Copyright	(c) Michal Konecny
License	BSD3
Maintainer	mikkonecny@gmail.com
Stability	experimental
Portability	portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

AERN2.Real

Contents

sequences of approximants
real numbers and conversions
limits
lazy Kleeneans
extracting approximations
abstract real numbers

Description

Exact real numbers represented by Cauchy sequences of MPBalls.

Synopsis

newtype CSequence t = CSequence {
- unCSequence :: [CN t]
}
cseqPrecisions :: [Precision]
cseqIndexForPrecision :: Precision -> Integer
cseqFromWithCurrentPrec :: (forall p. KnownNat p => WithCurrentPrec p (CN b)) -> CSequence b
cseqFromPrecFunction :: (Precision -> CN b) -> CSequence b
unsafeApproximationExtension :: (CSequence b -> t) -> CN b -> t
type CReal = CSequence MPBall
creal :: CanBeCReal t => t -> CReal
type HasCReals t = ConvertibleExactly CReal t
type CanBeCReal t = ConvertibleExactly t CReal
pi :: CReal
crealFromWithCurrentPrec :: (forall p. KnownNat p => WithCurrentPrec p (CN MPBall)) -> CSequence MPBall
crealFromPrecFunction :: (Precision -> CN MPBall) -> CReal
class HasLimits ix s where
- type LimitType ix s
- limit :: (ix -> s) -> LimitType ix s
type CKleenean = CSequence Kleenean
type CanBeCKleenean t = ConvertibleExactly t CKleenean
ckleenean :: CanBeCKleenean t => t -> CKleenean
class IsBool (SelectType k) => CanSelect k where
- type SelectType k
- select :: k -> k -> SelectType k
type CanSelectBool k = (CanSelect k, SelectType k ~ Bool)
type CanSelectCNBool k = (CanSelect k, SelectType k ~ CN Bool)
class CanAndOrCountable t where
- or_countable :: (Integer -> t) -> t
- and_countable :: (Integer -> t) -> t
class CanExtractApproximation e q where
- type ExtractedApproximation e q
- extractApproximation :: e -> q -> ExtractedApproximation e q
(?) :: CanExtractApproximation e q => e -> q -> ExtractedApproximation e q
bits :: ConvertibleExactly t Accuracy => t -> Accuracy
prec :: Integer -> Precision
class (OrderedField r, HasIntegers r, HasLimitsSameType Int r, HasLimitsSameType Integer r, HasLimitsSameType Rational r, CanTakeCNErrors r, CanSelectCNBool (OrderCompareType r r), EqCompareType Integer r ~ OrderCompareType r r, EqCompareType r Integer ~ OrderCompareType r r, EqCompareType Int r ~ OrderCompareType r r, EqCompareType r Int ~ OrderCompareType r r, EqCompareType Rational r ~ OrderCompareType r r, EqCompareType r Rational ~ OrderCompareType r r, OrderCompareType Integer r ~ OrderCompareType r r, OrderCompareType r Integer ~ OrderCompareType r r, OrderCompareType Int r ~ OrderCompareType r r, OrderCompareType r Int ~ OrderCompareType r r, OrderCompareType Rational r ~ OrderCompareType r r, OrderCompareType r Rational ~ OrderCompareType r r) => RealNumber r

sequences of approximants

newtype CSequence t Source #

Constructors

CSequence
Fields unCSequence :: [CN t]

