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___Compress__Beta.html
<!DOCTYPE html> <html lang="en"> <head> <title>CompressBeta -- CompressBeta is an option for eagon, default is true</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="Construct the Eagon double complex, which contains a resolution of the residue field" href="index.html">EagonResolution</a> :: <a title="CompressBeta is an option for eagon, default is true" href="___Compress__Beta.html">CompressBeta</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="___Display.html">next</a> | <a href="index.html">previous</a> | <a href="___Display.html">forward</a> | <a href="index.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>CompressBeta -- CompressBeta is an option for eagon, default is true</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">E = eagon(R,b,CompressBeta =>bool1, Verbose =>bool2)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">R</span>, <span>a <a title="the class of all rings" href="../../Macaulay2Doc/html/___Ring.html">ring</a></span>, </span></li> <li><span><span class="tt">b</span>, <span>an <a title="the class of all integers" href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, </span></li> <li><span><span class="tt">bool1</span>, <span>a <a title="the class of boolean values" href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, </span></li> <li><span><span class="tt">bool2</span>, <span>a <a title="the class of boolean values" href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, </span></li> </ul> </li> <li>Outputs: <ul> <li><span><span class="tt">E</span>, <span>an instance of the type <a title="HashTable storing output of eagon" href="___Eagon__Data.html">EagonData</a></span>, </span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>eagonBeta(E,i) := E#{"eagonBeta",n,0} is defined by lifting another map along the map dVert^n_i. If CompressBeta => true, the default, then the lifting uses the smallest initial subsequence of the blocks of source dVert as possible, and thus the columns of picture eagonBeta(E,i) will have fewer nonzero entries. if Verbose =>true, then data about the usage is printed.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : R = ZZ/101[x,y,z]/ideal"x3,y3,z3" o1 = R o1 : QuotientRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : E = eagon(R,4,CompressBeta =>true, Verbose =>true); Used 1 of 1 blocks of eagonBeta (2, 1) Used 1 of 1 blocks of eagonBeta (2, 2) Used 1 of 1 blocks of eagonBeta (2, 3) Used 1 of 1 blocks of eagonBeta (2, 4) Used 2 of 2 blocks of eagonBeta (3, 1) Used 2 of 2 blocks of eagonBeta (3, 2) Used 1 of 2 blocks of eagonBeta (3, 3) Used 1 of 1 blocks of eagonBeta (3, 4) Used 3 of 3 blocks of eagonBeta (4, 1) Used 3 of 3 blocks of eagonBeta (4, 2) Used 1 of 2 blocks of eagonBeta (4, 3) Used 1 of 1 blocks of eagonBeta (4, 4)</code></pre> </td> </tr> </table> </div> <div> <h2>See also</h2> <ul> <li><span><a title="compute the Eagon double complex" href="_eagon.html">eagon</a> -- compute the Eagon double complex</span></li> <li><span><a title="print the eagonBeta maps in the Eagon resolution" href="_eagon__Beta.html">eagonBeta</a> -- print the eagonBeta maps in the Eagon resolution</span></li> </ul> </div> <div> <div> <h2>Functions with optional argument named <span class="tt">CompressBeta</span>:</h2> <ul> <li><span><kbd>eagon(...,CompressBeta=>...)</kbd> -- see <span><a title="compute the Eagon double complex" href="_eagon.html">eagon</a> -- compute the Eagon double complex</span></span></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="CompressBeta is an option for eagon, default is true" href="___Compress__Beta.html">CompressBeta</a> is <span>a <a title="the class of all symbols" href="../../Macaulay2Doc/html/___Symbol.html">symbol</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">EagonResolution.m2:1323:0</span>.</p> </div> </div> </div> </body> </html>
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