homotopyEDDegree -- numerically compute ED degrees of affine cones using homotopy continuation

• Usage:

  GED = homotopyEDDegree(NCO, "Weight", true, false)

• Inputs:
  • NCO, an instance of the type NumericalComputationOptions, a MutableHashTable to keeps track of the options and configurations for the homotopy methods
  • ht, a string, one of "Weight" or "Data" which defines the type of homotopy to execute
  • isStageOne, a Boolean value, if set, runs stage 1 to solve the start system
  • isStageTwo, a Boolean value, if set, runs stage 2 to solve the target system via path tracking
• Outputs:
  • ED, an integer, a generic/unit Euclidean distance degree

i1 : R = QQ[x,y];

i2 : F = G = {x^2+y^2-1};

i3 : NCO = newNumericalComputationOptions(F, G);

i4 : NCO#"TargetWeight" = apply(#gens R, i -> random RR);

i5 : GED = homotopyEDDegree(NCO, "Weight", true, true)
-- warning: experimental computation over inexact field begun
--          results not reliable (one warning given per session)

o5 = 4

i6 : NCO#"TargetWeight" = apply(#gens R, i -> 1_R);

i7 : UED = homotopyEDDegree(NCO, "Weight", false, true)

o7 = 2