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<!DOCTYPE html> <html lang="en"> <head> <title>A1BrouwerDegrees : 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" ]; 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href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="package for working with A1-Brouwer degree computations" href="index.html">A1BrouwerDegrees</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>A1BrouwerDegrees : Table of Contents</h1> <ul> <li><span><a title="package for working with A1-Brouwer degree computations" href="index.html">A1BrouwerDegrees</a> -- package for working with A1-Brouwer degree computations</span></li> <li><span><a title="the direct sum of two Grothendieck-Witt classes" href="_add__G__W.html">addGW</a> -- the direct sum of two Grothendieck-Witt classes</span></li> <li><span><a title="diagonalizes a symmetric matrix via congruence" href="_diagonalize__Via__Congruence.html">diagonalizeViaCongruence</a> -- diagonalizes a symmetric matrix via congruence</span></li> <li><span><a title="returns the anisotropic dimension of a symmetric bilinear form" href="_get__Anisotropic__Dimension.html">getAnisotropicDimension</a> -- returns the anisotropic dimension of a symmetric bilinear form</span></li> <li><span><a title="returns the anisotropic dimension of a rational symmetric bilinear form over the p-adic rational numbers" href="_get__Anisotropic__Dimension__Q__Qp.html">getAnisotropicDimensionQQp</a> -- returns the anisotropic dimension of a rational symmetric bilinear form over the p-adic rational numbers</span></li> <li><span><a title="returns the anisotropic part of a Grothendieck-Witt class" href="_get__Anisotropic__Part.html">getAnisotropicPart</a> -- returns the anisotropic part of a Grothendieck-Witt class</span></li> <li><span><a title="the base field of a Grothendieck-Witt class" href="_get__Base__Field.html">getBaseField</a> -- the base field of a Grothendieck-Witt class</span></li> <li><span><a title="produces a diagonalized form for any Grothendieck-Witt class, with simplified terms on the diagonal" href="_get__Diagonal__Class.html">getDiagonalClass</a> -- produces a diagonalized form for any Grothendieck-Witt class, with simplified terms on the diagonal</span></li> <li><span><a title="extracts a list of diagonal entries for a GrothendieckWittClass" href="_get__Diagonal__Entries.html">getDiagonalEntries</a> -- extracts a list of diagonal entries for a GrothendieckWittClass</span></li> <li><span><a title="computes the global A1-Brouwer degree of a list of n polynomials in n variables over a field k" href="_get__Global__A1__Degree.html">getGlobalA1Degree</a> -- computes the global A1-Brouwer degree of a list of n polynomials in n variables over a field k</span></li> <li><span><a title="computes the Hasse-Witt invariant at a prime p for the quadratic form of the Grothendieck-Witt class" href="_get__Hasse__Witt__Invariant.html">getHasseWittInvariant</a> -- computes the Hasse-Witt invariant at a prime p for the quadratic form of the Grothendieck-Witt class</span></li> <li><span><a title="computes the Hilbert symbol of two rational numbers at a prime" href="_get__Hilbert__Symbol.html">getHilbertSymbol</a> -- computes the Hilbert symbol of two rational numbers at a prime</span></li> <li><span><a title="computes the Hilbert symbol of two rational numbers over the real numbers" href="_get__Hilbert__Symbol__Real.html">getHilbertSymbolReal</a> -- computes the Hilbert symbol of two rational numbers over the real numbers</span></li> <li><span><a title="computes the integral discriminant for a rational symmetric bilinear form" href="_get__Integral__Discriminant.html">getIntegralDiscriminant</a> -- computes the integral discriminant for a rational symmetric bilinear form</span></li> <li><span><a title="computes a local A1-Brouwer degree of a list of n polynomials in n variables over a field k at a prime ideal in the zero locus" href="_get__Local__A1__Degree.html">getLocalA1Degree</a> -- computes a local A1-Brouwer degree of a list of n polynomials in n variables over a field k at