Top
Back: gaussColWithoutPerm
Forward: writeBertiniInput
FastBack:
FastForward:
Up: recover_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

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]:
==> (2.205434719776045096930307642859075524287+i*0.25730092814606991457068358\
   04349122804132)
==>    [2]:
==> (-1.226268021448026250395260475546359882937+i*2.2086899103953438646694486\
   85263394248351)
==>    [3]:
==> (2.205434719776045096930307642859075524287+i*0.25730092814606991457068358\
   04349122804132)
==> [2]:
==>    [1]:
==> (-0.3005303817070822590769853153215176888853+i*0.530349818173461311476099\
   5170026362821902)
==>    [2]:
==> (-0.3005303817070822590769853153215176888853+i*0.530349818173461311476099\
   5170026362821902)
==>    [3]:
==> (0.6054234023633421459312700472938903569694-i*0.0447398875576939657055861\
   5192222264579111)
==> [3]:
==>    [1]:
==> (-1.22654501255552276109695812488273122541+i*0.69428184328086858442236556\
   33071289026215)
==>    [2]:
==> (0.002338594377493654012440398487905742432261-i*0.11739563056944158919740\
   07631104624782625)
==>    [3]:
==> (0.002338594377493654012440398487905742432261-i*0.11739563056944158919740\
   07631104624782625)


Top Back: gaussColWithoutPerm Forward: writeBertiniInput FastBack: FastForward: Up: recover_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 4.2.1p2, 2021, generated by texi2html.