Data.Semimodule.Basis

Documentation

type Basis b f = (Free f, Rep f ~ b)

data V2 a

Constructors

V2 !a !a

Instances

Functor V2

Defined in Data.Semimodule.Basis

Methods

fmap :: (a -> b) -> V2 a -> V2 b

(<$) :: a -> V2 b -> V2 a

Foldable V2

Defined in Data.Semimodule.Basis

Methods

fold :: Monoid m => V2 m -> m

foldMap :: Monoid m => (a -> m) -> V2 a -> m

foldr :: (a -> b -> b) -> b -> V2 a -> b

foldr' :: (a -> b -> b) -> b -> V2 a -> b

foldl :: (b -> a -> b) -> b -> V2 a -> b

foldl' :: (b -> a -> b) -> b -> V2 a -> b

foldr1 :: (a -> a -> a) -> V2 a -> a

foldl1 :: (a -> a -> a) -> V2 a -> a

toList :: V2 a -> [a]

null :: V2 a -> Bool

length :: V2 a -> Int

elem :: Eq a => a -> V2 a -> Bool

maximum :: Ord a => V2 a -> a

minimum :: Ord a => V2 a -> a

sum :: Num a => V2 a -> a

product :: Num a => V2 a -> a

Distributive V2

Defined in Data.Semimodule.Basis

Methods

distribute :: Functor f => f (V2 a) -> V2 (f a)

collect :: Functor f => (a -> V2 b) -> f a -> V2 (f b)

distributeM :: Monad m => m (V2 a) -> V2 (m a)

collectM :: Monad m => (a -> V2 b) -> m a -> V2 (m b)

Representable V2

Defined in Data.Semimodule.Basis

Associated Types

type Rep V2 :: Type

Methods

tabulate :: (Rep V2 -> a) -> V2 a

index :: V2 a -> Rep V2 -> a

Foldable1 V2

Defined in Data.Semimodule.Basis

Methods

fold1 :: Semigroup m => V2 m -> m

foldMap1 :: Semigroup m => (a -> m) -> V2 a -> m

toNonEmpty :: V2 a -> NonEmpty a

Semiring a => Semimodule a (V2 a)

Defined in Data.Semimodule.Basis

Methods

(*.) :: a -> V2 a -> V2 a

(.*) :: V2 a -> a -> V2 a

Eq a => Eq (V2 a)

Defined in Data.Semimodule.Basis

Methods

(==) :: V2 a -> V2 a -> Bool

(/=) :: V2 a -> V2 a -> Bool

Ord a => Ord (V2 a)

Defined in Data.Semimodule.Basis

Methods

compare :: V2 a -> V2 a -> Ordering

(<) :: V2 a -> V2 a -> Bool

(<=) :: V2 a -> V2 a -> Bool

(>) :: V2 a -> V2 a -> Bool

(>=) :: V2 a -> V2 a -> Bool

max :: V2 a -> V2 a -> V2 a

min :: V2 a -> V2 a -> V2 a

Show a => Show (V2 a)

Defined in Data.Semimodule.Basis

Methods

showsPrec :: Int -> V2 a -> ShowS

show :: V2 a -> String

showList :: [V2 a] -> ShowS

(Additive - Semigroup) a => Semigroup (Additive (V2 a))

Matrix addition.

>>> m23 1 2 3 4 5 6 <> m23 7 8 9 1 2 3 :: M23 Int
V2 (V3 8 10 12) (V3 5 7 9)

Defined in Data.Semimodule.Basis

Methods

(<>) :: Additive (V2 a) -> Additive (V2 a) -> Additive (V2 a)

sconcat :: NonEmpty (Additive (V2 a)) -> Additive (V2 a)

stimes :: Integral b => b -> Additive (V2 a) -> Additive (V2 a)

(Additive - Semigroup) a => Semigroup (V2 a)

Vector addition.

