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PHCpack :: factorWitnessSet

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

Synopsis

Description

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

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 constructEmbedding ...
calling phc -c < /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44733-0/2PHCbatch > /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44733-0/3PHCsession
output of phc -c is in file /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44733-0/1PHCoutput
... calling solveSystem ...
using temporary files /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44733-0/4PHCinput and /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44733-0/4PHCoutput
... constructing a witness set ... 
i4 : w

o4 = [dim=1,deg=4]

o4 : WitnessSet
i5 : L = factorWitnessSet(w)
preparing input file to /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44733-0/5PHCinput
preparing batch file to /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44733-0/7PHCbatch
... calling monodromy breakup ...
session information of phc -f is in /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44733-0/8PHCsession
output of phc -f is in file /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44733-0/6PHCoutput
found 2 irreducible factors 

o5 = A variety of dimension 1 with components in
     dim 1:  (dim=1,deg=3) (dim=1,deg=1)

o5 : NumericalVariety

See also

Ways to use factorWitnessSet :

  • factorWitnessSet(WitnessSet)