Data.Semimodule.Free

Types

type Free f = Representable f

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

type Basis2 b c f g = (Basis b f, Basis c g)

type Basis3 b c d f g h = (Basis b f, Basis c g, Basis d h)

Vector arithmetic

(.*) :: RightSemimodule r a => a -> r -> a infixl 7

Right-multiply a module element by a scalar.

(!*) :: Free f => Dual a (Rep f) -> f a -> a infixr 3

Apply a linear functional to a vector.

(.#) :: Free f => FreeCounital a g => (f ** g) a -> g a -> f a infixr 7

Multiply a matrix on the right by a column vector.

 (.#) = (!#) . tran

>>> tran (m23 1 2 3 4 5 6) !# V3 7 8 9 :: V2 Int
V2 50 122
>>> m23 1 2 3 4 5 6 .# V3 7 8 9 :: V2 Int
V2 50 122
>>> m22 1 0 0 0 .# m23 1 2 3 4 5 6 .# V3 7 8 9 :: V2 Int
V2 50 0

(!#) :: Free f => Free g => Tran a (Rep f) (Rep g) -> g a -> f a infixr 2

Apply a transformation to a vector.

(*.) :: LeftSemimodule l a => l -> a -> a infixr 7

Left-multiply a module element by a scalar.

(*!) :: Free f => f a -> Dual a (Rep f) -> a infixl 3

Apply a linear functional to a vector.

(#.) :: FreeCounital a f => Free g => f a -> (f ** g) a -> g a infixl 7

Multiply a matrix on the left by a row vector.

>>> V2 1 2 #. m23 3 4 5 6 7 8
V3 15 18 21

>>> V2 1 2 #. m23 3 4 5 6 7 8 #. m32 1 0 0 0 0 0 :: V2 Int
V2 15 0

(#!) :: Free f => Free g => g a -> Tran a (Rep f) (Rep g) -> f a infixl 2

Apply a transformation to a vector.

dual :: FreeCounital a f => f a -> Dual a (Rep f)

Take the dual of a vector.

>>> dual (V2 3 4) !% V2 1 2 :: Int
11

inner :: FreeCounital a f => f a -> f a -> a infix 6

Inner product.

This is a variant of xmult restricted to free functors.

>>> V3 1 2 3 `inner` V3 1 2 3
14

lerp :: LeftModule r a => r -> a -> a -> a

Linearly interpolate between two vectors.

>>> u = V3 (1 :% 1) (2 :% 1) (3 :% 1) :: V3 Rational
>>> v = V3 (2 :% 1) (4 :% 1) (6 :% 1) :: V3 Rational
>>> r = 1 :% 2 :: Rational
>>> lerp r u v
V3 (6 % 4) (12 % 4) (18 % 4)

quadrance :: FreeCounital a f => f a -> a

Squared l2 norm of a vector.

cross :: Ring a => V3 a -> V3 a -> V3 a

Cross product.

a `cross' a = zero
a `cross' b = negate ( b `cross' a ) , 
a `cross' ( b + c ) = ( a `cross' b ) + ( a `cross' c ) , 
( r a ) `cross' b = a `cross' ( r b ) = r ( a `cross' b ) . 
a `cross' ( b `cross' c ) + b `cross' ( c `cross' a ) + c `cross' ( a `cross' b ) = zero . 

See Jacobi identity.

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

Scalar triple product.

triple x y z = triple z x y = triple y z x
triple x y z = negate $ triple x z y = negate $ triple y x z
triple x x y = triple x y y = triple x y x = zero
(triple x y z) *. x = (x `cross' y) `cross' (x `cross' z)

>>> triple (V3 0 0 1) (V3 1 0 0) (V3 0 1 0) :: Double
1.0

Vector accessors and constructors

dirac :: Eq i => Semiring a => i -> i -> a

Dirac delta function.

idx :: Semiring a => Basis b f => b -> f a

Create a unit vector at an index.

>>> idx E21 :: V2 Int
V2 1 0

>>> idx E42 :: V4 Int
V4 0 1 0 0

elt :: Basis b f => b -> f a -> a

Retrieve an element of a vector.

>>> elt E21 (V2 1 2)
1

lensRep :: Basis b f => b -> forall g. Functor g => (a -> g a) -> f a -> g (f a)

Create a lens from a representable functor.

grateRep :: Basis b f => forall g. Functor g => (b -> g a1 -> a2) -> g (f a1) -> f a2

Create an indexed grate from a representable functor.

Matrix arithmetic

(.#.) :: Free f => FreeCounital a g => Free h => (f ** g) a -> (g ** h) a -> (f ** h) a infixr 7

Multiply two matrices.

>>> m22 1 2 3 4 .#. m22 1 2 3 4 :: M22 Int
Compose (V2 (V2 7 10) (V2 15 22))

>>> m23 1 2 3 4 5 6 .#. m32 1 2 3 4 4 5 :: M22 Int
Compose (V2 (V2 19 25) (V2 43 58))

(!#!) :: Tran a c d -> Tran a b c -> Tran a b d infix 2

Compose two transformations.

trace :: FreeBialgebra a f => (f ** f) a -> a

Trace of an endomorphism.

>>> trace $ m22 1.0 2.0 3.0 4.0
5.0

transpose :: Free f => Free g => (f ** g) a -> (g ** f) a

Transpose a matrix.

>>> transpose $ m23 1 2 3 4 5 6 :: M32 Int
V3 (V2 1 4) (V2 2 5) (V2 3 6)

inv1 :: Field a => M11 a -> M11 a

1x1 matrix inverse over a field.

>>> inv1 $ m11 4.0 :: M11 Double
Compose (V1 (V1 0.25))

inv2 :: Field a => M22 a -> M22 a

2x2 matrix inverse over a field.

>>> inv2 $ m22 1 2 3 4 :: M22 Double
Compose (V2 (V2 (-2.0) 1.0) (V2 1.5 (-0.5)))

bdet2 :: Semiring a => Basis2 E2 E2 f g => (f ** g) a -> (a, a)

2x2 matrix bdeterminant over a commutative semiring.

>>> bdet2 $ m22 1 2 3 4
(4,6)

det2 :: Ring a => Basis2 E2 E2 f g => (f ** g) a -> a

2x2 matrix determinant over a commutative ring.

det2 = uncurry (-) . bdet2

>>> det2 $ m22 1 2 3 4 :: Double
-2.0

bdet3 :: Semiring a => Basis2 E3 E3 f g => (f ** g) a -> (a, a)

3x3 matrix bdeterminant over a commutative semiring.

>>> bdet3 (V3 (V3 1 2 3) (V3 4 5 6) (V3 7 8 9))
(225, 225)

det3 :: Ring a => Basis2 E3 E3 f g => (f ** g) a -> a

3x3 double-precision matrix determinant.

det3 = uncurry (-) . bdet3

Implementation uses a cofactor expansion to avoid loss of precision.

>>> det3 $ m33 1 2 3 4 5 6 7 8 9
0

inv3 :: Field a => M33 a -> M33 a

3x3 matrix inverse.

>>> inv3 $ m33 1 2 4 4 2 2 1 1 1 :: M33 Double
Compose (V3 (V3 0.0 0.5 (-1.0)) (V3 (-0.5) (-0.75) 3.5) (V3 0.5 0.25 (-1.5)))

bdet4 :: Semiring a => Basis2 E4 E4 f g => (f ** g) a -> (a, a)

4x4 matrix bdeterminant over a commutative semiring.

>>> bdet4 $ m44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
(27728,27728)

det4 :: Ring a => Basis2 E4 E4 f g => (f ** g) a -> a

4x4 matrix determinant over a commutative ring.

det4 = uncurry (-) . bdet4

This implementation uses a cofactor expansion to avoid loss of precision.

>>> det4 $ m44 1 0 3 2 2 0 2 1 0 0 0 1 0 3 4 0 :: Rational
(-12) % 1

inv4 :: Field a => M44 a -> M44 a

4x4 matrix inverse.

>>> row E41 . inv4 $ m44 1 0 3 2 2 0 2 1 0 0 0 1 0 3 4 0 :: V4 Rational
V4 (6 % (-12)) ((-9) % (-12)) ((-3) % (-12)) (0 % (-12))

Matrix accessors and constructors

tran :: Free f => FreeCounital a g => (f ** g) a -> Tran a (Rep f) (Rep g)

Lift a matrix into a linear transformation

 (.#) = (!#) . tran

elt2 :: Basis2 b c f g => b -> c -> (f ** g) a -> a

Retrieve an element of a matrix.

>>> elt2 E21 E21 $ m22 1 2 3 4
1

row :: Free f => Rep f -> (f ** g) a -> g a

Retrieve a row of a matrix.

>>> row E22 $ m23 1 2 3 4 5 6
V3 4 5 6

rows :: Free f => Free g => g a -> (f ** g) a

Obtain a matrix by stacking rows.

>>> rows (V2 1 2) :: M22 Int
V2 (V2 1 2) (V2 1 2)

col :: Free f => Free g => Rep g -> (f ** g) a -> f a

Retrieve a column of a matrix.

>>> elt E22 . col E31 $ m23 1 2 3 4 5 6
4

cols :: Free f => Free g => f a -> (f ** g) a

Obtain a matrix by stacking columns.

