Singular

D.15.30.12 rootIsolationPrimdec

Usage:

rootIsolationPrimdec(I); I ideal

Assume:

I is a zero-dimensional radical ideal

Return:

L, where L contains boxes which contain exactly one element of V(I)

Purpose:

same as rootIsolation, but speeds up computation and improves output by doing a primary decomposition before doing the root isolation

Theory:

For the primary decomposition we use the algorithm of Gianni-Traeger-Zarcharias.

Note:

This algorithm and some procedures used therein perform Groebner basis computations in basering. It is thus advised to define I w.r.t. a fast monomial ordering.

LIB "rootisolation.lib";
ring R = 0,(x,y),dp;
ideal I = 2x2-xy+2y2-2,2x2-3xy+3y2-2;  // V(I) has four elements
list result = rootIsolationPrimdec(I);
result;
==> [1]:
==>    [1, 1] x [0, 0]
==> [2]:
==>    [1/2, 1/2] x [1, 1]
==> [3]:
==>    [-1/2, -1/2] x [-1, -1]
==> [4]:
==>    [-1, -1] x [0, 0]