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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>Numeric.Module.Representable</title><link href="ocean.css" rel="stylesheet" type="text/css" title="Ocean" /><script src="haddock-util.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/Numeric-Module-Representable.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.Module.Representable</p></div><div id="table-of-contents"><p class="caption">Contents</p><ul><li><a href="#g:1">Representable Additive
</a></li><li><a href="#g:2">Representable Monoidal
</a></li><li><a href="#g:3">Representable Group
</a></li><li><a href="#g:4">Representable Multiplicative (via Algebra)
</a></li><li><a href="#g:5">Representable Unital (via UnitalAlgebra)
</a></li><li><a href="#g:6">Representable Rig (via Algebra)
</a></li><li><a href="#g:7">Representable Ring (via Algebra)
</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"><a href="#v:addRep">addRep</a> :: (<a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Zip">Zip</a> m, <a href="Numeric-Additive-Class.html#t:Additive">Additive</a> r) =&gt; m r -&gt; m r -&gt; m r</li><li class="src short"><a href="#v:sinnum1pRep">sinnum1pRep</a> :: (<a href="Numeric-Algebra.html#t:Whole">Whole</a> n, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#t:Functor">Functor</a> m, <a href="Numeric-Additive-Class.html#t:Additive">Additive</a> r) =&gt; n -&gt; m r -&gt; m r</li><li class="src short"><a href="#v:zeroRep">zeroRep</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Applicative.html#t:Applicative">Applicative</a> m, <a href="Numeric-Algebra-Class.html#t:Monoidal">Monoidal</a> r) =&gt; m r</li><li class="src short"><a href="#v:sinnumRep">sinnumRep</a> :: (<a href="Numeric-Algebra.html#t:Whole">Whole</a> n, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#t:Functor">Functor</a> m, <a href="Numeric-Algebra-Class.html#t:Monoidal">Monoidal</a> r) =&gt; n -&gt; m r -&gt; m r</li><li class="src short"><a href="#v:negateRep">negateRep</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#t:Functor">Functor</a> m, <a href="Numeric-Additive-Group.html#t:Group">Group</a> r) =&gt; m r -&gt; m r</li><li class="src short"><a href="#v:minusRep">minusRep</a> :: (<a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Zip">Zip</a> m, <a href="Numeric-Additive-Group.html#t:Group">Group</a> r) =&gt; m r -&gt; m r -&gt; m r</li><li class="src short"><a href="#v:subtractRep">subtractRep</a> :: (<a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Zip">Zip</a> m, <a href="Numeric-Additive-Group.html#t:Group">Group</a> r) =&gt; m r -&gt; m r -&gt; m r</li><li class="src short"><a href="#v:timesRep">timesRep</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integral">Integral</a> n, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#t:Functor">Functor</a> m, <a href="Numeric-Additive-Group.html#t:Group">Group</a> r) =&gt; n -&gt; m r -&gt; m r</li><li class="src short"><a href="#v:mulRep">mulRep</a> :: (<a href="/usr/share/doc/libghc-representable-functors-doc/html/Data-Functor-Representable.html#t:Representable">Representable</a> m, <a href="Numeric-Algebra-Class.html#t:Algebra">Algebra</a> r (<a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Key">Key</a> m)) =&gt; m r -&gt; m r -&gt; m r</li><li class="src short"><a href="#v:oneRep">oneRep</a> :: (<a href="/usr/share/doc/libghc-representable-functors-doc/html/Data-Functor-Representable.html#t:Representable">Representable</a> m, <a href="Numeric-Algebra-Unital.html#t:Unital">Unital</a> r, <a href="Numeric-Algebra-Unital.html#t:UnitalAlgebra">UnitalAlgebra</a> r (<a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Key">Key</a> m)) =&gt; m r</li><li class="src short"><a href="#v:fromNaturalRep">fromNaturalRep</a> :: (<a