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Language	Haskell98

Numeric.Module.Class

Contents

Module over semirings

Synopsis

Module over semirings

class (Semiring r, Additive m) => LeftModule r m where #

Minimal complete definition

(.*)

Methods

(.*) :: r -> m -> m infixl 7 #

Instances

LeftModule Integer Int #
Methods (.*) :: Integer -> Int -> Int #
LeftModule Integer Int8 #
Methods (.*) :: Integer -> Int8 -> Int8 #
LeftModule Integer Int16 #
Methods (.*) :: Integer -> Int16 -> Int16 #
LeftModule Integer Int32 #
Methods (.*) :: Integer -> Int32 -> Int32 #
LeftModule Integer Int64 #
Methods (.*) :: Integer -> Int64 -> Int64 #
LeftModule Integer Integer #
Methods (.*) :: Integer -> Integer -> Integer #
LeftModule Integer Word #
Methods (.*) :: Integer -> Word -> Word #
LeftModule Integer Word8 #
Methods (.*) :: Integer -> Word8 -> Word8 #
LeftModule Integer Word16 #
Methods (.*) :: Integer -> Word16 -> Word16 #
LeftModule Integer Word32 #
Methods (.*) :: Integer -> Word32 -> Word32 #
LeftModule Integer Word64 #
Methods (.*) :: Integer -> Word64 -> Word64 #
LeftModule Integer Euclidean #
Methods (.*) :: Integer -> Euclidean -> Euclidean #
LeftModule Natural Bool #
Methods (.*) :: Natural -> Bool -> Bool #
LeftModule Natural Int #
Methods (.*) :: Natural -> Int -> Int #
LeftModule Natural Int8 #
Methods (.*) :: Natural -> Int8 -> Int8 #
LeftModule Natural Int16 #
Methods (.*) :: Natural -> Int16 -> Int16 #
LeftModule Natural Int32 #
Methods (.*) :: Natural -> Int32 -> Int32 #
LeftModule Natural Int64 #
Methods (.*) :: Natural -> Int64 -> Int64 #
LeftModule Natural Integer #
Methods (.*) :: Natural -> Integer -> Integer #
LeftModule Natural Natural #
Methods (.*) :: Natural -> Natural -> Natural #
LeftModule Natural Word #
Methods (.*) :: Natural -> Word -> Word #
LeftModule Natural Word8 #
Methods (.*) :: Natural -> Word8 -> Word8 #
LeftModule Natural Word16 #
Methods (.*) :: Natural -> Word16 -> Word16 #
LeftModule Natural Word32 #
Methods (.*) :: Natural -> Word32 -> Word32 #
LeftModule Natural Word64 #
Methods (.*) :: Natural -> Word64 -> Word64 #
LeftModule Natural Euclidean #
Methods (.*) :: Natural -> Euclidean -> Euclidean #
Additive m => LeftModule () m #
Methods (.*) :: () -> m -> m #
Semiring r => LeftModule r () #
Methods (.*) :: r -> () -> () #
Group r => LeftModule Integer (ZeroRng r) #
Methods (.*) :: Integer -> ZeroRng r -> ZeroRng r #
(Abelian r, Group r) => LeftModule Integer (RngRing r) #
Methods (.*) :: Integer -> RngRing r -> RngRing r #
Division r => LeftModule Integer (Log r) #
Methods (.*) :: Integer -> Log r -> Log r #
GCDDomain d => LeftModule Integer (Fraction d) #
Methods (.*) :: Integer -> Fraction d -> Fraction d #
Monoidal r => LeftModule Natural (ZeroRng r) #
Methods (.*) :: Natural -> ZeroRng r -> ZeroRng r #
(Abelian r, Monoidal r) => LeftModule Natural (RngRing r) #
Methods (.*) :: Natural -> RngRing r -> RngRing r #
Unital r => LeftModule Natural (Log r) #
Methods (.*) :: Natural -> Log r -> Log r #
LeftModule Natural (BasisCoblade m) #
Methods (.*) :: Natural -> BasisCoblade m -> BasisCoblade m #
GCDDomain d => LeftModule Natural (Fraction d) #
Methods (.*) :: Natural -> Fraction d -> Fraction d #
RightModule r s => LeftModule r (Opposite s) #
