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 (the default is CC, but one can imagine using RR) 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: