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D.4.21.1 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.
- 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.
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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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