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<!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.Projects.ChevalleyGroup.Classical</title><link href="ocean.css" rel="stylesheet" type="text/css" title="Ocean" /><script src="haddock-util.js" type="text/javascript"></script><script src="file:///usr/share/javascript/mathjax/MathJax.js" type="text/javascript"></script><script type="text/javascript">//<![CDATA[
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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Math-Projects-ChevalleyGroup-Classical.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-0.4.8: 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><tr><th>Language</th><td>Haskell98</td></tr></table><p class="caption">Math.Projects.ChevalleyGroup.Classical</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:numPtsAG">numPtsAG</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Integral">Integral</a> b) =&gt; b -&gt; a -&gt; a</li><li class="src short"><a href="#v:numPtsPG">numPtsPG</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Integral">Integral</a> b, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Integral">Integral</a> a) =&gt; b -&gt; a -&gt; a</li><li class="src short"><a href="#v:sl">sl</a> :: <a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> k =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; [k] -&gt; [[[k]]]</li><li class="src short"><a href="#v:elemTransvection">elemTransvection</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> t, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> t1, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> t1, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Enum">Enum</a> t1) =&gt; t1 -&gt; (t1, t1) -&gt; t -&gt; [[t]]</li><li class="src short"><a href="#v:l">l</a> :: (<a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> k) =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; [k] -&gt; [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> [k]]</li><li class="src short"><a href="#v:orderL">orderL</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Integral">Integral</a> a =&gt; a -&gt; a -&gt; a</li><li class="src short"><a href="#v:sp2">sp2</a> :: <a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> k =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; [k] -&gt; [[[k]]]</li><li class="src short"><a href="#v:s2">s2</a> :: (<a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> k) =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; [k] -&gt; [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> [k]]</li><li class="src short"><a href="#v:s">s</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> k, <a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> k) =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; [k] -&gt; [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> [k]]</li><li class="src short"><a href="#v:orderS2">orderS2</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Integral">Integral</a> b, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Integral">Integral</a> a) =&gt; b -&gt; a -&gt; a</li><li class="src short"><a href="#v:orderS">orderS</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Integral">Integral</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Integral">Integral</a> b) =&gt; b -&gt; a -&gt; a</li><li class="src short"><a href="#v:omegaeven">omegaeven</a> :: <a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> a =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; t -&gt; [[[a]]]</li><li class="src short"><a href="#v:d">d</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> a, <a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> a) =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; [a] -&gt; [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> [a]]</li><li class="src short"><a href="#v:omegaodd">omegaodd</a> :: (<a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> a1, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Foldable.html#t:Foldable">Foldable</a> t) =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; t a -&gt; [[[a1]]]</li><li class="src short"><a href="#v:b">b</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> a, <a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> a) =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; [a] -&gt; [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> [a]]</li><li class="src short"><a href="#v:o">o</a> :: (<a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> a) =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; [a] -&gt; [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> [a]]</li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><a id="v:numPtsAG" class="def">numPtsAG</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Integral">Integral</a> b) =&gt; b -&gt; a -&gt; a <a href="src/Math-Projects-ChevalleyGroup-Classical.html#numPtsAG" class="link">Source</a> <a href="#v:numPtsAG" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:numPtsPG" class="def">numPtsPG</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Integral">Integral</a> b, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Integral">Integral</a> a) =&gt; b -&gt; a -&gt; a <a href="src/Math-Projects-ChevalleyGroup-Classical.html#numPtsPG" class="link">Source</a> <a href="#v:numPtsPG" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:sl" class="def">sl</a> :: <a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> k =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; [k] -&gt; [[[k]]] <a href="src/Math-Projects-ChevalleyGroup-Classical.html#sl" class="link">Source</a> <a href="#v:sl" class="selflink">#</a></p><div class="doc"><p>The special linear group SL(n,Fq), generated by elementary transvections, returned as matrices</p></div></div><div class="top"><p class="src"><a id="v:elemTransvection" class="def">elemTransvection</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> t, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> t1, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> t1, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Enum">Enum</a> t1) =&gt; t1 -&gt; (t1, t1) -&gt; t -&gt; [[t]] <a href="src/Math-Projects-ChevalleyGroup-Classical.html#elemTransvection" class="link">Source</a> <a href="#v:elemTransvection" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:l" class="def">l</a> :: (<a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> k) =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; [k] -&gt; [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> [k]] <a href="src/Math-Projects-ChevalleyGroup-Classical.html#l" class="link">Source</a> <a href="#v:l" class="selflink">#</a></p><div class="doc"><p>The projective special linear group PSL(n,Fq) == A(n,Fq) == SL(n,Fq)/Z,
 returned as permutations of the points of PG(n-1,Fq).
