AERN2.AD.Type

Documentation

data Differential a

Constructors

OrderZero

Fields

• diff_x :: a

OrderOne

Fields

• diff_x :: a
• diff_dx :: a

OrderTwo

Fields

• diff_x :: a
• diff_dx :: a
• diff_dxt :: a
• diff_d2x :: a

Instances

Functor Differential

Defined in AERN2.AD.Type

Methods

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

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

CanDiv Integer (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

Associated Types

type DivType Integer (Differential (CN MPBall))

Methods

divide :: Integer -> Differential (CN MPBall) -> DivType Integer (Differential (CN MPBall))

CanDiv MPBall (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

Associated Types

type DivType MPBall (Differential (CN MPBall))

Methods

divide :: MPBall -> Differential (CN MPBall) -> DivType MPBall (Differential (CN MPBall))

CanMulAsymmetric Integer (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

Associated Types

type MulType Integer (Differential (CN MPBall))

Methods

mul :: Integer -> Differential (CN MPBall) -> MulType Integer (Differential (CN MPBall))

CanMulAsymmetric MPBall (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

Associated Types

type MulType MPBall (Differential (CN MPBall))

Methods

mul :: MPBall -> Differential (CN MPBall) -> MulType MPBall (Differential (CN MPBall))

CanAddAsymmetric Integer (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

Associated Types

type AddType Integer (Differential (CN MPBall))

Methods

add :: Integer -> Differential (CN MPBall) -> AddType Integer (Differential (CN MPBall))

CanAddAsymmetric MPBall (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

Associated Types

type AddType MPBall (Differential (CN MPBall))

Methods

add :: MPBall -> Differential (CN MPBall) -> AddType MPBall (Differential (CN MPBall))

CanSub Integer (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

Associated Types

type SubType Integer (Differential (CN MPBall))

Methods

sub :: Integer -> Differential (CN MPBall) -> SubType Integer (Differential (CN MPBall))

CanSub MPBall (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

Associated Types

type SubType MPBall (Differential (CN MPBall))

Methods

sub :: MPBall -> Differential (CN MPBall) -> SubType MPBall (Differential (CN MPBall))

Show a => Show (Differential a)

Defined in AERN2.AD.Type

Methods

showsPrec :: Int -> Differential a -> ShowS

show :: Differential a -> String

showList :: [Differential a] -> ShowS

HasPrecision a => HasPrecision (Differential a)

Defined in AERN2.AD.Type

Methods

getPrecision :: Differential a -> Precision

CanSetPrecision a => CanSetPrecision (Differential a)

Defined in AERN2.AD.Type

Methods

setPrecision :: Precision -> Differential a -> Differential a

(CanSqrtSameType a, CanMulSameType a, CanNegSameType a, CanAddSameType a, CanMulBy a Integer, CanRecipSameType a) => CanSqrt (Differential a)

Defined in AERN2.AD.GenericOperations

Associated Types

type SqrtType (Differential a)

Methods

sqrt :: Differential a -> SqrtType (Differential a)

(CanExpSameType a, CanMulSameType a, CanAddSameType a) => CanExp (Differential a)

Defined in AERN2.AD.GenericOperations

Associated Types

type ExpType (Differential a)

Methods

exp :: Differential a -> ExpType (Differential a)

(CanSinCosSameType a, CanMulSameType a, CanNegSameType a, CanSubSameType a, CanAddSameType a, HasIntegers a, CanMinMaxSameType a) => CanSinCos (Differential a)

Defined in AERN2.AD.GenericOperations

Associated Types

type SinCosType (Differential a)

Methods

cos :: Differential a -> SinCosType (Differential a)

sin :: Differential a -> SinCosType (Differential a)

CanAbs (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

Associated Types

type AbsType (Differential (CN MPBall))

Methods

abs :: Differential (CN MPBall) -> AbsType (Differential (CN MPBall))

CanMulBy (Differential a) Integer => CanNeg (Differential a)

Defined in AERN2.AD.GenericOperations

Associated Types

type NegType (Differential a)

Methods

negate :: Differential a -> NegType (Differential a)

CanDiv (Differential (CN MPBall)) Integer

Defined in AERN2.AD.MPBallOperations

Associated Types

type DivType (Differential (CN MPBall)) Integer

Methods

divide :: Differential (CN MPBall) -> Integer -> DivType (Differential (CN MPBall)) Integer

CanDiv (Differential (CN MPBall)) MPBall

Defined in AERN2.AD.MPBallOperations

Associated Types

type DivType (Differential (CN MPBall)) MPBall

Methods

divide :: Differential (CN MPBall) -> MPBall -> DivType (Differential (CN MPBall)) MPBall

