
D.4.21.3 primdecGTZE
Procedure from library primdec.lib (see primdec_lib).
 Usage:
 primdecGTZE(I); i ideal
 Return:
 a list pr of primary ideals and their associated primes for a proper ideal, and an empty list for the unit ideal.
 pr[i][1] the ith primary component,
pr[i][2] the ith 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!)
 For local orderings, the result is considered in the localization
of the polynomial ring, not in the power series ring
 For local and mixed orderings, the decomposition in the
corresponding global ring is returned if the string 'global'
is specified as second argument
Example:
 LIB "primdec.lib";
ring r = 0,(x,y,z),lp;
poly p = z2+1;
poly q = z3+2;
ideal I = p*q^2,yz2;
list pr = primdecGTZE(I);
pr;
==> [1]:
==> [1]:
==> _[1]=z6+4z3+4
==> _[2]=yz2
==> [2]:
==> _[1]=z3+2
==> _[2]=yz2
==> [2]:
==> [1]:
==> _[1]=z2+1
==> _[2]=yz2
==> [2]:
==> _[1]=z2+1
==> _[2]=yz2
ideal J = 1;
list prempty = primdecGTZE(J);
prempty;
==> empty list

