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_check__Degrees_lp..._cm__Strict_eq_gt..._rp.html
<!DOCTYPE html> <html lang="en"> <head> <title>checkDegrees(...,Strict=>...) -- forces strict equality of degrees</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 title="probabilistic test for isomorphism of modules" href="index.html">Isomorphism</a> :: <a title="forces strict equality of degrees" href="_check__Degrees_lp..._cm__Strict_eq_gt..._rp.html">checkDegrees(...,Strict=>...)</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__Isomorphic.html">next</a> | <a href="_check__Degrees.html">previous</a> | <a href="_is__Isomorphic.html">forward</a> | <a href="_check__Degrees.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>checkDegrees(...,Strict=>...) -- forces strict equality of degrees</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">d = checkDegrees(N, M, Strict =>true)</code></dd> </dl> </li> </ul> <div> <h2>Description</h2> <div> <p>Used with Strict=>false, the default, checkDegrees(N,M) returns (true, deg) if degrees M and degrees N are equal up to a shift d. With Strict => true the degree lists must be equal.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : S = ZZ/101[a,b,Degrees => {{1,0},{0,1}}] o1 = S o1 : PolynomialRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : B = S^{{1,1}} 1 o2 = S o2 : S-module, free, degrees {{-1, -1}}</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : B' = S^{{3,3}}**B 1 o3 = S o3 : S-module, free, degrees {{-4, -4}}</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : d = checkDegrees(B',B) o4 = (true, {-3, -3}) o4 : Sequence</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : degrees (S^{d_1}**B') == degrees B o5 = true</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i6 : degrees (B') == degrees (S^{-d_1}**B) o6 = true</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i7 : checkDegrees(B',B,Strict=>true) o7 = (false, ) o7 : Sequence</code></pre> </td> </tr> </table> </div> <div> <h2>See also</h2> <ul> <li><span><a title="compares the degrees of generators of two modules" href="_check__Degrees.html">checkDegrees</a> -- compares the degrees of generators of two modules</span></li> </ul> </div> <div> <div> <h2>Functions with optional argument named <span class="tt">Strict</span>:</h2> <ul> <li><span><a title="forces strict equality of degrees" href="_check__Degrees_lp..._cm__Strict_eq_gt..._rp.html">checkDegrees(...,Strict=>...)</a> -- forces strict equality of degrees</span></li> <li><span><kbd>isIsomorphic(...,Strict=>...)</kbd> -- see <span><a title="probabilistic test for isomorphism of modules" href="_is__Isomorphic.html">isIsomorphic</a> -- probabilistic test for isomorphism of modules</span></span></li> <li><span><kbd>isomorphism(...,Strict=>...)</kbd> -- see <span><a title="retrieve an isomorphism of modules" href="_isomorphism.html">isomorphism</a> -- retrieve an isomorphism of modules</span></span></li> </ul> </div> <div> <h2>Further information</h2> <ul> <li><span>Default value: <a href="../../Macaulay2Doc/html/_false.html">false</a></span></li> <li><span>Function: <span><a title="compares the degrees of generators of two modules" href="_check__Degrees.html">checkDegrees</a> -- compares the degrees of generators of two modules</span></span></li> <li><span>Option key: <span><a title="an optional argument" href="../../Macaulay2Doc/html/___Strict.html">Strict</a> -- an optional argument</span></span></li> </ul> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Isomorphism.m2:528:0</span>.</p> </div> </div> </div> </body> </html>
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