isOn -- determines if a point belongs to a variety

• Usage:

  B = isOn(P,V)

• Inputs:
  • P, a point
  • V, a numerical variety, a witness set, an ideal, or a ring element
• Optional inputs:
  • Software => ..., default value null, specify internal or external software
  • Tolerance => ..., default value null
• Outputs:
  • B, a Boolean value

i1 : R = CC[x,y]

o1 = R

o1 : PolynomialRing

i2 : I = ideal((x^2+y^2+2)*x,(x^2+y^2+2)*y);

o2 : Ideal of R

i3 : e = 0.0000001

o3 = 1e-7

o3 : RR (of precision 53)

i4 : W = witnessSet(ideal I_0 , ideal(x-y), {point {{ (1-e)*ii,(1-e)*ii}},point {{ -(1+e)*ii,-(1+e)*ii}}})	

o4 = W

o4 : WitnessSet

i5 : isOn(point {{sqrt 5*ii,sqrt 3}},W)

o5 = true