Singular

D.7.1.36 image_of_variety

Usage:

image_of_variety(I,F);
I: an arbitray <ideal>,
F: a 1xm <matrix> defining an invariant ring of some matrix group

Return:

The <ideal> defining the image under that group of the variety defined by I

Theory:

rel_orbit_variety(I,F) is called and the newly introduced
variables in the output are replaced by the generators of the
invariant ring. This ideal in the original variables defines the image
of the variety defined by I

LIB "finvar.lib";
ring R=0,(x,y,z),dp;
matrix F[1][3]=x+y+z,xy+xz+yz,xyz;
ideal I=xy;
print(image_of_variety(I,F));
==> xyz