One Hat Cyber Team
Your IP :
216.73.216.115
Server IP :
194.44.31.54
Server :
Linux zen.imath.kiev.ua 4.18.0-553.77.1.el8_10.x86_64 #1 SMP Fri Oct 3 14:30:23 UTC 2025 x86_64
Server Software :
Apache/2.4.37 (Rocky Linux) OpenSSL/1.1.1k
PHP Version :
5.6.40
Buat File
|
Buat Folder
Eksekusi
Dir :
~
/
usr
/
share
/
doc
/
Macaulay2
/
Points
/
html
/
Edit File:
_expected__Betti.html
<!DOCTYPE html> <html lang="en"> <head> <title>expectedBetti -- The betti table of r points in Pn according to the minimal resolution conjecture</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="A package for making and studying points in affine and projective spaces" href="index.html">Points</a> :: <a title="The betti table of r points in Pn according to the minimal resolution conjecture" href="_expected__Betti.html">expectedBetti</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="_min__Max__Resolution.html">next</a> | <a href="___All__Random.html">previous</a> | <a href="_min__Max__Resolution.html">forward</a> | <a href="___All__Random.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>expectedBetti -- The betti table of r points in Pn according to the minimal resolution conjecture</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">L = expectedBetti(r,n)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">r</span>, <span>an <a title="the class of all integers" href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, ambient dimension</span></li> <li><span><span class="tt">n</span>, <span>an <a title="the class of all integers" href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, number of points</span></li> </ul> </li> <li>Outputs: <ul> <li><span><span class="tt">L</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>The output is the smallest conceivable betti table for a set of r points in P^n, which is predicted (incorrectly) by the minimal resolution conjecture.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : expectedBetti(11,5) 0 1 2 3 4 5 6 7 8 9 10 11 o1 = total: 1 7 66 330 858 1386 1518 1155 605 209 43 4 0: 1 7 11 . . . . . . . . . 1: . . 55 330 858 1386 1518 1155 605 209 43 4 o1 : BettiTally</code></pre> </td> </tr> </table> </div> <div> <h2>Caveat</h2> <div> <p>The MRC is false, so these are sometimes not the actual Betti numbers.</p> </div> </div> <div> <h2>See also</h2> <ul> <li><span><a title="The betti table of r points in Pn according to the minimal resolution conjecture" href="_expected__Betti.html">expectedBetti</a> -- The betti table of r points in Pn according to the minimal resolution conjecture</span></li> <li><span><a title="Min and max conceivable Betti tables for generic points" href="_min__Max__Resolution.html">minMaxResolution</a> -- Min and max conceivable Betti tables for generic points</span></li> </ul> </div> <div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="The betti table of r points in Pn according to the minimal resolution conjecture" href="_expected__Betti.html">expectedBetti</a> is <span>a <a title="the class of all function closures" href="../../Macaulay2Doc/html/___Function__Closure.html">function closure</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Points.m2:785:0</span>.</p> </div> </div> </div> </body> </html>
Simpan