algebra-3.1: Constructive abstract algebra

Safe Haskell | None

Numeric.Algebra.Idempotent

Contents

- Idempotent algebras

Synopsis

- class Multiplicative r => Band r
- pow1pBand :: Whole n => r -> n -> r
- powBand :: (Unital r, Whole n) => r -> n -> r
- class Algebra r a => IdempotentAlgebra r a
- class Coalgebra r c => IdempotentCoalgebra r c
- class (Bialgebra r h, IdempotentAlgebra r h, IdempotentCoalgebra r h) => IdempotentBialgebra r h

# Documentation

class Multiplicative r => Band r Source

An multiplicative semigroup with idempotent multiplication.

     a * a = a

Instances

Band Bool |
Band () |
Idempotent r => Band (Exp r) |
Band r => Band (Opposite r) |
(Band a, Band b) => Band (a, b) |
Band (Rect i j) |
(Idempotent r, IdempotentCoalgebra r a) => Band (Covector r a) |
(Band a, Band b, Band c) => Band (a, b, c) |
(Band a, Band b, Band c, Band d) => Band (a, b, c, d) |
(Band a, Band b, Band c, Band d, Band e) => Band (a, b, c, d, e) |

pow1pBand :: Whole n => r -> n -> rSource

powBand :: (Unital r, Whole n) => r -> n -> rSource

# Idempotent algebras

class Algebra r a => IdempotentAlgebra r a Source

Instances

(Semiring r, Band r) => IdempotentAlgebra r () |
(Semiring r, Band r) => IdempotentAlgebra r IntSet |
(Semiring r, Band r, Ord a) => IdempotentAlgebra r (Set a) |
(IdempotentAlgebra r a, IdempotentAlgebra r b) => IdempotentAlgebra r (a, b) |
(IdempotentAlgebra r a, IdempotentAlgebra r b, IdempotentAlgebra r c) => IdempotentAlgebra r (a, b, c) |
(IdempotentAlgebra r a, IdempotentAlgebra r b, IdempotentAlgebra r c, IdempotentAlgebra r d) => IdempotentAlgebra r (a, b, c, d) |
(IdempotentAlgebra r a, IdempotentAlgebra r b, IdempotentAlgebra r c, IdempotentAlgebra r d, IdempotentAlgebra r e) => IdempotentAlgebra r (a, b, c, d, e) |

class Coalgebra r c => IdempotentCoalgebra r c Source

Instances

(Semiring r, Band r) => IdempotentCoalgebra r () |
(Semiring r, Band r) => IdempotentCoalgebra r IntSet |
(Semiring r, Band r, Ord c) => IdempotentCoalgebra r (Set c) |
(IdempotentCoalgebra r a, IdempotentCoalgebra r b) => IdempotentCoalgebra r (a, b) |
(IdempotentCoalgebra r a, IdempotentCoalgebra r b, IdempotentCoalgebra r c) => IdempotentCoalgebra r (a, b, c) |
(IdempotentCoalgebra r a, IdempotentCoalgebra r b, IdempotentCoalgebra r c, IdempotentCoalgebra r d) => IdempotentCoalgebra r (a, b, c, d) |
(IdempotentCoalgebra r a, IdempotentCoalgebra r b, IdempotentCoalgebra r c, IdempotentCoalgebra r d, IdempotentCoalgebra r e) => IdempotentCoalgebra r (a, b, c, d, e) |

class (Bialgebra r h, IdempotentAlgebra r h, IdempotentCoalgebra r h) => IdempotentBialgebra r h Source

Instances

(Bialgebra r h, IdempotentAlgebra r h, IdempotentCoalgebra r h) => IdempotentBialgebra r h |