Copyright	(c) Michal Konecny
License	BSD3
Maintainer	mikkonecny@gmail.com
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell98

AERN2.Sequence

Contents

The protocol and type of fast converging sequences
selecting one of several staged computations
auxiliary functions for making new sequence operations

Description

A type of fast convergent sequences parametrised by the arrow in which the elements of the sequence are queried

Synopsis

module AERN2.AccuracySG
data SequenceP a = SequenceP {
- unSequenceP :: a
}
pSeq :: a -> SequenceP a
class (Show a, Show (EnsureNoCN a), Show (EnsureCN a), HasAccuracy a, CanAdjustToAccuracySG a, CanEnsureCN a, CanEnsureCN (EnsureCN a), HasAccuracy (EnsureNoCN a), CanIntersectCNSameType a) => SuitableForSeq a
type SequenceA to a = QA to (SequenceP a)
type Sequence a = SequenceA (->) a
newSeq :: (QAArrow to, SuitableForSeq a) => a -> String -> [AnyProtocolQA to] -> ((Maybe (QAId to), Maybe (QAId to)) -> AccuracySG `to` a) -> SequenceA to a
newSeqSimple :: (QAArrow to, SuitableForSeq a) => a -> ((Maybe (QAId to), Maybe (QAId to)) -> AccuracySG `to` a) -> SequenceA to a
seqName :: SequenceA to a -> String
seqId :: SequenceA to a -> Maybe (QAId to)
seqSources :: SequenceA to a -> [QAId to]
seqRename :: (String -> String) -> SequenceA to a -> SequenceA to a
seqWithAccuracy :: QAArrow to => SequenceA to a -> Maybe (QAId to) -> AccuracySG `to` a
(?) :: QAArrow to => QA to p -> Q p `to` A p
seqWithAccuracyA :: QAArrow to => Maybe (QAId to) -> (SequenceA to a, AccuracySG) `to` a
seqsWithAccuracyA :: QAArrow to => Maybe (QAId to) -> ([SequenceA to a], AccuracySG) `to` [a]
(-:-) :: (QAArrow to, QAProtocolCacheable p) => QA to p `to` QA to p
(-:-||) :: (QAArrow to, QAProtocolCacheable p) => QA to p `to` QA to p
(-:-|) :: (QAArrow to, QAProtocolCacheable p) => QA to p `to` QA to p
data SequenceAtAccuracy a = SequenceAtAccuracy (Sequence a) AccuracySG
convergentList2SequenceA :: (QAArrow to, SuitableForSeq a) => String -> [a] -> SequenceA to a
seqByPrecision2SequenceA :: (QAArrow to, SuitableForSeq a) => String -> (Precision -> a) -> SequenceA to a
pick :: QAArrow to => Maybe (QAId to) -> [SequenceA to (Maybe a)] `to` a
unaryOp :: (QAArrow to, SuitableForSeq a, SuitableForSeq b) => String -> (a -> b) -> (Maybe (QAId to) -> SequenceA to a -> AccuracySG `to` (AccuracySG, Maybe a)) -> SequenceA to a -> SequenceA to b
binaryOp :: (QAArrow to, SuitableForSeq a, SuitableForSeq b, SuitableForSeq c) => String -> (a -> b -> c) -> (Maybe (QAId to) -> SequenceA to a -> SequenceA to b -> AccuracySG `to` ((AccuracySG, Maybe a), (AccuracySG, Maybe b))) -> SequenceA to a -> SequenceA to b -> SequenceA to c
binaryOpWithPureArg :: (QAArrow to, SuitableForSeq a, SuitableForSeq b) => String -> (a -> t -> b) -> (Maybe (QAId to) -> SequenceA to a -> t -> AccuracySG `to` (AccuracySG, Maybe a)) -> SequenceA to a -> t -> SequenceA to b
getSeqFnNormLog :: (QAArrow to, CanEnsureCN v, HasNorm (EnsureNoCN v)) => Maybe (QAId to) -> SequenceA to a -> (a -> v) -> AccuracySG `to` (Maybe Integer, a)
getInitQ1FromSimple :: Arrow to => (AccuracySG `to` q) -> Maybe (QAId to) -> r1 -> AccuracySG `to` (q, Maybe a)
getInitQ1TFromSimple :: Arrow to => (AccuracySG `to` q) -> Maybe (QAId to) -> r1 -> t -> AccuracySG `to` (q, Maybe a)
getInitQ1Q2FromSimple :: Arrow to => (AccuracySG `to` (q, q)) -> Maybe (QAId to) -> r1 -> r2 -> AccuracySG `to` ((q, Maybe a), (q, Maybe b))

Documentation

module AERN2.AccuracySG

The protocol and type of fast converging sequences

data SequenceP a #

Constructors

SequenceP
Fields unSequenceP :: a

Instances

Floating CauchyRealCN #
Instance details Defined in AERN2.Real.Arithmetic Methods pi :: CauchyRealCN # exp :: CauchyRealCN -> CauchyRealCN # log :: CauchyRealCN -> CauchyRealCN # sqrt :: CauchyRealCN -> CauchyRealCN # (**) :: CauchyRealCN -> CauchyRealCN -> CauchyRealCN # logBase :: CauchyRealCN -> CauchyRealCN -> CauchyRealCN # sin :: CauchyRealCN -> CauchyRealCN # cos :: CauchyRealCN -> CauchyRealCN # tan :: CauchyRealCN -> CauchyRealCN # asin :: CauchyRealCN -> CauchyRealCN # acos :: CauchyRealCN -> CauchyRealCN # atan :: CauchyRealCN -> CauchyRealCN # sinh :: CauchyRealCN -> CauchyRealCN # cosh :: CauchyRealCN -> CauchyRealCN # tanh :: CauchyRealCN -> CauchyRealCN # asinh :: CauchyRealCN -> CauchyRealCN # acosh :: CauchyRealCN -> CauchyRealCN # atanh :: CauchyRealCN -> CauchyRealCN # log1p :: CauchyRealCN -> CauchyRealCN # expm1 :: CauchyRealCN -> CauchyRealCN # log1pexp :: CauchyRealCN -> CauchyRealCN # log1mexp :: CauchyRealCN -> CauchyRealCN #
Floating CauchyReal #
Instance details Defined in AERN2.Real.Arithmetic Methods pi :: CauchyReal # exp :: CauchyReal -> CauchyReal # log :: CauchyReal -> CauchyReal # sqrt :: CauchyReal -> CauchyReal # (**) :: CauchyReal -> CauchyReal -> CauchyReal # logBase :: CauchyReal -> CauchyReal -> CauchyReal # sin :: CauchyReal -> CauchyReal # cos :: CauchyReal -> CauchyReal # tan :: CauchyReal -> CauchyReal # asin :: CauchyReal -> CauchyReal # acos :: CauchyReal -> CauchyReal # atan :: CauchyReal -> CauchyReal # sinh :: CauchyReal -> CauchyReal # cosh :: CauchyReal -> CauchyReal # tanh :: CauchyReal -> CauchyReal # asinh :: CauchyReal -> CauchyReal # acosh :: CauchyReal -> CauchyReal # atanh :: CauchyReal -> CauchyReal # log1p :: CauchyReal -> CauchyReal # expm1 :: CauchyReal -> CauchyReal # log1pexp :: CauchyReal -> CauchyReal # log1mexp :: CauchyReal -> CauchyReal #
Functor SequenceP #
Instance details Defined in AERN2.Sequence.Type Methods fmap :: (a -> b) -> SequenceP a -> SequenceP b # (<$) :: a -> SequenceP b -> SequenceP a #
Arbitrary CauchyReal #
Instance details Defined in AERN2.Real.Tests Methods arbitrary :: Gen CauchyReal # shrink :: CauchyReal -> [CauchyReal] #
ConvertibleWithPrecision CauchyReal MPBall #
Instance details Defined in AERN2.Real.Type Methods safeConvertP :: Precision -> CauchyReal -> ConvertResult MPBall #
Convertible CauchyReal Double #
Instance details Defined in AERN2.Real.Arithmetic Methods safeConvert :: CauchyReal -> ConvertResult Double #
CanDiv Double CauchyReal #
Instance details Defined in AERN2.Real.Arithmetic Associated Types type DivTypeNoCN Double CauchyReal :: * # type DivType Double CauchyReal :: * # Methods divideNoCN :: Double -> CauchyReal -> DivTypeNoCN Double CauchyReal # divide :: Double -> CauchyReal -> DivType Double CauchyReal #
CanDiv CauchyReal Double #
Instance details Defined in AERN2.Real.Arithmetic Associated Types type DivTypeNoCN CauchyReal Double :: * # type DivType CauchyReal Double :: * # Methods divideNoCN :: CauchyReal -> Double -> DivTypeNoCN CauchyReal Double # divide :: CauchyReal -> Double -> DivType CauchyReal Double #
