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D.8.7.7 getWitnessSet
Procedure from library recover.lib (see recover_lib).
- Usage:
- getWitnessSet();
- Assume:
- There is a text-document "main_data" in the current directory which was
produced by Bertini.
The basefield is the field of real numbers or the field of complex numbers.
- Return:
- list; a list P of lists p_i of numbers: P a set of witness points
- Note:
- Reads the file "main_data", searches the strings containing the witness points,
and converts them into floating point numbers.
Example:
| LIB "recover.lib";
//First, we write the input file for bertini, then run bertini
ring r=0,(x,y,z),dp;
ideal I=(x-y)*(y-z)*(x-z);
writeBertiniInput(I,40);
system("sh","bertini input");
==>
==> 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: 6.000000000000e+00, DegreeBound: 3.000000000000e+00
==> AMPSafetyDigits1: 1, AMPSafetyDigits2: 1, AMPMaxPrec: 160
==>
==>
==> Tracking regeneration codim 1 of 1: 3 paths to track.
==> Tracking path 0 of 3
==> Tracking path 1 of 3
==> Tracking path 2 of 3
==>
==> Sorting codimension 1 of 1: 3 paths to sort.
==> Sorting 0 of 3
==> Sorting 1 of 3
==> Sorting 2 of 3
==>
==>
==> ************ 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 | 3 | 3 | 3 | 0 | 0 \
| 0 | 0
==> ----------------------------------------------------------------------------------------------------------------
==> |total| 3
==>
==> ****************************************************
==>
==>
==>
==> *************** Witness Set Summary ****************
==>
==> NOTE: nonsingular vs singular is based on rank deficiency and identical e\
ndpoints
==>
==> |codim| witness points | nonsingular | singular
==> -------------------------------------------------
==> | 1 | 3 | 3 | 0
==> -------------------------------------------------
==>
==> ****************************************************
==>
==>
==> Calculating traces for codimension 1.
==> Calculating 0 of 3
==> Calculating 1 of 3
==> Calculating 2 of 3
==>
==> Using combinatorial trace test to decompose codimension 1.
==>
==>
==> ************* Witness Set Decomposition *************
==>
==> | dimension | components | classified | unclassified
==> -----------------------------------------------------
==> | 1 | 0 | 0 | 3
==> -----------------------------------------------------
==>
==> ************** Decomposition by Degree **************
==>
==> *****************************************************
==>
==> 0
//Then we change the ring and extract the witness set from main_data
ring R=(complex,40,i),(x,y,z),dp;
list P=getWitnessSet();
P;
==> [1]:
==> [1]:
==> (-0.5053477842536520234882531787599500977517+i*0.459412532175336719793946\
1433257152223253)
==> [2]:
==> (-0.07686982534976881571588082407272096218348-i*0.14523875021278221526860\
14899525911669524)
==> [3]:
==> (-0.07686982534976881571588082407272096218348-i*0.14523875021278221526860\
14899525911669524)
==> [2]:
==> [1]:
==> (-0.03328981724377298288606629765108993272105+i*0.70676032948548696099027\
69178309021036699)
==> [2]:
==> (0.5012448569660372139533544973514823985668+i*0.3646023649027948310973766\
504146583225158)
==> [3]:
==> (-0.03328981724377298288606629765108993272105+i*0.70676032948548696099027\
69178309021036699)
==> [3]:
==> [1]:
==> (-0.383199612605882475216427274028733151279+i*1.8490868825302240054009933\
75508087988171)
==> [2]:
==> (-0.383199612605882475216427274028733151279+i*1.8490868825302240054009933\
75508087988171)
==> [3]:
==> (-1.892529239771633450162525888846915411464+i*1.1548801949118699760864660\
24340955009543)
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