Instances

Instances details

Arbitrary CReal Source #
Instance details Defined in AERN2.Real.Tests Methods arbitrary :: Gen CReal # shrink :: CReal -> [CReal] #
CanSelect CKleenean Source #
Instance details Defined in AERN2.Real.CKleenean Associated Types type SelectType CKleenean # Methods select :: CKleenean -> CKleenean -> SelectType CKleenean #
CanSelectCountable CKleenean Source #
Instance details Defined in AERN2.Real.CKleenean Associated Types type SelectCountableType CKleenean # Methods selectCountable :: (Integer -> CKleenean) -> SelectCountableType CKleenean #
RealNumber CReal Source #
Instance details Defined in AERN2.Real
CanAndOrCountable CKleenean Source #
Instance details Defined in AERN2.Real.CKleenean Methods or_countable :: (Integer -> CKleenean) -> CKleenean Source # and_countable :: (Integer -> CKleenean) -> CKleenean Source #
Floating CReal Source #
Instance details Defined in AERN2.Real.Elementary Methods pi :: CReal # exp :: CReal -> CReal # log :: CReal -> CReal # sqrt :: CReal -> CReal # (**) :: CReal -> CReal -> CReal # logBase :: CReal -> CReal -> CReal # sin :: CReal -> CReal # cos :: CReal -> CReal # tan :: CReal -> CReal # asin :: CReal -> CReal # acos :: CReal -> CReal # atan :: CReal -> CReal # sinh :: CReal -> CReal # cosh :: CReal -> CReal # tanh :: CReal -> CReal # asinh :: CReal -> CReal # acosh :: CReal -> CReal # atanh :: CReal -> CReal # log1p :: CReal -> CReal # expm1 :: CReal -> CReal # log1pexp :: CReal -> CReal # log1mexp :: CReal -> CReal #
Num CReal Source #
Instance details Defined in AERN2.Real.Field Methods (+) :: CReal -> CReal -> CReal # (-) :: CReal -> CReal -> CReal # (*) :: CReal -> CReal -> CReal # negate :: CReal -> CReal # abs :: CReal -> CReal # signum :: CReal -> CReal # fromInteger :: Integer -> CReal #
Fractional CReal Source #
Instance details Defined in AERN2.Real.Field Methods (/) :: CReal -> CReal -> CReal # recip :: CReal -> CReal # fromRational :: Rational -> CReal #
CanExp CReal Source #
Instance details Defined in AERN2.Real.Elementary Associated Types type ExpType CReal # Methods exp :: CReal -> ExpType CReal #
CanLog CReal Source #
Instance details Defined in AERN2.Real.Elementary Associated Types type LogType CReal # Methods log :: CReal -> LogType CReal #
CanSinCos CReal Source #
Instance details Defined in AERN2.Real.Elementary Associated Types type SinCosType CReal # Methods cos :: CReal -> SinCosType CReal # sin :: CReal -> SinCosType CReal #
CanSqrt CReal Source #
Instance details Defined in AERN2.Real.Elementary Associated Types type SqrtType CReal # Methods sqrt :: CReal -> SqrtType CReal #
Field CReal Source #
Instance details Defined in AERN2.Real.Field
OrderedField CReal Source #
Instance details Defined in AERN2.Real.Field
OrderedRing CReal Source #
Instance details Defined in AERN2.Real.Field
Ring CReal Source #
Instance details Defined in AERN2.Real.Field
HasLimits Rational CReal Source #
Instance details Defined in AERN2.Real.Limit Associated Types type LimitType Rational CReal # Methods limit :: (Rational -> CReal) -> LimitType Rational CReal #
HasLimits Integer CReal Source #
Instance details Defined in AERN2.Real.Limit Associated Types type LimitType Integer CReal # Methods limit :: (Integer -> CReal) -> LimitType Integer CReal #
HasLimits Int CReal Source #
Instance details Defined in AERN2.Real.Limit Associated Types type LimitType Int CReal # Methods limit :: (Int -> CReal) -> LimitType Int CReal #
ConvertibleExactly Dyadic CReal Source #
Instance details Defined in AERN2.Real.Type Methods safeConvertExactly :: Dyadic -> ConvertResult CReal #
ConvertibleExactly CReal CReal Source #
Instance details Defined in AERN2.Real.Type Methods safeConvertExactly :: CReal -> ConvertResult CReal #
ConvertibleExactly Rational CReal Source #
Instance details Defined in AERN2.Real.Type Methods safeConvertExactly :: Rational -> ConvertResult CReal #
ConvertibleExactly Integer CReal Source #
Instance details Defined in AERN2.Real.Type Methods safeConvertExactly :: Integer -> ConvertResult CReal #
ConvertibleExactly Int CReal Source #
Instance details Defined in AERN2.Real.Type Methods safeConvertExactly :: Int -> ConvertResult CReal #
ConvertibleExactly t Kleenean => ConvertibleExactly t CKleenean Source #
Instance details Defined in AERN2.Real.CKleenean Methods safeConvertExactly :: t -> ConvertResult CKleenean #
ConvertibleWithPrecision CReal (CN MPBall) Source #
Instance details Defined in AERN2.Real.Type Methods safeConvertP :: Precision -> CReal -> ConvertResult (CN MPBall) #
CanTakeErrors NumErrors (CSequence t) Source #
Instance details Defined in AERN2.Real.Type Methods takeErrors :: NumErrors -> CSequence t -> CSequence t # takeErrorsNoValue :: NumErrors -> CSequence t #
CanAddAsymmetric MPBall b => CanAddAsymmetric MPBall (CSequence b) Source #
Instance details Defined in AERN2.Real.Field Associated Types type AddType MPBall (CSequence b) # Methods add :: MPBall -> CSequence b -> AddType MPBall (CSequence b) #
CanAddAsymmetric Dyadic a => CanAddAsymmetric Dyadic (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type AddType Dyadic (CSequence a) # Methods add :: Dyadic -> CSequence a -> AddType Dyadic (CSequence a) #
CanAddAsymmetric Rational a => CanAddAsymmetric Rational (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type AddType Rational (CSequence a) # Methods add :: Rational -> CSequence a -> AddType Rational (CSequence a) #
CanAddAsymmetric Integer a => CanAddAsymmetric Integer (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type AddType Integer (CSequence a) # Methods add :: Integer -> CSequence a -> AddType Integer (CSequence a) #
CanAddAsymmetric Int a => CanAddAsymmetric Int (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type AddType Int (CSequence a) # Methods add :: Int -> CSequence a -> AddType Int (CSequence a) #
CanSub MPBall b => CanSub MPBall (CSequence b) Source #
Instance details Defined in AERN2.Real.Field Associated Types type SubType MPBall (CSequence b) # Methods sub :: MPBall -> CSequence b -> SubType MPBall (CSequence b) #
CanSub Dyadic a => CanSub Dyadic (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type SubType Dyadic (CSequence a) # Methods sub :: Dyadic -> CSequence a -> SubType Dyadic (CSequence a) #
CanSub Rational a => CanSub Rational (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type SubType Rational (CSequence a) # Methods sub :: Rational -> CSequence a -> SubType Rational (CSequence a) #
CanSub Integer a => CanSub Integer (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type SubType Integer (CSequence a) # Methods sub :: Integer -> CSequence a -> SubType Integer (CSequence a) #
CanSub Int a => CanSub Int (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type SubType Int (CSequence a) # Methods sub :: Int -> CSequence a -> SubType Int (CSequence a) #
CanAndOrAsymmetric Kleenean t2 => CanAndOrAsymmetric Kleenean (CSequence t2) Source #
Instance details Defined in AERN2.Real.CKleenean Associated Types type AndOrType Kleenean (CSequence t2) # Methods and2 :: Kleenean -> CSequence t2 -> AndOrType Kleenean (CSequence t2) # or2 :: Kleenean -> CSequence t2 -> AndOrType Kleenean (CSequence t2) #
CanAndOrAsymmetric Bool t2 => CanAndOrAsymmetric Bool (CSequence t2) Source #
Instance details Defined in AERN2.Real.CKleenean Associated Types type AndOrType Bool (CSequence t2) # Methods and2 :: Bool -> CSequence t2 -> AndOrType Bool (CSequence t2) # or2 :: Bool -> CSequence t2 -> AndOrType Bool (CSequence t2) #
(CanDiv MPBall b, CanTestZero b) => CanDiv MPBall (CSequence b) Source #
Instance details Defined in AERN2.Real.Field Associated Types type DivType MPBall (CSequence b) # Methods divide :: MPBall -> CSequence b -> DivType MPBall (CSequence b) #
(CanDiv Dyadic a, CanTestZero a) => CanDiv Dyadic (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type DivType Dyadic (CSequence a) # Methods divide :: Dyadic -> CSequence a -> DivType Dyadic (CSequence a) #
(CanDiv Rational a, CanTestZero a) => CanDiv Rational (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type DivType Rational (CSequence a) # Methods divide :: Rational -> CSequence a -> DivType Rational (CSequence a) #
(CanDiv Integer a, CanTestZero a) => CanDiv Integer (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type DivType Integer (CSequence a) # Methods divide :: Integer -> CSequence a -> DivType Integer (CSequence a) #
(CanDiv Int a, CanTestZero a) => CanDiv Int (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type DivType Int (CSequence a) # Methods divide :: Int -> CSequence a -> DivType Int (CSequence a) #
(HasEqAsymmetric MPBall b, CanTestCertainly (EqCompareType MPBall b)) => HasEqAsymmetric MPBall (CSequence b) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType MPBall (CSequence b) # Methods equalTo :: MPBall -> CSequence b -> EqCompareType MPBall (CSequence b) # notEqualTo :: MPBall -> CSequence b -> EqCompareType MPBall (CSequence b) #
(HasEqAsymmetric Dyadic a, IsBool (CSequence (EqCompareType Dyadic a)), CanTestCertainly (EqCompareType Dyadic a)) => HasEqAsymmetric Dyadic (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType Dyadic (CSequence a) # Methods equalTo :: Dyadic -> CSequence a -> EqCompareType Dyadic (CSequence a) # notEqualTo :: Dyadic -> CSequence a -> EqCompareType Dyadic (CSequence a) #
(HasEqAsymmetric Rational a, IsBool (CSequence (EqCompareType Rational a)), CanTestCertainly (EqCompareType Rational a)) => HasEqAsymmetric Rational (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType Rational (CSequence a) # Methods equalTo :: Rational -> CSequence a -> EqCompareType Rational (CSequence a) # notEqualTo :: Rational -> CSequence a -> EqCompareType Rational (CSequence a) #
(HasEqAsymmetric Integer a, IsBool (CSequence (EqCompareType Integer a)), CanTestCertainly (EqCompareType Integer a)) => HasEqAsymmetric Integer (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType Integer (CSequence a) # Methods equalTo :: Integer -> CSequence a -> EqCompareType Integer (CSequence a) # notEqualTo :: Integer -> CSequence a -> EqCompareType Integer (CSequence a) #
(HasEqAsymmetric Int a, IsBool (CSequence (EqCompareType Int a)), CanTestCertainly (EqCompareType Int a)) => HasEqAsymmetric Int (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType Int (CSequence a) # Methods equalTo :: Int -> CSequence a -> EqCompareType Int (CSequence a) # notEqualTo :: Int -> CSequence a -> EqCompareType Int (CSequence a) #
(HasCReals t, HasIntegers t) => ConvertibleExactly CReal (Complex t) Source #
Instance details Defined in AERN2.Complex Methods safeConvertExactly :: CReal -> ConvertResult (Complex t) #
CanUnionCNSameType t => HasIfThenElse CKleenean (CSequence t) Source #
Instance details Defined in AERN2.Real.CKleenean Associated Types type IfThenElseType CKleenean (CSequence t) # Methods ifThenElse :: CKleenean -> CSequence t -> CSequence t -> IfThenElseType CKleenean (CSequence t) #
HasIfThenElse CKleenean t => HasIfThenElse CKleenean (Maybe t) Source #
Instance details Defined in AERN2.Real.CKleenean Associated Types type IfThenElseType CKleenean (Maybe t) # Methods ifThenElse :: CKleenean -> Maybe t -> Maybe t -> IfThenElseType CKleenean (Maybe t) #
HasIfThenElse CKleenean t => HasIfThenElse CKleenean [t] Source #
Instance details Defined in AERN2.Real.CKleenean Associated Types type IfThenElseType CKleenean [t] # Methods ifThenElse :: CKleenean -> [t] -> [t] -> IfThenElseType CKleenean [t] #
CanMinMaxAsymmetric MPBall a => CanMinMaxAsymmetric MPBall (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType MPBall (CSequence a) # Methods min :: MPBall -> CSequence a -> MinMaxType MPBall (CSequence a) # max :: MPBall -> CSequence a -> MinMaxType MPBall (CSequence a) #
CanMinMaxAsymmetric Dyadic a => CanMinMaxAsymmetric Dyadic (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType Dyadic (CSequence a) # Methods min :: Dyadic -> CSequence a -> MinMaxType Dyadic (CSequence a) # max :: Dyadic -> CSequence a -> MinMaxType Dyadic (CSequence a) #
CanMinMaxAsymmetric Rational a => CanMinMaxAsymmetric Rational (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType Rational (CSequence a) # Methods min :: Rational -> CSequence a -> MinMaxType Rational (CSequence a) # max :: Rational -> CSequence a -> MinMaxType Rational (CSequence a) #
CanMinMaxAsymmetric Integer a => CanMinMaxAsymmetric Integer (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType Integer (CSequence a) # Methods min :: Integer -> CSequence a -> MinMaxType Integer (CSequence a) # max :: Integer -> CSequence a -> MinMaxType Integer (CSequence a) #
CanMinMaxAsymmetric Int a => CanMinMaxAsymmetric Int (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType Int (CSequence a) # Methods min :: Int -> CSequence a -> MinMaxType Int (CSequence a) # max :: Int -> CSequence a -> MinMaxType Int (CSequence a) #
CanMulAsymmetric MPBall b => CanMulAsymmetric MPBall (CSequence b) Source #
Instance details Defined in AERN2.Real.Field Associated Types type MulType MPBall (CSequence b) # Methods mul :: MPBall -> CSequence b -> MulType MPBall (CSequence b) #
(CanMulAsymmetric Dyadic a, CanGiveUpIfVeryInaccurate (MulType Dyadic a)) => CanMulAsymmetric Dyadic (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type MulType Dyadic (CSequence a) # Methods mul :: Dyadic -> CSequence a -> MulType Dyadic (CSequence a) #
(CanMulAsymmetric Rational a, CanGiveUpIfVeryInaccurate (MulType Rational a)) => CanMulAsymmetric Rational (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type MulType Rational (CSequence a) # Methods mul :: Rational -> CSequence a -> MulType Rational (CSequence a) #
(CanMulAsymmetric Integer a, CanGiveUpIfVeryInaccurate (MulType Integer a)) => CanMulAsymmetric Integer (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type MulType Integer (CSequence a) # Methods mul :: Integer -> CSequence a -> MulType Integer (CSequence a) #
(CanMulAsymmetric Int a, CanGiveUpIfVeryInaccurate (MulType Int a)) => CanMulAsymmetric Int (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type MulType Int (CSequence a) # Methods mul :: Int -> CSequence a -> MulType Int (CSequence a) #
(HasOrderAsymmetric MPBall b, CanTestCertainly (OrderCompareType MPBall b)) => HasOrderAsymmetric MPBall (CSequence b) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType MPBall (CSequence b) # Methods lessThan :: MPBall -> CSequence b -> OrderCompareType MPBall (CSequence b) # greaterThan :: MPBall -> CSequence b -> OrderCompareType MPBall (CSequence b) # leq :: MPBall -> CSequence b -> OrderCompareType MPBall (CSequence b) # geq :: MPBall -> CSequence b -> OrderCompareType MPBall (CSequence b) #
