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<!DOCTYPE html> <html lang="en"> <head> <title>NAGtypes : Index</title> <meta content="text/html; charset=utf-8" http-equiv="Content-Type"> <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css"> <link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css"> <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> <script> var macros = { "\\break": "\\\\", "\\ZZ": "\\mathbb{Z}", "\\NN": "\\mathbb{N}", "\\QQ": "\\mathbb{Q}", "\\RR": "\\mathbb{R}", "\\CC": "\\mathbb{C}", "\\PP": "\\mathbb{P}" }, delimiters = [ { left: "$$", right: "$$", display: true}, { left: "\\[", right: "\\]", display: true}, { left: "$", right: "$", display: false}, { left: "\\(", right: "\\)", display: false} ], ignoredTags = [ "kbd", "var", "samp", "script", "noscript", "style", "textarea", "pre", "code", "option" ]; document.addEventListener("DOMContentLoaded", function() { renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true }); }); </script> <style>.katex { font-size: 1em; }</style> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script> <script src="../../../../Macaulay2/Style/prism.js"></script> <script>var current_version = '1.25.06';</script> <script src="../../../../Macaulay2/Style/version-select.js"></script> <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif"> </head> <body> <div id="buttons"> <div> <a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="../../Macaulay2Doc/html/index.html">Documentation </a> <br><a href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="Common types used in Numerical Algebraic Geometry" href="index.html">NAGtypes</a> :: <a href="master.html">Index</a></span> </div> <div class="right"> <form method="get" action="https://www.google.com/search"> <input placeholder="Search" type="text" name="q" value=""> <input type="hidden" name="q" value="site:macaulay2.com/doc"> </form> next | previous | forward | backward | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <h1>NAGtypes : Index</h1> <div> <a href="#A">A</a> <a href="#B">B</a> <a href="#C">C</a> <a href="#D">D</a> <a href="#E">E</a> <a href="#F">F</a> <a href="#G">G</a> <a href="#H">H</a> <a href="#I">I</a> <a href="#J">J</a> <a href="#K">K</a> <a href="#L">L</a> <a href="#M">M</a> <a href="#N">N</a> <a href="#O">O</a> <a href="#P">P</a> <a href="#Q">Q</a> <a href="#R">R</a> <a href="#S">S</a> <a href="#T">T</a> <a href="#U">U</a> <a href="#V">V</a> <a href="#W">W</a> <a href="#X">X</a> <a href="#Y">Y</a> <a href="#Z">Z</a> </div> <ul> <li><span><a id="A"></a></span><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">AbstractPoint</a> -- a type used to store a point in complex space</span></li> <li><span><a title="determine if solutions are equal" href="_are__Equal.html">AbstractPoint == AbstractPoint</a> -- determine if solutions are equal</span></li> <li><span><a title="Union of polynomial spaces" href="_addition.html">addition</a> -- Union of polynomial spaces</span></li> <li><span><a title="Union of polynomial spaces" href="_addition.html">addition(...,Tolerance=>...)</a> -- Union of polynomial spaces</span></li> <li><span><a title="Union of polynomial spaces" href="_addition.html">addition(PolySpace,PolySpace)</a> -- Union of polynomial spaces</span></li> <li><span><a title="a projective witness set" href="___Projective__Witness__Set.html">AffineChart</a> -- a projective witness set</span></li> <li><span><a title="(under construction!) new types and methods needed to generalize WitnessSet" href="___W__Set.html">Ambient</a> -- (under construction!) new types and methods needed to generalize WitnessSet</span></li> <li><span><a title="(under construction!) new types and methods needed to generalize WitnessSet" href="___W__Set.html">ambient(SlicingVariety)</a> -- (under construction!) new types and methods needed to generalize WitnessSet</span></li> <li><span><a title="(under construction!) new types and methods needed to generalize WitnessSet" href="___W__Set.html">ambient(WSet)</a> -- (under construction!) new types and methods needed to generalize WitnessSet</span></li> <li><span><a title="determine if solutions are equal" href="_are__Equal.html">areEqual</a> -- determine if solutions are equal</span></li> <li><span><a title="determine if solutions are equal" href="_are__Equal.html">areEqual(...,Projective=>...)</a> -- determine if solutions are equal</span></li> <li><span><a title="the tolerance of a numerical computation" href="_sort__Solutions_lp..._cm__Tolerance_eq_gt..._rp.html">areEqual(...,Tolerance=>...)