>>> V2 1 2 <> V2 3 4
V2 4 6

Defined in Data.Semimodule.Basis

Methods

(<>) :: V2 a -> V2 a -> V2 a

sconcat :: NonEmpty (V2 a) -> V2 a

stimes :: Integral b => b -> V2 a -> V2 a

(Additive - Monoid) a => Monoid (Additive (V2 a))

Defined in Data.Semimodule.Basis

Methods

mempty :: Additive (V2 a)

mappend :: Additive (V2 a) -> Additive (V2 a) -> Additive (V2 a)

mconcat :: [Additive (V2 a)] -> Additive (V2 a)

(Additive - Monoid) a => Monoid (V2 a)

Defined in Data.Semimodule.Basis

Methods

mempty :: V2 a

mappend :: V2 a -> V2 a -> V2 a

mconcat :: [V2 a] -> V2 a

(Additive - Group) a => Magma (Additive (V2 a))

Matrix subtraction.

>>> m23 1 2 3 4 5 6 << m23 7 8 9 1 2 3 :: M23 Int
V2 (V3 (-6) (-6) (-6)) (V3 3 3 3)

Defined in Data.Semimodule.Basis

Methods

(<<) :: Additive (V2 a) -> Additive (V2 a) -> Additive (V2 a)

(Additive - Group) a => Magma (V2 a)

Vector subtraction.

>>> V2 1 2 << V2 3 4
V2 (-2) (-2)

Defined in Data.Semimodule.Basis

Methods

(<<) :: V2 a -> V2 a -> V2 a

(Additive - Group) a => Loop (Additive (V2 a))

Defined in Data.Semimodule.Basis

Methods

lempty :: Additive (V2 a)

lreplicate :: Natural -> Additive (V2 a) -> Additive (V2 a)

(Additive - Group) a => Loop (V2 a)

Defined in Data.Semimodule.Basis

Methods

lempty :: V2 a

lreplicate :: Natural -> V2 a -> V2 a

(Additive - Group) a => Quasigroup (Additive (V2 a))

Defined in Data.Semimodule.Basis

Methods

(//) :: Additive (V2 a) -> Additive (V2 a) -> Additive (V2 a)

(\\) :: Additive (V2 a) -> Additive (V2 a) -> Additive (V2 a)

(Additive - Group) a => Quasigroup (V2 a)

Defined in Data.Semimodule.Basis

Methods

(//) :: V2 a -> V2 a -> V2 a

(\\) :: V2 a -> V2 a -> V2 a

(Additive - Group) a => Group (Additive (V2 a))

Defined in Data.Semimodule.Basis

Methods

inv :: Additive (V2 a) -> Additive (V2 a)

greplicate :: Integer -> Additive (V2 a) -> Additive (V2 a)

(Additive - Group) a => Group (V2 a)

Defined in Data.Semimodule.Basis

Methods

inv :: V2 a -> V2 a

greplicate :: Integer -> V2 a -> V2 a

type Rep V2

Defined in Data.Semimodule.Basis

type Rep V2 = E2

data E2

Constructors

E21

E22

Instances

Eq E2

Defined in Data.Semimodule.Basis

Methods

(==) :: E2 -> E2 -> Bool

(/=) :: E2 -> E2 -> Bool

Ord E2

Defined in Data.Semimodule.Basis

Methods

compare :: E2 -> E2 -> Ordering

(<) :: E2 -> E2 -> Bool

(<=) :: E2 -> E2 -> Bool

(>) :: E2 -> E2 -> Bool

(>=) :: E2 -> E2 -> Bool

max :: E2 -> E2 -> E2

min :: E2 -> E2 -> E2

Show E2

Defined in Data.Semimodule.Basis

Methods

showsPrec :: Int -> E2 -> ShowS

show :: E2 -> String

showList :: [E2] -> ShowS

Semiring r => Composition r E2

Defined in Data.Semimodule.Basis

Methods

conjugateWith :: (E2 -> r) -> E2 -> r

normWith :: (E2 -> r) -> r

Semiring r => Algebra r E2

Defined in Data.Semimodule.Basis

Methods

multiplyWith :: (E2 -> E2 -> r) -> E2 -> r

Semigroup (Additive E2)

