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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Numeric-Algebra-Dual.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">algebra-3.1: Constructive abstract 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">Numeric.Algebra.Dual</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">class</span> <a href="#t:Distinguished">Distinguished</a> t <span class="keyword">where</span><ul class="subs"><li><a href="#v:e">e</a> :: t</li></ul></li><li class="src short"><span class="keyword">class</span> <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> t => <a href="#t:Infinitesimal">Infinitesimal</a> t <span class="keyword">where</span><ul class="subs"><li><a href="#v:d">d</a> :: t</li></ul></li><li class="src short"><span class="keyword">data</span> <a href="#t:DualBasis">DualBasis</a> <ul class="subs"><li>= <a href="#v:E">E</a> </li><li>| <a href="#v:D">D</a> </li></ul></li><li class="src short"><span class="keyword">data</span> <a href="#t:Dual">Dual</a> a = <a href="#v:Dual">Dual</a> a a</li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><span class="keyword">class</span> <a name="t:Distinguished" class="def">Distinguished</a> t <span class="keyword">where</span><a href="src/Numeric-Algebra-Distinguished-Class.html#Distinguished" class="link">Source</a></p><div class="subs methods"><p class="caption">Methods</p><p class="src"><a name="v:e" class="def">e</a> :: t<a href="src/Numeric-Algebra-Distinguished-Class.html#e" class="link">Source</a></p></div><div class="subs instances"><p id="control.i:Distinguished" class="caption collapser" onclick="toggleSection('i:Distinguished')">Instances</p><div id="section.i:Distinguished" class="show"><table><tr><td class="src"><a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> <a href="Numeric-Algebra-Complex.html#t:ComplexBasis">ComplexBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> <a href="Numeric-Algebra-Quaternion.html#t:QuaternionBasis">QuaternionBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> <a href="Numeric-Coalgebra-Dual.html#t:DualBasis-39-">DualBasis'</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> <a href="Numeric-Coalgebra-Quaternion.html#t:QuaternionBasis-39-">QuaternionBasis'</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> <a href="Numeric-Coalgebra-Trigonometric.html#t:TrigBasis">TrigBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="Numeric-Algebra-Complex.html#t:Complex">Complex</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="Numeric-Algebra-Quaternion.html#t:Quaternion">Quaternion</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="Numeric-Coalgebra-Dual.html#t:Dual-39-">Dual'</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="Numeric-Coalgebra-Quaternion.html#t:Quaternion-39-">Quaternion'</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="Numeric-Coalgebra-Trigonometric.html#t:Trig">Trig</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="Numeric-Algebra-Complex.html#t:ComplexBasis">ComplexBasis</a> -> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="Numeric-Algebra-Quaternion.html#t:QuaternionBasis">QuaternionBasis</a> -> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a> -> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="Numeric-Coalgebra-Dual.html#t:DualBasis-39-">DualBasis'</a> -> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="Numeric-Coalgebra-Quaternion.html#t:QuaternionBasis-39-">QuaternionBasis'</a> -> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="Numeric-Coalgebra-Trigonometric.html#t:TrigBasis">TrigBasis</a> -> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="/usr/share/doc/libghc-representable-tries-doc/html/Data-Functor-Representable-Trie.html#t::-45--62-:">:->:</a> <a href="Numeric-Algebra-Complex.html#t:ComplexBasis">ComplexBasis</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="/usr/share/doc/libghc-representable-tries-doc/html/Data-Functor-Representable-Trie.html#t::-45--62-:">:->:</a> <a href="Numeric-Algebra-Quaternion.html#t:QuaternionBasis">QuaternionBasis</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="/usr/share/doc/libghc-representable-tries-doc/html/Data-Functor-Representable-Trie.html#t::-45--62-:">:->:</a> <a href="Numeric-Coalgebra-Quaternion.html#t:QuaternionBasis-39-">QuaternionBasis'</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="/usr/share/doc/libghc-representable-tries-doc/html/Data-Functor-Representable-Trie.html#t::-45--62-:">:->:</a> <a href="Numeric-Coalgebra-Trigonometric.html#t:TrigBasis">TrigBasis</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> a => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="Numeric-Covector.html#t:Covector">Covector</a> r a)</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">class</span> <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> t => <a name="t:Infinitesimal" class="def">Infinitesimal</a> t <span class="keyword">where</span><a href="src/Numeric-Algebra-Dual-Class.html#Infinitesimal" class="link">Source</a></p><div class="subs methods"><p class="caption">Methods</p><p class="src"><a name="v:d" class="def">d</a> :: t<a href="src/Numeric-Algebra-Dual-Class.html#d" class="link">Source</a></p></div><div class="subs instances"><p id="control.i:Infinitesimal" class="caption collapser" onclick="toggleSection('i:Infinitesimal')">Instances</p><div id="section.i:Infinitesimal" class="show"><table><tr><td class="src"><a href="Numeric-Algebra-Dual.html#t:Infinitesimal">Infinitesimal</a> <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Algebra-Dual.html#t:Infinitesimal">Infinitesimal</a> <a