leftKernelWeightEDDegree -- numerically compute Euclidean distance degrees of complete intersections

• Usage:

  UED = leftKernelUnitEDDegree(F)

  GED = leftKernelGenericEDDegree(F)

  GED = leftKernelWeightEDDegree(F,U,W)

• Inputs:
  • F, a list, a system of polynomials (need not be square) defining an affine variety that is a complete intersection
  • U, a list, a (generic) data vector
  • W, a list, a (generic) weight vector
• Optional inputs:
  • 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 = {x^2 + y^2 - 1};

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

i4 : UED = leftKernelUnitEDDegree F
Warning: The HomVariableGroup is written first and then the AffVariableGroup is written second.

o4 = 2

i5 : GED = leftKernelGenericEDDegree F
Warning: The HomVariableGroup is written first and then the AffVariableGroup is written second.

o5 = 4

i6 : GED = leftKernelWeightEDDegree(F, U, W)
Warning: The HomVariableGroup is written first and then the AffVariableGroup is written second.

o6 = 4