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D.8.7.9 num_prime_decom
Procedure from library recover.lib (see recover_lib).
- Usage:
- num_prime_decom(I,D); ideal I, int D
D a bound to the degree of the elements of the components of a prime
decomposition of I.
- Return:
- list of ideals: each of the ideals a prime component of the radical of I
- Remarks:
- Uses Bertini.
- Note:
- Should only be called from a ring over the rational numbers.
Example:
| | LIB "recover.lib";
ring R=0,(x,y,z),dp;
ideal I=(x+y)*(y+2z), (x+y)*(x-3z);
int D=2;
int Prec=300;
num_prime_decom(I,D,Prec);
==>
==> Bertini(TM) v1.6
==> (May 22, 2018)
==>
==> D.J. Bates, J.D. Hauenstein,
==> A.J. Sommese, C.W. Wampler
==>
==> (using GMP v6.0.0, MPFR v3.1.2)
==>
==>
==>
==> NOTE: You have requested to use adaptive path tracking. Please make sure\
that you have
==> setup the following tolerances appropriately:
==> CoeffBound: 8.000000000000e+00, DegreeBound: 2.000000000000e+00
==> AMPSafetyDigits1: 1, AMPSafetyDigits2: 1, AMPMaxPrec: 1024
==>
==>
==> Tracking regeneration codim 1 of 2: 2 paths to track.
==> Tracking path 0 of 2
==> Tracking path 1 of 2
==>
==> Sorting codimension 1 of 2: 2 paths to sort.
==> Sorting 0 of 2
==> Sorting 1 of 2
==>
==> Preparing regeneration codim 2 of 2: 1 witness point to move.
==> Moving 0 of 1
==>
==> Tracking regeneration codim 2 of 2: 2 paths to track.
==> Tracking path 0 of 2
==> Tracking path 1 of 2
==>
==> Sorting codimension 2 of 2: 2 paths to sort.
==> Sorting 0 of 2
==> Sorting 1 of 2
==>
==>
==> ************ Regenerative Cascade Summary ************
==>
==> NOTE: nonsingular vs singular is based on rank deficiency and identical e\
ndpoints
==>
==> |codim| paths |witness superset| nonsingular | singular |nonsolutions\
| inf endpoints | other bad endpoints
==> ----------------------------------------------------------------------------------------------------------------
==> | 1 | 2 | 1 | 1 | 0 | 1 \
| 0 | 0
==> | 2 | 2 | 2 | 1 | 1 | 0 \
| 0 | 0
==> ----------------------------------------------------------------------------------------------------------------
==> |total| 4
==>
==> ****************************************************
==>
==>
==> Removing junk points from codimension 2: 1 endpoints to check.
==> Checking 0 of 1
==>
==>
==> *************** Witness Set Summary ****************
==>
==> NOTE: nonsingular vs singular is based on rank deficiency and identical e\
ndpoints
==>
==> |codim| witness points | nonsingular | singular
==> -------------------------------------------------
==> | 1 | 1 | 1 | 0
==> | 2 | 1 | 1 | 0
==> -------------------------------------------------
==>
==> ****************************************************
==>
==>
==> Calculating traces for codimension 1.
==> Calculating 0 of 1
==>
==> Using combinatorial trace test to decompose codimension 1.
==>
==> Calculating traces for codimension 2.
==> Calculating 0 of 1
==>
==>
==> ************* Witness Set Decomposition *************
==>
==> | dimension | components | classified | unclassified
==> -----------------------------------------------------
==> | 1 | 0 | 0 | 1
==> | 0 | 1 | 1 | 0
==> -----------------------------------------------------
==>
==> ************** Decomposition by Degree **************
==>
==> Dimension 0: 1 classified component
==> -----------------------------------------------------
==> degree 1: 1 component
==>
==> *****************************************************
==>
==> 0
==> empty list
//Let us compare that to the result of primdecSY:
primdecSY(I);
==> [1]:
==> [1]:
==> _[1]=x+y
==> [2]:
==> _[1]=x+y
==> [2]:
==> [1]:
==> _[1]=y+2z
==> _[2]=x-3z
==> [2]:
==> _[1]=y+2z
==> _[2]=x-3z
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