D.8.7.7 getWitnessSet

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.

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");
//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;