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

(Multiplicative (Complex r), TriviallyInvolutive r, Rng r) => Commutative (Complex r)

(Multiplicative (Dual r), TriviallyInvolutive r, Rng r) => Commutative (Dual r)

(Multiplicative (Hyper' k), Commutative k, Semiring k) => Commutative (Hyper' k)

(Multiplicative (Hyper k), Commutative k, Semiring k) => Commutative (Hyper k)

(Multiplicative (Dual' r), TriviallyInvolutive r, Rng r) => Commutative (Dual' r)

Multiplicative (BasisCoblade m) => Commutative (BasisCoblade m)

(Multiplicative (Trig k), Commutative k, Rng k) => Commutative (Trig k)

(Multiplicative (Exp r), Abelian r) => Commutative (Exp r)

(Multiplicative (End r), Abelian r, Commutative r) => Commutative (End r)

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

(Multiplicative (RngRing r), Commutative r, Rng r) => Commutative (RngRing r)

(Multiplicative (ZeroRng r), Monoidal r) => Commutative (ZeroRng r)

(Multiplicative (a -> r), CommutativeAlgebra r a) => Commutative (a -> r)

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

(Multiplicative (:->: a r), HasTrie a, CommutativeAlgebra r a) => Commutative (:->: a r)

(Multiplicative (Covector r m), Commutative m, Coalgebra r m) => Commutative (Covector r m)

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

(Multiplicative (Map r b m), Commutative m, Coalgebra r m) => Commutative (Map r b m)

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

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

class Algebra r a => CommutativeAlgebra r a

Instances

(Algebra r IntSet, Commutative r, Semiring r) => CommutativeAlgebra r IntSet

(Algebra r (), Commutative r, Semiring r) => CommutativeAlgebra r ()

(Algebra r (IntMap b), Commutative r, Monoidal r, Semiring r, Abelian b, Partitionable b) => CommutativeAlgebra r (IntMap b)

(Algebra r (Set a), Commutative r, Semiring r, Ord a) => CommutativeAlgebra r (Set a)

(Algebra r (Map a b), Commutative r, Monoidal r, Semiring r, Ord a, Abelian b, Partitionable b) => CommutativeAlgebra r (Map a b)

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

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

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

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

(Coalgebra r IntSet, Commutative r, Semiring r) => CocommutativeCoalgebra r IntSet

(Coalgebra r (), Commutative r, Semiring r) => CocommutativeCoalgebra r ()

(Coalgebra r (IntMap b), Commutative r, Semiring r, Abelian b) => CocommutativeCoalgebra r (IntMap b)

(Coalgebra r (Set a), Commutative r, Semiring r, Ord a) => CocommutativeCoalgebra r (Set a)

(Coalgebra r (Map a b), Commutative r, Semiring r, Ord a, Abelian b) => CocommutativeCoalgebra r (Map a b)

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

(Coalgebra r (:->: m r), HasTrie m, CommutativeAlgebra r m) => CocommutativeCoalgebra r (:->: m r)

(Coalgebra r (m -> r), CommutativeAlgebra r m) => CocommutativeCoalgebra r (m -> r)

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

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

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