algebra-3.1: Constructive abstract algebra

Safe Haskell | None

Numeric.Module.Class

Contents

- Module over semirings

Synopsis

- class (Semiring r, Additive m) => LeftModule r m where
  - (.*) :: r -> m -> m
- class (Semiring r, Additive m) => RightModule r m where
  - (*.) :: m -> r -> m
- class (LeftModule r m, RightModule r m) => Module r m

# Module over semirings

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

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) |
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) |
(LeftModule r a, LeftModule r b) => LeftModule r (a, b) |
(HasTrie e, LeftModule r m) => LeftModule r (:->: e m) |
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 where Source

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) |
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) |
(RightModule r a, RightModule r b) => RightModule r (a, b) |
(HasTrie e, RightModule r m) => RightModule r (:->: e m) |
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 |