Computing contractions of ideals in Macaulay2

Question

Does Macaulay2 compute contractions of ideals under ring homomorphisms. Specifically, if $R\subseteq S$ is a ring extension (say polynomial rings over $\mathbb{Q}$ which can be specified in M2) and $I$ is an ideal in $S$ given by generators, is there a command to compute $I\cap R$?

EDIT: The eliminate command is supposed to do what I want, except when I use it the output is an ideal in the original ring.

Answer 1

You could set f=map(S/I,R) and obtain the intersection as ker(f).