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<div><h1>NumericalAlgebraicGeometry -- Numerical Algebraic Geometry</h1>
<div class="single"><h2>Description</h2>
<div>The package <em>NAG4M2 (Numerical Algebraic Geometry for Macaulay 2)</em> implements methods of polynomial homotopy continuation to solve systems of polynomial equations and describe positive-dimensional complex algebraic varieties.<br/>The current version focuses on solving square systems with finite number of solutions.</div>
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<div class="single"><h2>Author</h2>
<ul><li><div class="single">Anton Leykin<span> <<a href="mailto:leykin@math.gatech.edu">leykin@math.gatech.edu</a>></span></div>
</li>
</ul>
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<div class="single"><h2>Version</h2>
This documentation describes version <b>1.3.0.1</b> of NumericalAlgebraicGeometry.</div>
<div class="single"><h2>Source code</h2>
The source code from which this documentation is derived is in the file <a href="../../../../Macaulay2/NumericalAlgebraicGeometry.m2">NumericalAlgebraicGeometry.m2</a>. The auxiliary files accompanying it are in the directory <a href="../../../../Macaulay2/NumericalAlgebraicGeometry/">NumericalAlgebraicGeometry/</a>.</div>
<div class="single"><h2>Exports</h2>
<ul><li><div class="single">Functions<ul><li><span><a href="_are__Equal.html" title="determine if solutions are equal">areEqual</a> -- determine if solutions are equal</span></li>
<li><span>getSolution, see <span><a href="_get__Solution_lp__Z__Z_rp.html" title="get various attributes of the specified solution">getSolution(ZZ)</a> -- get various attributes of the specified solution</span></span></li>
<li><span><a href="_good__Initial__Pair.html" title="a good (conjectured by Shub and Smale) initial pair">goodInitialPair</a> -- a good (conjectured by Shub and Smale) initial pair</span></li>
<li><span>NAGtrace, see <span><a href="___N__A__Gtrace_lp__Z__Z_rp.html" title="set the trace level in NumericalAlgebraicGeometry package">NAGtrace(ZZ)</a> -- set the trace level in NumericalAlgebraicGeometry package</span></span></li>
<li><span><a href="_random__Initial__Pair.html" title="a random initial pair">randomInitialPair</a> -- a random initial pair</span></li>
<li><span><a href="_random__Sd.html" title="a random homogeneous system of polynomial equations">randomSd</a> -- a random homogeneous system of polynomial equations</span></li>
<li><span>refine, see <span><a href="_refine_lp__List_cm__List_rp.html" title="refine numerical solutions to a system of polynomial equations">refine(List,List)</a> -- refine numerical solutions to a system of polynomial equations</span></span></li>
<li><span>solveSystem, see <span><a href="_solve__System_lp__List_rp.html" title="solve a square system of polynomial equations">solveSystem(List)</a> -- solve a square system of polynomial equations</span></span></li>
<li><span>sortSolutions, see <span><a href="_sort__Solutions_lp__List_rp.html" title="sort the list of solutions">sortSolutions(List)</a> -- sort the list of solutions</span></span></li>
<li><span>totalDegreeStartSystem, see <span><a href="_total__Degree__Start__System_lp__List_rp.html" title="construct a start system for the total degree homotopy">totalDegreeStartSystem(List)</a> -- construct a start system for the total degree homotopy</span></span></li>
<li><span>track, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
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<li><div class="single">Symbols<ul><li><span><a href="___Bertini.html" title="use Bertini for homotopy continuation">Bertini</a> -- use Bertini for homotopy continuation</span></li>
<li><span>Coordinates, see <span><a href="_get__Solution_lp__Z__Z_rp.html" title="get various attributes of the specified solution">getSolution(ZZ)</a> -- get various attributes of the specified solution</span></span></li>
<li><span>LastT, see <span><a href="_get__Solution_lp__Z__Z_rp.html" title="get various attributes of the specified solution">getSolution(ZZ)</a> -- get various attributes of the specified solution</span></span></li>
<li><span>NumberOfSteps, see <span><a href="_get__Solution_lp__Z__Z_rp.html" title="get various attributes of the specified solution">getSolution(ZZ)</a> -- get various attributes of the specified solution</span></span></li>
<li><span>RCondition, see <span><a href="_get__Solution_lp__Z__Z_rp.html" title="get various attributes of the specified solution">getSolution(ZZ)</a> -- get various attributes of the specified solution</span></span></li>
<li><span>SolutionAttributes, see <span><a href="_get__Solution_lp__Z__Z_rp.html" title="get various attributes of the specified solution">getSolution(ZZ)</a> -- get various attributes of the specified solution</span></span></li>
