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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Math-Algebras-Structures.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>Safe</td></tr><tr><th>Language</th><td>Haskell98</td></tr></table><p class="caption">Math.Algebras.Structures</p></div><div id="table-of-contents"><p class="caption">Contents</p><ul><li><a href="#section.orphans">Orphan instances</a></li></ul></div><div id="description"><p class="caption">Description</p><div class="doc"><p>A module defining various algebraic structures that can be defined on vector spaces
- specifically algebra, coalgebra, bialgebra, Hopf algebra, module, comodule</p></div></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:Mon">Mon</a> m <span class="keyword">where</span><ul class="subs"></ul></li><li class="src short"><span class="keyword">class</span> <a href="#t:Algebra">Algebra</a> k b <span class="keyword">where</span><ul class="subs"></ul></li><li class="src short"><a href="#v:unit-39-">unit'</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k b) => <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k () -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k b</li><li class="src short"><span class="keyword">class</span> <a href="#t:Coalgebra">Coalgebra</a> k b <span class="keyword">where</span><ul class="subs"></ul></li><li class="src short"><a href="#v:counit-39-">counit'</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k b) => <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k b -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k ()</li><li class="src short"><span class="keyword">class</span> (<a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k b, <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k b) => <a href="#t:Bialgebra">Bialgebra</a> k b</li><li class="src short"><span class="keyword">class</span> <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</a> k b => <a href="#t:HopfAlgebra">HopfAlgebra</a> k b <span class="keyword">where</span><ul class="subs"></ul></li><li class="src short"><span class="keyword">newtype</span> <a href="#t:SetCoalgebra">SetCoalgebra</a> b = <a href="#v:SC">SC</a> b</li><li class="src short"><span class="keyword">newtype</span> <a href="#t:MonoidCoalgebra">MonoidCoalgebra</a> m = <a href="#v:MC">MC</a> m</li><li class="src short"><span class="keyword">class</span> <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k a => <a href="#t:Module">Module</a> k a m <span class="keyword">where</span><ul class="subs"></ul></li><li class="src short"><a href="#v:-42-.">(*.)</a> :: (<a href="Math-Algebras-Structures.html#t:Module">Module</a> k a m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k a -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k m -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k m</li><li class="src short"><span class="keyword">class</span> <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k c => <a href="#t:Comodule">Comodule</a> k c n <span class="keyword">where</span><ul class="subs"></ul></li><li class="src short"><span class="keyword">class</span> <a href="#t:HasPairing">HasPairing</a> k u v <span class="keyword">where</span><ul class="subs"></ul></li><li class="src short"><a href="#v:pairing-39-">pairing'</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="Math-Algebras-Structures.html#t:HasPairing">HasPairing</a> k u v) => <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k u -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k v -> k</li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><span class="keyword">class</span> <a id="t:Mon" class="def">Mon</a> m <span class="keyword">where</span> <a href="src/Math-Algebras-Structures.html#Mon" class="link">Source</a> <a href="#t:Mon" class="selflink">#</a></p><div class="doc"><p>Monoid</p></div><div class="subs minimal"><p class="caption">Minimal complete definition</p><p class="src"><a href="Math-Algebras-Structures.html#v:munit">munit</a>, <a href="Math-Algebras-Structures.html#v:mmult">mmult</a></p></div><div class="subs methods"><p class="caption">Methods</p><p class="src"><a id="v:munit" class="def">munit</a> :: m <a href="src/Math-Algebras-Structures.html#munit" class="link">Source</a> <a href="#v:munit" class="selflink">#</a></p><p class="src"><a id="v:mmult" class="def">mmult</a> :: m -> m -> m <a href="src/Math-Algebras-Structures.html#mmult" class="link">Source</a> <a href="#v:mmult" class="selflink">#</a></p></div><div class="subs instances"><p id="control.i:Mon" class="caption collapser" onclick="toggleSection('i:Mon')">Instances</p><div id="section.i:Mon" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Mon:Mon:1" class="instance expander" onclick="toggleSection('i:ic:Mon:Mon:1')"></span> <a href="Math-Algebras-Structures.html#t:Mon">Mon</a> <a href="Math-Algebras-LaurentPoly.html#t:LaurentMonomial">LaurentMonomial</a></span> <a href="src/Math-Algebras-Structures.html#line-30" class="link">Source</a> <a href="#t:Mon" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Mon:Mon:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:munit">munit</a> :: <a href="Math-Algebras-LaurentPoly.html#t:LaurentMonomial">LaurentMonomial</a> <a href="src/Math-Algebras-Structures.html#munit" class="link">Source</a> <a href="#v:munit" class="selflink">#</a></p><p class="src"><a href="#v:mmult">mmult</a> :: <a href="Math-Algebras-LaurentPoly.html#t:LaurentMonomial">LaurentMonomial</a> -> <a href="Math-Algebras-LaurentPoly.html#t:LaurentMonomial">LaurentMonomial</a> -> <a href="Math-Algebras-LaurentPoly.html#t:LaurentMonomial">LaurentMonomial</a> <a href="src/Math-Algebras-Structures.html#mmult" class="link">Source</a> <a href="#v:mmult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Mon:Mon:2" class="instance expander" onclick="toggleSection('i:ic:Mon:Mon:2')"></span> <a href="Math-Algebras-Structures.html#t:Mon">Mon</a> (<a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a> v)</span> <a href="src/Math-Algebras-Structures.html#line-30" class="link">Source</a> <a href="#t:Mon" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Mon:Mon:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:munit">munit</a> :: <a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a> v <a href="src/Math-Algebras-Structures.html#munit" class="link">Source</a> <a href="#v:munit" class="selflink">#</a></p><p class="src"><a href="#v:mmult">mmult</a> :: <a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a> v -> <a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a> v -> <a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a> v <a href="src/Math-Algebras-Structures.html#mmult" class="link">Source</a> <a href="#v:mmult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Mon:Mon:3" class="instance expander" onclick="toggleSection('i:ic:Mon:Mon:3')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Math-Algebras-Structures.html#t:Mon">Mon</a> (<a href="Math-Algebras-TensorAlgebra.html#t:SymmetricAlgebra">SymmetricAlgebra</a> a)</span> <a href="src/Math-Algebras-Structures.html#line-122" class="link">Source</a> <a href="#t:Mon" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Mon:Mon:3" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:munit">munit</a> :: <a href="Math-Algebras-TensorAlgebra.html#t:SymmetricAlgebra">SymmetricAlgebra</a> a <a href="src/Math-Algebras-Structures.html#munit" class="link">Source</a> <a href="#v:munit" class="selflink">#</a></p><p class="src"><a href="#v:mmult">mmult</a> :: <a href="Math-Algebras-TensorAlgebra.html#t:SymmetricAlgebra">SymmetricAlgebra</a> a -> <a href="Math-Algebras-TensorAlgebra.html#t:SymmetricAlgebra">SymmetricAlgebra</a> a -> <a href="Math-Algebras-TensorAlgebra.html#t:SymmetricAlgebra">SymmetricAlgebra</a> a <a href="src/Math-Algebras-Structures.html#mmult" class="link">Source</a> <a href="#v:mmult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Mon:Mon:4" class="instance expander" onclick="toggleSection('i:ic:Mon:Mon:4')"></span> <a href="Math-Algebras-Structures.html#t:Mon">Mon</a> (<a href="Math-Algebras-TensorAlgebra.html#t:TensorAlgebra">TensorAlgebra</a> a)</span> <a href="src/Math-Algebras-Structures.html#line-35" class="link">Source</a> <a href="#t:Mon" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Mon:Mon:4" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:munit">munit</a> :: <a href="Math-Algebras-TensorAlgebra.html#t:TensorAlgebra">TensorAlgebra</a> a <a href="src/Math-Algebras-Structures.html#munit" class="link">Source</a> <a href="#v:munit" class="selflink">#</a></p><p class="src"><a href="#v:mmult">mmult</a> :: <a href="Math-Algebras-TensorAlgebra.html#t:TensorAlgebra">TensorAlgebra</a> a -> <a href="Math-Algebras-TensorAlgebra.html#t:TensorAlgebra">TensorAlgebra</a> a -> <a href="Math-Algebras-TensorAlgebra.html#t:TensorAlgebra">TensorAlgebra</a> a <a href="src/Math-Algebras-Structures.html#mmult" class="link">Source</a> <a href="#v:mmult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Mon:Mon:5" class="instance expander" onclick="toggleSection('i:ic:Mon:Mon:5')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> v => <a href="Math-Algebras-Structures.html#t:Mon">Mon</a> (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Grevlex">Grevlex</a> v)</span> <a href="src/Math-Algebras-Structures.html#line-209" class="link">Source</a> <a href="#t:Mon" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Mon:Mon:5" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:munit">munit</a> :: <a href="Math-CommutativeAlgebra-Polynomial.html#t:Grevlex">Grevlex</a> v <a href="src/Math-Algebras-Structures.html#munit" class="link">Source</a> <a href="#v:munit" class="selflink">#</a></p><p class="src"><a href="#v:mmult">mmult</a> :: <a href="Math-CommutativeAlgebra-Polynomial.html#t:Grevlex">Grevlex</a> v -> <a href="Math-CommutativeAlgebra-Polynomial.html#t:Grevlex">Grevlex</a> v -> <a href="Math-CommutativeAlgebra-Polynomial.html#t:Grevlex">Grevlex</a> v <a href="src/Math-Algebras-Structures.html#mmult" class="link">Source</a> <a href="#v:mmult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Mon:Mon:6" class="instance expander" onclick="toggleSection('i:ic:Mon:Mon:6')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> v => <a href="Math-Algebras-Structures.html#t:Mon">Mon</a> (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Glex">Glex</a> v)</span> <a href="src/Math-Algebras-Structures.html#line-173" class="link">Source</a> <a href="#t:Mon" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Mon:Mon:6" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:munit">munit</a> :: <a href="Math-CommutativeAlgebra-Polynomial.html#t:Glex">Glex</a> v <a href="src/Math-Algebras-Structures.html#munit" class="link">Source</a> <a href="#v:munit" class="selflink">#</a></p><p class="src"><a href="#v:mmult">mmult</a> :: <a href="Math-CommutativeAlgebra-Polynomial.html#t:Glex">Glex</a> v -> <a href="Math-CommutativeAlgebra-Polynomial.html#t:Glex">Glex</a> v -> <a href="Math-CommutativeAlgebra-Polynomial.html#t:Glex">Glex</a> v <a href="src/Math-Algebras-Structures.html#mmult" class="link">Source</a> <a href="#v:mmult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Mon:Mon:7" class="instance expander" onclick="toggleSection('i:ic:Mon:Mon:7')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> v => <a href="Math-Algebras-Structures.html#t:Mon">Mon</a> (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Lex">Lex</a> v)</span> <a href="src/Math-Algebras-Structures.html#line-127" class="link">Source</a> <a href="#t:Mon" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Mon:Mon:7" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:munit">munit</a> :: <a href="Math-CommutativeAlgebra-Polynomial.html#t:Lex">Lex</a> v <a href="src/Math-Algebras-Structures.html#munit" class="link">Source</a> <a href="#v:munit" class="selflink">#</a></p><p class="src"><a href="#v:mmult">mmult</a> :: <a href="Math-CommutativeAlgebra-Polynomial.html#t:Lex">Lex</a> v -> <a href="Math-CommutativeAlgebra-Polynomial.html#t:Lex">Lex</a> v -> <a href="Math-CommutativeAlgebra-Polynomial.html#t:Lex">Lex</a> v <a