*b
];

GBNPGroebnerBasis(rels, KQ);

While this second one gets stuck in an infinite loop:

# set of generators for the ideal < a*b+b*a, a^2+b^2, a^3, a^2*b >
rels := [
  a^2+b^2, a^2*b+b*a^2, a^4, a^3*b, a^2*b*a, a*b*a*b, b*a*b*a, a^3+a^2*b+a*b*a+a*b^2,
  a^2+a*b+b*a+b^2+a^2*b+b*a^2, a^2+a*b+b*a+b^2+a^3+a^2*b+a*b*a+b^2*a,
  a^3+a*b*a+b*a*b+b^3, a^4, a^3*b, a^2*b*a, a*b*a*b, b*a*b*a
];

GBNPGroebnerBasis(rels, KQ);