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PHCpack :: phcFactor

phcFactor -- applies monodromy to factor a witness set into irreducible components

Synopsis

Description

A witness set is irreducible if there exists a path not passing through a singularity between any two of its generic points.

We illustrate the factorization via the twisted cubic and a line.
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

Ways to use phcFactor :