Singular

D.7.3.3 ImageVariety

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.

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