href="Numeric-Coalgebra-Dual.html#t:DualBasis-39-">DualBasis'</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Infinitesimal">Infinitesimal</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Infinitesimal">Infinitesimal</a> (<a href="Numeric-Coalgebra-Dual.html#t:Dual-39-">Dual'</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Infinitesimal">Infinitesimal</a> (<a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a> -> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Infinitesimal">Infinitesimal</a> (<a href="Numeric-Coalgebra-Dual.html#t:DualBasis-39-">DualBasis'</a> -> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Algebra-Dual.html#t:Infinitesimal">Infinitesimal</a> a => <a href="Numeric-Algebra-Dual.html#t:Infinitesimal">Infinitesimal</a> (<a href="Numeric-Covector.html#t:Covector">Covector</a> r a)</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:DualBasis" class="def">DualBasis</a> <a href="src/Numeric-Algebra-Dual.html#DualBasis" class="link">Source</a></p><div class="doc"><p>dual number basis, D^2 = 0. D /= 0.
</p></div><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a name="v:E" class="def">E</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a name="v:D" class="def">D</a></td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:DualBasis" class="caption collapser" onclick="toggleSection('i:DualBasis')">Instances</p><div id="section.i:DualBasis" class="show"><table><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Bounded">Bounded</a> <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Enum">Enum</a> <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Eq.html#t:Eq">Eq</a> <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Data.html#t:Data">Data</a> <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Read.html#t:Read">Read</a> <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ix.html#t:Ix">Ix</a> <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Typeable-Internal.html#t:Typeable">Typeable</a> <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-representable-tries-doc/html/Data-Functor-Representable-Trie.html#t:HasTrie">HasTrie</a> <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Algebra-Dual.html#t:Infinitesimal">Infinitesimal</a> <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-mtl-doc/html/Control-Monad-Reader-Class.html#t:MonadReader">MonadReader</a> <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rng-Class.html#t:Rng">Rng</a> k => <a href="Numeric-Algebra-Class.html#t:Coalgebra">Coalgebra</a> k <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rng-Class.html#t:Rng">Rng</a> k => <a href="Numeric-Algebra-Class.html#t:Algebra">Algebra</a> k <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rng-Class.html#t:Rng">Rng</a> k => <a href="Numeric-Algebra-Unital.html#t:Bialgebra">Bialgebra</a> k <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rng-Class.html#t:Rng">Rng</a> k => <a href="Numeric-Algebra-Unital.html#t:CounitalCoalgebra">CounitalCoalgebra</a> k <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rng-Class.html#t:Rng">Rng</a> k => <a href="Numeric-Algebra-Unital.html#t:UnitalAlgebra">UnitalAlgebra</a> k <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Numeric-Algebra-Involutive.html#t:InvolutiveSemiring">InvolutiveSemiring</a> k, <a href="Numeric-Rng-Class.html#t:Rng">Rng</a> k) => <a href="Numeric-Algebra-Hopf.html#t:HopfAlgebra">HopfAlgebra</a> k <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Numeric-Algebra-Involutive.html#t:InvolutiveSemiring">InvolutiveSemiring</a> k, <a href="Numeric-Rng-Class.html#t:Rng">Rng</a> k) => <a href="Numeric-Algebra-Involutive.html#t:InvolutiveCoalgebra">InvolutiveCoalgebra</a> k <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Numeric-Algebra-Involutive.html#t:InvolutiveSemiring">InvolutiveSemiring</a> k, <a href="Numeric-Rng-Class.html#t:Rng">Rng</a> k) => <a href="Numeric-Algebra-Involutive.html#t:InvolutiveAlgebra">InvolutiveAlgebra</a> k <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a> -> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Infinitesimal">Infinitesimal</a> (<a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a> -> r)</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:Dual" class="def">Dual</a> a <a href="src/Numeric-Algebra-Dual.html#Dual" class="link">Source</a></p><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a name="v:Dual" class="def">Dual</a> a a</td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:Dual" class="caption collapser" onclick="toggleSection('i:Dual')">Instances</p><div id="section.i:Dual" class="show"><table><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#t:Monad">Monad</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#t:Functor">Functor</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Typeable-Internal.html#t:Typeable1">Typeable1</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Applicative.html#t:Applicative">Applicative</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Foldable.html#t:Foldable">Foldable</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Traversable.html#t:Traversable">Traversable</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-distributive-doc/html/Data-Distributive.html#t:Distributive">Distributive</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Keyed">Keyed</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Zip">Zip</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:ZipWithKey">ZipWithKey</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Indexable">Indexable</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Lookup">Lookup</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Adjustable">Adjustable</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