Singular

Given algebras A=K[x1,...,xm]/I and B=K[y1,...,yn]/J and homomorphism f:K[x]-->K[y], I'd like to check if f(I)⊆J, which would mean that f defines a homomorphism f: A-->B.

The code below returns an error, since f(I) is undefined. If p∈K[x], how can I calculate f(p)∈K[y]? I've tried subst(p,...); and imap(...), but without success.



It would be desirable to be able to check f(I)⊆J automatically, i.e. at once (with a single command) and not manually (for each f(g_i) where g_i are generators of I).

gives the numnber of non-zero entries, i.e. to test if F(I0 is in J:

Yes, but does not work, because I is an ideal in A and the ground ring is B.

Not clear what this should mean. You should use reduce in the form

unless you know already that J is a Groebner basis.
But in your case std(J)==1, as one can see directly.

Yes, of course I meant std(J) inside reduce.

Hmm, this is really strange, now my initial code works. I don't know what I made wrong before. Singular always returned an error, saying that I is not defined, since the basering was B and I was in A. Very strange indeed.

Thank you!