# Algorithm for finding generators of an ideal

Let $k$ be a field, and $f:k[x_1,\ldots,x_n]\to k[y_1,\ldots,y_m]$ a $k$-algebra homomorphism. Given $r_1,\ldots,r_k\in k[y_1,\ldots,y_m]$, is there an algorithm for producing a finite generating set for the ideal $f^{-1}((r_1,\ldots,r_k))$?

-
I wonder if there is even a reasonable algorithm for finding generators of $f^{-1}(0)$. –  Thomas Andrews Jul 18 '13 at 16:42
Will Grobner bases help? –  Robert Lewis Jul 18 '13 at 17:37

$$f : k[x_1, \dots, x_n] \rightarrow S$$
where $S$ is some quotient of a polynomial ring. Macaulay2 can calculate such a kernel.