Ideas.Common.Algebra.Field

Semi-ring

class SemiRing a where

Minimal complete definition

(|+|), zero, (|*|), one

Methods

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

zero :: a

sum :: [a] -> a

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

one :: a

product :: [a] -> a

Instances

Num a => SemiRing (SafeNum a)

(CoField a, Field a) => SemiRing (SmartField a)

Ring

class SemiRing a => Ring a where

Minimal complete definition

Nothing

Methods

plusInverse :: a -> a

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

Instances

Num a => Ring (SafeNum a)

(CoField a, Field a) => Ring (SmartField a)

Field

class Ring a => Field a where

Minimal complete definition

Nothing

Methods

timesInverse :: a -> a

(|/|) :: a -> a -> a infixl 7

Instances

(Eq a, Fractional a) => Field (SafeNum a)

(CoField a, Field a) => Field (SmartField a)

Additive monoid

newtype Additive a

Constructors

Additive

Fields

fromAdditive :: a

Instances

Functor Additive

Applicative Additive

Eq a => Eq (Additive a)

Ord a => Ord (Additive a)

Show a => Show (Additive a)

Arbitrary a => Arbitrary (Additive a)

CoArbitrary a => CoArbitrary (Additive a)

SemiRing a => Monoid (Additive a)

CoRing a => CoGroup (Additive a)

CoSemiRing a => CoMonoid (Additive a)

Ring a => Group (Additive a)

Multiplicative monoid

newtype Multiplicative a

Constructors

Multiplicative

Fields

fromMultiplicative :: a

Instances

Functor Multiplicative

Applicative Multiplicative

Eq a => Eq (Multiplicative a)

Ord a => Ord (Multiplicative a)

Show a => Show (Multiplicative a)

Arbitrary a => Arbitrary (Multiplicative a)

CoArbitrary a => CoArbitrary (Multiplicative a)

SemiRing a => Monoid (Multiplicative a)

CoSemiRing a => CoMonoidZero (Multiplicative a)

CoField a => CoGroup (Multiplicative a)

CoSemiRing a => CoMonoid (Multiplicative a)

SemiRing a => MonoidZero (Multiplicative a)

Field a => Group (Multiplicative a)

Datatype for safe numeric operators

data SafeNum a

Instances

Monad SafeNum

Functor SafeNum

Applicative SafeNum

Eq a => Eq (SafeNum a)

(Eq a, Fractional a) => Fractional (SafeNum a)

Num a => Num (SafeNum a)

Ord a => Ord (SafeNum a)

Show a => Show (SafeNum a)

Arbitrary a => Arbitrary (SafeNum a)

(Eq a, Fractional a) => Field (SafeNum a)

Num a => Ring (SafeNum a)

Num a => SemiRing (SafeNum a)

safeNum :: SafeNum a -> Either String a

CoSemiRing, CoRing, and CoField (for matching)

class CoSemiRing a where

Methods

isPlus :: a -> Maybe (a, a)

isZero :: a -> Bool

isTimes :: a -> Maybe (a, a)

isOne :: a -> Bool

Instances

CoSemiRing a => CoSemiRing (SmartField a)

class CoSemiRing a => CoRing a where

Minimal complete definition

isNegate

Methods

isNegate :: a -> Maybe a

isMinus :: a -> Maybe (a, a)

Instances

CoRing a => CoRing (SmartField a)

class CoRing a => CoField a where

Minimal complete definition

isRecip

Methods

isRecip :: a -> Maybe a

isDivision :: a -> Maybe (a, a)

Instances

CoField a => CoField (SmartField a)