A witness set is irreducible if there exists a path not passing through a singularity between any two of its generic points.
i1 : R = CC[x,y,z]; f = {(x^2-y)*(x-1), x^3 - z}; |
i3 : (w,ns) = topWitnessSet(f,1); ... calling phcEmbed ... writing output to file /tmp/M2-7872-0/1PHCoutput calling phc -c < /tmp/M2-7872-0/2PHCbatch > /tmp/M2-7872-0/3PHCsession output of phc -c is in file /tmp/M2-7872-0/1PHCoutput ... calling phcSolve ... using temporary files /tmp/M2-7872-0/4PHCinput and /tmp/M2-7872-0/4PHCoutput ... constructing a witness set ... |
i4 : degree(w) o4 = 4 |
i5 : L = phcFactor(w) preparing input file to /tmp/M2-7872-0/5PHCinput preparing batch file to /tmp/M2-7872-0/7PHCbatch ... calling monodromy breakup ... session information of phc -f is in /tmp/M2-7872-0/8PHCsession output of phc -f is in file /tmp/M2-7872-0/6PHCoutput found 2 irreducible factors o5 = {(dim=1,deg=1), (dim=1,deg=3)} o5 : List |