(HasOrderAsymmetric Dyadic a, IsBool (CSequence (OrderCompareType Dyadic a)), CanTestCertainly (OrderCompareType Dyadic a)) => HasOrderAsymmetric Dyadic (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType Dyadic (CSequence a) # Methods lessThan :: Dyadic -> CSequence a -> OrderCompareType Dyadic (CSequence a) # greaterThan :: Dyadic -> CSequence a -> OrderCompareType Dyadic (CSequence a) # leq :: Dyadic -> CSequence a -> OrderCompareType Dyadic (CSequence a) # geq :: Dyadic -> CSequence a -> OrderCompareType Dyadic (CSequence a) #
(HasOrderAsymmetric Rational a, IsBool (CSequence (OrderCompareType Rational a)), CanTestCertainly (OrderCompareType Rational a)) => HasOrderAsymmetric Rational (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType Rational (CSequence a) # Methods lessThan :: Rational -> CSequence a -> OrderCompareType Rational (CSequence a) # greaterThan :: Rational -> CSequence a -> OrderCompareType Rational (CSequence a) # leq :: Rational -> CSequence a -> OrderCompareType Rational (CSequence a) # geq :: Rational -> CSequence a -> OrderCompareType Rational (CSequence a) #
(HasOrderAsymmetric Integer a, IsBool (CSequence (OrderCompareType Integer a)), CanTestCertainly (OrderCompareType Integer a)) => HasOrderAsymmetric Integer (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType Integer (CSequence a) # Methods lessThan :: Integer -> CSequence a -> OrderCompareType Integer (CSequence a) # greaterThan :: Integer -> CSequence a -> OrderCompareType Integer (CSequence a) # leq :: Integer -> CSequence a -> OrderCompareType Integer (CSequence a) # geq :: Integer -> CSequence a -> OrderCompareType Integer (CSequence a) #
(HasOrderAsymmetric Int a, IsBool (CSequence (OrderCompareType Int a)), CanTestCertainly (OrderCompareType Int a)) => HasOrderAsymmetric Int (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType Int (CSequence a) # Methods lessThan :: Int -> CSequence a -> OrderCompareType Int (CSequence a) # greaterThan :: Int -> CSequence a -> OrderCompareType Int (CSequence a) # leq :: Int -> CSequence a -> OrderCompareType Int (CSequence a) # geq :: Int -> CSequence a -> OrderCompareType Int (CSequence a) #
(CanPow Rational e, HasOrderCertainly e Integer, CanTestIsIntegerType e, CanTestInteger e) => CanPow Rational (CSequence e) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type PowType Rational (CSequence e) # type PPowType Rational (CSequence e) # Methods pow :: Rational -> CSequence e -> PowType Rational (CSequence e) # ppow :: Rational -> CSequence e -> PPowType Rational (CSequence e) #
(CanPow Integer e, HasOrderCertainly e Integer, CanTestIsIntegerType e, CanTestInteger e) => CanPow Integer (CSequence e) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type PowType Integer (CSequence e) # type PPowType Integer (CSequence e) # Methods pow :: Integer -> CSequence e -> PowType Integer (CSequence e) # ppow :: Integer -> CSequence e -> PPowType Integer (CSequence e) #
(CanPow Int e, HasOrderCertainly e Integer, CanTestIsIntegerType e, CanTestInteger e) => CanPow Int (CSequence e) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type PowType Int (CSequence e) # type PPowType Int (CSequence e) # Methods pow :: Int -> CSequence e -> PowType Int (CSequence e) # ppow :: Int -> CSequence e -> PPowType Int (CSequence e) #
HasLimits Rational (CReal -> CReal) Source #
Instance details Defined in AERN2.Real.Limit Associated Types type LimitType Rational (CReal -> CReal) # Methods limit :: (Rational -> CReal -> CReal) -> LimitType Rational (CReal -> CReal) #
(HasIfThenElse CKleenean t1, HasIfThenElse CKleenean t2) => HasIfThenElse CKleenean (t1, t2) Source #
Instance details Defined in AERN2.Real.CKleenean Associated Types type IfThenElseType CKleenean (t1, t2) # Methods ifThenElse :: CKleenean -> (t1, t2) -> (t1, t2) -> IfThenElseType CKleenean (t1, t2) #
HasIfThenElse CKleenean v => HasIfThenElse CKleenean (k -> v) Source #
Instance details Defined in AERN2.Real.CKleenean Associated Types type IfThenElseType CKleenean (k -> v) # Methods ifThenElse :: CKleenean -> (k -> v) -> (k -> v) -> IfThenElseType CKleenean (k -> v) #
Show t => Show (CSequence t) Source #
Instance details Defined in AERN2.Real.Type Methods showsPrec :: Int -> CSequence t -> ShowS # show :: CSequence t -> String # showList :: [CSequence t] -> ShowS #
CanClearPotentialErrors (CSequence t) Source #
Instance details Defined in AERN2.Real.Type Methods clearPotentialErrors :: CSequence t -> CSequence t #
HasEqCertainly a a => Eq (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Methods (==) :: CSequence a -> CSequence a -> Bool # (/=) :: CSequence a -> CSequence a -> Bool #
(HasEqCertainly a a, HasOrderCertainly a a) => Ord (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Methods compare :: CSequence a -> CSequence a -> Ordering # (<) :: CSequence a -> CSequence a -> Bool # (<=) :: CSequence a -> CSequence a -> Bool # (>) :: CSequence a -> CSequence a -> Bool # (>=) :: CSequence a -> CSequence a -> Bool # max :: CSequence a -> CSequence a -> CSequence a # min :: CSequence a -> CSequence a -> CSequence a #
CanNeg t => CanNeg (CSequence t) Source #
Instance details Defined in AERN2.Real.CKleenean Associated Types type NegType (CSequence t) # Methods negate :: CSequence t -> NegType (CSequence t) #
CanAbs t1 => CanAbs (CSequence t1) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type AbsType (CSequence t1) # Methods abs :: CSequence t1 -> AbsType (CSequence t1) #
CanTestIsIntegerType t => CanTestIsIntegerType (CSequence t) Source #
Instance details Defined in AERN2.Real.Type Methods isIntegerType :: CSequence t -> Bool #
HasAccuracy t => CanExtractApproximation (CSequence t) Accuracy Source #
Instance details Defined in AERN2.Real.Type Associated Types type ExtractedApproximation (CSequence t) Accuracy Source # Methods extractApproximation :: CSequence t -> Accuracy -> ExtractedApproximation (CSequence t) Accuracy Source #
CanExtractApproximation (CSequence t) Precision Source #
Instance details Defined in AERN2.Real.Type Associated Types type ExtractedApproximation (CSequence t) Precision Source # Methods extractApproximation :: CSequence t -> Precision -> ExtractedApproximation (CSequence t) Precision Source #
CanAddAsymmetric a Dyadic => CanAddAsymmetric (CSequence a) Dyadic Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type AddType (CSequence a) Dyadic # Methods add :: CSequence a -> Dyadic -> AddType (CSequence a) Dyadic #
CanAddAsymmetric a Rational => CanAddAsymmetric (CSequence a) Rational Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type AddType (CSequence a) Rational # Methods add :: CSequence a -> Rational -> AddType (CSequence a) Rational #
CanAddAsymmetric a Integer => CanAddAsymmetric (CSequence a) Integer Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type AddType (CSequence a) Integer # Methods add :: CSequence a -> Integer -> AddType (CSequence a) Integer #
CanAddAsymmetric a Int => CanAddAsymmetric (CSequence a) Int Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type AddType (CSequence a) Int # Methods add :: CSequence a -> Int -> AddType (CSequence a) Int #
CanAddAsymmetric b MPBall => CanAddAsymmetric (CSequence b) MPBall Source #
Instance details Defined in AERN2.Real.Field Associated Types type AddType (CSequence b) MPBall # Methods add :: CSequence b -> MPBall -> AddType (CSequence b) MPBall #
CanSub a Dyadic => CanSub (CSequence a) Dyadic Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type SubType (CSequence a) Dyadic # Methods sub :: CSequence a -> Dyadic -> SubType (CSequence a) Dyadic #
CanSub a Rational => CanSub (CSequence a) Rational Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type SubType (CSequence a) Rational # Methods sub :: CSequence a -> Rational -> SubType (CSequence a) Rational #
CanSub a Integer => CanSub (CSequence a) Integer Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type SubType (CSequence a) Integer # Methods sub :: CSequence a -> Integer -> SubType (CSequence a) Integer #
CanSub a Int => CanSub (CSequence a) Int Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type SubType (CSequence a) Int # Methods sub :: CSequence a -> Int -> SubType (CSequence a) Int #
CanSub b MPBall => CanSub (CSequence b) MPBall Source #
Instance details Defined in AERN2.Real.Field Associated Types type SubType (CSequence b) MPBall # Methods sub :: CSequence b -> MPBall -> SubType (CSequence b) MPBall #
CanAndOrAsymmetric t1 Kleenean => CanAndOrAsymmetric (CSequence t1) Kleenean Source #
Instance details Defined in AERN2.Real.CKleenean Associated Types type AndOrType (CSequence t1) Kleenean # Methods and2 :: CSequence t1 -> Kleenean -> AndOrType (CSequence t1) Kleenean # or2 :: CSequence t1 -> Kleenean -> AndOrType (CSequence t1) Kleenean #
CanAndOrAsymmetric t1 Bool => CanAndOrAsymmetric (CSequence t1) Bool Source #
Instance details Defined in AERN2.Real.CKleenean Associated Types type AndOrType (CSequence t1) Bool # Methods and2 :: CSequence t1 -> Bool -> AndOrType (CSequence t1) Bool # or2 :: CSequence t1 -> Bool -> AndOrType (CSequence t1) Bool #
CanDiv a Dyadic => CanDiv (CSequence a) Dyadic Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type DivType (CSequence a) Dyadic # Methods divide :: CSequence a -> Dyadic -> DivType (CSequence a) Dyadic #
CanDiv a Rational => CanDiv (CSequence a) Rational Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type DivType (CSequence a) Rational # Methods divide :: CSequence a -> Rational -> DivType (CSequence a) Rational #
CanDiv a Integer => CanDiv (CSequence a) Integer Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type DivType (CSequence a) Integer # Methods divide :: CSequence a -> Integer -> DivType (CSequence a) Integer #
CanDiv a Int => CanDiv (CSequence a) Int Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type DivType (CSequence a) Int # Methods divide :: CSequence a -> Int -> DivType (CSequence a) Int #
CanDiv b MPBall => CanDiv (CSequence b) MPBall Source #
Instance details Defined in AERN2.Real.Field Associated Types type DivType (CSequence b) MPBall # Methods divide :: CSequence b -> MPBall -> DivType (CSequence b) MPBall #
(HasEqAsymmetric a MPBall, CanTestCertainly (EqCompareType a MPBall)) => HasEqAsymmetric (CSequence a) MPBall Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType (CSequence a) MPBall # Methods equalTo :: CSequence a -> MPBall -> EqCompareType (CSequence a) MPBall # notEqualTo :: CSequence a -> MPBall -> EqCompareType (CSequence a) MPBall #
(HasEqAsymmetric a Dyadic, IsBool (CSequence (EqCompareType a Dyadic)), CanTestCertainly (EqCompareType a Dyadic)) => HasEqAsymmetric (CSequence a) Dyadic Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType (CSequence a) Dyadic # Methods equalTo :: CSequence a -> Dyadic -> EqCompareType (CSequence a) Dyadic # notEqualTo :: CSequence a -> Dyadic -> EqCompareType (CSequence a) Dyadic #
(HasEqAsymmetric a Rational, IsBool (CSequence (EqCompareType a Rational)), CanTestCertainly (EqCompareType a Rational)) => HasEqAsymmetric (CSequence a) Rational Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType (CSequence a) Rational # Methods equalTo :: CSequence a -> Rational -> EqCompareType (CSequence a) Rational # notEqualTo :: CSequence a -> Rational -> EqCompareType (CSequence a) Rational #
(HasEqAsymmetric a Integer, IsBool (CSequence (EqCompareType a Integer)), CanTestCertainly (EqCompareType a Integer)) => HasEqAsymmetric (CSequence a) Integer Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType (CSequence a) Integer # Methods equalTo :: CSequence a -> Integer -> EqCompareType (CSequence a) Integer # notEqualTo :: CSequence a -> Integer -> EqCompareType (CSequence a) Integer #
(HasEqAsymmetric a Int, IsBool (CSequence (EqCompareType a Int)), CanTestCertainly (EqCompareType a Int)) => HasEqAsymmetric (CSequence a) Int Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType (CSequence a) Int # Methods equalTo :: CSequence a -> Int -> EqCompareType (CSequence a) Int # notEqualTo :: CSequence a -> Int -> EqCompareType (CSequence a) Int #
ConvertibleExactly (WithAnyPrec (CN MPBall)) CReal Source #
Instance details Defined in AERN2.Real.Type Methods safeConvertExactly :: WithAnyPrec (CN MPBall) -> ConvertResult CReal #
CanMinMaxAsymmetric a MPBall => CanMinMaxAsymmetric (CSequence a) MPBall Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType (CSequence a) MPBall # Methods min :: CSequence a -> MPBall -> MinMaxType (CSequence a) MPBall # max :: CSequence a -> MPBall -> MinMaxType (CSequence a) MPBall #
CanMinMaxAsymmetric a Dyadic => CanMinMaxAsymmetric (CSequence a) Dyadic Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType (CSequence a) Dyadic # Methods min :: CSequence a -> Dyadic -> MinMaxType (CSequence a) Dyadic # max :: CSequence a -> Dyadic -> MinMaxType (CSequence a) Dyadic #
CanMinMaxAsymmetric a Rational => CanMinMaxAsymmetric (CSequence a) Rational Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType (CSequence a) Rational # Methods min :: CSequence a -> Rational -> MinMaxType (CSequence a) Rational # max :: CSequence a -> Rational -> MinMaxType (CSequence a) Rational #
CanMinMaxAsymmetric a Integer => CanMinMaxAsymmetric (CSequence a) Integer Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType (CSequence a) Integer # Methods min :: CSequence a -> Integer -> MinMaxType (CSequence a) Integer # max :: CSequence a -> Integer -> MinMaxType (CSequence a) Integer #
CanMinMaxAsymmetric a Int => CanMinMaxAsymmetric (CSequence a) Int Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType (CSequence a) Int # Methods min :: CSequence a -> Int -> MinMaxType (CSequence a) Int # max :: CSequence a -> Int -> MinMaxType (CSequence a) Int #
(CanMulAsymmetric a Dyadic, CanGiveUpIfVeryInaccurate (MulType a Dyadic)) => CanMulAsymmetric (CSequence a) Dyadic Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type MulType (CSequence a) Dyadic # Methods mul :: CSequence a -> Dyadic -> MulType (CSequence a) Dyadic #
(CanMulAsymmetric a Rational, CanGiveUpIfVeryInaccurate (MulType a Rational)) => CanMulAsymmetric (CSequence a) Rational Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type MulType (CSequence a) Rational # Methods mul :: CSequence a -> Rational -> MulType (CSequence a) Rational #
(CanMulAsymmetric a Integer, CanGiveUpIfVeryInaccurate (MulType a Integer)) => CanMulAsymmetric (CSequence a) Integer Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type MulType (CSequence a) Integer # Methods mul :: CSequence a -> Integer -> MulType (CSequence a) Integer #
(CanMulAsymmetric a Int, CanGiveUpIfVeryInaccurate (MulType a Int)) => CanMulAsymmetric (CSequence a) Int Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type MulType (CSequence a) Int # Methods mul :: CSequence a -> Int -> MulType (CSequence a) Int #
CanMulAsymmetric b MPBall => CanMulAsymmetric (CSequence b) MPBall Source #