</a> -- the tolerance of a numerical computation</span></li> <li><span><a title="determine if solutions are equal" href="_are__Equal.html">areEqual(AbstractPoint,AbstractPoint)</a> -- determine if solutions are equal</span></li> <li><span><a title="determine if solutions are equal" href="_are__Equal.html">areEqual(BasicList,BasicList)</a> -- determine if solutions are equal</span></li> <li><span><a title="determine if solutions are equal" href="_are__Equal.html">areEqual(CC,CC)</a> -- determine if solutions are equal</span></li> <li><span><a title="approximate equality of dual spaces" href="_are__Equal_lp__Dual__Space_cm__Dual__Space_rp.html">areEqual(DualSpace,DualSpace)</a> -- approximate equality of dual spaces</span></li> <li><span><a title="determine if solutions are equal" href="_are__Equal.html">areEqual(List,List)</a> -- determine if solutions are equal</span></li> <li><span><a title="determine if solutions are equal" href="_are__Equal.html">areEqual(Matrix,Matrix)</a> -- determine if solutions are equal</span></li> <li><span><a title="determine if solutions are equal" href="_are__Equal.html">areEqual(MutableMatrix,MutableMatrix)</a> -- determine if solutions are equal</span></li> <li><span><a title="determine if solutions are equal" href="_are__Equal.html">areEqual(Number,Number)</a> -- determine if solutions are equal</span></li> <li><span><a title="approximate equality of subspaces spanned by polynomials" href="_are__Equal_lp__Poly__Space_cm__Poly__Space_rp.html">areEqual(PolySpace,PolySpace)</a> -- approximate equality of subspaces spanned by polynomials</span></li> <li><span><a id="B"></a><a id="C"></a></span><span><a title="a numerical variety" href="___Numerical__Variety.html">check(NumericalVariety)</a> -- a numerical variety</span></li> <li><span><a title="(under construction!) new types and methods needed to generalize WitnessSet" href="___W__Set.html">codim(SlicingVariety)</a> -- (under construction!) new types and methods needed to generalize WitnessSet</span></li> <li><span><a title="a witness set" href="___Witness__Set.html">codim(WitnessSet)</a> -- a witness set</span></li> <li><span><a title="(under construction!) new types and methods needed to generalize WitnessSet" href="___W__Set.html">codim(WSet)</a> -- (under construction!) new types and methods needed to generalize WitnessSet</span></li> <li><span><a title="list components of a numerical variety" href="_components_lp__Numerical__Variety_rp.html">components(NumericalVariety)</a> -- list components of a numerical variety</span></li> <li><span><a title="list components of a numerical variety" href="_components_lp__Numerical__Variety_rp.html">components(NumericalVariety,ZZ)</a> -- list components of a numerical variety</span></li> <li><span><a title="list components of a numerical variety" href="_components_lp__Numerical__Variety_rp.html">components(NumericalVariety,ZZ,InfiniteNumber)</a> -- list components of a numerical variety</span></li> <li><span><a title="list components of a numerical variety" href="_components_lp__Numerical__Variety_rp.html">components(NumericalVariety,ZZ,ZZ)</a> -- list components of a numerical variety</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">ConditionNumber</a> -- a type used to store a point in complex space</span></li> <li><span><a title="a polynomial system" href="___Poly__System.html">ContinuationParameter</a> -- a polynomial system</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">Coordinates</a> -- a type used to store a point in complex space</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">coordinates</a> -- a type used to store a point in complex space</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">coordinates(AbstractPoint)</a> -- a type used to store a point in complex space</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">coordinates(Point)</a> -- a type used to store a point in complex space</span></li> <li><span><a id="D"></a></span><span><a title="declares a component represented by the witness set irreducible" href="_declare__Irreducible.html">declareIrreducible</a> -- declares a component represented by the witness set irreducible</span></li> <li><span><a title="declares a component represented by the witness set irreducible" href="_declare__Irreducible.html">declareIrreducible(WitnessSet)</a> -- declares a component represented by the witness set irreducible</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">DecreasePrecision</a> -- a type used to store a point in complex space</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">DeflationNumber</a> -- a type used to store a point in complex space</span></li> <li><span><a title="a numerical variety" href="___Numerical__Variety.html">degree(NumericalVariety)</a> -- a numerical variety</span></li> <li><span><a title="a witness set" href="___Witness__Set.html">degree(WitnessSet)</a> -- a witness set</span></li> <li><span><a title="(under construction!) new types and methods needed to generalize WitnessSet" href="___W__Set.html">degree(WSet)</a> -- (under construction!) new types and methods needed to generalize WitnessSet</span></li> <li><span><a title="the tolerance of a numerical computation" href="_sort__Solutions_lp..._cm__Tolerance_eq_gt..._rp.html">differencePointSet(...,Tolerance=>...)