| Safe Haskell | None |
|---|
Numeric.Algebra.Hopf
- class Bialgebra r h => HopfAlgebra r h where
- antipode :: (h -> r) -> h -> r
Documentation
class Bialgebra r h => HopfAlgebra r h whereSource
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
Instances
| (InvolutiveSemiring k, Rng k) => HopfAlgebra k ComplexBasis | |
| (TriviallyInvolutive r, InvolutiveSemiring r, Rng r) => HopfAlgebra r QuaternionBasis | |
| (InvolutiveSemiring k, Rng k) => HopfAlgebra k DualBasis | |
| (Commutative k, Group k, InvolutiveSemiring k) => HopfAlgebra k HyperBasis' | |
| (Commutative k, Group k, InvolutiveSemiring k) => HopfAlgebra k HyperBasis | |
| (InvolutiveSemiring k, Rng k) => HopfAlgebra k DualBasis' | |
| (TriviallyInvolutive r, InvolutiveSemiring r, Rng r) => HopfAlgebra r QuaternionBasis' | |
| (Commutative k, Group k, InvolutiveSemiring k) => HopfAlgebra k TrigBasis | |
| (HopfAlgebra r a, HopfAlgebra r b) => HopfAlgebra r (a, b) | |
| (HopfAlgebra r a, HopfAlgebra r b, HopfAlgebra r c) => HopfAlgebra r (a, b, c) | |
| (HopfAlgebra r a, HopfAlgebra r b, HopfAlgebra r c, HopfAlgebra r d) => HopfAlgebra r (a, b, c, d) | |
| (HopfAlgebra r a, HopfAlgebra r b, HopfAlgebra r c, HopfAlgebra r d, HopfAlgebra r e) => HopfAlgebra r (a, b, c, d, e) |