MathObj.Wrapper.NumericPrelude

A wrapper that provides instances of Haskell 98 and NumericPrelude numeric type classes for types that have NumericPrelude instances.

Documentation

newtype T a

This makes a type usable with Haskell98 type classes that was initially implemented for NumericPrelude typeclasses. E.g. if a is in class C, then T a is both in class Num and in C.

You can even lift container types. If Polynomial a is in C for all types a that are in C, then T (Polynomial (MathObj.Wrapper.Haskell98.T a)) is in Num for all types a that are in Num.

Constructors

Cons

Fields

• decons :: a

Instances

Functor T

Defined in MathObj.Wrapper.NumericPrelude

Methods

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

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

Bounded a => Bounded (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

minBound :: T a

maxBound :: T a

Enum a => Enum (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

succ :: T a -> T a

pred :: T a -> T a

toEnum :: Int -> T a

fromEnum :: T a -> Int

enumFrom :: T a -> [T a]

enumFromThen :: T a -> T a -> [T a]

enumFromTo :: T a -> T a -> [T a]

enumFromThenTo :: T a -> T a -> T a -> [T a]

Eq a => Eq (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

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

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

(C a, C a, Eq a, Show a) => Floating (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

pi :: T a

exp :: T a -> T a

log :: T a -> T a

sqrt :: T a -> T a

(**) :: T a -> T a -> T a

logBase :: T a -> T a -> T a

sin :: T a -> T a

cos :: T a -> T a

tan :: T a -> T a

asin :: T a -> T a

acos :: T a -> T a

atan :: T a -> T a

sinh :: T a -> T a

cosh :: T a -> T a

tanh :: T a -> T a

asinh :: T a -> T a

acosh :: T a -> T a

atanh :: T a -> T a

log1p :: T a -> T a

expm1 :: T a -> T a

log1pexp :: T a -> T a

log1mexp :: T a -> T a

(C a, C a, Eq a, Show a) => Fractional (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

(/) :: T a -> T a -> T a

recip :: T a -> T a

fromRational :: Rational -> T a

(C a, C a, C a, Ord a, Enum a, Show a) => Integral (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

quot :: T a -> T a -> T a

rem :: T a -> T a -> T a

div :: T a -> T a -> T a

mod :: T a -> T a -> T a

quotRem :: T a -> T a -> (T a, T a)

divMod :: T a -> T a -> (T a, T a)

toInteger :: T a -> Integer

(C a, C a, Eq a, Show a) => Num (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

(+) :: T a -> T a -> T a

(-) :: T a -> T a -> T a

(*) :: T a -> T a -> T a

negate :: T a -> T a

abs :: T a -> T a

signum :: T a -> T a

fromInteger :: Integer -> T a

Ord a => Ord (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

compare :: T a -> T a -> Ordering

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

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

(>) :: T a -> T a -> Bool

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

max :: T a -> T a -> T a

min :: T a -> T a -> T a

(C a, C a, Ord a, Show a) => Real (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

toRational :: T a -> Rational

(C a, C a, C a, C a, Ord a, Show a) => RealFloat (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

floatRadix :: T a -> Integer

floatDigits :: T a -> Int

floatRange :: T a -> (Int, Int)

decodeFloat :: T a -> (Integer, Int)

encodeFloat :: Integer -> Int -> T a

exponent :: T a -> Int

significand :: T a -> T a

scaleFloat :: Int -> T a -> T a

isNaN :: T a -> Bool

isInfinite :: T a -> Bool

isDenormalized :: T a -> Bool

isNegativeZero :: T a -> Bool

isIEEE :: T a -> Bool

atan2 :: T a -> T a -> T a

(C a, C a, C a, C a, Ord a, Show a) => RealFrac (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

properFraction :: Integral b => T a -> (b, T a)

truncate :: Integral b => T a -> b

round :: Integral b => T a -> b

ceiling :: Integral b => T a -> b

floor :: Integral b => T a -> b

Show a => Show (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

showsPrec :: Int -> T a -> ShowS

show :: T a -> String

showList :: [T a] -> ShowS

Ix a => Ix (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

range :: (T a, T a) -> [T a]

index :: (T a, T a) -> T a -> Int

unsafeIndex :: (T a, T a) -> T a -> Int

inRange :: (T a, T a) -> T a -> Bool

rangeSize :: (T a, T a) -> Int

unsafeRangeSize :: (T a, T a) -> Int

C a => C (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

zero :: T a

(+) :: T a -> T a -> T a

(-) :: T a -> T a -> T a

negate :: T a -> T a

C a => C (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

isZero :: T a -> Bool

C a => C (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

(*) :: T a -> T a -> T a

one :: T a

fromInteger :: Integer -> T a

(^) :: T a -> Integer -> T a

C a => C (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

div :: T a -> T a -> T a

mod :: T a -> T a -> T a

divMod :: T a -> T a -> (T a, T a)