href="src/Math-Algebras-Structures.html#mmult" class="link">Source</a> <a href="#v:mmult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Mon:Mon:8" class="instance expander" onclick="toggleSection('i:ic:Mon:Mon:8')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> v => <a href="Math-Algebras-Structures.html#t:Mon">Mon</a> (<a href="Math-CommutativeAlgebra-Polynomial.html#t:MonImpl">MonImpl</a> v)</span> <a href="src/Math-Algebras-Structures.html#line-76" class="link">Source</a> <a href="#t:Mon" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Mon:Mon:8" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:munit">munit</a> :: <a href="Math-CommutativeAlgebra-Polynomial.html#t:MonImpl">MonImpl</a> v <a href="src/Math-Algebras-Structures.html#munit" class="link">Source</a> <a href="#v:munit" class="selflink">#</a></p><p class="src"><a href="#v:mmult">mmult</a> :: <a href="Math-CommutativeAlgebra-Polynomial.html#t:MonImpl">MonImpl</a> v -> <a href="Math-CommutativeAlgebra-Polynomial.html#t:MonImpl">MonImpl</a> v -> <a href="Math-CommutativeAlgebra-Polynomial.html#t:MonImpl">MonImpl</a> v <a href="src/Math-Algebras-Structures.html#mmult" class="link">Source</a> <a href="#v:mmult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Mon:Mon:9" class="instance expander" onclick="toggleSection('i:ic:Mon:Mon:9')"></span> (<a href="Math-Algebras-Structures.html#t:Mon">Mon</a> a, <a href="Math-Algebras-Structures.html#t:Mon">Mon</a> b) => <a href="Math-Algebras-Structures.html#t:Mon">Mon</a> (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Elim2">Elim2</a> a b)</span> <a href="src/Math-Algebras-Structures.html#line-251" class="link">Source</a> <a href="#t:Mon" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Mon:Mon:9" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:munit">munit</a> :: <a href="Math-CommutativeAlgebra-Polynomial.html#t:Elim2">Elim2</a> a b <a href="src/Math-Algebras-Structures.html#munit" class="link">Source</a> <a href="#v:munit" class="selflink">#</a></p><p class="src"><a href="#v:mmult">mmult</a> :: <a href="Math-CommutativeAlgebra-Polynomial.html#t:Elim2">Elim2</a> a b -> <a href="Math-CommutativeAlgebra-Polynomial.html#t:Elim2">Elim2</a> a b -> <a href="Math-CommutativeAlgebra-Polynomial.html#t:Elim2">Elim2</a> a b <a href="src/Math-Algebras-Structures.html#mmult" class="link">Source</a> <a href="#v:mmult" class="selflink">#</a></p></div></div></td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">class</span> <a id="t:Algebra" class="def">Algebra</a> k b <span class="keyword">where</span> <a href="src/Math-Algebras-Structures.html#Algebra" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></p><div class="doc"><p>Caution: If we declare an instance Algebra k b, then we are saying that the vector space Vect k b is a k-algebra.
In other words, we are saying that b is the basis for a k-algebra. So a more accurate name for this class
would have been AlgebraBasis.</p></div><div class="subs minimal"><p class="caption">Minimal complete definition</p><p class="src"><a href="Math-Algebras-Structures.html#v:unit">unit</a>, <a href="Math-Algebras-Structures.html#v:mult">mult</a></p></div><div class="subs methods"><p class="caption">Methods</p><p class="src"><a id="v:unit" class="def">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k b <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a id="v:mult" class="def">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> b b) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k b <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div><div class="subs instances"><p id="control.i:Algebra" class="caption collapser" onclick="toggleSection('i:Algebra')">Instances</p><div id="section.i:Algebra" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:1" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:1')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k ()</span> <a href="src/Math-Algebras-Structures.html#line-80" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k () <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> () ()) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k () <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:2" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:2')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k <a href="Math-Algebras-LaurentPoly.html#t:LaurentMonomial">LaurentMonomial</a></span> <a href="src/Math-Algebras-Structures.html#line-34" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-LaurentPoly.html#t:LaurentMonomial">LaurentMonomial</a> <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Algebras-LaurentPoly.html#t:LaurentMonomial">LaurentMonomial</a> <a href="Math-Algebras-LaurentPoly.html#t:LaurentMonomial">LaurentMonomial</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-LaurentPoly.html#t:LaurentMonomial">LaurentMonomial</a> <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:3" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:3')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k <a href="Math-Algebras-Matrix.html#t:M3">M3</a></span> <a href="src/Math-Algebras-Structures.html#line-78" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:3" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-Matrix.html#t:M3">M3</a> <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Algebras-Matrix.html#t:M3">M3</a> <a href="Math-Algebras-Matrix.html#t:M3">M3</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-Matrix.html#t:M3">M3</a> <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:4" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:4')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k <a href="Math-Algebras-Matrix.html#t:Mat2">Mat2</a></span> <a href="src/Math-Algebras-Structures.html#line-27" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:4" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-Matrix.html#t:Mat2">Mat2</a> <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Algebras-Matrix.html#t:Mat2">Mat2</a> <a href="Math-Algebras-Matrix.html#t:Mat2">Mat2</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-Matrix.html#t:Mat2">Mat2</a> <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:5" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:5')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k <a href="Math-Algebras-Quaternions.html#t:HBasis">HBasis</a></span> <a href="src/Math-Algebras-Structures.html#line-32" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:5" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-Quaternions.html#t:HBasis">HBasis</a> <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Algebras-Quaternions.html#t:HBasis">HBasis</a> <a href="Math-Algebras-Quaternions.html#t:HBasis">HBasis</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-Quaternions.html#t:HBasis">HBasis</a> <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:6" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:6')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a></span> <a href="src/Math-Algebras-Structures.html#line-48" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:6" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-Octonions.html#t:OBasis">OBasis</a> <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:7" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:7')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:NSym">NSym</a></span> <a href="src/Math-Algebras-Structures.html#line-721" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:7" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:NSym">NSym</a> <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:NSym">NSym</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:NSym">NSym</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:NSym">NSym</a> <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:8" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:8')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymH">SymH</a></span> <a href="src/Math-Algebras-Structures.html#line-690" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:8" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymH">SymH</a> <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymH">SymH</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymH">SymH</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymH">SymH</a> <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:9" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:9')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymE">SymE</a></span> <a href="src/Math-Algebras-Structures.html#line-660" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:9" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymE">SymE</a> <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymE">SymE</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymE">SymE</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymE">SymE</a> <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:10" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:10')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymM">SymM</a></span> <a href="src/Math-Algebras-Structures.html#line-620" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:10" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymM">SymM</a> <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymM">SymM</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymM">SymM</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymM">SymM</a> <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:11" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:11')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymF">QSymF</a></span> <a href="src/Math-Algebras-Structures.html#line-578" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:11" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymF">QSymF</a> <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymF">QSymF</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymF">QSymF</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymF">QSymF</a> <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:12" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:12')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymM">QSymM</a></span> <a href="src/Math-Algebras-Structures.html#line-530" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:12" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymM">QSymM</a> <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymM">QSymM</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymM">QSymM</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymM">QSymM</a> <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:13" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:13')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymM">YSymM</a></span> <a href="src/Math-Algebras-Structures.html#line-474" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:13" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymM">YSymM</a> <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymM">YSymM</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymM">YSymM</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymM">YSymM</a> <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:14" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:14')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymM">SSymM</a></span> <a href="src/Math-Algebras-Structures.html#line-233" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:14" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymM">SSymM</a> <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymM">SSymM</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymM">SSymM</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymM">SSymM</a> <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:15" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:15')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a></span> <a href="src/Math-Algebras-Structures.html#line-125" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:15" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a> <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a> <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:16" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:16')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k <a href="Math-NumberTheory-QuadraticField.html#t:QNFBasis">QNFBasis</a></span> <a href="src/Math-Algebras-Structures.html#line-68" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:16" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-NumberTheory-QuadraticField.html#t:QNFBasis">QNFBasis</a> <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-NumberTheory-QuadraticField.html#t:QNFBasis">QNFBasis</a> <a href="Math-NumberTheory-QuadraticField.html#t:QNFBasis">QNFBasis</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-NumberTheory-QuadraticField.html#t:QNFBasis">QNFBasis</a> <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:17" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:17')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> v) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k (<a href="Math-Algebras-Commutative.html#t:GlexMonomial">GlexMonomial</a> v)</span> <a href="src/Math-Algebras-Structures.html#line-60" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:17" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-Commutative.html#t:GlexMonomial">GlexMonomial</a> v) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-Commutative.html#t:GlexMonomial">GlexMonomial</a> v) (<a href="Math-Algebras-Commutative.html#t:GlexMonomial">GlexMonomial</a> v)) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-Commutative.html#t:GlexMonomial">GlexMonomial</a> v) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:18" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:18')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/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)</span> <a href="src/Math-Algebras-Structures.html#line-34" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:18" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a> v) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a> v) (<a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a> v)) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-NonCommutative.html#t:NonComMonomial">NonComMonomial</a> v) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:19" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:19')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k (<a href="Math-Algebras-TensorAlgebra.html#t:ExteriorAlgebra">ExteriorAlgebra</a> a)</span> <a href="src/Math-Algebras-Structures.html#line-195" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:19" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorAlgebra.html#t:ExteriorAlgebra">ExteriorAlgebra</a> a) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-TensorAlgebra.html#t:ExteriorAlgebra">ExteriorAlgebra</a> a) (<a href="Math-Algebras-TensorAlgebra.html#t:ExteriorAlgebra">ExteriorAlgebra</a> a)) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorAlgebra.html#t:ExteriorAlgebra">ExteriorAlgebra</a> a) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:20" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:20')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k (<a href="Math-Algebras-TensorAlgebra.html#t:SymmetricAlgebra">SymmetricAlgebra</a> a)</span> <a href="src/Math-Algebras-Structures.html#line-126" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:20" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorAlgebra.html#t:SymmetricAlgebra">SymmetricAlgebra</a> a) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-TensorAlgebra.html#t:SymmetricAlgebra">SymmetricAlgebra</a> a) (<a href="Math-Algebras-TensorAlgebra.html#t:SymmetricAlgebra">SymmetricAlgebra</a> a)) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorAlgebra.html#t:SymmetricAlgebra">SymmetricAlgebra</a> a) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:21" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:21')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k (<a href="Math-Algebras-TensorAlgebra.html#t:TensorAlgebra">TensorAlgebra</a> a)</span> <a href="src/Math-Algebras-Structures.html#line-39" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:21" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorAlgebra.html#t:TensorAlgebra">TensorAlgebra</a> a) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-TensorAlgebra.html#t:TensorAlgebra">TensorAlgebra</a> a) (<a href="Math-Algebras-TensorAlgebra.html#t:TensorAlgebra">TensorAlgebra</a> a)) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorAlgebra.html#t:TensorAlgebra">TensorAlgebra</a> a) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:22" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:22')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> v, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:Show">Show</a> v) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Grevlex">Grevlex</a> v)</span> <a href="src/Math-Algebras-Structures.html#line-232" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:22" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Grevlex">Grevlex</a> v) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Grevlex">Grevlex</a> v) (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Grevlex">Grevlex</a> v)) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Grevlex">Grevlex</a> v) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:23" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:23')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> v, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:Show">Show</a> v) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Glex">Glex</a> v)</span> <a href="src/Math-Algebras-Structures.html#line-196" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:23" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Glex">Glex</a> v) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Glex">Glex</a> v) (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Glex">Glex</a> v)) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Glex">Glex</a> v) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:24" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:24')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> v, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:Show">Show</a> v) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Lex">Lex</a> v)</span> <a href="src/Math-Algebras-Structures.html#line-162" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:24" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Lex">Lex</a> v) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Lex">Lex</a> v) (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Lex">Lex</a> v)) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Lex">Lex</a> v) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:25" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:25')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymF">YSymF</a> a)</span> <a href="src/Math-Algebras-Structures.html#line-402" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:25" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymF">YSymF</a> a) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymF">YSymF</a> a) (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymF">YSymF</a> a)) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymF">YSymF</a> a) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:26" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:26')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>)</span> <a href="src/Math-Algebras-Structures.html#line-265" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:26" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>) (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>)) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:27" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:27')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:Shuffle">Shuffle</a> a)</span> <a href="src/Math-Algebras-Structures.html#line-72" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:27" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:Shuffle">Shuffle</a> a) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:Shuffle">Shuffle</a> a) (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:Shuffle">Shuffle</a> a)) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:Shuffle">Shuffle</a> a) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:28" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:28')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k (<a href="Math-Combinatorics-IncidenceAlgebra.html#t:Interval">Interval</a> a)</span> <a href="src/Math-Algebras-Structures.html#line-104" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc"><p>The incidence algebra of a poset is the free k-vector space having as its basis the set of intervals in the poset,
with multiplication defined by concatenation of intervals.
The incidence algebra can also be thought of as the vector space of functions from intervals to k, with multiplication
defined by the convolution (f*g)(x,y) = sum [ f(x,z) g(z,y) | x <= z <= y ].</p></td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:28" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Combinatorics-IncidenceAlgebra.html#t:Interval">Interval</a> a) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Combinatorics-IncidenceAlgebra.html#t:Interval">Interval</a> a) (<a href="Math-Combinatorics-IncidenceAlgebra.html#t:Interval">Interval</a> a)) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Combinatorics-IncidenceAlgebra.html#t:Interval">Interval</a> a) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:29" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:29')"></span> <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> <a href="Math-Algebra-Field-Base.html#t:Q">Q</a> (<a href="Math-Algebras-AffinePlane.html#t:SL2">SL2</a> <a href="Math-Algebras-AffinePlane.html#t:ABCD">ABCD</a>)</span> <a href="src/Math-Algebras-Structures.html#line-40" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:29" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: <a href="Math-Algebra-Field-Base.html#t:Q">Q</a> -> <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-AffinePlane.html#t:SL2">SL2</a> <a href="Math-Algebras-AffinePlane.html#t:ABCD">ABCD</a>) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <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-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-AffinePlane.html#t:SL2">SL2</a> <a href="Math-Algebras-AffinePlane.html#t:ABCD">ABCD</a>) (<a href="Math-Algebras-AffinePlane.html#t:SL2">SL2</a> <a href="Math-Algebras-AffinePlane.html#t:ABCD">ABCD</a>)) -> <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-AffinePlane.html#t:SL2">SL2</a> <a href="Math-Algebras-AffinePlane.html#t:ABCD">ABCD</a>) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:30" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:30')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> b, <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k a, <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k b) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> a b)</span> <a href="src/Math-Algebras-Structures.html#line-131" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc"><p>The tensor product of k-algebras can itself be given the structure of a k-algebra</p></td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:30" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> a b) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> a b) (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> a b)) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> a b) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:31" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:31')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> b, <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k a, <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k b) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k (<a href="Math-Algebras-TensorProduct.html#t:DSum">DSum</a> a b)</span> <a href="src/Math-Algebras-Structures.html#line-102" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc"><p>The direct sum of k-algebras can itself be given the structure of a k-algebra.
