Okay, so I will make a new function named coefficient_monomials and will 
implement the functionality that Lorenz Panny suggested.
Thank you for your help : ) .

On Wednesday, January 10, 2024 at 8:16:25 PM UTC+5:30 Nils Bruin wrote:

> 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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