D.6.1.31 image_of_variety

Procedure from library finvar.lib (see finvar_lib).

Usage:

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

Return:

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

Theory:

relative_orbit_variety(I,F,s) 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

Example:

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