Steps To Reproduce

In Sage 10.2 and 10.2.rc4, reduction of elements of exterior algebra modulo an ideal does not give a reduced form.

sage: N = 4
sage: E = ExteriorAlgebra(QQ,binomial(N,2))
sage: e = E.gens()
sage: K = matroids.CompleteGraphic(N);
sage: C = K.circuits()
sage: ideal_gens = [sum([(-1)^j*E.prod(e[i] for i in list(c)[:j] + list(c)[j+1:]) for j in range(len(c))]) for c in C]
sage: OS = E.quo(ideal_gens)
sage: [OS(b).lift() for b in E.homogeneous_component_basis(4)]
[0,
 0,
 0,
 0,
 0,
 -e0*e1*e3*e4 + e0*e1*e3*e5,
 0,
 0,
 0,
 0,
 0,
 0,
 e0*e1*e3*e4 - e0*e1*e3*e5,
 e0*e1*e3*e4 - e0*e1*e3*e5,
 0]
sage: [OS(OS(b).lift()) for b in E.homogeneous_component_basis(4)]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Expected Behavior

There should be no nonzero degree-4 elements in the previous example.

Actual Behavior

One needs to do the reduction step manually twice in order to reduce elements modulo the ideal.

Additional Information

A guess at the bug is that it could be caused by a loop terminating early during the Groebner basis reduction step.

Environment

- **OS**: MacOS Ventura 13.4.1
- **Sage Version**: 10.2, 10.2.rc4

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide