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<!DOCTYPE html> <html lang="en"> <head> <title>NAGtypes : Table of Contents</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="toc.html">Table of Contents</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 : Table of Contents</h1> <ul> <li><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">AbstractPoint</a> -- a type used to store a point in complex space</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="determine if solutions are equal" href="_are__Equal.html">areEqual</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="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 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="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="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="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="random linear combinations of equations/generators" href="_general__Equations.html">generalEquations</a> -- random linear combinations of equations/generators</span></li> <li><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 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="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="compare two points" href="_is__G__E__Q.html">isGEQ</a> -- compare two points</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="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="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="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(List)</a> -- construct a numerical variety</span></li> <li><span><a title="construct a Point" href="_point.html">point</a> -- construct a Point</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="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="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="a projective numerical variety" href="___Projective__Numerical__Variety.html">ProjectiveNumericalVariety</a> -- a projective numerical variety</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="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="select real points" href="_real__Points.html">realPoints</a> -- select real points</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="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="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="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">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(List)</a> -- sort the list of solutions</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 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 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="(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> </body> </html>