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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Math-QuantumAlgebra-Tangle.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.QuantumAlgebra.Tangle</p></div><div id="description"><p class="caption">Description</p><div class="doc"><p>A module defining the category of tangles, and representations into the category of vector spaces
(specifically, knot invariants).</p></div></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:Tangle" class="def">Tangle</a> <a href="src/Math-QuantumAlgebra-Tangle.html#Tangle" class="link">Source</a></p><div class="subs instances"><p id="control.i:Tangle" class="caption collapser" onclick="toggleSection('i:Tangle')">Instances</p><div id="section.i:Tangle" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><a href="Math-QuantumAlgebra-TensorCategory.html#t:Monoidal">Monoidal</a> <a href="Math-QuantumAlgebra-Tangle.html#t:Tangle">Tangle</a></span> <a href="src/Math-QuantumAlgebra-Tangle.html#line-76" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Math-QuantumAlgebra-TensorCategory.html#t:MCategory">MCategory</a> <a href="Math-QuantumAlgebra-Tangle.html#t:Tangle">Tangle</a></span> <a href="src/Math-QuantumAlgebra-Tangle.html#line-42" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Eq.html#t:Eq">Eq</a> (<a href="Math-QuantumAlgebra-TensorCategory.html#t:Ob">Ob</a> <a href="Math-QuantumAlgebra-Tangle.html#t:Tangle">Tangle</a>)</span> <a href="src/Math-QuantumAlgebra-Tangle.html#line-43" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Eq.html#t:Eq">Eq</a> (<a href="Math-QuantumAlgebra-TensorCategory.html#t:Ar">Ar</a> <a href="Math-QuantumAlgebra-Tangle.html#t:Tangle">Tangle</a>)</span> <a href="src/Math-QuantumAlgebra-Tangle.html#line-53" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Ord.html#t:Ord">Ord</a> (<a href="Math-QuantumAlgebra-TensorCategory.html#t:Ob">Ob</a> <a href="Math-QuantumAlgebra-Tangle.html#t:Tangle">Tangle</a>)</span> <a href="src/Math-QuantumAlgebra-Tangle.html#line-43" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Ord.html#t:Ord">Ord</a> (<a href="Math-QuantumAlgebra-TensorCategory.html#t:Ar">Ar</a> <a href="Math-QuantumAlgebra-Tangle.html#t:Tangle">Tangle</a>)</span> <a href="src/Math-QuantumAlgebra-Tangle.html#line-53" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Show.html#t:Show">Show</a> (<a href="Math-QuantumAlgebra-TensorCategory.html#t:Ob">Ob</a> <a href="Math-QuantumAlgebra-Tangle.html#t:Tangle">Tangle</a>)</span> <a href="src/Math-QuantumAlgebra-Tangle.html#line-43" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Show.html#t:Show">Show</a> (<a href="Math-QuantumAlgebra-TensorCategory.html#t:Ar">Ar</a> <a href="Math-QuantumAlgebra-Tangle.html#t:Tangle">Tangle</a>)</span> <a href="src/Math-QuantumAlgebra-Tangle.html#line-53" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><span class="keyword">data</span> <a href="Math-QuantumAlgebra-TensorCategory.html#t:Ob">Ob</a> <a href="Math-QuantumAlgebra-Tangle.html#t:Tangle">Tangle</a> = <a name="v:OT" class="def">OT</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Int.html#t:Int">Int</a></span> <a href="src/Math-QuantumAlgebra-Tangle.html#line-43" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><span class="keyword">data</span> <a href="Math-QuantumAlgebra-TensorCategory.html#t:Ar">Ar</a> <a href="Math-QuantumAlgebra-Tangle.html#t:Tangle">Tangle</a> <ul class="inst"><li class="inst">= <a name="v:IdT" class="def">IdT</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Int.html#t:Int">Int</a></li><li class="inst">| <a name="v:CapT" class="def">CapT</a></li><li class="inst">| <a name="v:CupT" class="def">CupT</a></li><li class="inst">| <a name="v:OverT" class="def">OverT</a></li><li class="inst">| <a name="v:UnderT" class="def">UnderT</a></li><li class="inst">| <a name="v:SeqT" class="def">SeqT</a> [<a href="Math-QuantumAlgebra-TensorCategory.html#t:Ar">Ar</a> <a href="Math-QuantumAlgebra-Tangle.html#t:Tangle">Tangle</a>]</li><li class="inst">| <a name="v:ParT" class="def">ParT</a> [<a href="Math-QuantumAlgebra-TensorCategory.html#t:Ar">Ar</a> <a href="Math-QuantumAlgebra-Tangle.html#t:Tangle">Tangle</a>]</li></ul></span> <a href="src/Math-QuantumAlgebra-Tangle.html#line-44" class="link">Source</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:Oriented" class="def">Oriented</a> <a href="src/Math-QuantumAlgebra-Tangle.html#Oriented" class="link">Source</a></p><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a name="v:Plus" class="def">Plus</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a