algebra-4.3.1: Constructive abstract algebra

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LanguageHaskell98

Numeric.Algebra.Hopf

Synopsis

Documentation

class Bialgebra r h => HopfAlgebra r h where Source #

A HopfAlgebra algebra on a semiring, where the module is free.

When antipode . antipode = id and antipode is an antihomomorphism then we are an InvolutiveBialgebra with inv = antipode as well

Minimal complete definition

antipode

Methods

antipode :: (h -> r) -> h -> r Source #

Instances

(Commutative k, Group k, InvolutiveSemiring k) => HopfAlgebra k TrigBasis Source # 

Methods

antipode :: (TrigBasis -> k) -> TrigBasis -> k Source #

(TriviallyInvolutive r, InvolutiveSemiring r, Rng r) => HopfAlgebra r QuaternionBasis' Source # 
(Commutative k, Group k, InvolutiveSemiring k) => HopfAlgebra k HyperBasis Source # 

Methods

antipode :: (HyperBasis -> k) -> HyperBasis -> k Source #

(InvolutiveSemiring k, Rng k) => HopfAlgebra k DualBasis' Source # 

Methods

antipode :: (DualBasis' -> k) -> DualBasis' -> k Source #

(TriviallyInvolutive r, InvolutiveSemiring r, Rng r) => HopfAlgebra r QuaternionBasis Source # 
(Commutative k, Group k, InvolutiveSemiring k) => HopfAlgebra k HyperBasis' Source # 

Methods

antipode :: (HyperBasis' -> k) -> HyperBasis' -> k Source #

(InvolutiveSemiring k, Rng k) => HopfAlgebra k DualBasis Source # 

Methods

antipode :: (DualBasis -> k) -> DualBasis -> k Source #

(InvolutiveSemiring k, Rng k) => HopfAlgebra k ComplexBasis Source # 

Methods

antipode :: (ComplexBasis -> k) -> ComplexBasis -> k Source #

(HopfAlgebra r a, HopfAlgebra r b) => HopfAlgebra r (a, b) Source # 

Methods

antipode :: ((a, b) -> r) -> (a, b) -> r Source #

(HopfAlgebra r a, HopfAlgebra r b, HopfAlgebra r c) => HopfAlgebra r (a, b, c) Source # 

Methods

antipode :: ((a, b, c) -> r) -> (a, b, c) -> r Source #

(HopfAlgebra r a, HopfAlgebra r b, HopfAlgebra r c, HopfAlgebra r d) => HopfAlgebra r (a, b, c, d) Source # 

Methods

antipode :: ((a, b, c, d) -> r) -> (a, b, c, d) -> r Source #

(HopfAlgebra r a, HopfAlgebra r b, HopfAlgebra r c, HopfAlgebra r d, HopfAlgebra r e) => HopfAlgebra r (a, b, c, d, e) Source # 

Methods

antipode :: ((a, b, c, d, e) -> r) -> (a, b, c, d, e) -> r Source #