Numeric.Clifford.Multivector

Documentation

data Multivector n f where

Constructors

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

Fields

_terms :: [Blade n f]

Instances

(C f, Ord f, SingI Nat n) => C f (Multivector n f)

(C f, Ord f, SingI Nat n) => C f (Multivector n f)

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

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

Eq (Multivector n f)

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

Ord (Multivector n f)

Show f => Show (Multivector n f)

NFData f => NFData (Multivector n f)

(C f, C f, Ord f, SingI Nat n) => C (Multivector n f)

(C f, Ord f, SingI Nat n) => C (Multivector n f)

(C f, Ord f, SingI Nat n) => C (Multivector n f)

dimension :: forall n f. SingI n => Multivector n f -> Natural

terms :: Lens' (Multivector n f) [Blade n f]

mvNormalForm :: Multivector t t1 -> Multivector t t1

mvTerms :: Multivector n f -> [Blade n f]

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

groupLikeTerms :: Eq f => [Blade n f] -> [[Blade n f]]

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

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

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

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

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

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

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

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

two :: C a => a

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

magnitude :: C c => Multivector n c -> c

(/) :: (C f, Ord f, SingI n) => Multivector n f -> f -> Multivector n f

(</) :: (Ord f, SingI Nat n, C f) => Multivector n f -> Multivector n f -> Multivector n f

(/>) :: (Ord f, SingI Nat n, C f) => Multivector n f -> Multivector n f -> Multivector n f

(</>) :: (Ord f, SingI Nat n, C f) => Multivector n f -> Multivector n f -> Multivector n f

integratePoly :: (Ord b, SingI Nat n, C b) => Multivector n b -> [Multivector n b] -> [Multivector n b]

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

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

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

exp :: (Ord f, Show f, SingI Nat n, C f) => Multivector n f -> Multivector n f

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

cosh :: (Ord f, Show f, SingI Nat n, C f) => Multivector n f -> Multivector n f

sinh :: (Ord f, Show f, SingI Nat n, C f) => Multivector n f -> Multivector n f

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

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

sin :: (Ord f, Show f, SingI Nat n, C f) => Multivector n f -> Multivector n f

sinTerms :: (Ord f, SingI Nat n, C f) => Multivector n f -> [Multivector n f]

cos :: (Ord f, Show f, SingI Nat n, C f) => Multivector n f -> Multivector n f

cosTerms :: (Ord f, SingI Nat n, C f) => Multivector n f -> [Multivector n f]

expTerms :: (Ord f, SingI Nat n, C f) => Multivector n f -> [Multivector n f]

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

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

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

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

reverseBlade :: Blade n f -> Blade n f

reverseMultivector :: Multivector t t1 -> Multivector t t1

inverse :: (Ord f, SingI Nat n, C f) => Multivector n f -> Multivector n f

recip :: (Ord f, SingI Nat n, C f) => Multivector n f -> Multivector n f

root :: (Show f, Ord f, C f, SingI d) => Integer -> Multivector d f -> Multivector d f

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

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

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

pow :: (Ord f, Show f, SingI Nat n, C f, C a) => Multivector n f -> a -> Multivector n f

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

secantMethod :: (Ord f, SingI Nat n, C f) => (Multivector n f -> Multivector n f) -> Multivector n f -> Multivector n f -> [Multivector n f]

normalised :: (Ord f, SingI Nat n, C f) => Multivector n f -> Multivector n f

log :: (Ord f, Show f, SingI Nat n, C f) => Multivector n f -> Multivector n f

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

makeArbitrary ''Multivector)