algebra-3.1: Constructive abstract algebra

Safe Haskell | None

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 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) |
CommutativeAlgebra r a => Commutative (a -> r) |
(Commutative a, Commutative b) => Commutative (a, b) |
(HasTrie a, CommutativeAlgebra r a) => Commutative (:->: a r) |
(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) |
(HasTrie m, CommutativeAlgebra r m) => CocommutativeCoalgebra r (:->: m r) |
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 |