Defined in Data.Semimodule.Basis

Methods

(<>) :: Additive E2 -> Additive E2 -> Additive E2

sconcat :: NonEmpty (Additive E2) -> Additive E2

stimes :: Integral b => b -> Additive E2 -> Additive E2

Monoid (Additive E2)

Defined in Data.Semimodule.Basis

Methods

mempty :: Additive E2

mappend :: Additive E2 -> Additive E2 -> Additive E2

mconcat :: [Additive E2] -> Additive E2

e2 :: Basis E2 f => a -> a -> f a

data V3 a

Constructors

V3 !a !a !a

Instances

Functor V3

Defined in Data.Semimodule.Basis

Methods

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

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

Foldable V3

Defined in Data.Semimodule.Basis

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.Basis

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.Basis

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.Basis

Methods

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

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

toNonEmpty :: V3 a -> NonEmpty a

Semiring a => Semimodule a (V3 a)

Defined in Data.Semimodule.Basis

Methods

(*.) :: a -> V3 a -> V3 a

(.*) :: V3 a -> a -> V3 a

Eq a => Eq (V3 a)

Defined in Data.Semimodule.Basis

Methods

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

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

Ord a => Ord (V3 a)

Defined in Data.Semimodule.Basis

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.Basis

Methods

showsPrec :: Int -> V3 a -> ShowS

show :: V3 a -> String

showList :: [V3 a] -> ShowS

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

Matrix addition.

>>> V2 (V3 1 2 3) (V3 4 5 6) <> V2 (V3 7 8 9) (V3 1 2 3)
V2 (V3 8 10 12) (V3 5 7 9)

Defined in Data.Semimodule.Basis

Methods

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

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

stimes :: Integral b => b -> Additive (V3 a) -> Additive (V3 a)

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

Vector addition.

>>> V3 1 2 3 <> V3 4 5 6
V3 5 7 9

Defined in Data.Semimodule.Basis

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 (Additive (V3 a))

Defined in Data.Semimodule.Basis

Methods

mempty :: Additive (V3 a)

mappend :: Additive (V3 a) -> Additive (V3 a) -> Additive (V3 a)

mconcat :: [Additive (V3 a)] -> Additive (V3 a)

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

Defined in Data.Semimodule.Basis

Methods

mempty :: V3 a

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

mconcat :: [V3 a] -> V3 a

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

Matrix subtraction.

>>> V3 (V3 1 2 3) (V3 4 5 6) (V3 7 8 9) << V3 (V3 7 8 9) (V3 7 8 9) (V3 7 8 9)
V3 (V3 (-6) (-6) (-6)) (V3 (-3) (-3) (-3)) (V3 0 0 0)

Defined in Data.Semimodule.Basis

Methods

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

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

Vector subtraction.

>>> V3 1 2 3 << V3 4 5 6
V3 (-3) (-3) (-3)

Defined in Data.Semimodule.Basis

Methods

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

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

Defined in Data.Semimodule.Basis

Methods

lempty :: Additive (V3 a)

lreplicate :: Natural -> Additive (V3 a) -> Additive (V3 a)

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

Defined in Data.Semimodule.Basis

Methods

lempty :: V3 a

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

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

Defined in Data.Semimodule.Basis

Methods

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

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

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

Defined in Data.Semimodule.Basis

Methods

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

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

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

Defined in Data.Semimodule.Basis

Methods

inv :: Additive (V3 a) -> Additive (V3 a)

greplicate :: Integer -> Additive (V3 a) -> Additive (V3 a)