>>> cols (V2 1 2) :: M22 Int
V2 (V2 1 1) (V2 2 2)

diag :: FreeCoalgebra a f => f a -> (f ** f) a

Obtain a diagonal matrix from a vector.

 diag = flip bindRep id . getCompose

codiag :: FreeAlgebra a f => (f ** f) a -> f a

Obtain the diagonal of a matrix as a vector.

 codiag f = tabulate $ append (index . index (getCompose f))

>>> codiag $ m22 1.0 2.0 3.0 4.0
V2 1.0 4.0

outer :: Semiring a => Free f => Free g => f a -> g a -> (f ** g) a

Outer product.

>>> V2 1 1 `outer` V2 1 1
Compose (V2 (V2 1 1) (V2 1 1))

scalar :: FreeCoalgebra a f => a -> (f ** f) a

Obtain a scalar matrix from a scalar.

>>> scalar 4.0 :: M22 Double
Compose (V2 (V2 4.0 0.0) (V2 0.0 4.0))

identity :: FreeCoalgebra a f => (f ** f) a

Obtain an identity matrix.

>>> identity :: M33 Int
Compose (V3 (V3 1 0 0) (V3 0 1 0) (V3 0 0 1))

Vector types

newtype V1 a

Constructors

V1 a

Instances

Functor V1

Defined in Data.Semimodule.Free

Methods

fmap :: (a -> b) -> V1 a -> V1 b

(<$) :: a -> V1 b -> V1 a

Applicative V1

Defined in Data.Semimodule.Free

Methods

pure :: a -> V1 a

(<*>) :: V1 (a -> b) -> V1 a -> V1 b

liftA2 :: (a -> b -> c) -> V1 a -> V1 b -> V1 c

(*>) :: V1 a -> V1 b -> V1 b

(<*) :: V1 a -> V1 b -> V1 a

Foldable V1

Defined in Data.Semimodule.Free

Methods

fold :: Monoid m => V1 m -> m

foldMap :: Monoid m => (a -> m) -> V1 a -> m

foldr :: (a -> b -> b) -> b -> V1 a -> b

foldr' :: (a -> b -> b) -> b -> V1 a -> b

foldl :: (b -> a -> b) -> b -> V1 a -> b

foldl' :: (b -> a -> b) -> b -> V1 a -> b

foldr1 :: (a -> a -> a) -> V1 a -> a

foldl1 :: (a -> a -> a) -> V1 a -> a

toList :: V1 a -> [a]

null :: V1 a -> Bool

length :: V1 a -> Int

elem :: Eq a => a -> V1 a -> Bool

maximum :: Ord a => V1 a -> a

minimum :: Ord a => V1 a -> a

sum :: Num a => V1 a -> a

product :: Num a => V1 a -> a

Distributive V1

Defined in Data.Semimodule.Free

Methods

distribute :: Functor f => f (V1 a) -> V1 (f a)

collect :: Functor f => (a -> V1 b) -> f a -> V1 (f b)

distributeM :: Monad m => m (V1 a) -> V1 (m a)

collectM :: Monad m => (a -> V1 b) -> m a -> V1 (m b)

Representable V1

Defined in Data.Semimodule.Free

Associated Types

type Rep V1 :: Type

Methods

tabulate :: (Rep V1 -> a) -> V1 a

index :: V1 a -> Rep V1 -> a

Show1 V1

Defined in Data.Semimodule.Free

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V1 a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V1 a] -> ShowS

Foldable1 V1

Defined in Data.Semimodule.Free

Methods

fold1 :: Semigroup m => V1 m -> m

foldMap1 :: Semigroup m => (a -> m) -> V1 a -> m

toNonEmpty :: V1 a -> NonEmpty a

Semiring a => Bisemimodule a a (V1 a)

Defined in Data.Semimodule.Free

Methods

discale :: a -> a -> V1 a -> V1 a

Semiring a => RightSemimodule a (V1 a)

Defined in Data.Semimodule.Free

Methods

rscale :: a -> V1 a -> V1 a

Semiring a => LeftSemimodule a (V1 a)

Defined in Data.Semimodule.Free

Methods

lscale :: a -> V1 a -> V1 a

Eq a => Eq (V1 a)

Defined in Data.Semimodule.Free

Methods

(==) :: V1 a -> V1 a -> Bool

(/=) :: V1 a -> V1 a -> Bool

Ord a => Ord (V1 a)

Defined in Data.Semimodule.Free

Methods

compare :: V1 a -> V1 a -> Ordering

(<) :: V1 a -> V1 a -> Bool

(<=) :: V1 a -> V1 a -> Bool

(>) :: V1 a -> V1 a -> Bool

(>=) :: V1 a -> V1 a -> Bool

max :: V1 a -> V1 a -> V1 a

min :: V1 a -> V1 a -> V1 a

Show a => Show (V1 a)

Defined in Data.Semimodule.Free

Methods

showsPrec :: Int -> V1 a -> ShowS

show :: V1 a -> String

showList :: [V1 a] -> ShowS

Semiring a => Semigroup (Multiplicative (M11 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Multiplicative (M11 a) -> Multiplicative (M11 a) -> Multiplicative (M11 a)

sconcat :: NonEmpty (Multiplicative (M11 a)) -> Multiplicative (M11 a)

stimes :: Integral b => b -> Multiplicative (M11 a) -> Multiplicative (M11 a)

(Additive - Semigroup) a => Semigroup (Additive (V1 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (V1 a) -> Additive (V1 a) -> Additive (V1 a)

sconcat :: NonEmpty (Additive (V1 a)) -> Additive (V1 a)

stimes :: Integral b => b -> Additive (V1 a) -> Additive (V1 a)

(Additive - Semigroup) a => Semigroup (Additive (M41 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M41 a) -> Additive (M41 a) -> Additive (M41 a)

sconcat :: NonEmpty (Additive (M41 a)) -> Additive (M41 a)

stimes :: Integral b => b -> Additive (M41 a) -> Additive (M41 a)

(Additive - Semigroup) a => Semigroup (Additive (M31 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M31 a) -> Additive (M31 a) -> Additive (M31 a)

sconcat :: NonEmpty (Additive (M31 a)) -> Additive (M31 a)

stimes :: Integral b => b -> Additive (M31 a) -> Additive (M31 a)

(Additive - Semigroup) a => Semigroup (Additive (M21 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M21 a) -> Additive (M21 a) -> Additive (M21 a)

sconcat :: NonEmpty (Additive (M21 a)) -> Additive (M21 a)

stimes :: Integral b => b -> Additive (M21 a) -> Additive (M21 a)

(Additive - Semigroup) a => Semigroup (Additive (M14 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M14 a) -> Additive (M14 a) -> Additive (M14 a)

sconcat :: NonEmpty (Additive (M14 a)) -> Additive (M14 a)

stimes :: Integral b => b -> Additive (M14 a) -> Additive (M14 a)

(Additive - Semigroup) a => Semigroup (Additive (M13 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M13 a) -> Additive (M13 a) -> Additive (M13 a)

sconcat :: NonEmpty (Additive (M13 a)) -> Additive (M13 a)

stimes :: Integral b => b -> Additive (M13 a) -> Additive (M13 a)

(Additive - Semigroup) a => Semigroup (Additive (M12 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M12 a) -> Additive (M12 a) -> Additive (M12 a)

sconcat :: NonEmpty (Additive (M12 a)) -> Additive (M12 a)

stimes :: Integral b => b -> Additive (M12 a) -> Additive (M12 a)

(Additive - Semigroup) a => Semigroup (Additive (M11 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M11 a) -> Additive (M11 a) -> Additive (M11 a)

sconcat :: NonEmpty (Additive (M11 a)) -> Additive (M11 a)

stimes :: Integral b => b -> Additive (M11 a) -> Additive (M11 a)

Semiring a => Monoid (Multiplicative (M11 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Multiplicative (M11 a)

mappend :: Multiplicative (M11 a) -> Multiplicative (M11 a) -> Multiplicative (M11 a)

mconcat :: [Multiplicative (M11 a)] -> Multiplicative (M11 a)

(Additive - Monoid) a => Monoid (Additive (V1 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (V1 a)

mappend :: Additive (V1 a) -> Additive (V1 a) -> Additive (V1 a)

mconcat :: [Additive (V1 a)] -> Additive (V1 a)

(Additive - Monoid) a => Monoid (Additive (M41 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M41 a)

mappend :: Additive (M41 a) -> Additive (M41 a) -> Additive (M41 a)

mconcat :: [Additive (M41 a)] -> Additive (M41 a)

(Additive - Monoid) a => Monoid (Additive (M31 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M31 a)

mappend :: Additive (M31 a) -> Additive (M31 a) -> Additive (M31 a)

mconcat :: [Additive (M31 a)] -> Additive (M31 a)

(Additive - Monoid) a => Monoid (Additive (M21 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M21 a)

mappend :: Additive (M21 a) -> Additive (M21 a) -> Additive (M21 a)

mconcat :: [Additive (M21 a)] -> Additive (M21 a)

(Additive - Monoid) a => Monoid (Additive (M14 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M14 a)

mappend :: Additive (M14 a) -> Additive (M14 a) -> Additive (M14 a)

mconcat :: [Additive (M14 a)] -> Additive (M14 a)

