Algebra.RingUtils

Documentation

module Prelude

class AbelianGroup a where

Methods

zero :: a

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

Instances

AbelianGroup Bool

AbelianGroup Int

AbelianGroup a => AbelianGroup (Pair 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

Methods

isZero :: a -> Bool

Instances

AbelianGroupZ Int

AbelianGroupZ a => AbelianGroupZ (Pair a)

AbelianGroupZ (f (g a)) => AbelianGroupZ (O f g a)

class AbelianGroupZ a => Ring a where

Methods

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

Instances

Ring Int

class AbelianGroupZ a => RingP a where

Methods

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

data Pair a

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]

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

onlyRight :: [t] -> Pair [t]

newtype O f g a

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

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

module Data.Pair