</a> -- the tolerance of a numerical computation</span></li> <li><span><a title="(under construction!) new types and methods needed to generalize WitnessSet" href="___W__Set.html">dim(Ambient)</a> -- (under construction!) new types and methods needed to generalize WitnessSet</span></li> <li><span><a title="a dual functional vector subspace" href="___Dual__Space.html">dim(DualSpace)</a> -- a dual functional vector subspace</span></li> <li><span><a title="a numerical variety" href="___Numerical__Variety.html">dim(NumericalVariety)</a> -- a numerical variety</span></li> <li><span><a title="a polynomial vector subspace" href="___Poly__Space.html">dim(PolySpace)</a> -- a polynomial vector subspace</span></li> <li><span><a title="(under construction!) new types and methods needed to generalize WitnessSet" href="___W__Set.html">dim(SlicingVariety)</a> -- (under construction!) new types and methods needed to generalize WitnessSet</span></li> <li><span><a title="a witness set" href="___Witness__Set.html">dim(WitnessSet)</a> -- a witness set</span></li> <li><span><a title="(under construction!) new types and methods needed to generalize WitnessSet" href="___W__Set.html">dim(WSet)</a> -- (under construction!) new types and methods needed to generalize WitnessSet</span></li> <li><span><a title="a dual functional vector subspace" href="___Dual__Space.html">DualSpace</a> -- a dual functional vector subspace</span></li> <li><span><a title="construct a DualSpace" href="_dual__Space.html">dualSpace</a> -- construct a DualSpace</span></li> <li><span><a title="construct a DualSpace" href="_dual__Space.html">dualSpace(DualSpace)</a> -- construct a DualSpace</span></li> <li><span><a title="construct a DualSpace" href="_dual__Space.html">dualSpace(Matrix,AbstractPoint)</a> -- construct a DualSpace</span></li> <li><span><a title="construct a DualSpace" href="_dual__Space.html">dualSpace(PolySpace,AbstractPoint)</a> -- construct a DualSpace</span></li> <li><span><a id="E"></a></span><span><a title="a witness set" href="___Witness__Set.html">Equations</a> -- a witness set</span></li> <li><span><a title="a witness set" href="___Witness__Set.html">equations</a> -- a witness set</span></li> <li><span><a title="a polynomial system" href="___Poly__System.html">equations(PolySystem)</a> -- a polynomial system</span></li> <li><span><a title="a witness set" href="___Witness__Set.html">equations(WitnessSet)</a> -- a witness set</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">ErrorBoundEstimate</a> -- a type used to store a point in complex space</span></li> <li><span><a title="evaluate a polynomial system or matrix at a point" href="_evaluate.html">evaluate</a> -- evaluate a polynomial system or matrix at a point</span></li> <li><span><a title="evaluate a polynomial system or matrix at a point" href="_evaluate.html">evaluate(Matrix,AbstractPoint)</a> -- evaluate a polynomial system or matrix at a point</span></li> <li><span><a title="evaluate a polynomial system or matrix at a point" href="_evaluate.html">evaluate(Matrix,Matrix)</a> -- evaluate a polynomial system or matrix at a point</span></li> <li><span><a title="evaluate a polynomial system or matrix at a point" href="_evaluate.html">evaluate(PolySystem,Matrix)</a> -- evaluate a polynomial system or matrix at a point</span></li> <li><span><a title="a system of functions" href="___System.html">evaluate(System,AbstractPoint)</a> -- a system of functions</span></li> <li><span><a title="a system of functions" href="___System.html">evaluate(System,AbstractPoint,AbstractPoint)</a> -- a system of functions</span></li> <li><span><a title="a system of functions" href="___System.html">evaluate(System,Matrix)</a> -- a system of functions</span></li> <li><span><a title="a system of functions" href="___System.html">evaluate(System,Matrix,Matrix)</a> -- a system of functions</span></li> <li><span><a title="a system of functions" href="___System.html">evaluateJacobian</a> -- a system of functions</span></li> <li><span><a title="evaluate a polynomial system or matrix at a point" href="_evaluate.html">evaluateJacobian(PolySystem,AbstractPoint)</a> -- evaluate a polynomial system or matrix at a point</span></li> <li><span><a title="a system of functions" href="___System.html">evaluateJacobian(System,AbstractPoint)</a> -- a system of functions</span></li> <li><span><a title="a system of functions" href="___System.html">evaluateJacobian(System,AbstractPoint,AbstractPoint)</a> -- a system of functions</span></li> <li><span><a title="a system of functions" href="___System.html">evaluateJacobian(System,Matrix)</a> -- a system of functions</span></li> <li><span><a title="a system of functions" href="___System.html">evaluateJacobian(System,Matrix,Matrix)</a> -- a