(Additive - Monoid) a => Monoid (Additive (M13 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M13 a)

mappend :: Additive (M13 a) -> Additive (M13 a) -> Additive (M13 a)

mconcat :: [Additive (M13 a)] -> Additive (M13 a)

(Additive - Monoid) a => Monoid (Additive (M12 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M12 a)

mappend :: Additive (M12 a) -> Additive (M12 a) -> Additive (M12 a)

mconcat :: [Additive (M12 a)] -> Additive (M12 a)

(Additive - Monoid) a => Monoid (Additive (M11 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M11 a)

mappend :: Additive (M11 a) -> Additive (M11 a) -> Additive (M11 a)

mconcat :: [Additive (M11 a)] -> Additive (M11 a)

(Additive - Group) a => Group (Additive (V1 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (V1 a) -> Additive (V1 a)

greplicate :: Integer -> Additive (V1 a) -> Additive (V1 a)

(Additive - Group) a => Group (Additive (M41 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M41 a) -> Additive (M41 a)

greplicate :: Integer -> Additive (M41 a) -> Additive (M41 a)

(Additive - Group) a => Group (Additive (M31 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M31 a) -> Additive (M31 a)

greplicate :: Integer -> Additive (M31 a) -> Additive (M31 a)

(Additive - Group) a => Group (Additive (M21 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M21 a) -> Additive (M21 a)

greplicate :: Integer -> Additive (M21 a) -> Additive (M21 a)

(Additive - Group) a => Group (Additive (M14 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M14 a) -> Additive (M14 a)

greplicate :: Integer -> Additive (M14 a) -> Additive (M14 a)

(Additive - Group) a => Group (Additive (M13 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M13 a) -> Additive (M13 a)

greplicate :: Integer -> Additive (M13 a) -> Additive (M13 a)

(Additive - Group) a => Group (Additive (M12 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M12 a) -> Additive (M12 a)

greplicate :: Integer -> Additive (M12 a) -> Additive (M12 a)

(Additive - Group) a => Group (Additive (M11 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M11 a) -> Additive (M11 a)

greplicate :: Integer -> Additive (M11 a) -> Additive (M11 a)

(Additive - Group) a => Loop (Additive (V1 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (V1 a)

lreplicate :: Natural -> Additive (V1 a) -> Additive (V1 a)

(Additive - Group) a => Loop (Additive (M41 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M41 a)

lreplicate :: Natural -> Additive (M41 a) -> Additive (M41 a)

(Additive - Group) a => Loop (Additive (M31 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M31 a)

lreplicate :: Natural -> Additive (M31 a) -> Additive (M31 a)

(Additive - Group) a => Loop (Additive (M21 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M21 a)

lreplicate :: Natural -> Additive (M21 a) -> Additive (M21 a)

(Additive - Group) a => Loop (Additive (M14 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M14 a)

lreplicate :: Natural -> Additive (M14 a) -> Additive (M14 a)

(Additive - Group) a => Loop (Additive (M13 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M13 a)

lreplicate :: Natural -> Additive (M13 a) -> Additive (M13 a)

(Additive - Group) a => Loop (Additive (M12 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M12 a)

lreplicate :: Natural -> Additive (M12 a) -> Additive (M12 a)

(Additive - Group) a => Loop (Additive (M11 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M11 a)

lreplicate :: Natural -> Additive (M11 a) -> Additive (M11 a)

(Additive - Group) a => Quasigroup (Additive (V1 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (V1 a) -> Additive (V1 a) -> Additive (V1 a)

(\\) :: Additive (V1 a) -> Additive (V1 a) -> Additive (V1 a)

(Additive - Group) a => Quasigroup (Additive (M41 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M41 a) -> Additive (M41 a) -> Additive (M41 a)

(\\) :: Additive (M41 a) -> Additive (M41 a) -> Additive (M41 a)

(Additive - Group) a => Quasigroup (Additive (M31 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M31 a) -> Additive (M31 a) -> Additive (M31 a)

(\\) :: Additive (M31 a) -> Additive (M31 a) -> Additive (M31 a)

(Additive - Group) a => Quasigroup (Additive (M21 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M21 a) -> Additive (M21 a) -> Additive (M21 a)

(\\) :: Additive (M21 a) -> Additive (M21 a) -> Additive (M21 a)

(Additive - Group) a => Quasigroup (Additive (M14 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M14 a) -> Additive (M14 a) -> Additive (M14 a)

(\\) :: Additive (M14 a) -> Additive (M14 a) -> Additive (M14 a)

(Additive - Group) a => Quasigroup (Additive (M13 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M13 a) -> Additive (M13 a) -> Additive (M13 a)

(\\) :: Additive (M13 a) -> Additive (M13 a) -> Additive (M13 a)

(Additive - Group) a => Quasigroup (Additive (M12 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M12 a) -> Additive (M12 a) -> Additive (M12 a)

(\\) :: Additive (M12 a) -> Additive (M12 a) -> Additive (M12 a)

(Additive - Group) a => Quasigroup (Additive (M11 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M11 a) -> Additive (M11 a) -> Additive (M11 a)

(\\) :: Additive (M11 a) -> Additive (M11 a) -> Additive (M11 a)

(Additive - Group) a => Magma (Additive (V1 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (V1 a) -> Additive (V1 a) -> Additive (V1 a)

(Additive - Group) a => Magma (Additive (M41 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M41 a) -> Additive (M41 a) -> Additive (M41 a)

(Additive - Group) a => Magma (Additive (M31 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M31 a) -> Additive (M31 a) -> Additive (M31 a)

(Additive - Group) a => Magma (Additive (M21 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M21 a) -> Additive (M21 a) -> Additive (M21 a)

(Additive - Group) a => Magma (Additive (M14 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M14 a) -> Additive (M14 a) -> Additive (M14 a)

(Additive - Group) a => Magma (Additive (M13 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M13 a) -> Additive (M13 a) -> Additive (M13 a)

(Additive - Group) a => Magma (Additive (M12 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M12 a) -> Additive (M12 a) -> Additive (M12 a)

(Additive - Group) a => Magma (Additive (M11 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M11 a) -> Additive (M11 a) -> Additive (M11 a)

Ring a => Ring (M11 a)

Defined in Data.Semimodule.Free

Semiring a => Semiring (M11 a)

Defined in Data.Semimodule.Free

Semiring a => Presemiring (M11 a)

Defined in Data.Semimodule.Free

Semiring a => RightSemimodule (M44 a) (M14 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M44 a -> M14 a -> M14 a

Semiring a => RightSemimodule (M33 a) (M13 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M33 a -> M13 a -> M13 a

Semiring a => RightSemimodule (M22 a) (M12 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M22 a -> M12 a -> M12 a

Semiring a => RightSemimodule (M11 a) (M41 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M11 a -> M41 a -> M41 a

Semiring a => RightSemimodule (M11 a) (M31 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M11 a -> M31 a -> M31 a

Semiring a => RightSemimodule (M11 a) (M21 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M11 a -> M21 a -> M21 a

Semiring a => RightSemimodule (M11 a) (M11 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M11 a -> M11 a -> M11 a

Semiring a => LeftSemimodule (M44 a) (M41 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M44 a -> M41 a -> M41 a

Semiring a => LeftSemimodule (M33 a) (M31 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M33 a -> M31 a -> M31 a

Semiring a => LeftSemimodule (M22 a) (M21 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M22 a -> M21 a -> M21 a

Semiring a => LeftSemimodule (M11 a) (M14 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M11 a -> M14 a -> M14 a

Semiring a => LeftSemimodule (M11 a) (M13 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M11 a -> M13 a -> M13 a

Semiring a => LeftSemimodule (M11 a) (M12 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M11 a -> M12 a -> M12 a

Semiring a => LeftSemimodule (M11 a) (M11 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M11 a -> M11 a -> M11 a

Semiring a => Bisemimodule (M44 a) (M11 a) (M41 a)

Defined in Data.Semimodule.Free

Methods

discale :: M44 a -> M11 a -> M41 a -> M41 a

Semiring a => Bisemimodule (M33 a) (M11 a) (M31 a)

Defined in Data.Semimodule.Free

Methods

discale :: M33 a -> M11 a -> M31 a -> M31 a

Semiring a => Bisemimodule (M22 a) (M11 a) (M21 a)

Defined in Data.Semimodule.Free

Methods

discale :: M22 a -> M11 a -> M21 a -> M21 a

Semiring a => Bisemimodule (M11 a) (M44 a) (M14 a)

Defined in Data.Semimodule.Free

Methods

discale :: M11 a -> M44 a -> M14 a -> M14 a

Semiring a => Bisemimodule (M11 a) (M33 a) (M13 a)

Defined in Data.Semimodule.Free

Methods

discale :: M11 a -> M33 a -> M13 a -> M13 a

Semiring a => Bisemimodule (M11 a) (M22 a) (M12 a)

Defined in Data.Semimodule.Free

Methods

discale :: M11 a -> M22 a -> M12 a -> M12 a

Semiring a => Bisemimodule (M11 a) (M11 a) (M11 a)