Methods (.*) :: r -> Opposite s -> Opposite s #
LeftModule r m => LeftModule r (End m) #
Methods (.*) :: r -> End m -> End m #
LeftModule r s => LeftModule r (Trig s) #
Methods (.*) :: r -> Trig s -> Trig s #
LeftModule r s => LeftModule r (Quaternion' s) #
Methods (.*) :: r -> Quaternion' s -> Quaternion' s #
LeftModule r s => LeftModule r (Hyper s) #
Methods (.*) :: r -> Hyper s -> Hyper s #
LeftModule r s => LeftModule r (Dual' s) #
Methods (.*) :: r -> Dual' s -> Dual' s #
LeftModule r s => LeftModule r (Quaternion s) #
Methods (.*) :: r -> Quaternion s -> Quaternion s #
LeftModule r s => LeftModule r (Hyper' s) #
Methods (.*) :: r -> Hyper' s -> Hyper' s #
LeftModule r s => LeftModule r (Dual s) #
Methods (.*) :: r -> Dual s -> Dual s #
LeftModule r s => LeftModule r (Complex s) #
Methods (.*) :: r -> Complex s -> Complex s #
(LeftModule r a, LeftModule r b) => LeftModule r (a, b) #
Methods (.*) :: r -> (a, b) -> (a, b) #
LeftModule r m => LeftModule r (e -> m) #
Methods (.*) :: r -> (e -> m) -> e -> m #
LeftModule r s => LeftModule r (Covector s m) #
Methods (.*) :: r -> Covector s m -> Covector s m #
(LeftModule r a, LeftModule r b, LeftModule r c) => LeftModule r (a, b, c) #
Methods (.*) :: r -> (a, b, c) -> (a, b, c) #
LeftModule r s => LeftModule r (Map s b m) #
Methods (.*) :: r -> Map s b m -> Map s b m #
(LeftModule r a, LeftModule r b, LeftModule r c, LeftModule r d) => LeftModule r (a, b, c, d) #
Methods (.*) :: r -> (a, b, c, d) -> (a, b, c, d) #
(LeftModule r a, LeftModule r b, LeftModule r c, LeftModule r d, LeftModule r e) => LeftModule r (a, b, c, d, e) #
Methods (.*) :: r -> (a, b, c, d, e) -> (a, b, c, d, e) #
Rng s => LeftModule (RngRing s) (RngRing s) #
Methods (.*) :: RngRing s -> RngRing s -> RngRing s #
Semiring r => LeftModule (Opposite r) (Opposite r) #
Methods (.*) :: Opposite r -> Opposite r -> Opposite r #
(Monoidal m, Abelian m) => LeftModule (End m) (End m) #
Methods (.*) :: End m -> End m -> End m #
(Commutative r, Rng r) => LeftModule (Trig r) (Trig r) #
Methods (.*) :: Trig r -> Trig r -> Trig r #
(TriviallyInvolutive r, Rng r) => LeftModule (Quaternion' r) (Quaternion' r) #
Methods (.*) :: Quaternion' r -> Quaternion' r -> Quaternion' r #
(Commutative r, Semiring r) => LeftModule (Hyper r) (Hyper r) #
Methods (.*) :: Hyper r -> Hyper r -> Hyper r #
(Commutative r, Rng r) => LeftModule (Dual' r) (Dual' r) #
Methods (.*) :: Dual' r -> Dual' r -> Dual' r #
(TriviallyInvolutive r, Rng r) => LeftModule (Quaternion r) (Quaternion r) #
Methods (.*) :: Quaternion r -> Quaternion r -> Quaternion r #
(Commutative r, Semiring r) => LeftModule (Hyper' r) (Hyper' r) #
Methods (.*) :: Hyper' r -> Hyper' r -> Hyper' r #
(Commutative r, Rng r) => LeftModule (Dual r) (Dual r) #
Methods (.*) :: Dual r -> Dual r -> Dual r #
(Commutative r, Rng r) => LeftModule (Complex r) (Complex r) #
Methods (.*) :: Complex r -> Complex r -> Complex r #
Coalgebra r m => LeftModule (Covector r m) (Covector r m) #
Methods (.*) :: Covector r m -> Covector r m -> Covector r m #
Coalgebra r m => LeftModule (Map r b m) (Map r b m) #
Methods (.*) :: Map r b m -> Map r b m -> Map r b m #

class (Semiring r, Additive m) => RightModule r m where #

Minimal complete definition

(*.)