system of functions</span></li> <li><span><a id="F"></a><a id="G"></a></span><span><a title="random linear combinations of equations/generators" href="_general__Equations.html">generalEquations</a> -- random linear combinations of equations/generators</span></li> <li><span><a title="random linear combinations of equations/generators" href="_general__Equations.html">generalEquations(WitnessSet)</a> -- random linear combinations of equations/generators</span></li> <li><span><a title="random linear combinations of equations/generators" href="_general__Equations.html">generalEquations(ZZ,Ideal)</a> -- random linear combinations of equations/generators</span></li> <li><span><a title="random linear combinations of equations/generators" href="_general__Equations.html">generalEquations(ZZ,List)</a> -- random linear combinations of equations/generators</span></li> <li><span><a title="a dual functional vector subspace" href="___Dual__Space.html">generators(DualSpace)</a> -- a dual functional vector subspace</span></li> <li><span><a title="a polynomial vector subspace" href="___Poly__Space.html">generators(PolySpace)</a> -- a polynomial vector subspace</span></li> <li><span><a id="H"></a></span><span><a title="homogenize a polynomial system" href="_homogenize_lp__Poly__System_cm__Ring_cm__Ring__Element_rp.html">homogenize(PolySystem,Ring,RingElement)</a> -- homogenize a polynomial system</span></li> <li><span><a id="I"></a></span><span><a title="a polynomial system" href="___Poly__System.html">ideal(PolySystem)</a> -- a polynomial system</span></li> <li><span><a title="a witness set" href="___Witness__Set.html">ideal(WitnessSet)</a> -- a witness set</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">IncreasePrecision</a> -- a type used to store a point in complex space</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">Infinity</a> -- a type used to store a point in complex space</span></li> <li><span><a title="Intersection of polynomial spaces" href="_intersect_lp__Poly__Space_cm__Poly__Space_rp.html">intersect(PolySpace,PolySpace)</a> -- Intersection of polynomial spaces</span></li> <li><span><a title="Intersection of polynomial spaces" href="_intersect_lp__Poly__Space_cm__Poly__Space_rp.html">intersect(PolySpace,PolySpace,Tolerance=>...)</a> -- Intersection of polynomial spaces</span></li> <li><span><a title="Is one space contained in the other" href="_is__Contained.html">isContained</a> -- Is one space contained in the other</span></li> <li><span><a title="Is one space contained in the other" href="_is__Contained.html">isContained(...,Tolerance=>...)</a> -- Is one space contained in the other</span></li> <li><span><a title="Is one space contained in the other" href="_is__Contained.html">isContained(DualSpace,DualSpace)</a> -- Is one space contained in the other</span></li> <li><span><a title="Is one space contained in the other" href="_is__Contained.html">isContained(PolySpace,PolySpace)</a> -- Is one space contained in the other</span></li> <li><span><a title="compare two points" href="_is__G__E__Q.html">isGEQ</a> -- compare two points</span></li> <li><span><a title="the tolerance of a numerical computation" href="_sort__Solutions_lp..._cm__Tolerance_eq_gt..._rp.html">isGEQ(...,Tolerance=>...)</a> -- the tolerance of a numerical computation</span></li> <li><span><a title="compare two points" href="_is__G__E__Q.html">isGEQ(AbstractPoint,AbstractPoint)</a> -- compare two points</span></li> <li><span><a title="compare two points" href="_is__G__E__Q.html">isGEQ(List,List)</a> -- compare two points</span></li> <li><span><a title="a polynomial system" href="___Poly__System.html">isHomogeneous(PolySystem)</a> -- a polynomial system</span></li> <li><span><a title="a witness set" href="___Witness__Set.html">IsIrreducible</a> -- a witness set</span></li> <li><span><a title="determine whether a point is real" href="_is__Real__Point.html">isRealPoint</a> -- determine whether a point is real</span></li> <li><span><a title="the tolerance of a numerical computation" href="_sort__Solutions_lp..._cm__Tolerance_eq_gt..._rp.html">isRealPoint(...,Tolerance=>...)</a> -- the tolerance of a numerical computation</span></li> <li><span><a title="determine whether a point is real" href="_is__Real__Point.html">isRealPoint(AbstractPoint)</a> -- determine whether a point is real</span></li> <li><span><a id="J"></a></span><span><a title="a polynomial system" href="___Poly__System.html">jacobian(PolySystem)</a> -- a polynomial system</span></li> <li><span><a id="K"></a><a id="L"></a></span><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">LastT</a> -- a type used to store a point in complex space</span></li> <li><span><a id="M"></a></span><span><a title="(under construction!) new types and methods needed to generalize WitnessSet" href="___W__Set.html">map(SlicingVariety)</a> -- (under