Safe Haskell	None
Language	Haskell2010

AERN2.AD.Type

Documentation

data Differential a Source #

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

Instances details

Functor Differential Source #
Instance details Defined in AERN2.AD.Type Methods fmap :: (a -> b) -> Differential a -> Differential b # (<$) :: a -> Differential b -> Differential a #
CanDiv Integer (Differential (CN MPBall)) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details Defined in AERN2.AD.Type Methods showsPrec :: Int -> Differential a -> ShowS # show :: Differential a -> String # showList :: [Differential a] -> ShowS #
HasPrecision a => HasPrecision (Differential a) Source #
Instance details Defined in AERN2.AD.Type Methods getPrecision :: Differential a -> Precision #
CanSetPrecision a => CanSetPrecision (Differential a) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details Defined in AERN2.AD.GenericOperations Associated Types type NegType (Differential a) # Methods negate :: Differential a -> NegType (Differential a) #
CanDiv (Differential (CN MPBall)) Integer Source #
Instance details 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 Source #
Instance details 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 Source #
Instance details 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 Source #
Instance details 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 Source #
Instance details 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 Source #
Instance details 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 Source #
Instance details 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 Source #
Instance details 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 Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details Defined in AERN2.AD.MPBallOperations type DivType Integer (Differential (CN MPBall)) = Differential (CN MPBall)
type DivType MPBall (Differential (CN MPBall)) Source #
Instance details Defined in AERN2.AD.MPBallOperations type DivType MPBall (Differential (CN MPBall)) = Differential (CN MPBall)
type MulType Integer (Differential (CN MPBall)) Source #
Instance details Defined in AERN2.AD.MPBallOperations type MulType Integer (Differential (CN MPBall)) = Differential (CN MPBall)
type MulType MPBall (Differential (CN MPBall)) Source #
Instance details Defined in AERN2.AD.MPBallOperations type MulType MPBall (Differential (CN MPBall)) = Differential (CN MPBall)
type AddType Integer (Differential (CN MPBall)) Source #
Instance details Defined in AERN2.AD.MPBallOperations type AddType Integer (Differential (CN MPBall)) = Differential (CN MPBall)
type AddType MPBall (Differential (CN MPBall)) Source #
Instance details Defined in AERN2.AD.MPBallOperations type AddType MPBall (Differential (CN MPBall)) = Differential (CN MPBall)
type SubType Integer (Differential (CN MPBall)) Source #
Instance details Defined in AERN2.AD.MPBallOperations type SubType Integer (Differential (CN MPBall)) = Differential (CN MPBall)
type SubType MPBall (Differential (CN MPBall)) Source #
Instance details Defined in AERN2.AD.MPBallOperations type SubType MPBall (Differential (CN MPBall)) = Differential (CN MPBall)
type SqrtType (Differential a) Source #
Instance details Defined in AERN2.AD.GenericOperations type SqrtType (Differential a) = Differential a
type ExpType (Differential a) Source #
Instance details Defined in AERN2.AD.GenericOperations type ExpType (Differential a) = Differential a
type SinCosType (Differential a) Source #
Instance details Defined in AERN2.AD.GenericOperations type SinCosType (Differential a) = Differential a
type AbsType (Differential (CN MPBall)) Source #
Instance details Defined in AERN2.AD.MPBallOperations type AbsType (Differential (CN MPBall)) = Differential (CN MPBall)
type NegType (Differential a) Source #
Instance details Defined in AERN2.AD.GenericOperations type NegType (Differential a) = Differential a
type DivType (Differential (CN MPBall)) Integer Source #
Instance details Defined in AERN2.AD.MPBallOperations type DivType (Differential (CN MPBall)) Integer = Differential (CN MPBall)
type DivType (Differential (CN MPBall)) MPBall Source #
Instance details Defined in AERN2.AD.MPBallOperations type DivType (Differential (CN MPBall)) MPBall = Differential (CN MPBall)
type PPowType (Differential (CN MPBall)) Integer Source #
Instance details Defined in AERN2.AD.MPBallOperations type PPowType (Differential (CN MPBall)) Integer = PowType (Differential (CN MPBall)) Integer
type PowType (Differential (CN MPBall)) Integer Source #
Instance details Defined in AERN2.AD.MPBallOperations type PowType (Differential (CN MPBall)) Integer = Differential (CN MPBall)