name="v:Minus" class="def">Minus</a></td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:Oriented" class="caption collapser" onclick="toggleSection('i:Oriented')">Instances</p><div id="section.i:Oriented" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Eq.html#t:Eq">Eq</a> <a href="Math-QuantumAlgebra-Tangle.html#t:Oriented">Oriented</a></span> <a href="src/Math-QuantumAlgebra-Tangle.html#line-86" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Ord.html#t:Ord">Ord</a> <a href="Math-QuantumAlgebra-Tangle.html#t:Oriented">Oriented</a></span> <a href="src/Math-QuantumAlgebra-Tangle.html#line-86" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Show.html#t:Show">Show</a> <a href="Math-QuantumAlgebra-Tangle.html#t:Oriented">Oriented</a></span> <a href="src/Math-QuantumAlgebra-Tangle.html#line-86" class="link">Source</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">type</span> <a name="t:TangleRep" class="def">TangleRep</a> b = <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> (<a href="Math-Algebras-LaurentPoly.html#t:LaurentPoly">LaurentPoly</a> <a href="Math-Algebra-Field-Base.html#t:Q">Q</a>) b <a href="src/Math-QuantumAlgebra-Tangle.html#TangleRep" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:cap" class="def">cap</a> :: [<a href="Math-QuantumAlgebra-Tangle.html#t:Oriented">Oriented</a>] -> <a href="Math-QuantumAlgebra-Tangle.html#t:TangleRep">TangleRep</a> [<a href="Math-QuantumAlgebra-Tangle.html#t:Oriented">Oriented</a>] <a href="src/Math-QuantumAlgebra-Tangle.html#cap" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:cup" class="def">cup</a> :: [<a href="Math-QuantumAlgebra-Tangle.html#t:Oriented">Oriented</a>] -> <a href="Math-QuantumAlgebra-Tangle.html#t:TangleRep">TangleRep</a> [<a href="Math-QuantumAlgebra-Tangle.html#t:Oriented">Oriented</a>] <a href="src/Math-QuantumAlgebra-Tangle.html#cup" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:over" class="def">over</a> :: [<a href="Math-QuantumAlgebra-Tangle.html#t:Oriented">Oriented</a>] -> <a href="Math-QuantumAlgebra-Tangle.html#t:TangleRep">TangleRep</a> [<a href="Math-QuantumAlgebra-Tangle.html#t:Oriented">Oriented</a>] <a href="src/Math-QuantumAlgebra-Tangle.html#over" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:under" class="def">under</a> :: [<a href="Math-QuantumAlgebra-Tangle.html#t:Oriented">Oriented</a>] -> <a href="Math-QuantumAlgebra-Tangle.html#t:TangleRep">TangleRep</a> [<a href="Math-QuantumAlgebra-Tangle.html#t:Oriented">Oriented</a>] <a href="src/Math-QuantumAlgebra-Tangle.html#under" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:loop" class="def">loop</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> (<a href="Math-Algebras-LaurentPoly.html#t:LaurentPoly">LaurentPoly</a> <a href="Math-Algebra-Field-Base.html#t:Q">Q</a>) [<a href="Math-QuantumAlgebra-Tangle.html#t:Oriented">Oriented</a>] <a href="src/Math-QuantumAlgebra-Tangle.html#loop" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:trefoil" class="def">trefoil</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> (<a href="Math-Algebras-LaurentPoly.html#t:LaurentPoly">LaurentPoly</a> <a href="Math-Algebra-Field-Base.html#t:Q">Q</a>) [<a href="Math-QuantumAlgebra-Tangle.html#t:Oriented">Oriented</a>] <a href="src/Math-QuantumAlgebra-Tangle.html#trefoil" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:kauffman" class="def">kauffman</a> :: <a href="Math-QuantumAlgebra-TensorCategory.html#t:Ar">Ar</a> <a href="Math-QuantumAlgebra-Tangle.html#t:Tangle">Tangle</a> -> <a href="Math-QuantumAlgebra-Tangle.html#t:TangleRep">TangleRep</a> [<a href="Math-QuantumAlgebra-Tangle.html#t:Oriented">Oriented</a>] -> <a href="Math-QuantumAlgebra-Tangle.html#t:TangleRep">TangleRep</a> [<a href="Math-QuantumAlgebra-Tangle.html#t:Oriented">Oriented</a>] <a href="src/Math-QuantumAlgebra-Tangle.html#kauffman" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:loopT" class="def">loopT</a> :: <a href="Math-QuantumAlgebra-TensorCategory.html#t:Ar">Ar</a> <a href="Math-QuantumAlgebra-Tangle.html#t:Tangle">Tangle</a> <a href="src/Math-QuantumAlgebra-Tangle.html#loopT" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:trefoilT" class="def">trefoilT</a> :: <a href="Math-QuantumAlgebra-TensorCategory.html#t:Ar">Ar</a> <a href="Math-QuantumAlgebra-Tangle.html#t:Tangle">Tangle</a> <a href="src/Math-QuantumAlgebra-Tangle.html#trefoilT" class="link">Source</a></p></div></div></div><div id="footer"><p>Produced by <a 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