Defined in Data.Semimodule.Free

Methods

discale :: M11 a -> M11 a -> M11 a -> M11 a

type Rep V1

Defined in Data.Semimodule.Free

type Rep V1 = E1

unV1 :: V1 a -> a

data V2 a

Constructors

V2 !a !a

Instances

Functor V2

Defined in Data.Semimodule.Free

Methods

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

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

Applicative V2

Defined in Data.Semimodule.Free

Methods

pure :: a -> V2 a

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

liftA2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c

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

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

Foldable V2

Defined in Data.Semimodule.Free

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.Free

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.Free

Associated Types

type Rep V2 :: Type

Methods

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

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

Show1 V2

Defined in Data.Semimodule.Free

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V2 a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V2 a] -> ShowS

Foldable1 V2

Defined in Data.Semimodule.Free

Methods

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

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

toNonEmpty :: V2 a -> NonEmpty a

Semiring a => Bisemimodule a a (V2 a)

Defined in Data.Semimodule.Free

Methods

discale :: a -> a -> V2 a -> V2 a

Semiring a => RightSemimodule a (V2 a)

Defined in Data.Semimodule.Free

Methods

rscale :: a -> V2 a -> V2 a

Semiring a => LeftSemimodule a (V2 a)

Defined in Data.Semimodule.Free

Methods

lscale :: a -> V2 a -> V2 a

Eq a => Eq (V2 a)

Defined in Data.Semimodule.Free

Methods

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

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

Ord a => Ord (V2 a)

Defined in Data.Semimodule.Free

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.Free

Methods

showsPrec :: Int -> V2 a -> ShowS

show :: V2 a -> String

showList :: [V2 a] -> ShowS

Semiring a => Semigroup (Multiplicative (M22 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Multiplicative (M22 a) -> Multiplicative (M22 a) -> Multiplicative (M22 a)

sconcat :: NonEmpty (Multiplicative (M22 a)) -> Multiplicative (M22 a)

stimes :: Integral b => b -> Multiplicative (M22 a) -> Multiplicative (M22 a)

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

Defined in Data.Semimodule.Free

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 (Additive (M42 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M42 a) -> Additive (M42 a) -> Additive (M42 a)

sconcat :: NonEmpty (Additive (M42 a)) -> Additive (M42 a)

stimes :: Integral b => b -> Additive (M42 a) -> Additive (M42 a)

(Additive - Semigroup) a => Semigroup (Additive (M32 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M32 a) -> Additive (M32 a) -> Additive (M32 a)

sconcat :: NonEmpty (Additive (M32 a)) -> Additive (M32 a)

stimes :: Integral b => b -> Additive (M32 a) -> Additive (M32 a)

(Additive - Semigroup) a => Semigroup (Additive (M24 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M24 a) -> Additive (M24 a) -> Additive (M24 a)

sconcat :: NonEmpty (Additive (M24 a)) -> Additive (M24 a)

stimes :: Integral b => b -> Additive (M24 a) -> Additive (M24 a)

(Additive - Semigroup) a => Semigroup (Additive (M23 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M23 a) -> Additive (M23 a) -> Additive (M23 a)

sconcat :: NonEmpty (Additive (M23 a)) -> Additive (M23 a)

stimes :: Integral b => b -> Additive (M23 a) -> Additive (M23 a)

(Additive - Semigroup) a => Semigroup (Additive (M22 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M22 a) -> Additive (M22 a) -> Additive (M22 a)

sconcat :: NonEmpty (Additive (M22 a)) -> Additive (M22 a)

stimes :: Integral b => b -> Additive (M22 a) -> Additive (M22 a)

(Additive - Semigroup) a => Semigroup (Additive (M21 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M21 a) -> Additive (M21 a) -> Additive (M21 a)

sconcat :: NonEmpty (Additive (M21 a)) -> Additive (M21 a)

stimes :: Integral b => b -> Additive (M21 a) -> Additive (M21 a)

(Additive - Semigroup) a => Semigroup (Additive (M12 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M12 a) -> Additive (M12 a) -> Additive (M12 a)

sconcat :: NonEmpty (Additive (M12 a)) -> Additive (M12 a)

stimes :: Integral b => b -> Additive (M12 a) -> Additive (M12 a)

Semiring a => Monoid (Multiplicative (M22 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Multiplicative (M22 a)

mappend :: Multiplicative (M22 a) -> Multiplicative (M22 a) -> Multiplicative (M22 a)

mconcat :: [Multiplicative (M22 a)] -> Multiplicative (M22 a)

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

Defined in Data.Semimodule.Free

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 (Additive (M42 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M42 a)

mappend :: Additive (M42 a) -> Additive (M42 a) -> Additive (M42 a)

mconcat :: [Additive (M42 a)] -> Additive (M42 a)

(Additive - Monoid) a => Monoid (Additive (M32 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M32 a)

mappend :: Additive (M32 a) -> Additive (M32 a) -> Additive (M32 a)

mconcat :: [Additive (M32 a)] -> Additive (M32 a)

(Additive - Monoid) a => Monoid (Additive (M24 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M24 a)

mappend :: Additive (M24 a) -> Additive (M24 a) -> Additive (M24 a)

mconcat :: [Additive (M24 a)] -> Additive (M24 a)

(Additive - Monoid) a => Monoid (Additive (M23 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M23 a)

mappend :: Additive (M23 a) -> Additive (M23 a) -> Additive (M23 a)

mconcat :: [Additive (M23 a)] -> Additive (M23 a)

(Additive - Monoid) a => Monoid (Additive (M22 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M22 a)

mappend :: Additive (M22 a) -> Additive (M22 a) -> Additive (M22 a)

mconcat :: [Additive (M22 a)] -> Additive (M22 a)

(Additive - Monoid) a => Monoid (Additive (M21 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M21 a)

mappend :: Additive (M21 a) -> Additive (M21 a) -> Additive (M21 a)

mconcat :: [Additive (M21 a)] -> Additive (M21 a)

(Additive - Monoid) a => Monoid (Additive (M12 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M12 a)

mappend :: Additive (M12 a) -> Additive (M12 a) -> Additive (M12 a)

mconcat :: [Additive (M12 a)] -> Additive (M12 a)

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

Defined in Data.Semimodule.Free

Methods

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

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

(Additive - Group) a => Group (Additive (M42 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M42 a) -> Additive (M42 a)

greplicate :: Integer -> Additive (M42 a) -> Additive (M42 a)

(Additive - Group) a => Group (Additive (M32 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M32 a) -> Additive (M32 a)

greplicate :: Integer -> Additive (M32 a) -> Additive (M32 a)

(Additive - Group) a => Group (Additive (M24 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M24 a) -> Additive (M24 a)

greplicate :: Integer -> Additive (M24 a) -> Additive (M24 a)

(Additive - Group) a => Group (Additive (M23 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M23 a) -> Additive (M23 a)

greplicate :: Integer -> Additive (M23 a) -> Additive (M23 a)

(Additive - Group) a => Group (Additive (M22 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M22 a) -> Additive (M22 a)

greplicate :: Integer -> Additive (M22 a) -> Additive (M22 a)

(Additive - Group) a => Group (Additive (M21 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M21 a) -> Additive (M21 a)

greplicate :: Integer -> Additive (M21 a) -> Additive (M21 a)

(Additive - Group) a => Group (Additive (M12 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M12 a) -> Additive (M12 a)

greplicate :: Integer -> Additive (M12 a) -> Additive (M12 a)

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

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (V2 a)

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

(Additive - Group) a => Loop (Additive (M42 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M42 a)

lreplicate :: Natural -> Additive (M42 a) -> Additive (M42 a)

(Additive - Group) a => Loop (Additive (M32 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M32 a)

lreplicate :: Natural -> Additive (M32 a) -> Additive (M32 a)

(Additive - Group) a => Loop (Additive (M24 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M24 a)

lreplicate :: Natural -> Additive (M24 a) -> Additive (M24 a)

(Additive - Group) a => Loop (Additive (M23 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M23 a)

lreplicate :: Natural -> Additive (M23 a) -> Additive (M23 a)

(Additive - Group) a => Loop (Additive (M22 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M22 a)

lreplicate :: Natural -> Additive (M22 a) -> Additive (M22 a)

(Additive - Group) a => Loop (Additive (M21 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M21 a)

lreplicate :: Natural -> Additive (M21 a) -> Additive (M21 a)

(Additive - Group) a => Loop (Additive (M12 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M12 a)

lreplicate :: Natural -> Additive (M12 a) -> Additive (M12 a)

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

Defined in Data.Semimodule.Free

Methods

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

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

(Additive - Group) a => Quasigroup (Additive (M42 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M42 a) -> Additive (M42 a) -> Additive (M42 a)

(\\) :: Additive (M42 a) -> Additive (M42 a) -> Additive (M42 a)

(Additive - Group) a => Quasigroup (Additive (M32 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M32 a) -> Additive (M32 a) -> Additive (M32 a)

(\\) :: Additive (M32 a) -> Additive (M32 a) -> Additive (M32 a)

(Additive - Group) a => Quasigroup (Additive (M24 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M24 a) -> Additive (M24 a) -> Additive (M24 a)

(\\) :: Additive (M24 a) -> Additive (M24 a) -> Additive (M24 a)

(Additive - Group) a => Quasigroup (Additive (M23 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M23 a) -> Additive (M23 a) -> Additive (M23 a)

(\\) :: Additive (M23 a) -> Additive (M23 a) -> Additive (M23 a)

(Additive - Group) a => Quasigroup (Additive (M22 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M22 a) -> Additive (M22 a) -> Additive (M22 a)

