Math.Algebras.Octonions

A module defining the (non-associative) algebra of octonions over an arbitrary field.

The octonions are the algebra defined by the basis {1,i0,i1,i2,i3,i4,i5,i6}, where each i_n * i_n = -1, and i_n+1 * i_n+2 = i_n+4 (where the indices are modulo 7).

Documentation

data OBasis

Constructors

O Int

Instances

Eq OBasis

Defined in Math.Algebras.Octonions

Methods

(==) :: OBasis -> OBasis -> Bool

(/=) :: OBasis -> OBasis -> Bool

Ord OBasis

Defined in Math.Algebras.Octonions

Methods

compare :: OBasis -> OBasis -> Ordering

(<) :: OBasis -> OBasis -> Bool

(<=) :: OBasis -> OBasis -> Bool

(>) :: OBasis -> OBasis -> Bool

(>=) :: OBasis -> OBasis -> Bool

max :: OBasis -> OBasis -> OBasis

min :: OBasis -> OBasis -> OBasis

Show OBasis

Defined in Math.Algebras.Octonions

Methods

showsPrec :: Int -> OBasis -> ShowS

show :: OBasis -> String

showList :: [OBasis] -> ShowS

(Eq k, Num k) => Algebra k OBasis

Defined in Math.Algebras.Octonions

Methods

unit :: k -> Vect k OBasis

mult :: Vect k (Tensor OBasis OBasis) -> Vect k OBasis

(Eq k, Num k) => HasConjugation k OBasis

Defined in Math.Algebras.Octonions

Methods

conj :: Vect k OBasis -> Vect k OBasis

sqnorm :: Vect k OBasis -> k

type Octonion k = Vect k OBasis

i0 :: Octonion Q

i1 :: Octonion Q

i2 :: Octonion Q

i3 :: Octonion Q

i4 :: Octonion Q

i5 :: Octonion Q

i6 :: Octonion Q

i_ :: Num k => Int -> Octonion k