# witnessSet -- construct a WitnessSet

## Synopsis

• Usage:
w = witnessSet(E,S,P)
• Inputs:
• E, an ideal or
• S, an ideal generated by linear polynomials (or of the generators or of their coefficients)
• P, a list, contains witness points (of type Point)
• Outputs:
• w,

## Description

Used to construct a witness set of a component of the variety V(E). It is expected that codim E == dim S and that P is a subset of the intersection of V(E) and V(S).

 i1 : R = CC[x,y] o1 = R o1 : PolynomialRing i2 : w = witnessSet( ideal(x^2+y^2+2), ideal(x-y), {point {{0.999999*ii,0.999999*ii}}, point {{-1.000001*ii,-1.000001*ii}}} ) o2 = w o2 : WitnessSet i3 : peek w o3 = WitnessSet{cache => CacheTable{...1...} } Equations => {-2} | x2+y2+2 | Points => {{.999999*ii, .999999*ii}} {{-ii, -ii} } Slice => | 1 -1 0 |

## Ways to use witnessSet :

• "witnessSet(Ideal,Ideal,List)"
• "witnessSet(Ideal,Matrix,List)"
• "witnessSet(PolySystem,Matrix,List)"
• "witnessSet(PolySystem,PolySystem,List)"

## For the programmer

The object witnessSet is .