(\\) :: Additive (M22 a) -> Additive (M22 a) -> Additive (M22 a)

(Additive - Group) a => Quasigroup (Additive (M21 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M21 a) -> Additive (M21 a) -> Additive (M21 a)

(\\) :: Additive (M21 a) -> Additive (M21 a) -> Additive (M21 a)

(Additive - Group) a => Quasigroup (Additive (M12 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M12 a) -> Additive (M12 a) -> Additive (M12 a)

(\\) :: Additive (M12 a) -> Additive (M12 a) -> Additive (M12 a)

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

Defined in Data.Semimodule.Free

Methods

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

(Additive - Group) a => Magma (Additive (M42 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M42 a) -> Additive (M42 a) -> Additive (M42 a)

(Additive - Group) a => Magma (Additive (M32 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M32 a) -> Additive (M32 a) -> Additive (M32 a)

(Additive - Group) a => Magma (Additive (M24 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M24 a) -> Additive (M24 a) -> Additive (M24 a)

(Additive - Group) a => Magma (Additive (M23 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M23 a) -> Additive (M23 a) -> Additive (M23 a)

(Additive - Group) a => Magma (Additive (M22 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M22 a) -> Additive (M22 a) -> Additive (M22 a)

(Additive - Group) a => Magma (Additive (M21 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M21 a) -> Additive (M21 a) -> Additive (M21 a)

(Additive - Group) a => Magma (Additive (M12 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M12 a) -> Additive (M12 a) -> Additive (M12 a)

Ring a => Ring (M22 a)

Defined in Data.Semimodule.Free

Semiring a => Semiring (M22 a)

Defined in Data.Semimodule.Free

Semiring a => Presemiring (M22 a)

Defined in Data.Semimodule.Free

Semiring a => RightSemimodule (M44 a) (M24 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M44 a -> M24 a -> M24 a

Semiring a => RightSemimodule (M33 a) (M23 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M33 a -> M23 a -> M23 a

Semiring a => RightSemimodule (M22 a) (M42 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M22 a -> M42 a -> M42 a

Semiring a => RightSemimodule (M22 a) (M32 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M22 a -> M32 a -> M32 a

Semiring a => RightSemimodule (M22 a) (M22 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M22 a -> M22 a -> M22 a

Semiring a => RightSemimodule (M22 a) (M12 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M22 a -> M12 a -> M12 a

Semiring a => RightSemimodule (M11 a) (M21 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M11 a -> M21 a -> M21 a

Semiring a => LeftSemimodule (M44 a) (M42 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M44 a -> M42 a -> M42 a

Semiring a => LeftSemimodule (M33 a) (M32 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M33 a -> M32 a -> M32 a

Semiring a => LeftSemimodule (M22 a) (M24 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M22 a -> M24 a -> M24 a

Semiring a => LeftSemimodule (M22 a) (M23 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M22 a -> M23 a -> M23 a

Semiring a => LeftSemimodule (M22 a) (M22 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M22 a -> M22 a -> M22 a

Semiring a => LeftSemimodule (M22 a) (M21 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M22 a -> M21 a -> M21 a

Semiring a => LeftSemimodule (M11 a) (M12 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M11 a -> M12 a -> M12 a

Semiring a => Bisemimodule (M44 a) (M22 a) (M42 a)

Defined in Data.Semimodule.Free

Methods

discale :: M44 a -> M22 a -> M42 a -> M42 a

Semiring a => Bisemimodule (M33 a) (M22 a) (M32 a)

Defined in Data.Semimodule.Free

Methods

discale :: M33 a -> M22 a -> M32 a -> M32 a

Semiring a => Bisemimodule (M22 a) (M44 a) (M24 a)

Defined in Data.Semimodule.Free

Methods

discale :: M22 a -> M44 a -> M24 a -> M24 a

Semiring a => Bisemimodule (M22 a) (M33 a) (M23 a)

Defined in Data.Semimodule.Free

Methods

discale :: M22 a -> M33 a -> M23 a -> M23 a

Semiring a => Bisemimodule (M22 a) (M22 a) (M22 a)

Defined in Data.Semimodule.Free

Methods

discale :: M22 a -> M22 a -> M22 a -> M22 a

Semiring a => Bisemimodule (M22 a) (M11 a) (M21 a)

Defined in Data.Semimodule.Free

Methods

discale :: M22 a -> M11 a -> M21 a -> M21 a

Semiring a => Bisemimodule (M11 a) (M22 a) (M12 a)

Defined in Data.Semimodule.Free

Methods

discale :: M11 a -> M22 a -> M12 a -> M12 a

type Rep V2

Defined in Data.Semimodule.Free

type Rep V2 = E2

data V3 a

Constructors

V3 !a !a !a

Instances

Functor V3

Defined in Data.Semimodule.Free

Methods

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

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

Applicative V3

Defined in Data.Semimodule.Free

Methods

pure :: a -> V3 a

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

liftA2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c

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

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

Foldable V3

Defined in Data.Semimodule.Free

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.Free

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.Free

Associated Types

type Rep V3 :: Type

Methods

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

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

Eq1 V3

Defined in Data.Semimodule.Free

Methods

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

Show1 V3

Defined in Data.Semimodule.Free

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V3 a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V3 a] -> ShowS

Foldable1 V3

Defined in Data.Semimodule.Free

Methods

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

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

toNonEmpty :: V3 a -> NonEmpty a

Semiring a => Bisemimodule a a (V3 a)

Defined in Data.Semimodule.Free

Methods

discale :: a -> a -> V3 a -> V3 a

Semiring a => RightSemimodule a (V3 a)

Defined in Data.Semimodule.Free

Methods

rscale :: a -> V3 a -> V3 a

Semiring a => LeftSemimodule a (V3 a)

Defined in Data.Semimodule.Free

Methods

lscale :: a -> V3 a -> V3 a

Eq a => Eq (V3 a)

Defined in Data.Semimodule.Free

Methods

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

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

Ord a => Ord (V3 a)

Defined in Data.Semimodule.Free

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.Free

Methods

showsPrec :: Int -> V3 a -> ShowS

show :: V3 a -> String

showList :: [V3 a] -> ShowS

Semiring a => Semigroup (Multiplicative (M33 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Multiplicative (M33 a) -> Multiplicative (M33 a) -> Multiplicative (M33 a)

sconcat :: NonEmpty (Multiplicative (M33 a)) -> Multiplicative (M33 a)

stimes :: Integral b => b -> Multiplicative (M33 a) -> Multiplicative (M33 a)

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

Defined in Data.Semimodule.Free

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 (Additive (M43 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M43 a) -> Additive (M43 a) -> Additive (M43 a)

sconcat :: NonEmpty (Additive (M43 a)) -> Additive (M43 a)

stimes :: Integral b => b -> Additive (M43 a) -> Additive (M43 a)

(Additive - Semigroup) a => Semigroup (Additive (M34 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M34 a) -> Additive (M34 a) -> Additive (M34 a)

sconcat :: NonEmpty (Additive (M34 a)) -> Additive (M34 a)

stimes :: Integral b => b -> Additive (M34 a) -> Additive (M34 a)

(Additive - Semigroup) a => Semigroup (Additive (M33 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M33 a) -> Additive (M33 a) -> Additive (M33 a)

sconcat :: NonEmpty (Additive (M33 a)) -> Additive (M33 a)

stimes :: Integral b => b -> Additive (M33 a) -> Additive (M33 a)

(Additive - Semigroup) a => Semigroup (Additive (M32 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M32 a) -> Additive (M32 a) -> Additive (M32 a)

sconcat :: NonEmpty (Additive (M32 a)) -> Additive (M32 a)

stimes :: Integral b => b -> Additive (M32 a) -> Additive (M32 a)

(Additive - Semigroup) a => Semigroup (Additive (M23 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M23 a) -> Additive (M23 a) -> Additive (M23 a)

sconcat :: NonEmpty (Additive (M23 a)) -> Additive (M23 a)

stimes :: Integral b => b -> Additive (M23 a) -> Additive (M23 a)

(Additive - Semigroup) a => Semigroup (Additive (M31 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M31 a) -> Additive (M31 a) -> Additive (M31 a)

sconcat :: NonEmpty (Additive (M31 a)) -> Additive (M31 a)

stimes :: Integral b => b -> Additive (M31 a) -> Additive (M31 a)

(Additive - Semigroup) a => Semigroup (Additive (M13 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M13 a) -> Additive (M13 a) -> Additive (M13 a)

sconcat :: NonEmpty (Additive (M13 a)) -> Additive (M13 a)

stimes :: Integral b => b -> Additive (M13 a) -> Additive (M13 a)

Semiring a => Monoid (Multiplicative (M33 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Multiplicative (M33 a)

mappend :: Multiplicative (M33 a) -> Multiplicative (M33 a) -> Multiplicative (M33 a)

mconcat :: [Multiplicative (M33 a)] -> Multiplicative (M33 a)

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

Defined in Data.Semimodule.Free

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 (Additive (M43 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M43 a)

mappend :: Additive (M43 a) -> Additive (M43 a) -> Additive (M43 a)

mconcat :: [Additive (M43 a)] -> Additive (M43 a)

