linear-1.23: Linear Algebra
LicenseBSD-style (see the file LICENSE)
MaintainerEdward Kmett <ekmett@gmail.com>
Stabilityprovisional
Portabilityportable
Safe HaskellSafe-Inferred
LanguageHaskell2010

Linear.Covector

Description

Operations on affine spaces.

Synopsis

Documentation

newtype Covector r a Source #

Linear functionals from elements of an (infinite) free module to a scalar

Constructors

Covector 

Fields

Instances

Instances details
Num r => Alternative (Covector r) Source # 
Instance details

Defined in Linear.Covector

Methods

empty :: Covector r a #

(<|>) :: Covector r a -> Covector r a -> Covector r a #

some :: Covector r a -> Covector r [a] #

many :: Covector r a -> Covector r [a] #

Applicative (Covector r) Source # 
Instance details

Defined in Linear.Covector

Methods

pure :: a -> Covector r a #

(<*>) :: Covector r (a -> b) -> Covector r a -> Covector r b #

liftA2 :: (a -> b -> c) -> Covector r a -> Covector r b -> Covector r c #

(*>) :: Covector r a -> Covector r b -> Covector r b #

(<*) :: Covector r a -> Covector r b -> Covector r a #

Functor (Covector r) Source # 
Instance details

Defined in Linear.Covector

Methods

fmap :: (a -> b) -> Covector r a -> Covector r b #

(<$) :: a -> Covector r b -> Covector r a #

Monad (Covector r) Source # 
Instance details

Defined in Linear.Covector

Methods

(>>=) :: Covector r a -> (a -> Covector r b) -> Covector r b #

(>>) :: Covector r a -> Covector r b -> Covector r b #

return :: a -> Covector r a #

Num r => MonadPlus (Covector r) Source # 
Instance details

Defined in Linear.Covector

Methods

mzero :: Covector r a #

mplus :: Covector r a -> Covector r a -> Covector r a #

Num r => Alt (Covector r) Source # 
Instance details

Defined in Linear.Covector

Methods

(<!>) :: Covector r a -> Covector r a -> Covector r a #

some :: Applicative (Covector r) => Covector r a -> Covector r [a] #

many :: Applicative (Covector r) => Covector r a -> Covector r [a] #

Apply (Covector r) Source # 
Instance details

Defined in Linear.Covector

Methods

(<.>) :: Covector r (a -> b) -> Covector r a -> Covector r b #

(.>) :: Covector r a -> Covector r b -> Covector r b #

(<.) :: Covector r a -> Covector r b -> Covector r a #

liftF2 :: (a -> b -> c) -> Covector r a -> Covector r b -> Covector r c #

Bind (Covector r) Source # 
Instance details

Defined in Linear.Covector

Methods

(>>-) :: Covector r a -> (a -> Covector r b) -> Covector r b #

join :: Covector r (Covector r a) -> Covector r a #

Num r => Plus (Covector r) Source # 
Instance details

Defined in Linear.Covector

Methods

zero :: Covector r a #

Coalgebra r m => Num (Covector r m) Source # 
Instance details

Defined in Linear.Covector

Methods

(+) :: Covector r m -> Covector r m -> Covector r m #

(-) :: Covector r m -> Covector r m -> Covector r m #

(*) :: Covector r m -> Covector r m -> Covector r m #

negate :: Covector r m -> Covector r m #

abs :: Covector r m -> Covector r m #

signum :: Covector r m -> Covector r m #

fromInteger :: Integer -> Covector r m #

($*) :: Representable f => Covector r (Rep f) -> f r -> r infixr 0 Source #