Singular

D.4.20.19 zerodec

Usage:

zerodec(I); I ideal

Assume:

I is zero-dimensional, the characteristic of the ground field is 0

Return:

list of primary ideals, the zero-dimensional decomposition of I

Note:

The algorithm (of Monico), works well only for a small total number of solutions (vdim(std(I)) should be < 100) and without parameters. In practice, it works also in large characteristic p>0 but may fail for small p.
If printlevel > 0 (default = 0) additional information is displayed.

LIB "primdec.lib";
ring r  = 0,(x,y),dp;
ideal i = x2-2,y2-2;
list pr = zerodec(i);
pr;
==> [1]:
==>    _[1]=y2-2
==>    _[2]=xy+2
==>    _[3]=x2-2
==> [2]:
==>    _[1]=y2-2
==>    _[2]=xy-2
==>    _[3]=x2-2