algebra-2.1.1: Constructive abstract algebra

Safe HaskellSafe-Infered

Numeric.Algebra.Involutive

Contents

Synopsis

Involution

class Multiplicative r => InvolutiveMultiplication r whereSource

An semigroup with involution

 adjoint a * adjoint b = adjoint (b * a)

Methods

adjoint :: r -> rSource

Instances

InvolutiveMultiplication Bool 
InvolutiveMultiplication Int 
InvolutiveMultiplication Int8 
InvolutiveMultiplication Int16 
InvolutiveMultiplication Int32 
InvolutiveMultiplication Int64 
InvolutiveMultiplication Integer 
InvolutiveMultiplication Word 
InvolutiveMultiplication Word8 
InvolutiveMultiplication Word16 
InvolutiveMultiplication Word32 
InvolutiveMultiplication Word64 
InvolutiveMultiplication () 
InvolutiveMultiplication Natural 
InvolutiveMultiplication Euclidean 
(Commutative r, Rng r, InvolutiveMultiplication r) => InvolutiveMultiplication (Complex r) 
(TriviallyInvolutive r, Rng r) => InvolutiveMultiplication (Quaternion r) 
(Commutative r, Rng r, InvolutiveSemiring r) => InvolutiveMultiplication (Dual r) 
(Commutative r, InvolutiveSemiring r, Rng r) => InvolutiveMultiplication (Hyper' r) 
(Commutative r, Group r, InvolutiveSemiring r) => InvolutiveMultiplication (Hyper r) 
(Commutative r, Rng r, InvolutiveSemiring r) => InvolutiveMultiplication (Dual' r) 
(TriviallyInvolutive r, Rng r) => InvolutiveMultiplication (Quaternion' r) 
(Commutative r, Rng r, InvolutiveMultiplication r) => InvolutiveMultiplication (Trig r) 
InvolutiveAlgebra r h => InvolutiveMultiplication (h -> r) 
(InvolutiveMultiplication a, InvolutiveMultiplication b) => InvolutiveMultiplication (a, b) 
(HasTrie h, InvolutiveAlgebra r h) => InvolutiveMultiplication (:->: h r) 
(InvolutiveMultiplication a, InvolutiveMultiplication b, InvolutiveMultiplication c) => InvolutiveMultiplication (a, b, c) 
(InvolutiveMultiplication a, InvolutiveMultiplication b, InvolutiveMultiplication c, InvolutiveMultiplication d) => InvolutiveMultiplication (a, b, c, d) 
(InvolutiveMultiplication a, InvolutiveMultiplication b, InvolutiveMultiplication c, InvolutiveMultiplication d, InvolutiveMultiplication e) => InvolutiveMultiplication (a, b, c, d, e) 

Involutive Algebras

Trivial Involution