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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


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            User manual for Singular version 2-0-4, May 2003, generated by texi2html.