Methods

(*.) :: m -> r -> m infixl 7 #

Instances

RightModule Integer Int #
Methods (*.) :: Int -> Integer -> Int #
RightModule Integer Int8 #
Methods (*.) :: Int8 -> Integer -> Int8 #
RightModule Integer Int16 #
Methods (*.) :: Int16 -> Integer -> Int16 #
RightModule Integer Int32 #
Methods (*.) :: Int32 -> Integer -> Int32 #
RightModule Integer Int64 #
Methods (*.) :: Int64 -> Integer -> Int64 #
RightModule Integer Integer #
Methods (*.) :: Integer -> Integer -> Integer #
RightModule Integer Word #
Methods (*.) :: Word -> Integer -> Word #
RightModule Integer Word8 #
Methods (*.) :: Word8 -> Integer -> Word8 #
RightModule Integer Word16 #
Methods (*.) :: Word16 -> Integer -> Word16 #
RightModule Integer Word32 #
Methods (*.) :: Word32 -> Integer -> Word32 #
RightModule Integer Word64 #
Methods (*.) :: Word64 -> Integer -> Word64 #
RightModule Integer Euclidean #
Methods (*.) :: Euclidean -> Integer -> Euclidean #
RightModule Natural Bool #
Methods (*.) :: Bool -> Natural -> Bool #
RightModule Natural Int #
Methods (*.) :: Int -> Natural -> Int #
RightModule Natural Int8 #
Methods (*.) :: Int8 -> Natural -> Int8 #
RightModule Natural Int16 #
Methods (*.) :: Int16 -> Natural -> Int16 #
RightModule Natural Int32 #
Methods (*.) :: Int32 -> Natural -> Int32 #
RightModule Natural Int64 #
Methods (*.) :: Int64 -> Natural -> Int64 #
RightModule Natural Integer #
Methods (*.) :: Integer -> Natural -> Integer #
RightModule Natural Natural #
Methods (*.) :: Natural -> Natural -> Natural #
RightModule Natural Word #
Methods (*.) :: Word -> Natural -> Word #
RightModule Natural Word8 #
Methods (*.) :: Word8 -> Natural -> Word8 #
RightModule Natural Word16 #
Methods (*.) :: Word16 -> Natural -> Word16 #
RightModule Natural Word32 #
Methods (*.) :: Word32 -> Natural -> Word32 #
RightModule Natural Word64 #
Methods (*.) :: Word64 -> Natural -> Word64 #
RightModule Natural Euclidean #
Methods (*.) :: Euclidean -> Natural -> Euclidean #
Additive m => RightModule () m #
Methods (*.) :: m -> () -> m #
Semiring r => RightModule r () #
Methods (*.) :: () -> r -> () #
Group r => RightModule Integer (ZeroRng r) #
Methods (*.) :: ZeroRng r -> Integer -> ZeroRng r #
(Abelian r, Group r) => RightModule Integer (RngRing r) #
Methods (*.) :: RngRing r -> Integer -> RngRing r #
Division r => RightModule Integer (Log r) #
Methods (*.) :: Log r -> Integer -> Log r #
GCDDomain d => RightModule Integer (Fraction d) #
Methods (*.) :: Fraction d -> Integer -> Fraction d #
Monoidal r => RightModule Natural (ZeroRng r) #
Methods (*.) :: ZeroRng r -> Natural -> ZeroRng r #
(Abelian r, Monoidal r) => RightModule Natural (RngRing r) #
Methods (*.) :: RngRing r -> Natural -> RngRing r #
Unital r => RightModule Natural (Log r) #
Methods (*.) :: Log r -> Natural -> Log r #
RightModule Natural (BasisCoblade m) #
Methods (*.) :: BasisCoblade m -> Natural -> BasisCoblade m #
GCDDomain d => RightModule Natural (Fraction d) #
Methods (*.) :: Fraction d -> Natural -> Fraction d #
LeftModule r s => RightModule r (Opposite s) #
Methods (*.) :: Opposite s -> r -> Opposite s #
RightModule r m => RightModule r (End m) #
Methods (*.) :: End m -> r -> End m #
