BNFC-2.6.0.3: A compiler front-end generator.

Safe Haskell	None

Algebra.RingUtils

Documentation

module Prelude

class AbelianGroup a whereSource

Methods

zero :: aSource

(+) :: a -> a -> aSource

Instances

AbelianGroup Bool
AbelianGroup Int
AbelianGroup a => AbelianGroup (Pair a)
AbelianGroup (Set a)
AbelianGroup a => AbelianGroup (Vec x a)
AbelianGroup (f (g a)) => AbelianGroup (O f g a)
AbelianGroupZ a => AbelianGroup (Mat x y a)

class AbelianGroup a => AbelianGroupZ a whereSource

Methods

isZero :: a -> Bool Source

Instances

AbelianGroupZ Int
(AbelianGroup (Pair a), AbelianGroupZ a) => AbelianGroupZ (Pair a)
AbelianGroup (Set a) => AbelianGroupZ (Set a)
(AbelianGroup (O f g a), AbelianGroupZ (f (g a))) => AbelianGroupZ (O f g a)

class AbelianGroupZ a => Ring a whereSource

Methods

(*) :: a -> a -> aSource

Instances

class AbelianGroupZ a => RingP a whereSource

Methods

mul :: Bool -> a -> a -> Pair aSource

data Pair a Source

Constructors

:/:
Fields leftOf :: a rightOf :: a

Instances

Functor Pair
Applicative Pair
Show a => Show (Pair a)
(AbelianGroup (Pair a), AbelianGroupZ a) => AbelianGroupZ (Pair a)
AbelianGroup a => AbelianGroup (Pair a)
Matrix m => Matrix (O Pair m)

select :: Bool -> [a] -> Pair [a]Source

onlyLeft :: [a] -> Pair [a]Source

onlyRight :: [a] -> Pair [a]Source

newtype O f g a Source

Constructors

O
Fields fromO :: f (g a)

Instances

(Functor f, Functor g) => Functor (O f g)
Matrix m => Matrix (O Pair m)
Show (f (g a)) => Show (O f g a)
(AbelianGroup (O f g a), AbelianGroupZ (f (g a))) => AbelianGroupZ (O f g a)
AbelianGroup (f (g a)) => AbelianGroup (O f g a)

sum :: AbelianGroup a => [a] -> aSource

mulDefault :: RingP a => a -> a -> aSource

module Data.Pair