CanMulAsymmetric Double CauchyReal #
Instance details Defined in AERN2.Real.Arithmetic Associated Types type MulType Double CauchyReal :: * # Methods mul :: Double -> CauchyReal -> MulType Double CauchyReal #
CanMulAsymmetric CauchyReal Double #
Instance details Defined in AERN2.Real.Arithmetic Associated Types type MulType CauchyReal Double :: * # Methods mul :: CauchyReal -> Double -> MulType CauchyReal Double #
CanPow Double CauchyReal #
Instance details Defined in AERN2.Real.Arithmetic Associated Types type PowTypeNoCN Double CauchyReal :: * # type PowType Double CauchyReal :: * # Methods powNoCN :: Double -> CauchyReal -> PowTypeNoCN Double CauchyReal # pow :: Double -> CauchyReal -> PowType Double CauchyReal #
CanPow CauchyReal Double #
Instance details Defined in AERN2.Real.Arithmetic Associated Types type PowTypeNoCN CauchyReal Double :: * # type PowType CauchyReal Double :: * # Methods powNoCN :: CauchyReal -> Double -> PowTypeNoCN CauchyReal Double # pow :: CauchyReal -> Double -> PowType CauchyReal Double #
CanAddAsymmetric Double CauchyReal #
Instance details Defined in AERN2.Real.Arithmetic Associated Types type AddType Double CauchyReal :: * # Methods add :: Double -> CauchyReal -> AddType Double CauchyReal #
CanAddAsymmetric CauchyReal Double #
Instance details Defined in AERN2.Real.Arithmetic Associated Types type AddType CauchyReal Double :: * # Methods add :: CauchyReal -> Double -> AddType CauchyReal Double #
CanSub Double CauchyReal #
Instance details Defined in AERN2.Real.Arithmetic Associated Types type SubType Double CauchyReal :: * # Methods sub :: Double -> CauchyReal -> SubType Double CauchyReal #
CanSub CauchyReal Double #
Instance details Defined in AERN2.Real.Arithmetic Associated Types type SubType CauchyReal Double :: * # Methods sub :: CauchyReal -> Double -> SubType CauchyReal Double #
HasLimits Rational CauchyReal #
Instance details Defined in AERN2.Limit Associated Types type LimitType Rational CauchyReal :: * # Methods limit :: (Rational -> CauchyReal) -> LimitType Rational CauchyReal #
(CanDiv MPBall b, SuitableForSeq b, HasNorm (EnsureNoCN b), CanEnsureCN b, CanSetPrecision (DivType MPBall b), CanSetPrecision (DivTypeNoCN MPBall b)) => CanDiv MPBall (Sequence b) #
Instance details Defined in AERN2.Sequence.Field Associated Types type DivTypeNoCN MPBall (Sequence b) :: * # type DivType MPBall (Sequence b) :: * # Methods divideNoCN :: MPBall -> Sequence b -> DivTypeNoCN MPBall (Sequence b) # divide :: MPBall -> Sequence b -> DivType MPBall (Sequence b) #
(CanMulAsymmetric MPBall b, SuitableForSeq b, CanSetPrecision (MulType MPBall b)) => CanMulAsymmetric MPBall (Sequence b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type MulType MPBall (Sequence b) :: * # Methods mul :: MPBall -> Sequence b -> MulType MPBall (Sequence b) #
(CanPow MPBall e, SuitableForSeq e, HasIntegerBounds e, CanSetPrecision (PowTypeNoCN MPBall e), CanSetPrecision (PowType MPBall e)) => CanPow MPBall (Sequence e) #
