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isWitnessSetMember -- tests whether a point belongs to a solution set

Description

Uses numerical homotopy methods to test whether the point p belongs to the variety associated to the witness set W.

Although W should be properly embedded, p should be given in the coordinates of the original system.

i1 : R = CC[x11,x22,x21,x12,x23,x13];
i2 : system = {x11*x22-x21*x12,x12*x23-x22*x13};
i3 : V = numericalIrreducibleDecomposition (system);
found 4 irreducible factors 
i4 : W = first V#4;
i5 : isWitnessSetMember(W, point{{0,0,0,0,0,0}})

o5 = true

Ways to use isWitnessSetMember:

  • isWitnessSetMember(WitnessSet,AbstractPoint)

For the programmer

The object isWitnessSetMember is a method function with options.


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/PHCpack/PHCpackDoc.m2:499:0.