|
|
D.4.21.2 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 for a proper ideal I, otherwise pr = list( list( ideal(1), ideal(1) )
| | 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!)
- 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,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
|
|
