BNFC-2.8: A compiler front-end generator.

Safe Haskell	None
Language	Haskell98

Algebra.RingUtils

Documentation

module Prelude

class AbelianGroup a where Source

Methods

zero :: a Source

(+) :: a -> a -> a infixl 6 Source

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 where Source

Methods

isZero :: a -> Bool Source

Instances

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

class AbelianGroupZ a => Ring a where Source

Methods

(*) :: a -> a -> a infixl 7 Source

Instances

class AbelianGroupZ a => RingP a where Source

Methods

mul :: Bool -> a -> a -> Pair a Source

data Pair a Source

Constructors

(:/:) infixl 2
Fields leftOf :: a rightOf :: a

Instances

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

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

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

onlyRight :: [t] -> Pair [t] 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)
AbelianGroupZ (f (g a)) => AbelianGroupZ (O f g a)
AbelianGroup (f (g a)) => AbelianGroup (O f g a)

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

mulDefault :: RingP a => a -> a -> a Source

module Data.Pair