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<!DOCTYPE html> <html lang="en"> <head> <title>NCRingMap _ ZZ -- Matrix of one homogeneous component of an NCRingMap</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="Matrix of one homogeneous component of an NCRingMap" href="___N__C__Ring__Map_sp_us_sp__Z__Z.html">NCRingMap _ ZZ</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="___N__C__Ring__Map_sp__N__C__Ideal.html">next</a> | <a href="___N__C__Ring__Map_sp_at_at_sp__N__C__Ring__Map.html">previous</a> | <a href="___N__C__Ring__Map_sp__N__C__Ideal.html">forward</a> | <a href="___N__C__Ring__Map_sp_at_at_sp__N__C__Ring__Map.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>NCRingMap _ ZZ -- Matrix of one homogeneous component of an NCRingMap</h1> <ul> <li><span>Operator: <a title="a binary operator, used for subscripting and access to elements" href="../../Macaulay2Doc/html/__us.html">_</a></span></li> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">f_n</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">f</span>, <span>an instance of the type <a title="Type of a map to or from a noncommutative ring." href="___N__C__Ring__Map.html">NCRingMap</a></span>, </span></li> <li><span><span class="tt">n</span>, <span>an <a title="the class of all integers" href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, </span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>a <a title="the class of all matrices" href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, </span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>This method returns the homogeneous degree n component of the ring map f. The output is the matrix (over the coefficient ring of the target) of the component map relative to the monomial bases for the source and target.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : A = skewPolynomialRing(QQ,(-1)_QQ,{w,x,y,z}) --Calling Bergman for NCGB calculation. Complete! o1 = A o1 : NCQuotientRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : setWeights(A,{1,1,2,2}) o2 = A o2 : NCQuotientRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : f = ncMap(A,A,{x,w,z,y}) o3 = NCRingMap A <--- A o3 : NCRingMap</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : basis(1,A) o4 = | w x | o4 : NCMatrix</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : f_1 o5 = | 0 1 | | 1 0 | 2 2 o5 : Matrix QQ <-- QQ</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i6 : basis(2,A) o6 = | y z w^2 w*x x^2 | o6 : NCMatrix</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i7 : f_2 o7 = | 0 1 0 0 0 | | 1 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 -1 0 | | 0 0 1 0 0 | 5 5 o7 : Matrix QQ <-- QQ</code></pre> </td> </tr> </table> </div> <div> <div class="waystouse"> <h2>Ways to use this method:</h2> <ul> <li><span><a title="Matrix of one homogeneous component of an NCRingMap" href="___N__C__Ring__Map_sp_us_sp__Z__Z.html">NCRingMap _ ZZ</a> -- Matrix of one homogeneous component of an NCRingMap</span></li> </ul> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">NCAlgebra/NCAlgebraDoc.m2:3194:0</span>.</p> </div> </div> </div> </body> </html>