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possible bug: kernel of ring homomorphism

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
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).

Why?

 2 retagged vdelecroix 7157 ●16 ●78 ●156 http://www.labri.fr/pe...

possible bug: kernel of ring homomorphism

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
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).

Why?

 3 retagged vdelecroix 7157 ●16 ●78 ●156 http://www.labri.fr/pe...

possible bug: kernel of ring homomorphism

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
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).

Why?