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@user202729 user202729 commented Sep 21, 2025

This pull request makes RingExtension work over nontrivial tower of extension constructed using PolynomialQuotientRing. See the tests for details (previously they fail).

            sage: p = 886368969471450739924935101400677
            sage: K = GF(p)
            sage: Kx.<x> = K[]
            sage: K3.<u> = K.extension(Kx([4, 1, 0, 1]))
            sage: K3y.<y> = K3[]
            sage: K6.<t> = K3.extension(K3y([2, 0, 1]))
            sage: K6t.<t1> = K6.over(K, gen=t)
            Traceback (most recent call last):
            ...
            ValueError: the given family is not a basis
            sage: K6t.<t1> = K6.over(K, gen=t+u)
            sage: K6t(t1).minpoly()
            x^6 + 8*x^4 + 8*x^3 + 13*x^2 + 886368969471450739924935101400637*x + 18
            sage: K6t(t1).minpoly()(t1)
            0

The example is taken from #40764. For now, you need to provide a generator t+u.

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github-actions bot commented Sep 21, 2025

Documentation preview for this PR (built with commit d096221; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

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