type MulType (Differential (CN MPBall)) Integer Source #
Instance details Defined in AERN2.AD.MPBallOperations type MulType (Differential (CN MPBall)) Integer = Differential (CN MPBall)
type MulType (Differential (CN MPBall)) MPBall Source #
Instance details Defined in AERN2.AD.MPBallOperations type MulType (Differential (CN MPBall)) MPBall = Differential (CN MPBall)
type AddType (Differential (CN MPBall)) Integer Source #
Instance details Defined in AERN2.AD.MPBallOperations type AddType (Differential (CN MPBall)) Integer = Differential (CN MPBall)
type AddType (Differential (CN MPBall)) MPBall Source #
Instance details Defined in AERN2.AD.MPBallOperations type AddType (Differential (CN MPBall)) MPBall = Differential (CN MPBall)
type SubType (Differential (CN MPBall)) Integer Source #
Instance details Defined in AERN2.AD.MPBallOperations type SubType (Differential (CN MPBall)) Integer = Differential (CN MPBall)
type SubType (Differential (CN MPBall)) MPBall Source #
Instance details Defined in AERN2.AD.MPBallOperations type SubType (Differential (CN MPBall)) MPBall = Differential (CN MPBall)
type DivType (CN a) (Differential (CN MPBall)) Source #
Instance details Defined in AERN2.AD.MPBallOperations type DivType (CN a) (Differential (CN MPBall)) = Differential (CN MPBall)
type DivType (Differential a) (Differential a) Source #
Instance details Defined in AERN2.AD.GenericOperations type DivType (Differential a) (Differential a) = Differential (DivType a a)
type DivType (Differential (CN MPBall)) (CN a) Source #
Instance details Defined in AERN2.AD.MPBallOperations type DivType (Differential (CN MPBall)) (CN a) = Differential (CN MPBall)
type PPowType (Differential a) (Differential a) Source #
Instance details Defined in AERN2.AD.GenericOperations type PPowType (Differential a) (Differential a) = PowType (Differential a) (Differential a)
type PowType (Differential a) (Differential a) Source #
Instance details Defined in AERN2.AD.GenericOperations type PowType (Differential a) (Differential a) = Differential a
type ModType (Differential (CN MPBall)) (Differential (CN MPBall)) Source #
Instance details Defined in AERN2.AD.MPBallOperations type ModType (Differential (CN MPBall)) (Differential (CN MPBall)) = Differential (CN MPBall)
type DivIType (Differential (CN MPBall)) (Differential (CN MPBall)) Source #
Instance details Defined in AERN2.AD.MPBallOperations type DivIType (Differential (CN MPBall)) (Differential (CN MPBall)) = Differential (CN MPBall)
type MulType (CN a) (Differential (CN MPBall)) Source #
Instance details Defined in AERN2.AD.MPBallOperations type MulType (CN a) (Differential (CN MPBall)) = Differential (CN MPBall)
type MulType (Differential a) (Differential a) Source #
Instance details Defined in AERN2.AD.GenericOperations type MulType (Differential a) (Differential a) = Differential a
type MulType (Differential (CN MPBall)) (CN a) Source #
Instance details Defined in AERN2.AD.MPBallOperations type MulType (Differential (CN MPBall)) (CN a) = Differential (CN MPBall)
type AddType (CN a) (Differential (CN MPBall)) Source #
Instance details Defined in AERN2.AD.MPBallOperations type AddType (CN a) (Differential (CN MPBall)) = Differential (CN MPBall)
type AddType (Differential a) (Differential a) Source #
Instance details Defined in AERN2.AD.GenericOperations type AddType (Differential a) (Differential a) = Differential a
type AddType (Differential (CN MPBall)) (CN a) Source #
Instance details Defined in AERN2.AD.MPBallOperations type AddType (Differential (CN MPBall)) (CN a) = Differential (CN MPBall)
type SubType (CN a) (Differential (CN MPBall)) Source #
Instance details Defined in AERN2.AD.MPBallOperations type SubType (CN a) (Differential (CN MPBall)) = Differential (CN MPBall)
type SubType (Differential a) (Differential a) Source #
Instance details Defined in AERN2.AD.GenericOperations type SubType (Differential a) (Differential a) = Differential a
type SubType (Differential (CN MPBall)) (CN a) Source #
Instance details Defined in AERN2.AD.MPBallOperations type SubType (Differential (CN MPBall)) (CN a) = Differential (CN MPBall)
type MinMaxType (Differential a) (Differential a) Source #
Instance details Defined in AERN2.AD.GenericOperations type MinMaxType (Differential a) (Differential a) = Differential a

order :: Differential a -> Integer Source #

class CanBeDifferential a where Source #

Methods

differential :: Integer -> a -> Differential a Source #

Instances

Instances details

HasIntegers a => CanBeDifferential a Source #
Instance details Defined in AERN2.AD.Type Methods differential :: Integer -> a -> Differential a Source #

setValue :: Differential a -> a -> Differential a Source #