algebra-4.3: 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

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

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

class Coalgebra r c => IdempotentCoalgebra r c Source #

Instances

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

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 Source #