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D.4.18.15 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);
==> 
==> // def S = absPrimdecGTZ(i); creates a ring,
==> // which comes with two lists:
==> // absolute_primes -- the absolute prime components,
==> // and primary_decomp -- the primary and prime
==> // components over the current basering).
==> // Type setring S; absolute_primes;
==> // to access the data.
==> 
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
See also: absFactorize; primdecGTZ.


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