Data.Semimodule.V3

Documentation

triple :: Ring a => V3 a -> V3 a -> V3 a -> a

Scalar triple product.

data V3 a

Constructors

V3 !a !a !a

Instances

Functor V3

Defined in Data.Semimodule.V3

Methods

fmap :: (a -> b) -> V3 a -> V3 b

(<$) :: a -> V3 b -> V3 a

Foldable V3

Defined in Data.Semimodule.V3

Methods

fold :: Monoid m => V3 m -> m

foldMap :: Monoid m => (a -> m) -> V3 a -> m

foldr :: (a -> b -> b) -> b -> V3 a -> b

foldr' :: (a -> b -> b) -> b -> V3 a -> b

foldl :: (b -> a -> b) -> b -> V3 a -> b

foldl' :: (b -> a -> b) -> b -> V3 a -> b

foldr1 :: (a -> a -> a) -> V3 a -> a

foldl1 :: (a -> a -> a) -> V3 a -> a

toList :: V3 a -> [a]

null :: V3 a -> Bool

length :: V3 a -> Int

elem :: Eq a => a -> V3 a -> Bool

maximum :: Ord a => V3 a -> a

minimum :: Ord a => V3 a -> a

sum :: Num a => V3 a -> a

product :: Num a => V3 a -> a

Distributive V3

Defined in Data.Semimodule.V3

Methods

distribute :: Functor f => f (V3 a) -> V3 (f a)

collect :: Functor f => (a -> V3 b) -> f a -> V3 (f b)

distributeM :: Monad m => m (V3 a) -> V3 (m a)

collectM :: Monad m => (a -> V3 b) -> m a -> V3 (m b)

Representable V3

Defined in Data.Semimodule.V3

Associated Types

type Rep V3 :: Type

Methods

tabulate :: (Rep V3 -> a) -> V3 a

index :: V3 a -> Rep V3 -> a

Foldable1 V3

Defined in Data.Semimodule.V3

Methods

fold1 :: Semigroup m => V3 m -> m

foldMap1 :: Semigroup m => (a -> m) -> V3 a -> m

toNonEmpty :: V3 a -> NonEmpty a

Eq a => Eq (V3 a)

Defined in Data.Semimodule.V3

Methods

(==) :: V3 a -> V3 a -> Bool

(/=) :: V3 a -> V3 a -> Bool

Ord a => Ord (V3 a)

Defined in Data.Semimodule.V3

Methods

compare :: V3 a -> V3 a -> Ordering

(<) :: V3 a -> V3 a -> Bool

(<=) :: V3 a -> V3 a -> Bool

(>) :: V3 a -> V3 a -> Bool

(>=) :: V3 a -> V3 a -> Bool

max :: V3 a -> V3 a -> V3 a

min :: V3 a -> V3 a -> V3 a

Show a => Show (V3 a)

Defined in Data.Semimodule.V3

Methods

showsPrec :: Int -> V3 a -> ShowS

show :: V3 a -> String

showList :: [V3 a] -> ShowS

(Additive - Semigroup) a => Semigroup (V3 a)

Defined in Data.Semimodule.V3

Methods

(<>) :: V3 a -> V3 a -> V3 a

sconcat :: NonEmpty (V3 a) -> V3 a

stimes :: Integral b => b -> V3 a -> V3 a

(Additive - Monoid) a => Monoid (V3 a)

Defined in Data.Semimodule.V3

Methods

mempty :: V3 a

mappend :: V3 a -> V3 a -> V3 a

mconcat :: [V3 a] -> V3 a

(Additive - Group) a => Magma (V3 a)

Defined in Data.Semimodule.V3

Methods

(<<) :: V3 a -> V3 a -> V3 a

(Additive - Group) a => Loop (V3 a)

Defined in Data.Semimodule.V3

Methods

lempty :: V3 a

lreplicate :: Natural -> V3 a -> V3 a

(Additive - Group) a => Quasigroup (V3 a)

Defined in Data.Semimodule.V3

Methods

(//) :: V3 a -> V3 a -> V3 a

(\\) :: V3 a -> V3 a -> V3 a

(Additive - Group) a => Group (V3 a)

Defined in Data.Semimodule.V3

Methods

inv :: V3 a -> V3 a

greplicate :: Integer -> V3 a -> V3 a

type Rep V3

Defined in Data.Semimodule.V3

type Rep V3 = I3

data I3

Constructors

I31

I32

I33

Instances

Eq I3

Defined in Data.Semimodule.V3

Methods

(==) :: I3 -> I3 -> Bool

(/=) :: I3 -> I3 -> Bool

Ord I3

Defined in Data.Semimodule.V3

Methods

compare :: I3 -> I3 -> Ordering

(<) :: I3 -> I3 -> Bool

(<=) :: I3 -> I3 -> Bool

(>) :: I3 -> I3 -> Bool

(>=) :: I3 -> I3 -> Bool

max :: I3 -> I3 -> I3

min :: I3 -> I3 -> I3

Show I3

Defined in Data.Semimodule.V3

Methods

showsPrec :: Int -> I3 -> ShowS

show :: I3 -> String

showList :: [I3] -> ShowS

Ring r => Unital r QuaternionBasis

Defined in Data.Semimodule.V3

Methods

unitWith :: r -> QuaternionBasis -> r

Ring r => Composition r QuaternionBasis

Defined in Data.Semimodule.V3

Methods

conjugateWith :: (QuaternionBasis -> r) -> QuaternionBasis -> r

Ring r => Algebra r QuaternionBasis

Defined in Data.Semimodule.V3

Methods

multiplyWith :: (QuaternionBasis -> QuaternionBasis -> r) -> QuaternionBasis -> r

Ring r => Algebra r I3

Defined in Data.Semimodule.V3

Methods

multiplyWith :: (I3 -> I3 -> r) -> I3 -> r

type Dim3 f = (Representable f, Rep f ~ I3)

i3 :: Dim3 f => a -> a -> a -> f a

type QuaternionBasis = Maybe I3