weak_popov_form incorrectly returns zero matrix when using ordered=True and include_zero_vectors=False #41278
Description
Steps To Reproduce
As described in the title.
Expected Behavior
R.<x> = GF(3)[]
A = matrix(R, [[x^3 + x, 0, 0], [2*x^2, x, 0], [x, 0, x], [x^2 + 1, x^2 + 1, 0], [2*x + 2, 2*x + 2, x], [x^2 + x + 1, x^2 + 2*x + 1, 2*x^3 + 2*x^2], [0, 0, x^2 + 1], [x^2 + x, x^2 + 2*x, 2*x^3 + 2*x^2 + 2*x + 2], [2*x^4 + x^3 + 2*x^2 + 2, 2*x^4 + x^2 + 2, x^5 + 2*x^4 + x^3 + x^2 + 2*x + 1]])
print(A.weak_popov_form(ordered=True)) # This is fine
# [x + 2 2 2]
# [ 0 2*x 1]
# [ x 0 x]
# [ 0 0 0]
# [ 0 0 0]
# [ 0 0 0]
# [ 0 0 0]
# [ 0 0 0]
# [ 0 0 0]
A.weak_popov_form(ordered=True, include_zero_vectors=False) # This should just give the first three rows of the previous calculationActual Behavior
A.weak_popov_form(ordered=True, include_zero_vectors=False) # Sage incorrectly returns a zero matrix
# [ 0 0 0]
# [ 0 0 0]
# [ 0 0 0]Additional Information
include_zero_vectors works fine if not using ordered=True:
A.weak_popov_form(include_zero_vectors=False)
# [ 0 2*x 1]
# [ x 0 x]
# [x + 2 2 2]Environment
- OS: Fedora 42
- Sage Version: Tested on both Sage 10.7 and develop
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