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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Math-Projects-ChevalleyGroup-Exceptional.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.Exceptional</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"><span class="keyword">newtype</span> <a href="#t:Octonion">Octonion</a> k = <a href="#v:O">O</a> [(<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a>, k)]</li><li class="src short"><a href="#v:i0">i0</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a></li><li class="src short"><a href="#v:i1">i1</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a></li><li class="src short"><a href="#v:i2">i2</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a></li><li class="src short"><a href="#v:i3">i3</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a></li><li class="src short"><a href="#v:i4">i4</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a></li><li class="src short"><a href="#v:i5">i5</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a></li><li class="src short"><a href="#v:i6">i6</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a></li><li class="src short"><a href="#v:fromList">fromList</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k) => [k] -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k</li><li class="src short"><a href="#v:toList">toList</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a => <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> a -> [a]</li><li class="src short"><a href="#v:expose">expose</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> t -> [(<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a>, t)]</li><li class="src short"><a href="#v:nf">nf</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> t1, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> t, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> t1) => [(t, t1)] -> [(t, t1)]</li><li class="src short"><a href="#v:m">m</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a1, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integral">Integral</a> a) => (a, a1) -> (a, a1) -> (a, a1)</li><li class="src short"><a href="#v:conj">conj</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k => <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k</li><li class="src short"><a href="#v:sqnorm">sqnorm</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a => <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> a -> a</li><li class="src short"><a href="#v:isOrthogonal">isOrthogonal</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> a) => <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> a -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:antiCommutes">antiCommutes</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> a) => a -> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:octonions">octonions</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k) => [k] -> [<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k]</li><li class="src short"><a href="#v:isUnit">isUnit</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> a) => <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:unitImagOctonions">unitImagOctonions</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> a) => [a] -> [<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> a]</li><li class="src short"><a href="#v:autFrom">autFrom</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a) => <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> a -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> a -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> a -> [[a]]</li><li class="src short"><a href="#v:-37--94-">(%^)</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k) => <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> [[k]] -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k</li><li class="src short"><a href="#v:alpha3">alpha3</a> :: [[<a href="Math-Core-Field.html#t:F3">F3</a>]]</li><li class="src short"><a href="#v:beta3">beta3</a> :: [[<a href="Math-Core-Field.html#t:F3">F3</a>]]</li><li class="src short"><a href="#v:gamma3s">gamma3s</a> :: [<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:F3">F3</a>]</li><li class="src short"><a href="#v:gamma3">gamma3</a> :: [[<a href="Math-Core-Field.html#t:F3">F3</a>]]</li><li class="src short"><a href="#v:alpha3-39-">alpha3'</a> :: <a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:F3">F3</a>)</li><li class="src short"><a href="#v:beta3-39-">beta3'</a> :: <a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:F3">F3</a>)</li><li class="src short"><a href="#v:gamma3-39-">gamma3'</a> :: <a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:F3">F3</a>)</li><li class="src short"><a href="#v:g2_3">g2_3</a> :: [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:F3">F3</a>)]</li><li class="src short"><a href="#v:alpha4">alpha4</a> :: [[<a href="Math-Core-Field.html#t:F4">F4</a>]]</li><li class="src short"><a href="#v:beta4">beta4</a> :: [[<a href="Math-Core-Field.html#t:F4">F4</a>]]</li><li class="src short"><a href="#v:gamma4s">gamma4s</a> :: [<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:F4">F4</a>]</li><li class="src short"><a href="#v:gamma4">gamma4</a> :: [[<a href="Math-Core-Field.html#t:F4">F4</a>]]</li><li class="src short"><a href="#v:alpha4-39-">alpha4'</a> :: <a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:F4">F4</a>)</li><li class="src short"><a href="#v:beta4-39-">beta4'</a> :: <a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:F4">F4</a>)</li><li class="src short"><a href="#v:gamma4-39-">gamma4'</a> :: <a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:F4">F4</a>)</li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><span class="keyword">newtype</span> <a id="t:Octonion" class="def">Octonion</a> k <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#Octonion" class="link">Source</a> <a href="#t:Octonion" class="selflink">#</a></p><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a id="v:O" class="def">O</a> [(<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a>, k)]</td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:Octonion" class="caption collapser" onclick="toggleSection('i:Octonion')">Instances</p><div id="section.i:Octonion" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Octonion:Eq:1" class="instance expander" onclick="toggleSection('i:id:Octonion:Eq:1')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k)</span> <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#line-28" class="link">Source</a> <a href="#t:Octonion" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Octonion:Eq:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:-61--61-">(==)</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-61--61-" class="selflink">#</a></p><p class="src"><a href="#v:-47--61-">(/=)</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-47--61-" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Octonion:Fractional:2" class="instance expander" onclick="toggleSection('i:id:Octonion:Fractional:2')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Fractional">Fractional</a> k) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Fractional">Fractional</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k)</span> <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#line-96" class="link">Source</a> <a