isRealPoint -- determine whether a point is real

• Usage:

  b = isRealPoint p

• Inputs:
  • p
• Optional inputs:
  • Tolerance => ..., default value .000001, the tolerance of a numerical computation
• Outputs:
  • b, tells if p is within Tolerance to a real point

i1 : needsPackage "NumericalAlgebraicGeometry"

o1 = NumericalAlgebraicGeometry

o1 : Package

i2 : R = CC[x,y];

i3 : sols = solveSystem{x^3-y^2, x-y-2}

o3 = {{-2*ii, -2-2*ii}, {2*ii, -2+2*ii}, {1, -1}}

o3 : List

i4 : sols / isRealPoint

o4 = {false, false, true}

o4 : List