One Hat Cyber Team
Your IP :
216.73.216.14
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
/
Normaliz
/
html
/
View File Name :
___Rational__Cone.html
<!DOCTYPE html> <html lang="en"> <head> <title>RationalCone -- class of rational cones</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="an interface to use Normaliz in Macaulay 2" href="index.html">Normaliz</a> :: <a title="class of rational cones" href="___Rational__Cone.html">RationalCone</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="_read__Multiple__Nmz__Data.html">next</a> | <a href="_output_spfiles_spwritten_spby_sp__Normaliz.html">previous</a> | <a href="_read__Multiple__Nmz__Data.html">forward</a> | <a href="_output_spfiles_spwritten_spby_sp__Normaliz.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>RationalCone -- class of rational cones</h1> <div> <h2>Description</h2> <p></p> The method <a title="calls Normaliz" href="_normaliz.html">normaliz</a> returns an object of type RationalCone. By default, that cone contains only the content of the output file .gen, under the key "gen" (i.e. the generators that have been computed) and the content of the output file .inv, which contains some additional data. Note that Normaliz writes the generators as rows, in contrast to the convention used in M2. <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : setNmzOption("allf",true);</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : eq=matrix {{1, 1, 1, -1, -1, -1, 0, 0, 0}, {1, 1, 1, 0, 0, 0, -1, -1, -1}, {0, 1, 1, -1, 0, 0, -1, 0, 0}, {1, 0, 1, 0, -1, 0, 0, -1, 0}, {1, 1, 0, 0, 0, -1, 0, 0, -1}, {0, 1, 1, 0, -1, 0, 0, 0, -1}, {1, 1, 0, 0, -1, 0, -1, 0, 0}}; 7 9 o2 : Matrix ZZ <-- ZZ</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : rc=normaliz(eq,"equations");</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : rc#"gen" o4 = | 0 2 1 2 1 0 1 0 2 | | 1 0 2 2 1 0 0 2 1 | | 1 1 1 1 1 1 1 1 1 | | 1 2 0 0 1 2 2 0 1 | | 2 0 1 0 1 2 1 2 0 | 5 9 o4 : Matrix ZZ <-- ZZ</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : rc#"inv" o5 = HashTable{"" => (1, 1, 1) } "class group" => (1, 2, 2) "degree 1 elements" => 5 "dim max subspace" => 0 "embedding dim" => 9 "external index" => 1 "graded" => true "grading denom" => 3 "grading" => (1, 1, 1, 0, 0, 0, 0, 0, 0) "hilbert basis elements" => 5 "hilbert quasipolynomial denom" => 1 "hilbert series denom" => (1, 1, 1) "hilbert series num" => (1, 2, 1) "inhomogeneous" => false "multiplicity denom" => 1 "multiplicity" => 4 "number extreme rays" => 4 "number support hyperplanes" => 4 "rank" => 3 "size triangulation" => 2 "sum dets" => 4 o5 : HashTable</code></pre> </td> </tr> </table> <p></p> To obtain all the information written by <span class="tt">Normaliz</span> set the option <a href="_all__Computations.html">allComputations</a> to true. Then the method returns an object of type RationalCone whose keys are the suffixes of all the output files written, with value the content of the corresponding output file (also to be read line by line). <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i6 : arc=normaliz(allComputations=>true,eq,"equations");</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i7 : arc#"gen" o7 = | 0 2 1 2 1 0 1 0 2 | | 1 0 2 2 1 0 0 2 1 | | 1 1 1 1 1 1 1 1 1 | | 1 2 0 0 1 2 2 0 1 | | 2 0 1 0 1 2 1 2 0 | 5 9 o7 : Matrix ZZ <-- ZZ</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i8 : arc#"ext" o8 = | 0 2 1 2 1 0 1 0 2 | | 1 0 2 2 1 0 0 2 1 | | 1 2 0 0 1 2 2 0 1 | | 2 0 1 0 1 2 1 2 0 | 4 9 o8 : Matrix ZZ <-- ZZ</code></pre> </td> </tr> </table> <p></p> See <a href="_output_spfiles_spwritten_spby_sp__Normaliz.html">output files written by Normaliz</a> for an explanation of the different output files. </div> <div> <h2>See also</h2> <ul> <li><span><a href="_all__Computations.html">allComputations</a></span></li> <li><span><a title="reads an output file of Normaliz containing one matrix" href="_read__Nmz__Data.html">readNmzData</a> -- reads an output file of Normaliz containing one matrix</span></li> <li><span><a href="___Keeping_spresults_spof_spthe_spcomputation_spby_sp__Normaliz.html">Keeping results of the computation by Normaliz</a></span></li> <li><span><a href="_output_spfiles_spwritten_spby_sp__Normaliz.html">output files written by Normaliz</a></span></li> </ul> </div> <div> <div class="waystouse"> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="class of rational cones" href="___Rational__Cone.html">RationalCone</a> is <span>a <a title="the class of all mutable types" href="../../Macaulay2Doc/html/___Type.html">type</a></span>, with ancestor classes <a title="the class of all hash tables" href="../../Macaulay2Doc/html/___Hash__Table.html">HashTable</a> < <a title="the class of all things" href="../../Macaulay2Doc/html/___Thing.html">Thing</a>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Normaliz.m2:949:0</span>.</p> </div> </div> </div> </body> </html>