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PHCpack :: isWitnessSetMember

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



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 :