href="#t:Octonion" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Octonion:Fractional:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:-47-">(/)</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k <a href="#v:-47-" class="selflink">#</a></p><p class="src"><a href="#v:recip">recip</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k <a href="#v:recip" class="selflink">#</a></p><p class="src"><a href="#v:fromRational">fromRational</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Rational">Rational</a> -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k <a href="#v:fromRational" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Octonion:Num:3" class="instance expander" onclick="toggleSection('i:id:Octonion:Num:3')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k)</span> <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#line-65" class="link">Source</a> <a href="#t:Octonion" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Octonion:Num:3" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:-43-">(+)</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k <a href="#v:-43-" class="selflink">#</a></p><p class="src"><a href="#v:-45-">(-)</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k <a href="#v:-45-" class="selflink">#</a></p><p class="src"><a href="#v:-42-">(*)</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k <a href="#v:-42-" class="selflink">#</a></p><p class="src"><a href="#v:negate">negate</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k <a href="#v:negate" class="selflink">#</a></p><p class="src"><a href="#v:abs">abs</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k <a href="#v:abs" class="selflink">#</a></p><p class="src"><a href="#v:signum">signum</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k <a href="#v:signum" class="selflink">#</a></p><p class="src"><a href="#v:fromInteger">fromInteger</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k <a href="#v:fromInteger" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Octonion:Ord:4" class="instance expander" onclick="toggleSection('i:id:Octonion:Ord:4')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> k => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k)</span> <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#line-28" class="link">Source</a> <a href="#t:Octonion" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Octonion:Ord:4" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:compare">compare</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ordering">Ordering</a> <a href="#v:compare" class="selflink">#</a></p><p class="src"><a href="#v:-60-">(<)</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-60-" class="selflink">#</a></p><p class="src"><a href="#v:-60--61-">(<=)</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-60--61-" class="selflink">#</a></p><p class="src"><a href="#v:-62-">(>)</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-62-" class="selflink">#</a></p><p class="src"><a href="#v:-62--61-">(>=)</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-62--61-" class="selflink">#</a></p><p class="src"><a href="#v:max">max</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k <a href="#v:max" class="selflink">#</a></p><p class="src"><a href="#v:min">min</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k <a href="#v:min" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Octonion:Show:5" class="instance expander" onclick="toggleSection('i:id:Octonion:Show:5')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:Show">Show</a> k => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:Show">Show</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k)</span> <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#line-49" class="link">Source</a> <a href="#t:Octonion" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Octonion:Show:5" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:showsPrec">showsPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a> -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:ShowS">ShowS</a> <a href="#v:showsPrec" class="selflink">#</a></p><p class="src"><a href="#v:show">show</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a> <a href="#v:show" class="selflink">#</a></p><p class="src"><a href="#v:showList">showList</a> :: [<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k] -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:ShowS">ShowS</a> <a href="#v:showList" class="selflink">#</a></p></div></div></td></tr></table></div></div></div><div class="top"><p class="src"><a id="v:i0" class="def">i0</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a> <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#i0" class="link">Source</a> <a href="#v:i0" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:i1" class="def">i1</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a> <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#i1" class="link">Source</a> <a href="#v:i1" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:i2" class="def">i2</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a> <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#i2" class="link">Source</a> <a href="#v:i2" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:i3" class="def">i3</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a> <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#i3" class="link">Source</a> <a href="#v:i3" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:i4" class="def">i4</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a> <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#i4" class="link">Source</a> <a href="#v:i4" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:i5" class="def">i5</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a> <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#i5" class="link">Source</a> <a href="#v:i5" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:i6" class="def">i6</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a> <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#i6" class="link">Source</a> <a href="#v:i6" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:fromList" class="def">fromList</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k) => [k] -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#fromList" class="link">Source</a> <a href="#v:fromList" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:toList" class="def">toList</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a => <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> a -> [a] <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#toList" class="link">Source</a> <a href="#v:toList" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:expose" class="def">expose</a> :: <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> t -> [(<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a>, t)] <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#expose" class="link">Source</a> <a href="#v:expose" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:nf" class="def">nf</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> t1, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> t, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> t1) => [(t, t1)] -> [(t, t1)] <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#nf" class="link">Source</a> <a