CanPow (Differential (CN MPBall)) Integer

Defined in AERN2.AD.MPBallOperations

Associated Types

type PowType (Differential (CN MPBall)) Integer

type PPowType (Differential (CN MPBall)) Integer

Methods

pow :: Differential (CN MPBall) -> Integer -> PowType (Differential (CN MPBall)) Integer

ppow :: Differential (CN MPBall) -> Integer -> PPowType (Differential (CN MPBall)) Integer

CanMulAsymmetric (Differential (CN MPBall)) Integer

Defined in AERN2.AD.MPBallOperations

Associated Types

type MulType (Differential (CN MPBall)) Integer

Methods

mul :: Differential (CN MPBall) -> Integer -> MulType (Differential (CN MPBall)) Integer

CanMulAsymmetric (Differential (CN MPBall)) MPBall

Defined in AERN2.AD.MPBallOperations

Associated Types

type MulType (Differential (CN MPBall)) MPBall

Methods

mul :: Differential (CN MPBall) -> MPBall -> MulType (Differential (CN MPBall)) MPBall

CanAddAsymmetric (Differential (CN MPBall)) Integer

Defined in AERN2.AD.MPBallOperations

Associated Types

type AddType (Differential (CN MPBall)) Integer

Methods

add :: Differential (CN MPBall) -> Integer -> AddType (Differential (CN MPBall)) Integer

CanAddAsymmetric (Differential (CN MPBall)) MPBall

Defined in AERN2.AD.MPBallOperations

Associated Types

type AddType (Differential (CN MPBall)) MPBall

Methods

add :: Differential (CN MPBall) -> MPBall -> AddType (Differential (CN MPBall)) MPBall

CanSub (Differential (CN MPBall)) Integer

Defined in AERN2.AD.MPBallOperations

Associated Types

type SubType (Differential (CN MPBall)) Integer

Methods

sub :: Differential (CN MPBall) -> Integer -> SubType (Differential (CN MPBall)) Integer

CanSub (Differential (CN MPBall)) MPBall

Defined in AERN2.AD.MPBallOperations

Associated Types

type SubType (Differential (CN MPBall)) MPBall

Methods

sub :: Differential (CN MPBall) -> MPBall -> SubType (Differential (CN MPBall)) MPBall

CanBeMPBall a => CanDiv (CN a) (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

Associated Types

type DivType (CN a) (Differential (CN MPBall))

Methods

divide :: CN a -> Differential (CN MPBall) -> DivType (CN a) (Differential (CN MPBall))

(CanDiv a a, CanSubSameType a, CanMulSameType a, CanMulBy a Integer, CanAddSameType a, CanSubSameType (DivType a a)) => CanDiv (Differential a) (Differential a)

Defined in AERN2.AD.GenericOperations

Associated Types

type DivType (Differential a) (Differential a)

Methods

divide :: Differential a -> Differential a -> DivType (Differential a) (Differential a)

CanBeMPBall a => CanDiv (Differential (CN MPBall)) (CN a)

Defined in AERN2.AD.MPBallOperations

Associated Types

type DivType (Differential (CN MPBall)) (CN a)

Methods

divide :: Differential (CN MPBall) -> CN a -> DivType (Differential (CN MPBall)) (CN a)

(CanMulSameType a, CanAddSameType a, CanPowBy a a, CanSubThis a Integer, CanLogSameType a, CanDivSameType a) => CanPow (Differential a) (Differential a)

Defined in AERN2.AD.GenericOperations

Associated Types

type PowType (Differential a) (Differential a)

type PPowType (Differential a) (Differential a)

Methods

pow :: Differential a -> Differential a -> PowType (Differential a) (Differential a)

ppow :: Differential a -> Differential a -> PPowType (Differential a) (Differential a)

CanDivIMod (Differential (CN MPBall)) (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

Associated Types

type DivIType (Differential (CN MPBall)) (Differential (CN MPBall))

type ModType (Differential (CN MPBall)) (Differential (CN MPBall))

Methods

divIMod :: Differential (CN MPBall) -> Differential (CN MPBall) -> (DivIType (Differential (CN MPBall)) (Differential (CN MPBall)), ModType (Differential (CN MPBall)) (Differential (CN MPBall)))

mod :: Differential (CN MPBall) -> Differential (CN MPBall) -> ModType (Differential (CN MPBall)) (Differential (CN MPBall))

divI :: Differential (CN MPBall) -> Differential (CN MPBall) -> DivIType (Differential (CN MPBall)) (Differential (CN MPBall))

CanBeMPBall a => CanMulAsymmetric (CN a) (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

Associated Types

type MulType (CN a) (Differential (CN MPBall))

