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<!DOCTYPE html> <html lang="en"> <head> <title>Topcom -- interface to selected functions from topcom package</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="interface to selected functions from topcom package" href="index.html">Topcom</a> :: <a title="interface to selected functions from topcom package" href="index.html">Topcom</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="___An_spexample_spuse_spof_sp__Top__Com.html">next</a> | previous | <a href="___An_spexample_spuse_spof_sp__Top__Com.html">forward</a> | backward | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>Topcom -- interface to selected functions from topcom package</h1> <div> <h2>Description</h2> <div> <p><a href="https://www.wm.uni-bayreuth.de/de/team/rambau_joerg/TOPCOM/index.html">Topcom</a> is mathematical software written by Jorg Rambau for computing and manipulating triangulations of polytopes and chirotopes.</p> <p>This Macaulay2 package provides an interface for some of the functionality of this software.</p> <p>The package is meant as an internal package, to be called by packages such as <a title="for computations with convex polyhedra, cones, and fans" href="../../Polyhedra/html/index.html">Polyhedra</a>. It is highly recommended to use those packages, rather than calling this package directly.</p> </div> <div> <h2>Example use of Topcom</h2> </div> <div> <ul> <li><span><a title="interface to selected functions from topcom package" href="___An_spexample_spuse_spof_sp__Top__Com.html">An example use of TopCom</a> -- interface to selected functions from topcom package</span></li> </ul> </div> <div> <h2>Generating triangulations</h2> </div> <div> <ul> <li><span><a title="generate all triangulations of a point or vector configuration" href="_topcom__All__Triangulations_lp__Matrix_rp.html">topcomAllTriangulations(Matrix)</a> -- generate all triangulations of a point or vector configuration</span></li> <li><span><a title="the number of triangulations of a point or vector configuration" href="_topcom__Num__Triangulations_lp__Matrix_rp.html">topcomNumTriangulations(Matrix)</a> -- the number of triangulations of a point or vector configuration</span></li> </ul> </div> <div> <h2>Useful functions involving specific triangulations</h2> </div> <div> <ul> <li><span><a title="compute a regular triangulation using all of the given points" href="_topcom__Regular__Fine__Triangulation_lp__Matrix_rp.html">topcomRegularFineTriangulation(Matrix)</a> -- compute a regular triangulation using all of the given points</span></li> <li><span><a title="determine if a set of subsets is a triangulation of a point set" href="_topcom__Is__Triangulation_lp__Matrix_cm__List_rp.html">topcomIsTriangulation(Matrix,List)</a> -- determine if a set of subsets is a triangulation of a point set</span></li> <li><span><a title="determine if a given triangulation is a regular triangulation" href="_topcom__Is__Regular__Triangulation.html">topcomIsRegularTriangulation(Matrix,List)</a> -- determine if a given triangulation is a regular triangulation</span></li> <li><span><a title="find a list of heights of a regular triangulation" href="_topcom__Regular__Triangulation__Weights_lp__Matrix_cm__List_rp.html">topcomRegularTriangulationWeights(Matrix,List)</a> -- find a list of heights of a regular triangulation</span></li> </ul> </div> <div> <h2>Useful functions involving bistellar flips</h2> </div> <div> <ul> <li><span><a title="find the neighboring triangulations (bistellar flips) of a triangulation" href="_topcom__Flips_lp__Matrix_cm__List_rp.html">topcomFlips(Matrix,List)</a> -- find the neighboring triangulations (bistellar flips) of a triangulation</span></li> <li><span><a title="find the number of neighboring triangulations (bistellar flips) of a triangulation" href="_topcom__Num__Flips_lp__Matrix_cm__List_rp.html">topcomNumFlips(Matrix,List)</a> -- find the number of neighboring triangulations (bistellar flips) of a triangulation</span></li> </ul> </div> <div> <h2>Chirotope functions</h2> </div> <div> <p>The <i>chirotope</i> of a point set (or vector set), consisting of the columns of the $d \times n$ matrix $A$, is the function which assigns to each $d+1 \times d+1$ minor of $\overline{A}$ the sign of its determinant. Topcom encodes this into a string. See <a title="compute the chirotope string of a point or vector configuration" href="_chirotope__String_lp__Matrix_rp.html">chirotopeString</a> for details about the output of this function.