href="Numeric-Algebra-Unital.html#t:UnitalAlgebra">UnitalAlgebra</a> r (<a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Key">Key</a> m), <a href="/usr/share/doc/libghc-representable-functors-doc/html/Data-Functor-Representable.html#t:Representable">Representable</a> m, <a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r) =&gt; <a href="Numeric-Algebra.html#t:Natural">Natural</a> -&gt; m r</li><li class="src short"><a href="#v:fromIntegerRep">fromIntegerRep</a> :: (<a href="Numeric-Algebra-Unital.html#t:UnitalAlgebra">UnitalAlgebra</a> r (<a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Key">Key</a> m), <a href="/usr/share/doc/libghc-representable-functors-doc/html/Data-Functor-Representable.html#t:Representable">Representable</a> m, <a href="Numeric-Ring-Class.html#t:Ring">Ring</a> r) =&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integer">Integer</a> -&gt; m r</li></ul></div><div id="interface"><h1 id="g:1">Representable Additive
</h1><div class="top"><p class="src"><a name="v:addRep" class="def">addRep</a> :: (<a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Zip">Zip</a> m, <a href="Numeric-Additive-Class.html#t:Additive">Additive</a> r) =&gt; m r -&gt; m r -&gt; m r<a href="src/Numeric-Module-Representable.html#addRep" class="link">Source</a></p><div class="doc"><p>`Additive.(+)` default definition
</p></div></div><div class="top"><p class="src"><a name="v:sinnum1pRep" class="def">sinnum1pRep</a> :: (<a href="Numeric-Algebra.html#t:Whole">Whole</a> n, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#t:Functor">Functor</a> m, <a href="Numeric-Additive-Class.html#t:Additive">Additive</a> r) =&gt; n -&gt; m r -&gt; m r<a href="src/Numeric-Module-Representable.html#sinnum1pRep" class="link">Source</a></p><div class="doc"><p><code><a href="Additive.html#t:sinnum1p">sinnum1p</a></code> default definition
</p></div></div><h1 id="g:2">Representable Monoidal
</h1><div class="top"><p class="src"><a name="v:zeroRep" class="def">zeroRep</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Applicative.html#t:Applicative">Applicative</a> m, <a href="Numeric-Algebra-Class.html#t:Monoidal">Monoidal</a> r) =&gt; m r<a href="src/Numeric-Module-Representable.html#zeroRep" class="link">Source</a></p><div class="doc"><p><code><a href="Monoidal.html#t:zero">zero</a></code> default definition
</p></div></div><div class="top"><p class="src"><a name="v:sinnumRep" class="def">sinnumRep</a> :: (<a href="Numeric-Algebra.html#t:Whole">Whole</a> n, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#t:Functor">Functor</a> m, <a href="Numeric-Algebra-Class.html#t:Monoidal">Monoidal</a> r) =&gt; n -&gt; m r -&gt; m r<a href="src/Numeric-Module-Representable.html#sinnumRep" class="link">Source</a></p><div class="doc"><p><code><a href="Monoidal.html#t:sinnum">sinnum</a></code> default definition
</p></div></div><h1 id="g:3">Representable Group
</h1><div class="top"><p class="src"><a name="v:negateRep" class="def">negateRep</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#t:Functor">Functor</a> m, <a href="Numeric-Additive-Group.html#t:Group">Group</a> r) =&gt; m r -&gt; m r<a href="src/Numeric-Module-Representable.html#negateRep" class="link">Source</a></p><div class="doc"><p><code><a href="Group.html#t:negate">negate</a></code> default definition
</p></div></div><div class="top"><p class="src"><a name="v:minusRep" class="def">minusRep</a> :: (<a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Zip">Zip</a> m, <a href="Numeric-Additive-Group.html#t:Group">Group</a> r) =&gt; m r -&gt; m r -&gt; m r<a href="src/Numeric-Module-Representable.html#minusRep" class="link">Source</a></p><div class="doc"><p>`Group.(-)` default definition
