algebra-4.2: Constructive abstract algebra

Numeric.Algebra.Idempotent

Contents

Synopsis

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 :: r -> Natural -> r Source

powBand :: Unital r => r -> Natural -> r Source

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