Currently, most methods from matrix_polynomial_dense support empty matrices (i.e. with dimensions 0 x n, m x 0, or 0 x 0). Most, but not all, and why some do and some don't is not very clear for the user, and is not well indicated in the documentation.

This was raised specifically for minimal_relation_basis in #39516 (comment) . For example:

• row_degrees does not support empty matrices (fails with an error message), it is indirectly stated in the documentation via the examples
• leading_matrix and right_quo_rem do not support empty matrices (fails with an error message), it is not indicated in the documentation
• minimal_approximant_basis and minimal_kernel_basis do support empty matrices.

The treatment of empty matrices should be more unified among the available methods if possible; but at the very least, the documentation should clearly indicate input restrictions about empty matrices.