Instance details Defined in AERN2.Sequence.Elementary Associated Types type PowTypeNoCN MPBall (Sequence e) :: * # type PowType MPBall (Sequence e) :: * # Methods powNoCN :: MPBall -> Sequence e -> PowTypeNoCN MPBall (Sequence e) # pow :: MPBall -> Sequence e -> PowType MPBall (Sequence e) #
(CanAddAsymmetric MPBall b, SuitableForSeq b, CanSetPrecision (AddType MPBall b)) => CanAddAsymmetric MPBall (Sequence b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type AddType MPBall (Sequence b) :: * # Methods add :: MPBall -> Sequence b -> AddType MPBall (Sequence b) #
(CanSub MPBall b, SuitableForSeq b, CanSetPrecision (SubType MPBall b)) => CanSub MPBall (Sequence b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type SubType MPBall (Sequence b) :: * # Methods sub :: MPBall -> Sequence b -> SubType MPBall (Sequence b) #
(CanMinMaxAsymmetric MPBall b, SuitableForSeq b, CanSetPrecision (MinMaxType MPBall b)) => CanMinMaxAsymmetric MPBall (Sequence b) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type MinMaxType MPBall (Sequence b) :: * # Methods min :: MPBall -> Sequence b -> MinMaxType MPBall (Sequence b) # max :: MPBall -> Sequence b -> MinMaxType MPBall (Sequence b) #
QAArrow to => ConvertibleExactly CauchyReal (MPBallWithGlobalPrecA to) #
Instance details Defined in AERN2.MPBallWithGlobalPrec Methods safeConvertExactly :: CauchyReal -> ConvertResult (MPBallWithGlobalPrecA to) #
(SuitableForCE es, CanEnsureCE es a) => CanEnsureCE es (SequenceP a) #
Instance details Defined in AERN2.Sequence.Type Associated Types type EnsureCE es (SequenceP a) :: * # type EnsureNoCE es (SequenceP a) :: * # Methods ensureCE :: Maybe es -> SequenceP a -> EnsureCE es (SequenceP a) # deEnsureCE :: Maybe es -> EnsureCE es (SequenceP a) -> Either es (SequenceP a) # ensureNoCE :: Maybe es -> SequenceP a -> (Maybe (EnsureNoCE es (SequenceP a)), es) # noValueECE :: Maybe (SequenceP a) -> es -> EnsureCE es (SequenceP a) # prependErrorsECE :: Maybe (SequenceP a) -> es -> EnsureCE es (SequenceP a) -> EnsureCE es (SequenceP a) #
HasLimits Rational (WithLipschitz (CauchyReal -> CauchyRealCN)) #
Instance details Defined in AERN2.Limit Associated Types type LimitType Rational (WithLipschitz (CauchyReal -> CauchyRealCN)) :: * # Methods limit :: (Rational -> WithLipschitz (CauchyReal -> CauchyRealCN)) -> LimitType Rational (WithLipschitz (CauchyReal -> CauchyRealCN)) #
(QAArrow to, CanDiv Int b, SuitableForSeq b, SuitableForSeq (DivType Int b), SuitableForSeq (DivTypeNoCN Int b), HasNorm (EnsureNoCN b)) => CanDiv Int (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Field Associated Types type DivTypeNoCN Int (SequenceA to b) :: * # type DivType Int (SequenceA to b) :: * # Methods divideNoCN :: Int -> SequenceA to b -> DivTypeNoCN Int (SequenceA to b) # divide :: Int -> SequenceA to b -> DivType Int (SequenceA to b) #
(QAArrow to, CanDiv Integer b, SuitableForSeq b, SuitableForSeq (DivType Integer b), SuitableForSeq (DivTypeNoCN Integer b), HasNorm (EnsureNoCN b)) => CanDiv Integer (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Field Associated Types type DivTypeNoCN Integer (SequenceA to b) :: * # type DivType Integer (SequenceA to b) :: * # Methods divideNoCN :: Integer -> SequenceA to b -> DivTypeNoCN Integer (SequenceA to b) # divide :: Integer -> SequenceA to b -> DivType Integer (SequenceA to b) #