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

Defined in Data.Semimodule.Basis

Methods

inv :: V3 a -> V3 a

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

type Rep V3

Defined in Data.Semimodule.Basis

type Rep V3 = E3

data E3

Constructors

E31

E32

E33

Instances

Eq E3

Defined in Data.Semimodule.Basis

Methods

(==) :: E3 -> E3 -> Bool

(/=) :: E3 -> E3 -> Bool

Ord E3

Defined in Data.Semimodule.Basis

Methods

compare :: E3 -> E3 -> Ordering

(<) :: E3 -> E3 -> Bool

(<=) :: E3 -> E3 -> Bool

(>) :: E3 -> E3 -> Bool

(>=) :: E3 -> E3 -> Bool

max :: E3 -> E3 -> E3

min :: E3 -> E3 -> E3

Show E3

Defined in Data.Semimodule.Basis

Methods

showsPrec :: Int -> E3 -> ShowS

show :: E3 -> String

showList :: [E3] -> ShowS

Field r => Division r QuaternionBasis

Defined in Data.Semimodule.Basis

Methods

reciprocalWith :: (QuaternionBasis -> r) -> QuaternionBasis -> r

Ring r => Unital r QuaternionBasis

Defined in Data.Semimodule.Basis

Methods

unitWith :: r -> QuaternionBasis -> r

Ring r => Composition r QuaternionBasis

Defined in Data.Semimodule.Basis

Methods

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

normWith :: (QuaternionBasis -> r) -> r

Ring r => Composition r E3

Defined in Data.Semimodule.Basis

Methods

conjugateWith :: (E3 -> r) -> E3 -> r

normWith :: (E3 -> r) -> r

Ring r => Algebra r QuaternionBasis

Defined in Data.Semimodule.Basis

Methods

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

Ring r => Algebra r E3

Defined in Data.Semimodule.Basis

Methods

multiplyWith :: (E3 -> E3 -> r) -> E3 -> r

Semigroup (Additive E3)

Defined in Data.Semimodule.Basis

Methods

(<>) :: Additive E3 -> Additive E3 -> Additive E3

sconcat :: NonEmpty (Additive E3) -> Additive E3

stimes :: Integral b => b -> Additive E3 -> Additive E3

Monoid (Additive E3)

Defined in Data.Semimodule.Basis

Methods

mempty :: Additive E3

mappend :: Additive E3 -> Additive E3 -> Additive E3

mconcat :: [Additive E3] -> Additive E3

e3 :: Basis E3 f => a -> a -> a -> f a

type QuaternionBasis = Maybe E3

data V4 a

Constructors

V4 !a !a !a !a

Instances

Functor V4

Defined in Data.Semimodule.Basis

Methods

fmap :: (a -> b) -> V4 a -> V4 b

(<$) :: a -> V4 b -> V4 a

Foldable V4

Defined in Data.Semimodule.Basis

Methods

fold :: Monoid m => V4 m -> m

foldMap :: Monoid m => (a -> m) -> V4 a -> m

foldr :: (a -> b -> b) -> b -> V4 a -> b

foldr' :: (a -> b -> b) -> b -> V4 a -> b

foldl :: (b -> a -> b) -> b -> V4 a -> b

foldl' :: (b -> a -> b) -> b -> V4 a -> b

foldr1 :: (a -> a -> a) -> V4 a -> a

foldl1 :: (a -> a -> a) -> V4 a -> a

toList :: V4 a -> [a]

null :: V4 a -> Bool

length :: V4 a -> Int

elem :: Eq a => a -> V4 a -> Bool

maximum :: Ord a => V4 a -> a

minimum :: Ord a => V4 a -> a

sum :: Num a => V4 a -> a

product :: Num a => V4 a -> a

Distributive V4

Defined in Data.Semimodule.Basis

Methods

distribute :: Functor f => f (V4 a) -> V4 (f a)

collect :: Functor f => (a -> V4 b) -> f a -> V4 (f b)

distributeM :: Monad m => m (V4 a) -> V4 (m a)

collectM :: Monad m => (a -> V4 b) -> m a -> V4 (m b)