</p> </div> <div> <ul> <li><span><a title="compute the chirotope string of a point or vector configuration" href="_chirotope__String_lp__Matrix_rp.html">chirotopeString(Matrix)</a> -- compute the chirotope string of a point or vector configuration</span></li> <li><span><a title="compute the chirotope string of a point or vector configuration" href="_naive__Chirotope__String_lp__Matrix_rp.html">naiveChirotopeString(Matrix)</a> -- compute the chirotope string of a point or vector configuration</span></li> <li><span><a title="compute the oriented circuits of an oriented matroid or point or vector configuration" href="_oriented__Circuits.html">orientedCircuits(String)</a> -- compute the oriented circuits of an oriented matroid or point or vector configuration</span></li> <li><span><a title="compute the oriented cocircuits of an oriented matroid" href="_oriented__Cocircuits.html">orientedCocircuits(String)</a> -- compute the oriented cocircuits of an oriented matroid</span></li> </ul> </div> </div> <div> <h2>See also</h2> <ul> <li><span><a title="for computations with convex polyhedra, cones, and fans" href="../../Polyhedra/html/index.html">Polyhedra</a> -- for computations with convex polyhedra, cones, and fans</span></li> <li><span><a title="generating and manipulating triangulations of point or vector configurations" href="../../Triangulations/html/index.html">Triangulations</a> -- generating and manipulating triangulations of point or vector configurations</span></li> <li><span><a title="simple access to Kreuzer-Skarke database of reflexive polytopes of dimensions 3 and 4" href="../../ReflexivePolytopesDB/html/index.html">ReflexivePolytopesDB</a> -- simple access to Kreuzer-Skarke database of reflexive polytopes of dimensions 3 and 4</span></li> </ul> </div> <div> <div> <div> <h2>Author</h2> <ul> <li><a href="http://www.math.cornell.edu/~mike">Mike Stillman</a><span> <<a href="mailto:mike%40math.cornell.edu">mike@math.cornell.edu</a>></span></li> </ul> </div> <div> <h2>Version</h2> <p>This documentation describes version <b>0.95</b> of Topcom, released <b>13 Nov 2022</b>.</p> </div> <div> <h2>Citation</h2> <p>If you have used this package in your research, please cite it as follows:</p> <table class="examples"> <tr> <td> <pre><code class="language-bib">@misc{TopcomSource, title = {{Topcom: A \emph{Macaulay2} package. Version~0.95}}, author = {Mike Stillman}, howpublished = {A \emph{Macaulay2} package available at \url{https://github.com/Macaulay2/M2/tree/stable/M2/Macaulay2/packages}} } </code></pre> </td> </tr> </table> </div> <div> <h2>Exports</h2> <div class="exports"> <ul> <li>Functions and commands <ul> <li><span><kbd>chirotopeString</kbd> -- see <span><a title="compute the chirotope string of a point or vector configuration" href="_chirotope__String_lp__Matrix_rp.html">chirotopeString(Matrix)</a> -- compute the chirotope string of a point or vector configuration</span></span></li> <li><span><kbd>naiveChirotopeString</kbd> -- see <span><a title="compute the chirotope string of a point or vector configuration" href="_naive__Chirotope__String_lp__Matrix_rp.html">naiveChirotopeString(Matrix)</a> -- compute the chirotope string of a point or vector configuration</span></span></li> <li><span><a title="compute the oriented circuits of an oriented matroid or point or vector configuration" href="_oriented__Circuits.html">orientedCircuits</a> -- compute the oriented circuits of an oriented matroid or point or vector