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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Numeric-Additive-Group.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.Additive.Group</p></div><div id="table-of-contents"><p class="caption">Contents</p><ul><li><a href="#g:1">Additive Groups
</a></li></ul></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="Numeric-Algebra-Class.html#t:LeftModule">LeftModule</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integer">Integer</a> r, <a href="Numeric-Algebra-Class.html#t:RightModule">RightModule</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integer">Integer</a> r, <a href="Numeric-Algebra-Class.html#t:Monoidal">Monoidal</a> r) => <a href="#t:Group">Group</a> r <span class="keyword">where</span><ul class="subs"><li><a href="#v:-45-">(-)</a> :: r -> r -> r</li><li><a href="#v:negate">negate</a> :: r -> r</li><li><a href="#v:subtract">subtract</a> :: r -> r -> r</li><li><a href="#v:times">times</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integral">Integral</a> n => n -> r -> r</li></ul></li></ul></div><div id="interface"><h1 id="g:1">Additive Groups
</h1><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Numeric-Algebra-Class.html#t:LeftModule">LeftModule</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integer">Integer</a> r, <a href="Numeric-Algebra-Class.html#t:RightModule">RightModule</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integer">Integer</a> r, <a href="Numeric-Algebra-Class.html#t:Monoidal">Monoidal</a> r) => <a name="t:Group" class="def">Group</a> r <span class="keyword">where</span><a href="src/Numeric-Additive-Group.html#Group" class="link">Source</a></p><div class="subs methods"><p class="caption">Methods</p><p class="src"><a name="v:-45-" class="def">(-)</a> :: r -> r -> r<a href="src/Numeric-Additive-Group.html#-" class="link">Source</a></p><p class="src"><a name="v:negate" class="def">negate</a> :: r -> r<a href="src/Numeric-Additive-Group.html#negate" class="link">Source</a></p><p class="src"><a name="v:subtract" class="def">subtract</a> :: r -> r -> r<a href="src/Numeric-Additive-Group.html#subtract" class="link">Source</a></p><p class="src"><a name="v:times" class="def">times</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integral">Integral</a> n => n -> r -> r<a href="src/Numeric-Additive-Group.html#times" class="link">Source</a></p></div><div class="subs instances"><p id="control.i:Group" class="caption collapser" onclick="toggleSection('i:Group')">Instances</p><div id="section.i:Group" class="show"><table><tr><td class="src"><a href="Numeric-Additive-Group.html#t:Group">Group</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Int.html#t:Int">Int</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Group.html#t:Group">Group</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Int.html#t:Int8">Int8</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Group.html#t:Group">Group</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Int.html#t:Int16">Int16</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Group.html#t:Group">Group</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Int.html#t:Int32">Int32</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Group.html#t:Group">Group</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Int.html#t:Int64">Int64</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Group.html#t:Group">Group</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integer">Integer</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Group.html#t:Group">Group</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Word.html#t:Word">Word</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Group.html#t:Group">Group</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Word.html#t:Word8">Word8</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Group.html#t:Group">Group</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Word.html#t:Word16">Word16</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Group.html#t:Group">Group</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Word.html#t:Word32">Word32</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Group.html#t:Group">Group</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Word.html#t:Word64">Word64</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Group.html#t:Group">Group</a> ()</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Group.html#t:Group">Group</a> <a href="Numeric-Coalgebra-Geometric.html#t:Euclidean">Euclidean</a></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-Complex.html#t:Complex">Complex</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-Quaternion.html#t:Quaternion">Quaternion</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-Additive-Group.html#t:Group">Group</a> r => <a href="Numeric-Additive-Group.html#t:Group">Group</a> (<a href="Numeric-Algebra-Hyperbolic.html#t:Hyper-39-">Hyper'</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-Coalgebra-Hyperbolic.html#t:Hyper">Hyper</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-Coalgebra-Dual.html#t:Dual-39-">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-Coalgebra-Quaternion.html#t:Quaternion-39-">Quaternion'</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-Coalgebra-Trigonometric.html#t:Trig">Trig</a> r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Algebra-Division.html#t:Division">Division</a> r => <a href="Numeric-Additive-Group.html#t:Group">Group</a> (<a href="Numeric-Log.html#t:Log">Log</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-Ring-Endomorphism.html#t:End">End</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-Ring-Opposite.html#t:Opposite">Opposite</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-Group.html#t:Group">Group</a> r) => <a href="Numeric-Additive-Group.html#t:Group">Group</a> (<a href="Numeric-Ring-Rng.html#t:RngRing">RngRing</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-Rng-Zero.html#t:ZeroRng">ZeroRng</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> (e -> r)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Numeric-Additive-Group.html#t:Group">Group</a> a, <a href="Numeric-Additive-Group.html#t:Group">Group</a> b) => <a href="Numeric-Additive-Group.html#t:Group">Group</a> (a, b)</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> e, <a href="Numeric-Additive-Group.html#t:Group">Group</a> r) => <a href="Numeric-Additive-Group.html#t:Group">Group</a> (<a href="/usr/share/doc/libghc-representable-tries-doc/html/Data-Functor-Representable-Trie.html#t::-45--62-:">:->:</a> e r)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Group.html#t:Group">Group</a> s => <a href="Numeric-Additive-Group.html#t:Group">Group</a> (<a href="Numeric-Covector.html#t:Covector">Covector</a> s a)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Numeric-Additive-Group.html#t:Group">Group</a> a, <a href="Numeric-Additive-Group.html#t:Group">Group</a> b, <a href="Numeric-Additive-Group.html#t:Group">Group</a> c) => <a href="Numeric-Additive-Group.html#t:Group">Group</a> (a, b, c)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Numeric-Additive-Group.html#t:Group">Group</a> s => <a href="Numeric-Additive-Group.html#t:Group">Group</a> (<a href="Numeric-Map.html#t:Map">Map</a> s b a)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Numeric-Additive-Group.html#t:Group">Group</a> a, <a href="Numeric-Additive-Group.html#t:Group">Group</a> b, <a href="Numeric-Additive-Group.html#t:Group">Group</a> c, <a href="Numeric-Additive-Group.html#t:Group">Group</a> d) => <a href="Numeric-Additive-Group.html#t:Group">Group</a> (a, b, c, d)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Numeric-Additive-Group.html#t:Group">Group</a> a, <a href="Numeric-Additive-Group.html#t:Group">Group</a> b, <a href="Numeric-Additive-Group.html#t:Group">Group</a> c, <a href="Numeric-Additive-Group.html#t:Group">Group</a> d, <a href="Numeric-Additive-Group.html#t:Group">Group</a> e) => <a href="Numeric-Additive-Group.html#t:Group">Group</a> (a, b, c, d, e)</td><td class="doc empty"> </td></tr></table></div></div></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.13.2</p></div></body></html>
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