Uses numerical homotopy methods to test whether the point p belongs to the variety associated to the witness set W.
Although W should be properly embedded, p should be given in the coordinates of the original system.
i1 : R = CC[x11,x22,x21,x12,x23,x13]; |
i2 : system = {x11*x22-x21*x12,x12*x23-x22*x13}; |
i3 : V = numericalIrreducibleDecomposition (system); writing output to file /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44669-0/1PHCoutput calling phc -c < /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44669-0/2PHCbatch > /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44669-0/4PHCsession output of phc -c is in file /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44669-0/1PHCoutput ... constructing witness sets ... preparing input file to /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44669-0/6PHCinput preparing batch file to /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44669-0/8PHCbatch ... calling monodromy breakup ... session information of phc -f is in /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44669-0/9PHCsession output of phc -f is in file /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44669-0/7PHCoutput found 2 irreducible factors |
i4 : W = first V#4; |
i5 : isWitnessSetMember(W, point{{0,0,0,0,0,0}}) o5 = true |