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<!DOCTYPE html> <html lang="en"> <head> <title>isomorphism(Poset,Poset) -- computes an isomorphism between isomorphic posets</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="a package for working with partially ordered sets" href="index.html">Posets</a> :: <a title="computes an isomorphism between isomorphic posets" href="_isomorphism_lp__Poset_cm__Poset_rp.html">isomorphism(Poset,Poset)</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="_is__Ranked.html">next</a> | <a href="_is__Modular.html">previous</a> | <a href="_is__Ranked.html">forward</a> | <a href="_is__Modular.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>isomorphism(Poset,Poset) -- computes an isomorphism between isomorphic posets</h1> <ul> <li><span>Function: <a title="retrieve an isomorphism of modules" href="../../Isomorphism/html/_isomorphism.html">isomorphism</a></span></li> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">pi' = isomorphism(P, Q)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">P</span>, <span>an instance of the type <a title="a class for partially ordered sets (posets)" href="___Poset.html">Poset</a></span>, </span></li> <li><span><span class="tt">Q</span>, <span>an instance of the type <a title="a class for partially ordered sets (posets)" href="___Poset.html">Poset</a></span>, </span></li> </ul> </li> <li><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>: <ul> <li><span><a title="retrieve an isomorphism of modules" href="../../Isomorphism/html/_isomorphism.html">Homogeneous</a><span class="tt"> => </span><span class="tt">...</span>, <span>default value true</span>, <span></span></span></li> <li><span><span class="tt">Strategy</span> (missing documentation)<!--tag: [isomorphism, Strategy]--> <span class="tt"> => </span><span class="tt">...</span>, <span>default value null</span>, <span></span></span></li> <li><span><a title="retrieve an isomorphism of modules" href="../../Isomorphism/html/_isomorphism.html">Strict</a><span class="tt"> => </span><span class="tt">...</span>, <span>default value false</span>, <span></span></span></li> <li><span><a title="retrieve an isomorphism of modules" href="../../Isomorphism/html/_isomorphism.html">Tries</a><span class="tt"> => </span><span class="tt">...</span>, <span>default value null</span>, <span></span></span></li> <li><span><a title="retrieve an isomorphism of modules" href="../../Isomorphism/html/_isomorphism.html">Verbose</a><span class="tt"> => </span><span class="tt">...</span>, <span>default value false</span>, <span></span></span></li> </ul> </li> <li>Outputs: <ul> <li><span><span class="tt">pi'</span>, <span>a <a title="the class of all hash tables" href="../../Macaulay2Doc/html/___Hash__Table.html">hash table</a></span>, which specifies a partial order preserving bijection from the ground set of $P$ to the ground set of $Q$</span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>Two posets are isomorphic if there is a partial order preserving bijection between the ground sets of the posets which preserves the specified ground set partitions.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : isomorphism(divisorPoset (2*3*5), booleanLattice 3) o1 = HashTable{1 => 000 } 2 => 001 3 => 010 5 => 100 6 => 011 10 => 101 15 => 110 30 => 111 o1 : HashTable</code></pre> </td> </tr> </table> <div> <p>This method was inspired by John Stembridge's Maple package available at <a href="http://www.math.lsa.umich.edu/~jrs/maple.html#posets">http://www.math.lsa.umich.edu/~jrs/maple.html#posets</a>.</p> </div> </div> <div> <h2>See also</h2> <ul> <li><span><a title="determines if two posets are isomorphic" href="_are__Isomorphic.html">areIsomorphic</a> -- determines if two posets are isomorphic</span></li> <li><span><a title="returns a sub-list of non-isomorphic posets" href="_remove__Isomorphic__Posets.html">removeIsomorphicPosets</a> -- returns a sub-list of non-isomorphic posets</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Ways to use this method:</h2> <ul> <li><span><a title="computes an isomorphism between isomorphic posets" href="_isomorphism_lp__Poset_cm__Poset_rp.html">isomorphism(Poset,Poset)</a> -- computes an isomorphism between isomorphic posets</span></li> </ul> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Posets.m2:3195:0</span>.</p> </div> </div> </div> </body> </html>