Instance details Defined in AERN2.Real.Field Associated Types type MulType (CSequence b) MPBall # Methods mul :: CSequence b -> MPBall -> MulType (CSequence b) MPBall #
(HasOrderAsymmetric a MPBall, CanTestCertainly (OrderCompareType a MPBall)) => HasOrderAsymmetric (CSequence a) MPBall Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType (CSequence a) MPBall # Methods lessThan :: CSequence a -> MPBall -> OrderCompareType (CSequence a) MPBall # greaterThan :: CSequence a -> MPBall -> OrderCompareType (CSequence a) MPBall # leq :: CSequence a -> MPBall -> OrderCompareType (CSequence a) MPBall # geq :: CSequence a -> MPBall -> OrderCompareType (CSequence a) MPBall #
(HasOrderAsymmetric a Dyadic, IsBool (CSequence (OrderCompareType a Dyadic)), CanTestCertainly (OrderCompareType a Dyadic)) => HasOrderAsymmetric (CSequence a) Dyadic Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType (CSequence a) Dyadic # Methods lessThan :: CSequence a -> Dyadic -> OrderCompareType (CSequence a) Dyadic # greaterThan :: CSequence a -> Dyadic -> OrderCompareType (CSequence a) Dyadic # leq :: CSequence a -> Dyadic -> OrderCompareType (CSequence a) Dyadic # geq :: CSequence a -> Dyadic -> OrderCompareType (CSequence a) Dyadic #
(HasOrderAsymmetric a Rational, IsBool (CSequence (OrderCompareType a Rational)), CanTestCertainly (OrderCompareType a Rational)) => HasOrderAsymmetric (CSequence a) Rational Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType (CSequence a) Rational # Methods lessThan :: CSequence a -> Rational -> OrderCompareType (CSequence a) Rational # greaterThan :: CSequence a -> Rational -> OrderCompareType (CSequence a) Rational # leq :: CSequence a -> Rational -> OrderCompareType (CSequence a) Rational # geq :: CSequence a -> Rational -> OrderCompareType (CSequence a) Rational #
(HasOrderAsymmetric a Integer, IsBool (CSequence (OrderCompareType a Integer)), CanTestCertainly (OrderCompareType a Integer)) => HasOrderAsymmetric (CSequence a) Integer Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType (CSequence a) Integer # Methods lessThan :: CSequence a -> Integer -> OrderCompareType (CSequence a) Integer # greaterThan :: CSequence a -> Integer -> OrderCompareType (CSequence a) Integer # leq :: CSequence a -> Integer -> OrderCompareType (CSequence a) Integer # geq :: CSequence a -> Integer -> OrderCompareType (CSequence a) Integer #
(HasOrderAsymmetric a Int, IsBool (CSequence (OrderCompareType a Int)), CanTestCertainly (OrderCompareType a Int)) => HasOrderAsymmetric (CSequence a) Int Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType (CSequence a) Int # Methods lessThan :: CSequence a -> Int -> OrderCompareType (CSequence a) Int # greaterThan :: CSequence a -> Int -> OrderCompareType (CSequence a) Int # leq :: CSequence a -> Int -> OrderCompareType (CSequence a) Int # geq :: CSequence a -> Int -> OrderCompareType (CSequence a) Int #
(CanPow b Rational, HasOrderCertainly b Integer, HasEqCertainly b Integer, CanTestIsIntegerType b) => CanPow (CSequence b) Rational Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type PowType (CSequence b) Rational # type PPowType (CSequence b) Rational # Methods pow :: CSequence b -> Rational -> PowType (CSequence b) Rational # ppow :: CSequence b -> Rational -> PPowType (CSequence b) Rational #
(CanPow b Integer, HasOrderCertainly b Integer, HasEqCertainly b Integer, CanTestIsIntegerType b) => CanPow (CSequence b) Integer Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type PowType (CSequence b) Integer # type PPowType (CSequence b) Integer # Methods pow :: CSequence b -> Integer -> PowType (CSequence b) Integer # ppow :: CSequence b -> Integer -> PPowType (CSequence b) Integer #
(CanPow b Int, HasOrderCertainly b Integer, HasEqCertainly b Integer, CanTestIsIntegerType b) => CanPow (CSequence b) Int Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type PowType (CSequence b) Int # type PPowType (CSequence b) Int # Methods pow :: CSequence b -> Int -> PowType (CSequence b) Int # ppow :: CSequence b -> Int -> PPowType (CSequence b) Int #
CanAddAsymmetric a Dyadic => CanAddAsymmetric (CSequence a) (CN Dyadic) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type AddType (CSequence a) (CN Dyadic) # Methods add :: CSequence a -> CN Dyadic -> AddType (CSequence a) (CN Dyadic) #
CanAddAsymmetric a Rational => CanAddAsymmetric (CSequence a) (CN Rational) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type AddType (CSequence a) (CN Rational) # Methods add :: CSequence a -> CN Rational -> AddType (CSequence a) (CN Rational) #
CanAddAsymmetric a Integer => CanAddAsymmetric (CSequence a) (CN Integer) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type AddType (CSequence a) (CN Integer) # Methods add :: CSequence a -> CN Integer -> AddType (CSequence a) (CN Integer) #
CanAddAsymmetric a Int => CanAddAsymmetric (CSequence a) (CN Int) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type AddType (CSequence a) (CN Int) # Methods add :: CSequence a -> CN Int -> AddType (CSequence a) (CN Int) #
CanAddAsymmetric b MPBall => CanAddAsymmetric (CSequence b) (CN MPBall) Source #
Instance details Defined in AERN2.Real.Field Associated Types type AddType (CSequence b) (CN MPBall) # Methods add :: CSequence b -> CN MPBall -> AddType (CSequence b) (CN MPBall) #
CanAddAsymmetric t1 t2 => CanAddAsymmetric (CSequence t1) (CSequence t2) Source #
Instance details Defined in AERN2.Real.Field Associated Types type AddType (CSequence t1) (CSequence t2) # Methods add :: CSequence t1 -> CSequence t2 -> AddType (CSequence t1) (CSequence t2) #
CanAddAsymmetric MPBall b => CanAddAsymmetric (CN MPBall) (CSequence b) Source #
Instance details Defined in AERN2.Real.Field Associated Types type AddType (CN MPBall) (CSequence b) # Methods add :: CN MPBall -> CSequence b -> AddType (CN MPBall) (CSequence b) #
CanAddAsymmetric Dyadic a => CanAddAsymmetric (CN Dyadic) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type AddType (CN Dyadic) (CSequence a) # Methods add :: CN Dyadic -> CSequence a -> AddType (CN Dyadic) (CSequence a) #
CanAddAsymmetric Rational a => CanAddAsymmetric (CN Rational) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type AddType (CN Rational) (CSequence a) # Methods add :: CN Rational -> CSequence a -> AddType (CN Rational) (CSequence a) #
CanAddAsymmetric Integer a => CanAddAsymmetric (CN Integer) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type AddType (CN Integer) (CSequence a) # Methods add :: CN Integer -> CSequence a -> AddType (CN Integer) (CSequence a) #
CanAddAsymmetric Int a => CanAddAsymmetric (CN Int) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type AddType (CN Int) (CSequence a) # Methods add :: CN Int -> CSequence a -> AddType (CN Int) (CSequence a) #
CanSub a Dyadic => CanSub (CSequence a) (CN Dyadic) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type SubType (CSequence a) (CN Dyadic) # Methods sub :: CSequence a -> CN Dyadic -> SubType (CSequence a) (CN Dyadic) #
CanSub a Rational => CanSub (CSequence a) (CN Rational) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type SubType (CSequence a) (CN Rational) # Methods sub :: CSequence a -> CN Rational -> SubType (CSequence a) (CN Rational) #
CanSub a Integer => CanSub (CSequence a) (CN Integer) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type SubType (CSequence a) (CN Integer) # Methods sub :: CSequence a -> CN Integer -> SubType (CSequence a) (CN Integer) #
CanSub a Int => CanSub (CSequence a) (CN Int) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type SubType (CSequence a) (CN Int) # Methods sub :: CSequence a -> CN Int -> SubType (CSequence a) (CN Int) #
CanSub b MPBall => CanSub (CSequence b) (CN MPBall) Source #
Instance details Defined in AERN2.Real.Field Associated Types type SubType (CSequence b) (CN MPBall) # Methods sub :: CSequence b -> CN MPBall -> SubType (CSequence b) (CN MPBall) #
CanSub t1 t2 => CanSub (CSequence t1) (CSequence t2) Source #
Instance details Defined in AERN2.Real.Field Associated Types type SubType (CSequence t1) (CSequence t2) # Methods sub :: CSequence t1 -> CSequence t2 -> SubType (CSequence t1) (CSequence t2) #
CanSub MPBall b => CanSub (CN MPBall) (CSequence b) Source #
Instance details Defined in AERN2.Real.Field Associated Types type SubType (CN MPBall) (CSequence b) # Methods sub :: CN MPBall -> CSequence b -> SubType (CN MPBall) (CSequence b) #
CanSub Dyadic a => CanSub (CN Dyadic) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type SubType (CN Dyadic) (CSequence a) # Methods sub :: CN Dyadic -> CSequence a -> SubType (CN Dyadic) (CSequence a) #
CanSub Rational a => CanSub (CN Rational) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type SubType (CN Rational) (CSequence a) # Methods sub :: CN Rational -> CSequence a -> SubType (CN Rational) (CSequence a) #
CanSub Integer a => CanSub (CN Integer) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type SubType (CN Integer) (CSequence a) # Methods sub :: CN Integer -> CSequence a -> SubType (CN Integer) (CSequence a) #
CanSub Int a => CanSub (CN Int) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type SubType (CN Int) (CSequence a) # Methods sub :: CN Int -> CSequence a -> SubType (CN Int) (CSequence a) #
(CanAndOrAsymmetric t1 t2, CanTestCertainly t1, HasBools t2) => CanAndOrAsymmetric (CSequence t1) (CSequence t2) Source #
Instance details Defined in AERN2.Real.CKleenean Associated Types type AndOrType (CSequence t1) (CSequence t2) # Methods and2 :: CSequence t1 -> CSequence t2 -> AndOrType (CSequence t1) (CSequence t2) # or2 :: CSequence t1 -> CSequence t2 -> AndOrType (CSequence t1) (CSequence t2) #
CanDiv a Dyadic => CanDiv (CSequence a) (CN Dyadic) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type DivType (CSequence a) (CN Dyadic) # Methods divide :: CSequence a -> CN Dyadic -> DivType (CSequence a) (CN Dyadic) #
CanDiv a Rational => CanDiv (CSequence a) (CN Rational) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type DivType (CSequence a) (CN Rational) # Methods divide :: CSequence a -> CN Rational -> DivType (CSequence a) (CN Rational) #
CanDiv a Integer => CanDiv (CSequence a) (CN Integer) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type DivType (CSequence a) (CN Integer) # Methods divide :: CSequence a -> CN Integer -> DivType (CSequence a) (CN Integer) #
CanDiv a Int => CanDiv (CSequence a) (CN Int) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type DivType (CSequence a) (CN Int) # Methods divide :: CSequence a -> CN Int -> DivType (CSequence a) (CN Int) #
CanDiv b MPBall => CanDiv (CSequence b) (CN MPBall) Source #
Instance details Defined in AERN2.Real.Field Associated Types type DivType (CSequence b) (CN MPBall) # Methods divide :: CSequence b -> CN MPBall -> DivType (CSequence b) (CN MPBall) #
(CanDiv t1 t2, CanTestZero t2) => CanDiv (CSequence t1) (CSequence t2) Source #
Instance details Defined in AERN2.Real.Field Associated Types type DivType (CSequence t1) (CSequence t2) # Methods divide :: CSequence t1 -> CSequence t2 -> DivType (CSequence t1) (CSequence t2) #
(CanDiv MPBall b, CanTestZero b) => CanDiv (CN MPBall) (CSequence b) Source #
Instance details Defined in AERN2.Real.Field Associated Types type DivType (CN MPBall) (CSequence b) # Methods divide :: CN MPBall -> CSequence b -> DivType (CN MPBall) (CSequence b) #
(CanDiv Dyadic a, CanTestZero a) => CanDiv (CN Dyadic) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type DivType (CN Dyadic) (CSequence a) # Methods divide :: CN Dyadic -> CSequence a -> DivType (CN Dyadic) (CSequence a) #
(CanDiv Rational a, CanTestZero a) => CanDiv (CN Rational) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type DivType (CN Rational) (CSequence a) # Methods divide :: CN Rational -> CSequence a -> DivType (CN Rational) (CSequence a) #
(CanDiv Integer a, CanTestZero a) => CanDiv (CN Integer) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type DivType (CN Integer) (CSequence a) # Methods divide :: CN Integer -> CSequence a -> DivType (CN Integer) (CSequence a) #
(CanDiv Int a, CanTestZero a) => CanDiv (CN Int) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type DivType (CN Int) (CSequence a) # Methods divide :: CN Int -> CSequence a -> DivType (CN Int) (CSequence a) #
(HasEqAsymmetric a MPBall, CanTestCertainly (EqCompareType a MPBall)) => HasEqAsymmetric (CSequence a) (CN MPBall) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType (CSequence a) (CN MPBall) # Methods equalTo :: CSequence a -> CN MPBall -> EqCompareType (CSequence a) (CN MPBall) # notEqualTo :: CSequence a -> CN MPBall -> EqCompareType (CSequence a) (CN MPBall) #
(HasEqAsymmetric a Dyadic, IsBool (CSequence (EqCompareType a Dyadic)), CanTestCertainly (EqCompareType a Dyadic)) => HasEqAsymmetric (CSequence a) (CN Dyadic) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType (CSequence a) (CN Dyadic) # Methods equalTo :: CSequence a -> CN Dyadic -> EqCompareType (CSequence a) (CN Dyadic) # notEqualTo :: CSequence a -> CN Dyadic -> EqCompareType (CSequence a) (CN Dyadic) #
(HasEqAsymmetric a Rational, IsBool (CSequence (EqCompareType a Rational)), CanTestCertainly (EqCompareType a Rational)) => HasEqAsymmetric (CSequence a) (CN Rational) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType (CSequence a) (CN Rational) # Methods equalTo :: CSequence a -> CN Rational -> EqCompareType (CSequence a) (CN Rational) # notEqualTo :: CSequence a -> CN Rational -> EqCompareType (CSequence a) (CN Rational) #
(HasEqAsymmetric a Integer, IsBool (CSequence (EqCompareType a Integer)), CanTestCertainly (EqCompareType a Integer)) => HasEqAsymmetric (CSequence a) (CN Integer) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType (CSequence a) (CN Integer) # Methods equalTo :: CSequence a -> CN Integer -> EqCompareType (CSequence a) (CN Integer) # notEqualTo :: CSequence a -> CN Integer -> EqCompareType (CSequence a) (CN Integer) #
(HasEqAsymmetric a Int, IsBool (CSequence (EqCompareType a Int)), CanTestCertainly (EqCompareType a Int)) => HasEqAsymmetric (CSequence a) (CN Int) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType (CSequence a) (CN Int) # Methods equalTo :: CSequence a -> CN Int -> EqCompareType (CSequence a) (CN Int) # notEqualTo :: CSequence a -> CN Int -> EqCompareType (CSequence a) (CN Int) #
(HasEqAsymmetric t1 t2, IsBool (CSequence (EqCompareType t1 t2)), CanTestCertainly (EqCompareType t1 t2)) => HasEqAsymmetric (CSequence t1) (CSequence t2) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType (CSequence t1) (CSequence t2) # Methods equalTo :: CSequence t1 -> CSequence t2 -> EqCompareType (CSequence t1) (CSequence t2) # notEqualTo :: CSequence t1 -> CSequence t2 -> EqCompareType (CSequence t1) (CSequence t2) #
