algebra-4.3: Constructive abstract algebra

Numeric.Algebra.Commutative

Synopsis

# Documentation

class Multiplicative r => Commutative r Source #

A commutative multiplicative semigroup

Instances

 Source # Source # Source # Source # Source # Source # Source # Source # Source # Source # Source # Source # Source # Source # Source # GCDDomain d => Commutative (Fraction d) Source # (TriviallyInvolutive r, Rng r) => Commutative (Complex r) Source # (TriviallyInvolutive r, Rng r) => Commutative (Dual r) Source # (Commutative k, Semiring k) => Commutative (Hyper' k) Source # (TriviallyInvolutive r, Rng r) => Commutative (Dual' r) Source # Source # (Commutative k, Semiring k) => Commutative (Hyper k) Source # (Commutative k, Rng k) => Commutative (Trig k) Source # Abelian r => Commutative (Exp r) Source # (Abelian r, Commutative r) => Commutative (End r) Source # Source # (Commutative r, Rng r) => Commutative (RngRing r) Source # Monoidal r => Commutative (ZeroRng r) Source # CommutativeAlgebra r a => Commutative (a -> r) Source # (Commutative a, Commutative b) => Commutative (a, b) Source # (Commutative m, Coalgebra r m) => Commutative (Covector r m) Source # (Commutative a, Commutative b, Commutative c) => Commutative (a, b, c) Source # (Commutative m, Coalgebra r m) => Commutative (Map r b m) Source # (Commutative a, Commutative b, Commutative c, Commutative d) => Commutative (a, b, c, d) Source # (Commutative a, Commutative b, Commutative c, Commutative d, Commutative e) => Commutative (a, b, c, d, e) Source #

class Algebra r a => CommutativeAlgebra r a Source #

Instances

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

class Coalgebra r c => CocommutativeCoalgebra r c Source #

Instances

 Source # (Commutative r, Semiring r) => CocommutativeCoalgebra r () Source # (Commutative r, Semiring r, Abelian b) => CocommutativeCoalgebra r (IntMap b) Source # (Commutative r, Semiring r, Ord a) => CocommutativeCoalgebra r (Set a) Source # (Commutative r, Semiring r, Ord a, Abelian b) => CocommutativeCoalgebra r (Map a b) Source # (CocommutativeCoalgebra r a, CocommutativeCoalgebra r b) => CocommutativeCoalgebra r (a, b) Source # CommutativeAlgebra r m => CocommutativeCoalgebra r (m -> r) Source # (CocommutativeCoalgebra r a, CocommutativeCoalgebra r b, CocommutativeCoalgebra r c) => CocommutativeCoalgebra r (a, b, c) Source # (CocommutativeCoalgebra r a, CocommutativeCoalgebra r b, CocommutativeCoalgebra r c, CocommutativeCoalgebra r d) => CocommutativeCoalgebra r (a, b, c, d) Source # (CocommutativeCoalgebra r a, CocommutativeCoalgebra r b, CocommutativeCoalgebra r c, CocommutativeCoalgebra r d, CocommutativeCoalgebra r e) => CocommutativeCoalgebra r (a, b, c, d, e) Source #

class (Bialgebra r h, CommutativeAlgebra r h, CocommutativeCoalgebra r h) => CommutativeBialgebra r h Source #

Instances

 (Bialgebra r h, CommutativeAlgebra r h, CocommutativeCoalgebra r h) => CommutativeBialgebra r h Source #