<li><span>SolutionStatus, see <span><a href="_get__Solution_lp__Z__Z_rp.html" title="get various attributes of the specified solution">getSolution(ZZ)</a> -- get various attributes of the specified solution</span></span></li>
<li><span>GeneralPosition, see <span><a href="_good__Initial__Pair.html" title="a good (conjectured by Shub and Smale) initial pair">goodInitialPair</a> -- a good (conjectured by Shub and Smale) initial pair</span></span></li>
<li><span><a href="___H__O__M4__P__S2.html" title="use HOM4PS for homotopy continuation">HOM4PS2</a> -- use HOM4PS for homotopy continuation</span></li>
<li><span><a href="___P__H__Cpack.html" title="use PHCpack for homotopy continuation">PHCpack</a> -- use PHCpack for homotopy continuation</span></li>
<li><span>Bits, see <span><a href="_refine_lp__List_cm__List_rp.html" title="refine numerical solutions to a system of polynomial equations">refine(List,List)</a> -- refine numerical solutions to a system of polynomial equations</span></span></li>
<li><span>ErrorTolerance, see <span><a href="_refine_lp__List_cm__List_rp.html" title="refine numerical solutions to a system of polynomial equations">refine(List,List)</a> -- refine numerical solutions to a system of polynomial equations</span></span></li>
<li><span>Iterations, see <span><a href="_refine_lp__List_cm__List_rp.html" title="refine numerical solutions to a system of polynomial equations">refine(List,List)</a> -- refine numerical solutions to a system of polynomial equations</span></span></li>
<li><span>ResidualTolerance, see <span><a href="_refine_lp__List_cm__List_rp.html" title="refine numerical solutions to a system of polynomial equations">refine(List,List)</a> -- refine numerical solutions to a system of polynomial equations</span></span></li>
<li><span>M2, see <span><a href="_solve__System_lp..._cm_sp__Software_sp_eq_gt_sp..._rp.html" title="specify software for the solver">solveSystem(..., Software => ...)</a> -- specify software for the solver</span></span></li>
<li><span>M2engine, see <span><a href="_solve__System_lp..._cm_sp__Software_sp_eq_gt_sp..._rp.html" title="specify software for the solver">solveSystem(..., Software => ...)</a> -- specify software for the solver</span></span></li>
<li><span>M2enginePrecookedSLPs, see <span><a href="_solve__System_lp..._cm_sp__Software_sp_eq_gt_sp..._rp.html" title="specify software for the solver">solveSystem(..., Software => ...)</a> -- specify software for the solver</span></span></li>
<li><span>Software, see <span><a href="_solve__System_lp..._cm_sp__Software_sp_eq_gt_sp..._rp.html" title="specify software for the solver">solveSystem(..., Software => ...)</a> -- specify software for the solver</span></span></li>
<li><span><a href="___Tolerance.html" title="specifies the tolerance of a numerical computation">Tolerance</a> -- specifies the tolerance of a numerical computation</span></li>
<li><span>AffinePatches, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>CompiledHornerForm, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>CorrectorTolerance, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>DynamicPatch, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>EndZoneFactor, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>Euler, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>gamma, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>HornerForm, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>InfinityThreshold, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>maxCorrSteps, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>Multistep, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>MultistepDegree, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>NoOutput, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>Normalize, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>numberSuccessesBeforeIncrease, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>Predictor, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>ProjectiveNewton, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>Projectivize, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>RungeKutta4, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>Secant, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>SLP, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>SLPcorrector, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>SLPpredictor, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>stepIncreaseFactor, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>Tangent, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>tDegree, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>tStep, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
<li><span>tStepMin, see <span><a href="_track_lp__List_cm__List_cm__List_rp.html" title="track a user homotopy">track(List,List,List)</a> -- track a user homotopy</span></span></li>
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