(HasEqAsymmetric MPBall b, CanTestCertainly (EqCompareType MPBall b)) => HasEqAsymmetric (CN MPBall) (CSequence b) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType (CN MPBall) (CSequence b) # Methods equalTo :: CN MPBall -> CSequence b -> EqCompareType (CN MPBall) (CSequence b) # notEqualTo :: CN MPBall -> CSequence b -> EqCompareType (CN MPBall) (CSequence b) #
(HasEqAsymmetric Dyadic a, IsBool (CSequence (EqCompareType Dyadic a)), CanTestCertainly (EqCompareType Dyadic a)) => HasEqAsymmetric (CN Dyadic) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType (CN Dyadic) (CSequence a) # Methods equalTo :: CN Dyadic -> CSequence a -> EqCompareType (CN Dyadic) (CSequence a) # notEqualTo :: CN Dyadic -> CSequence a -> EqCompareType (CN Dyadic) (CSequence a) #
(HasEqAsymmetric Rational a, IsBool (CSequence (EqCompareType Rational a)), CanTestCertainly (EqCompareType Rational a)) => HasEqAsymmetric (CN Rational) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType (CN Rational) (CSequence a) # Methods equalTo :: CN Rational -> CSequence a -> EqCompareType (CN Rational) (CSequence a) # notEqualTo :: CN Rational -> CSequence a -> EqCompareType (CN Rational) (CSequence a) #
(HasEqAsymmetric Integer a, IsBool (CSequence (EqCompareType Integer a)), CanTestCertainly (EqCompareType Integer a)) => HasEqAsymmetric (CN Integer) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType (CN Integer) (CSequence a) # Methods equalTo :: CN Integer -> CSequence a -> EqCompareType (CN Integer) (CSequence a) # notEqualTo :: CN Integer -> CSequence a -> EqCompareType (CN Integer) (CSequence a) #
(HasEqAsymmetric Int a, IsBool (CSequence (EqCompareType Int a)), CanTestCertainly (EqCompareType Int a)) => HasEqAsymmetric (CN Int) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type EqCompareType (CN Int) (CSequence a) # Methods equalTo :: CN Int -> CSequence a -> EqCompareType (CN Int) (CSequence a) # notEqualTo :: CN Int -> CSequence a -> EqCompareType (CN Int) (CSequence a) #
CanMinMaxAsymmetric a MPBall => CanMinMaxAsymmetric (CSequence a) (CN MPBall) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType (CSequence a) (CN MPBall) # Methods min :: CSequence a -> CN MPBall -> MinMaxType (CSequence a) (CN MPBall) # max :: CSequence a -> CN MPBall -> MinMaxType (CSequence a) (CN MPBall) #
CanMinMaxAsymmetric a Dyadic => CanMinMaxAsymmetric (CSequence a) (CN Dyadic) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType (CSequence a) (CN Dyadic) # Methods min :: CSequence a -> CN Dyadic -> MinMaxType (CSequence a) (CN Dyadic) # max :: CSequence a -> CN Dyadic -> MinMaxType (CSequence a) (CN Dyadic) #
CanMinMaxAsymmetric a Rational => CanMinMaxAsymmetric (CSequence a) (CN Rational) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType (CSequence a) (CN Rational) # Methods min :: CSequence a -> CN Rational -> MinMaxType (CSequence a) (CN Rational) # max :: CSequence a -> CN Rational -> MinMaxType (CSequence a) (CN Rational) #
CanMinMaxAsymmetric a Integer => CanMinMaxAsymmetric (CSequence a) (CN Integer) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType (CSequence a) (CN Integer) # Methods min :: CSequence a -> CN Integer -> MinMaxType (CSequence a) (CN Integer) # max :: CSequence a -> CN Integer -> MinMaxType (CSequence a) (CN Integer) #
CanMinMaxAsymmetric a Int => CanMinMaxAsymmetric (CSequence a) (CN Int) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType (CSequence a) (CN Int) # Methods min :: CSequence a -> CN Int -> MinMaxType (CSequence a) (CN Int) # max :: CSequence a -> CN Int -> MinMaxType (CSequence a) (CN Int) #
CanMinMaxAsymmetric t1 t2 => CanMinMaxAsymmetric (CSequence t1) (CSequence t2) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType (CSequence t1) (CSequence t2) # Methods min :: CSequence t1 -> CSequence t2 -> MinMaxType (CSequence t1) (CSequence t2) # max :: CSequence t1 -> CSequence t2 -> MinMaxType (CSequence t1) (CSequence t2) #
CanMinMaxAsymmetric MPBall a => CanMinMaxAsymmetric (CN MPBall) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType (CN MPBall) (CSequence a) # Methods min :: CN MPBall -> CSequence a -> MinMaxType (CN MPBall) (CSequence a) # max :: CN MPBall -> CSequence a -> MinMaxType (CN MPBall) (CSequence a) #
CanMinMaxAsymmetric Dyadic a => CanMinMaxAsymmetric (CN Dyadic) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType (CN Dyadic) (CSequence a) # Methods min :: CN Dyadic -> CSequence a -> MinMaxType (CN Dyadic) (CSequence a) # max :: CN Dyadic -> CSequence a -> MinMaxType (CN Dyadic) (CSequence a) #
CanMinMaxAsymmetric Rational a => CanMinMaxAsymmetric (CN Rational) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType (CN Rational) (CSequence a) # Methods min :: CN Rational -> CSequence a -> MinMaxType (CN Rational) (CSequence a) # max :: CN Rational -> CSequence a -> MinMaxType (CN Rational) (CSequence a) #
CanMinMaxAsymmetric Integer a => CanMinMaxAsymmetric (CN Integer) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType (CN Integer) (CSequence a) # Methods min :: CN Integer -> CSequence a -> MinMaxType (CN Integer) (CSequence a) # max :: CN Integer -> CSequence a -> MinMaxType (CN Integer) (CSequence a) #
CanMinMaxAsymmetric Int a => CanMinMaxAsymmetric (CN Int) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type MinMaxType (CN Int) (CSequence a) # Methods min :: CN Int -> CSequence a -> MinMaxType (CN Int) (CSequence a) # max :: CN Int -> CSequence a -> MinMaxType (CN Int) (CSequence a) #
(CanMulAsymmetric a Dyadic, CanGiveUpIfVeryInaccurate (MulType a Dyadic)) => CanMulAsymmetric (CSequence a) (CN Dyadic) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type MulType (CSequence a) (CN Dyadic) # Methods mul :: CSequence a -> CN Dyadic -> MulType (CSequence a) (CN Dyadic) #
(CanMulAsymmetric a Rational, CanGiveUpIfVeryInaccurate (MulType a Rational)) => CanMulAsymmetric (CSequence a) (CN Rational) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type MulType (CSequence a) (CN Rational) # Methods mul :: CSequence a -> CN Rational -> MulType (CSequence a) (CN Rational) #
(CanMulAsymmetric a Integer, CanGiveUpIfVeryInaccurate (MulType a Integer)) => CanMulAsymmetric (CSequence a) (CN Integer) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type MulType (CSequence a) (CN Integer) # Methods mul :: CSequence a -> CN Integer -> MulType (CSequence a) (CN Integer) #
(CanMulAsymmetric a Int, CanGiveUpIfVeryInaccurate (MulType a Int)) => CanMulAsymmetric (CSequence a) (CN Int) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type MulType (CSequence a) (CN Int) # Methods mul :: CSequence a -> CN Int -> MulType (CSequence a) (CN Int) #
(CanMulAsymmetric b MPBall, CanGiveUpIfVeryInaccurate (MulType b MPBall)) => CanMulAsymmetric (CSequence b) (CN MPBall) Source #
Instance details Defined in AERN2.Real.Field Associated Types type MulType (CSequence b) (CN MPBall) # Methods mul :: CSequence b -> CN MPBall -> MulType (CSequence b) (CN MPBall) #
(CanMulAsymmetric t1 t2, CanGiveUpIfVeryInaccurate (MulType t1 t2)) => CanMulAsymmetric (CSequence t1) (CSequence t2) Source #
Instance details Defined in AERN2.Real.Field Associated Types type MulType (CSequence t1) (CSequence t2) # Methods mul :: CSequence t1 -> CSequence t2 -> MulType (CSequence t1) (CSequence t2) #
(CanMulAsymmetric MPBall b, CanGiveUpIfVeryInaccurate (MulType MPBall b)) => CanMulAsymmetric (CN MPBall) (CSequence b) Source #
Instance details Defined in AERN2.Real.Field Associated Types type MulType (CN MPBall) (CSequence b) # Methods mul :: CN MPBall -> CSequence b -> MulType (CN MPBall) (CSequence b) #
(CanMulAsymmetric Dyadic a, CanGiveUpIfVeryInaccurate (MulType Dyadic a)) => CanMulAsymmetric (CN Dyadic) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type MulType (CN Dyadic) (CSequence a) # Methods mul :: CN Dyadic -> CSequence a -> MulType (CN Dyadic) (CSequence a) #
(CanMulAsymmetric Rational a, CanGiveUpIfVeryInaccurate (MulType Rational a)) => CanMulAsymmetric (CN Rational) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type MulType (CN Rational) (CSequence a) # Methods mul :: CN Rational -> CSequence a -> MulType (CN Rational) (CSequence a) #
(CanMulAsymmetric Integer a, CanGiveUpIfVeryInaccurate (MulType Integer a)) => CanMulAsymmetric (CN Integer) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type MulType (CN Integer) (CSequence a) # Methods mul :: CN Integer -> CSequence a -> MulType (CN Integer) (CSequence a) #
(CanMulAsymmetric Int a, CanGiveUpIfVeryInaccurate (MulType Int a)) => CanMulAsymmetric (CN Int) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH Associated Types type MulType (CN Int) (CSequence a) # Methods mul :: CN Int -> CSequence a -> MulType (CN Int) (CSequence a) #
(HasOrderAsymmetric a MPBall, CanTestCertainly (OrderCompareType a MPBall)) => HasOrderAsymmetric (CSequence a) (CN MPBall) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType (CSequence a) (CN MPBall) # Methods lessThan :: CSequence a -> CN MPBall -> OrderCompareType (CSequence a) (CN MPBall) # greaterThan :: CSequence a -> CN MPBall -> OrderCompareType (CSequence a) (CN MPBall) # leq :: CSequence a -> CN MPBall -> OrderCompareType (CSequence a) (CN MPBall) # geq :: CSequence a -> CN MPBall -> OrderCompareType (CSequence a) (CN MPBall) #
(HasOrderAsymmetric a Dyadic, IsBool (CSequence (OrderCompareType a Dyadic)), CanTestCertainly (OrderCompareType a Dyadic)) => HasOrderAsymmetric (CSequence a) (CN Dyadic) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType (CSequence a) (CN Dyadic) # Methods lessThan :: CSequence a -> CN Dyadic -> OrderCompareType (CSequence a) (CN Dyadic) # greaterThan :: CSequence a -> CN Dyadic -> OrderCompareType (CSequence a) (CN Dyadic) # leq :: CSequence a -> CN Dyadic -> OrderCompareType (CSequence a) (CN Dyadic) # geq :: CSequence a -> CN Dyadic -> OrderCompareType (CSequence a) (CN Dyadic) #
(HasOrderAsymmetric a Rational, IsBool (CSequence (OrderCompareType a Rational)), CanTestCertainly (OrderCompareType a Rational)) => HasOrderAsymmetric (CSequence a) (CN Rational) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType (CSequence a) (CN Rational) # Methods lessThan :: CSequence a -> CN Rational -> OrderCompareType (CSequence a) (CN Rational) # greaterThan :: CSequence a -> CN Rational -> OrderCompareType (CSequence a) (CN Rational) # leq :: CSequence a -> CN Rational -> OrderCompareType (CSequence a) (CN Rational) # geq :: CSequence a -> CN Rational -> OrderCompareType (CSequence a) (CN Rational) #
(HasOrderAsymmetric a Integer, IsBool (CSequence (OrderCompareType a Integer)), CanTestCertainly (OrderCompareType a Integer)) => HasOrderAsymmetric (CSequence a) (CN Integer) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType (CSequence a) (CN Integer) # Methods lessThan :: CSequence a -> CN Integer -> OrderCompareType (CSequence a) (CN Integer) # greaterThan :: CSequence a -> CN Integer -> OrderCompareType (CSequence a) (CN Integer) # leq :: CSequence a -> CN Integer -> OrderCompareType (CSequence a) (CN Integer) # geq :: CSequence a -> CN Integer -> OrderCompareType (CSequence a) (CN Integer) #
(HasOrderAsymmetric a Int, IsBool (CSequence (OrderCompareType a Int)), CanTestCertainly (OrderCompareType a Int)) => HasOrderAsymmetric (CSequence a) (CN Int) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType (CSequence a) (CN Int) # Methods lessThan :: CSequence a -> CN Int -> OrderCompareType (CSequence a) (CN Int) # greaterThan :: CSequence a -> CN Int -> OrderCompareType (CSequence a) (CN Int) # leq :: CSequence a -> CN Int -> OrderCompareType (CSequence a) (CN Int) # geq :: CSequence a -> CN Int -> OrderCompareType (CSequence a) (CN Int) #
(HasOrderAsymmetric t1 t2, IsBool (CSequence (OrderCompareType t1 t2)), CanTestCertainly (OrderCompareType t1 t2)) => HasOrderAsymmetric (CSequence t1) (CSequence t2) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType (CSequence t1) (CSequence t2) # Methods lessThan :: CSequence t1 -> CSequence t2 -> OrderCompareType (CSequence t1) (CSequence t2) # greaterThan :: CSequence t1 -> CSequence t2 -> OrderCompareType (CSequence t1) (CSequence t2) # leq :: CSequence t1 -> CSequence t2 -> OrderCompareType (CSequence t1) (CSequence t2) # geq :: CSequence t1 -> CSequence t2 -> OrderCompareType (CSequence t1) (CSequence t2) #
(HasOrderAsymmetric MPBall b, CanTestCertainly (OrderCompareType MPBall b)) => HasOrderAsymmetric (CN MPBall) (CSequence b) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType (CN MPBall) (CSequence b) # Methods lessThan :: CN MPBall -> CSequence b -> OrderCompareType (CN MPBall) (CSequence b) # greaterThan :: CN MPBall -> CSequence b -> OrderCompareType (CN MPBall) (CSequence b) # leq :: CN MPBall -> CSequence b -> OrderCompareType (CN MPBall) (CSequence b) # geq :: CN MPBall -> CSequence b -> OrderCompareType (CN MPBall) (CSequence b) #
(HasOrderAsymmetric Dyadic a, IsBool (CSequence (OrderCompareType Dyadic a)), CanTestCertainly (OrderCompareType Dyadic a)) => HasOrderAsymmetric (CN Dyadic) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType (CN Dyadic) (CSequence a) # Methods lessThan :: CN Dyadic -> CSequence a -> OrderCompareType (CN Dyadic) (CSequence a) # greaterThan :: CN Dyadic -> CSequence a -> OrderCompareType (CN Dyadic) (CSequence a) # leq :: CN Dyadic -> CSequence a -> OrderCompareType (CN Dyadic) (CSequence a) # geq :: CN Dyadic -> CSequence a -> OrderCompareType (CN Dyadic) (CSequence a) #
(HasOrderAsymmetric Rational a, IsBool (CSequence (OrderCompareType Rational a)), CanTestCertainly (OrderCompareType Rational a)) => HasOrderAsymmetric (CN Rational) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType (CN Rational) (CSequence a) # Methods lessThan :: CN Rational -> CSequence a -> OrderCompareType (CN Rational) (CSequence a) # greaterThan :: CN Rational -> CSequence a -> OrderCompareType (CN Rational) (CSequence a) # leq :: CN Rational -> CSequence a -> OrderCompareType (CN Rational) (CSequence a) # geq :: CN Rational -> CSequence a -> OrderCompareType (CN Rational) (CSequence a) #
(HasOrderAsymmetric Integer a, IsBool (CSequence (OrderCompareType Integer a)), CanTestCertainly (OrderCompareType Integer a)) => HasOrderAsymmetric (CN Integer) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType (CN Integer) (CSequence a) # Methods lessThan :: CN Integer -> CSequence a -> OrderCompareType (CN Integer) (CSequence a) # greaterThan :: CN Integer -> CSequence a -> OrderCompareType (CN Integer) (CSequence a) # leq :: CN Integer -> CSequence a -> OrderCompareType (CN Integer) (CSequence a) # geq :: CN Integer -> CSequence a -> OrderCompareType (CN Integer) (CSequence a) #
(HasOrderAsymmetric Int a, IsBool (CSequence (OrderCompareType Int a)), CanTestCertainly (OrderCompareType Int a)) => HasOrderAsymmetric (CN Int) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons Associated Types type OrderCompareType (CN Int) (CSequence a) # Methods lessThan :: CN Int -> CSequence a -> OrderCompareType (CN Int) (CSequence a) # greaterThan :: CN Int -> CSequence a -> OrderCompareType (CN Int) (CSequence a) # leq :: CN Int -> CSequence a -> OrderCompareType (CN Int) (CSequence a) # geq :: CN Int -> CSequence a -> OrderCompareType (CN Int) (CSequence a) #
(CanPow b e, HasOrderCertainly b Integer, HasOrderCertainly e Integer, HasEqCertainly b Integer, CanTestInteger e, CanTestIsIntegerType b, CanTestIsIntegerType e) => CanPow (CSequence b) (CSequence e) Source #
Instance details Defined in AERN2.Real.Field Associated Types type PowType (CSequence b) (CSequence e) # type PPowType (CSequence b) (CSequence e) # Methods pow :: CSequence b -> CSequence e -> PowType (CSequence b) (CSequence e) # ppow :: CSequence b -> CSequence e -> PPowType (CSequence b) (CSequence e) #
ConvertibleExactly (WithSample CReal Rational) CReal Source #
Instance details Defined in AERN2.Real.Type Methods safeConvertExactly :: WithSample CReal Rational -> ConvertResult CReal #
ConvertibleExactly (WithSample CReal Integer) CReal Source #
Instance details Defined in AERN2.Real.Type Methods safeConvertExactly :: WithSample CReal Integer -> ConvertResult CReal #
type SelectCountableType CKleenean Source #
Instance details Defined in AERN2.Real.CKleenean type SelectCountableType CKleenean = Integer
type SelectType CKleenean Source #
Instance details Defined in AERN2.Real.CKleenean type SelectType CKleenean = CN Bool
type ExpType CReal Source #
Instance details Defined in AERN2.Real.Elementary type ExpType CReal = CReal
type LogType CReal Source #
Instance details Defined in AERN2.Real.Elementary type LogType CReal = CReal
type SinCosType CReal Source #
Instance details Defined in AERN2.Real.Elementary type SinCosType CReal = CReal
type SqrtType CReal Source #
Instance details Defined in AERN2.Real.Elementary type SqrtType CReal = CReal
type LimitType Rational CReal Source #
Instance details Defined in AERN2.Real.Limit type LimitType Rational CReal = CReal
type LimitType Integer CReal Source #
Instance details Defined in AERN2.Real.Limit type LimitType Integer CReal = CReal
type LimitType Int CReal Source #
Instance details Defined in AERN2.Real.Limit type LimitType Int CReal = CReal
type AddType MPBall (CSequence b) Source #
Instance details Defined in AERN2.Real.Field type AddType MPBall (CSequence b) = AddType MPBall b
type AddType Dyadic (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type AddType Dyadic (CSequence a) = CSequence (AddType Dyadic a)
type AddType Rational (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type AddType Rational (CSequence a) = CSequence (AddType Rational a)
type AddType Integer (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type AddType Integer (CSequence a) = CSequence (AddType Integer a)
type AddType Int (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type AddType Int (CSequence a) = CSequence (AddType Int a)
type SubType MPBall (CSequence b) Source #
Instance details Defined in AERN2.Real.Field type SubType MPBall (CSequence b) = SubType MPBall b
type SubType Dyadic (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type SubType Dyadic (CSequence a) = CSequence (SubType Dyadic a)
type SubType Rational (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type SubType Rational (CSequence a) = CSequence (SubType Rational a)
type SubType Integer (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type SubType Integer (CSequence a) = CSequence (SubType Integer a)
type SubType Int (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type SubType Int (CSequence a) = CSequence (SubType Int a)
type AndOrType Kleenean (CSequence t2) Source #
Instance details Defined in AERN2.Real.CKleenean type AndOrType Kleenean (CSequence t2) = CSequence (AndOrType Kleenean t2)
type AndOrType Bool (CSequence t2) Source #
Instance details Defined in AERN2.Real.CKleenean type AndOrType Bool (CSequence t2) = CSequence (AndOrType Bool t2)
type DivType MPBall (CSequence b) Source #
Instance details Defined in AERN2.Real.Field type DivType MPBall (CSequence b) = DivType MPBall b
type DivType Dyadic (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type DivType Dyadic (CSequence a) = CSequence (DivType Dyadic a)
type DivType Rational (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type DivType Rational (CSequence a) = CSequence (DivType Rational a)
type DivType Integer (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type DivType Integer (CSequence a) = CSequence (DivType Integer a)
type DivType Int (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type DivType Int (CSequence a) = CSequence (DivType Int a)
type EqCompareType MPBall (CSequence b) Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType MPBall (CSequence b) = EqCompareType (CN MPBall) (CN b)
type EqCompareType Dyadic (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType Dyadic (CSequence a) = CSequence (EqCompareType Dyadic a)
type EqCompareType Rational (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType Rational (CSequence a) = CSequence (EqCompareType Rational a)
type EqCompareType Integer (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType Integer (CSequence a) = CSequence (EqCompareType Integer a)
type EqCompareType Int (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType Int (CSequence a) = CSequence (EqCompareType Int a)
type IfThenElseType CKleenean (CSequence t) Source #
Instance details Defined in AERN2.Real.CKleenean type IfThenElseType CKleenean (CSequence t) = CSequence t
type IfThenElseType CKleenean (Maybe t) Source #
Instance details Defined in AERN2.Real.CKleenean type IfThenElseType CKleenean (Maybe t) = Maybe (IfThenElseType CKleenean t)
type IfThenElseType CKleenean [t] Source #
Instance details Defined in AERN2.Real.CKleenean type IfThenElseType CKleenean [t] = [IfThenElseType CKleenean t]
type MinMaxType MPBall (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType MPBall (CSequence a) = MinMaxType (CN MPBall) (CN a)
type MinMaxType Dyadic (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType Dyadic (CSequence a) = CSequence (MinMaxType Dyadic a)
type MinMaxType Rational (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType Rational (CSequence a) = CSequence (MinMaxType Rational a)
type MinMaxType Integer (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType Integer (CSequence a) = CSequence (MinMaxType Integer a)
type MinMaxType Int (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType Int (CSequence a) = CSequence (MinMaxType Int a)
type MulType MPBall (CSequence b) Source #
Instance details Defined in AERN2.Real.Field type MulType MPBall (CSequence b) = MulType MPBall b
type MulType Dyadic (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type MulType Dyadic (CSequence a) = CSequence (MulType Dyadic a)
type MulType Rational (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type MulType Rational (CSequence a) = CSequence (MulType Rational a)
type MulType Integer (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type MulType Integer (CSequence a) = CSequence (MulType Integer a)
type MulType Int (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type MulType Int (CSequence a) = CSequence (MulType Int a)
type OrderCompareType MPBall (CSequence b) Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType MPBall (CSequence b) = OrderCompareType (CN MPBall) (CN b)
type OrderCompareType Dyadic (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType Dyadic (CSequence a) = CSequence (OrderCompareType Dyadic a)
type OrderCompareType Rational (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType Rational (CSequence a) = CSequence (OrderCompareType Rational a)
type OrderCompareType Integer (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType Integer (CSequence a) = CSequence (OrderCompareType Integer a)
type OrderCompareType Int (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType Int (CSequence a) = CSequence (OrderCompareType Int a)
type PPowType Rational (CSequence e) Source #
Instance details Defined in AERN2.Real.FieldTH type PPowType Rational (CSequence e) = CSequence (PPowType Rational e)
type PPowType Integer (CSequence e) Source #
Instance details Defined in AERN2.Real.FieldTH type PPowType Integer (CSequence e) = CSequence (PPowType Integer e)
type PPowType Int (CSequence e) Source #
Instance details Defined in AERN2.Real.FieldTH type PPowType Int (CSequence e) = CSequence (PPowType Int e)
type PowType Rational (CSequence e) Source #
Instance details Defined in AERN2.Real.FieldTH type PowType Rational (CSequence e) = CSequence (PowType Rational e)
type PowType Integer (CSequence e) Source #
Instance details Defined in AERN2.Real.FieldTH type PowType Integer (CSequence e) = CSequence (PowType Integer e)
type PowType Int (CSequence e) Source #
Instance details Defined in AERN2.Real.FieldTH type PowType Int (CSequence e) = CSequence (PowType Int e)
type LimitType Rational (CReal -> CReal) Source #
Instance details Defined in AERN2.Real.Limit type LimitType Rational (CReal -> CReal) = CReal -> CReal
type IfThenElseType CKleenean (t1, t2) Source #
Instance details Defined in AERN2.Real.CKleenean type IfThenElseType CKleenean (t1, t2) = (IfThenElseType CKleenean t1, IfThenElseType CKleenean t2)
type IfThenElseType CKleenean (k -> v) Source #
Instance details Defined in AERN2.Real.CKleenean type IfThenElseType CKleenean (k -> v) = k -> IfThenElseType CKleenean v
type NegType (CSequence t) Source #
Instance details Defined in AERN2.Real.CKleenean type NegType (CSequence t) = CSequence (NegType t)
type AbsType (CSequence t1) Source #
Instance details Defined in AERN2.Real.Comparisons type AbsType (CSequence t1) = CSequence (AbsType t1)
type ExtractedApproximation (CSequence t) Accuracy Source #
Instance details Defined in AERN2.Real.Type type ExtractedApproximation (CSequence t) Accuracy = CN t
type ExtractedApproximation (CSequence t) Precision Source #
Instance details Defined in AERN2.Real.Type type ExtractedApproximation (CSequence t) Precision = CN t
type AddType (CSequence a) Dyadic Source #
Instance details Defined in AERN2.Real.FieldTH type AddType (CSequence a) Dyadic = CSequence (AddType a Dyadic)
type AddType (CSequence a) Rational Source #
Instance details Defined in AERN2.Real.FieldTH type AddType (CSequence a) Rational = CSequence (AddType a Rational)
type AddType (CSequence a) Integer Source #
Instance details Defined in AERN2.Real.FieldTH type AddType (CSequence a) Integer = CSequence (AddType a Integer)
type AddType (CSequence a) Int Source #
Instance details Defined in AERN2.Real.FieldTH type AddType (CSequence a) Int = CSequence (AddType a Int)
type AddType (CSequence b) MPBall Source #
Instance details Defined in AERN2.Real.Field type AddType (CSequence b) MPBall = AddType b MPBall
type SubType (CSequence a) Dyadic Source #
Instance details Defined in AERN2.Real.FieldTH type SubType (CSequence a) Dyadic = CSequence (SubType a Dyadic)
type SubType (CSequence a) Rational Source #
Instance details Defined in AERN2.Real.FieldTH type SubType (CSequence a) Rational = CSequence (SubType a Rational)
type SubType (CSequence a) Integer Source #
Instance details Defined in AERN2.Real.FieldTH type SubType (CSequence a) Integer = CSequence (SubType a Integer)
type SubType (CSequence a) Int Source #
Instance details Defined in AERN2.Real.FieldTH type SubType (CSequence a) Int = CSequence (SubType a Int)
type SubType (CSequence b) MPBall Source #
Instance details Defined in AERN2.Real.Field type SubType (CSequence b) MPBall = SubType b MPBall
type AndOrType (CSequence t1) Kleenean Source #
Instance details Defined in AERN2.Real.CKleenean type AndOrType (CSequence t1) Kleenean = CSequence (AndOrType t1 Kleenean)
type AndOrType (CSequence t1) Bool Source #
Instance details Defined in AERN2.Real.CKleenean type AndOrType (CSequence t1) Bool = CSequence (AndOrType t1 Bool)
type DivType (CSequence a) Dyadic Source #
Instance details Defined in AERN2.Real.FieldTH type DivType (CSequence a) Dyadic = CSequence (DivType a Dyadic)
type DivType (CSequence a) Rational Source #
Instance details Defined in AERN2.Real.FieldTH type DivType (CSequence a) Rational = CSequence (DivType a Rational)
type DivType (CSequence a) Integer Source #
Instance details Defined in AERN2.Real.FieldTH type DivType (CSequence a) Integer = CSequence (DivType a Integer)
type DivType (CSequence a) Int Source #
Instance details Defined in AERN2.Real.FieldTH type DivType (CSequence a) Int = CSequence (DivType a Int)
type DivType (CSequence b) MPBall Source #
Instance details Defined in AERN2.Real.Field type DivType (CSequence b) MPBall = DivType b MPBall
type EqCompareType (CSequence a) MPBall Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType (CSequence a) MPBall = EqCompareType (CN a) (CN MPBall)
type EqCompareType (CSequence a) Dyadic Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType (CSequence a) Dyadic = CSequence (EqCompareType a Dyadic)
type EqCompareType (CSequence a) Rational Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType (CSequence a) Rational = CSequence (EqCompareType a Rational)
type EqCompareType (CSequence a) Integer Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType (CSequence a) Integer = CSequence (EqCompareType a Integer)
type EqCompareType (CSequence a) Int Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType (CSequence a) Int = CSequence (EqCompareType a Int)
type MinMaxType (CSequence a) MPBall Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType (CSequence a) MPBall = MinMaxType (CN a) (CN MPBall)
type MinMaxType (CSequence a) Dyadic Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType (CSequence a) Dyadic = CSequence (MinMaxType a Dyadic)
type MinMaxType (CSequence a) Rational Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType (CSequence a) Rational = CSequence (MinMaxType a Rational)
type MinMaxType (CSequence a) Integer Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType (CSequence a) Integer = CSequence (MinMaxType a Integer)
type MinMaxType (CSequence a) Int Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType (CSequence a) Int = CSequence (MinMaxType a Int)
type MulType (CSequence a) Dyadic Source #
Instance details Defined in AERN2.Real.FieldTH type MulType (CSequence a) Dyadic = CSequence (MulType a Dyadic)
type MulType (CSequence a) Rational Source #
Instance details Defined in AERN2.Real.FieldTH type MulType (CSequence a) Rational = CSequence (MulType a Rational)
type MulType (CSequence a) Integer Source #
Instance details Defined in AERN2.Real.FieldTH type MulType (CSequence a) Integer = CSequence (MulType a Integer)
type MulType (CSequence a) Int Source #
Instance details Defined in AERN2.Real.FieldTH type MulType (CSequence a) Int = CSequence (MulType a Int)
type MulType (CSequence b) MPBall Source #
Instance details Defined in AERN2.Real.Field type MulType (CSequence b) MPBall = MulType b MPBall
type OrderCompareType (CSequence a) MPBall Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType (CSequence a) MPBall = OrderCompareType (CN a) (CN MPBall)
type OrderCompareType (CSequence a) Dyadic Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType (CSequence a) Dyadic = CSequence (OrderCompareType a Dyadic)
type OrderCompareType (CSequence a) Rational Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType (CSequence a) Rational = CSequence (OrderCompareType a Rational)
type OrderCompareType (CSequence a) Integer Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType (CSequence a) Integer = CSequence (OrderCompareType a Integer)
type OrderCompareType (CSequence a) Int Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType (CSequence a) Int = CSequence (OrderCompareType a Int)
type PPowType (CSequence b) Rational Source #
Instance details Defined in AERN2.Real.FieldTH type PPowType (CSequence b) Rational = CSequence (PPowType b Rational)
type PPowType (CSequence b) Integer Source #
Instance details Defined in AERN2.Real.FieldTH type PPowType (CSequence b) Integer = CSequence (PPowType b Integer)
type PPowType (CSequence b) Int Source #
Instance details Defined in AERN2.Real.FieldTH type PPowType (CSequence b) Int = CSequence (PPowType b Int)
type PowType (CSequence b) Rational Source #
Instance details Defined in AERN2.Real.FieldTH type PowType (CSequence b) Rational = CSequence (PowType b Rational)
type PowType (CSequence b) Integer Source #
Instance details Defined in AERN2.Real.FieldTH type PowType (CSequence b) Integer = CSequence (PowType b Integer)
type PowType (CSequence b) Int Source #
Instance details Defined in AERN2.Real.FieldTH type PowType (CSequence b) Int = CSequence (PowType b Int)
type AddType (CSequence a) (CN Dyadic) Source #
Instance details Defined in AERN2.Real.FieldTH type AddType (CSequence a) (CN Dyadic) = CSequence (AddType a Dyadic)
type AddType (CSequence a) (CN Rational) Source #
Instance details Defined in AERN2.Real.FieldTH type AddType (CSequence a) (CN Rational) = CSequence (AddType a Rational)
type AddType (CSequence a) (CN Integer) Source #
Instance details Defined in AERN2.Real.FieldTH type AddType (CSequence a) (CN Integer) = CSequence (AddType a Integer)
type AddType (CSequence a) (CN Int) Source #
Instance details Defined in AERN2.Real.FieldTH type AddType (CSequence a) (CN Int) = CSequence (AddType a Int)
type AddType (CSequence b) (CN MPBall) Source #
Instance details Defined in AERN2.Real.Field type AddType (CSequence b) (CN MPBall) = AddType (CN b) (CN MPBall)
type AddType (CSequence t1) (CSequence t2) Source #
Instance details Defined in AERN2.Real.Field type AddType (CSequence t1) (CSequence t2) = CSequence (AddType t1 t2)
type AddType (CN MPBall) (CSequence b) Source #
Instance details Defined in AERN2.Real.Field type AddType (CN MPBall) (CSequence b) = AddType (CN MPBall) (CN b)
type AddType (CN Dyadic) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type AddType (CN Dyadic) (CSequence a) = CSequence (AddType Dyadic a)
type AddType (CN Rational) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type AddType (CN Rational) (CSequence a) = CSequence (AddType Rational a)
type AddType (CN Integer) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type AddType (CN Integer) (CSequence a) = CSequence (AddType Integer a)
type AddType (CN Int) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type AddType (CN Int) (CSequence a) = CSequence (AddType Int a)
type SubType (CSequence a) (CN Dyadic) Source #
Instance details Defined in AERN2.Real.FieldTH type SubType (CSequence a) (CN Dyadic) = CSequence (SubType a Dyadic)
type SubType (CSequence a) (CN Rational) Source #
Instance details Defined in AERN2.Real.FieldTH type SubType (CSequence a) (CN Rational) = CSequence (SubType a Rational)
type SubType (CSequence a) (CN Integer) Source #
Instance details Defined in AERN2.Real.FieldTH type SubType (CSequence a) (CN Integer) = CSequence (SubType a Integer)
type SubType (CSequence a) (CN Int) Source #
Instance details Defined in AERN2.Real.FieldTH type SubType (CSequence a) (CN Int) = CSequence (SubType a Int)
type SubType (CSequence b) (CN MPBall) Source #
Instance details Defined in AERN2.Real.Field type SubType (CSequence b) (CN MPBall) = SubType (CN b) (CN MPBall)
type SubType (CSequence t1) (CSequence t2) Source #
Instance details Defined in AERN2.Real.Field type SubType (CSequence t1) (CSequence t2) = CSequence (SubType t1 t2)
type SubType (CN MPBall) (CSequence b) Source #
Instance details Defined in AERN2.Real.Field type SubType (CN MPBall) (CSequence b) = SubType (CN MPBall) (CN b)
type SubType (CN Dyadic) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type SubType (CN Dyadic) (CSequence a) = CSequence (SubType Dyadic a)
type SubType (CN Rational) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type SubType (CN Rational) (CSequence a) = CSequence (SubType Rational a)
type SubType (CN Integer) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type SubType (CN Integer) (CSequence a) = CSequence (SubType Integer a)
type SubType (CN Int) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type SubType (CN Int) (CSequence a) = CSequence (SubType Int a)
type AndOrType (CSequence t1) (CSequence t2) Source #
Instance details Defined in AERN2.Real.CKleenean type AndOrType (CSequence t1) (CSequence t2) = CSequence (AndOrType t1 t2)
type DivType (CSequence a) (CN Dyadic) Source #
Instance details Defined in AERN2.Real.FieldTH type DivType (CSequence a) (CN Dyadic) = CSequence (DivType a Dyadic)
type DivType (CSequence a) (CN Rational) Source #
Instance details Defined in AERN2.Real.FieldTH type DivType (CSequence a) (CN Rational) = CSequence (DivType a Rational)
type DivType (CSequence a) (CN Integer) Source #
Instance details Defined in AERN2.Real.FieldTH type DivType (CSequence a) (CN Integer) = CSequence (DivType a Integer)
type DivType (CSequence a) (CN Int) Source #
Instance details Defined in AERN2.Real.FieldTH type DivType (CSequence a) (CN Int) = CSequence (DivType a Int)
type DivType (CSequence b) (CN MPBall) Source #
Instance details Defined in AERN2.Real.Field type DivType (CSequence b) (CN MPBall) = DivType (CN b) (CN MPBall)
type DivType (CSequence t1) (CSequence t2) Source #
Instance details Defined in AERN2.Real.Field type DivType (CSequence t1) (CSequence t2) = CSequence (DivType t1 t2)
type DivType (CN MPBall) (CSequence b) Source #
Instance details Defined in AERN2.Real.Field type DivType (CN MPBall) (CSequence b) = DivType (CN MPBall) (CN b)
type DivType (CN Dyadic) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type DivType (CN Dyadic) (CSequence a) = CSequence (DivType Dyadic a)
type DivType (CN Rational) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type DivType (CN Rational) (CSequence a) = CSequence (DivType Rational a)
type DivType (CN Integer) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type DivType (CN Integer) (CSequence a) = CSequence (DivType Integer a)
type DivType (CN Int) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type DivType (CN Int) (CSequence a) = CSequence (DivType Int a)
type EqCompareType (CSequence a) (CN MPBall) Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType (CSequence a) (CN MPBall) = EqCompareType (CN a) (CN MPBall)
type EqCompareType (CSequence a) (CN Dyadic) Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType (CSequence a) (CN Dyadic) = CSequence (EqCompareType a Dyadic)
type EqCompareType (CSequence a) (CN Rational) Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType (CSequence a) (CN Rational) = CSequence (EqCompareType a Rational)
type EqCompareType (CSequence a) (CN Integer) Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType (CSequence a) (CN Integer) = CSequence (EqCompareType a Integer)
type EqCompareType (CSequence a) (CN Int) Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType (CSequence a) (CN Int) = CSequence (EqCompareType a Int)
type EqCompareType (CSequence t1) (CSequence t2) Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType (CSequence t1) (CSequence t2) = CSequence (EqCompareType t1 t2)
type EqCompareType (CN MPBall) (CSequence b) Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType (CN MPBall) (CSequence b) = EqCompareType (CN MPBall) (CN b)
type EqCompareType (CN Dyadic) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType (CN Dyadic) (CSequence a) = CSequence (EqCompareType Dyadic a)
type EqCompareType (CN Rational) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType (CN Rational) (CSequence a) = CSequence (EqCompareType Rational a)
type EqCompareType (CN Integer) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType (CN Integer) (CSequence a) = CSequence (EqCompareType Integer a)
type EqCompareType (CN Int) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type EqCompareType (CN Int) (CSequence a) = CSequence (EqCompareType Int a)
type MinMaxType (CSequence a) (CN MPBall) Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType (CSequence a) (CN MPBall) = MinMaxType (CN a) (CN MPBall)
type MinMaxType (CSequence a) (CN Dyadic) Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType (CSequence a) (CN Dyadic) = CSequence (MinMaxType a Dyadic)
type MinMaxType (CSequence a) (CN Rational) Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType (CSequence a) (CN Rational) = CSequence (MinMaxType a Rational)
type MinMaxType (CSequence a) (CN Integer) Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType (CSequence a) (CN Integer) = CSequence (MinMaxType a Integer)
type MinMaxType (CSequence a) (CN Int) Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType (CSequence a) (CN Int) = CSequence (MinMaxType a Int)
type MinMaxType (CSequence t1) (CSequence t2) Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType (CSequence t1) (CSequence t2) = CSequence (MinMaxType t1 t2)
type MinMaxType (CN MPBall) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType (CN MPBall) (CSequence a) = MinMaxType (CN MPBall) (CN a)
type MinMaxType (CN Dyadic) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType (CN Dyadic) (CSequence a) = CSequence (MinMaxType Dyadic a)
type MinMaxType (CN Rational) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType (CN Rational) (CSequence a) = CSequence (MinMaxType Rational a)
type MinMaxType (CN Integer) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType (CN Integer) (CSequence a) = CSequence (MinMaxType Integer a)
type MinMaxType (CN Int) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type MinMaxType (CN Int) (CSequence a) = CSequence (MinMaxType Int a)
type MulType (CSequence a) (CN Dyadic) Source #
Instance details Defined in AERN2.Real.FieldTH type MulType (CSequence a) (CN Dyadic) = CSequence (MulType a Dyadic)
type MulType (CSequence a) (CN Rational) Source #
Instance details Defined in AERN2.Real.FieldTH type MulType (CSequence a) (CN Rational) = CSequence (MulType a Rational)
type MulType (CSequence a) (CN Integer) Source #
Instance details Defined in AERN2.Real.FieldTH type MulType (CSequence a) (CN Integer) = CSequence (MulType a Integer)
type MulType (CSequence a) (CN Int) Source #
Instance details Defined in AERN2.Real.FieldTH type MulType (CSequence a) (CN Int) = CSequence (MulType a Int)
type MulType (CSequence b) (CN MPBall) Source #
Instance details Defined in AERN2.Real.Field type MulType (CSequence b) (CN MPBall) = MulType (CN b) (CN MPBall)
type MulType (CSequence t1) (CSequence t2) Source #
Instance details Defined in AERN2.Real.Field type MulType (CSequence t1) (CSequence t2) = CSequence (MulType t1 t2)
type MulType (CN MPBall) (CSequence b) Source #
Instance details Defined in AERN2.Real.Field type MulType (CN MPBall) (CSequence b) = MulType (CN MPBall) (CN b)
type MulType (CN Dyadic) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type MulType (CN Dyadic) (CSequence a) = CSequence (MulType Dyadic a)
type MulType (CN Rational) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type MulType (CN Rational) (CSequence a) = CSequence (MulType Rational a)
type MulType (CN Integer) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type MulType (CN Integer) (CSequence a) = CSequence (MulType Integer a)
type MulType (CN Int) (CSequence a) Source #
Instance details Defined in AERN2.Real.FieldTH type MulType (CN Int) (CSequence a) = CSequence (MulType Int a)
type OrderCompareType (CSequence a) (CN MPBall) Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType (CSequence a) (CN MPBall) = OrderCompareType (CN a) (CN MPBall)
type OrderCompareType (CSequence a) (CN Dyadic) Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType (CSequence a) (CN Dyadic) = CSequence (OrderCompareType a Dyadic)
type OrderCompareType (CSequence a) (CN Rational) Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType (CSequence a) (CN Rational) = CSequence (OrderCompareType a Rational)
type OrderCompareType (CSequence a) (CN Integer) Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType (CSequence a) (CN Integer) = CSequence (OrderCompareType a Integer)
type OrderCompareType (CSequence a) (CN Int) Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType (CSequence a) (CN Int) = CSequence (OrderCompareType a Int)
type OrderCompareType (CSequence t1) (CSequence t2) Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType (CSequence t1) (CSequence t2) = CSequence (OrderCompareType t1 t2)
type OrderCompareType (CN MPBall) (CSequence b) Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType (CN MPBall) (CSequence b) = OrderCompareType (CN MPBall) (CN b)
type OrderCompareType (CN Dyadic) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType (CN Dyadic) (CSequence a) = CSequence (OrderCompareType Dyadic a)
type OrderCompareType (CN Rational) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType (CN Rational) (CSequence a) = CSequence (OrderCompareType Rational a)
type OrderCompareType (CN Integer) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType (CN Integer) (CSequence a) = CSequence (OrderCompareType Integer a)
type OrderCompareType (CN Int) (CSequence a) Source #
Instance details Defined in AERN2.Real.Comparisons type OrderCompareType (CN Int) (CSequence a) = CSequence (OrderCompareType Int a)
type PPowType (CSequence b) (CSequence e) Source #
Instance details Defined in AERN2.Real.Field type PPowType (CSequence b) (CSequence e) = CSequence (PPowType b e)
type PowType (CSequence b) (CSequence e) Source #
Instance details Defined in AERN2.Real.Field type PowType (CSequence b) (CSequence e) = CSequence (PowType b e)

