D.4.7.2 primdecGTZ

Procedure from library primdec.lib (see primdec_lib).

Usage:

primdecGTZ(i); i ideal

Return:

a list pr of primary ideals and their associated primes:

pr[i][1] the i-th primary component, pr[i][2] the i-th prime component.

Note:

Algorithm of Gianni/Trager/Zacharias.
Designed for characteristic 0, works also in char k > 0, if it terminates (may result in an infinite loop in small characteristic!)

Example:

LIB "primdec.lib";
ring  r = 0,(x,y,z),lp;
poly  p = z2+1;
poly  q = z3+2;
ideal i = p*q^2,y-z2;
list pr = primdecGTZ(i);
pr;
→ [1]:
→    [1]:
→       _[1]=z6+4z3+4
→       _[2]=y-z2
→    [2]:
→       _[1]=z3+2
→       _[2]=y-z2
→ [2]:
→    [1]:
→       _[1]=z2+1
→       _[2]=y-z2
→    [2]:
→       _[1]=z2+1
→       _[2]=y-z2