The EliminationIdeal command eliminates variables from an ideal using a Groebner basis computation. The result of EliminationIdeal(J, X) is the intersection of the ideal J with the subring .

Note: You cannot use the Intersect command to compute this result.  For any variables X, the polynomial ring  is represented by the ideal , and Intersect(J, <1>) = J.

The EliminationIdeal command can be used to perform nonlinear elimination on a general set of relations.  This is demonstrated below.