The command PolynomialMapImage(F, PM, R, S) returns a constructible set cs which is the image of the variety  under the polynomial map PM.

The command PolynomialMapImage(F, H, PM, R, S) returns a constructible set cs which is the image of the difference of the variety  by the variety  under the polynomial map PM.

The command PolynomialMapImage(CS, PM, R, S) returns a constructible set cs which is the image of the constructible set CS under the polynomial map PM.

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

The variable sets of R and S should be disjoint.

The number of polynomials in PM is equal to the number of variables of ring S.

This command is part of the RegularChains[ConstructibleSetTools] package, so it can be used in the form PolynomialMapImage(..) only after executing the command with(RegularChains[ConstructibleSetTools]).  However, it can always be accessed through the long form of the command by using RegularChains[ConstructibleSetTools][PolynomialMapImage](..).