Singular

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]:
==> (-1.091539137494895032433657732542300290495-i*0.3620645097138828473958153\
   897224798132795)
==>    [2]:
==> (2.094461180430185682092618604395279248835-i*0.60967535061696549895184462\
   51740577217638)
==>    [3]:
==> (-1.091539137494895032433657732542300290495-i*0.3620645097138828473958153\
   897224798132795)
==> [2]:
==>    [1]:
==> (0.9322662765475681516613433242385265308411-i*0.4304023483863401500497589\
   037783466482181)
==>    [2]:
==> (0.01994271926407262131927561578591894808585+i*0.389572731929891481300811\
   434147133538153)
==>    [3]:
==> (0.01994271926407262131927561578591894808585+i*0.389572731929891481300811\
   434147133538153)
==> [3]:
==>    [1]:
==> (0.4206951377294804668621269077937447905995-i*0.1435362740367477235531642\
   941259118013902)
==>    [2]:
==> (0.4206951377294804668621269077937447905995-i*0.1435362740367477235531642\
   941259118013902)
==>    [3]:
==> (-0.3660198658214268072763851033658124294577+i*0.344091416897794777030086\
   0340821005202815)