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]:
==> (-0.6148682175293528269000847552058993558245+i*1.322901188749815465696612\
   571759403022028)
==>    [2]:
==> (-0.6454844170598741581971816981005691299296-i*1.510182926907183564857735\
   628787292535952)
==>    [3]:
==> (-0.6148682175293528269000847552058993558245+i*1.322901188749815465696612\
   571759403022028)
==> [2]:
==>    [1]:
==> (-0.1287433298093820045615267644892869459428+i*1.147656662176870257058437\
   924129583214206)
==>    [2]:
==> (0.304356848597029953864983424482198409305-i*0.09871743444908696318016782\
   785315877345917)
==>    [3]:
==> (0.304356848597029953864983424482198409305-i*0.09871743444908696318016782\
   785315877345917)
==> [3]:
==>    [1]:
==> (0.2684708551916681529039926174107476056399+i*1.2587766892280933780421532\
   85549246941945)
==>    [2]:
==> (0.2684708551916681529039926174107476056399+i*1.2587766892280933780421532\
   85549246941945)
==>    [3]:
==> (1.560216638185363375647879145056077916064-i*0.59747859734886145756212285\
   98345861730618)