This is the product object in the category of k-algebras.</p></td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:31" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:DSum">DSum</a> a b) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-TensorProduct.html#t:DSum">DSum</a> a b) (<a href="Math-Algebras-TensorProduct.html#t:DSum">DSum</a> a b)) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:DSum">DSum</a> a b) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:32" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:32')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a, <a href="Math-Algebras-Structures.html#t:Mon">Mon</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> b, <a href="Math-Algebras-Structures.html#t:Mon">Mon</a> b) => <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Elim2">Elim2</a> a b)</span> <a href="src/Math-Algebras-Structures.html#line-263" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:32" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</a> :: k -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Elim2">Elim2</a> a b) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Elim2">Elim2</a> a b) (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Elim2">Elim2</a> a b)) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-CommutativeAlgebra-Polynomial.html#t:Elim2">Elim2</a> a b) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:33" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:33')"></span> <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</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-QuantumPlane.html#t:SL2q">SL2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>)</span> <a href="src/Math-Algebras-Structures.html#line-190" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:33" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</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-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-QuantumPlane.html#t:SL2q">SL2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</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-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-QuantumAlgebra-QuantumPlane.html#t:SL2q">SL2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) (<a href="Math-QuantumAlgebra-QuantumPlane.html#t:SL2q">SL2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</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-QuantumPlane.html#t:SL2q">SL2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:34" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:34')"></span> <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</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-QuantumPlane.html#t:M2q">M2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>)</span> <a href="src/Math-Algebras-Structures.html#line-101" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:34" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</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-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-QuantumPlane.html#t:M2q">M2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</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-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-QuantumAlgebra-QuantumPlane.html#t:M2q">M2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) (<a href="Math-QuantumAlgebra-QuantumPlane.html#t:M2q">M2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</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-QuantumPlane.html#t:M2q">M2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:35" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:35')"></span> <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</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-QuantumPlane.html#t:Aq02">Aq02</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>)</span> <a href="src/Math-Algebras-Structures.html#line-77" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:35" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</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-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-QuantumPlane.html#t:Aq02">Aq02</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</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-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-QuantumAlgebra-QuantumPlane.html#t:Aq02">Aq02</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) (<a href="Math-QuantumAlgebra-QuantumPlane.html#t:Aq02">Aq02</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</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-QuantumPlane.html#t:Aq02">Aq02</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Algebra:Algebra:36" class="instance expander" onclick="toggleSection('i:ic:Algebra:Algebra:36')"></span> <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</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-QuantumPlane.html#t:Aq20">Aq20</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>)</span> <a href="src/Math-Algebras-Structures.html#line-55" class="link">Source</a> <a href="#t:Algebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Algebra:Algebra:36" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:unit">unit</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-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-QuantumPlane.html#t:Aq20">Aq20</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) <a href="src/Math-Algebras-Structures.html#unit" class="link">Source</a> <a href="#v:unit" class="selflink">#</a></p><p class="src"><a href="#v:mult">mult</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-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-QuantumAlgebra-QuantumPlane.html#t:Aq20">Aq20</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) (<a href="Math-QuantumAlgebra-QuantumPlane.html#t:Aq20">Aq20</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</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-QuantumPlane.html#t:Aq20">Aq20</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) <a href="src/Math-Algebras-Structures.html#mult" class="link">Source</a> <a href="#v:mult" class="selflink">#</a></p></div></div></td></tr></table></div></div></div><div class="top"><p class="src"><a id="v:unit-39-" class="def">unit'</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k b) => <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k () -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k b <a href="src/Math-Algebras-Structures.html#unit%27" class="link">Source</a> <a href="#v:unit-39-" class="selflink">#</a></p><div class="doc"><p>Sometimes it is more convenient to work with this version of unit.</p></div></div><div class="top"><p class="src"><span class="keyword">class</span> <a id="t:Coalgebra" class="def">Coalgebra</a> k b <span class="keyword">where</span> <a href="src/Math-Algebras-Structures.html#Coalgebra" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></p><div class="doc"><p>An instance declaration for Coalgebra k b is saying that the vector space Vect k b is a k-coalgebra.</p></div><div class="subs minimal"><p class="caption">Minimal complete definition</p><p class="src"><a href="Math-Algebras-Structures.html#v:counit">counit</a>, <a href="Math-Algebras-Structures.html#v:comult">comult</a></p></div><div class="subs methods"><p class="caption">Methods</p><p class="src"><a id="v:counit" class="def">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k b -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a id="v:comult" class="def">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k b -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> b b) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div><div class="subs instances"><p id="control.i:Coalgebra" class="caption collapser" onclick="toggleSection('i:Coalgebra')">Instances</p><div id="section.i:Coalgebra" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:1" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:1')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k <a href="Math-Algebras-VectorSpace.html#t:EBasis">EBasis</a></span> <a href="src/Math-Algebras-Structures.html#line-151" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-VectorSpace.html#t:EBasis">EBasis</a> -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-VectorSpace.html#t:EBasis">EBasis</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Algebras-VectorSpace.html#t:EBasis">EBasis</a> <a href="Math-Algebras-VectorSpace.html#t:EBasis">EBasis</a>) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:2" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:2')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k ()</span> <a href="src/Math-Algebras-Structures.html#line-89" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k () -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k () -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> () ()) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:3" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:3')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k <a href="Math-Algebras-Matrix.html#t:Mat2-39-">Mat2'</a></span> <a href="src/Math-Algebras-Structures.html#line-60" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:3" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-Matrix.html#t:Mat2-39-">Mat2'</a> -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-Matrix.html#t:Mat2-39-">Mat2'</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Algebras-Matrix.html#t:Mat2-39-">Mat2'</a> <a href="Math-Algebras-Matrix.html#t:Mat2-39-">Mat2'</a>) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:4" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:4')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:NSym">NSym</a></span> <a href="src/Math-Algebras-Structures.html#line-726" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:4" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:NSym">NSym</a> -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:NSym">NSym</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:NSym">NSym</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:NSym">NSym</a>) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:5" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:5')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymH">SymH</a></span> <a href="src/Math-Algebras-Structures.html#line-694" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:5" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymH">SymH</a> -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymH">SymH</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymH">SymH</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymH">SymH</a>) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:6" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:6')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymE">SymE</a></span> <a href="src/Math-Algebras-Structures.html#line-664" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:6" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymE">SymE</a> -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymE">SymE</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymE">SymE</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymE">SymE</a>) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:7" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:7')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymM">SymM</a></span> <a href="src/Math-Algebras-Structures.html#line-638" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:7" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymM">SymM</a> -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymM">SymM</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymM">SymM</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymM">SymM</a>) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:8" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:8')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymF">QSymF</a></span> <a href="src/Math-Algebras-Structures.html#line-582" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:8" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymF">QSymF</a> -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymF">QSymF</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymF">QSymF</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymF">QSymF</a>) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:9" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:9')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymM">QSymM</a></span> <a href="src/Math-Algebras-Structures.html#line-535" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:9" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymM">QSymM</a> -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymM">QSymM</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymM">QSymM</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymM">QSymM</a>) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:10" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:10')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymM">YSymM</a></span> <a href="src/Math-Algebras-Structures.html#line-478" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:10" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymM">YSymM</a> -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymM">YSymM</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymM">YSymM</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymM">YSymM</a>) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:11" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:11')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymM">SSymM</a></span> <a href="src/Math-Algebras-Structures.html#line-249" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:11" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymM">SSymM</a> -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymM">SSymM</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymM">SSymM</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymM">SSymM</a>) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:12" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:12')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a></span> <a href="src/Math-Algebras-Structures.html#line-137" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:12" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a> -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:13" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:13')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> m, <a href="Math-Algebras-Structures.html#t:Mon">Mon</a> m) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k (<a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m)</span> <a href="src/Math-Algebras-Structures.html#line-164" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:13" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m) -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m) (<a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m)) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:14" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:14')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k (<a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b)</span> <a href="src/Math-Algebras-Structures.html#line-157" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:14" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b) -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b) (<a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b)) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:15" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:15')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k (<a href="Math-Algebras-Commutative.html#t:GlexMonomial">GlexMonomial</a> v)</span> <a href="src/Math-Algebras-Structures.html#line-68" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:15" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-Commutative.html#t:GlexMonomial">GlexMonomial</a> v) -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-Commutative.html#t:GlexMonomial">GlexMonomial</a> v) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-Commutative.html#t:GlexMonomial">GlexMonomial</a> v) (<a href="Math-Algebras-Commutative.html#t:GlexMonomial">GlexMonomial</a> v)) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:16" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:16')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> c) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k (<a href="Math-Algebras-TensorAlgebra.html#t:TensorCoalgebra">TensorCoalgebra</a> c)</span> <a href="src/Math-Algebras-Structures.html#line-270" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:16" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorAlgebra.html#t:TensorCoalgebra">TensorCoalgebra</a> c) -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorAlgebra.html#t:TensorCoalgebra">TensorCoalgebra</a> c) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-TensorAlgebra.html#t:TensorCoalgebra">TensorCoalgebra</a> c) (<a href="Math-Algebras-TensorAlgebra.html#t:TensorCoalgebra">TensorCoalgebra</a> c)) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:17" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:17')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Algebras-Quaternions.html#t:HBasis">HBasis</a>)</span> <a href="src/Math-Algebras-Structures.html#line-169" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:17" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Algebras-Quaternions.html#t:HBasis">HBasis</a>) -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Algebras-Quaternions.html#t:HBasis">HBasis</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Algebras-Quaternions.html#t:HBasis">HBasis</a>) (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Algebras-Quaternions.html#t:HBasis">HBasis</a>)) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:18" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:18')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymF">YSymF</a> a)</span> <a href="src/Math-Algebras-Structures.html#line-387" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:18" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymF">YSymF</a> a) -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymF">YSymF</a> a) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymF">YSymF</a> a) (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymF">YSymF</a> a)) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:19" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:19')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>)</span> <a href="src/Math-Algebras-Structures.html#line-277" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:19" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>) -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>) (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>)) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:20" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:20')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:Shuffle">Shuffle</a> a)</span> <a href="src/Math-Algebras-Structures.html#line-79" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:20" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:Shuffle">Shuffle</a> a) -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:Shuffle">Shuffle</a> a) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:Shuffle">Shuffle</a> a) (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:Shuffle">Shuffle</a> a)) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:21" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:21')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k (<a href="Math-Combinatorics-IncidenceAlgebra.html#t:Interval">Interval</a> a)</span> <a href="src/Math-Algebras-Structures.html#line-218" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:21" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Combinatorics-IncidenceAlgebra.html#t:Interval">Interval</a> a) -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Combinatorics-IncidenceAlgebra.html#t:Interval">Interval</a> a) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Combinatorics-IncidenceAlgebra.html#t:Interval">Interval</a> a) (<a href="Math-Combinatorics-IncidenceAlgebra.html#t:Interval">Interval</a> a)) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:22" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:22')"></span> <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> <a href="Math-Algebra-Field-Base.html#t:Q">Q</a> (<a href="Math-Algebras-AffinePlane.html#t:SL2">SL2</a> <a href="Math-Algebras-AffinePlane.html#t:ABCD">ABCD</a>)</span> <a href="src/Math-Algebras-Structures.html#line-62" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:22" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <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-AffinePlane.html#t:SL2">SL2</a> <a href="Math-Algebras-AffinePlane.html#t:ABCD">ABCD</a>) -> <a href="Math-Algebra-Field-Base.html#t:Q">Q</a> <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <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-AffinePlane.html#t:SL2">SL2</a> <a href="Math-Algebras-AffinePlane.html#t:ABCD">ABCD</a>) -> <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-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-AffinePlane.html#t:SL2">SL2</a> <a href="Math-Algebras-AffinePlane.html#t:ABCD">ABCD</a>) (<a href="Math-Algebras-AffinePlane.html#t:SL2">SL2</a> <a href="Math-Algebras-AffinePlane.html#t:ABCD">ABCD</a>)) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:23" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:23')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> b, <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k a, <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k b) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> a b)</span> <a href="src/Math-Algebras-Structures.html#line-140" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc"><p>The tensor product of k-coalgebras can itself be given the structure of a k-coalgebra</p></td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:23" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> a b) -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> a b) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> a b) (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> a b)) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:24" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:24')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> b, <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k a, <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k b) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k (<a href="Math-Algebras-TensorProduct.html#t:DSum">DSum</a> a b)</span> <a href="src/Math-Algebras-Structures.html#line-116" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc"><p>The direct sum of k-coalgebras can itself be given the structure of a k-coalgebra.
