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

Synopsis

Usage:

isWitnessSetMember(W,p)
Inputs:
- W, a witness set, positive dimensional, properly embedded with slack variables
- p, a point,
Optional inputs:
- Verbose => ..., default value false, option to specify whether additional output is wanted
Outputs:
- a Boolean value, true if p is a member of the solution set of W, false otherwise
Consequences:
- Invokes the command phc -f (with option 1)

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