Top
Back: zerodec
Forward: primitiv_lib
FastBack: normal_lib
FastForward: primitiv_lib
Up: primdec_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.4.10.15 absPrimdecGTZ

Procedure from library primdec.lib (see primdec_lib).

Usage:
absPrimdecGTZ(I); I ideal

Assume:
Ground field has characteristic 0.

Return:
a ring containing two lists: absolute_primes (the absolute prime components of I) and primary_decomp (the output of primdecGTZ(I)). The list absolute_primes has to be interpreted as follows: each entry describes a class of conjugated absolute primes,
 
   absolute_primes[i][1]   the absolute prime component,
   absolute_primes[i][2]   the number of conjugates.
The first entry of absolute_primes[i][1] is the minimal polynomial of a minimal finite field extension over which the absolute prime component is defined.

Note:
Algorithm of Gianni/Trager/Zacharias combined with the absFactorize command.

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;
def S = absPrimdecGTZ(i);
==> 
==> // 'absPrimdecGTZ' created a ring, in which two lists absolute_primes (th\
   e
==> // absolute prime components) and primary_decomp (the primary and prime
==> // components over the current basering) are stored.
==> // To access the list of absolute prime components, type (if the name S w\
   as
==> // assigned to the return value):
==>         setring S; absolute_primes; 
setring S;
absolute_primes;
==> [1]:
==>    [1]:
==>       _[1]=a3+2
==>       _[2]=z-a
==>       _[3]=y-za
==>    [2]:
==>       3
==> [2]:
==>    [1]:
==>       _[1]=a2+1
==>       _[2]=z-a
==>       _[3]=y+1
==>    [2]:
==>       2
primdecGTZ, absFactorize


Top Back: zerodec Forward: primitiv_lib FastBack: normal_lib FastForward: primitiv_lib Up: primdec_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 3-0-1, October 2005, generated by texi2html.