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<!DOCTYPE html> <html lang="en"> <head> <title>setWeights -- Set a nonstandard grading for a NCRing.</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 href="index.html">NCAlgebra</a> :: <a title="Set a nonstandard grading for a NCRing." href="_set__Weights.html">setWeights</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="_size_lp__N__C__Ring__Element_rp.html">next</a> | <a href="___Ring__Element_sp_st_sp__N__C__Matrix.html">previous</a> | <a href="_size_lp__N__C__Ring__Element_rp.html">forward</a> | <a href="___Ring__Element_sp_st_sp__N__C__Matrix.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>setWeights -- Set a nonstandard grading for a NCRing.</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">setWeights(A,degList)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">A</span>, <span>an instance of the type <a title="Type of a noncommutative ring" href="___N__C__Ring.html">NCRing</a></span>, </span></li> <li><span><span class="tt">degList</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of integer weights to be assigned to the generators of A</span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>an instance of the type <a title="Type of a noncommutative ring" href="___N__C__Ring.html">NCRing</a></span>, </span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>This method enables the user to work with rings which are not naturally graded (the generators are not all degree 1). The user should be aware that methods which call Bergman may not work with nonstandard gradings. Perhaps the most important example is hilbertBergman, which throws an error. Instead, use <a title="compute the Hilbert series" href="../../Macaulay2Doc/html/_hilbert__Series.html">hilbertSeries</a>.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : A=QQ{x,y,z} o1 = A o1 : NCPolynomialRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : w=x^3-y^2 2 3 o2 = -y +x o2 : A</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : isHomogeneous w o3 = false</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : setWeights(A, {2,3,1}) o4 = A o4 : NCPolynomialRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : isHomogeneous w o5 = true</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i6 : C = QQ{a,b,c} o6 = C o6 : NCPolynomialRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i7 : g = ncMap(C,A,{a^3,b^2,a+b,a-b}) o7 = NCRingMap C <--- A o7 : NCRingMap</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i8 : isHomogeneous g o8 = false</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i9 : setWeights(A,{3,2,1,1}) o9 = A o9 : NCPolynomialRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i10 : isHomogeneous g o10 = true</code></pre> </td> </tr> </table> </div> <div> <h2>See also</h2> <ul> <li><span><a title="whether something is homogeneous (graded)" href="../../Macaulay2Doc/html/_is__Homogeneous.html">isHomogeneous</a> -- whether something is homogeneous (graded)</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">setWeights</span>:</h2> <ul> <li><kbd>setWeights(NCRing,List)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="Set a nonstandard grading for a NCRing." href="_set__Weights.html">setWeights</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function.html">method function</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">NCAlgebra/NCAlgebraDoc.m2:2192:0</span>.</p> </div> </div> </div> </body> </html>