Numeric.Algebra.Idempotent

Documentation

class Multiplicative r => Band r

An multiplicative semigroup with idempotent multiplication.

 a * a = a

Instances

Band Bool

Band ()

(Multiplicative (Exp r), Idempotent r) => Band (Exp r)

(Multiplicative (Opposite r), Band r) => Band (Opposite r)

(Multiplicative (a, b), Band a, Band b) => Band (a, b)

Multiplicative (Rect i j) => Band (Rect i j)

(Multiplicative (Covector r a), Idempotent r, IdempotentCoalgebra r a) => Band (Covector r a)

(Multiplicative (a, b, c), Band a, Band b, Band c) => Band (a, b, c)

(Multiplicative (a, b, c, d), Band a, Band b, Band c, Band d) => Band (a, b, c, d)

(Multiplicative (a, b, c, d, e), Band a, Band b, Band c, Band d, Band e) => Band (a, b, c, d, e)

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

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

Idempotent algebras

class Algebra r a => IdempotentAlgebra r a

Instances

(Algebra r (), Semiring r, Band r) => IdempotentAlgebra r ()

(Algebra r IntSet, Semiring r, Band r) => IdempotentAlgebra r IntSet

(Algebra r (Set a), Semiring r, Band r, Ord a) => IdempotentAlgebra r (Set a)

(Algebra r (a, b), IdempotentAlgebra r a, IdempotentAlgebra r b) => IdempotentAlgebra r (a, b)

(Algebra r (a, b, c), IdempotentAlgebra r a, IdempotentAlgebra r b, IdempotentAlgebra r c) => IdempotentAlgebra r (a, b, c)

(Algebra r (a, b, c, d), IdempotentAlgebra r a, IdempotentAlgebra r b, IdempotentAlgebra r c, IdempotentAlgebra r d) => IdempotentAlgebra r (a, b, c, d)

(Algebra r (a, b, c, d, e), 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

(Coalgebra r (), Semiring r, Band r) => IdempotentCoalgebra r ()

(Coalgebra r IntSet, Semiring r, Band r) => IdempotentCoalgebra r IntSet

(Coalgebra r (Set c), Semiring r, Band r, Ord c) => IdempotentCoalgebra r (Set c)

(Coalgebra r (a, b), IdempotentCoalgebra r a, IdempotentCoalgebra r b) => IdempotentCoalgebra r (a, b)

(Coalgebra r (a, b, c), IdempotentCoalgebra r a, IdempotentCoalgebra r b, IdempotentCoalgebra r c) => IdempotentCoalgebra r (a, b, c)

(Coalgebra r (a, b, c, d), IdempotentCoalgebra r a, IdempotentCoalgebra r b, IdempotentCoalgebra r c, IdempotentCoalgebra r d) => IdempotentCoalgebra r (a, b, c, d)

(Coalgebra r (a, b, c, d, e), 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