On Wednesday 10 January 2024 at 03:03:09 UTC-8 Martin R wrote:

... What would be a good name?  Brainstorming: `coefficient_system`, 
`coefficients`, `coefficients_monomials`, 
`coefficient_matrix_monomial_vector`...


I think coefficients_monomials() is the most descriptive, as it tells you 
what you get back and in what order.

C, m = PS.coefficients_monomials()
assert PolynomialSequence(C*m) == PS

(incidentally, the assert also holds true with the return values of 
coefficient_matrix)

Also, thinking about whether C should be transposed: I think it's logical 
that the rows of C are the coefficients of members of the sequence (since 
matrices are closest to sequences of rows in sage), so C is already correct 
in that sense. Therefore, m should indeed be a "column" vector, but sage is 
ambivalent about whether vectors are rows or columns and therefore we can 
safely return it as a vector.

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