numericalVariety(List) -- construct a numerical variety

Synopsis

• Function: numericalVariety

• Usage:

  V = numericalVariety Ws; V = projectiveNumericalVariety Ws;

• Inputs:
  • Ws, a list, contains (projective) witness sets representing components of a variety
• Outputs:
  • V, a numerical variety

Description

Constructs a numerical (affine or projective) variety. It is NOT expected that every witness set W in the list Ws has the same W.Equations.

i1 : R = CC[x,y]; I = ideal((x^2+y^2+2)*x,(x^2+y^2+2)*y);

o2 : Ideal of R

i3 : w1 = witnessSet(I , ideal(x-y), {point {{0.999999*ii,0.999999*ii}}, point {{-1.000001*ii,-1.000001*ii}}} )

o3 = w1

o3 : WitnessSet

i4 : w0 = witnessSet(I, ideal R, {point {{0.,0.}}})

o4 = w0

o4 : WitnessSet

i5 : V = numericalVariety {w0,w1}

o5 = V

o5 : NumericalVariety

See also

• WitnessSet -- a witness set
• ProjectiveWitnessSet -- a projective witness set
• numericalAffineSpace -- affine space as a numerical variety