Singular

D.7.3.3 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 quasihomogenous 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); ==> ==> // 'ImageVariety' created a new ring. ==> // To see the ring, type (if the name 'R' was assigned to the return valu\ e): ==> show(R); ==> // To access the ideal of the image variety, type ==> setring R; imageid; ==> 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 ```