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_get__Non__Unit.html
<!DOCTYPE html> <html lang="en"> <head> <title>getNonUnit -- retrieve a previously discovered non-unit</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="index.html">Documentation </a> <br><a href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="Macaulay2 documentation" href="index.html">Macaulay2Doc</a> » <a href="_rings.html">rings</a> » <a href="_finite_spfield_spextensions.html">finite field extensions</a> » <a title="retrieve a previously discovered non-unit" href="_get__Non__Unit.html">getNonUnit</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="_is__Primitive.html">next</a> | <a href="_to__Field_lp__Ring_rp.html">previous</a> | <a href="_is__Primitive.html">forward</a> | <a href="_to__Field_lp__Ring_rp.html">backward</a> | <a href="_finite_spfield_spextensions.html">up</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>getNonUnit -- retrieve a previously discovered non-unit</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">getNonUnit R</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">R</span>, <span>a <a title="the class of all rings" href="___Ring.html">ring</a></span>, in which division by a non-unit may have been attempted</span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>a <a title="the class of all ring elements handled by the engine" href="___Ring__Element.html">ring element</a></span>, the non-unit, if any, or <a title="the unique member of the empty class" href="_null.html">null</a></span></li> </ul> </li> </ul> <div> <h2>Description</h2> If a ring has been declared to be a field, using <a title="declare that a ring is a field" href="_to__Field_lp__Ring_rp.html">toField</a> or <a title="construct a fraction field" href="_frac.html">frac</a>, but a nonzero element is found to not be a unit, this routine will return that element, otherwise <a title="the unique member of the empty class" href="_null.html">null</a> is returned. <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : A = ZZ/101[a]/(a^2-1);</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : toField A o2 = A[] o2 : PolynomialRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : 1//(a-1) o3 = 0 o3 : A</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : getNonUnit A</code></pre> </td> </tr> </table> Warning: this function does not work yet for divisions attempted in the course of computing a Gröbner basis or resolution. </div> <div> <h2>See also</h2> <ul> <li><span><a title="declare that a ring is a field" href="_to__Field_lp__Ring_rp.html">toField</a> -- declare that a ring is a field</span></li> <li><span><a title="construct a fraction field" href="_frac.html">frac</a> -- construct a fraction field</span></li> </ul> </div> <div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="retrieve a previously discovered non-unit" href="_get__Non__Unit.html">getNonUnit</a> is <span>a <a title="the class of all function closures" href="___Function__Closure.html">function closure</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Macaulay2Doc/functions/getNonUnit-doc.m2:28:0</span>.</p> </div> </div> </div> </body> </html>