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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
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