sample(WitnessSet) -- sample a point on a component

• Function: sample

• Usage:

  P = sample W

• Inputs:
  • W, a witness set
• Optional inputs:
  • Tolerance => ..., default value .000001
• Outputs:
  • P, an instance of the type Point

i1 : R = CC[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : W = witnessSet(ideal {x^2+y^2+z^2-1, z^2}, matrix "1,0,0,0", {{{0,1,0_CC}},{{0,-1,0_CC}}}/point ) 

o2 = W

o2 : WitnessSet

i3 : P := sample(W, Tolerance=>1e-15)   

o3 = (-1.08328-.110311*ii, -.252017+.474162*ii, -2.0883e-26-4.5498e-25*ii)

o3 : Point

i4 : isOn(P,W)

o4 = true