Arithmetic.Numbers

Types

data Tropical a

Constructors

Tropical

Fields

• value :: a

Inf

Instances

Functor Tropical

Defined in Arithmetic.Numbers

Methods

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

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

(Num a, Ord a, Rig a) => LeftModule Natural (Tropical a)

Defined in Arithmetic.Numbers

Methods

(.*) :: Natural -> Tropical a -> Tropical a

(Num a, Ord a, Rig a) => RightModule Natural (Tropical a)

Defined in Arithmetic.Numbers

Methods

(*.) :: Tropical a -> Natural -> Tropical a

Enum (Tropical Integer)

Defined in Arithmetic.Numbers

Methods

succ :: Tropical Integer -> Tropical Integer

pred :: Tropical Integer -> Tropical Integer

toEnum :: Int -> Tropical Integer

fromEnum :: Tropical Integer -> Int

enumFrom :: Tropical Integer -> [Tropical Integer]

enumFromThen :: Tropical Integer -> Tropical Integer -> [Tropical Integer]

enumFromTo :: Tropical Integer -> Tropical Integer -> [Tropical Integer]

enumFromThenTo :: Tropical Integer -> Tropical Integer -> Tropical Integer -> [Tropical Integer]

Eq a => Eq (Tropical a)

Defined in Arithmetic.Numbers

Methods

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

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

Integral (Tropical Integer)

Defined in Arithmetic.Numbers

Methods

quot :: Tropical Integer -> Tropical Integer -> Tropical Integer

rem :: Tropical Integer -> Tropical Integer -> Tropical Integer

div :: Tropical Integer -> Tropical Integer -> Tropical Integer

mod :: Tropical Integer -> Tropical Integer -> Tropical Integer

quotRem :: Tropical Integer -> Tropical Integer -> (Tropical Integer, Tropical Integer)

divMod :: Tropical Integer -> Tropical Integer -> (Tropical Integer, Tropical Integer)

toInteger :: Tropical Integer -> Integer

(Ord a, Num a) => Num (Tropical a)

Defined in Arithmetic.Numbers

Methods

(+) :: Tropical a -> Tropical a -> Tropical a

(-) :: Tropical a -> Tropical a -> Tropical a

(*) :: Tropical a -> Tropical a -> Tropical a

negate :: Tropical a -> Tropical a

abs :: Tropical a -> Tropical a

signum :: Tropical a -> Tropical a

fromInteger :: Integer -> Tropical a

Ord (Tropical Integer)

Defined in Arithmetic.Numbers

Methods

compare :: Tropical Integer -> Tropical Integer -> Ordering

(<) :: Tropical Integer -> Tropical Integer -> Bool

(<=) :: Tropical Integer -> Tropical Integer -> Bool

(>) :: Tropical Integer -> Tropical Integer -> Bool

(>=) :: Tropical Integer -> Tropical Integer -> Bool

max :: Tropical Integer -> Tropical Integer -> Tropical Integer

min :: Tropical Integer -> Tropical Integer -> Tropical Integer

Real (Tropical Integer)

Defined in Arithmetic.Numbers

Methods

toRational :: Tropical Integer -> Rational

Show a => Show (Tropical a)

Defined in Arithmetic.Numbers

Methods

showsPrec :: Int -> Tropical a -> ShowS

show :: Tropical a -> String

showList :: [Tropical a] -> ShowS

(Rig a, Num a, Ord a) => Rig (Tropical a)

Defined in Arithmetic.Numbers

Methods

fromNatural :: Natural -> Tropical a

(Num a, Ord a, Rig a) => DecidableZero (Tropical a)

Not neccesary to implement since it is already defined

Defined in Arithmetic.Numbers

Methods

isZero :: Tropical a -> Bool

Num a => Commutative (Tropical a)

Defined in Arithmetic.Numbers

Num a => Unital (Tropical a)

Defined in Arithmetic.Numbers

Methods

one :: Tropical a

pow :: Tropical a -> Natural -> Tropical a

productWith :: Foldable f => (a0 -> Tropical a) -> f a0 -> Tropical a

Num a => Multiplicative (Tropical a)

Defined in Arithmetic.Numbers

Methods

(*) :: Tropical a -> Tropical a -> Tropical a

pow1p :: Tropical a -> Natural -> Tropical a

productWith1 :: Foldable1 f => (a0 -> Tropical a) -> f a0 -> Tropical a

(Ord a, Num a) => Semiring (Tropical a)

Defined in Arithmetic.Numbers

(Num a, Ord a, Rig a) => Monoidal (Tropical a)

Defined in Arithmetic.Numbers

Methods

zero :: Tropical a

sinnum :: Natural -> Tropical a -> Tropical a

sumWith :: Foldable f => (a0 -> Tropical a) -> f a0 -> Tropical a

Ord a => Additive (Tropical a)

Defined in Arithmetic.Numbers

Methods

(+) :: Tropical a -> Tropical a -> Tropical a

sinnum1p :: Natural -> Tropical a -> Tropical a

sumWith1 :: Foldable1 f => (a0 -> Tropical a) -> f a0 -> Tropical a

Ord a => Abelian (Tropical a)

Defined in Arithmetic.Numbers

(IsMonomialOrder ord, KnownNat n) => Fractional (Polynomial (Tropical Integer) ord n)

Defined in Polynomial.Prelude

Methods

(/) :: Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n

recip :: Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n

fromRational :: Rational -> Polynomial (Tropical Integer) ord n

(IsMonomialOrder ord, KnownNat n) => Num (Polynomial (Tropical Integer) ord n)

Defined in Polynomial.Prelude

Methods

(+) :: Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n

(-) :: Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n

(*) :: Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n

negate :: Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n

abs :: Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n

signum :: Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n

fromInteger :: Integer -> Polynomial (Tropical Integer) ord n