Domain.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

SemiRing Expr

Defined in Domain.Math.Expr.Data

Methods

(|+|) :: Expr -> Expr -> Expr

zero :: Expr

sum :: [Expr] -> Expr

(|*|) :: Expr -> Expr -> Expr

one :: Expr

product :: [Expr] -> Expr

Num a => SemiRing (SafeNum a)

Defined in Domain.Algebra.Field

Methods

(|+|) :: SafeNum a -> SafeNum a -> SafeNum a

zero :: SafeNum a

sum :: [SafeNum a] -> SafeNum a

(|*|) :: SafeNum a -> SafeNum a -> SafeNum a

one :: SafeNum a

product :: [SafeNum a] -> SafeNum a

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

Defined in Domain.Algebra.SmartGroup

Methods

(|+|) :: SmartField a -> SmartField a -> SmartField a

zero :: SmartField a

sum :: [SmartField a] -> SmartField a

(|*|) :: SmartField a -> SmartField a -> SmartField a

one :: SmartField a

product :: [SmartField a] -> SmartField a

Ring

class SemiRing a => Ring a where

Minimal complete definition

Nothing

Methods

plusInverse :: a -> a

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

Instances

Ring Expr

Defined in Domain.Math.Expr.Data

Methods

plusInverse :: Expr -> Expr

(|-|) :: Expr -> Expr -> Expr

Num a => Ring (SafeNum a)

Defined in Domain.Algebra.Field

Methods

plusInverse :: SafeNum a -> SafeNum a

(|-|) :: SafeNum a -> SafeNum a -> SafeNum a

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

Defined in Domain.Algebra.SmartGroup

Methods

plusInverse :: SmartField a -> SmartField a

(|-|) :: SmartField a -> SmartField a -> SmartField a

Field

class Ring a => Field a where

Minimal complete definition

Nothing

Methods

timesInverse :: a -> a

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

Instances

Field Expr

Defined in Domain.Math.Expr.Data

Methods

timesInverse :: Expr -> Expr

(|/|) :: Expr -> Expr -> Expr

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

Defined in Domain.Algebra.Field

Methods

timesInverse :: SafeNum a -> SafeNum a

(|/|) :: SafeNum a -> SafeNum a -> SafeNum a

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

Defined in Domain.Algebra.SmartGroup

Methods

timesInverse :: SmartField a -> SmartField a

(|/|) :: SmartField a -> SmartField a -> SmartField a

Additive monoid

newtype Additive a

Constructors

Additive

Fields

• fromAdditive :: a

Instances

Functor Additive

Defined in Domain.Algebra.Field

Methods

fmap :: (a -> b) -> Additive a -> Additive b

(<$) :: a -> Additive b -> Additive a

Applicative Additive

Defined in Domain.Algebra.Field

Methods

pure :: a -> Additive a

(<*>) :: Additive (a -> b) -> Additive a -> Additive b

liftA2 :: (a -> b -> c) -> Additive a -> Additive b -> Additive c

(*>) :: Additive a -> Additive b -> Additive b

(<*) :: Additive a -> Additive b -> Additive a

Eq a => Eq (Additive a)

Defined in Domain.Algebra.Field

Methods

(==) :: Additive a -> Additive a -> Bool

(/=) :: Additive a -> Additive a -> Bool

Ord a => Ord (Additive a)

Defined in Domain.Algebra.Field

Methods

compare :: Additive a -> Additive a -> Ordering

(<) :: Additive a -> Additive a -> Bool

(<=) :: Additive a -> Additive a -> Bool

(>) :: Additive a -> Additive a -> Bool

(>=) :: Additive a -> Additive a -> Bool

max :: Additive a -> Additive a -> Additive a

min :: Additive a -> Additive a -> Additive a

Show a => Show (Additive a)

Defined in Domain.Algebra.Field

Methods

showsPrec :: Int -> Additive a -> ShowS

show :: Additive a -> String

showList :: [Additive a] -> ShowS

SemiRing a => Semigroup (Additive a)

Defined in Domain.Algebra.Field

Methods

(<>) :: Additive a -> Additive a -> Additive a

sconcat :: NonEmpty (Additive a) -> Additive a

stimes :: Integral b => b -> Additive a -> Additive a

SemiRing a => Monoid (Additive a)

Defined in Domain.Algebra.Field

Methods

mempty :: Additive a

mappend :: Additive a -> Additive a -> Additive a

mconcat :: [Additive a] -> Additive a

Arbitrary a => Arbitrary (Additive a)

Defined in Domain.Algebra.Field

Methods

arbitrary :: Gen (Additive a)

shrink :: Additive a -> [Additive a]

CoArbitrary a => CoArbitrary (Additive a)

Defined in Domain.Algebra.Field

Methods

coarbitrary :: Additive a -> Gen b -> Gen b

CoRing a => CoGroup (Additive a)

Defined in Domain.Algebra.Field

Methods

isInverse :: Additive a -> Maybe (Additive a)

isAppendInv :: Additive a -> Maybe (Additive a, Additive a)

CoSemiRing a => CoMonoid (Additive a)

Defined in Domain.Algebra.Field

Methods

isEmpty :: Additive a -> Bool

isAppend :: Additive a -> Maybe (Additive a, Additive a)

Ring a => Group (Additive a)

Defined in Domain.Algebra.Field

Methods

inverse :: Additive a -> Additive a

appendInv :: Additive a -> Additive a -> Additive a

Multiplicative monoid

newtype Multiplicative a

Constructors

Multiplicative

Fields

• fromMultiplicative :: a

Instances

Functor Multiplicative

Defined in Domain.Algebra.Field

Methods

fmap :: (a -> b) -> Multiplicative a -> Multiplicative b

(<$) :: a -> Multiplicative b -> Multiplicative a

Applicative Multiplicative

Defined in Domain.Algebra.Field

Methods

pure :: a -> Multiplicative a

(<*>) :: Multiplicative (a -> b) -> Multiplicative a -> Multiplicative b

liftA2 :: (a -> b -> c) -> Multiplicative a -> Multiplicative b -> Multiplicative c

(*>) :: Multiplicative a -> Multiplicative b -> Multiplicative b

(<*) :: Multiplicative a -> Multiplicative b -> Multiplicative a

Eq a => Eq (Multiplicative a)

Defined in Domain.Algebra.Field

Methods

(==) :: Multiplicative a -> Multiplicative a -> Bool

(/=) :: Multiplicative a -> Multiplicative a -> Bool

Ord a => Ord (Multiplicative a)

Defined in Domain.Algebra.Field

Methods

compare :: Multiplicative a -> Multiplicative a -> Ordering

(<) :: Multiplicative a -> Multiplicative a -> Bool

(<=) :: Multiplicative a -> Multiplicative a -> Bool

(>) :: Multiplicative a -> Multiplicative a -> Bool

(>=) :: Multiplicative a -> Multiplicative a -> Bool

max :: Multiplicative a -> Multiplicative a -> Multiplicative a

min :: Multiplicative a -> Multiplicative a -> Multiplicative a

Show a => Show (Multiplicative a)

Defined in Domain.Algebra.Field

Methods

showsPrec :: Int -> Multiplicative a -> ShowS

show :: Multiplicative a -> String

showList :: [Multiplicative a] -> ShowS

SemiRing a => Semigroup (Multiplicative a)

Defined in Domain.Algebra.Field

Methods

(<>) :: Multiplicative a -> Multiplicative a -> Multiplicative a

sconcat :: NonEmpty (Multiplicative a) -> Multiplicative a

stimes :: Integral b => b -> Multiplicative a -> Multiplicative a

SemiRing a => Monoid (Multiplicative a)

Defined in Domain.Algebra.Field

Methods

mempty :: Multiplicative a

mappend :: Multiplicative a -> Multiplicative a -> Multiplicative a

mconcat :: [Multiplicative a] -> Multiplicative a

Arbitrary a => Arbitrary (Multiplicative a)

Defined in Domain.Algebra.Field

Methods

arbitrary :: Gen (Multiplicative a)

shrink :: Multiplicative a -> [Multiplicative a]

CoArbitrary a => CoArbitrary (Multiplicative a)

Defined in Domain.Algebra.Field

Methods

coarbitrary :: Multiplicative a -> Gen b -> Gen b

CoSemiRing a => CoMonoidZero (Multiplicative a)

Defined in Domain.Algebra.Field

Methods

isMonoidZero :: Multiplicative a -> Bool

CoField a => CoGroup (Multiplicative a)

Defined in Domain.Algebra.Field

Methods

isInverse :: Multiplicative a -> Maybe (Multiplicative a)

isAppendInv :: Multiplicative a -> Maybe (Multiplicative a, Multiplicative a)

CoSemiRing a => CoMonoid (Multiplicative a)

Defined in Domain.Algebra.Field

Methods

isEmpty :: Multiplicative a -> Bool

isAppend :: Multiplicative a -> Maybe (Multiplicative a, Multiplicative a)

SemiRing a => MonoidZero (Multiplicative a)

Defined in Domain.Algebra.Field

Methods

mzero :: Multiplicative a

Field a => Group (Multiplicative a)

Defined in Domain.Algebra.Field

Methods

inverse :: Multiplicative a -> Multiplicative a

appendInv :: Multiplicative a -> Multiplicative a -> Multiplicative a

Datatype for safe numeric operators

data SafeNum a

Instances

Monad SafeNum

Defined in Domain.Algebra.Field

Methods

(>>=) :: SafeNum a -> (a -> SafeNum b) -> SafeNum b

(>>) :: SafeNum a -> SafeNum b -> SafeNum b

return :: a -> SafeNum a

fail :: String -> SafeNum a

Functor SafeNum

Defined in Domain.Algebra.Field

Methods

fmap :: (a -> b) -> SafeNum a -> SafeNum b

(<$) :: a -> SafeNum b -> SafeNum a

Applicative SafeNum

Defined in Domain.Algebra.Field

Methods

pure :: a -> SafeNum a

(<*>) :: SafeNum (a -> b) -> SafeNum a -> SafeNum b

liftA2 :: (a -> b -> c) -> SafeNum a -> SafeNum b -> SafeNum c

(*>) :: SafeNum a -> SafeNum b -> SafeNum b

(<*) :: SafeNum a -> SafeNum b -> SafeNum a

Eq a => Eq (SafeNum a)

Defined in Domain.Algebra.Field

Methods

(==) :: SafeNum a -> SafeNum a -> Bool

(/=) :: SafeNum a -> SafeNum a -> Bool

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

Defined in Domain.Algebra.Field

Methods

(/) :: SafeNum a -> SafeNum a -> SafeNum a

recip :: SafeNum a -> SafeNum a

fromRational :: Rational -> SafeNum a

Num a => Num (SafeNum a)

Defined in Domain.Algebra.Field

Methods

(+) :: SafeNum a -> SafeNum a -> SafeNum a

(-) :: SafeNum a -> SafeNum a -> SafeNum a

(*) :: SafeNum a -> SafeNum a -> SafeNum a

negate :: SafeNum a -> SafeNum a

abs :: SafeNum a -> SafeNum a

signum :: SafeNum a -> SafeNum a

fromInteger :: Integer -> SafeNum a

Ord a => Ord (SafeNum a)

Defined in Domain.Algebra.Field

Methods

compare :: SafeNum a -> SafeNum a -> Ordering

(<) :: SafeNum a -> SafeNum a -> Bool

(<=) :: SafeNum a -> SafeNum a -> Bool

(>) :: SafeNum a -> SafeNum a -> Bool

(>=) :: SafeNum a -> SafeNum a -> Bool

max :: SafeNum a -> SafeNum a -> SafeNum a

min :: SafeNum a -> SafeNum a -> SafeNum a

Show a => Show (SafeNum a)

Defined in Domain.Algebra.Field

Methods

showsPrec :: Int -> SafeNum a -> ShowS

show :: SafeNum a -> String

showList :: [SafeNum a] -> ShowS

Arbitrary a => Arbitrary (SafeNum a)

Defined in Domain.Algebra.Field

Methods

arbitrary :: Gen (SafeNum a)

shrink :: SafeNum a -> [SafeNum a]

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

Defined in Domain.Algebra.Field

Methods

timesInverse :: SafeNum a -> SafeNum a

(|/|) :: SafeNum a -> SafeNum a -> SafeNum a

Num a => Ring (SafeNum a)

Defined in Domain.Algebra.Field

Methods

plusInverse :: SafeNum a -> SafeNum a

(|-|) :: SafeNum a -> SafeNum a -> SafeNum a

Num a => SemiRing (SafeNum a)

Defined in Domain.Algebra.Field

Methods

(|+|) :: SafeNum a -> SafeNum a -> SafeNum a

zero :: SafeNum a

sum :: [SafeNum a] -> SafeNum a

(|*|) :: SafeNum a -> SafeNum a -> SafeNum a

one :: SafeNum a

product :: [SafeNum a] -> 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 Expr

Defined in Domain.Math.Expr.Data

Methods

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

isZero :: Expr -> Bool

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

isOne :: Expr -> Bool

CoSemiRing a => CoSemiRing (SmartField a)

Defined in Domain.Algebra.SmartGroup

Methods

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

isZero :: SmartField a -> Bool

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

isOne :: SmartField a -> Bool

class CoSemiRing a => CoRing a where

Minimal complete definition

isNegate

Methods

isNegate :: a -> Maybe a

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

Instances

CoRing Expr

Defined in Domain.Math.Expr.Data

Methods

isNegate :: Expr -> Maybe Expr

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

CoRing a => CoRing (SmartField a)

Defined in Domain.Algebra.SmartGroup

Methods

isNegate :: SmartField a -> Maybe (SmartField a)

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

class CoRing a => CoField a where

Minimal complete definition

isRecip

Methods

isRecip :: a -> Maybe a

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

Instances

CoField Expr

Defined in Domain.Math.Expr.Data

Methods

isRecip :: Expr -> Maybe Expr

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

CoField a => CoField (SmartField a)

Defined in Domain.Algebra.SmartGroup

Methods

isRecip :: SmartField a -> Maybe (SmartField a)

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