Representable V4

Defined in Data.Semimodule.Basis

Associated Types

type Rep V4 :: Type

Methods

tabulate :: (Rep V4 -> a) -> V4 a

index :: V4 a -> Rep V4 -> a

Foldable1 V4

Defined in Data.Semimodule.Basis

Methods

fold1 :: Semigroup m => V4 m -> m

foldMap1 :: Semigroup m => (a -> m) -> V4 a -> m

toNonEmpty :: V4 a -> NonEmpty a

Semiring a => Semimodule a (V4 a)

Defined in Data.Semimodule.Basis

Methods

(*.) :: a -> V4 a -> V4 a

(.*) :: V4 a -> a -> V4 a

Eq a => Eq (V4 a)

Defined in Data.Semimodule.Basis

Methods

(==) :: V4 a -> V4 a -> Bool

(/=) :: V4 a -> V4 a -> Bool

Ord a => Ord (V4 a)

Defined in Data.Semimodule.Basis

Methods

compare :: V4 a -> V4 a -> Ordering

(<) :: V4 a -> V4 a -> Bool

(<=) :: V4 a -> V4 a -> Bool

(>) :: V4 a -> V4 a -> Bool

(>=) :: V4 a -> V4 a -> Bool

max :: V4 a -> V4 a -> V4 a

min :: V4 a -> V4 a -> V4 a

Show a => Show (V4 a)

Defined in Data.Semimodule.Basis

Methods

showsPrec :: Int -> V4 a -> ShowS

show :: V4 a -> String

showList :: [V4 a] -> ShowS

(Additive - Semigroup) a => Semigroup (Additive (V4 a))

Matrix addition.

>>> m24 1 2 3 4 5 6 7 8 <> m24 1 2 3 4 5 6 7 8 :: M24 Int
V2 (V4 2 4 6 8) (V4 10 12 14 16)

Defined in Data.Semimodule.Basis

Methods

(<>) :: Additive (V4 a) -> Additive (V4 a) -> Additive (V4 a)

sconcat :: NonEmpty (Additive (V4 a)) -> Additive (V4 a)

stimes :: Integral b => b -> Additive (V4 a) -> Additive (V4 a)

(Additive - Semigroup) a => Semigroup (V4 a)

Vector addition.

>>> V4 1 2 3 4 <> V4 5 6 7 8
V4 6 8 10 12 

Defined in Data.Semimodule.Basis

Methods

(<>) :: V4 a -> V4 a -> V4 a

sconcat :: NonEmpty (V4 a) -> V4 a

stimes :: Integral b => b -> V4 a -> V4 a

(Additive - Monoid) a => Monoid (Additive (V4 a))

Defined in Data.Semimodule.Basis

Methods

mempty :: Additive (V4 a)

mappend :: Additive (V4 a) -> Additive (V4 a) -> Additive (V4 a)

mconcat :: [Additive (V4 a)] -> Additive (V4 a)

(Additive - Monoid) a => Monoid (V4 a)

Defined in Data.Semimodule.Basis

Methods

mempty :: V4 a

mappend :: V4 a -> V4 a -> V4 a

mconcat :: [V4 a] -> V4 a

(Additive - Group) a => Magma (Additive (V4 a))

Matrix subtraction.

>>> V4 (V4 1 2 3) (V4 4 5 6) (V4 7 8 9) << V4 (V4 7 8 9) (V4 7 8 9) (V4 7 8 9)
V4 (V4 (-6) (-6) (-6)) (V4 (-3) (-3) (-3)) (V4 0 0 0)

Defined in Data.Semimodule.Basis

Methods

(<<) :: Additive (V4 a) -> Additive (V4 a) -> Additive (V4 a)

(Additive - Group) a => Magma (V4 a)

Vector subtraction.