construction!) new types and methods needed to generalize WitnessSet</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">matrix(AbstractPoint)</a> -- a type used to store a point in complex space</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">MaxPrecision</a> -- a type used to store a point in complex space</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">MinStepFailure</a> -- a type used to store a point in complex space</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">Multiplicity</a> -- a type used to store a point in complex space</span></li> <li><span><a id="N"></a></span><span><a title="Common types used in Numerical Algebraic Geometry" href="index.html">NAGtypes</a> -- Common types used in Numerical Algebraic Geometry</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">net(AbstractPoint)</a> -- a type used to store a point in complex space</span></li> <li><span><a title="(under construction!) new types and methods needed to generalize WitnessSet" href="___W__Set.html">net(Ambient)</a> -- (under construction!) new types and methods needed to generalize WitnessSet</span></li> <li><span><a title="a dual functional vector subspace" href="___Dual__Space.html">net(DualSpace)</a> -- a dual functional vector subspace</span></li> <li><span><a title="a numerical variety" href="___Numerical__Variety.html">net(NumericalVariety)</a> -- a numerical variety</span></li> <li><span><a title="a polynomial vector subspace" href="___Poly__Space.html">net(PolySpace)</a> -- a polynomial vector subspace</span></li> <li><span><a title="a polynomial system" href="___Poly__System.html">net(PolySystem)</a> -- a polynomial system</span></li> <li><span><a title="(under construction!) new types and methods needed to generalize WitnessSet" href="___W__Set.html">net(SlicingVariety)</a> -- (under construction!) new types and methods needed to generalize WitnessSet</span></li> <li><span><a title="a witness set" href="___Witness__Set.html">net(WitnessSet)</a> -- a witness set</span></li> <li><span><a title="(under construction!) new types and methods needed to generalize WitnessSet" href="___W__Set.html">net(WSet)</a> -- (under construction!) new types and methods needed to generalize WitnessSet</span></li> <li><span><a title="p in the p-norm" href="___Norm.html">Norm</a> -- p in the p-norm</span></li> <li><span><a title="p-norm of the point" href="_norm_lp__Thing_cm__Abstract__Point_rp.html">norm(Thing,AbstractPoint)</a> -- p-norm of the point</span></li> <li><span><a title="a polynomial system" href="___Poly__System.html">NumberOfPolys</a> -- a polynomial system</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">NumberOfSteps</a> -- a type used to store a point in complex space</span></li> <li><span><a title="a polynomial system" href="___Poly__System.html">NumberOfVariables</a> -- a polynomial system</span></li> <li><span><a title="affine space as a numerical variety" href="_numerical__Affine__Space.html">numericalAffineSpace</a> -- affine space as a numerical variety</span></li> <li><span><a title="affine space as a numerical variety" href="_numerical__Affine__Space.html">numericalAffineSpace(PolynomialRing)</a> -- affine space as a numerical variety</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">NumericalRankFailure</a> -- a type used to store a point in complex space</span></li> <li><span><a title="a numerical variety" href="___Numerical__Variety.html">NumericalVariety</a> -- a numerical variety</span></li> <li><span><a title="construct a numerical variety" href="_numerical__Variety_lp__List_rp.html">numericalVariety</a> -- construct a numerical variety</span></li> <li><span><a title="construct a numerical variety" href="_numerical__Variety_lp__List_rp.html">numericalVariety(List)</a> -- construct a numerical variety</span></li> <li><span><a title="a system of functions" href="___System.html">numFunctions</a> -- a system of functions</span></li> <li><span><a title="a polynomial system" href="___Poly__System.html">numFunctions(PolySystem)</a> -- a polynomial system</span></li> <li><span><a title="a system of functions" href="___System.html">numFunctions(System)</a> -- a system of functions</span></li> <li><span><a title="a system of functions" href="___System.html">numParameters</a> -- a system of functions</span></li> <li><span><a title="a polynomial system" href="___Poly__System.html">numParameters(PolySystem)</a> -- a polynomial system</span></li> <li><span><a title="a system of functions" href="___System.html">numParameters(System)</a> -- a system of functions</span></li> <li><span><a title="a system of functions" href="___System.html">numVariables</a> -- a system of functions</span></li> <li><span><a title="a polynomial system" href="___Poly__System.html">numVariables(PolySystem)</a> -- a polynomial system</span></li> <li><span><a title="a system of