(Additive - Monoid) a => Monoid (Additive (M34 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M34 a)

mappend :: Additive (M34 a) -> Additive (M34 a) -> Additive (M34 a)

mconcat :: [Additive (M34 a)] -> Additive (M34 a)

(Additive - Monoid) a => Monoid (Additive (M33 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M33 a)

mappend :: Additive (M33 a) -> Additive (M33 a) -> Additive (M33 a)

mconcat :: [Additive (M33 a)] -> Additive (M33 a)

(Additive - Monoid) a => Monoid (Additive (M32 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M32 a)

mappend :: Additive (M32 a) -> Additive (M32 a) -> Additive (M32 a)

mconcat :: [Additive (M32 a)] -> Additive (M32 a)

(Additive - Monoid) a => Monoid (Additive (M23 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M23 a)

mappend :: Additive (M23 a) -> Additive (M23 a) -> Additive (M23 a)

mconcat :: [Additive (M23 a)] -> Additive (M23 a)

(Additive - Monoid) a => Monoid (Additive (M31 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M31 a)

mappend :: Additive (M31 a) -> Additive (M31 a) -> Additive (M31 a)

mconcat :: [Additive (M31 a)] -> Additive (M31 a)

(Additive - Monoid) a => Monoid (Additive (M13 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M13 a)

mappend :: Additive (M13 a) -> Additive (M13 a) -> Additive (M13 a)

mconcat :: [Additive (M13 a)] -> Additive (M13 a)

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

Defined in Data.Semimodule.Free

Methods

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

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

(Additive - Group) a => Group (Additive (M43 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M43 a) -> Additive (M43 a)

greplicate :: Integer -> Additive (M43 a) -> Additive (M43 a)

(Additive - Group) a => Group (Additive (M34 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M34 a) -> Additive (M34 a)

greplicate :: Integer -> Additive (M34 a) -> Additive (M34 a)

(Additive - Group) a => Group (Additive (M33 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M33 a) -> Additive (M33 a)

greplicate :: Integer -> Additive (M33 a) -> Additive (M33 a)

(Additive - Group) a => Group (Additive (M32 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M32 a) -> Additive (M32 a)

greplicate :: Integer -> Additive (M32 a) -> Additive (M32 a)

(Additive - Group) a => Group (Additive (M23 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M23 a) -> Additive (M23 a)

greplicate :: Integer -> Additive (M23 a) -> Additive (M23 a)

(Additive - Group) a => Group (Additive (M31 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M31 a) -> Additive (M31 a)

greplicate :: Integer -> Additive (M31 a) -> Additive (M31 a)

(Additive - Group) a => Group (Additive (M13 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M13 a) -> Additive (M13 a)

greplicate :: Integer -> Additive (M13 a) -> Additive (M13 a)

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

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (V3 a)

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

(Additive - Group) a => Loop (Additive (M43 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M43 a)

lreplicate :: Natural -> Additive (M43 a) -> Additive (M43 a)

(Additive - Group) a => Loop (Additive (M34 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M34 a)

lreplicate :: Natural -> Additive (M34 a) -> Additive (M34 a)

(Additive - Group) a => Loop (Additive (M33 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M33 a)

lreplicate :: Natural -> Additive (M33 a) -> Additive (M33 a)

(Additive - Group) a => Loop (Additive (M32 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M32 a)

lreplicate :: Natural -> Additive (M32 a) -> Additive (M32 a)

(Additive - Group) a => Loop (Additive (M23 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M23 a)

lreplicate :: Natural -> Additive (M23 a) -> Additive (M23 a)

(Additive - Group) a => Loop (Additive (M31 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M31 a)

lreplicate :: Natural -> Additive (M31 a) -> Additive (M31 a)

(Additive - Group) a => Loop (Additive (M13 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M13 a)

lreplicate :: Natural -> Additive (M13 a) -> Additive (M13 a)

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

Defined in Data.Semimodule.Free

Methods

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

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

(Additive - Group) a => Quasigroup (Additive (M43 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M43 a) -> Additive (M43 a) -> Additive (M43 a)

(\\) :: Additive (M43 a) -> Additive (M43 a) -> Additive (M43 a)

(Additive - Group) a => Quasigroup (Additive (M34 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M34 a) -> Additive (M34 a) -> Additive (M34 a)

(\\) :: Additive (M34 a) -> Additive (M34 a) -> Additive (M34 a)

(Additive - Group) a => Quasigroup (Additive (M33 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M33 a) -> Additive (M33 a) -> Additive (M33 a)

(\\) :: Additive (M33 a) -> Additive (M33 a) -> Additive (M33 a)

(Additive - Group) a => Quasigroup (Additive (M32 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M32 a) -> Additive (M32 a) -> Additive (M32 a)

(\\) :: Additive (M32 a) -> Additive (M32 a) -> Additive (M32 a)

(Additive - Group) a => Quasigroup (Additive (M23 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M23 a) -> Additive (M23 a) -> Additive (M23 a)

(\\) :: Additive (M23 a) -> Additive (M23 a) -> Additive (M23 a)

(Additive - Group) a => Quasigroup (Additive (M31 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M31 a) -> Additive (M31 a) -> Additive (M31 a)

(\\) :: Additive (M31 a) -> Additive (M31 a) -> Additive (M31 a)

(Additive - Group) a => Quasigroup (Additive (M13 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M13 a) -> Additive (M13 a) -> Additive (M13 a)

(\\) :: Additive (M13 a) -> Additive (M13 a) -> Additive (M13 a)

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

Defined in Data.Semimodule.Free

Methods

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

(Additive - Group) a => Magma (Additive (M43 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M43 a) -> Additive (M43 a) -> Additive (M43 a)

(Additive - Group) a => Magma (Additive (M34 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M34 a) -> Additive (M34 a) -> Additive (M34 a)

(Additive - Group) a => Magma (Additive (M33 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M33 a) -> Additive (M33 a) -> Additive (M33 a)

(Additive - Group) a => Magma (Additive (M32 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M32 a) -> Additive (M32 a) -> Additive (M32 a)

(Additive - Group) a => Magma (Additive (M23 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M23 a) -> Additive (M23 a) -> Additive (M23 a)

(Additive - Group) a => Magma (Additive (M31 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M31 a) -> Additive (M31 a) -> Additive (M31 a)

(Additive - Group) a => Magma (Additive (M13 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M13 a) -> Additive (M13 a) -> Additive (M13 a)

Ring a => Ring (M33 a)

Defined in Data.Semimodule.Free

Semiring a => Semiring (M33 a)

Defined in Data.Semimodule.Free

Semiring a => Presemiring (M33 a)

Defined in Data.Semimodule.Free

Semiring a => RightSemimodule (M44 a) (M34 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M44 a -> M34 a -> M34 a

Semiring a => RightSemimodule (M33 a) (M43 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M33 a -> M43 a -> M43 a

Semiring a => RightSemimodule (M33 a) (M33 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M33 a -> M33 a -> M33 a

Semiring a => RightSemimodule (M33 a) (M23 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M33 a -> M23 a -> M23 a

Semiring a => RightSemimodule (M33 a) (M13 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M33 a -> M13 a -> M13 a

Semiring a => RightSemimodule (M22 a) (M32 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M22 a -> M32 a -> M32 a

Semiring a => RightSemimodule (M11 a) (M31 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M11 a -> M31 a -> M31 a

Semiring a => LeftSemimodule (M44 a) (M43 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M44 a -> M43 a -> M43 a

Semiring a => LeftSemimodule (M33 a) (M34 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M33 a -> M34 a -> M34 a

Semiring a => LeftSemimodule (M33 a) (M33 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M33 a -> M33 a -> M33 a

Semiring a => LeftSemimodule (M33 a) (M32 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M33 a -> M32 a -> M32 a

Semiring a => LeftSemimodule (M33 a) (M31 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M33 a -> M31 a -> M31 a

Semiring a => LeftSemimodule (M22 a) (M23 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M22 a -> M23 a -> M23 a

Semiring a => LeftSemimodule (M11 a) (M13 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M11 a -> M13 a -> M13 a

Semiring a => Bisemimodule (M44 a) (M33 a) (M43 a)

Defined in Data.Semimodule.Free

Methods

discale :: M44 a -> M33 a -> M43 a -> M43 a

Semiring a => Bisemimodule (M33 a) (M44 a) (M34 a)

Defined in Data.Semimodule.Free

Methods

discale :: M33 a -> M44 a -> M34 a -> M34 a

Semiring a => Bisemimodule (M33 a) (M33 a) (M33 a)

Defined in Data.Semimodule.Free

Methods

discale :: M33 a -> M33 a -> M33 a -> M33 a

Semiring a => Bisemimodule (M33 a) (M22 a) (M32 a)

Defined in Data.Semimodule.Free

Methods

discale :: M33 a -> M22 a -> M32 a -> M32 a

Semiring a => Bisemimodule (M33 a) (M11 a) (M31 a)

Defined in Data.Semimodule.Free

Methods

discale :: M33 a -> M11 a -> M31 a -> M31 a

Semiring a => Bisemimodule (M22 a) (M33 a) (M23 a)

Defined in Data.Semimodule.Free

Methods

discale :: M22 a -> M33 a -> M23 a -> M23 a

Semiring a => Bisemimodule (M11 a) (M33 a) (M13 a)

