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<!DOCTYPE html> <html lang="en"> <head> <title>BettiCharacters : Table of Contents</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="finite group characters on free resolutions and graded modules" href="index.html">BettiCharacters</a> :: <a href="toc.html">Table of Contents</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> next | previous | forward | backward | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <h1>BettiCharacters : Table of Contents</h1> <ul> <li><span><a title="finite group characters on free resolutions and graded modules" href="index.html">BettiCharacters</a> -- finite group characters on free resolutions and graded modules</span> <ul> <li><span><a title="define finite group action" href="_action.html">action</a> -- define finite group action</span> <ul> <li><span><a title="the class of all finite group actions" href="___Action.html">Action</a> -- the class of all finite group actions</span> <ul> <li><span><a title="the class of all finite group actions on complexes" href="___Action__On__Complex.html">ActionOnComplex</a> -- the class of all finite group actions on complexes</span></li> <li><span><a title="the class of all finite group actions on graded modules" href="___Action__On__Graded__Module.html">ActionOnGradedModule</a> -- the class of all finite group actions on graded modules</span></li> <li><span><a title="format for printing, as a net" href="_net_lp__Action_rp.html">net(Action)</a> -- format for printing, as a net</span></li> <li><span><a title="get ring of object acted upon" href="_ring_lp__Action_rp.html">ring(Action)</a> -- get ring of object acted upon</span></li> <li><span><a title="get action on ring generators" href="_ring__Actors.html">ringActors</a> -- get action on ring generators</span></li> <li><span><a title="get object acted upon" href="_target_lp__Action_rp.html">target(Action)</a> -- get object acted upon</span></li> </ul> </li> <li><span><a title="define finite group action on a resolution" href="_action_lp__Complex_cm__List_cm__List_cm__Z__Z_rp.html">action(Complex,List,List,ZZ)</a> -- define finite group action on a resolution</span></li> <li><span><a title="define finite group action on a graded module" href="_action_lp__Module_cm__List_cm__List_rp.html">action(Module,List,List)</a> -- define finite group action on a graded module</span></li> <li><span><a title="format ring actors as one-row substitution matrices" href="___Sub.html">Sub</a> -- format ring actors as one-row substitution matrices</span></li> </ul> </li> <li><span><a title="group elements of an action" href="_actors.html">actors</a> -- group elements of an action</span> <ul> <li><span><a title="group elements of action on resolution" href="_actors_lp__Action__On__Complex_cm__Z__Z_rp.html">actors(ActionOnComplex,ZZ)</a> -- group elements of action on resolution</span></li> <li><span><a title="group elements acting on components of a module" href="_actors_lp__Action__On__Graded__Module_cm__List_rp.html">actors(ActionOnGradedModule,List)</a> -- group elements acting on components of a module</span></li> <li><span><a title="get inverse of action on ring generators" href="_inverse__Ring__Actors.html">inverseRingActors</a> -- get inverse of action on ring generators</span></li> <li><span><a title="number of acting elements" href="_num__Actors.html">numActors</a> -- number of acting elements</span></li> </ul> </li> <li><span><a title="compute characters of finite group action" href="_character.html">character</a> -- compute characters of finite group action</span> <ul> <li><span><a title="the class of all characters of finite group representations" href="___Character.html">Character</a> -- the class of all characters of finite group representations</span> <ul> <li><span><a title="homological shift" href="___Character_sp__Array.html">Character Array</a> -- homological shift</span></li> <li><span><a title="direct sum of characters" href="_direct__Sum_lp__Character_rp.html">directSum(Character)</a> -- direct sum of characters</span></li> <li><span><a title="dual character" href="_dual.html">dual</a> -- dual character</span></li> <li><span><a title="format for printing, as a net" href="_net_lp__Character_rp.html">net(Character)</a> -- format for printing, as a net</span></li> <li><span><a title="tensor product of characters" href="_tensor_lp__Character_cm__Character_rp.html">tensor(Character,Character)</a> -- tensor product of characters</span></li> </ul> </li> <li><span><a title="compute all Betti characters of minimal free resolution" href="_character_lp__Action__On__Complex_rp.html">character(ActionOnComplex)</a> -- compute all Betti characters of minimal free resolution</span></li> <li><span><a title="compute Betti characters of minimal free resolution" href="_character_lp__Action__On__Complex_cm__Z__Z_rp.html">character(ActionOnComplex,ZZ)</a> -- compute Betti characters of minimal free resolution</span></li> <li><span><a title="compute characters of graded components of a module" href="_character_lp__Action__On__Graded__Module_cm__List_rp.html">character(ActionOnGradedModule,List)</a> -- compute characters of graded components of a module</span></li> <li><span><a title="construct a character" href="_character_lp__Polynomial__Ring_cm__Z__Z_cm__Hash__Table_rp.html">character(PolynomialRing,ZZ,HashTable)</a> -- construct a character</span></li> <li><span><a title="recover character from decomposition" href="_character_lp__Character__Decomposition_cm__Character__Table_rp.html">character(CharacterDecomposition,CharacterTable)</a> -- recover character from decomposition</span></li> </ul> </li> <li><span><a title="shift, direct sum, dual, and tensor product" href="___Character_spoperations.html">Character operations</a> -- shift, direct sum, dual, and tensor product</span></li> <li><span><a title="construct a character table" href="_character__Table.html">characterTable</a> -- construct a character table</span> <ul> <li><span><a title="the class of all character tables of finite groups" href="___Character__Table.html">CharacterTable</a> -- the class of all character tables of finite groups</span> <ul> <li><span><a title="format for printing, as a net" href="_net_lp__Character__Table_rp.html">net(CharacterTable)</a> -- format for printing, as a net</span></li> </ul> </li> <li><span><a title="custom labels for irreducible characters" href="___Labels.html">Labels</a> -- custom labels for irreducible characters</span></li> </ul> </li> <li><span><a title="decompose a character into irreducible characters" href="_decompose__Character.html">decomposeCharacter</a> -- decompose a character into irreducible characters</span> <ul> <li><span><a title="the class of all finite group character decompositions" href="___Character__Decomposition.html">CharacterDecomposition</a> -- the class of all finite group character decompositions</span> <ul> <li><span><a title="format for printing, as a net" href="_net_lp__Character__Decomposition_rp.html">net(CharacterDecomposition)</a> -- format for printing, as a net</span></li> </ul> </li> </ul> </li> <li><span><a title="compare actions and characters" href="___Equality_spchecks.html">Equality checks</a> -- compare actions and characters</span></li> <li><span><a title="permutation action of the symmetric group" href="_symmetric__Group__Actors.html">symmetricGroupActors</a> -- permutation action of the symmetric group</span></li> <li><span><a title="character table of the symmetric group" href="_symmetric__Group__Table.html">symmetricGroupTable</a> -- character table of the symmetric group</span></li> <li><span><a title="Specht ideals / subspace arrangements" href="___Betti__Characters_sp__Example_sp1.html">BettiCharacters Example 1</a> -- Specht ideals / subspace arrangements</span></li> <li><span><a title="Symbolic powers of star configurations" href="___Betti__Characters_sp__Example_sp2.html">BettiCharacters Example 2</a> -- Symbolic powers of star configurations</span></li> <li><span><a title="Klein configuration of points" href="___Betti__Characters_sp__Example_sp3.html">BettiCharacters Example 3</a> -- Klein configuration of points</span></li> <li><span><a title="a multigraded example" href="___Betti__Characters_sp__Example_sp4.html">BettiCharacters Example 4</a> -- a multigraded example</span></li> </ul> </li> </ul> </body> </html>