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Environment

- **OS**: Ubuntu 22.04
- **Sage Version**: 10.1.beta1

Steps To Reproduce

sage: pring.<x> = GF(97)[]
sage: M = Matrix(pring, [[1], [1], [1]])
sage: M.is_weak_popov(row_wise=False,include_zero_vectors=False)
False

Expected Behavior

This should return True, as the matrix is simply a constant nonzero column vector.

Actual Behavior

This returns False.

Additional Information

For a simple nonzero (constant) column vector, the above code snippet does not provide the correct result. This is due to the code being written and correct for row-wise case, but not adapted to some specific instances in the column-wise case (essentially due to the comparisons to self.ncols()).

The failing piece of code is due to the lines in the is_weak_popov method:

        if leading_positions[-1] > self.ncols() and not include_zero_vectors:
            return False

in the code. The leading position here is 2, which is greater than the number of columns which is 1. With include_zero_vectors set to False, this returns False, which is wrong (and, in fact, there is no zero vector here, so this optional argument should not matter in the result).