One Hat Cyber Team
Your IP :
216.73.216.135
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
/
Polyhedra
/
html
/
View File Name :
_fan.html
<!DOCTYPE html> <html lang="en"> <head> <title>fan -- generates a Fan</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="for computations with convex polyhedra, cones, and fans" href="index.html">Polyhedra</a> :: <a title="generates a Fan" href="_fan.html">fan</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="___Fan_sp_st_sp__Fan.html">next</a> | <a href="___Fan.html">previous</a> | <a href="___Fan_sp_st_sp__Fan.html">forward</a> | <a href="___Fan.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>fan -- generates a Fan</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">F = fan C </code></dd> <dd><code class="language-macaulay2">F = fan L</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">C</span>, <span>a <a title="the class of all rational convex polyhedral cones" href="___Cone.html">convex rational cone</a></span></span></li> <li><span><span class="tt">L</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, with elements of class <a title="the class of all rational convex polyhedral cones" href="___Cone.html">Cone</a> or <a title="the class of all fans" href="___Fan.html">Fan</a></span></li> </ul> </li> <li>Outputs: <ul> <li><span><span class="tt">F</span>, <span>an instance of the type <a title="the class of all fans" href="___Fan.html">Fan</a></span></span></li> </ul> </li> </ul> <div> <h2>Description</h2> <p></p> If <span class="tt">fan</span> is applied to a <a title="the class of all rational convex polyhedral cones" href="___Cone.html">Cone</a> it generates the <a title="the class of all fans" href="___Fan.html">Fan</a> given by the Cone and all of its faces. If applied to a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">List</a> the list must only contain Cones and Fans in the same ambient space. Then it adds the Cones in the List and the generating Cones of the Fans in the List one by one to the Fan, checking each time if the new Cone is compatible with the cones that have already been added, i.e. that the intersection with each of them is a face of both Cones (intersection condition). <p></p> If one of the cones is in the wrong ambient space, there will be an error and no fan will be returned. If the intersection condition fails, there will also be an error. The pairs of incompatible cones can be accessed with the function <a title="returns the pairs of incompatible cones" href="_incomp__Cones.html">incompCones</a>. <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : C = coneFromVData matrix {{1,-1},{0,-1}} o1 = C o1 : Cone</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : F = fan C o2 = F o2 : Fan</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : C1 = coneFromVData matrix {{1,0},{0,1}};</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : C2 = coneFromVData matrix {{0,-1},{1,-1}};</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : F = fan {C,C1,C2} o5 = F o5 : Fan</code></pre> </td> </tr> </table> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">fan</span>:</h2> <ul> <li><kbd>fan(Cone)</kbd></li> <li><kbd>fan(List)</kbd></li> <li><span><kbd>fan(Matrix,List)</kbd> -- see <span><a title="Constructing a fan." href="_fan_lp__Matrix_cm__Matrix_cm__List_rp.html">fan(Matrix,Matrix,List)</a> -- Constructing a fan.</span></span></li> <li><span><a title="Constructing a fan." href="_fan_lp__Matrix_cm__Matrix_cm__List_rp.html">fan(Matrix,Matrix,List)</a> -- Constructing a fan.</span></li> <li><span><kbd>fan(Matrix,Matrix,Sequence)</kbd> -- see <span><a title="Constructing a fan." href="_fan_lp__Matrix_cm__Matrix_cm__List_rp.html">fan(Matrix,Matrix,List)</a> -- Constructing a fan.</span></span></li> <li><span><kbd>fan(Matrix,Sequence)</kbd> -- see <span><a title="Constructing a fan." href="_fan_lp__Matrix_cm__Matrix_cm__List_rp.html">fan(Matrix,Matrix,List)</a> -- Constructing a fan.</span></span></li> <li><span><a title="Take the fan over a polyhedral complex" href="_fan_lp__Polyhedral__Complex_rp.html">fan(PolyhedralComplex)</a> -- Take the fan over a polyhedral complex</span></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="generates a Fan" href="_fan.html">fan</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">Polyhedra/documentation/old_documentation.m2:594:0</span>.</p> </div> </div> </div> </body> </html>