functions" href="___System.html">numVariables(System)</a> -- a system of functions</span></li> <li><span><a id="O"></a></span><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">Origin</a> -- a type used to store a point in complex space</span></li> <li><span><a id="P"></a></span><span><a title="a polynomial system" href="___Poly__System.html">parameters</a> -- a polynomial system</span></li> <li><span><a title="a polynomial system" href="___Poly__System.html">parameters(PolySystem)</a> -- a polynomial system</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">Point</a> -- a type used to store a point in complex space</span></li> <li><span><a title="construct a Point" href="_point.html">point</a> -- construct a Point</span></li> <li><span><a title="construct a Point" href="_point.html">point(AbstractPoint)</a> -- construct a Point</span></li> <li><span><a title="a dual functional vector subspace" href="___Dual__Space.html">point(DualSpace)</a> -- a dual functional vector subspace</span></li> <li><span><a title="construct a Point" href="_point.html">point(List)</a> -- construct a Point</span></li> <li><span><a title="construct a Point" href="_point.html">point(List,CacheTable)</a> -- construct a Point</span></li> <li><span><a title="construct a Point" href="_point.html">point(Matrix)</a> -- construct a Point</span></li> <li><span><a title="a witness set" href="___Witness__Set.html">Points</a> -- a witness set</span></li> <li><span><a title="a witness set" href="___Witness__Set.html">points</a> -- a witness set</span></li> <li><span><a title="a witness set" href="___Witness__Set.html">points(WitnessSet)</a> -- a witness set</span></li> <li><span><a title="(under construction!) new types and methods needed to generalize WitnessSet" href="___W__Set.html">points(WSet)</a> -- (under construction!) new types and methods needed to generalize WitnessSet</span></li> <li><span><a title="a polynomial system" href="___Poly__System.html">PolyMap</a> -- a polynomial system</span></li> <li><span><a title="a polynomial vector subspace" href="___Poly__Space.html">PolySpace</a> -- a polynomial vector subspace</span></li> <li><span><a title="construct a PolySpace" href="_poly__Space.html">polySpace</a> -- construct a PolySpace</span></li> <li><span><a title="construct a PolySpace" href="_poly__Space.html">polySpace(...,Reduced=>...)</a> -- construct a PolySpace</span></li> <li><span><a title="construct a PolySpace" href="_poly__Space.html">polySpace(Matrix)</a> -- construct a PolySpace</span></li> <li><span><a title="construct a PolySpace" href="_poly__Space.html">polySpace(PolySpace)</a> -- construct a PolySpace</span></li> <li><span><a title="a polynomial system" href="___Poly__System.html">PolySystem</a> -- a polynomial system</span></li> <li><span><a title="construct a polynomial system" href="_poly__System.html">polySystem</a> -- construct a polynomial system</span></li> <li><span><a title="construct a polynomial system" href="_poly__System.html">polySystem(Ideal)</a> -- construct a polynomial system</span></li> <li><span><a title="construct a polynomial system" href="_poly__System.html">polySystem(List)</a> -- construct a polynomial system</span></li> <li><span><a title="construct a polynomial system" href="_poly__System.html">polySystem(Matrix)</a> -- construct a polynomial system</span></li> <li><span><a title="construct a polynomial system" href="_poly__System.html">polySystem(PolySystem)</a> -- construct a polynomial system</span></li> <li><span><a title="project a point" href="_project_lp__Abstract__Point_cm__Z__Z_rp.html">project</a> -- project a point</span></li> <li><span><a title="project a point" href="_project_lp__Abstract__Point_cm__Z__Z_rp.html">project(AbstractPoint,ZZ)</a> -- project a point</span></li> <li><span><a title="project a point" href="_project_lp__Abstract__Point_cm__Z__Z_rp.html">project(Point,ZZ)</a> -- project a point</span></li> <li><span><a title="a witness set" href="___Witness__Set.html">ProjectionDimension</a> -- a witness set</span></li> <li><span><a title="a projective numerical variety" href="___Projective__Numerical__Variety.html">ProjectiveNumericalVariety</a> -- a projective numerical variety</span></li> <li><span><a title="construct a numerical variety" href="_numerical__Variety_lp__List_rp.html">projectiveNumericalVariety</a> -- construct a numerical variety</span></li> <li><span><a title="construct a numerical variety" href="_numerical__Variety_lp__List_rp.html">projectiveNumericalVariety(List)</a> -- construct a numerical variety</span></li> <li><span><a title="slicing linear functions" href="_slice__Equations_lp__Matrix_cm__Ring_rp.html">projectiveSliceEquations</a> -- slicing linear functions</span></li> <li><span><a title="slicing linear functions" href="_slice__Equations_lp__Matrix_cm__Ring_rp.html">projectiveSliceEquations(Matrix,Ring)</a> -- slicing