Defined in Data.Semimodule.Free

Methods

discale :: M11 a -> M33 a -> M13 a -> M13 a

type Rep V3

Defined in Data.Semimodule.Free

type Rep V3 = E3

data V4 a

Constructors

V4 !a !a !a !a

Instances

Functor V4

Defined in Data.Semimodule.Free

Methods

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

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

Applicative V4

Defined in Data.Semimodule.Free

Methods

pure :: a -> V4 a

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

liftA2 :: (a -> b -> c) -> V4 a -> V4 b -> V4 c

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

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

Foldable V4

Defined in Data.Semimodule.Free

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.Free

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.Free

Associated Types

type Rep V4 :: Type

Methods

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

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

Show1 V4

Defined in Data.Semimodule.Free

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V4 a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V4 a] -> ShowS

Foldable1 V4

Defined in Data.Semimodule.Free

Methods

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

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

toNonEmpty :: V4 a -> NonEmpty a

Semiring a => Bisemimodule a a (V4 a)

Defined in Data.Semimodule.Free

Methods

discale :: a -> a -> V4 a -> V4 a

Semiring a => RightSemimodule a (V4 a)

Defined in Data.Semimodule.Free

Methods

rscale :: a -> V4 a -> V4 a

Semiring a => LeftSemimodule a (V4 a)

Defined in Data.Semimodule.Free

Methods

lscale :: a -> V4 a -> V4 a

Eq a => Eq (V4 a)

Defined in Data.Semimodule.Free

Methods

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

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

Ord a => Ord (V4 a)

Defined in Data.Semimodule.Free

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.Free

Methods

showsPrec :: Int -> V4 a -> ShowS

show :: V4 a -> String

showList :: [V4 a] -> ShowS

Semiring a => Semigroup (Multiplicative (M44 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Multiplicative (M44 a) -> Multiplicative (M44 a) -> Multiplicative (M44 a)

sconcat :: NonEmpty (Multiplicative (M44 a)) -> Multiplicative (M44 a)

stimes :: Integral b => b -> Multiplicative (M44 a) -> Multiplicative (M44 a)

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

Defined in Data.Semimodule.Free

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 (Additive (M44 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M44 a) -> Additive (M44 a) -> Additive (M44 a)

sconcat :: NonEmpty (Additive (M44 a)) -> Additive (M44 a)

stimes :: Integral b => b -> Additive (M44 a) -> Additive (M44 a)

(Additive - Semigroup) a => Semigroup (Additive (M43 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M43 a) -> Additive (M43 a) -> Additive (M43 a)

sconcat :: NonEmpty (Additive (M43 a)) -> Additive (M43 a)

stimes :: Integral b => b -> Additive (M43 a) -> Additive (M43 a)

(Additive - Semigroup) a => Semigroup (Additive (M42 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M42 a) -> Additive (M42 a) -> Additive (M42 a)

sconcat :: NonEmpty (Additive (M42 a)) -> Additive (M42 a)

stimes :: Integral b => b -> Additive (M42 a) -> Additive (M42 a)

(Additive - Semigroup) a => Semigroup (Additive (M34 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M34 a) -> Additive (M34 a) -> Additive (M34 a)

sconcat :: NonEmpty (Additive (M34 a)) -> Additive (M34 a)

stimes :: Integral b => b -> Additive (M34 a) -> Additive (M34 a)

(Additive - Semigroup) a => Semigroup (Additive (M24 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M24 a) -> Additive (M24 a) -> Additive (M24 a)

sconcat :: NonEmpty (Additive (M24 a)) -> Additive (M24 a)

stimes :: Integral b => b -> Additive (M24 a) -> Additive (M24 a)

(Additive - Semigroup) a => Semigroup (Additive (M41 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M41 a) -> Additive (M41 a) -> Additive (M41 a)

sconcat :: NonEmpty (Additive (M41 a)) -> Additive (M41 a)

stimes :: Integral b => b -> Additive (M41 a) -> Additive (M41 a)

(Additive - Semigroup) a => Semigroup (Additive (M14 a))

Defined in Data.Semimodule.Free

Methods

(<>) :: Additive (M14 a) -> Additive (M14 a) -> Additive (M14 a)

sconcat :: NonEmpty (Additive (M14 a)) -> Additive (M14 a)

stimes :: Integral b => b -> Additive (M14 a) -> Additive (M14 a)

Semiring a => Monoid (Multiplicative (M44 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Multiplicative (M44 a)

mappend :: Multiplicative (M44 a) -> Multiplicative (M44 a) -> Multiplicative (M44 a)

mconcat :: [Multiplicative (M44 a)] -> Multiplicative (M44 a)

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

Defined in Data.Semimodule.Free

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 (Additive (M44 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M44 a)

mappend :: Additive (M44 a) -> Additive (M44 a) -> Additive (M44 a)

mconcat :: [Additive (M44 a)] -> Additive (M44 a)

(Additive - Monoid) a => Monoid (Additive (M43 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M43 a)

mappend :: Additive (M43 a) -> Additive (M43 a) -> Additive (M43 a)

mconcat :: [Additive (M43 a)] -> Additive (M43 a)

(Additive - Monoid) a => Monoid (Additive (M42 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M42 a)

mappend :: Additive (M42 a) -> Additive (M42 a) -> Additive (M42 a)

mconcat :: [Additive (M42 a)] -> Additive (M42 a)

(Additive - Monoid) a => Monoid (Additive (M34 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M34 a)

mappend :: Additive (M34 a) -> Additive (M34 a) -> Additive (M34 a)

mconcat :: [Additive (M34 a)] -> Additive (M34 a)

(Additive - Monoid) a => Monoid (Additive (M24 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M24 a)

mappend :: Additive (M24 a) -> Additive (M24 a) -> Additive (M24 a)

mconcat :: [Additive (M24 a)] -> Additive (M24 a)

(Additive - Monoid) a => Monoid (Additive (M41 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M41 a)

mappend :: Additive (M41 a) -> Additive (M41 a) -> Additive (M41 a)

mconcat :: [Additive (M41 a)] -> Additive (M41 a)

(Additive - Monoid) a => Monoid (Additive (M14 a))

Defined in Data.Semimodule.Free

Methods

mempty :: Additive (M14 a)

mappend :: Additive (M14 a) -> Additive (M14 a) -> Additive (M14 a)

mconcat :: [Additive (M14 a)] -> Additive (M14 a)

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

Defined in Data.Semimodule.Free

Methods

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

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

(Additive - Group) a => Group (Additive (M44 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M44 a) -> Additive (M44 a)

greplicate :: Integer -> Additive (M44 a) -> Additive (M44 a)

(Additive - Group) a => Group (Additive (M43 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M43 a) -> Additive (M43 a)

greplicate :: Integer -> Additive (M43 a) -> Additive (M43 a)

(Additive - Group) a => Group (Additive (M42 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M42 a) -> Additive (M42 a)

greplicate :: Integer -> Additive (M42 a) -> Additive (M42 a)

(Additive - Group) a => Group (Additive (M34 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M34 a) -> Additive (M34 a)

greplicate :: Integer -> Additive (M34 a) -> Additive (M34 a)

(Additive - Group) a => Group (Additive (M24 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M24 a) -> Additive (M24 a)

greplicate :: Integer -> Additive (M24 a) -> Additive (M24 a)

(Additive - Group) a => Group (Additive (M41 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M41 a) -> Additive (M41 a)

greplicate :: Integer -> Additive (M41 a) -> Additive (M41 a)

(Additive - Group) a => Group (Additive (M14 a))

Defined in Data.Semimodule.Free

Methods

inv :: Additive (M14 a) -> Additive (M14 a)

greplicate :: Integer -> Additive (M14 a) -> Additive (M14 a)

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

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (V4 a)

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

(Additive - Group) a => Loop (Additive (M44 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M44 a)

lreplicate :: Natural -> Additive (M44 a) -> Additive (M44 a)

(Additive - Group) a => Loop (Additive (M43 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M43 a)

lreplicate :: Natural -> Additive (M43 a) -> Additive (M43 a)

(Additive - Group) a => Loop (Additive (M42 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M42 a)

lreplicate :: Natural -> Additive (M42 a) -> Additive (M42 a)

(Additive - Group) a => Loop (Additive (M34 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M34 a)

lreplicate :: Natural -> Additive (M34 a) -> Additive (M34 a)

(Additive - Group) a => Loop (Additive (M24 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M24 a)

lreplicate :: Natural -> Additive (M24 a) -> Additive (M24 a)

(Additive - Group) a => Loop (Additive (M41 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M41 a)

lreplicate :: Natural -> Additive (M41 a) -> Additive (M41 a)

(Additive - Group) a => Loop (Additive (M14 a))

Defined in Data.Semimodule.Free

Methods

lempty :: Additive (M14 a)

lreplicate :: Natural -> Additive (M14 a) -> Additive (M14 a)

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

Defined in Data.Semimodule.Free

Methods

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

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

(Additive - Group) a => Quasigroup (Additive (M44 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M44 a) -> Additive (M44 a) -> Additive (M44 a)

(\\) :: Additive (M44 a) -> Additive (M44 a) -> Additive (M44 a)

(Additive - Group) a => Quasigroup (Additive (M43 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M43 a) -> Additive (M43 a) -> Additive (M43 a)

(\\) :: Additive (M43 a) -> Additive (M43 a) -> Additive (M43 a)

