bug in kernel of ring homomorphism of quotient rings

[gh-mwageringel]

As reported on ​sage-devel:

sage: A.<t> = QQ[]
sage: B.<x,y> = QQ[]
sage: H = B.quotient(B.ideal([B.1]))
sage: f = A.hom([H.0], H)
sage: f.kernel()
Principal ideal (t) of Univariate Polynomial Ring in t over Rational Field

whereas the kernel should be the zero ideal.

[gh-mwageringel]

The problem indeed only occurs with quotient rings, as the implementation switches from the quotient to the cover ring in order to compute an elimination ideal. For this, the elimination variables need to be lifted from the quotient to the cover ring. However, one of the generator variables of the quotient ring is 0 in the example, so 0.lift() gives 0 again, rather than a variable of the cover ring. I have fixed this by taking the correct variables from the cover ring directly.

In more detail, the problematic call to elimination_ideal is of this kind:

sage: R.<x,y,z> = QQ[]
sage: R.ideal(x-y, z).elimination_ideal([y, R(0)])
Ideal (x - y, z) of Multivariate Polynomial Ring in x, y, z over Rational Field

This is a usage error because it calls elimination_ideal with a 0 instead of a variable. The implementation then calls libsingular with the product of the passed variables, which is 0 again, so nothing gets eliminated.

A question that remains is whether elimination_ideal should validate its arguments in order to make sure they are all variables of the ring. This can be a different ticket though.

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New commits:

​0aba8a0

31367: fix elimination in case of quotient rings

[gh-mwageringel]

The bot is green. Please review.

[tscrim]

LGTM.

[gh-mwageringel]

Thank you.

[gh-mwageringel]

Replying to gh-mwageringel:

A question that remains is whether elimination_ideal should validate its arguments in order to make sure they are all variables of the ring. This can be a different ticket though.

I have created #31414 for validating the input of elimination_ideal.