I like this idea much better!  What would be a good name?  Brainstorming: 
`coefficient_system`, `coefficients`, `coefficients_monomials`, 
`coefficient_matrix_monomial_vector`...

On Wednesday 10 January 2024 at 09:06:36 UTC+1 Nils Bruin wrote:

> deprecation in a way that allows code to be adapted gradually would mean:
>  - introduce a new method with a different name that implements the 
> desired behaviour
>  - deprecate old method
>  - after appropriate deprecation period remove old method
>  - possibly, at this point introduce the now-vacated name as a synonym for 
> the method with the desired method.
> Quite frankly I think "coefficient_matrix" is the wrong name anyway: I'd 
> expect such a method to return a matrix, but it returns a tuple (both in 
> the old and the new version). So I think step 4 can be skipped in this case.
>
> Note that often deprecation remains the state for very long: the 
> motivation for actually removing functionality is pretty minimal.
>
>
> On Tuesday 9 January 2024 at 23:49:37 UTC-8 Ruchit Jagodara wrote:
>
>> Currently, the PolynomialSequence.coefficient_matrix() function returns a 
>> matrix of monomials as the second element of a tuple. However, as discussed 
>> in issue [#37027](https://github.com/sagemath/sage/issues/37027), it has 
>> been suggested that returning a vector of monomials would be more logical. 
>> I am uncertain about the correct approach to deprecate the current 
>> behavior. I have submitted a pull request with the proposed changes at PR 
>> [#37035](https://github.com/sagemath/sage/pull/37035), but I would 
>> appreciate guidance on whether this is the appropriate way to deprecate the 
>> property.
>>
>

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