NAG -- Numerical Algebraic Geometry

Description

The package NAG4M2 (Numerical Algebraic Geometry for Macaulay 2) implements methods of polynomial homotopy continuation to solve systems of polynomial equations and deal with complex algebraic varieties.

Under construction:

The package will be included in the future releases of Macaulay 2.
In order to run the current version of the package Macaulay 2 needs to be compiled from the source code. Instructions are posted at http://www.math.uiuc.edu/Macaulay2/Downloads/SourceCode.

( Another way is to download the packages subdirectory only:
svn co svn://macaulay2.math.uiuc.edu/Macaulay2/trunk/M2/Macaulay2/packages
and then use
loadPackage("NAG", FileName=>"packages/NAG.m2").
Note: in this case the functionality of the package is limited; in particular, SLP and M2engine options do not work. )

Functions:

solveSystem -- solve a square system of polynomial equations
track -- track a user homotopy

Author

Anton Leykin <leykin@math.uic.edu>

Version

This documentation describes version 1.2.1 of NAG.

Source code

The source code is in the file NAG.m2.

Exports

Functions
- areEqual (missing documentation)
- multistepPredictor (missing documentation)
- multistepPredictorLooseEnd (missing documentation)
- refine, see refine(List,List) -- refine numerical solutions to a system of polynomial equations
- solveSystem, see solveSystem(List) -- solve a square system of polynomial equations
- sortSolutions (missing documentation)
- totalDegreeStartSystem, see totalDegreeStartSystem(List) -- construct a start system for the total degree homotopy
- track, see track(List,List,List) -- track a user homotopy
Symbols
- AffinePatches (missing documentation)
- Bertini -- use Bertini for homotopy continuation
- CompiledHornerForm (missing documentation)
- CorrectorTolerance (missing documentation)
- DynamicPatch (missing documentation)
- Euler (missing documentation)
- finalMaxCorrSteps (missing documentation)
- gamma (missing documentation)
- HOM4PS2 -- use HOM4PS for homotopy continuation
- HornerForm (missing documentation)
- maxCorrSteps (missing documentation)
- Multistep (missing documentation)
- MultistepDegree (missing documentation)
- numberSuccessesBeforeIncrease (missing documentation)
- PHCpack -- use PHCpack for homotopy continuation
- Predictor (missing documentation)
- Projectivize (missing documentation)
- RandomSeed (missing documentation)
- RungeKutta4 (missing documentation)
- Secant (missing documentation)
- SLP (missing documentation)
- SLPcorrector (missing documentation)
- SLPpredictor (missing documentation)
- M2, see solveSystem(..., Software => ...) -- specify software for the solver
- M2engine, see solveSystem(..., Software => ...) -- specify software for the solver
- M2enginePrecookedSLPs, see solveSystem(..., Software => ...) -- specify software for the solver
- Software, see solveSystem(..., Software => ...) -- specify software for the solver
- stepIncreaseFactor (missing documentation)
- Tangent (missing documentation)
- tDegree (missing documentation)
- Tolerance (missing documentation)
- tStep (missing documentation)
- tStepMax (missing documentation)
- tStepMin (missing documentation)