>>> V4 1 2 3 << V4 4 5 6
V4 (-3) (-3) (-3)

Defined in Data.Semimodule.Basis

Methods

(<<) :: V4 a -> V4 a -> V4 a

(Additive - Group) a => Loop (Additive (V4 a))

Defined in Data.Semimodule.Basis

Methods

lempty :: Additive (V4 a)

lreplicate :: Natural -> Additive (V4 a) -> Additive (V4 a)

(Additive - Group) a => Loop (V4 a)

Defined in Data.Semimodule.Basis

Methods

lempty :: V4 a

lreplicate :: Natural -> V4 a -> V4 a

(Additive - Group) a => Quasigroup (Additive (V4 a))

Defined in Data.Semimodule.Basis

Methods

(//) :: Additive (V4 a) -> Additive (V4 a) -> Additive (V4 a)

(\\) :: Additive (V4 a) -> Additive (V4 a) -> Additive (V4 a)

(Additive - Group) a => Quasigroup (V4 a)

Defined in Data.Semimodule.Basis

Methods

(//) :: V4 a -> V4 a -> V4 a

(\\) :: V4 a -> V4 a -> V4 a

(Additive - Group) a => Group (Additive (V4 a))

Defined in Data.Semimodule.Basis

Methods

inv :: Additive (V4 a) -> Additive (V4 a)

greplicate :: Integer -> Additive (V4 a) -> Additive (V4 a)

(Additive - Group) a => Group (V4 a)

Defined in Data.Semimodule.Basis

Methods

inv :: V4 a -> V4 a

greplicate :: Integer -> V4 a -> V4 a

type Rep V4

Defined in Data.Semimodule.Basis

type Rep V4 = E4

data E4

Constructors

E41

E42

E43

E44

Instances

Eq E4

Defined in Data.Semimodule.Basis

Methods

(==) :: E4 -> E4 -> Bool

(/=) :: E4 -> E4 -> Bool

Ord E4

Defined in Data.Semimodule.Basis

Methods

compare :: E4 -> E4 -> Ordering

(<) :: E4 -> E4 -> Bool

(<=) :: E4 -> E4 -> Bool

(>) :: E4 -> E4 -> Bool

(>=) :: E4 -> E4 -> Bool

max :: E4 -> E4 -> E4

min :: E4 -> E4 -> E4

Show E4

Defined in Data.Semimodule.Basis

Methods

showsPrec :: Int -> E4 -> ShowS

show :: E4 -> String

showList :: [E4] -> ShowS

e4 :: Basis E4 f => a -> a -> a -> a -> f a

data VFour a

Constructors

VFour !a !a !a !a

Instances

Functor VFour

Defined in Data.Semimodule.Basis

Methods

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

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

Foldable VFour

Defined in Data.Semimodule.Basis

Methods

fold :: Monoid m => VFour m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> VFour a -> a

foldl1 :: (a -> a -> a) -> VFour a -> a

toList :: VFour a -> [a]

null :: VFour a -> Bool

length :: VFour a -> Int

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

maximum :: Ord a => VFour a -> a

minimum :: Ord a => VFour a -> a

sum :: Num a => VFour a -> a

product :: Num a => VFour a -> a

Distributive VFour

Defined in Data.Semimodule.Basis

Methods

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

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

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

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

Representable VFour

Defined in Data.Semimodule.Basis

Associated Types

type Rep VFour :: Type

Methods

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

index :: VFour a -> Rep VFour -> a

Foldable1 VFour

Defined in Data.Semimodule.Basis

Methods

fold1 :: Semigroup m => VFour m -> m

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

toNonEmpty :: VFour a -> NonEmpty a

Semiring a => Semimodule a (VFour a)

