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
/
Normaliz
/
html
/
Edit File:
_normaliz_lp__List_rp.html
<!DOCTYPE html> <html lang="en"> <head> <title>normaliz(List) -- calls Normaliz with several input matrices</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="calls Normaliz with several input matrices" href="_normaliz_lp__List_rp.html">normaliz(List)</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="_normaliz_lp__Matrix_cm__String_rp.html">next</a> | <a href="_normaliz.html">previous</a> | <a href="_normaliz_lp__Matrix_cm__String_rp.html">forward</a> | <a href="_normaliz.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>normaliz(List) -- calls Normaliz with several input matrices</h1> <ul> <li><span>Function: <a title="calls Normaliz" href="_normaliz.html">normaliz</a></span></li> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">normaliz L</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of pairs (mat,nmzType)</span></li> </ul> </li> <li><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>: <ul> <li><span><span class="tt">allComputations</span> (missing documentation)<!--tag: [normaliz, allComputations]--> <span class="tt"> => </span><span class="tt">...</span>, <span>default value false</span>, <span></span></span></li> <li><span><span class="tt">grading</span> (missing documentation)<!--tag: [normaliz, grading]--> <span class="tt"> => </span><span class="tt">...</span>, <span>default value {}</span>, <span></span></span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>a <a title="class of rational cones" href="___Rational__Cone.html">rational cone</a></span>, generators of the integral closure and optional output from <span class="tt">Normaliz</span></span></li> </ul> </li> </ul> <div> <h2>Description</h2> <p></p> This function applies <span class="tt">Normaliz</span> to all <span class="tt">mat</span> each in the type set by the second parameter <span class="tt">nmzType</span>. The function returns an object of type <a title="class of rational cones" href="___Rational__Cone.html">RationalCone</a> defined by the file with suffix <span class="tt">gen</span> , if computed, and possibly some additional information.It is possibly to give several matrices of the same type. All matrices of one type are then appended to one matrix by <span class="tt">Normaliz</span>. <p></p> By default, the cone returned contains only the content of the output file .gen, under the key "gen", i.e. the generators that have been computed, line by line and the content of the output file .inv, under the key "inv". <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : hy=matrix {{-1,0,-1,0,3,0,0,0,0},{-1,0,1,0,1,0,0,0,0},{1,0,1,0,-1,0,0,0,0},{1,0,-1,0,1,0,0,0,0}}; 4 9 o1 : Matrix ZZ <-- ZZ</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 : cg=matrix {{1,0,0,0,0,0,0,0,0,2},{0,0,1,0,0,0,0,0,0,2},{0,0,0,0,0,0,1,0,0,2},{0,0,0,0,0,0,0,0,1,2}}; 4 10 o3 : Matrix ZZ <-- ZZ</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : rc=normaliz({(hy,"inequalities"),(eq,"equations"),(cg,"congruences")});</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : rc#"gen" o5 = | 0 4 2 4 2 0 2 0 4 | | 2 0 4 4 2 0 0 4 2 | | 2 2 2 2 2 2 2 2 2 | | 2 3 4 5 3 1 2 3 4 | | 2 4 0 0 2 4 4 0 2 | | 2 5 2 3 3 3 4 1 4 | | 4 0 2 0 2 4 2 4 0 | | 4 1 4 3 3 3 2 5 2 | | 4 3 2 1 3 5 4 3 2 | 9 9 o5 : Matrix ZZ <-- ZZ</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 (to decide which information shall be written by <span class="tt">Normaliz</span> use the options for <span class="tt">Normaliz</span>, see <a title="sets a command line option for Normaliz" href="_set__Nmz__Option.html">setNmzOption</a>). 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, which is an matrix whose rows contain the data computed, except for the suffix <span class="tt">inv</span>, for which the type is a <a title="the class of all hash tables" href="../../Macaulay2Doc/html/___Hash__Table.html">HashTable</a> (see also <a title="returns the numerical invariants computed" href="_get__Num__Invs.html">getNumInvs</a>). It can also be used with the option <a href="_grading.html">grading</a>. <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i6 : setNmzOption("allf",true);</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i7 : arc=normaliz(allComputations=>true,{(hy,"inequalities"),(eq,"equations"),(cg,"congruences")});</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i8 : arc#"gen" o8 = | 0 4 2 4 2 0 2 0 4 | | 2 0 4 4 2 0 0 4 2 | | 2 2 2 2 2 2 2 2 2 | | 2 3 4 5 3 1 2 3 4 | | 2 4 0 0 2 4 4 0 2 | | 2 5 2 3 3 3 4 1 4 | | 4 0 2 0 2 4 2 4 0 | | 4 1 4 3 3 3 2 5 2 | | 4 3 2 1 3 5 4 3 2 | 9 9 o8 : Matrix ZZ <-- ZZ</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i9 : arc#"ext" o9 = | 0 4 2 4 2 0 2 0 4 | | 2 0 4 4 2 0 0 4 2 | | 2 4 0 0 2 4 4 0 2 | | 4 0 2 0 2 4 2 4 0 | 4 9 o9 : Matrix ZZ <-- ZZ</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i10 : arc#"inv" o10 = HashTable{"class group" => (1, 4, 4) } "dim max subspace" => 0 "embedding dim" => 9 "external index" => 4 "graded" => false "hilbert basis elements" => 9 "inhomogeneous" => false "number extreme rays" => 4 "number support hyperplanes" => 4 "rank" => 3 "size triangulation" => 2 "sum dets" => 8 o10 : HashTable</code></pre> </td> </tr> </table> </div> <div> <h2>See also</h2> <ul> <li><span><a title="class of rational cones" href="___Rational__Cone.html">RationalCone</a> -- class of rational cones</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"> <h2>Ways to use this method:</h2> <ul> <li><span><a title="calls Normaliz with several input matrices" href="_normaliz_lp__List_rp.html">normaliz(List)</a> -- calls Normaliz with several input matrices</span></li> </ul> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Normaliz.m2:1320:0</span>.</p> </div> </div> </div> </body> </html>
Simpan