Numeric.Algebra.Commutative

Documentation

class Multiplicative r => Commutative r

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

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

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

Instances

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