Safe Haskell | None |
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- newtype BasisCoblade m = BasisCoblade {}
- type Comultivector r m = Covector r (BasisCoblade m)
- class Eigenbasis m where
- euclidean :: proxy m -> Bool
- antiEuclidean :: proxy m -> Bool
- v :: m -> BasisCoblade m
- e :: Int -> m
- class (Ring r, Eigenbasis m) => Eigenmetric r m where
- metric :: m -> r
- newtype Euclidean = Euclidean Int
- grade :: BasisCoblade m -> Int
- filterGrade :: Monoidal r => BasisCoblade m -> Int -> Comultivector r m
- reverse :: Group r => BasisCoblade m -> Comultivector r m
- gradeInversion :: Group r => BasisCoblade m -> Comultivector r m
- cliffordConjugate :: Group r => BasisCoblade m -> Comultivector r m
- geometric :: Eigenmetric r m => BasisCoblade m -> BasisCoblade m -> Comultivector r m
- outer :: Eigenmetric r m => BasisCoblade m -> BasisCoblade m -> Comultivector r m
- contractL :: Eigenmetric r m => BasisCoblade m -> BasisCoblade m -> Comultivector r m
- contractR :: Eigenmetric r m => BasisCoblade m -> BasisCoblade m -> Comultivector r m
- hestenes :: Eigenmetric r m => BasisCoblade m -> BasisCoblade m -> Comultivector r m
- dot :: Eigenmetric r m => BasisCoblade m -> BasisCoblade m -> Comultivector r m
- liftProduct :: (BasisCoblade m -> BasisCoblade m -> Comultivector r m) -> Comultivector r m -> Comultivector r m -> Comultivector r m
Geometric coalgebra primitives
newtype BasisCoblade m Source
type Comultivector r m = Covector r (BasisCoblade m)Source
Operations over an eigenbasis
class Eigenbasis m whereSource
euclidean :: proxy m -> BoolSource
antiEuclidean :: proxy m -> BoolSource
v :: m -> BasisCoblade mSource
class (Ring r, Eigenbasis m) => Eigenmetric r m whereSource
(Eigenbasis Euclidean, Ring r) => Eigenmetric r Euclidean |
Grade
grade :: BasisCoblade m -> IntSource
filterGrade :: Monoidal r => BasisCoblade m -> Int -> Comultivector r mSource
Inversions
reverse :: Group r => BasisCoblade m -> Comultivector r mSource
gradeInversion :: Group r => BasisCoblade m -> Comultivector r mSource
cliffordConjugate :: Group r => BasisCoblade m -> Comultivector r mSource
Products
geometric :: Eigenmetric r m => BasisCoblade m -> BasisCoblade m -> Comultivector r mSource
outer :: Eigenmetric r m => BasisCoblade m -> BasisCoblade m -> Comultivector r mSource
Inner products
contractL :: Eigenmetric r m => BasisCoblade m -> BasisCoblade m -> Comultivector r mSource
contractR :: Eigenmetric r m => BasisCoblade m -> BasisCoblade m -> Comultivector r mSource
hestenes :: Eigenmetric r m => BasisCoblade m -> BasisCoblade m -> Comultivector r mSource
dot :: Eigenmetric r m => BasisCoblade m -> BasisCoblade m -> Comultivector r mSource
liftProduct :: (BasisCoblade m -> BasisCoblade m -> Comultivector r m) -> Comultivector r m -> Comultivector r m -> Comultivector r mSource