configuration</span></li> <li><span><a title="compute the oriented cocircuits of an oriented matroid" href="_oriented__Cocircuits.html">orientedCocircuits</a> -- compute the oriented cocircuits of an oriented matroid</span></li> <li><span><kbd>topcomAllTriangulations</kbd> -- see <span><a title="generate all triangulations of a point or vector configuration" href="_topcom__All__Triangulations_lp__Matrix_rp.html">topcomAllTriangulations(Matrix)</a> -- generate all triangulations of a point or vector configuration</span></span></li> <li><span><kbd>topcomFlips</kbd> -- see <span><a title="find the neighboring triangulations (bistellar flips) of a triangulation" href="_topcom__Flips_lp__Matrix_cm__List_rp.html">topcomFlips(Matrix,List)</a> -- find the neighboring triangulations (bistellar flips) of a triangulation</span></span></li> <li><span><a title="determine if a given triangulation is a regular triangulation" href="_topcom__Is__Regular__Triangulation.html">topcomIsRegularTriangulation</a> -- determine if a given triangulation is a regular triangulation</span></li> <li><span><kbd>topcomIsTriangulation</kbd> -- see <span><a title="determine if a set of subsets is a triangulation of a point set" href="_topcom__Is__Triangulation_lp__Matrix_cm__List_rp.html">topcomIsTriangulation(Matrix,List)</a> -- determine if a set of subsets is a triangulation of a point set</span></span></li> <li><span><kbd>topcomNumFlips</kbd> -- see <span><a title="find the number of neighboring triangulations (bistellar flips) of a triangulation" href="_topcom__Num__Flips_lp__Matrix_cm__List_rp.html">topcomNumFlips(Matrix,List)</a> -- find the number of neighboring triangulations (bistellar flips) of a triangulation</span></span></li> <li><span><kbd>topcomNumTriangulations</kbd> -- see <span><a title="the number of triangulations of a point or vector configuration" href="_topcom__Num__Triangulations_lp__Matrix_rp.html">topcomNumTriangulations(Matrix)</a> -- the number of triangulations of a point or vector configuration</span></span></li> <li><span><kbd>topcomRegularFineTriangulation</kbd> -- see <span><a title="compute a regular triangulation using all of the given points" href="_topcom__Regular__Fine__Triangulation_lp__Matrix_rp.html">topcomRegularFineTriangulation(Matrix)</a> -- compute a regular triangulation using all of the given points</span></span></li> <li><span><kbd>topcomRegularTriangulationWeights</kbd> -- see <span><a title="find a list of heights of a regular triangulation" href="_topcom__Regular__Triangulation__Weights_lp__Matrix_cm__List_rp.html">topcomRegularTriangulationWeights(Matrix,List)</a> -- find a list of heights of a regular triangulation</span></span></li> </ul> </li> <li>Methods <ul> <li><span><a title="compute the chirotope string of a point or vector configuration" href="_chirotope__String_lp__Matrix_rp.html">chirotopeString(Matrix)</a> -- compute the chirotope string of a point or vector configuration</span></li> <li><span><a title="compute the chirotope string of a point or vector configuration" href="_naive__Chirotope__String_lp__Matrix_rp.html">naiveChirotopeString(Matrix)</a> -- compute the chirotope string of a point or vector configuration</span></li> <li><span><kbd>orientedCircuits(Matrix)</kbd> -- see <span><a title="compute the oriented circuits of an oriented matroid or point or vector configuration" href="_oriented__Circuits.html">orientedCircuits</a> -- compute the oriented circuits of an oriented matroid or point or vector configuration</span></span></li> <li><span><kbd>orientedCircuits(String)</kbd> -- see <span><a title="compute the oriented circuits of an oriented matroid or point or vector configuration" href="_oriented__Circuits.html">orientedCircuits</a> -- compute the oriented circuits of an oriented matroid or point or vector configuration</span></span></li> <li><span><kbd>orientedCocircuits(Matrix)</kbd> -- see <span><a title="compute the oriented cocircuits of an oriented matroid" href="_oriented__Cocircuits.html">orientedCocircuits</a> -- compute