Numeric.Algebra.Idempotent

Documentation

class Multiplicative r => Band r

An multiplicative semigroup with idempotent multiplication.

a * a = a

Instances

Band Bool

Band ()

Band r => Band (Opposite r)

Idempotent r => Band (Exp 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

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

Idempotent algebras

class Algebra r a => IdempotentAlgebra r a

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

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

Instances

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