 This is a finite simple group provided n&gt;2 or q&gt;3.</p></div></div><div class="top"><p class="src"><a id="v:orderL" class="def">orderL</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Integral">Integral</a> a =&gt; a -&gt; a -&gt; a <a href="src/Math-Projects-ChevalleyGroup-Classical.html#orderL" class="link">Source</a> <a href="#v:orderL" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:sp2" class="def">sp2</a> :: <a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> k =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; [k] -&gt; [[[k]]] <a href="src/Math-Projects-ChevalleyGroup-Classical.html#sp2" class="link">Source</a> <a href="#v:sp2" class="selflink">#</a></p><div class="doc"><p>The symplectic group Sp(2n,Fq), returned as matrices</p></div></div><div class="top"><p class="src"><a id="v:s2" class="def">s2</a> :: (<a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> k) =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; [k] -&gt; [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> [k]] <a href="src/Math-Projects-ChevalleyGroup-Classical.html#s2" class="link">Source</a> <a href="#v:s2" class="selflink">#</a></p><div class="doc"><p>The projective symplectic group PSp(2n,Fq) == Cn(Fq) == Sp(2n,Fq)/Z,
 returned as permutations of the points of PG(2n-1,Fq).
 This is a finite simple group for n&gt;1, except for PSp(4,F2).</p></div></div><div class="top"><p class="src"><a id="v:s" class="def">s</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> k, <a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> k) =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; [k] -&gt; [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> [k]] <a href="src/Math-Projects-ChevalleyGroup-Classical.html#s" class="link">Source</a> <a href="#v:s" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:orderS2" class="def">orderS2</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Integral">Integral</a> b, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Integral">Integral</a> a) =&gt; b -&gt; a -&gt; a <a href="src/Math-Projects-ChevalleyGroup-Classical.html#orderS2" class="link">Source</a> <a href="#v:orderS2" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:orderS" class="def">orderS</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Integral">Integral</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Integral">Integral</a> b) =&gt; b -&gt; a -&gt; a <a href="src/Math-Projects-ChevalleyGroup-Classical.html#orderS" class="link">Source</a> <a href="#v:orderS" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:omegaeven" class="def">omegaeven</a> :: <a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> a =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; t -&gt; [[[a]]] <a href="src/Math-Projects-ChevalleyGroup-Classical.html#omegaeven" class="link">Source</a> <a href="#v:omegaeven" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:d" class="def">d</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> a, <a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> a) =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; [a] -&gt; [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> [a]] <a href="src/Math-Projects-ChevalleyGroup-Classical.html#d" class="link">Source</a> <a href="#v:d" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:omegaodd" class="def">omegaodd</a> :: (<a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> a1, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Foldable.html#t:Foldable">Foldable</a> t) =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; t a -&gt; [[[a1]]] <a href="src/Math-Projects-ChevalleyGroup-Classical.html#omegaodd" class="link">Source</a> <a href="#v:omegaodd" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:b" class="def">b</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> a, <a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> a) =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; [a] -&gt; [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> [a]] <a href="src/Math-Projects-ChevalleyGroup-Classical.html#b" class="link">Source</a> <a href="#v:b" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:o" class="def">o</a> :: (<a href="Math-Algebra-Field-Base.html#t:FiniteField">FiniteField</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> a) =&gt; <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -&gt; [a] -&gt; [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> [a]] <a href="src/Math-Projects-ChevalleyGroup-Classical.html#o" class="link">Source</a> <a href="#v:o" class="selflink">#</a></p></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.17.3</p></div></body></html>