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D.4.29.1 primdecZ

Procedure from library primdecint.lib (see primdecint_lib).

Usage:
primdecZ(I[, n]); I ideal, n integer (number of processors)

Note:
If size(#) > 0, then #[1] is the number of available processors for the computation.
The coefficients must be ZZ.

Return:
a list pr of primary ideals and their associated primes:
 
   pr[i][1]   the i-th primary component,
   pr[i][2]   the i-th prime component.

Example:
 
LIB "primdecint.lib";
ring R=integer,(a,b,c,d),dp;
ideal I1=9,a,b;
ideal I2=3,c;
ideal I3=11,2a,7b;
ideal I4=13a2,17b4;
ideal I5=9c5,6d5;
ideal I6=17,a15,b15,c15,d15;
ideal I=intersectZ(I1,I2);
I=intersectZ(I,I3);
I=intersectZ(I,I4);
I=intersectZ(I,I5);
I=intersectZ(I,I6);
primdecZ(I);
==> [1]:
==>    [1]:
==>       _[1]=d5
==>       _[2]=c5
==>    [2]:
==>       _[1]=d
==>       _[2]=c
==> [2]:
==>    [1]:
==>       _[1]=a2
==>       _[2]=b4
==>    [2]:
==>       _[1]=b
==>       _[2]=a
==> [3]:
==>    [1]:
==>       _[1]=2
==>       _[2]=c5
==>    [2]:
==>       _[1]=2
==>       _[2]=c
==> [4]:
==>    [1]:
==>       _[1]=3
==>    [2]:
==>       _[1]=3
==> [5]:
==>    [1]:
==>       _[1]=13
==>       _[2]=b4
==>    [2]:
==>       _[1]=13
==>       _[2]=b
==> [6]:
==>    [1]:
==>       _[1]=17
==>       _[2]=a2
==>    [2]:
==>       _[1]=17
==>       _[2]=a
==> [7]:
==>    [1]:
==>       _[1]=17
==>       _[2]=d15
==>       _[3]=c15
==>       _[4]=b15
==>       _[5]=a15
==>    [2]:
==>       _[1]=17
==>       _[2]=d
==>       _[3]=c
==>       _[4]=b
==>       _[5]=a
==> [8]:
==>    [1]:
==>       _[1]=9
==>       _[2]=3d5
==>       _[3]=d10
==>    [2]:
==>       _[1]=3
==>       _[2]=d
ideal J=intersectZ(ideal(17,a),ideal(17,a2,b));
primdecZ(J);
==> [1]:
==>    [1]:
==>       _[1]=17
==>       _[2]=a
==>    [2]:
==>       _[1]=17
==>       _[2]=a
==> [2]:
==>    [1]:
==>       _[1]=17
==>       _[2]=b
==>       _[3]=a2
==>    [2]:
==>       _[1]=17
==>       _[2]=b
==>       _[3]=a
ideal K=intersectZ(ideal(9,a+3),ideal(9,b+3));
primdecZ(K);
==> [1]:
==>    [1]:
==>       _[1]=9
==>       _[2]=b+3
==>    [2]:
==>       _[1]=3
==>       _[2]=b
==> [2]:
==>    [1]:
==>       _[1]=9
==>       _[2]=a+3
==>    [2]:
==>       _[1]=3
==>       _[2]=a


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