</p></div></div><div class="top"><p class="src"><a name="v:subtractRep" class="def">subtractRep</a> :: (<a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Zip">Zip</a> m, <a href="Numeric-Additive-Group.html#t:Group">Group</a> r) =&gt; m r -&gt; m r -&gt; m r<a href="src/Numeric-Module-Representable.html#subtractRep" class="link">Source</a></p><div class="doc"><p><code><a href="Group.html#t:subtract">subtract</a></code> default definition
</p></div></div><div class="top"><p class="src"><a name="v:timesRep" class="def">timesRep</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integral">Integral</a> n, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#t:Functor">Functor</a> m, <a href="Numeric-Additive-Group.html#t:Group">Group</a> r) =&gt; n -&gt; m r -&gt; m r<a href="src/Numeric-Module-Representable.html#timesRep" class="link">Source</a></p><div class="doc"><p><code><a href="Group.html#t:times">times</a></code> default definition
</p></div></div><h1 id="g:4">Representable Multiplicative (via Algebra)
</h1><div class="top"><p class="src"><a name="v:mulRep" class="def">mulRep</a> :: (<a href="/usr/share/doc/libghc-representable-functors-doc/html/Data-Functor-Representable.html#t:Representable">Representable</a> m, <a href="Numeric-Algebra-Class.html#t:Algebra">Algebra</a> r (<a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Key">Key</a> m)) =&gt; m r -&gt; m r -&gt; m r<a href="src/Numeric-Module-Representable.html#mulRep" class="link">Source</a></p><div class="doc"><p>`Multiplicative.(*)` default definition
</p></div></div><h1 id="g:5">Representable Unital (via UnitalAlgebra)
</h1><div class="top"><p class="src"><a name="v:oneRep" class="def">oneRep</a> :: (<a href="/usr/share/doc/libghc-representable-functors-doc/html/Data-Functor-Representable.html#t:Representable">Representable</a> m, <a href="Numeric-Algebra-Unital.html#t:Unital">Unital</a> r, <a href="Numeric-Algebra-Unital.html#t:UnitalAlgebra">UnitalAlgebra</a> r (<a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Key">Key</a> m)) =&gt; m r<a href="src/Numeric-Module-Representable.html#oneRep" class="link">Source</a></p><div class="doc"><p><code><a href="Unital.html#t:one">one</a></code> default definition
</p></div></div><h1 id="g:6">Representable Rig (via Algebra)
</h1><div class="top"><p class="src"><a name="v:fromNaturalRep" class="def">fromNaturalRep</a> :: (<a href="Numeric-Algebra-Unital.html#t:UnitalAlgebra">UnitalAlgebra</a> r (<a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Key">Key</a> m), <a href="/usr/share/doc/libghc-representable-functors-doc/html/Data-Functor-Representable.html#t:Representable">Representable</a> m, <a href="Numeric-Rig-Class.html#t:Rig">Rig</a> r) =&gt; <a href="Numeric-Algebra.html#t:Natural">Natural</a> -&gt; m r<a href="src/Numeric-Module-Representable.html#fromNaturalRep" class="link">Source</a></p><div class="doc"><p><code><a href="Rig.html#t:fromNatural">fromNatural</a></code> default definition
</p></div></div><h1 id="g:7">Representable Ring (via Algebra)
</h1><div class="top"><p class="src"><a name="v:fromIntegerRep" class="def">fromIntegerRep</a> :: (<a href="Numeric-Algebra-Unital.html#t:UnitalAlgebra">UnitalAlgebra</a> r (<a href="/usr/share/doc/libghc-keys-doc/html/Data-Key.html#t:Key">Key</a> m), <a href="/usr/share/doc/libghc-representable-functors-doc/html/Data-Functor-Representable.html#t:Representable">Representable</a> m, <a href="Numeric-Ring-Class.html#t:Ring">Ring</a> r) =&gt; <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Integer">Integer</a> -&gt; m r<a href="src/Numeric-Module-Representable.html#fromIntegerRep" class="link">Source</a></p><div class="doc"><p><code><a href="Ring.html#t:fromInteger">fromInteger</a></code> default definition
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