trackHomotopy(Homotopy,List) -- follow points along a homotopy

Synopsis

Function: trackHomotopy
Usage:

trackHomotopy(H,S)
Inputs:
- H, an instance of the type Homotopy,
- S, a list, start solutions
Optional inputs:
- CorrectorTolerance => ..., default value null, options for core functions of Numerical Algebraic Geometry
- EndZoneFactor => ..., default value null, options for core functions of Numerical Algebraic Geometry
- Field => ..., default value null
- InfinityThreshold => ..., default value null, options for core functions of Numerical Algebraic Geometry
- maxCorrSteps => ..., default value null, options for core functions of Numerical Algebraic Geometry
- NoOutput => ..., default value null, options for core functions of Numerical Algebraic Geometry
- numberSuccessesBeforeIncrease => ..., default value null, options for core functions of Numerical Algebraic Geometry
- Precision => ..., default value null, options for core functions of Numerical Algebraic Geometry
- Predictor => ..., default value null, options for core functions of Numerical Algebraic Geometry
- Software => ..., default value null, options for core functions of Numerical Algebraic Geometry
- stepIncreaseFactor => ..., default value null, options for core functions of Numerical Algebraic Geometry
- tStep => ..., default value null, options for core functions of Numerical Algebraic Geometry
- tStepMin => ..., default value null, options for core functions of Numerical Algebraic Geometry
Outputs:
- a list

Description

This method implements homotopy continuation: it follows a given list S of start solutions along a Homotopy H.

Option Field is unique to this method (the default is CC, but one can imagine using RR). It specifies which InexactFieldFamily to use when adaptive precision is requested via Precision=>infinity. The rest are a subset of numerical homotopy tracking options.

Caveat

Note for developers: the old implementation track eventually will be replaced by a call to trackHomotopy. Alternative ways for calling (H could be a Sequence (a preSLP), Matrix, etc.) are deprecated and are for debugging purposes only.

Ways to use this method: