HaskellForMaths-0.4.8: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe Haskell | None
Language | Haskell98

Math.Algebras.Octonions

Description

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 Source #

Constructors

O Int |

Instances

Eq OBasis Source # |
Methods (==) :: OBasis -> OBasis -> Bool # (/=) :: OBasis -> OBasis -> Bool #
Ord OBasis Source # |
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 Source # |
Methods showsPrec :: Int -> OBasis -> ShowS # show :: OBasis -> String # showList :: [OBasis] -> ShowS #
(Eq k, Num k) => Algebra k OBasis Source # |
Methods unit :: k -> Vect k OBasis Source # mult :: Vect k (Tensor OBasis OBasis) -> Vect k OBasis Source #
(Eq k, Num k) => HasConjugation k OBasis Source # |
Methods conj :: Vect k OBasis -> Vect k OBasis Source # sqnorm :: Vect k OBasis -> k Source #

type Octonion k = Vect k OBasis Source #

i0 :: Octonion Q Source #

i1 :: Octonion Q Source #

i2 :: Octonion Q Source #

i3 :: Octonion Q Source #

i4 :: Octonion Q Source #

i5 :: Octonion Q Source #

i6 :: Octonion Q Source #

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