Steps To Reproduce

In SageMath version 9.0, running this:

A = PermutationGroup([(1,2)], domain=[1,2])
print("with domain ", A.domain())
print(IntegerVectorsModPermutationGroup(A, 3).list())

B = PermutationGroup([(1,2)], domain=[1,2,3])
print("with domain ", B.domain())
print(IntegerVectorsModPermutationGroup(B, 3).list())

Expected Behavior

In A , the domain has two elements, so I am expecting lists of two elements that add up to 3:

with domain  {1, 2}
[[3, 0], [2, 1]]

In B, the domain has three elements, so I am expecting lists of three elements that add up to 3:

with domain  {1, 2, 3}
[[3, 0, 0], [2, 1, 0], [2, 0, 1], [1, 1, 1], [1, 0, 2], [0, 0, 3]]

Actual Behavior

From both groups we get the same listing:

with domain  {1, 2}
[[3, 0], [2, 1]]
with domain  {1, 2, 3}
[[3, 0], [2, 1]]

Additional Information

If the order of execution is reversed, so that we do B first and A second, then B gives the correct three-element lists, and A gives incorrectly the three-element lists.

So, the first one gets computed correctly, and the second one incorrectly. It looks like IntegerVectorsModPermutationGroup is remembering that it has already seen this group, not noticing that is in fact a different permutation group with different domain.

Environment

- **OS**: Ubuntu 20.04
- **Sage Version**: 9.0

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