The command RationalMapPreimage(F, RM, R, S) returns a constructible set cs over R. cs is the preimage of the variety  under the rational map RM.

If H is specified, let  be the variety defined by the product of polynomials in H. The command RationalMapPreimage(F, H, RM, R, S) returns the preimage of the constructible set - under the rational map RM.

The command RationalMapPreimage(CS, RM, R, S) returns the preimage of the constructible set CS under the rational map RM.

Both rings R and S should be over the same ground field.

The variable sets of R and S should be disjoint.

The number of rational functions in RM is equal to the number of variables of ring S.