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Return explicit polynomial in .in_subalgebra #39225

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@schcs

Description

@schcs

Problem Description

Given a polynomial f∈𝔽[x1,…,xn] which is an element of the subalgebra generated by f1,…,fk, calling f.in_subalgebra([f1,...,fk]) should returnh(t1,…,tk)such that f=h(f1,…,fk). I believe that this would be a useful feature.

Proposed Solution

The method is implemented in sage/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx. When algorithm = "groebner" is chosen, the polynomial z should be returned together with True. In case of False, 0 can be returned.

Alternatives Considered

I'm not sure about feasible alternatives.

Additional Information

No response

Is there an existing issue for this?

  • I have searched the existing issues for a bug report that matches the one I want to file, without success.

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