[auto ekmett@gmail.com**20090402072556] { addfile ./doc/html/monoids/Data-Field-VectorSpace.html addfile ./doc/html/monoids/Data-Ring-Algebra.html addfile ./doc/html/monoids/src/Data-Field-VectorSpace.html addfile ./doc/html/monoids/src/Data-Ring-Algebra.html hunk ./doc/html/monoids/Data-Field-VectorSpace.html 1 + + +Data.Field.VectorSpace
monoids-0.1.23: Monoids, specialized containers and a general map/reduce frameworkSource codeContentsIndex
Data.Field.VectorSpace
Documentation
module Data.Field
module Data.Ring.Module
class (Field f, Module f g) => VectorSpace f g Source
Produced by Haddock version 2.3.0
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monoids-0.1.23: Monoids, specialized containers and a general map/reduce frameworkSource codeContentsIndex
Data.Ring.Algebra
Synopsis
module Data.Ring.Module
class (Module r m, Multiplicative m) => Algebra r m
Documentation
module Data.Ring.Module
class (Module r m, Multiplicative m) => Algebra r m Source
r *. (x * y) = (r *. x) * y = x * (r *. y) +
Produced by Haddock version 2.3.0
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Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Algebra, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Field.VectorSpaceData.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.FieldData.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Algebra, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Field.VectorSpace, Data.Monoid.Applicative, Data.Ring.Module.AutomaticDifferentiation, Data.Monoid.Applicative, Data.Ring.Algebra, Data.Ring.Module.AutomaticDifferentiation, Data.Field.VectorSpace, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Semi.Natural, Data.Ring.Algebra, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Field.VectorSpace, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Algebra, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Field.VectorSpace, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Ring.Semi.Natural, Data.Ring.Algebra, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Field.VectorSpaceData.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.FieldData.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Algebra, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Field.VectorSpaceData.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.FieldData.Monoid.Reducer, Data.Monoid.Reducer.Char, Data.Monoid.Lexical.UTF8.Decoder, Data.Monoid.Reducer.With, Data.Monoid.Generator, Data.Monoid.Lexical.SourcePosition, Data.Monoid.Lexical.Words, Data.Monoid.Self, Data.Monoid.Generator.LZ78, Data.Monoid.FromString, Data.Monoid.Categorical, Data.Monoid.Additive, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Monoid.Combinators, Data.Monoid.Generator.Free, Data.Monoid.Generator.RLE, Data.Ring.Semi.Natural, Data.Ring.Algebra, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Field.VectorSpace, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Semi.Natural, Data.Ring.Algebra, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Field.VectorSpace, Data.Group.Multiplicative.Sugar, Data.Field, Data.Group.Multiplicative.Sugar, Data.Field, Data.Field.VectorSpaceVectorSpaceData.Field.VectorSpace, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Semi.Natural, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Monoid.Additive.Sugar, Data.Monoid.Multiplicative, Data.Monoid.Multiplicative.Sugar, Data.Ring.Semi.Near, Data.Ring.Semi, Data.Ring.Semi.Ord, Data.Ring.Semi.Tropical, Data.Ring.Sugar, Data.Group.Multiplicative, Data.Group, Data.Group.Combinators, Data.Group.Sugar, Data.Group.Multiplicative.Sugar, Data.Ring, Data.Ring.Boolean, Data.Ring.FromNum, Data.Ring.ModularArithmetic, Data.Ring.Module, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Semi.Natural, Data.Ring.Algebra, Data.Ring.Module.AutomaticDifferentiation, Data.Field, Data.Field.VectorSpacemonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.23: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.23: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.22: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.23: Monoids, specialized containers and a general map/reduce frameworkshow/hide
Data.Field.VectorSpace
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Data.Ring.Algebra
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+ + + +Data/Field/VectorSpace.hs + + + +
{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances, FlexibleContexts #-}
+module Data.Field.VectorSpace 
+    ( module Data.Field
+    , module Data.Ring.Module
+    , VectorSpace
+    ) where
+
+import Data.Field
+import Data.Ring.Module
+    
+class (Field f, Module f g) => VectorSpace f g
+
+ hunk ./doc/html/monoids/src/Data-Ring-Algebra.html 1 + + + + +Data/Ring/Algebra.hs + + + +
{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances, FlexibleContexts #-}
+module Data.Ring.Algebra
+    ( module Data.Ring.Module
+    , Algebra
+    ) where
+
+import Data.Ring.Module
+
+-- |  r *. (x * y) = (r *. x) * y = x * (r *. y)
+class (r `Module` m, Multiplicative m) => Algebra r m 
+
+ }