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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Math-Algebras-Octonions.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.Algebras.Octonions</p></div><div id="description"><p class="caption">Description</p><div class="doc"><p>A module defining the (non-associative) algebra of octonions over an arbitrary field.</p><p>The octonions are the algebra defined by the basis {1,i0,i1,i2,i3,i4,i5,i6},
where each i_n * i_n = -1, and i_n+1 * i_n+2 = i_n+4 (where the indices are modulo 7).</p></div></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><span class="keyword">data</span> <a id="t:OBasis" class="def">OBasis</a> <a href="src/Math-Algebras-Octonions.html#OBasis" class="link">Source</a> <a href="#t:OBasis" 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></td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:OBasis" class="caption collapser" onclick="toggleSection('i:OBasis')">Instances</p><div id="section.i:OBasis" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:OBasis:Eq:1" class="instance expander" onclick="toggleSection('i:id:OBasis: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> <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a></span> <a href="src/Math-Algebras-Octonions.html#line-26" class="link">Source</a> <a href="#t:OBasis" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:OBasis: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-Algebras-Octonions.html#t:OBasis">OBasis</a> -> <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</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="#v:-61--61-" class="selflink">#</a></p><p class="src"><a href="#v:-47--61-">(/=)</a> :: <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> -> <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</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="#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:OBasis:Ord:2" class="instance expander" onclick="toggleSection('i:id:OBasis:Ord:2')"></span> <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-Algebras-Octonions.html#t:OBasis">OBasis</a></span> <a href="src/Math-Algebras-Octonions.html#line-26" class="link">Source</a> <a href="#t:OBasis" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:OBasis:Ord:2" 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-Algebras-Octonions.html#t:OBasis">OBasis</a> -> <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> -> <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-Algebras-Octonions.html#t:OBasis">OBasis</a> -> <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</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="#v:-60-" class="selflink">#</a></p><p class="src"><a href="#v:-60--61-">(<=)</a> :: <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> -> <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</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="#v:-60--61-" class="selflink">#</a></p><p class="src"><a href="#v:-62-">(>)</a> :: <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> -> <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</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="#v:-62-" class="selflink">#</a></p><p class="src"><a href="#v:-62--61-">(>=)</a> :: <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> -> <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</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="#v:-62--61-" class="selflink">#</a></p><p class="src"><a href="#v:max">max</a> :: <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> -> <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> -> <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> <a href="#v:max" class="selflink">#</a></p><p class="src"><a href="#v:min">min</a> :: <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> -> <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> -> <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> <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:OBasis:Show:3" class="instance expander" onclick="toggleSection('i:id:OBasis:Show:3')"></span> <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-Algebras-Octonions.html#t:OBasis">OBasis</a></span> <a href="src/Math-Algebras-Octonions.html#line-31" class="link">Source</a> <a href="#t:OBasis" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:OBasis:Show:3" 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-Algebras-Octonions.html#t:OBasis">OBasis</a> -> <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-Algebras-Octonions.html#t:OBasis">OBasis</a> -> <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-Algebras-Octonions.html#t:OBasis">OBasis</a>] -> <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><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:OBasis:Algebra:4" class="instance expander" onclick="toggleSection('i:id:OBasis:Algebra:4')"></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/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a></span> <a href="src/Math-Algebras-Octonions.html#line-48" class="link">Source</a> <a href="#t:OBasis" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:OBasis:Algebra:4" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:OBasis:HasConjugation:5" class="instance expander" onclick="toggleSection('i:id:OBasis:HasConjugation:5')"></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/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Quaternions.html#t:HasConjugation">HasConjugation</a> k <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a></span> <a href="src/Math-Algebras-Octonions.html#line-62" class="link">Source</a> <a href="#t:OBasis" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:OBasis:HasConjugation:5" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:conj">conj</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> <a href="src/Math-Algebras-Quaternions.html#conj" class="link">Source</a> <a href="#v:conj" class="selflink">#</a></p><p class="src"><a href="#v:sqnorm">sqnorm</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> -> k <a href="src/Math-Algebras-Quaternions.html#sqnorm" class="link">Source</a> <a href="#v:sqnorm" class="selflink">#</a></p></div></div></td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">type</span> <a id="t:Octonion" class="def">Octonion</a> k = <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> <a href="src/Math-Algebras-Octonions.html#Octonion" class="link">Source</a> <a href="#t:Octonion" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:i0" class="def">i0</a> :: <a href="Math-Algebras-Octonions.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a> <a href="src/Math-Algebras-Octonions.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-Algebras-Octonions.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a> <a href="src/Math-Algebras-Octonions.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-Algebras-Octonions.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a> <a href="src/Math-Algebras-Octonions.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-Algebras-Octonions.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a> <a href="src/Math-Algebras-Octonions.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-Algebras-Octonions.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a> <a href="src/Math-Algebras-Octonions.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-Algebras-Octonions.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a> <a href="src/Math-Algebras-Octonions.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-Algebras-Octonions.html#t:Octonion">Octonion</a> <a href="Math-Core-Field.html#t:Q">Q</a> <a href="src/Math-Algebras-Octonions.html#i6" class="link">Source</a> <a href="#v:i6" class="selflink">#</a></p></div><div class="top"><p class="src"><a id="v:i_" class="def">i_</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-Int.html#t:Int">Int</a> -> <a href="Math-Algebras-Octonions.html#t:Octonion">Octonion</a> k <a href="src/Math-Algebras-Octonions.html#i_" class="link">Source</a> <a href="#v:i_" 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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