a prime ideal in the zero locus</span></li> <li><span><a title="produces a basis for a local finitely generated algebra over a field k" href="_get__Local__Algebra__Basis.html">getLocalAlgebraBasis</a> -- produces a basis for a local finitely generated algebra over a field k</span></li> <li><span><a title="the underlying matrix of a Grothendieck-Witt class" href="_get__Matrix.html">getMatrix</a> -- the underlying matrix of a Grothendieck-Witt class</span></li> <li><span><a title="p-adic valuation of a rational number" href="_get__Padic__Valuation.html">getPadicValuation</a> -- p-adic valuation of a rational number</span></li> <li><span><a title="calculates the rank of a symmetric bilinear form" href="_get__Rank.html">getRank</a> -- calculates the rank of a symmetric bilinear form</span></li> <li><span><a title="outputs a list containing all primes p where the Hasse-Witt invariant of a symmetric bilinear form is nontrivial" href="_get__Relevant__Primes.html">getRelevantPrimes</a> -- outputs a list containing all primes p where the Hasse-Witt invariant of a symmetric bilinear form is nontrivial</span></li> <li><span><a title="computes the signature of a symmetric bilinear form over the real numbers or rational numbers" href="_get__Signature.html">getSignature</a> -- computes the signature of a symmetric bilinear form over the real numbers or rational numbers</span></li> <li><span><a title="produces a simplified diagonal representative of a Grothendieck-Witt class" href="_get__Sum__Decomposition.html">getSumDecomposition</a> -- produces a simplified diagonal representative of a Grothendieck-Witt class</span></li> <li><span><a title="produces a simplified diagonal representative of a Grothendieck-Witt class" href="_get__Sum__Decomposition__String.html">getSumDecompositionString</a> -- produces a simplified diagonal representative of a Grothendieck-Witt class</span></li> <li><span><a title="returns the Witt index of a symmetric bilinear form" href="_get__Witt__Index.html">getWittIndex</a> -- returns the Witt index of a symmetric bilinear form</span></li> <li><span><a title="a new type, intended to capture the isomorphism class of an element of the Grothendieck-Witt ring of a base field" href="___Grothendieck__Witt__Class.html">GrothendieckWittClass</a> -- a new type, intended to capture the isomorphism class of an element of the Grothendieck-Witt ring of a base field</span></li> <li><span><a title="determines whether a Grothendieck-Witt class is anisotropic" href="_is__Anisotropic.html">isAnisotropic</a> -- determines whether a Grothendieck-Witt class is anisotropic</span></li> <li><span><a title="determines whether two Grothendieck-Witt classes over CC, RR, QQ, or a finite field of characteristic not 2 are isomorphic." href="_is__Isomorphic__Form.html">isIsomorphicForm</a> -- determines whether two Grothendieck-Witt classes over CC, RR, QQ, or a finite field of characteristic not 2 are isomorphic.</span></li> <li><span><a title="determines whether a Grothendieck-Witt class is isotropic" href="_is__Isotropic.html">isIsotropic</a> -- determines whether a Grothendieck-Witt class is isotropic</span></li> <li><span><a title="the Grothendieck-Witt class of a diagonal form" href="_make__Diagonal__Form.html">makeDiagonalForm</a> -- the Grothendieck-Witt class of a diagonal form</span></li> <li><span><a title="the Grothendieck-Witt class of a symmetric matrix" href="_make__G__W__Class.html">makeGWClass</a> -- the Grothendieck-Witt class of a symmetric matrix</span></li> <li><span><a title="the Grothendieck-Witt class of a hyperbolic form" href="_make__Hyperbolic__Form.html">makeHyperbolicForm</a> -- the Grothendieck-Witt class of a hyperbolic form</span></li> <li><span><a title="the Grothendieck-Witt class of a Pfister form" href="_make__Pfister__Form.html">makePfisterForm</a> -- the Grothendieck-Witt class of a Pfister form</span></li> <li><span><a title="the tensor product of two Grothendieck-Witt classes" href="_multiply__G__W.html">multiplyGW</a> -- the tensor product of two Grothendieck-Witt classes</span></li> </ul> </body> </html>