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 |
The object factorWitnessSet is a method function with options.