possible bug: kernel of ring homomorphism

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Akos M

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Feb 8, 2021, 4:20:34 AMFeb 8
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Hi, 

I'm not sure whether this is a bug or not, but the kernel of a ring homomorphism to a quotient ring gives unexpected results:

A.<t> = QQ[] 
B.<x,y> = QQ[] 
H = B.quotient(B.ideal([B.1])) 
f = A.hom([H.0], H) 
f.kernel()

outputs:

Ring morphism: From: Univariate Polynomial Ring in t over Rational Field 
To: Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (y) Defn: t |--> xbar 
Principal ideal (t) of Univariate Polynomial Ring in t over Rational Field

whereas the kernel of f:A[t]->B[x,y]->B[x,y]/(y), for f(t)=x should be (0).

Is this a bug?

Thanks,
Akos

John Cremona

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Feb 8, 2021, 5:06:27 AMFeb 8
to SAGE devel
It looks like a bug to me. f.kernel() expands to
f._inverse_image_ideal(f.codomain().zero_ideal()) and
f.codomain().zero_ideal() looks OK so the problem must be in the
inverse image. The author is apparently Simon King (2011). Simon,
can you help?

John
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Dima Pasechnik

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Feb 8, 2021, 5:09:52 AMFeb 8
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A wild guess would be that it's due to univariate and multivariate
rings handled by different backends in Sage, one sees this kinds of
corner cases errors.
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Akos M

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Feb 8, 2021, 5:42:59 AMFeb 8
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It seems that unfortunately the problem persists for multivariate rings as well:

A.<t,u> = QQ[]
B.<x,y,z> = QQ[]
H = B.quotient(B.ideal([B.2]))
f = A.hom([H.0, H.1], H)
f
f.kernel()

Ring morphism: 
 From: Multivariate Polynomial Ring in t, u over Rational Field 
 To: Quotient of Multivariate Polynomial Ring in x, y, z over Rational Field by the ideal (z) 
 Defn: t |--> xbar 
           u |--> ybar 
Ideal (-t, -u, 0) of Multivariate Polynomial Ring in t, u over Rational Field

I have the impression that the fact that the ring homomorphism is to a quotient ring introduces the error, but that's just a wild guess. 

Samuel Lelievre

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Feb 8, 2021, 9:54:42 PMFeb 8
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For reference this is also asked on Ask Sage:

Markus Wageringel

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Feb 9, 2021, 5:24:53 AMFeb 9
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Thank you for reporting this problem. I have opened https://trac.sagemath.org/ticket/31367 for it and will provide a fix there shortly.
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