/usr/share/doc/libghc-maths-doc/html/Math-Algebra-Group-SchreierSims.html is in libghc-maths-doc 0.4.5-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 | <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Math.Algebra.Group.SchreierSims</title><link href="ocean.css" rel="stylesheet" type="text/css" title="Ocean" /><script src="haddock-util.js" type="text/javascript"></script><script type="text/javascript">//<![CDATA[
window.onload = function () {pageLoad();setSynopsis("mini_Math-Algebra-Group-SchreierSims.html");};
//]]>
</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Math-Algebra-Group-SchreierSims.html">Source</a></li><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul><p class="caption">HaskellForMaths-0.4.5: Combinatorics, group theory, commutative algebra, non-commutative algebra</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Safe Haskell</th><td>None</td></tr></table><p class="caption">Math.Algebra.Group.SchreierSims</p></div><div id="synopsis"><p id="control.syn" class="caption expander" onclick="toggleSection('syn')">Synopsis</p><ul id="section.syn" class="hide" onclick="toggleSection('syn')"><li class="src short"><a href="#v:cosetRepsGx">cosetRepsGx</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> k) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k] -> k -> <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> k (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k)</li><li class="src short"><a href="#v:schreierGeneratorsGx">schreierGeneratorsGx</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> k) => (k, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> k (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k)) -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k]</li><li class="src short"><a href="#v:sift">sift</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> k) => [(k, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> k (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k))] -> <a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k)</li><li class="src short"><a href="#v:findBase">findBase</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> a] -> a</li><li class="src short"><a href="#v:sgs">sgs</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> a) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> a] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> a]</li><li class="src short"><a href="#v:bsgs">bsgs</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [(t, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> t (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t))]</li><li class="src short"><a href="#v:bsgs-39-">bsgs'</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [(t, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> t (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t))]</li><li class="src short"><a href="#v:newLevel">newLevel</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> ([t], ((t, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> t (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t)), [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t]))</li><li class="src short"><a href="#v:newLevel-39-">newLevel'</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => t -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> ((t, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> t (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t)), [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t])</li><li class="src short"><a href="#v:ss">ss</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [((t, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> t (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t)), [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t])]</li><li class="src short"><a href="#v:ss-39-">ss'</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [t] -> [((t, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> t (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t)), [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t])] -> [((t, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> t (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t)), [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t])] -> [((t, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> t (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t)), [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t])]</li><li class="src short"><a href="#v:isMemberBSGS">isMemberBSGS</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> k) => [(k, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> k (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k))] -> <a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:eltsBSGS">eltsBSGS</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Num">Num</a> b => [(a, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> k b)] -> [b]</li><li class="src short"><a href="#v:cartProd">cartProd</a> :: [[a]] -> [[a]]</li><li class="src short"><a href="#v:orderBSGS">orderBSGS</a> :: [(a1, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> k a)] -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integer">Integer</a></li><li class="src short"><a href="#v:isMember">isMember</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> <a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:elts">elts</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t]</li><li class="src short"><a href="#v:order">order</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integer">Integer</a></li><li class="src short"><a href="#v:isSubgp">isSubgp</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> k) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k] -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:isNormal">isNormal</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> k) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k] -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:index">index</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t1, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t1) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t1] -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integer">Integer</a></li><li class="src short"><a href="#v:reduceGens">reduceGens</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t]</li><li class="src short"><a href="#v:reduceGensBSGS">reduceGensBSGS</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> ([<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t], [(t, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> t (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t))])</li><li class="src short"><a href="#v:normalClosure">normalClosure</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t]</li><li class="src short"><a href="#v:commutatorGp">commutatorGp</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t]</li><li class="src short"><a href="#v:derivedSubgp">derivedSubgp</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t]</li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><a name="v:cosetRepsGx" class="def">cosetRepsGx</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> k) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k] -> k -> <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> k (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k)<a href="src/Math-Algebra-Group-SchreierSims.html#cosetRepsGx" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:schreierGeneratorsGx" class="def">schreierGeneratorsGx</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> k) => (k, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> k (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k)) -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k]<a href="src/Math-Algebra-Group-SchreierSims.html#schreierGeneratorsGx" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:sift" class="def">sift</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> k) => [(k, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> k (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k))] -> <a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k)<a href="src/Math-Algebra-Group-SchreierSims.html#sift" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:findBase" class="def">findBase</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> a] -> a<a href="src/Math-Algebra-Group-SchreierSims.html#findBase" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:sgs" class="def">sgs</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> a, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> a) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> a] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> a]<a href="src/Math-Algebra-Group-SchreierSims.html#sgs" class="link">Source</a></p><div class="doc"><p>Given generators for a permutation group, return a strong generating set.
