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^2 = -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

Ord OBasis

Show OBasis

Num k => Algebra k OBasis

Num k => HasConjugation k OBasis

type Octonion k = Vect k OBasis

i0, i6, i5, i4, i3, i2, i1 :: Octonion Q

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