This is the coproduct object in the category of k-coalgebras.</p></td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:24" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:DSum">DSum</a> a b) -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:DSum">DSum</a> a b) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-TensorProduct.html#t:DSum">DSum</a> a b) (<a href="Math-Algebras-TensorProduct.html#t:DSum">DSum</a> a b)) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:25" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:25')"></span> <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</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-QuantumPlane.html#t:SL2q">SL2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>)</span> <a href="src/Math-Algebras-Structures.html#line-198" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:25" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</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-QuantumPlane.html#t:SL2q">SL2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) -> <a href="Math-Algebras-LaurentPoly.html#t:LaurentPoly">LaurentPoly</a> <a href="Math-Algebra-Field-Base.html#t:Q">Q</a> <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</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-QuantumPlane.html#t:SL2q">SL2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</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-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-QuantumAlgebra-QuantumPlane.html#t:SL2q">SL2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) (<a href="Math-QuantumAlgebra-QuantumPlane.html#t:SL2q">SL2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>)) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Coalgebra:Coalgebra:26" class="instance expander" onclick="toggleSection('i:ic:Coalgebra:Coalgebra:26')"></span> <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</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-QuantumPlane.html#t:M2q">M2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>)</span> <a href="src/Math-Algebras-Structures.html#line-110" class="link">Source</a> <a href="#t:Coalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Coalgebra:Coalgebra:26" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</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-QuantumPlane.html#t:M2q">M2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) -> <a href="Math-Algebras-LaurentPoly.html#t:LaurentPoly">LaurentPoly</a> <a href="Math-Algebra-Field-Base.html#t:Q">Q</a> <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</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-QuantumPlane.html#t:M2q">M2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</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-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-QuantumAlgebra-QuantumPlane.html#t:M2q">M2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) (<a href="Math-QuantumAlgebra-QuantumPlane.html#t:M2q">M2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>)) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr></table></div></div></div><div class="top"><p class="src"><a id="v:counit-39-" class="def">counit'</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k b) => <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k b -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k () <a href="src/Math-Algebras-Structures.html#counit%27" class="link">Source</a> <a href="#v:counit-39-" class="selflink">#</a></p><div class="doc"><p>Sometimes it is more convenient to work with this version of counit.</p></div></div><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k b, <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k b) => <a id="t:Bialgebra" class="def">Bialgebra</a> k b <a href="src/Math-Algebras-Structures.html#Bialgebra" class="link">Source</a> <a href="#t:Bialgebra" class="selflink">#</a></p><div class="doc"><p>A bialgebra is an algebra which is also a coalgebra, subject to the compatibility conditions
that counit and comult must be algebra morphisms (or equivalently, that unit and mult must be coalgebra morphisms)</p></div><div class="subs instances"><p id="control.i:Bialgebra" class="caption collapser" onclick="toggleSection('i:Bialgebra')">Instances</p><div id="section.i:Bialgebra" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Bialgebra:Bialgebra:1" class="instance expander" onclick="toggleSection('i:ic:Bialgebra:Bialgebra:1')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:NSym">NSym</a></span> <a href="src/Math-Algebras-Structures.html#line-734" class="link">Source</a> <a href="#t:Bialgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Bialgebra:Bialgebra:1" class="inst-details hide"></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Bialgebra:Bialgebra:2" class="instance expander" onclick="toggleSection('i:ic:Bialgebra:Bialgebra:2')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymH">SymH</a></span> <a href="src/Math-Algebras-Structures.html#line-702" class="link">Source</a> <a href="#t:Bialgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Bialgebra:Bialgebra:2" class="inst-details hide"></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Bialgebra:Bialgebra:3" class="instance expander" onclick="toggleSection('i:ic:Bialgebra:Bialgebra:3')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymE">SymE</a></span> <a href="src/Math-Algebras-Structures.html#line-672" class="link">Source</a> <a href="#t:Bialgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Bialgebra:Bialgebra:3" class="inst-details hide"></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Bialgebra:Bialgebra:4" class="instance expander" onclick="toggleSection('i:ic:Bialgebra:Bialgebra:4')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymM">SymM</a></span> <a href="src/Math-Algebras-Structures.html#line-643" class="link">Source</a> <a href="#t:Bialgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Bialgebra:Bialgebra:4" class="inst-details hide"></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Bialgebra:Bialgebra:5" class="instance expander" onclick="toggleSection('i:ic:Bialgebra:Bialgebra:5')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymF">QSymF</a></span> <a href="src/Math-Algebras-Structures.html#line-586" class="link">Source</a> <a href="#t:Bialgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Bialgebra:Bialgebra:5" class="inst-details hide"></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Bialgebra:Bialgebra:6" class="instance expander" onclick="toggleSection('i:ic:Bialgebra:Bialgebra:6')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymM">QSymM</a></span> <a href="src/Math-Algebras-Structures.html#line-540" class="link">Source</a> <a href="#t:Bialgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Bialgebra:Bialgebra:6" class="inst-details hide"></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Bialgebra:Bialgebra:7" class="instance expander" onclick="toggleSection('i:ic:Bialgebra:Bialgebra:7')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymM">YSymM</a></span> <a href="src/Math-Algebras-Structures.html#line-486" class="link">Source</a> <a href="#t:Bialgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Bialgebra:Bialgebra:7" class="inst-details hide"></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Bialgebra:Bialgebra:8" class="instance expander" onclick="toggleSection('i:ic:Bialgebra:Bialgebra:8')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymM">SSymM</a></span> <a href="src/Math-Algebras-Structures.html#line-258" class="link">Source</a> <a href="#t:Bialgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Bialgebra:Bialgebra:8" class="inst-details hide"></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Bialgebra:Bialgebra:9" class="instance expander" onclick="toggleSection('i:ic:Bialgebra:Bialgebra:9')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a></span> <a href="src/Math-Algebras-Structures.html#line-143" class="link">Source</a> <a href="#t:Bialgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Bialgebra:Bialgebra:9" class="inst-details hide"></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Bialgebra:Bialgebra:10" class="instance expander" onclick="toggleSection('i:ic:Bialgebra:Bialgebra:10')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymF">YSymF</a> a)</span> <a href="src/Math-Algebras-Structures.html#line-408" class="link">Source</a> <a href="#t:Bialgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Bialgebra:Bialgebra:10" class="inst-details hide"></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Bialgebra:Bialgebra:11" class="instance expander" onclick="toggleSection('i:ic:Bialgebra:Bialgebra:11')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</a> k (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>)</span> <a href="src/Math-Algebras-Structures.html#line-286" class="link">Source</a> <a href="#t:Bialgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Bialgebra:Bialgebra:11" class="inst-details hide"></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Bialgebra:Bialgebra:12" class="instance expander" onclick="toggleSection('i:ic:Bialgebra:Bialgebra:12')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:Shuffle">Shuffle</a> a)</span> <a href="src/Math-Algebras-Structures.html#line-84" class="link">Source</a> <a href="#t:Bialgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Bialgebra:Bialgebra:12" class="inst-details hide"></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Bialgebra:Bialgebra:13" class="instance expander" onclick="toggleSection('i:ic:Bialgebra:Bialgebra:13')"></span> <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</a> <a href="Math-Algebra-Field-Base.html#t:Q">Q</a> (<a href="Math-Algebras-AffinePlane.html#t:SL2">SL2</a> <a href="Math-Algebras-AffinePlane.html#t:ABCD">ABCD</a>)</span> <a href="src/Math-Algebras-Structures.html#line-81" class="link">Source</a> <a href="#t:Bialgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Bialgebra:Bialgebra:13" class="inst-details hide"></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Bialgebra:Bialgebra:14" class="instance expander" onclick="toggleSection('i:ic:Bialgebra:Bialgebra:14')"></span> <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</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-QuantumPlane.html#t:SL2q">SL2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>)</span> <a href="src/Math-Algebras-Structures.html#line-212" class="link">Source</a> <a href="#t:Bialgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Bialgebra:Bialgebra:14" class="inst-details hide"></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Bialgebra:Bialgebra:15" class="instance expander" onclick="toggleSection('i:ic:Bialgebra:Bialgebra:15')"></span> <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</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-QuantumPlane.html#t:M2q">M2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>)</span> <a href="src/Math-Algebras-Structures.html#line-124" class="link">Source</a> <a href="#t:Bialgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Bialgebra:Bialgebra:15" class="inst-details hide"></div></td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">class</span> <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</a> k b => <a id="t:HopfAlgebra" class="def">HopfAlgebra</a> k b <span class="keyword">where</span> <a href="src/Math-Algebras-Structures.html#HopfAlgebra" class="link">Source</a> <a href="#t:HopfAlgebra" class="selflink">#</a></p><div class="subs minimal"><p class="caption">Minimal complete definition</p><p class="src"><a href="Math-Algebras-Structures.html#v:antipode">antipode</a></p></div><div class="subs methods"><p class="caption">Methods</p><p class="src"><a id="v:antipode" class="def">antipode</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-Structures.html#antipode" class="link">Source</a> <a href="#v:antipode" class="selflink">#</a></p></div><div class="subs instances"><p id="control.i:HopfAlgebra" class="caption collapser" onclick="toggleSection('i:HopfAlgebra')">Instances</p><div id="section.i:HopfAlgebra" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:HopfAlgebra:HopfAlgebra:1" class="instance expander" onclick="toggleSection('i:ic:HopfAlgebra:HopfAlgebra:1')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:HopfAlgebra">HopfAlgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:NSym">NSym</a></span> <a href="src/Math-Algebras-Structures.html#line-737" class="link">Source</a> <a href="#t:HopfAlgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:HopfAlgebra:HopfAlgebra:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:antipode">antipode</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:NSym">NSym</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:NSym">NSym</a> <a href="src/Math-Algebras-Structures.html#antipode" class="link">Source</a> <a href="#v:antipode" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:HopfAlgebra:HopfAlgebra:2" class="instance expander" onclick="toggleSection('i:ic:HopfAlgebra:HopfAlgebra:2')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:HopfAlgebra">HopfAlgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymM">SymM</a></span> <a href="src/Math-Algebras-Structures.html#line-645" class="link">Source</a> <a href="#t:HopfAlgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:HopfAlgebra:HopfAlgebra:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:antipode">antipode</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymM">SymM</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymM">SymM</a> <a href="src/Math-Algebras-Structures.html#antipode" class="link">Source</a> <a href="#v:antipode" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:HopfAlgebra:HopfAlgebra:3" class="instance