:FoldableWithKey">FoldableWithKey</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:FoldableWithKey1">FoldableWithKey1</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:TraversableWithKey">TraversableWithKey</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:TraversableWithKey1">TraversableWithKey1</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-representable-functors-doc/html/Data-Functor-Representable.html#t:Representable">Representable</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-semigroupoids-doc/html/Data-Semigroup-Traversable.html#t:Traversable1">Traversable1</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-semigroupoids-doc/html/Data-Semigroup-Foldable.html#t:Foldable1">Foldable1</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-semigroupoids-doc/html/Data-Functor-Bind.html#t:Apply">Apply</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-semigroupoids-doc/html/Data-Functor-Bind.html#t:Bind">Bind</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/libghc-mtl-doc/html/Control-Monad-Reader-Class.html#t:MonadReader">MonadReader</a> <a href="Numeric-Algebra-Dual.html#t:DualBasis">DualBasis</a> <a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Algebra-Class.html#t:RightModule">RightModule</a> r s => <a href="Numeric-Algebra-Class.html#t:RightModule">RightModule</a> r (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> s)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Algebra-Class.html#t:LeftModule">LeftModule</a> r s => <a href="Numeric-Algebra-Class.html#t:LeftModule">LeftModule</a> r (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> s)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Numeric-Algebra-Commutative.html#t:Commutative">Commutative</a> r, <a href="Numeric-Rng-Class.html#t:Rng">Rng</a> r, <a href="Numeric-Algebra-Involutive.html#t:InvolutiveSemiring">InvolutiveSemiring</a> r) => <a href="Numeric-Quadrance-Class.html#t:Quadrance">Quadrance</a> r (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Eq.html#t:Eq">Eq</a> a => <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Eq.html#t:Eq">Eq</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> a)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Data.html#t:Data">Data</a> a => <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Data.html#t:Data">Data</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> a)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Read.html#t:Read">Read</a> a => <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Read.html#t:Read">Read</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> a)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> a => <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> a)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Class.html#t:Idempotent">Idempotent</a> r => <a href="Numeric-Additive-Class.html#t:Idempotent">Idempotent</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Class.html#t:Abelian">Abelian</a> r => <a href="Numeric-Additive-Class.html#t:Abelian">Abelian</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Class.html#t:Partitionable">Partitionable</a> r => <a href="Numeric-Additive-Class.html#t:Partitionable">Partitionable</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Class.html#t:Additive">Additive</a> r => <a href="Numeric-Additive-Class.html#t:Additive">Additive</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Algebra-Class.html#t:Monoidal">Monoidal</a> r => <a href="Numeric-Algebra-Class.html#t:Monoidal">Monoidal</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Numeric-Algebra-Commutative.html#t:Commutative">Commutative</a> r, <a href="Numeric-Rng-Class.html#t:Rng">Rng</a> r) => <a href="Numeric-Algebra-Class.html#t:Semiring">Semiring</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Numeric-Algebra-Commutative.html#t:Commutative">Commutative</a> r, <a href="Numeric-Rng-Class.html#t:Rng">Rng</a> r) => <a href="Numeric-Algebra-Class.html#t:Multiplicative">Multiplicative</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Group.html#t:Group">Group</a> r => <a href="Numeric-Additive-Group.html#t:Group">Group</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Numeric-Algebra-Commutative.html#t:Commutative">Commutative</a> r, <a href="Numeric-Ring-Class.html#t:Ring">Ring</a> r) => <a href="Numeric-Algebra-Unital.html#t:Unital">Unital</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Numeric-Algebra-Commutative.html#t:Commutative">Commutative</a> r, <a href="Numeric-Algebra-Involutive.html#t:InvolutiveSemiring">InvolutiveSemiring</a> r, <a href="Numeric-Ring-Division.html#t:DivisionRing">DivisionRing</a> r) => <a href="Numeric-Algebra-Division.html#t:Division">Division</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a 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href="Numeric-Rng-Class.html#t:Rng">Rng</a> r, <a href="Numeric-Algebra-Involutive.html#t:InvolutiveSemiring">InvolutiveSemiring</a> r) => <a href="Numeric-Algebra-Involutive.html#t:InvolutiveSemiring">InvolutiveSemiring</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Numeric-Algebra-Commutative.html#t:Commutative">Commutative</a> r, <a href="Numeric-Rng-Class.html#t:Rng">Rng</a> r, <a href="Numeric-Algebra-Involutive.html#t:InvolutiveSemiring">InvolutiveSemiring</a> r) => <a href="Numeric-Algebra-Involutive.html#t:InvolutiveMultiplication">InvolutiveMultiplication</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r => <a href="Numeric-Algebra-Dual.html#t:Distinguished">Distinguished</a> (<a href="Numeric-Algebra-Dual.html#t:Dual">Dual</a> r)</td><td class="doc empty"> </td></tr><tr><td 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