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

## Synopsis

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

## 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,Point)"

## For the programmer

The object isWitnessSetMember is .