Methods

mul :: CN a -> Differential (CN MPBall) -> MulType (CN a) (Differential (CN MPBall))

(CanMulSameType a, CanAddSameType a) => CanMulAsymmetric (Differential a) (Differential a)

Defined in AERN2.AD.GenericOperations

Associated Types

type MulType (Differential a) (Differential a)

Methods

mul :: Differential a -> Differential a -> MulType (Differential a) (Differential a)

CanBeMPBall a => CanMulAsymmetric (Differential (CN MPBall)) (CN a)

Defined in AERN2.AD.MPBallOperations

Associated Types

type MulType (Differential (CN MPBall)) (CN a)

Methods

mul :: Differential (CN MPBall) -> CN a -> MulType (Differential (CN MPBall)) (CN a)

CanBeMPBall a => CanAddAsymmetric (CN a) (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

Associated Types

type AddType (CN a) (Differential (CN MPBall))

Methods

add :: CN a -> Differential (CN MPBall) -> AddType (CN a) (Differential (CN MPBall))

CanAddSameType a => CanAddAsymmetric (Differential a) (Differential a)

Defined in AERN2.AD.GenericOperations

Associated Types

type AddType (Differential a) (Differential a)

Methods

add :: Differential a -> Differential a -> AddType (Differential a) (Differential a)

CanBeMPBall a => CanAddAsymmetric (Differential (CN MPBall)) (CN a)

Defined in AERN2.AD.MPBallOperations

Associated Types

type AddType (Differential (CN MPBall)) (CN a)

Methods

add :: Differential (CN MPBall) -> CN a -> AddType (Differential (CN MPBall)) (CN a)

CanBeMPBall a => CanSub (CN a) (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

Associated Types

type SubType (CN a) (Differential (CN MPBall))

Methods

sub :: CN a -> Differential (CN MPBall) -> SubType (CN a) (Differential (CN MPBall))

CanSubSameType a => CanSub (Differential a) (Differential a)

Defined in AERN2.AD.GenericOperations

Associated Types

type SubType (Differential a) (Differential a)

Methods

sub :: Differential a -> Differential a -> SubType (Differential a) (Differential a)

CanBeMPBall a => CanSub (Differential (CN MPBall)) (CN a)

Defined in AERN2.AD.MPBallOperations

Associated Types

type SubType (Differential (CN MPBall)) (CN a)

Methods

sub :: Differential (CN MPBall) -> CN a -> SubType (Differential (CN MPBall)) (CN a)

CanMinMaxSameType a => CanMinMaxAsymmetric (Differential a) (Differential a)

Defined in AERN2.AD.GenericOperations

Associated Types

type MinMaxType (Differential a) (Differential a)

Methods

min :: Differential a -> Differential a -> MinMaxType (Differential a) (Differential a)

max :: Differential a -> Differential a -> MinMaxType (Differential a) (Differential a)

type DivType Integer (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

type DivType Integer (Differential (CN MPBall)) = Differential (CN MPBall)

type DivType MPBall (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

type DivType MPBall (Differential (CN MPBall)) = Differential (CN MPBall)

type MulType Integer (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

type MulType Integer (Differential (CN MPBall)) = Differential (CN MPBall)

type MulType MPBall (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

type MulType MPBall (Differential (CN MPBall)) = Differential (CN MPBall)

type AddType Integer (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

type AddType Integer (Differential (CN MPBall)) = Differential (CN MPBall)

type AddType MPBall (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

type AddType MPBall (Differential (CN MPBall)) = Differential (CN MPBall)

type SubType Integer (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

type SubType Integer (Differential (CN MPBall)) = Differential (CN MPBall)

type SubType MPBall (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

type SubType MPBall (Differential (CN MPBall)) = Differential (CN MPBall)

type SqrtType (Differential a)

Defined in AERN2.AD.GenericOperations

type SqrtType (Differential a) = Differential a

type ExpType (Differential a)

Defined in AERN2.AD.GenericOperations

type ExpType (Differential a) = Differential a

type SinCosType (Differential a)

Defined in AERN2.AD.GenericOperations

type SinCosType (Differential a) = Differential a

type AbsType (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

type AbsType (Differential (CN MPBall)) = Differential (CN MPBall)

type NegType (Differential a)

