algebra-4.2: Constructive abstract algebra

Numeric.Algebra.Commutative

Synopsis

Documentation

class Multiplicative r => Commutative r Source

A commutative multiplicative semigroup

Instances

 Commutative Bool Commutative Int Commutative Int8 Commutative Int16 Commutative Int32 Commutative Int64 Commutative Integer Commutative Word Commutative Word8 Commutative Word16 Commutative Word32 Commutative Word64 Commutative () Commutative Natural Commutative Euclidean (TriviallyInvolutive r, Rng r) => Commutative (Complex r) (TriviallyInvolutive r, Rng r) => Commutative (Dual r) (Commutative k, Semiring k) => Commutative (Hyper' k) (Commutative k, Semiring k) => Commutative (Hyper k) (TriviallyInvolutive r, Rng r) => Commutative (Dual' r) Commutative (BasisCoblade m) (Commutative k, Rng k) => Commutative (Trig k) Abelian r => Commutative (Exp r) (Abelian r, Commutative r) => Commutative (End r) Commutative r => Commutative (Opposite r) (Commutative r, Rng r) => Commutative (RngRing r) Monoidal r => Commutative (ZeroRng r) (Commutative d, Euclidean d) => Commutative (Fraction d) CommutativeAlgebra r a => Commutative (a -> r) (Commutative a, Commutative b) => Commutative (a, b) (Commutative m, Coalgebra r m) => Commutative (Covector r m) (Commutative a, Commutative b, Commutative c) => Commutative (a, b, c) (Commutative m, Coalgebra r m) => Commutative (Map r b m) (Commutative a, Commutative b, Commutative c, Commutative d) => Commutative (a, b, c, d) (Commutative a, Commutative b, Commutative c, Commutative d, Commutative e) => Commutative (a, b, c, d, e)

class Algebra r a => CommutativeAlgebra r a Source

Instances

 (Commutative r, Semiring r) => CommutativeAlgebra r IntSet (Commutative r, Semiring r) => CommutativeAlgebra r () (Commutative r, Monoidal r, Semiring r, Abelian b, Partitionable b) => CommutativeAlgebra r (IntMap b) (Commutative r, Semiring r, Ord a) => CommutativeAlgebra r (Set a) (Commutative r, Monoidal r, Semiring r, Ord a, Abelian b, Partitionable b) => CommutativeAlgebra r (Map a b) (CommutativeAlgebra r a, CommutativeAlgebra r b) => CommutativeAlgebra r (a, b) (CommutativeAlgebra r a, CommutativeAlgebra r b, CommutativeAlgebra r c) => CommutativeAlgebra r (a, b, c) (CommutativeAlgebra r a, CommutativeAlgebra r b, CommutativeAlgebra r c, CommutativeAlgebra r d) => CommutativeAlgebra r (a, b, c, d) (CommutativeAlgebra r a, CommutativeAlgebra r b, CommutativeAlgebra r c, CommutativeAlgebra r d, CommutativeAlgebra r e) => CommutativeAlgebra r (a, b, c, d, e)

class Coalgebra r c => CocommutativeCoalgebra r c Source

Instances

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

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