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

• Usage:

  UED = numericUnitEDDegree(F,G)

  GED = numericGenericEDDegree(F,G)

  GED = homotopyEDDegree(F,G,U,V)

• Inputs:
  • F, a list, a system of polynomials (need not be square) defining the variety
  • G, a list, a system of polynomials (complete intersection) such that $V(F)$ is an irreducible component of $V(G)$, i.e. a witness model
  • U, a list, a (generic) data vector
  • W, a list, a (generic) weight vector
• Optional inputs:
  • Submodel => a list, default value {}, list of linear polynomials to slice the variety
  • TempDirectory => ..., default value null, set directory for Bertini runs
• Outputs:
  • ED, an integer, a generic/unit Euclidean distance degree

i1 : R = QQ[x,y];

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

i3 : (U,W) = ({.12, .23}, {.15, .331});

i4 : UED = numericUnitEDDegree(F, G)

o4 = 2

i5 : GED = numericGenericEDDegree(F, G)
-- warning: experimental computation over inexact field begun
--          results not reliable (one warning given per session)

o5 = 4

i6 : GED = numericWeightEDDegree(F, G, U, W)

o6 = 4