Defined in AERN2.AD.GenericOperations

type NegType (Differential a) = Differential a

type DivType (Differential (CN MPBall)) Integer

Defined in AERN2.AD.MPBallOperations

type DivType (Differential (CN MPBall)) Integer = Differential (CN MPBall)

type DivType (Differential (CN MPBall)) MPBall

Defined in AERN2.AD.MPBallOperations

type DivType (Differential (CN MPBall)) MPBall = Differential (CN MPBall)

type PPowType (Differential (CN MPBall)) Integer

Defined in AERN2.AD.MPBallOperations

type PPowType (Differential (CN MPBall)) Integer = PowType (Differential (CN MPBall)) Integer

type PowType (Differential (CN MPBall)) Integer

Defined in AERN2.AD.MPBallOperations

type PowType (Differential (CN MPBall)) Integer = Differential (CN MPBall)

type MulType (Differential (CN MPBall)) Integer

Defined in AERN2.AD.MPBallOperations

type MulType (Differential (CN MPBall)) Integer = Differential (CN MPBall)

type MulType (Differential (CN MPBall)) MPBall

Defined in AERN2.AD.MPBallOperations

type MulType (Differential (CN MPBall)) MPBall = Differential (CN MPBall)

type AddType (Differential (CN MPBall)) Integer

Defined in AERN2.AD.MPBallOperations

type AddType (Differential (CN MPBall)) Integer = Differential (CN MPBall)

type AddType (Differential (CN MPBall)) MPBall

Defined in AERN2.AD.MPBallOperations

type AddType (Differential (CN MPBall)) MPBall = Differential (CN MPBall)

type SubType (Differential (CN MPBall)) Integer

Defined in AERN2.AD.MPBallOperations

type SubType (Differential (CN MPBall)) Integer = Differential (CN MPBall)

type SubType (Differential (CN MPBall)) MPBall

Defined in AERN2.AD.MPBallOperations

type SubType (Differential (CN MPBall)) MPBall = Differential (CN MPBall)

type DivType (CN a) (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

type DivType (CN a) (Differential (CN MPBall)) = Differential (CN MPBall)

type DivType (Differential a) (Differential a)

Defined in AERN2.AD.GenericOperations

type DivType (Differential a) (Differential a) = Differential (DivType a a)

type DivType (Differential (CN MPBall)) (CN a)

Defined in AERN2.AD.MPBallOperations

type DivType (Differential (CN MPBall)) (CN a) = Differential (CN MPBall)

type PPowType (Differential a) (Differential a)

Defined in AERN2.AD.GenericOperations

type PPowType (Differential a) (Differential a) = PowType (Differential a) (Differential a)

type PowType (Differential a) (Differential a)

Defined in AERN2.AD.GenericOperations

type PowType (Differential a) (Differential a) = Differential a

type ModType (Differential (CN MPBall)) (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

type ModType (Differential (CN MPBall)) (Differential (CN MPBall)) = Differential (CN MPBall)

type DivIType (Differential (CN MPBall)) (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

type DivIType (Differential (CN MPBall)) (Differential (CN MPBall)) = Differential (CN MPBall)

type MulType (CN a) (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

type MulType (CN a) (Differential (CN MPBall)) = Differential (CN MPBall)

type MulType (Differential a) (Differential a)

Defined in AERN2.AD.GenericOperations

type MulType (Differential a) (Differential a) = Differential a

type MulType (Differential (CN MPBall)) (CN a)

Defined in AERN2.AD.MPBallOperations

type MulType (Differential (CN MPBall)) (CN a) = Differential (CN MPBall)

type AddType (CN a) (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

type AddType (CN a) (Differential (CN MPBall)) = Differential (CN MPBall)

type AddType (Differential a) (Differential a)

Defined in AERN2.AD.GenericOperations

type AddType (Differential a) (Differential a) = Differential a

type AddType (Differential (CN MPBall)) (CN a)

Defined in AERN2.AD.MPBallOperations

type AddType (Differential (CN MPBall)) (CN a) = Differential (CN MPBall)

type SubType (CN a) (Differential (CN MPBall))

Defined in AERN2.AD.MPBallOperations

type SubType (CN a) (Differential (CN MPBall)) = Differential (CN MPBall)

type SubType (Differential a) (Differential a)

Defined in AERN2.AD.GenericOperations

type SubType (Differential a) (Differential a) = Differential a

type SubType (Differential (CN MPBall)) (CN a)

Defined in AERN2.AD.MPBallOperations

type SubType (Differential (CN MPBall)) (CN a) = Differential (CN MPBall)

type MinMaxType (Differential a) (Differential a)

Defined in AERN2.AD.GenericOperations

type MinMaxType (Differential a) (Differential a) = Differential a

order :: Differential a -> Integer

class CanBeDifferential a where

Methods

differential :: Integer -> a -> Differential a

Instances

HasIntegers a => CanBeDifferential a

Defined in AERN2.AD.Type

Methods

differential :: Integer -> a -> Differential a

setValue :: Differential a -> a -> Differential a