One Hat Cyber Team
Your IP :
216.73.216.216
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
/
K3Carpets
/
html
/
View File Name :
_schreyer__Name.html
<!DOCTYPE html> <html lang="en"> <head> <title>schreyerName -- get the names of generators in the (nonminimal) Schreyer resolution according to Schreyer's convention</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="The unique Gorenstein double structure on a surface scroll" href="index.html">K3Carpets</a> :: <a title="get the names of generators in the (nonminimal) Schreyer resolution according to Schreyer's convention" href="_schreyer__Name.html">schreyerName</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="___Scrolls.html">next</a> | <a href="_scheme__In__Product.html">previous</a> | <a href="___Scrolls.html">forward</a> | <a href="_scheme__In__Product.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>schreyerName -- get the names of generators in the (nonminimal) Schreyer resolution according to Schreyer's convention</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">L = schreyerName(F,i,n)</code></dd> <dd><code class="language-macaulay2">h = schreyerName(F,a)</code></dd> <dd><code class="language-macaulay2">L = schreyerName(h,i,n)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">F</span>, <span>a <a title="the class of all chain complexes" href="../../Complexes/html/___Complex.html">complex</a></span>, the nonminimal resolution from a Groebner basis</span></li> <li><span><span class="tt">i</span>, <span>an <a title="the class of all integers" href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, the homological degree</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>, the number of the generator</span></li> <li><span><span class="tt">a</span>, <span>an <a title="the class of all integers" href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, homological degree</span></li> <li><span><span class="tt">h</span>, <span>a <a title="the class of all hash tables" href="../../Macaulay2Doc/html/___Hash__Table.html">hash table</a></span>, of lists of names</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>, list of monomials</span></li> <li><span><span class="tt">h</span>, <span>a <a title="the class of all hash tables" href="../../Macaulay2Doc/html/___Hash__Table.html">hash table</a></span>, of names</span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>We name the generators of the syzygies by the list of the monomial parts of the leadTerm with position m recursively:</p> <p>schreyerName(F,i,n) = append(schreyerName(F,i-1,m),mon)</p> <p>where mon denotes the monomial part and m the position in F_(i-1) of leadTerm F.dd_i_n.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : (a,b)=(5,4) o1 = (5, 4) o1 : Sequence</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : I = carpet(a,b); ZZ o2 : Ideal of -----[x ..x , y ..y ] 32003 0 5 0 4</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : F = freeResolution(I, Strategy => Nonminimal) ZZ 1 ZZ 28 ZZ 127 ZZ 286 ZZ 385 ZZ 323 ZZ 166 ZZ 48 ZZ 6 o3 = (-----[x ..x , y ..y ]) <-- (-----[x ..x , y ..y ]) <-- (-----[x ..x , y ..y ]) <-- (-----[x ..x , y ..y ]) <-- (-----[x ..x , y ..y ]) <-- (-----[x ..x , y ..y ]) <-- (-----[x ..x , y ..y ]) <-- (-----[x ..x , y ..y ]) <-- (-----[x ..x , y ..y ]) 32003 0 5 0 4 32003 0 5 0 4 32003 0 5 0 4 32003 0 5 0 4 32003 0 5 0 4 32003 0 5 0 4 32003 0 5 0 4 32003 0 5 0 4 32003 0 5 0 4 0 1 2 3 4 5 6 7 8 o3 : Complex</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : betti F 0 1 2 3 4 5 6 7 8 o4 = total: 1 28 127 286 385 323 166 48 6 0: 1 . . . . . . . . 1: . 28 105 184 185 110 36 5 . 2: . . 22 101 195 203 120 38 5 3: . . . 1 5 10 10 5 1 o4 : BettiTally</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : i=3,n=10 o5 = (3, 10) o5 : Sequence</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i6 : schreyerName(F,3,10) o6 = {x x , x , x } 3 4 3 1 o6 : List</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i7 : h=schreyerName F;</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i8 : h#8 2 2 o8 = {{y y , x , y , y , x , x , x , x }, {y y , x , y , y , x , x , x , x }, 1 3 1 2 1 5 4 3 2 2 3 1 2 1 5 4 3 2 ------------------------------------------------------------------------ 2 2 {y , x y , y , y , x , x , x , x }, {y , x y , y , y , x , x , x , x }, 3 2 0 2 1 4 3 2 1 3 3 0 2 1 4 3 2 1 ------------------------------------------------------------------------ 2 2 2 {y , x y , y , y , x , x , x , x }, {y , x y , x , y , y , x , x , x }} 3 4 0 2 1 4 3 2 1 3 5 0 1 2 1 4 3 2 o8 : List</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i9 : h#7_20 2 o9 = {y , x x , y , y , x , x , x } 3 1 4 2 1 3 2 1 o9 : List</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i10 : h#7_20 == schreyerName(F,7,20) o10 = true</code></pre> </td> </tr> </table> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">schreyerName</span>:</h2> <ul> <li><kbd>schreyerName(Complex)</kbd></li> <li><kbd>schreyerName(Complex,ZZ)</kbd></li> <li><kbd>schreyerName(Complex,ZZ,ZZ)</kbd></li> <li><kbd>schreyerName(HashTable,ZZ,ZZ)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="get the names of generators in the (nonminimal) Schreyer resolution according to Schreyer's convention" href="_schreyer__Name.html">schreyerName</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function.html">method function</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">K3Carpets.m2:1550:0</span>.</p> </div> </div> </div> </body> </html>