C a => C (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

isUnit :: T a -> Bool

stdAssociate :: T a -> T a

stdUnit :: T a -> T a

stdUnitInv :: T a -> T a

C a => C (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

extendedGCD :: T a -> T a -> (T a, (T a, T a))

gcd :: T a -> T a -> T a

lcm :: T a -> T a -> T a

C a => C (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

differentiate :: T a -> T a

C a => C (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

abs :: T a -> T a

signum :: T a -> T a

C a => C (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

(/) :: T a -> T a -> T a

recip :: T a -> T a

fromRational' :: Rational -> T a

(^-) :: T a -> Integer -> T a

C a => C (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

toRational :: T a -> Rational

C a => C (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

quot :: T a -> T a -> T a

rem :: T a -> T a -> T a

quotRem :: T a -> T a -> (T a, T a)

C a => C (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

toInteger :: T a -> Integer

C a => C (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

sqrt :: T a -> T a

root :: Integer -> T a -> T a

(^/) :: T a -> Rational -> T a

C a => C (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

pi :: T a

exp :: T a -> T a

log :: T a -> T a

logBase :: T a -> T a -> T a

(**) :: T a -> T a -> T a

sin :: T a -> T a

cos :: T a -> T a

tan :: T a -> T a

asin :: T a -> T a

acos :: T a -> T a

atan :: T a -> T a

sinh :: T a -> T a

cosh :: T a -> T a

tanh :: T a -> T a

asinh :: T a -> T a

acosh :: T a -> T a

atanh :: T a -> T a

C a => C (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

splitFraction :: C b => T a -> (b, T a)

fraction :: T a -> T a

ceiling :: C b => T a -> b

floor :: C b => T a -> b

truncate :: C b => T a -> b

round :: C b => T a -> b

(C a, C a) => C (T a)

Defined in MathObj.Wrapper.NumericPrelude

C a => C (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

atan2 :: T a -> T a -> T a

C a => C (T a)

Defined in MathObj.Wrapper.NumericPrelude

Methods

radix :: T a -> Integer

digits :: T a -> Int

range :: T a -> (Int, Int)

decode :: T a -> (Integer, Int)

encode :: Integer -> Int -> T a

exponent :: T a -> Int

significand :: T a -> T a

scale :: Int -> T a -> T a

isNaN :: T a -> Bool

isInfinite :: T a -> Bool

isDenormalized :: T a -> Bool

isNegativeZero :: T a -> Bool

isIEEE :: T a -> Bool

C a v => C (T a) (T v)

Defined in MathObj.Wrapper.NumericPrelude

Methods

(*>) :: T a -> T v -> T v

C a v => C (T a) (T v)

Defined in MathObj.Wrapper.NumericPrelude

C a v => C (T a) (T v)

Defined in MathObj.Wrapper.NumericPrelude

Methods

(</>) :: T v -> T v -> T a

C a v => C (T a) (T v)

Defined in MathObj.Wrapper.NumericPrelude

Methods

toScalar :: T v -> T a

toMaybeScalar :: T v -> Maybe (T a)

fromScalar :: T a -> T v

C a v => C (T a) (T v)

Defined in MathObj.Wrapper.NumericPrelude

Methods

norm :: T v -> T a

C a v => C (T a) (T v)

Defined in MathObj.Wrapper.NumericPrelude

Methods

norm :: T v -> T a

C a v => C (T a) (T v)

Defined in MathObj.Wrapper.NumericPrelude

Methods

norm :: T v -> T a

Sqr a v => Sqr (T a) (T v)

Defined in MathObj.Wrapper.NumericPrelude

Methods

normSqr :: T v -> T a

lift1 :: (a -> b) -> T a -> T b

lift2 :: (a -> b -> c) -> T a -> T b -> T c

unimplemented :: String -> a