linear functions</span></li> <li><span><a title="a projective witness set" href="___Projective__Witness__Set.html">ProjectiveWitnessSet</a> -- a projective witness set</span></li> <li><span><a title="construct a ProjectiveWitnessSet" href="_projective__Witness__Set.html">projectiveWitnessSet</a> -- construct a ProjectiveWitnessSet</span></li> <li><span><a title="construct a ProjectiveWitnessSet" href="_projective__Witness__Set.html">projectiveWitnessSet(Ideal,Matrix,Matrix,List)</a> -- construct a ProjectiveWitnessSet</span></li> <li><span><a id="Q"></a><a id="R"></a></span><span><a title="random element of a subspace" href="_random_lp__Poly__Space_rp.html">random(DualSpace)</a> -- random element of a subspace</span></li> <li><span><a title="random element of a subspace" href="_random_lp__Poly__Space_rp.html">random(PolySpace)</a> -- random element of a subspace</span></li> <li><span><a title="random element of a subspace" href="_random_lp__Poly__Space_rp.html">random(ZZ,DualSpace)</a> -- random element of a subspace</span></li> <li><span><a title="random element of a subspace" href="_random_lp__Poly__Space_rp.html">random(ZZ,PolySpace)</a> -- random element of a subspace</span></li> <li><span><a title="select real points" href="_real__Points.html">realPoints</a> -- select real points</span></li> <li><span><a title="the tolerance of a numerical computation" href="_sort__Solutions_lp..._cm__Tolerance_eq_gt..._rp.html">realPoints(...,Tolerance=>...)</a> -- the tolerance of a numerical computation</span></li> <li><span><a title="select real points" href="_real__Points.html">realPoints(List)</a> -- select real points</span></li> <li><span><a title="construct a PolySpace" href="_poly__Space.html">Reduced</a> -- construct a PolySpace</span></li> <li><span><a title="reduce the generators of a space" href="_reduce__Space.html">reduceSpace</a> -- reduce the generators of a space</span></li> <li><span><a title="reduce the generators of a space" href="_reduce__Space.html">reduceSpace(...,Monomials=>...)</a> -- reduce the generators of a space</span></li> <li><span><a title="the tolerance of a numerical computation" href="_sort__Solutions_lp..._cm__Tolerance_eq_gt..._rp.html">reduceSpace(...,Tolerance=>...)</a> -- the tolerance of a numerical computation</span></li> <li><span><a title="reduce the generators of a space" href="_reduce__Space.html">reduceSpace(DualSpace)</a> -- reduce the generators of a space</span></li> <li><span><a title="reduce the generators of a space" href="_reduce__Space.html">reduceSpace(PolySpace)</a> -- reduce the generators of a space</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">RefinementFailure</a> -- a type used to store a point in complex space</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">Regular</a> -- a type used to store a point in complex space</span></li> <li><span><a title="residual of a polynomial function at a point" href="_residual.html">residual</a> -- residual of a polynomial function at a point</span></li> <li><span><a title="p in the p-norm" href="___Norm.html">residual(...,Norm=>...)</a> -- p in the p-norm</span></li> <li><span><a title="residual of a polynomial function at a point" href="_residual.html">residual(List,Point)</a> -- residual of a polynomial function at a point</span></li> <li><span><a title="residual of a polynomial function at a point" href="_residual.html">residual(Matrix,Matrix)</a> -- residual of a polynomial function at a point</span></li> <li><span><a title="residual of a polynomial function at a point" href="_residual.html">residual(System,AbstractPoint)</a> -- residual of a polynomial function at a point</span></li> <li><span><a title="residual of a polynomial function at a point" href="_residual.html">residual(System,Point)</a> -- residual of a polynomial function at a point</span></li> <li><span><a title="a dual functional vector subspace" href="___Dual__Space.html">ring(DualSpace)</a> -- a dual functional vector subspace</span></li> <li><span><a title="a polynomial vector subspace" href="___Poly__Space.html">ring(PolySpace)</a> -- a polynomial vector subspace</span></li> <li><span><a title="a polynomial system" href="___Poly__System.html">ring(PolySystem)</a> -- a polynomial system</span></li> <li><span><a title="a witness set" href="___Witness__Set.html">ring(WitnessSet)</a> -- a witness set</span></li> <li><span><a id="S"></a></span><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">Singular</a> -- a type used to store a point in complex space</span></li> <li><span><a title="a witness set" href="___Witness__Set.html">Slice</a> -- a witness set</span></li> <li><span><a title="a witness set" href="___Witness__Set.html">slice</a> -- a witness set</span></li> <li><span><a title="a witness set" href="___Witness__Set.html">slice(WitnessSet)</a> -- a witness set</span></li> <li><span><a title="slicing