expander" onclick="toggleSection('i:ic:HopfAlgebra:HopfAlgebra:3')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:HopfAlgebra">HopfAlgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymF">QSymF</a></span> <a href="src/Math-Algebras-Structures.html#line-588" class="link">Source</a> <a href="#t:HopfAlgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:HopfAlgebra:HopfAlgebra:3" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:antipode">antipode</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymF">QSymF</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymF">QSymF</a> <a href="src/Math-Algebras-Structures.html#antipode" class="link">Source</a> <a href="#v:antipode" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:HopfAlgebra:HopfAlgebra:4" class="instance expander" onclick="toggleSection('i:ic:HopfAlgebra:HopfAlgebra:4')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:HopfAlgebra">HopfAlgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymM">QSymM</a></span> <a href="src/Math-Algebras-Structures.html#line-542" class="link">Source</a> <a href="#t:HopfAlgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:HopfAlgebra:HopfAlgebra:4" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:antipode">antipode</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymM">QSymM</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymM">QSymM</a> <a href="src/Math-Algebras-Structures.html#antipode" class="link">Source</a> <a href="#v:antipode" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:HopfAlgebra:HopfAlgebra:5" class="instance expander" onclick="toggleSection('i:ic:HopfAlgebra:HopfAlgebra:5')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:HopfAlgebra">HopfAlgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymM">YSymM</a></span> <a href="src/Math-Algebras-Structures.html#line-488" class="link">Source</a> <a href="#t:HopfAlgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:HopfAlgebra:HopfAlgebra:5" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:antipode">antipode</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymM">YSymM</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymM">YSymM</a> <a href="src/Math-Algebras-Structures.html#antipode" class="link">Source</a> <a href="#v:antipode" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:HopfAlgebra:HopfAlgebra:6" class="instance expander" onclick="toggleSection('i:ic:HopfAlgebra:HopfAlgebra:6')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:HopfAlgebra">HopfAlgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymM">SSymM</a></span> <a href="src/Math-Algebras-Structures.html#line-260" class="link">Source</a> <a href="#t:HopfAlgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:HopfAlgebra:HopfAlgebra:6" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:antipode">antipode</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymM">SSymM</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymM">SSymM</a> <a href="src/Math-Algebras-Structures.html#antipode" class="link">Source</a> <a href="#v:antipode" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:HopfAlgebra:HopfAlgebra:7" class="instance expander" onclick="toggleSection('i:ic:HopfAlgebra:HopfAlgebra:7')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:HopfAlgebra">HopfAlgebra</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a></span> <a href="src/Math-Algebras-Structures.html#line-145" class="link">Source</a> <a href="#t:HopfAlgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:HopfAlgebra:HopfAlgebra:7" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:antipode">antipode</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a> <a href="src/Math-Algebras-Structures.html#antipode" class="link">Source</a> <a href="#v:antipode" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:HopfAlgebra:HopfAlgebra:8" class="instance expander" onclick="toggleSection('i:ic:HopfAlgebra:HopfAlgebra:8')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Math-Algebras-Structures.html#t:HopfAlgebra">HopfAlgebra</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymF">YSymF</a> a)</span> <a href="src/Math-Algebras-Structures.html#line-410" class="link">Source</a> <a href="#t:HopfAlgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:HopfAlgebra:HopfAlgebra:8" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:antipode">antipode</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymF">YSymF</a> a) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:YSymF">YSymF</a> a) <a href="src/Math-Algebras-Structures.html#antipode" class="link">Source</a> <a href="#v:antipode" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:HopfAlgebra:HopfAlgebra:9" class="instance expander" onclick="toggleSection('i:ic:HopfAlgebra:HopfAlgebra:9')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:HopfAlgebra">HopfAlgebra</a> k (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>)</span> <a href="src/Math-Algebras-Structures.html#line-288" class="link">Source</a> <a href="#t:HopfAlgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:HopfAlgebra:HopfAlgebra:9" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:antipode">antipode</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>) <a href="src/Math-Algebras-Structures.html#antipode" class="link">Source</a> <a href="#v:antipode" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:HopfAlgebra:HopfAlgebra:10" class="instance expander" onclick="toggleSection('i:ic:HopfAlgebra:HopfAlgebra:10')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a) => <a href="Math-Algebras-Structures.html#t:HopfAlgebra">HopfAlgebra</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:Shuffle">Shuffle</a> a)</span> <a href="src/Math-Algebras-Structures.html#line-86" class="link">Source</a> <a href="#t:HopfAlgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:HopfAlgebra:HopfAlgebra:10" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:antipode">antipode</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:Shuffle">Shuffle</a> a) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:Shuffle">Shuffle</a> a) <a href="src/Math-Algebras-Structures.html#antipode" class="link">Source</a> <a href="#v:antipode" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:HopfAlgebra:HopfAlgebra:11" class="instance expander" onclick="toggleSection('i:ic:HopfAlgebra:HopfAlgebra:11')"></span> <a href="Math-Algebras-Structures.html#t:HopfAlgebra">HopfAlgebra</a> <a href="Math-Algebra-Field-Base.html#t:Q">Q</a> (<a href="Math-Algebras-AffinePlane.html#t:SL2">SL2</a> <a href="Math-Algebras-AffinePlane.html#t:ABCD">ABCD</a>)</span> <a href="src/Math-Algebras-Structures.html#line-83" class="link">Source</a> <a href="#t:HopfAlgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:HopfAlgebra:HopfAlgebra:11" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:antipode">antipode</a> :: <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-AffinePlane.html#t:SL2">SL2</a> <a href="Math-Algebras-AffinePlane.html#t:ABCD">ABCD</a>) -> <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-AffinePlane.html#t:SL2">SL2</a> <a href="Math-Algebras-AffinePlane.html#t:ABCD">ABCD</a>) <a href="src/Math-Algebras-Structures.html#antipode" class="link">Source</a> <a href="#v:antipode" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:HopfAlgebra:HopfAlgebra:12" class="instance expander" onclick="toggleSection('i:ic:HopfAlgebra:HopfAlgebra:12')"></span> <a href="Math-Algebras-Structures.html#t:HopfAlgebra">HopfAlgebra</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-QuantumPlane.html#t:SL2q">SL2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>)</span> <a href="src/Math-Algebras-Structures.html#line-215" class="link">Source</a> <a href="#t:HopfAlgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:HopfAlgebra:HopfAlgebra:12" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:antipode">antipode</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-QuantumPlane.html#t:SL2q">SL2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</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-QuantumPlane.html#t:SL2q">SL2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) <a href="src/Math-Algebras-Structures.html#antipode" class="link">Source</a> <a href="#v:antipode" class="selflink">#</a></p></div></div></td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">newtype</span> <a id="t:SetCoalgebra" class="def">SetCoalgebra</a> b <a href="src/Math-Algebras-Structures.html#SetCoalgebra" class="link">Source</a> <a href="#t:SetCoalgebra" class="selflink">#</a></p><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a id="v:SC" class="def">SC</a> b</td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:SetCoalgebra" class="caption collapser" onclick="toggleSection('i:SetCoalgebra')">Instances</p><div id="section.i:SetCoalgebra" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:SetCoalgebra:Coalgebra:1" class="instance expander" onclick="toggleSection('i:id:SetCoalgebra:Coalgebra:1')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k (<a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b)</span> <a href="src/Math-Algebras-Structures.html#line-157" class="link">Source</a> <a href="#t:SetCoalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:SetCoalgebra:Coalgebra:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b) -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b) (<a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b)) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:SetCoalgebra:Eq:2" class="instance expander" onclick="toggleSection('i:id:SetCoalgebra:Eq:2')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> b => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> (<a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b)</span> <a href="src/Math-Algebras-Structures.html#line-155" class="link">Source</a> <a href="#t:SetCoalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:SetCoalgebra:Eq:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:-61--61-">(==)</a> :: <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-61--61-" class="selflink">#</a></p><p class="src"><a href="#v:-47--61-">(/=)</a> :: <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-47--61-" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:SetCoalgebra:Ord:3" class="instance expander" onclick="toggleSection('i:id:SetCoalgebra:Ord:3')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> b => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> (<a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b)</span> <a href="src/Math-Algebras-Structures.html#line-155" class="link">Source</a> <a href="#t:SetCoalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:SetCoalgebra:Ord:3" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:compare">compare</a> :: <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ordering">Ordering</a> <a href="#v:compare" class="selflink">#</a></p><p class="src"><a href="#v:-60-">(<)</a> :: <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-60-" class="selflink">#</a></p><p class="src"><a href="#v:-60--61-">(<=)</a> :: <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-60--61-" class="selflink">#</a></p><p class="src"><a href="#v:-62-">(>)</a> :: <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-62-" class="selflink">#</a></p><p class="src"><a href="#v:-62--61-">(>=)</a> :: <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-62--61-" class="selflink">#</a></p><p class="src"><a href="#v:max">max</a> :: <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b <a href="#v:max" class="selflink">#</a></p><p class="src"><a href="#v:min">min</a> :: <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b <a href="#v:min" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:SetCoalgebra:Show:4" class="instance expander" onclick="toggleSection('i:id:SetCoalgebra:Show:4')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:Show">Show</a> b => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:Show">Show</a> (<a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b)</span> <a href="src/Math-Algebras-Structures.html#line-155" class="link">Source</a> <a href="#t:SetCoalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:SetCoalgebra:Show:4" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:showsPrec">showsPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a> -> <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:ShowS">ShowS</a> <a href="#v:showsPrec" class="selflink">#</a></p><p class="src"><a href="#v:show">show</a> :: <a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a> <a href="#v:show" class="selflink">#</a></p><p class="src"><a href="#v:showList">showList</a> :: [<a href="Math-Algebras-Structures.html#t:SetCoalgebra">SetCoalgebra</a> b] -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:ShowS">ShowS</a> <a href="#v:showList" class="selflink">#</a></p></div></div></td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">newtype</span> <a id="t:MonoidCoalgebra" class="def">MonoidCoalgebra</a> m <a href="src/Math-Algebras-Structures.html#MonoidCoalgebra" class="link">Source</a> <a href="#t:MonoidCoalgebra" class="selflink">#</a></p><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a id="v:MC" class="def">MC</a> m</td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:MonoidCoalgebra" class="caption collapser" onclick="toggleSection('i:MonoidCoalgebra')">Instances</p><div id="section.i:MonoidCoalgebra" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:MonoidCoalgebra:Coalgebra:1" class="instance expander" onclick="toggleSection('i:id:MonoidCoalgebra:Coalgebra:1')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> m, <a href="Math-Algebras-Structures.html#t:Mon">Mon</a> m) => <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k (<a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m)</span> <a href="src/Math-Algebras-Structures.html#line-164" class="link">Source</a> <a