(QAArrow to, CanDiv Rational b, SuitableForSeq b, SuitableForSeq (DivType Rational b), SuitableForSeq (DivTypeNoCN Rational b), HasNorm (EnsureNoCN b)) => CanDiv Rational (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Field Associated Types type DivTypeNoCN Rational (SequenceA to b) :: * # type DivType Rational (SequenceA to b) :: * # Methods divideNoCN :: Rational -> SequenceA to b -> DivTypeNoCN Rational (SequenceA to b) # divide :: Rational -> SequenceA to b -> DivType Rational (SequenceA to b) #
(QAArrow to, CanDiv Dyadic b, SuitableForSeq b, SuitableForSeq (DivType Dyadic b), SuitableForSeq (DivTypeNoCN Dyadic b), HasNorm (EnsureNoCN b)) => CanDiv Dyadic (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Field Associated Types type DivTypeNoCN Dyadic (SequenceA to b) :: * # type DivType Dyadic (SequenceA to b) :: * # Methods divideNoCN :: Dyadic -> SequenceA to b -> DivTypeNoCN Dyadic (SequenceA to b) # divide :: Dyadic -> SequenceA to b -> DivType Dyadic (SequenceA to b) #
(QAArrow to, CanMulAsymmetric Int b, SuitableForSeq b, SuitableForSeq (MulType Int b)) => CanMulAsymmetric Int (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type MulType Int (SequenceA to b) :: * # Methods mul :: Int -> SequenceA to b -> MulType Int (SequenceA to b) #
(QAArrow to, CanMulAsymmetric Integer b, SuitableForSeq b, SuitableForSeq (MulType Integer b)) => CanMulAsymmetric Integer (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type MulType Integer (SequenceA to b) :: * # Methods mul :: Integer -> SequenceA to b -> MulType Integer (SequenceA to b) #
(QAArrow to, CanMulAsymmetric Rational b, SuitableForSeq b, SuitableForSeq (MulType Rational b)) => CanMulAsymmetric Rational (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type MulType Rational (SequenceA to b) :: * # Methods mul :: Rational -> SequenceA to b -> MulType Rational (SequenceA to b) #
(QAArrow to, CanMulAsymmetric Dyadic b, SuitableForSeq b, SuitableForSeq (MulType Dyadic b)) => CanMulAsymmetric Dyadic (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type MulType Dyadic (SequenceA to b) :: * # Methods mul :: Dyadic -> SequenceA to b -> MulType Dyadic (SequenceA to b) #
(QAArrow to, CanPow Int a, CanSetPrecision a, HasIntegerBounds a, SuitableForSeq a, SuitableForSeq (PowType Int a), SuitableForSeq (PowTypeNoCN Int a)) => CanPow Int (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary Associated Types type PowTypeNoCN Int (SequenceA to a) :: * # type PowType Int (SequenceA to a) :: * # Methods powNoCN :: Int -> SequenceA to a -> PowTypeNoCN Int (SequenceA to a) # pow :: Int -> SequenceA to a -> PowType Int (SequenceA to a) #
(QAArrow to, CanPow Integer a, CanSetPrecision a, HasIntegerBounds a, SuitableForSeq a, SuitableForSeq (PowType Integer a), SuitableForSeq (PowTypeNoCN Integer a)) => CanPow Integer (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary Associated Types type PowTypeNoCN Integer (SequenceA to a) :: * # type PowType Integer (SequenceA to a) :: * # Methods powNoCN :: Integer -> SequenceA to a -> PowTypeNoCN Integer (SequenceA to a) # pow :: Integer -> SequenceA to a -> PowType Integer (SequenceA to a) #