linear functions" href="_slice__Equations_lp__Matrix_cm__Ring_rp.html">sliceEquations</a> -- slicing linear functions</span></li> <li><span><a title="slicing linear functions" href="_slice__Equations_lp__Matrix_cm__Ring_rp.html">sliceEquations(Matrix,Ring)</a> -- slicing linear functions</span></li> <li><span><a title="(under construction!) new types and methods needed to generalize WitnessSet" href="___W__Set.html">SlicingVariety</a> -- (under construction!) new types and methods needed to generalize WitnessSet</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">SolutionStatus</a> -- a type used to store a point in complex space</span></li> <li><span><a title="replaces clusters of approximately equal points by single points with multiplicity" href="_solutions__With__Multiplicity.html">solutionsWithMultiplicity</a> -- replaces clusters of approximately equal points by single points with multiplicity</span></li> <li><span><a title="the tolerance of a numerical computation" href="_sort__Solutions_lp..._cm__Tolerance_eq_gt..._rp.html">solutionsWithMultiplicity(...,Tolerance=>...)</a> -- the tolerance of a numerical computation</span></li> <li><span><a title="replaces clusters of approximately equal points by single points with multiplicity" href="_solutions__With__Multiplicity.html">solutionsWithMultiplicity(List)</a> -- replaces clusters of approximately equal points by single points with multiplicity</span></li> <li><span><a title="sort the list of solutions" href="_sort__Solutions_lp__List_rp.html">sortSolutions</a> -- sort the list of solutions</span></li> <li><span><a title="the tolerance of a numerical computation" href="_sort__Solutions_lp..._cm__Tolerance_eq_gt..._rp.html">sortSolutions(...,Tolerance=>...)</a> -- the tolerance of a numerical computation</span></li> <li><span><a title="sort the list of solutions" href="_sort__Solutions_lp__List_rp.html">sortSolutions(...,Weights=>...)</a> -- sort the list of solutions</span></li> <li><span><a title="sort the list of solutions" href="_sort__Solutions_lp__List_rp.html">sortSolutions(List)</a> -- sort the list of solutions</span></li> <li><span><a title="a polynomial system" href="___Poly__System.html">SpecializationRing</a> -- a polynomial system</span></li> <li><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">status(AbstractPoint)</a> -- a type used to store a point in complex space</span></li> <li><span><a title="substitute a ring in a polynomial system" href="_substitute_lp__Poly__System_cm__Ring_rp.html">substitute(PolySystem,Ring)</a> -- substitute a ring in a polynomial system</span></li> <li><span><a title="a system of functions" href="___System.html">System</a> -- a system of functions</span></li> <li><span><a id="T"></a></span><span><a title="coordinates of a point in the projective space in an affine chart" href="_to__Affine__Chart_lp__Z__Z_cm__List_rp.html">toAffineChart</a> -- coordinates of a point in the projective space in an affine chart</span></li> <li><span><a title="coordinates of a point in the projective space in an affine chart" href="_to__Affine__Chart_lp__Z__Z_cm__List_rp.html">toAffineChart(ZZ,List)</a> -- coordinates of a point in the projective space in an affine chart</span></li> <li><span><a id="U"></a></span><span><a title="the tolerance of a numerical computation" href="_sort__Solutions_lp..._cm__Tolerance_eq_gt..._rp.html">unionPointSet(...,Tolerance=>...)</a> -- the tolerance of a numerical computation</span></li> <li><span><a id="V"></a><a id="W"></a></span><span><a title="a type used to store a point in complex space" href="___Abstract__Point.html">WindingNumber</a> -- a type used to store a point in complex space</span></li> <li><span><a title="a witness set" href="___Witness__Set.html">WitnessSet</a> -- a witness set</span></li> <li><span><a title="construct a WitnessSet" href="_witness__Set.html">witnessSet</a> -- construct a WitnessSet</span></li> <li><span><a title="construct a WitnessSet" href="_witness__Set.html">witnessSet(Ideal,Ideal,List)</a> -- construct a WitnessSet</span></li> <li><span><a title="construct a WitnessSet" href="_witness__Set.html">witnessSet(Ideal,Matrix,List)</a> -- construct a WitnessSet</span></li> <li><span><a title="construct a WitnessSet" href="_witness__Set.html">witnessSet(PolySystem,Matrix,List)</a> -- construct a WitnessSet</span></li> <li><span><a title="construct a WitnessSet" href="_witness__Set.html">witnessSet(PolySystem,PolySystem,List)</a> -- construct a WitnessSet</span></li> <li><span><a title="(under construction!) new types and methods needed to generalize WitnessSet" href="___W__Set.html">WSet</a> -- (under construction!) new types and methods needed to generalize WitnessSet</span></li> </ul> <div> <span><a id="X"></a><a id="Y"></a><a id="Z"></a></span> </div> </body> </html>
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