href="#t:MonoidCoalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:MonoidCoalgebra:Coalgebra:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:counit">counit</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m) -> k <a href="src/Math-Algebras-Structures.html#counit" class="link">Source</a> <a href="#v:counit" class="selflink">#</a></p><p class="src"><a href="#v:comult">comult</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m) (<a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m)) <a href="src/Math-Algebras-Structures.html#comult" class="link">Source</a> <a href="#v:comult" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:MonoidCoalgebra:Eq:2" class="instance expander" onclick="toggleSection('i:id:MonoidCoalgebra:Eq:2')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> m => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> (<a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m)</span> <a href="src/Math-Algebras-Structures.html#line-162" class="link">Source</a> <a href="#t:MonoidCoalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:MonoidCoalgebra:Eq:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:-61--61-">(==)</a> :: <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-61--61-" class="selflink">#</a></p><p class="src"><a href="#v:-47--61-">(/=)</a> :: <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-47--61-" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:MonoidCoalgebra:Ord:3" class="instance expander" onclick="toggleSection('i:id:MonoidCoalgebra:Ord:3')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> m => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> (<a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m)</span> <a href="src/Math-Algebras-Structures.html#line-162" class="link">Source</a> <a href="#t:MonoidCoalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:MonoidCoalgebra:Ord:3" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:compare">compare</a> :: <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ordering">Ordering</a> <a href="#v:compare" class="selflink">#</a></p><p class="src"><a href="#v:-60-">(<)</a> :: <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-60-" class="selflink">#</a></p><p class="src"><a href="#v:-60--61-">(<=)</a> :: <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-60--61-" class="selflink">#</a></p><p class="src"><a href="#v:-62-">(>)</a> :: <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-62-" class="selflink">#</a></p><p class="src"><a href="#v:-62--61-">(>=)</a> :: <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-62--61-" class="selflink">#</a></p><p class="src"><a href="#v:max">max</a> :: <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m <a href="#v:max" class="selflink">#</a></p><p class="src"><a href="#v:min">min</a> :: <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m <a href="#v:min" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:MonoidCoalgebra:Show:4" class="instance expander" onclick="toggleSection('i:id:MonoidCoalgebra:Show:4')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:Show">Show</a> m => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:Show">Show</a> (<a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m)</span> <a href="src/Math-Algebras-Structures.html#line-162" class="link">Source</a> <a href="#t:MonoidCoalgebra" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:MonoidCoalgebra:Show:4" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:showsPrec">showsPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Int.html#t:Int">Int</a> -> <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:ShowS">ShowS</a> <a href="#v:showsPrec" class="selflink">#</a></p><p class="src"><a href="#v:show">show</a> :: <a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a> <a href="#v:show" class="selflink">#</a></p><p class="src"><a href="#v:showList">showList</a> :: [<a href="Math-Algebras-Structures.html#t:MonoidCoalgebra">MonoidCoalgebra</a> m] -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:ShowS">ShowS</a> <a href="#v:showList" class="selflink">#</a></p></div></div></td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">class</span> <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k a => <a id="t:Module" class="def">Module</a> k a m <span class="keyword">where</span> <a href="src/Math-Algebras-Structures.html#Module" class="link">Source</a> <a href="#t:Module" class="selflink">#</a></p><div class="subs minimal"><p class="caption">Minimal complete definition</p><p class="src"><a href="Math-Algebras-Structures.html#v:action">action</a></p></div><div class="subs methods"><p class="caption">Methods</p><p class="src"><a id="v:action" class="def">action</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> a m) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k m <a href="src/Math-Algebras-Structures.html#action" class="link">Source</a> <a href="#v:action" class="selflink">#</a></p></div><div class="subs instances"><p id="control.i:Module" class="caption collapser" onclick="toggleSection('i:Module')">Instances</p><div id="section.i:Module" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Module:Module:1" class="instance expander" onclick="toggleSection('i:ic:Module:Module:1')"></span> <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k a => <a href="Math-Algebras-Structures.html#t:Module">Module</a> k a a</span> <a href="src/Math-Algebras-Structures.html#line-186" class="link">Source</a> <a href="#t:Module" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Module:Module:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:action">action</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> a a) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k a <a href="src/Math-Algebras-Structures.html#action" class="link">Source</a> <a href="#v:action" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Module:Module:2" class="instance expander" onclick="toggleSection('i:ic:Module:Module:2')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:Module">Module</a> k <a href="Math-Algebras-Matrix.html#t:Mat2">Mat2</a> <a href="Math-Algebras-VectorSpace.html#t:EBasis">EBasis</a></span> <a href="src/Math-Algebras-Structures.html#line-38" class="link">Source</a> <a href="#t:Module" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Module:Module:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:action">action</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Algebras-Matrix.html#t:Mat2">Mat2</a> <a href="Math-Algebras-VectorSpace.html#t:EBasis">EBasis</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k <a href="Math-Algebras-VectorSpace.html#t:EBasis">EBasis</a> <a href="src/Math-Algebras-Structures.html#action" class="link">Source</a> <a href="#v:action" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Module:Module:3" class="instance expander" onclick="toggleSection('i:ic:Module:Module:3')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> u, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> v, <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</a> k a, <a href="Math-Algebras-Structures.html#t:Module">Module</a> k a u, <a href="Math-Algebras-Structures.html#t:Module">Module</a> k a v) => <a href="Math-Algebras-Structures.html#t:Module">Module</a> k a (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> u v)</span> <a href="src/Math-Algebras-Structures.html#line-202" class="link">Source</a> <a href="#t:Module" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Module:Module:3" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:action">action</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> a (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> u v)) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> u v) <a href="src/Math-Algebras-Structures.html#action" class="link">Source</a> <a href="#v:action" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Module:Module:4" class="instance expander" onclick="toggleSection('i:ic:Module:Module:4')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> u, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> v, <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k a, <a href="Math-Algebras-Structures.html#t:Module">Module</a> k a u, <a href="Math-Algebras-Structures.html#t:Module">Module</a> k a v) => <a href="Math-Algebras-Structures.html#t:Module">Module</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> a a) (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> u v)</span> <a href="src/Math-Algebras-Structures.html#line-196" class="link">Source</a> <a href="#t:Module" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Module:Module:4" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:action">action</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> a a) (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> u v)) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> u v) <a href="src/Math-Algebras-Structures.html#action" class="link">Source</a> <a href="#v:action" class="selflink">#</a></p></div></div></td></tr></table></div></div></div><div class="top"><p class="src"><a id="v:-42-." class="def">(*.)</a> :: (<a href="Math-Algebras-Structures.html#t:Module">Module</a> k a m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k a -> <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-Structures.html#%2A." class="link">Source</a> <a href="#v:-42-." class="selflink">#</a></p></div><div class="top"><p class="src"><span class="keyword">class</span> <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k c => <a id="t:Comodule" class="def">Comodule</a> k c n <span class="keyword">where</span> <a href="src/Math-Algebras-Structures.html#Comodule" class="link">Source</a> <a href="#t:Comodule" class="selflink">#</a></p><div class="subs minimal"><p class="caption">Minimal complete definition</p><p class="src"><a href="Math-Algebras-Structures.html#v:coaction">coaction</a></p></div><div class="subs methods"><p class="caption">Methods</p><p class="src"><a id="v:coaction" class="def">coaction</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k n -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> c n) <a href="src/Math-Algebras-Structures.html#coaction" class="link">Source</a> <a href="#v:coaction" class="selflink">#</a></p></div><div class="subs instances"><p id="control.i:Comodule" class="caption collapser" onclick="toggleSection('i:Comodule')">Instances</p><div id="section.i:Comodule" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Comodule:Comodule:1" class="instance expander" onclick="toggleSection('i:ic:Comodule:Comodule:1')"></span> <a href="Math-Algebras-Structures.html#t:Coalgebra">Coalgebra</a> k c => <a href="Math-Algebras-Structures.html#t:Comodule">Comodule</a> k c c</span> <a href="src/Math-Algebras-Structures.html#line-189" class="link">Source</a> <a href="#t:Comodule" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Comodule:Comodule:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:coaction">coaction</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k c -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> c c) <a href="src/Math-Algebras-Structures.html#coaction" class="link">Source</a> <a href="#v:coaction" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Comodule:Comodule:2" class="instance expander" onclick="toggleSection('i:ic:Comodule:Comodule:2')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> n, <a href="Math-Algebras-Structures.html#t:Bialgebra">Bialgebra</a> k a, <a href="Math-Algebras-Structures.html#t:Comodule">Comodule</a> k a m, <a href="Math-Algebras-Structures.html#t:Comodule">Comodule</a> k a n) => <a href="Math-Algebras-Structures.html#t:Comodule">Comodule</a> k a (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> m n)</span> <a href="src/Math-Algebras-Structures.html#line-212" class="link">Source</a> <a href="#t:Comodule" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Comodule:Comodule:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:coaction">coaction</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> m n) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> a (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> m n)) <a href="src/Math-Algebras-Structures.html#coaction" class="link">Source</a> <a href="#v:coaction" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:Comodule:Comodule:3" class="instance expander" onclick="toggleSection('i:ic:Comodule:Comodule:3')"></span> <a href="Math-Algebras-Structures.html#t:Comodule">Comodule</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-QuantumPlane.html#t:M2q">M2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) (<a href="Math-QuantumAlgebra-QuantumPlane.html#t:Aq20">Aq20</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>)</span> <a href="src/Math-Algebras-Structures.html#line-164" class="link">Source</a> <a href="#t:Comodule" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:Comodule:Comodule:3" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:coaction">coaction</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-QuantumPlane.html#t:Aq20">Aq20</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</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-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-QuantumAlgebra-QuantumPlane.html#t:M2q">M2q</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>) (<a href="Math-QuantumAlgebra-QuantumPlane.html#t:Aq20">Aq20</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-String.html#t:String">String</a>)) <a href="src/Math-Algebras-Structures.html#coaction" class="link">Source</a> <a href="#v:coaction" class="selflink">#</a></p></div></div></td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">class</span> <a id="t:HasPairing" class="def">HasPairing</a> k u v <span class="keyword">where</span> <a href="src/Math-Algebras-Structures.html#HasPairing" class="link">Source</a> <a href="#t:HasPairing" class="selflink">#</a></p><div class="doc"><p>A pairing is a non-degenerate bilinear form U x V -> k.
