parameterizedWeightEDDegree -- compute ED degrees of parameterized varieties

Usage:

UED = parameterizedUnitEDDegree(F)

GED = parameterizedGenericEDDegree(F)

GED = parameterizedWeightEDDegree(F,U,W)
Inputs:
- F, a list, a system of polynomials in $d$ variables parameterizing a $d$-dimensional variety
- U, a list, a (generic) data vector
- W, a list, a (generic) weight vector
Optional inputs:
- UseMonodromy => ..., default value false, whether to use monodromy methods to compute degrees
Outputs:
- ED, an integer, a generic/unit Euclidean distance degree

Description

This method computes Euclidean distance (ED) degrees for the variety parameterized by the a set of polynomials $F$ in $d$ variables. If the resulting variety is $d$-dimensional, then by finding a global description for the kernel of the transpose of the Jacobian map, the critical equations of the variety can be computed. The unit variant of this method computes an ED degree using random (integer) data and unit weights, whereas the generic variant will use random data and random weights.

i1 : R = QQ[x,y];

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

i3 : (U,W) = ({12, 23, 25}, {15, 331, 1});

i4 : UED = parameterizedUnitEDDegree F

o4 = 7

i5 : GED = parameterizedGenericEDDegree F

o5 = 7

i6 : GED = parameterizedWeightEDDegree(F, U, W)

o6 = 7

Ways to use parameterizedWeightEDDegree:

parameterizedWeightEDDegree(List,List,List)

For the programmer

The object parameterizedWeightEDDegree is a method function with options.

The source of this document is in EuclideanDistanceDegree.m2:270:0.

parameterizedWeightEDDegree -- compute ED degrees of parameterized varieties

Description

Menu

Ways to use parameterizedWeightEDDegree:

For the programmer