the oriented cocircuits of an oriented matroid</span></span></li> <li><span><kbd>orientedCocircuits(String)</kbd> -- see <span><a title="compute the oriented cocircuits of an oriented matroid" href="_oriented__Cocircuits.html">orientedCocircuits</a> -- compute the oriented cocircuits of an oriented matroid</span></span></li> <li><span><a title="generate all triangulations of a point or vector configuration" href="_topcom__All__Triangulations_lp__Matrix_rp.html">topcomAllTriangulations(Matrix)</a> -- generate all triangulations of a point or vector configuration</span></li> <li><span><a title="find the neighboring triangulations (bistellar flips) of a triangulation" href="_topcom__Flips_lp__Matrix_cm__List_rp.html">topcomFlips(Matrix,List)</a> -- find the neighboring triangulations (bistellar flips) of a triangulation</span></li> <li><span><kbd>topcomIsRegularTriangulation(Matrix,List)</kbd> -- see <span><a title="determine if a given triangulation is a regular triangulation" href="_topcom__Is__Regular__Triangulation.html">topcomIsRegularTriangulation</a> -- determine if a given triangulation is a regular triangulation</span></span></li> <li><span><a title="determine if a set of subsets is a triangulation of a point set" href="_topcom__Is__Triangulation_lp__Matrix_cm__List_rp.html">topcomIsTriangulation(Matrix,List)</a> -- determine if a set of subsets is a triangulation of a point set</span></li> <li><span><a title="find the number of neighboring triangulations (bistellar flips) of a triangulation" href="_topcom__Num__Flips_lp__Matrix_cm__List_rp.html">topcomNumFlips(Matrix,List)</a> -- find the number of neighboring triangulations (bistellar flips) of a triangulation</span></li> <li><span><a title="the number of triangulations of a point or vector configuration" href="_topcom__Num__Triangulations_lp__Matrix_rp.html">topcomNumTriangulations(Matrix)</a> -- the number of triangulations of a point or vector configuration</span></li> <li><span><a title="compute a regular triangulation using all of the given points" href="_topcom__Regular__Fine__Triangulation_lp__Matrix_rp.html">topcomRegularFineTriangulation(Matrix)</a> -- compute a regular triangulation using all of the given points</span></li> <li><span><a title="find a list of heights of a regular triangulation" href="_topcom__Regular__Triangulation__Weights_lp__Matrix_cm__List_rp.html">topcomRegularTriangulationWeights(Matrix,List)</a> -- find a list of heights of a regular triangulation</span></li> </ul> </li> <li>Symbols <ul> <li><span><a title="an optional argument used in some functions in the Topcom interface package" href="___Connected__To__Regular.html">ConnectedToRegular</a> -- an optional argument used in some functions in the Topcom interface package</span></li> <li><span><a title="an optional argument used in some functions in the Topcom interface package" href="___Fine.html">Fine</a> -- an optional argument used in some functions in the Topcom interface package</span></li> <li><span><a title="an optional argument to most functions in Topcom to indicate whether to homogenize the matrix" href="___Homogenize.html">Homogenize</a> -- an optional argument to most functions in Topcom to indicate whether to homogenize the matrix</span></li> <li><span><a title="an optional argument used in some functions in the Topcom interface package" href="___Regular__Only.html">RegularOnly</a> -- an optional argument used in some functions in the Topcom interface package</span></li> </ul> </li> </ul> </div> </div> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="interface to selected functions from topcom package" href="index.html">Topcom</a> is <span>a <a title="the class of all packages" href="../../Macaulay2Doc/html/___Package.html">package</a></span>, defined in <span class="tt">Topcom.m2</span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Topcom.m2:393:0</span>.</p> </div> </div> </div> </body> </html>
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