ReturnCriticalIdeal -- whether to return the ideal of critical points

Usage:

ICP = symbolicWeightEDDegree(F, U, W, ReturnCriticalIdeal => true)

Description

Symbolic methods compute the Euclidean Distance degree of a variety by computing the degree of its critical ideal, which defines the critical points of the distance function on the variety. Setting this option will cause symbolic methods to return this ideal rather than its degree.

i1 : R = QQ[x,y];

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

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

i4 : ICP = symbolicWeightEDDegree(F, U, W, ReturnCriticalIdeal => true)

                                    2    2
o4 = ideal (316x*y - 7613x + 180y, x  + y  - 1)

o4 : Ideal of R

Functions with optional argument named ReturnCriticalIdeal:

determinantalGenericEDDegree(...,ReturnCriticalIdeal=>...)
determinantalUnitEDDegree(...,ReturnCriticalIdeal=>...)
symbolicWeightEDDegree(...,ReturnCriticalIdeal=>...)

For the programmer

The object ReturnCriticalIdeal is a symbol.

The source of this document is in EuclideanDistanceDegree.m2:163:0.