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)