(Additive - Group) a => Quasigroup (Additive (M42 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M42 a) -> Additive (M42 a) -> Additive (M42 a)

(\\) :: Additive (M42 a) -> Additive (M42 a) -> Additive (M42 a)

(Additive - Group) a => Quasigroup (Additive (M34 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M34 a) -> Additive (M34 a) -> Additive (M34 a)

(\\) :: Additive (M34 a) -> Additive (M34 a) -> Additive (M34 a)

(Additive - Group) a => Quasigroup (Additive (M24 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M24 a) -> Additive (M24 a) -> Additive (M24 a)

(\\) :: Additive (M24 a) -> Additive (M24 a) -> Additive (M24 a)

(Additive - Group) a => Quasigroup (Additive (M41 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M41 a) -> Additive (M41 a) -> Additive (M41 a)

(\\) :: Additive (M41 a) -> Additive (M41 a) -> Additive (M41 a)

(Additive - Group) a => Quasigroup (Additive (M14 a))

Defined in Data.Semimodule.Free

Methods

(//) :: Additive (M14 a) -> Additive (M14 a) -> Additive (M14 a)

(\\) :: Additive (M14 a) -> Additive (M14 a) -> Additive (M14 a)

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

Defined in Data.Semimodule.Free

Methods

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

(Additive - Group) a => Magma (Additive (M44 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M44 a) -> Additive (M44 a) -> Additive (M44 a)

(Additive - Group) a => Magma (Additive (M43 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M43 a) -> Additive (M43 a) -> Additive (M43 a)

(Additive - Group) a => Magma (Additive (M42 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M42 a) -> Additive (M42 a) -> Additive (M42 a)

(Additive - Group) a => Magma (Additive (M34 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M34 a) -> Additive (M34 a) -> Additive (M34 a)

(Additive - Group) a => Magma (Additive (M24 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M24 a) -> Additive (M24 a) -> Additive (M24 a)

(Additive - Group) a => Magma (Additive (M41 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M41 a) -> Additive (M41 a) -> Additive (M41 a)

(Additive - Group) a => Magma (Additive (M14 a))

Defined in Data.Semimodule.Free

Methods

(<<) :: Additive (M14 a) -> Additive (M14 a) -> Additive (M14 a)

Ring a => Ring (M44 a)

Defined in Data.Semimodule.Free

Semiring a => Semiring (M44 a)

Defined in Data.Semimodule.Free

Semiring a => Presemiring (M44 a)

Defined in Data.Semimodule.Free

Semiring a => RightSemimodule (M44 a) (M44 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M44 a -> M44 a -> M44 a

Semiring a => RightSemimodule (M44 a) (M34 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M44 a -> M34 a -> M34 a

Semiring a => RightSemimodule (M44 a) (M24 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M44 a -> M24 a -> M24 a

Semiring a => RightSemimodule (M44 a) (M14 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M44 a -> M14 a -> M14 a

Semiring a => RightSemimodule (M33 a) (M43 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M33 a -> M43 a -> M43 a

Semiring a => RightSemimodule (M22 a) (M42 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M22 a -> M42 a -> M42 a

Semiring a => RightSemimodule (M11 a) (M41 a)

Defined in Data.Semimodule.Free

Methods

rscale :: M11 a -> M41 a -> M41 a

Semiring a => LeftSemimodule (M44 a) (M44 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M44 a -> M44 a -> M44 a

Semiring a => LeftSemimodule (M44 a) (M43 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M44 a -> M43 a -> M43 a

Semiring a => LeftSemimodule (M44 a) (M42 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M44 a -> M42 a -> M42 a

Semiring a => LeftSemimodule (M44 a) (M41 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M44 a -> M41 a -> M41 a

Semiring a => LeftSemimodule (M33 a) (M34 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M33 a -> M34 a -> M34 a

Semiring a => LeftSemimodule (M22 a) (M24 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M22 a -> M24 a -> M24 a

Semiring a => LeftSemimodule (M11 a) (M14 a)

Defined in Data.Semimodule.Free

Methods

lscale :: M11 a -> M14 a -> M14 a

Semiring a => Bisemimodule (M44 a) (M44 a) (M44 a)

Defined in Data.Semimodule.Free

Methods

discale :: M44 a -> M44 a -> M44 a -> M44 a

Semiring a => Bisemimodule (M44 a) (M33 a) (M43 a)

Defined in Data.Semimodule.Free

Methods

discale :: M44 a -> M33 a -> M43 a -> M43 a

Semiring a => Bisemimodule (M44 a) (M22 a) (M42 a)

Defined in Data.Semimodule.Free

Methods

discale :: M44 a -> M22 a -> M42 a -> M42 a

Semiring a => Bisemimodule (M44 a) (M11 a) (M41 a)

Defined in Data.Semimodule.Free

Methods

discale :: M44 a -> M11 a -> M41 a -> M41 a

Semiring a => Bisemimodule (M33 a) (M44 a) (M34 a)

Defined in Data.Semimodule.Free

Methods

discale :: M33 a -> M44 a -> M34 a -> M34 a

Semiring a => Bisemimodule (M22 a) (M44 a) (M24 a)

Defined in Data.Semimodule.Free

Methods

discale :: M22 a -> M44 a -> M24 a -> M24 a

Semiring a => Bisemimodule (M11 a) (M44 a) (M14 a)

Defined in Data.Semimodule.Free

Methods

discale :: M11 a -> M44 a -> M14 a -> M14 a

type Rep V4

Defined in Data.Semimodule.Free

type Rep V4 = E4

Matrix types

type M11 = Compose V1 V1

A 1x1 matrix.

type M12 = Compose V1 V2

A 1x2 matrix.

type M13 = Compose V1 V3

A 1x3 matrix.

type M14 = Compose V1 V4

A 1x4 matrix.

type M21 = Compose V2 V1

A 2x1 matrix.

type M31 = Compose V3 V1

A 3x1 matrix.

type M41 = Compose V4 V1

A 4x1 matrix.

type M22 = Compose V2 V2

A 2x2 matrix.

type M23 = Compose V2 V3

A 2x3 matrix.

type M24 = Compose V2 V4

A 2x4 matrix.

type M32 = Compose V3 V2

A 3x2 matrix.

type M33 = Compose V3 V3

A 3x3 matrix.

type M34 = Compose V3 V4

A 3x4 matrix.

type M42 = Compose V4 V2

A 4x2 matrix.

type M43 = Compose V4 V3

A 4x3 matrix.

type M44 = Compose V4 V4

A 4x4 matrix.

m11 :: a -> M11 a

Construct a 1x1 matrix.

>>> m11 1 :: M11 Int
Compose (V1 (V1 1))

m12 :: a -> a -> M12 a

Construct a 1x2 matrix.

>>> m12 1 2 :: M12 Int
Compose (V1 (V2 1 2))

m13 :: a -> a -> a -> M13 a

Construct a 1x3 matrix.

>>> m13 1 2 3 :: M13 Int
Compose (V1 (V3 1 2 3))

m14 :: a -> a -> a -> a -> M14 a

Construct a 1x4 matrix.

>>> m14 1 2 3 4 :: M14 Int
Compose (V1 (V4 1 2 3 4))

m21 :: a -> a -> M21 a

Construct a 2x1 matrix.

>>> m21 1 2 :: M21 Int
Compose (V2 (V1 1) (V1 2))

m31 :: a -> a -> a -> M31 a

Construct a 3x1 matrix.

>>> m31 1 2 3 :: M31 Int
Compose (V3 (V1 1) (V1 2) (V1 3))

m41 :: a -> a -> a -> a -> M41 a

Construct a 4x1 matrix.

>>> m41 1 2 3 4 :: M41 Int
Compose (V4 (V1 1) (V1 2) (V1 3) (V1 4))

m22 :: a -> a -> a -> a -> M22 a

Construct a 2x2 matrix.

Arguments are in row-major order.

>>> m22 1 2 3 4 :: M22 Int
Compose (V2 (V2 1 2) (V2 3 4))

m23 :: a -> a -> a -> a -> a -> a -> M23 a

Construct a 2x3 matrix.

Arguments are in row-major order.

m24 :: a -> a -> a -> a -> a -> a -> a -> a -> M24 a

Construct a 2x4 matrix.

Arguments are in row-major order.

m32 :: a -> a -> a -> a -> a -> a -> M32 a

Construct a 3x2 matrix.

Arguments are in row-major order.

m33 :: a -> a -> a -> a -> a -> a -> a -> a -> a -> M33 a

Construct a 3x3 matrix.

Arguments are in row-major order.

m34 :: a -> a -> a -> a -> a -> a -> a -> a -> a -> a -> a -> a -> M34 a

Construct a 3x4 matrix.

Arguments are in row-major order.

m42 :: a -> a -> a -> a -> a -> a -> a -> a -> M42 a

Construct a 4x2 matrix.

Arguments are in row-major order.

m43 :: a -> a -> a -> a -> a -> a -> a -> a -> a -> a -> a -> a -> M43 a

Construct a 4x3 matrix.

Arguments are in row-major order.

m44 :: a -> a -> a -> a -> a -> a -> a -> a -> a -> a -> a -> a -> a -> a -> a -> a -> M44 a

Construct a 4x4 matrix.

Arguments are in row-major order.