D.6.3.3 ImageVariety

Procedure from library rinvar.lib (see rinvar_lib).

Usage:

ImageVariety(ideal I, F [, w]);ideal I; F is a list/ideal, intvec w.

Purpose:

compute the Zariski closure of the image of the variety of I under the morphism F.

Note:

if ’I’ and ’F’ are quasihomogeneous w.r.t. ’w’ then the Hilbert-driven ’std’ is used.

Return:

polynomial ring over the same ground field, containing the ideal ’imageid’. The variables are Y(1),...,Y(k) where k = size(F) - ’imageid’ is the ideal of the Zariski closure of F(X) where X is the variety of I.

Example:

LIB "rinvar.lib";
ring B   = 0,(x,y),dp;
ideal I  = x4 - y4;
ideal F  = x2, y2, x*y;
def R = ImageVariety(I, F);
setring R;
imageid;
→ imageid[1]=Y(1)*Y(2)-Y(3)^2
→ imageid[2]=Y(1)^2-Y(2)^2
→ imageid[3]=Y(2)^3-Y(1)*Y(3)^2