Numeric.Algebra.Geometric

Geometric algebra primitives

newtype Blade m

Constructors

Blade

Fields

runBlade :: Word64

Instances

RightModule Natural (Blade m)

LeftModule Natural (Blade m)

Eigenmetric r m => Coalgebra r (Blade m)

Eigenmetric r m => CounitalCoalgebra r (Blade m)

Bounded (Blade m)

Enum (Blade m)

Eq (Blade m)

Integral (Blade m)

Num (Blade m)

Ord (Blade m)

Read (Blade m)

Real (Blade m)

Show (Blade m)

Ix (Blade m)

Bits (Blade m)

HasTrie (Blade m)

Abelian (Blade m)

Additive (Blade m)

Monoidal (Blade m)

Semiring (Blade m)

Multiplicative (Blade m)

Unital (Blade m)

DecidableAssociates (Blade m)

DecidableUnits (Blade m)

DecidableZero (Blade m)

Rig (Blade m)

Commutative (Blade m)

type Multivector r m = Blade m :->: r

type Comultivector r m = Covector r (Blade m)

Operations over an eigenbasis

class Eigenbasis m where

Methods

euclidean :: proxy m -> Bool

antiEuclidean :: proxy m -> Bool

v :: m -> Blade m

e :: Int -> m

Instances

Eigenbasis Euclidean

class (Ring r, Eigenbasis m) => Eigenmetric r m where

Methods

metric :: m -> r

Instances

Ring r => Eigenmetric r Euclidean

Grade

grade :: Blade m -> Int

filterGrade :: Monoidal r => Blade m -> Int -> Covector r (Blade m)

Inversions

reverse :: Group r => Blade m -> Comultivector r m

gradeInversion :: Group r => Blade m -> Comultivector r m

cliffordConjugate :: Group r => Blade m -> Comultivector r m

Products

geometric :: Eigenmetric r m => Blade m -> Blade m -> Comultivector r m

outer :: Eigenmetric r m => Blade m -> Blade m -> Comultivector r m

Inner products

contractL :: Eigenmetric r m => Blade m -> Blade m -> Comultivector r m

contractR :: Eigenmetric r m => Blade m -> Blade m -> Comultivector r m

hestenes :: Eigenmetric r m => Blade m -> Blade m -> Comultivector r m

dot :: Eigenmetric r m => Blade m -> Blade m -> Comultivector r m

liftProduct :: (Blade m -> Blade m -> Comultivector r m) -> Comultivector r m -> Comultivector r m -> Comultivector r m