Safe Haskell	Safe-Inferred

Numeric.Module.Class

Contents

Module over semirings

Synopsis

Module over semirings

class (Semiring r, Additive m) => LeftModule r m whereSource

Methods

(.*) :: r -> m -> mSource

Instances

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

class (Semiring r, Additive m) => RightModule r m whereSource

Methods

(*.) :: m -> r -> mSource

Instances

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

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

Instances

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