Defined in Data.Semimodule.Basis

Methods

(*.) :: a -> VFour a -> VFour a

(.*) :: VFour a -> a -> VFour a

Eq a => Eq (VFour a)

Defined in Data.Semimodule.Basis

Methods

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

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

Ord a => Ord (VFour a)

Defined in Data.Semimodule.Basis

Methods

compare :: VFour a -> VFour a -> Ordering

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

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

(>) :: VFour a -> VFour a -> Bool

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

max :: VFour a -> VFour a -> VFour a

min :: VFour a -> VFour a -> VFour a

Show a => Show (VFour a)

Defined in Data.Semimodule.Basis

Methods

showsPrec :: Int -> VFour a -> ShowS

show :: VFour a -> String

showList :: [VFour a] -> ShowS

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

Matrix addition.

>>> m24 1 2 3 4 5 6 7 8 <> m24 1 2 3 4 5 6 7 8 :: M24 Int
V2 (VFour 2 4 6 8) (VFour 10 12 14 16)

Defined in Data.Semimodule.Basis

Methods

(<>) :: Additive (VFour a) -> Additive (VFour a) -> Additive (VFour a)

sconcat :: NonEmpty (Additive (VFour a)) -> Additive (VFour a)

stimes :: Integral b => b -> Additive (VFour a) -> Additive (VFour a)

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

Vector addition.

>>> VFour 1 2 3 4 <> VFour 5 6 7 8
VFour 6 8 10 12 

Defined in Data.Semimodule.Basis

Methods

(<>) :: VFour a -> VFour a -> VFour a

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

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

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

Defined in Data.Semimodule.Basis

Methods

mempty :: Additive (VFour a)

mappend :: Additive (VFour a) -> Additive (VFour a) -> Additive (VFour a)

mconcat :: [Additive (VFour a)] -> Additive (VFour a)

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

Defined in Data.Semimodule.Basis

Methods

mempty :: VFour a

mappend :: VFour a -> VFour a -> VFour a

mconcat :: [VFour a] -> VFour a

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

Matrix subtraction.

>>> VFour (VFour 1 2 3) (VFour 4 5 6) (VFour 7 8 9) << VFour (VFour 7 8 9) (VFour 7 8 9) (VFour 7 8 9)
VFour (VFour (-6) (-6) (-6)) (VFour (-3) (-3) (-3)) (VFour 0 0 0)

Defined in Data.Semimodule.Basis

Methods

(<<) :: Additive (VFour a) -> Additive (VFour a) -> Additive (VFour a)

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

Vector subtraction.

>>> VFour 1 2 3 << VFour 4 5 6
VFour (-3) (-3) (-3)

Defined in Data.Semimodule.Basis

Methods

(<<) :: VFour a -> VFour a -> VFour a

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

Defined in Data.Semimodule.Basis

Methods

lempty :: Additive (VFour a)

lreplicate :: Natural -> Additive (VFour a) -> Additive (VFour a)

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

Defined in Data.Semimodule.Basis

Methods

lempty :: VFour a

lreplicate :: Natural -> VFour a -> VFour a

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

Defined in Data.Semimodule.Basis

Methods

(//) :: Additive (VFour a) -> Additive (VFour a) -> Additive (VFour a)

(\\) :: Additive (VFour a) -> Additive (VFour a) -> Additive (VFour a)

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

Defined in Data.Semimodule.Basis

Methods

(//) :: VFour a -> VFour a -> VFour a

(\\) :: VFour a -> VFour a -> VFour a

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

Defined in Data.Semimodule.Basis

Methods

inv :: Additive (VFour a) -> Additive (VFour a)

greplicate :: Integer -> Additive (VFour a) -> Additive (VFour a)

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

Defined in Data.Semimodule.Basis

Methods

inv :: VFour a -> VFour a

greplicate :: Integer -> VFour a -> VFour a

type Rep VFour

Defined in Data.Semimodule.Basis

type Rep VFour = Either E2 E2