RightModule r s => RightModule r (Trig s) #
Methods (*.) :: Trig s -> r -> Trig s #
RightModule r s => RightModule r (Quaternion' s) #
Methods (*.) :: Quaternion' s -> r -> Quaternion' s #
RightModule r s => RightModule r (Hyper s) #
Methods (*.) :: Hyper s -> r -> Hyper s #
RightModule r s => RightModule r (Dual' s) #
Methods (*.) :: Dual' s -> r -> Dual' s #
RightModule r s => RightModule r (Quaternion s) #
Methods (*.) :: Quaternion s -> r -> Quaternion s #
RightModule r s => RightModule r (Hyper' s) #
Methods (*.) :: Hyper' s -> r -> Hyper' s #
RightModule r s => RightModule r (Dual s) #
Methods (*.) :: Dual s -> r -> Dual s #
RightModule r s => RightModule r (Complex s) #
Methods (*.) :: Complex s -> r -> Complex s #
(RightModule r a, RightModule r b) => RightModule r (a, b) #
Methods (*.) :: (a, b) -> r -> (a, b) #
RightModule r m => RightModule r (e -> m) #
Methods (*.) :: (e -> m) -> r -> e -> m #
RightModule r s => RightModule r (Covector s m) #
Methods (*.) :: Covector s m -> r -> Covector s m #
(RightModule r a, RightModule r b, RightModule r c) => RightModule r (a, b, c) #
Methods (*.) :: (a, b, c) -> r -> (a, b, c) #
RightModule r s => RightModule r (Map s b m) #
Methods (*.) :: Map s b m -> r -> Map s b m #
(RightModule r a, RightModule r b, RightModule r c, RightModule r d) => RightModule r (a, b, c, d) #
Methods (*.) :: (a, b, c, d) -> r -> (a, b, c, d) #
(RightModule r a, RightModule r b, RightModule r c, RightModule r d, RightModule r e) => RightModule r (a, b, c, d, e) #
Methods (*.) :: (a, b, c, d, e) -> r -> (a, b, c, d, e) #
Rng s => RightModule (RngRing s) (RngRing s) #
Methods (*.) :: RngRing s -> RngRing s -> RngRing s #
Semiring r => RightModule (Opposite r) (Opposite r) #
Methods (*.) :: Opposite r -> Opposite r -> Opposite r #
(Monoidal m, Abelian m) => RightModule (End m) (End m) #
Methods (*.) :: End m -> End m -> End m #
(Commutative r, Rng r) => RightModule (Trig r) (Trig r) #
Methods (*.) :: Trig r -> Trig r -> Trig r #
(TriviallyInvolutive r, Rng r) => RightModule (Quaternion' r) (Quaternion' r) #
Methods (*.) :: Quaternion' r -> Quaternion' r -> Quaternion' r #
(Commutative r, Semiring r) => RightModule (Hyper r) (Hyper r) #
Methods (*.) :: Hyper r -> Hyper r -> Hyper r #
(Commutative r, Rng r) => RightModule (Dual' r) (Dual' r) #
Methods (*.) :: Dual' r -> Dual' r -> Dual' r #
(TriviallyInvolutive r, Rng r) => RightModule (Quaternion r) (Quaternion r) #
Methods (*.) :: Quaternion r -> Quaternion r -> Quaternion r #
(Commutative r, Semiring r) => RightModule (Hyper' r) (Hyper' r) #
Methods (*.) :: Hyper' r -> Hyper' r -> Hyper' r #
(Commutative r, Rng r) => RightModule (Dual r) (Dual r) #
Methods (*.) :: Dual r -> Dual r -> Dual r #
(Commutative r, Rng r) => RightModule (Complex r) (Complex r) #
Methods (*.) :: Complex r -> Complex r -> Complex r #
Coalgebra r m => RightModule (Covector r m) (Covector r m) #
Methods (*.) :: Covector r m -> Covector r m -> Covector r m #
Coalgebra r m => RightModule (Map r b m) (Map r b m) #
Methods (*.) :: Map r b m -> Map r b m -> Map r b m #

class (LeftModule r m, RightModule r m) => Module r m #

Instances

(LeftModule r m, RightModule r m) => Module r m #