UseMonodromy -- whether to use monodromy methods to compute degrees

Usage:

GED = parameterizedWeightEDDegree(F, U, W, UseMonodromy => true)

Description

If this option is set, the parameterized ED degree methods will use the MonodromySolver to numerically solve the critical equations and report the number of regular solutions as the ED degree of the parameterized variety.

i1 : R = QQ[x,y];

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

i3 : GED = parameterizedGenericEDDegree(F, UseMonodromy => true)

o3 = 7

Caveat

Using monodromy may result in an ED degree that is less than expected. In particular, if the parameterization map is $n$-to-one, using monodromy to solve for the degree may result in a degree than is off by a factor of $n$.

Functions with optional argument named UseMonodromy:

parameterizedGenericEDDegree(...,UseMonodromy=>...)
parameterizedUnitEDDegree(...,UseMonodromy=>...)
parameterizedWeightEDDegree(...,UseMonodromy=>...)

For the programmer

The object UseMonodromy is a symbol.

The source of this document is in EuclideanDistanceDegree.m2:229:0.