Safe Haskell	Safe
Language	Haskell98

Numeric.Algebra.Commutative

Synopsis

class Multiplicative r => Commutative r
class Algebra r a => CommutativeAlgebra r a
class Coalgebra r c => CocommutativeCoalgebra r c
class (Bialgebra r h, CommutativeAlgebra r h, CocommutativeCoalgebra r h) => CommutativeBialgebra r h

Documentation

class Multiplicative r => Commutative r #

A commutative multiplicative semigroup

Instances

Commutative Bool #
Instance details Defined in Numeric.Algebra.Commutative
Commutative Int #
Instance details Defined in Numeric.Algebra.Commutative
Commutative Int8 #
Instance details Defined in Numeric.Algebra.Commutative
Commutative Int16 #
Instance details Defined in Numeric.Algebra.Commutative
Commutative Int32 #
Instance details Defined in Numeric.Algebra.Commutative
Commutative Int64 #
Instance details Defined in Numeric.Algebra.Commutative
Commutative Integer #
Instance details Defined in Numeric.Algebra.Commutative
Commutative Natural #
Instance details Defined in Numeric.Algebra.Commutative
Commutative Word #
Instance details Defined in Numeric.Algebra.Commutative
Commutative Word8 #
Instance details Defined in Numeric.Algebra.Commutative
Commutative Word16 #
Instance details Defined in Numeric.Algebra.Commutative
Commutative Word32 #
Instance details Defined in Numeric.Algebra.Commutative
Commutative Word64 #
Instance details Defined in Numeric.Algebra.Commutative
Commutative () #
Instance details Defined in Numeric.Algebra.Commutative
Commutative Euclidean #
Instance details Defined in Numeric.Coalgebra.Geometric
Monoidal r => Commutative (ZeroRng r) #
Instance details Defined in Numeric.Rng.Zero
(Commutative r, Rng r) => Commutative (RngRing r) #
Instance details Defined in Numeric.Ring.Rng
Commutative r => Commutative (Opposite r) #
Instance details Defined in Numeric.Ring.Opposite
(Abelian r, Commutative r) => Commutative (End r) #
Instance details Defined in Numeric.Ring.Endomorphism
Abelian r => Commutative (Exp r) #
Instance details Defined in Numeric.Exp
(Commutative k, Rng k) => Commutative (Trig k) #
Instance details Defined in Numeric.Coalgebra.Trigonometric
(Commutative k, Semiring k) => Commutative (Hyper k) #
Instance details Defined in Numeric.Coalgebra.Hyperbolic
Commutative (BasisCoblade m) #
Instance details Defined in Numeric.Coalgebra.Geometric
(TriviallyInvolutive r, Rng r) => Commutative (Dual' r) #
Instance details Defined in Numeric.Coalgebra.Dual
(Commutative k, Semiring k) => Commutative (Hyper' k) #
Instance details Defined in Numeric.Algebra.Hyperbolic
(TriviallyInvolutive r, Rng r) => Commutative (Dual r) #
Instance details Defined in Numeric.Algebra.Dual
(TriviallyInvolutive r, Rng r) => Commutative (Complex r) #
Instance details Defined in Numeric.Algebra.Complex
GCDDomain d => Commutative (Fraction d) #
Instance details Defined in Numeric.Field.Fraction
CommutativeAlgebra r a => Commutative (a -> r) #
Instance details Defined in Numeric.Algebra.Commutative
(Commutative a, Commutative b) => Commutative (a, b) #
Instance details Defined in Numeric.Algebra.Commutative
(Commutative m, Coalgebra r m) => Commutative (Covector r m) #
Instance details Defined in Numeric.Covector
(Commutative a, Commutative b, Commutative c) => Commutative (a, b, c) #
Instance details Defined in Numeric.Algebra.Commutative
(Commutative m, Coalgebra r m) => Commutative (Map r b m) #
Instance details Defined in Numeric.Map
(Commutative a, Commutative b, Commutative c, Commutative d) => Commutative (a, b, c, d) #
Instance details Defined in Numeric.Algebra.Commutative
(Commutative a, Commutative b, Commutative c, Commutative d, Commutative e) => Commutative (a, b, c, d, e) #
Instance details Defined in Numeric.Algebra.Commutative

class Algebra r a => CommutativeAlgebra r a #

Instances

(Commutative r, Semiring r) => CommutativeAlgebra r IntSet #
Instance details Defined in Numeric.Algebra.Commutative
(Commutative r, Semiring r) => CommutativeAlgebra r () #
Instance details Defined in Numeric.Algebra.Commutative
(Commutative r, Semiring r, Ord a) => CommutativeAlgebra r (Set a) #
Instance details Defined in Numeric.Algebra.Commutative
(CommutativeAlgebra r a, CommutativeAlgebra r b) => CommutativeAlgebra r (a, b) #
Instance details Defined in Numeric.Algebra.Commutative
(CommutativeAlgebra r a, CommutativeAlgebra r b, CommutativeAlgebra r c) => CommutativeAlgebra r (a, b, c) #
Instance details Defined in Numeric.Algebra.Commutative
(CommutativeAlgebra r a, CommutativeAlgebra r b, CommutativeAlgebra r c, CommutativeAlgebra r d) => CommutativeAlgebra r (a, b, c, d) #
Instance details Defined in Numeric.Algebra.Commutative
(CommutativeAlgebra r a, CommutativeAlgebra r b, CommutativeAlgebra r c, CommutativeAlgebra r d, CommutativeAlgebra r e) => CommutativeAlgebra r (a, b, c, d, e) #
Instance details Defined in Numeric.Algebra.Commutative

class Coalgebra r c => CocommutativeCoalgebra r c #

Instances

(Commutative r, Semiring r) => CocommutativeCoalgebra r IntSet #
Instance details Defined in Numeric.Algebra.Commutative
(Commutative r, Semiring r) => CocommutativeCoalgebra r () #
Instance details Defined in Numeric.Algebra.Commutative
(Commutative r, Semiring r, Abelian b) => CocommutativeCoalgebra r (IntMap b) #
Instance details Defined in Numeric.Algebra.Commutative
(Commutative r, Semiring r, Ord a) => CocommutativeCoalgebra r (Set a) #
Instance details Defined in Numeric.Algebra.Commutative
(Commutative r, Semiring r, Ord a, Abelian b) => CocommutativeCoalgebra r (Map a b) #
Instance details Defined in Numeric.Algebra.Commutative
(CocommutativeCoalgebra r a, CocommutativeCoalgebra r b) => CocommutativeCoalgebra r (a, b) #
Instance details Defined in Numeric.Algebra.Commutative
CommutativeAlgebra r m => CocommutativeCoalgebra r (m -> r) #
Instance details Defined in Numeric.Algebra.Commutative
(CocommutativeCoalgebra r a, CocommutativeCoalgebra r b, CocommutativeCoalgebra r c) => CocommutativeCoalgebra r (a, b, c) #
Instance details Defined in Numeric.Algebra.Commutative
(CocommutativeCoalgebra r a, CocommutativeCoalgebra r b, CocommutativeCoalgebra r c, CocommutativeCoalgebra r d) => CocommutativeCoalgebra r (a, b, c, d) #
Instance details Defined in Numeric.Algebra.Commutative
(CocommutativeCoalgebra r a, CocommutativeCoalgebra r b, CocommutativeCoalgebra r c, CocommutativeCoalgebra r d, CocommutativeCoalgebra r e) => CocommutativeCoalgebra r (a, b, c, d, e) #
Instance details Defined in Numeric.Algebra.Commutative

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 #
Instance details Defined in Numeric.Algebra.Commutative