witnessSet -- construct a WitnessSet

Synopsis

• Usage:

  w = witnessSet(E,S,P)

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

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{IsIrreducible => null               }
                Points => {{.999999*ii, .999999*ii}}
                          {{-ii, -ii}              }
                Slice => | 1 -1 0 |
                                    2    2
                Equations => ideal(x  + y  + 2)