Numeric.Module.Class

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