We are typically interested in pairings having additional properties. For example:</p><ul><li>A bialgebra pairing is a pairing between bialgebras A and B such that the mult in A is adjoint to the comult in B, and vice versa, and the unit in A is adjoint to the counit in B, and vice versa.</li><li>A Hopf pairing is a bialgebra pairing between Hopf algebras A and B such that the antipodes in A and B are adjoint.</li></ul></div><div class="subs minimal"><p class="caption">Minimal complete definition</p><p class="src"><a href="Math-Algebras-Structures.html#v:pairing">pairing</a></p></div><div class="subs methods"><p class="caption">Methods</p><p class="src"><a id="v:pairing" class="def">pairing</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> u v) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k () <a href="src/Math-Algebras-Structures.html#pairing" class="link">Source</a> <a href="#v:pairing" class="selflink">#</a></p></div><div class="subs instances"><p id="control.i:HasPairing" class="caption collapser" onclick="toggleSection('i:HasPairing')">Instances</p><div id="section.i:HasPairing" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:HasPairing:HasPairing:1" class="instance expander" onclick="toggleSection('i:ic:HasPairing:HasPairing:1')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:HasPairing">HasPairing</a> k () ()</span> <a href="src/Math-Algebras-Structures.html#line-233" class="link">Source</a> <a href="#t:HasPairing" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:HasPairing:HasPairing:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:pairing">pairing</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> () ()) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k () <a href="src/Math-Algebras-Structures.html#pairing" class="link">Source</a> <a href="#v:pairing" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:HasPairing:HasPairing:2" class="instance expander" onclick="toggleSection('i:ic:HasPairing:HasPairing:2')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:HasPairing">HasPairing</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:NSym">NSym</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymM">QSymM</a></span> <a href="src/Math-Algebras-Structures.html#line-915" class="link">Source</a> <a href="#t:HasPairing" class="selflink">#</a></td><td class="doc"><p>A duality pairing between NSym and QSymM (monomial basis), showing that NSym and QSym are dual.</p></td></tr><tr><td colspan="2"><div id="section.i:ic:HasPairing:HasPairing:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:pairing">pairing</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:NSym">NSym</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:QSymM">QSymM</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k () <a href="src/Math-Algebras-Structures.html#pairing" class="link">Source</a> <a href="#v:pairing" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:HasPairing:HasPairing:3" class="instance expander" onclick="toggleSection('i:ic:HasPairing:HasPairing:3')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:HasPairing">HasPairing</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymH">SymH</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymM">SymM</a></span> <a href="src/Math-Algebras-Structures.html#line-908" class="link">Source</a> <a href="#t:HasPairing" class="selflink">#</a></td><td class="doc"><p>A duality pairing between the complete and monomial bases of Sym, showing that Sym is self-dual.</p></td></tr><tr><td colspan="2"><div id="section.i:ic:HasPairing:HasPairing:3" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:pairing">pairing</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymH">SymH</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SymM">SymM</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k () <a href="src/Math-Algebras-Structures.html#pairing" class="link">Source</a> <a href="#v:pairing" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:HasPairing:HasPairing:4" class="instance expander" onclick="toggleSection('i:ic:HasPairing:HasPairing:4')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:HasPairing">HasPairing</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a></span> <a href="src/Math-Algebras-Structures.html#line-165" class="link">Source</a> <a href="#t:HasPairing" class="selflink">#</a></td><td class="doc"><p>A pairing showing that SSym is self-adjoint</p></td></tr><tr><td colspan="2"><div id="section.i:ic:HasPairing:HasPairing:4" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:pairing">pairing</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k () <a href="src/Math-Algebras-Structures.html#pairing" class="link">Source</a> <a href="#v:pairing" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:HasPairing:HasPairing:5" class="instance expander" onclick="toggleSection('i:ic:HasPairing:HasPairing:5')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k) => <a href="Math-Algebras-Structures.html#t:HasPairing">HasPairing</a> k <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a> (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>)</span> <a href="src/Math-Algebras-Structures.html#line-295" class="link">Source</a> <a href="#t:HasPairing" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:HasPairing:HasPairing:5" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:pairing">pairing</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a> (<a href="Math-Algebras-VectorSpace.html#t:Dual">Dual</a> <a href="Math-Combinatorics-CombinatorialHopfAlgebra.html#t:SSymF">SSymF</a>)) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k () <a href="src/Math-Algebras-Structures.html#pairing" class="link">Source</a> <a href="#v:pairing" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:ic:HasPairing:HasPairing:6" class="instance expander" onclick="toggleSection('i:ic:HasPairing:HasPairing:6')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="Math-Algebras-Structures.html#t:HasPairing">HasPairing</a> k u v, <a href="Math-Algebras-Structures.html#t:HasPairing">HasPairing</a> k u' v') => <a href="Math-Algebras-Structures.html#t:HasPairing">HasPairing</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> u u') (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> v v')</span> <a href="src/Math-Algebras-Structures.html#line-236" class="link">Source</a> <a href="#t:HasPairing" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:ic:HasPairing:HasPairing:6" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:pairing">pairing</a> :: <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> u u') (<a href="Math-Algebras-TensorProduct.html#t:Tensor">Tensor</a> v v')) -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k () <a href="src/Math-Algebras-Structures.html#pairing" class="link">Source</a> <a href="#v:pairing" class="selflink">#</a></p></div></div></td></tr></table></div></div></div><div class="top"><p class="src"><a id="v:pairing-39-" class="def">pairing'</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="Math-Algebras-Structures.html#t:HasPairing">HasPairing</a> k u v) => <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k u -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k v -> k <a href="src/Math-Algebras-Structures.html#pairing%27" class="link">Source</a> <a href="#v:pairing-39-" class="selflink">#</a></p><div class="doc"><p>The pairing function with a more Haskellish type signature</p></div></div><h1>Orphan instances</h1><div id="section.orphans" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:o:ic:Num:Num:1" class="instance expander" onclick="toggleSection('i:o:ic:Num:Num:1')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> k, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Eq.html#t:Eq">Eq</a> b, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Data-Ord.html#t:Ord">Ord</a> b, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Text-Show.html#t:Show">Show</a> b, <a href="Math-Algebras-Structures.html#t:Algebra">Algebra</a> k b) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Num">Num</a> (<a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k b)</span> <a href="src/Math-Algebras-Structures.html#line-57" class="link">Source</a> <a href="#v:-36-fNumVect" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:o:ic:Num:Num:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:-43-">(+)</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="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k b <a href="#v:-43-" class="selflink">#</a></p><p class="src"><a href="#v:-45-">(-)</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="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k b <a href="#v:-45-" class="selflink">#</a></p><p class="src"><a href="#v:-42-">(*)</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="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k b <a href="#v:-42-" class="selflink">#</a></p><p class="src"><a href="#v:negate">negate</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="#v:negate" class="selflink">#</a></p><p class="src"><a href="#v:abs">abs</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="#v:abs" class="selflink">#</a></p><p class="src"><a href="#v:signum">signum</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="#v:signum" class="selflink">#</a></p><p class="src"><a href="#v:fromInteger">fromInteger</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.0.0/Prelude.html#t:Integer">Integer</a> -> <a href="Math-Algebras-VectorSpace.html#t:Vect">Vect</a> k b <a href="#v:fromInteger" class="selflink">#</a></p></div></div></td></tr></table></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.17.2</p></div></body></html>
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