Numeric.Coalgebra.Geometric

Geometric coalgebra primitives

newtype BasisCoblade m

Constructors

BasisCoblade

Fields

runBasisCoblade :: Word64

Instances

(Semiring Natural, Additive (BasisCoblade m)) => RightModule Natural (BasisCoblade m)

(Semiring Natural, Additive (BasisCoblade m)) => LeftModule Natural (BasisCoblade m)

(Semiring r, Eigenmetric r m) => Coalgebra r (BasisCoblade m)

(Coalgebra r (BasisCoblade m), Eigenmetric r m) => CounitalCoalgebra r (BasisCoblade m)

Bounded (BasisCoblade m)

Enum (BasisCoblade m)

Eq (BasisCoblade m)

(Real (BasisCoblade m), Enum (BasisCoblade m)) => Integral (BasisCoblade m)

Num (BasisCoblade m)

Eq (BasisCoblade m) => Ord (BasisCoblade m)

Read (BasisCoblade m)

(Num (BasisCoblade m), Ord (BasisCoblade m)) => Real (BasisCoblade m)

Show (BasisCoblade m)

Ord (BasisCoblade m) => Ix (BasisCoblade m)

Eq (BasisCoblade m) => Bits (BasisCoblade m)

(Adjustable (BaseTrie (BasisCoblade m)), TraversableWithKey1 (BaseTrie (BasisCoblade m)), Representable (BaseTrie (BasisCoblade m))) => HasTrie (BasisCoblade m)

Additive (BasisCoblade m) => Abelian (BasisCoblade m)

Additive (BasisCoblade m)

(LeftModule Natural (BasisCoblade m), RightModule Natural (BasisCoblade m)) => Monoidal (BasisCoblade m)

(Additive (BasisCoblade m), Abelian (BasisCoblade m), Multiplicative (BasisCoblade m)) => Semiring (BasisCoblade m)

Multiplicative (BasisCoblade m)

Multiplicative (BasisCoblade m) => Unital (BasisCoblade m)

Unital (BasisCoblade m) => DecidableAssociates (BasisCoblade m)

Unital (BasisCoblade m) => DecidableUnits (BasisCoblade m)

Monoidal (BasisCoblade m) => DecidableZero (BasisCoblade m)

(Semiring (BasisCoblade m), Unital (BasisCoblade m), Monoidal (BasisCoblade m)) => Rig (BasisCoblade m)

Multiplicative (BasisCoblade m) => Commutative (BasisCoblade m)

type Comultivector r m = Covector r (BasisCoblade m)

Operations over an eigenbasis

class Eigenbasis m where

Methods

euclidean :: proxy m -> Bool

antiEuclidean :: proxy m -> Bool

v :: m -> BasisCoblade m

e :: Int -> m

Instances

Eigenbasis Euclidean

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

Methods

metric :: m -> r

Instances

(Eigenbasis Euclidean, Ring r) => Eigenmetric r Euclidean

newtype Euclidean

Constructors

Euclidean Int

Instances

Enum Euclidean

Eq Euclidean

Integral Euclidean

Data Euclidean

Num Euclidean

Ord Euclidean

Read Euclidean

Real Euclidean

Show Euclidean

Ix Euclidean

Typeable Euclidean

HasTrie Euclidean

Abelian Euclidean

Additive Euclidean

Monoidal Euclidean

Semiring Euclidean

Multiplicative Euclidean

Group Euclidean

Unital Euclidean

Rig Euclidean

Ring Euclidean

Commutative Euclidean

TriviallyInvolutive Euclidean

InvolutiveSemiring Euclidean

InvolutiveMultiplication Euclidean

Eigenbasis Euclidean

RightModule Integer Euclidean

RightModule Natural Euclidean

LeftModule Integer Euclidean

LeftModule Natural Euclidean

(Eigenbasis Euclidean, Ring r) => Eigenmetric r Euclidean

Grade

grade :: BasisCoblade m -> Int

filterGrade :: Monoidal r => BasisCoblade m -> Int -> Comultivector r m

Inversions

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

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

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

Products

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

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

Inner products

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