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<!DOCTYPE html> <html lang="en"> <head> <title>normalFormBergman -- Calls Bergman for a normal form calculation</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="Calls Bergman for a normal form calculation" href="_normal__Form__Bergman.html">normalFormBergman</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="_numgens_lp__N__C__Ring_rp.html">next</a> | <a href="_normal__Elements_lp__N__C__Ring__Map_cm__Z__Z_rp.html">previous</a> | <a href="_numgens_lp__N__C__Ring_rp.html">forward</a> | <a href="_normal__Elements_lp__N__C__Ring__Map_cm__Z__Z_rp.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>normalFormBergman -- Calls Bergman for a normal form calculation</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">nfList = normalFormBergman(L,Igb)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">L</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 lists -- {...}" href="../../Macaulay2Doc/html/___List.html">List</a> of NCRingElements</span></li> <li><span><span class="tt">Igb</span>, <span>an instance of the type <a title="Type of a Groebner basis for an NCIdeal in an NCRing." href="___N__C__Groebner__Basis.html">NCGroebnerBasis</a></span>, </span></li> </ul> </li> <li>Outputs: <ul> <li><span><span class="tt">nfList</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, </span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>This method takes a list of NCRingElements and calls Bergman to reduce each element to normal form relative to the given NCGroebnerBasis for the NCIdeal defining the NCRing to which the list elements belong.</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 : f = y*z + z*y - x^2 2 o2 = zy+yz-x o2 : A</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : g = x*z + z*x - y^2 2 o3 = zx-y +xz o3 : A</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : h = z^2 - x*y - y*x 2 o4 = z -yx-xy o4 : A</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : I = ncIdeal {f,g,h} 2 2 2 o5 = Two-sided ideal {zy+yz-x , zx-y +xz, z -yx-xy} o5 : NCIdeal</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i6 : Igb = ncGroebnerBasis I --Calling Bergman for NCGB calculation. Complete! 2 2 2 o6 = y x-xy ; Lead Term = (y x, 1) 2 2 2 yx -x y; Lead Term = (yx , 1) 2 zx-y +xz; Lead Term = (zx, 1) 2 zy+yz-x ; Lead Term = (zy, 1) 2 2 z -yx-xy; Lead Term = (z , 1) o6 : NCGroebnerBasis</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i7 : normalFormBergman(z^17,Igb) --Calling Bergman for NF calculation for 1 elements. Complete! Writing bergman input file. Writing bergman init file. 2 2 3 3 4 4 5 5 6 6 7 7 8 8 o7 = yxyxyxyxyxyxyxyxz+xyxyxyxyxyxyxyxyz+8x yxyxyxyxyxyxy z+8x yxyxyxyxyxy z+28x yxyxyxyxy z+28x yxyxyxy z+56x yxyxy z+56x yxy z+70x y z o7 : A</code></pre> </td> </tr> </table> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">normalFormBergman</span>:</h2> <ul> <li><kbd>normalFormBergman(List,NCGroebnerBasis)</kbd></li> <li><kbd>normalFormBergman(NCRingElement,NCGroebnerBasis)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="Calls Bergman for a normal form calculation" href="_normal__Form__Bergman.html">normalFormBergman</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function__With__Options.html">method function with options</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">NCAlgebra/NCAlgebraDoc.m2:3647:0</span>.</p> </div> </div> </div> </body> </html>