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PHCpack :: factorWitnessSet

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



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);
i4 : w

o4 = w

o4 : WitnessSet
i5 : L = factorWitnessSet(w)
found 2 irreducible factors 

o5 = L

o5 : NumericalVariety

See also

Ways to use factorWitnessSet :

For the programmer

The object factorWitnessSet is a method function with options.