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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Math-Algebras-NonCommutative.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-0.4.5: 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></table><p class="caption">Math.Algebras.NonCommutative</p></div><div id="description"><p class="caption">Description</p><div class="doc"><p>A module defining the algebra of non-commutative polynomials over a field k
</p></div></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:NonComMonomial" class="def">NonComMonomial</a> v <a href="src/Math-Algebras-NonCommutative.html#NonComMonomial" class="link">Source</a></p><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a name="v:NCM" class="def">NCM</a> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Int.html#t:Int">Int</a> [v]</td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:NonComMonomial" class="caption collapser" onclick="toggleSection('i:NonComMonomial')">Instances</p><div id="section.i:NonComMonomial" class="show"><table><tr><td class="src"><a href="Math-Algebras-NonCommutative.html#t:Monomial">Monomial</a> <a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</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> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Num">Num</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> v) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k (<a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a> v)</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> v => <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Eq.html#t:Eq">Eq</a> (<a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a> v)</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> v => <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> (<a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a> v)</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> v, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> v) => <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> (<a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a> v)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Math-Algebras-Structures.html#t:Mon">Mon</a> (<a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a> v)</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> v => <a href="Math-Algebras-NonCommutative.html#t:DivisionBasis">DivisionBasis</a> (<a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a> v)</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">class</span> <a name="t:Monomial" class="def">Monomial</a> m <span class="keyword">where</span><a href="src/Math-Algebras-NonCommutative.html#Monomial" class="link">Source</a></p><div class="subs methods"><p class="caption">Methods</p><p class="src"><a name="v:var" class="def">var</a> :: v -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> <a href="Math-Algebra-Field-Base.html#t:Q">Q</a> (m v)<a href="src/Math-Algebras-NonCommutative.html#var" class="link">Source</a></p><p class="src"><a name="v:powers" class="def">powers</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Eq.html#t:Eq">Eq</a> v => m v -> [(v, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Int.html#t:Int">Int</a>)]<a href="src/Math-Algebras-NonCommutative.html#powers" class="link">Source</a></p></div><div class="subs instances"><p id="control.i:Monomial" class="caption collapser" onclick="toggleSection('i:Monomial')">Instances</p><div id="section.i:Monomial" class="show"><table><tr><td class="src"><a href="Math-Algebras-NonCommutative.html#t:Monomial">Monomial</a> <a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Math-Algebras-NonCommutative.html#t:Monomial">Monomial</a> <a href="Math-QuantumAlgebra-QuantumPlane.html#t:SL2q">SL2q</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Math-Algebras-NonCommutative.html#t:Monomial">Monomial</a> <a href="Math-QuantumAlgebra-QuantumPlane.html#t:M2q">M2q</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Math-Algebras-NonCommutative.html#t:Monomial">Monomial</a> <a href="Math-QuantumAlgebra-QuantumPlane.html#t:Aq02">Aq02</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Math-Algebras-NonCommutative.html#t:Monomial">Monomial</a> <a href="Math-QuantumAlgebra-QuantumPlane.html#t:Aq20">Aq20</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:bind" class="def">bind</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Eq.html#t:Eq">Eq</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Eq.html#t:Eq">Eq</a> v, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Num">Num</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> b, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> b, <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k b, <a href="Math-Algebras-NonCommutative.html#t:Monomial">Monomial</a> m) => <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (m v) -> (v -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k b) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k b<a href="src/Math-Algebras-NonCommutative.html#bind" class="link">Source</a></p></div><div class="top"><p class="src"><span class="keyword">type</span> <a name="t:NCPoly" class="def">NCPoly</a> v = <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> <a href="Math-Algebra-Field-Base.html#t:Q">Q</a> (<a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a> v)<a href="src/Math-Algebras-NonCommutative.html#NCPoly" class="link">Source</a></p></div><div class="top"><p class="src"><span class="keyword">class</span> <a name="t:DivisionBasis" class="def">DivisionBasis</a> m <span class="keyword">where</span><a href="src/Math-Algebras-NonCommutative.html#DivisionBasis" class="link">Source</a></p><div class="subs methods"><p class="caption">Methods</p><p class="src"><a name="v:divM" class="def">divM</a> :: m -> m -> <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Maybe.html#t:Maybe">Maybe</a> (m, m)<a href="src/Math-Algebras-NonCommutative.html#divM" class="link">Source</a></p></div><div class="subs instances"><p id="control.i:DivisionBasis" class="caption collapser" onclick="toggleSection('i:DivisionBasis')">Instances</p><div id="section.i:DivisionBasis" class="show"><table><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> v => <a href="Math-Algebras-NonCommutative.html#t:DivisionBasis">DivisionBasis</a> (<a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a> v)</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:ncm" class="def">ncm</a> :: [v] -> <a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a> v<a href="src/Math-Algebras-NonCommutative.html#ncm" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:lm" class="def">lm</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> t t1 -> t1<a href="src/Math-Algebras-NonCommutative.html#lm" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:lc" class="def">lc</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> t t1 -> t<a href="src/Math-Algebras-NonCommutative.html#lc" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:lt" class="def">lt</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k b -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k b<a href="src/Math-Algebras-NonCommutative.html#lt" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:quotRemNP" class="def">quotRemNP</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Eq.html#t:Eq">Eq</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Fractional">Fractional</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> m, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> m, <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k m, <a href="Math-Algebras-NonCommutative.html#t:DivisionBasis">DivisionBasis</a> m) => <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k m -> [<a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k m] -> ([(<a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k m, <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k m)], <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k m)<a href="src/Math-Algebras-NonCommutative.html#quotRemNP" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:remNP" class="def">remNP</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Eq.html#t:Eq">Eq</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Fractional">Fractional</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> m, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> m, <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k m, <a href="Math-Algebras-NonCommutative.html#t:DivisionBasis">DivisionBasis</a> m) => <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k m -> [<a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k m] -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k m<a href="src/Math-Algebras-NonCommutative.html#remNP" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:-37--37-" class="def">(%%)</a> :: (<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Eq.html#t:Eq">Eq</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#t:Fractional">Fractional</a> k, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Ord.html#t:Ord">Ord</a> m, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Text-Show.html#t:Show">Show</a> m, <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k m, <a href="Math-Algebras-NonCommutative.html#t:DivisionBasis">DivisionBasis</a> m) => <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k m -> [<a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k m] -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k m<a href="src/Math-Algebras-NonCommutative.html#%25%25" class="link">Source</a></p></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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