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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