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<!DOCTYPE html> <html lang="en"> <head> <title>RealRoots : 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="Package for exploring, counting and locating real solutions to polynomial systems" href="index.html">RealRoots</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>RealRoots : Table of Contents</h1> <ul> <li><span><a title="Package for exploring, counting and locating real solutions to polynomial systems" href="index.html">RealRoots</a> -- Package for exploring, counting and locating real solutions to polynomial systems</span></li> <li><span><a title="a bound for the number of real roots with multiplicity of a univariate polynomial with rational coefficients" href="_budan__Fourier__Bound.html">budanFourierBound</a> -- a bound for the number of real roots with multiplicity of a univariate polynomial with rational coefficients</span></li> <li><span><a title="the characteristic polynomial of a matrix or the characteristic polynomial of the regular representation of a polynomial" href="_characteristic__Polynomial.html">characteristicPolynomial</a> -- the characteristic polynomial of a matrix or the characteristic polynomial of the regular representation of a polynomial</span></li> <li><span><a title="the principal submatrix of the Hurwitz matrix of a univariate polynomial" href="_hurwitz__Matrix.html">hurwitzMatrix</a> -- the principal submatrix of the Hurwitz matrix of a univariate polynomial</span></li> <li><span><a title="determines if a univariate polynomial with rational coefficients is Hurwitz-stable" href="_is__Hurwitz__Stable.html">isHurwitzStable</a> -- determines if a univariate polynomial with rational coefficients is Hurwitz-stable</span></li> <li><span><a title="the minimal polynomial of an element of an Artinian ring" href="_minimal__Polynomial.html">minimalPolynomial</a> -- the minimal polynomial of an element of an Artinian ring</span></li> <li><span><a href="___Multiplicity.html">Multiplicity</a></span></li> <li><span><a href="___Multiplicity_lp__Real__Roots_rp.html">Multiplicity(RealRoots)</a></span></li> <li><span><a title="the rational univariate representation of a zero-dimensional ideal in a polynomial ring" href="_rational__Univariate__Representation.html">rationalUnivariateRepresentation</a> -- the rational univariate representation of a zero-dimensional ideal in a polynomial ring</span></li> <li><span><a title="the number of real points of the spectrum of an Artinian ring (of characteristic 0)" href="_real__Count.html">realCount</a> -- the number of real points of the spectrum of an Artinian ring (of characteristic 0)</span></li> <li><span><a title="a list that isolates the real roots of a univariate polynomial with rational coefficients" href="_real__Root__Isolation.html">realRootIsolation</a> -- a list that isolates the real roots of a univariate polynomial with rational coefficients</span></li> <li><span><a title="the regular representation of an element of an Artinian ring" href="_regular__Representation.html">regularRepresentation</a> -- the regular representation of an element of an Artinian ring</span></li> <li><span><a title="the signature of a symmetric matrix with rational entries" href="_signature.html">signature</a> -- the signature of a symmetric matrix with rational entries</span></li> <li><span><a title="the number of real roots of a univariate polynomial with rational coefficients" href="_sturm__Count.html">sturmCount</a> -- the number of real roots of a univariate polynomial with rational coefficients</span></li> <li><span><a title="the Sturm sequence of a univariate polynomial with rational coefficients" href="_sturm__Sequence.html">sturmSequence</a> -- the Sturm sequence of a univariate polynomial with rational coefficients</span></li> <li><span><a title="a signed count of the real roots of a univariate polynomial with rational coefficients" href="_sylvester__Count.html">sylvesterCount</a> -- a signed count of the real roots of a univariate polynomial with rational coefficients</span></li> <li><span><a title="the Sylvester sequence of two univariate polynomials with rational coefficients" href="_sylvester__Sequence.html">sylvesterSequence</a> -- the Sylvester sequence of two univariate polynomials with rational coefficients</span></li> <li><span><a title="the degree of the reduced scheme of an Artinian ring" href="_trace__Count.html">traceCount</a> -- the degree of the reduced scheme of an Artinian ring</span></li> <li><span><a title="the trace symmetric form of a polynomial in an Artinian ring" href="_trace__Form.html">traceForm</a> -- the trace symmetric form of a polynomial in an Artinian ring</span></li> <li><span><a title="the univariate eliminant of an element of an Artinian ring" href="_univariate__Eliminant.html">univariateEliminant</a> -- the univariate eliminant of an element of an Artinian ring</span></li> <li><span><a title="the number of sign changes of an ordered list of numbers" href="_variations.html">variations</a> -- the number of sign changes of an ordered list of numbers</span></li> </ul> </body> </html>