cseqPrecisions :: [Precision] Source #

cseqIndexForPrecision :: Precision -> Integer Source #

cseqFromWithCurrentPrec :: (forall p. KnownNat p => WithCurrentPrec p (CN b)) -> CSequence b Source #

cseqFromPrecFunction :: (Precision -> CN b) -> CSequence b Source #

unsafeApproximationExtension :: (CSequence b -> t) -> CN b -> t Source #

real numbers and conversions

type CReal = CSequence MPBall Source #

creal :: CanBeCReal t => t -> CReal Source #

type HasCReals t = ConvertibleExactly CReal t Source #

type CanBeCReal t = ConvertibleExactly t CReal Source #

pi :: CReal Source #

crealFromWithCurrentPrec :: (forall p. KnownNat p => WithCurrentPrec p (CN MPBall)) -> CSequence MPBall Source #

crealFromPrecFunction :: (Precision -> CN MPBall) -> CReal Source #

limits

class HasLimits ix s where #

Associated Types

type LimitType ix s #

Methods

limit :: (ix -> s) -> LimitType ix s #

Instances

Instances details

HasLimits Rational CReal Source #
Instance details Defined in AERN2.Real.Limit Associated Types type LimitType Rational CReal # Methods limit :: (Rational -> CReal) -> LimitType Rational CReal #
HasLimits Integer CReal Source #
Instance details Defined in AERN2.Real.Limit Associated Types type LimitType Integer CReal # Methods limit :: (Integer -> CReal) -> LimitType Integer CReal #
HasLimits Int CReal Source #
Instance details Defined in AERN2.Real.Limit Associated Types type LimitType Int CReal # Methods limit :: (Int -> CReal) -> LimitType Int CReal #
HasLimits Rational (CReal -> CReal) Source #
Instance details Defined in AERN2.Real.Limit Associated Types type LimitType Rational (CReal -> CReal) # Methods limit :: (Rational -> CReal -> CReal) -> LimitType Rational (CReal -> CReal) #

lazy Kleeneans

type CKleenean = CSequence Kleenean Source #

type CanBeCKleenean t = ConvertibleExactly t CKleenean Source #

ckleenean :: CanBeCKleenean t => t -> CKleenean Source #

class IsBool (SelectType k) => CanSelect k where #

Associated Types

type SelectType k #

Must be Bool or similar

Methods

select #

Arguments

:: k
-> k
-> SelectType k	True means that the first computation succeeded.

Execute two lazy computations "in parallel" until one of them succeeds.

Instances

Instances details

CanSelect Kleenean
Instance details Defined in AERN2.Select Associated Types type SelectType Kleenean # Methods select :: Kleenean -> Kleenean -> SelectType Kleenean #
CanSelect CKleenean Source #
Instance details Defined in AERN2.Real.CKleenean Associated Types type SelectType CKleenean # Methods select :: CKleenean -> CKleenean -> SelectType CKleenean #
CanSelect (CN Kleenean)
Instance details Defined in AERN2.Select Associated Types type SelectType (CN Kleenean) # Methods select :: CN Kleenean -> CN Kleenean -> SelectType (CN Kleenean) #

type CanSelectBool k = (CanSelect k, SelectType k ~ Bool) #

type CanSelectCNBool k = (CanSelect k, SelectType k ~ CN Bool) #

class CanAndOrCountable t where Source #

Methods

or_countable :: (Integer -> t) -> t Source #

and_countable :: (Integer -> t) -> t Source #

Instances

Instances details

CanAndOrCountable CKleenean Source #
Instance details Defined in AERN2.Real.CKleenean Methods or_countable :: (Integer -> CKleenean) -> CKleenean Source # and_countable :: (Integer -> CKleenean) -> CKleenean Source #

extracting approximations

class CanExtractApproximation e q where Source #

Associated Types

type ExtractedApproximation e q Source #

Methods

extractApproximation Source #

Arguments

:: e	exact value
-> q	query
-> ExtractedApproximation e q

Get an approximation of an exact value using the given query

Instances

Instances details

HasAccuracy t => CanExtractApproximation (CSequence t) Accuracy Source #
Instance details Defined in AERN2.Real.Type Associated Types type ExtractedApproximation (CSequence t) Accuracy Source # Methods extractApproximation :: CSequence t -> Accuracy -> ExtractedApproximation (CSequence t) Accuracy Source #
CanExtractApproximation (CSequence t) Precision Source #
Instance details Defined in AERN2.Real.Type Associated Types type ExtractedApproximation (CSequence t) Precision Source # Methods extractApproximation :: CSequence t -> Precision -> ExtractedApproximation (CSequence t) Precision Source #

(?) :: CanExtractApproximation e q => e -> q -> ExtractedApproximation e q infix 1 Source #

bits :: ConvertibleExactly t Accuracy => t -> Accuracy #

prec :: Integer -> Precision #

abstract real numbers

Instances

Instances details

RealNumber CReal Source #
Instance details Defined in AERN2.Real
KnownNat p => RealNumber (WithCurrentPrec p (CN MPBall)) Source #
Instance details Defined in AERN2.Real