href="#v:nf" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:m" class="def">m</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a1, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integral">Integral</a> a) => (a, a1) -> (a, a1) -> (a, a1) <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#m" class="link">Source</a> <a href="#v:m" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:conj" class="def">conj</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k => <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#conj" class="link">Source</a> <a href="#v:conj" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:sqnorm" class="def">sqnorm</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a => <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> a -> a <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#sqnorm" class="link">Source</a> <a href="#v:sqnorm" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:isOrthogonal" class="def">isOrthogonal</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> a) => <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> a -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#isOrthogonal" class="link">Source</a> <a href="#v:isOrthogonal" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:antiCommutes" class="def">antiCommutes</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> a) => a -> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#antiCommutes" class="link">Source</a> <a href="#v:antiCommutes" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:octonions" class="def">octonions</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k) => [k] -> [<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k] <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#octonions" class="link">Source</a> <a href="#v:octonions" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:isUnit" class="def">isUnit</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> a) => <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#isUnit" class="link">Source</a> <a href="#v:isUnit" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:unitImagOctonions" class="def">unitImagOctonions</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> a) => [a] -> [<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> a] <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#unitImagOctonions" class="link">Source</a> <a href="#v:unitImagOctonions" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:autFrom" class="def">autFrom</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> a) => <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> a -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> a -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> a -> [[a]] <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#autFrom" class="link">Source</a> <a href="#v:autFrom" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:-37--94-" class="def">(%^)</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k) => <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k -> [[k]] -> <a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> k <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#%25%5E" class="link">Source</a> <a href="#v:-37--94-" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:alpha3" class="def">alpha3</a> :: [[<a href="Math-Core-Field.html#t:F3">F3</a>]] <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#alpha3" class="link">Source</a> <a href="#v:alpha3" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:beta3" class="def">beta3</a> :: [[<a href="Math-Core-Field.html#t:F3">F3</a>]] <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#beta3" class="link">Source</a> <a href="#v:beta3" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:gamma3s" class="def">gamma3s</a> :: [<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:F3">F3</a>] <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#gamma3s" class="link">Source</a> <a href="#v:gamma3s" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:gamma3" class="def">gamma3</a> :: [[<a href="Math-Core-Field.html#t:F3">F3</a>]] <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#gamma3" class="link">Source</a> <a href="#v:gamma3" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:alpha3-39-" class="def">alpha3'</a> :: <a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:F3">F3</a>) <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#alpha3%27" class="link">Source</a> <a href="#v:alpha3-39-" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:beta3-39-" class="def">beta3'</a> :: <a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:F3">F3</a>) <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#beta3%27" class="link">Source</a> <a href="#v:beta3-39-" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:gamma3-39-" class="def">gamma3'</a> :: <a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:F3">F3</a>) <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#gamma3%27" class="link">Source</a> <a href="#v:gamma3-39-" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:g2_3" class="def">g2_3</a> :: [<a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:F3">F3</a>)] <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#g2_3" class="link">Source</a> <a href="#v:g2_3" class="selflink">#</a></p><div class="doc"><p>Generators for G2(3), a finite simple group of order 4245696,
as a permutation group on the 702 unit imaginary octonions over F3</p></div></div><div class="top"><p class="src"><a id="v:alpha4" class="def">alpha4</a> :: [[<a href="Math-Core-Field.html#t:F4">F4</a>]] <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#alpha4" class="link">Source</a> <a href="#v:alpha4" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:beta4" class="def">beta4</a> :: [[<a href="Math-Core-Field.html#t:F4">F4</a>]] <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#beta4" class="link">Source</a> <a href="#v:beta4" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:gamma4s" class="def">gamma4s</a> :: [<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:F4">F4</a>] <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#gamma4s" class="link">Source</a> <a href="#v:gamma4s" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:gamma4" class="def">gamma4</a> :: [[<a href="Math-Core-Field.html#t:F4">F4</a>]] <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#gamma4" class="link">Source</a> <a href="#v:gamma4" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:alpha4-39-" class="def">alpha4'</a> :: <a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:F4">F4</a>) <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#alpha4%27" class="link">Source</a> <a href="#v:alpha4-39-" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:beta4-39-" class="def">beta4'</a> :: <a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:F4">F4</a>) <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#beta4%27" class="link">Source</a> <a href="#v:beta4-39-" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:gamma4-39-" class="def">gamma4'</a> :: <a href="Math-Algebra-Group-PermutationGroup.html#t:Permutation">Permutation</a> (<a href="Math-Projects-ChevalleyGroup-Exceptional.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:F4">F4</a>) <a href="src/Math-Projects-ChevalleyGroup-Exceptional.html#gamma4%27" class="link">Source</a> <a href="#v:gamma4-39-" class="selflink">#</a></p></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.17.2</p></div></body></html>
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