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___N__C__Ring__Map_sp__N__C__Ring__Element.html
<!DOCTYPE html> <html lang="en"> <head> <title>NCRingMap NCRingElement -- Apply an NCRingMap to an element or matrix</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="Apply an NCRingMap to an element or matrix" href="___N__C__Ring__Map_sp__N__C__Ring__Element.html">NCRingMap NCRingElement</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="_normal__Automorphism.html">next</a> | <a href="___N__C__Ring__Map_sp__N__C__Ideal.html">previous</a> | <a href="_normal__Automorphism.html">forward</a> | <a href="___N__C__Ring__Map_sp__N__C__Ideal.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>NCRingMap NCRingElement -- Apply an NCRingMap to an element or matrix</h1> <ul> <li><span>Operator: <a title="blank operator; often used for function application, making polynomial rings" href="../../Macaulay2Doc/html/___S__P__A__C__E.html">SPACE</a></span></li> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">f x</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">x</span>, <span>an instance of the type <a title="Type of an element in a noncommutative ring" href="___N__C__Ring__Element.html">NCRingElement</a></span>, or a <a title="the class of all ring elements handled by the engine" href="../../Macaulay2Doc/html/___Ring__Element.html">RingElement</a> or an <a title="Type of a matrix over a noncommutative ring" href="___N__C__Matrix.html">NCMatrix</a></span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>an instance of the type <a title="Type of an element in a noncommutative ring" href="___N__C__Ring__Element.html">NCRingElement</a></span>, </span></li> </ul> </li> </ul> <div> <h2>Description</h2> <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 : B = QQ{a,b,c} o2 = B o2 : NCPolynomialRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : f = ncMap(B,A,{a^3,b^2,a+b,a-b}) o3 = NCRingMap B <--- A o3 : NCRingMap</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : f(w*x+2*y) 3 2 o4 = 2b+a b +2a o4 : B</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : f basis(2,A) o5 = | a^6 a^3*b^2 b^4 a^3*b+a^4 b^3+b^2*a b^2+b*a+a*b+a^2 -a^3*b+a^4 -b^3+b^2*a -b^2+b*a-a*b+a^2 b^2-b*a-a*b+a^2 | o5 : NCMatrix</code></pre> </td> </tr> </table> </div> <div> <div class="waystouse"> <h2>Ways to use this method:</h2> <ul> <li><kbd>NCRingMap NCMatrix</kbd></li> <li><span><a title="Apply an NCRingMap to an element or matrix" href="___N__C__Ring__Map_sp__N__C__Ring__Element.html">NCRingMap NCRingElement</a> -- Apply an NCRingMap to an element or matrix</span></li> <li><kbd>NCRingMap RingElement</kbd></li> </ul> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">NCAlgebra/NCAlgebraDoc.m2:3167:0</span>.</p> </div> </div> </div> </body> </html>