Numeric.Clifford.Multivector

Documentation

data Multivector p q f where

Constructors

BladeSum :: forall p q f. (Ord f, C f, SingI p, SingI q) => [Blade p q f] -> Multivector p q f

Fields

_terms :: [Blade p q f]

Instances

(C f, Ord f, SingI Nat p, SingI Nat q) => C f (Multivector p q f)

(C f, Ord f, SingI Nat p, SingI Nat q) => C f (Multivector p q f)

(C f, SingI Nat p, SingI Nat q, Ord f) => Monoid (Sum (Multivector p q f))

(C f, SingI Nat p, SingI Nat q, Ord f) => Monoid (Product (Multivector p q f))

Eq (Multivector p q f)

(C f, SingI Nat p, SingI Nat q, Ord f) => Num (Multivector p q f)

Ord (Multivector p q f)

Show f => Show (Multivector p q f)

(SingI Nat p, SingI Nat q, C f, Arbitrary f, Ord f) => Arbitrary (Multivector p q f)

NFData f => NFData (Multivector p q f)

(C f, Ord f, SingI Nat p, SingI Nat q, Show f) => C (Multivector p q f)

(C f, Show f, Ord f, SingI Nat p, SingI Nat q) => C (Multivector p q f)

(C f, Ord f, SingI Nat p, SingI Nat q) => C (Multivector p q f)

(C f, C f, Ord f, SingI Nat p, SingI Nat q) => C (Multivector p q f)

(C f, Ord f, SingI Nat p, SingI Nat q) => C (Multivector p q f)

(C f, Ord f, SingI Nat p, SingI Nat q) => C (Multivector p q f)

type STVector = Multivector 3 1 Double

type E3Vector = Multivector 3 0 Double

signature :: forall p q f. (SingI p, SingI q) => Multivector p q f -> (Natural, Natural)

terms :: Lens' (Multivector p q f) [Blade p q f]

mvNormalForm :: Multivector t t1 t2 -> Multivector t t1 t2

mvTerms :: Multivector p q f -> [Blade p q f]

addLikeTerms' :: (Eq f, SingI Nat p, SingI Nat q, C f) => [Blade p q f] -> [Blade p q f]

groupLikeTerms :: Eq f => [Blade p q f] -> [[Blade p q f]]

compareTol :: (C f, C f, Ord f, SingI p, SingI q) => Multivector p q f -> Multivector p q f -> f -> Bool

compensatedSum' :: C f => [f] -> f

compensatedRunningSum :: (C f, Ord f, SingI p, SingI q, Show f) => [Multivector p q f] -> [Multivector p q f]

multiplyOutBlades :: (SingI p, SingI q, C a) => [Blade p q a] -> [Blade p q a] -> [Blade p q a]

multiplyList :: (Ord t2, SingI Nat t, SingI Nat t1, C t2) => [Multivector t t1 t2] -> Multivector t t1 t2

multiplyList1 :: (Ord t2, SingI Nat t, SingI Nat t1, C t2) => [Multivector t t1 t2] -> Multivector t t1 t2

sumList :: (Ord t2, SingI Nat t, SingI Nat t1, C t2) => [Multivector t t1 t2] -> Multivector t t1 t2

sumLikeTerms :: (C f, SingI p, SingI q) => [[Blade p q f]] -> [Blade p q f]

e :: (C f, Ord f, SingI p, SingI q) => f -> [Natural] -> Multivector p q f

scalar :: (Ord f, SingI Nat p, SingI Nat q, C f) => f -> Multivector p q f

two :: C a => a

mul :: C a => a -> a -> a

psuedoScalar :: forall p q f. (Ord f, C f, SingI p, SingI q) => Multivector p q f

magnitude :: C f => Multivector p q f -> f

(</) :: (Ord t2, SingI Nat t, SingI Nat t1, C t2) => Multivector t t1 t2 -> Multivector t t1 t2 -> Multivector t t1 t2

(/>) :: (Ord t2, SingI Nat t, SingI Nat t1, C t2) => Multivector t t1 t2 -> Multivector t t1 t2 -> Multivector t t1 t2

(</>) :: (Ord t2, SingI Nat t, SingI Nat t1, C t2) => Multivector t t1 t2 -> Multivector t t1 t2 -> Multivector t t1 t2

scaleLeft :: (Ord f, SingI Nat p, SingI Nat q, C f) => f -> Multivector p q f -> Multivector p q f

scaleRight :: (Ord f, SingI Nat p, SingI Nat q, C f) => Multivector p q f -> f -> Multivector p q f

divideRight :: (Ord f, SingI Nat p, SingI Nat q, C f) => Multivector p q f -> f -> Multivector p q f

converge :: (Eq a, Show a) => [a] -> a

aitkensAcceleration :: (Ord t2, SingI Nat t, SingI Nat t1, C t2) => [Multivector t t1 t2] -> [Multivector t t1 t2]

shanksTransformation :: (C f, Ord f, Show f, SingI p, SingI q) => [Multivector p q f] -> [Multivector p q f]

takeEvery :: Int -> [a] -> [a]

seriesPlusMinus :: C a => [a] -> [a]

seriesMinusPlus :: C a => [a] -> [a]

expTerms :: (C f, SingI p, SingI q, Ord f) => Multivector p q f -> [Multivector p q f]

dot :: Multivector p q f -> Multivector p q f -> Multivector p q f

wedge :: Multivector p q f -> Multivector p q f -> Multivector p q f

(∧) :: Multivector p q f -> Multivector p q f -> Multivector p q f

(⋅) :: Multivector p q f -> Multivector p q f -> Multivector p q f

reverseBlade :: Blade p q f -> Blade p q f

reverseMultivector :: Multivector t t1 t2 -> Multivector t t1 t2

inverse :: Multivector t t1 t2 -> Multivector t t1 t2

rootIterationsStart :: (Ord f, Show f, C f) => Integer -> Multivector p q f -> Multivector p q f -> [Multivector p q f]

rootNewtonIterations :: (C f, Ord f, SingI p, SingI q) => Integer -> Multivector p q f -> Multivector p q f -> [Multivector p q f]

rootHalleysIterations :: (Show a, Ord a, C a, SingI p, SingI q) => Integer -> Multivector p q a -> Multivector p q a -> [Multivector p q a]

halleysMethod :: (Show a, Ord a, C a, SingI p, SingI q) => (Multivector p q a -> Multivector p q a) -> (Multivector p q a -> Multivector p q a) -> (Multivector p q a -> Multivector p q a) -> Multivector p q a -> [Multivector p q a]

secantMethod :: (Ord t2, SingI Nat t, SingI Nat t1, C t2) => (Multivector t t1 t2 -> Multivector t t1 t2) -> Multivector t t1 t2 -> Multivector t t1 t2 -> [Multivector t t1 t2]

normalised :: (Ord f, C f, SingI p, SingI q) => Multivector p q f -> (Multivector p q f, f)

makeSerialize ''Blade) $(derive makeSerialize ''Multivector) $(derive makeData ''Blade) $(derive makeTypeable ''Blade) $(derive makeData ''Multivector) $(derive makeTypeable ''Multivector)

makeArbitrary ''Multivector)