The result is calculated using Schreier-Sims algorithm, and is relative to the base implied by the Ord instance
</p></div></div><div class="top"><p class="src"><a name="v:bsgs" class="def">bsgs</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [(t, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> t (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t))]<a href="src/Math-Algebra-Group-SchreierSims.html#bsgs" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:bsgs-39-" class="def">bsgs'</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [(t, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> t (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t))]<a href="src/Math-Algebra-Group-SchreierSims.html#bsgs%27" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:newLevel" class="def">newLevel</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> ([t], ((t, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> t (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t)), [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t]))<a href="src/Math-Algebra-Group-SchreierSims.html#newLevel" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:newLevel-39-" class="def">newLevel'</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => t -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> ((t, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> t (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t)), [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t])<a href="src/Math-Algebra-Group-SchreierSims.html#newLevel%27" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:ss" class="def">ss</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [((t, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> t (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t)), [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t])]<a href="src/Math-Algebra-Group-SchreierSims.html#ss" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:ss-39-" class="def">ss'</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [t] -> [((t, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> t (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t)), [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t])] -> [((t, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> t (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t)), [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t])] -> [((t, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> t (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t)), [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t])]<a href="src/Math-Algebra-Group-SchreierSims.html#ss%27" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:isMemberBSGS" class="def">isMemberBSGS</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> k) => [(k, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> k (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k))] -> <a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Math-Algebra-Group-SchreierSims.html#isMemberBSGS" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:eltsBSGS" class="def">eltsBSGS</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Num">Num</a> b => [(a, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> k b)] -> [b]<a href="src/Math-Algebra-Group-SchreierSims.html#eltsBSGS" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:cartProd" class="def">cartProd</a> :: [[a]] -> [[a]]<a href="src/Math-Algebra-Group-SchreierSims.html#cartProd" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:orderBSGS" class="def">orderBSGS</a> :: [(a1, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> k a)] -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integer">Integer</a><a href="src/Math-Algebra-Group-SchreierSims.html#orderBSGS" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:isMember" class="def">isMember</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> <a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Math-Algebra-Group-SchreierSims.html#isMember" class="link">Source</a></p><div class="doc"><p>Given generators for a group, determine whether a permutation is a member of the group, using Schreier-Sims algorithm
</p></div></div><div class="top"><p class="src"><a name="v:elts" class="def">elts</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t]<a href="src/Math-Algebra-Group-SchreierSims.html#elts" class="link">Source</a></p><div class="doc"><p>Given generators for a group, return a (sorted) list of all elements of the group, using Schreier-Sims algorithm
</p></div></div><div class="top"><p class="src"><a name="v:order" class="def">order</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integer">Integer</a><a href="src/Math-Algebra-Group-SchreierSims.html#order" class="link">Source</a></p><div class="doc"><p>Given generators for a group, return the order of the group (the number of elements), using Schreier-Sims algorithm
</p></div></div><div class="top"><p class="src"><a name="v:isSubgp" class="def">isSubgp</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> k) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k] -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Math-Algebra-Group-SchreierSims.html#isSubgp" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:isNormal" class="def">isNormal</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> k) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> k] -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Bool.html#t:Bool">Bool</a><a href="src/Math-Algebra-Group-SchreierSims.html#isNormal" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:index" class="def">index</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t1, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t1) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t1] -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integer">Integer</a><a href="src/Math-Algebra-Group-SchreierSims.html#index" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:reduceGens" class="def">reduceGens</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t]<a href="src/Math-Algebra-Group-SchreierSims.html#reduceGens" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:reduceGensBSGS" class="def">reduceGensBSGS</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> ([<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t], [(t, <a href="/usr/share/doc/ghc-doc/html/libraries/containers-0.5.0.0/Data-Map-Lazy.html#t:Map">Map</a> t (<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t))])<a href="src/Math-Algebra-Group-SchreierSims.html#reduceGensBSGS" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:normalClosure" class="def">normalClosure</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t]<a href="src/Math-Algebra-Group-SchreierSims.html#normalClosure" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:commutatorGp" class="def">commutatorGp</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t]<a href="src/Math-Algebra-Group-SchreierSims.html#commutatorGp" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:derivedSubgp" class="def">derivedSubgp</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> t, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> t) => [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t] -> [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> t]<a href="src/Math-Algebra-Group-SchreierSims.html#derivedSubgp" class="link">Source</a></p></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.13.2</p></div></body></html>
|