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_grading.html
<!DOCTYPE html> <html lang="en"> <head> <title>grading</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="an interface to use Normaliz in Macaulay 2" href="index.html">Normaliz</a> :: <a href="_grading.html">grading</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> <a href="_intcl__Mon__Ideal.html">next</a> | <a href="_get__Num__Invs.html">previous</a> | <a href="_intcl__Mon__Ideal.html">forward</a> | <a href="_get__Num__Invs.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>grading</h1> <div> <h2>Description</h2> <p></p> grading is an option for <a title="calls Normaliz" href="_normaliz.html">normaliz</a>, <a title="integral closure of a toric ring" href="_intcl__Toric__Ring.html">intclToricRing</a>, <a title="normalization of a toric ring" href="_normal__Toric__Ring.html">normalToricRing</a>, <a title="normalization of Rees algebra" href="_intcl__Mon__Ideal.html">intclMonIdeal</a>, <a title="ring of invariants of torus action" href="_torus__Invariants.html">torusInvariants</a>, <a title="ring of invariants of a finite group action" href="_finite__Diag__Invariants.html">finiteDiagInvariants</a>, <a title="ring of invariants of a diagonalizable group action" href="_diag__Invariants.html">diagInvariants</a>, <a title="intersection of ring of valuations" href="_intersection__Val__Rings.html">intersectionValRings</a>, <a title="intersection of valuation ideals" href="_intersection__Val__Ring__Ideals.html">intersectionValRingIdeals</a>. Its default value is an empty list. If it is set to a list of integers it will be used as grading. This has no influence on the generators of the computed objects, but on additional data like the multiplicity or the Hilbert series. The grading may have non-positive entries, but it must give positive values for all generators. <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : R=ZZ/37[x,y,t];</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : L={x^3, x^2*y, y^3, x*y^2};</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : T=intclToricRing(allComputations=>true,L);</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : T.cache#"cone"#"inv"#"hilbert series num" o4 = 1 : (1) o4 : Sequence</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : T.cache#"cone"#"inv"#"hilbert series denom" o5 = (1, 1) o5 : Sequence</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i6 : T=intclToricRing(allComputations=>true,grading=>{3,2,1},L);</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i7 : T.cache#"cone"#"inv"#"hilbert series num" o7 = (1, -1, 1) o7 : Sequence</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i8 : T.cache#"cone"#"inv"#"hilbert series denom" o8 = (1, 6) o8 : Sequence</code></pre> </td> </tr> </table> </div> <div> <h2>See also</h2> <ul> <li><span><a href="_all__Computations.html">allComputations</a></span></li> </ul> </div> <div> <div> <h2>Functions with optional argument named <span class="tt">grading</span>:</h2> <ul> <li><span><span class="tt">diagInvariants(...,grading=>...)</span> (missing documentation)<!--tag: [diagInvariants, grading]--> </span></li> <li><span><span class="tt">finiteDiagInvariants(...,grading=>...)</span> (missing documentation)<!--tag: [finiteDiagInvariants, grading]--> </span></li> <li><span><span class="tt">intclMonIdeal(...,grading=>...)</span> (missing documentation)<!--tag: [intclMonIdeal, grading]--> </span></li> <li><span><span class="tt">intclToricRing(...,grading=>...)</span> (missing documentation)<!--tag: [intclToricRing, grading]--> </span></li> <li><span><span class="tt">intersectionValRingIdeals(...,grading=>...)</span> (missing documentation)<!--tag: [intersectionValRingIdeals, grading]--> </span></li> <li><span><span class="tt">intersectionValRings(...,grading=>...)</span> (missing documentation)<!--tag: [intersectionValRings, grading]--> </span></li> <li><span><span class="tt">normaliz(...,grading=>...)</span> (missing documentation)<!--tag: [normaliz, grading]--> </span></li> <li><span><span class="tt">normalToricRing(...,grading=>...)</span> (missing documentation)<!--tag: [normalToricRing, grading]--> </span></li> <li><span><span class="tt">torusInvariants(...,grading=>...)</span> (missing documentation)<!--tag: [torusInvariants, grading]--> </span></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a href="_grading.html">grading</a> is <span>a <a title="the class of all symbols" href="../../Macaulay2Doc/html/___Symbol.html">symbol</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Normaliz.m2:1350:0</span>.</p> </div> </div> </div> </body> </html>
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