(QAArrow to, CanPow Rational a, CanSetPrecision a, HasIntegerBounds a, SuitableForSeq a, SuitableForSeq (PowType Rational a), SuitableForSeq (PowTypeNoCN Rational a)) => CanPow Rational (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary Associated Types type PowTypeNoCN Rational (SequenceA to a) :: * # type PowType Rational (SequenceA to a) :: * # Methods powNoCN :: Rational -> SequenceA to a -> PowTypeNoCN Rational (SequenceA to a) # pow :: Rational -> SequenceA to a -> PowType Rational (SequenceA to a) #
(QAArrow to, CanPow Dyadic a, CanSetPrecision a, HasIntegerBounds a, SuitableForSeq a, SuitableForSeq (PowType Dyadic a), SuitableForSeq (PowTypeNoCN Dyadic a)) => CanPow Dyadic (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary Associated Types type PowTypeNoCN Dyadic (SequenceA to a) :: * # type PowType Dyadic (SequenceA to a) :: * # Methods powNoCN :: Dyadic -> SequenceA to a -> PowTypeNoCN Dyadic (SequenceA to a) # pow :: Dyadic -> SequenceA to a -> PowType Dyadic (SequenceA to a) #
(QAArrow to, CanAddAsymmetric Int b, SuitableForSeq b, SuitableForSeq (AddType Int b)) => CanAddAsymmetric Int (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type AddType Int (SequenceA to b) :: * # Methods add :: Int -> SequenceA to b -> AddType Int (SequenceA to b) #
(QAArrow to, CanAddAsymmetric Integer b, SuitableForSeq b, SuitableForSeq (AddType Integer b)) => CanAddAsymmetric Integer (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type AddType Integer (SequenceA to b) :: * # Methods add :: Integer -> SequenceA to b -> AddType Integer (SequenceA to b) #
(QAArrow to, CanAddAsymmetric Rational b, SuitableForSeq b, SuitableForSeq (AddType Rational b)) => CanAddAsymmetric Rational (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type AddType Rational (SequenceA to b) :: * # Methods add :: Rational -> SequenceA to b -> AddType Rational (SequenceA to b) #
(QAArrow to, CanAddAsymmetric Dyadic b, SuitableForSeq b, SuitableForSeq (AddType Dyadic b)) => CanAddAsymmetric Dyadic (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type AddType Dyadic (SequenceA to b) :: * # Methods add :: Dyadic -> SequenceA to b -> AddType Dyadic (SequenceA to b) #
(QAArrow to, CanSub Int b, SuitableForSeq b, SuitableForSeq (SubType Int b)) => CanSub Int (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type SubType Int (SequenceA to b) :: * # Methods sub :: Int -> SequenceA to b -> SubType Int (SequenceA to b) #
(QAArrow to, CanSub Integer b, SuitableForSeq b, SuitableForSeq (SubType Integer b)) => CanSub Integer (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type SubType Integer (SequenceA to b) :: * # Methods sub :: Integer -> SequenceA to b -> SubType Integer (SequenceA to b) #
(QAArrow to, CanSub Rational b, SuitableForSeq b, SuitableForSeq (SubType Rational b)) => CanSub Rational (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type SubType Rational (SequenceA to b) :: * # Methods sub :: Rational -> SequenceA to b -> SubType Rational (SequenceA to b) #
(QAArrow to, CanSub Dyadic b, SuitableForSeq b, SuitableForSeq (SubType Dyadic b)) => CanSub Dyadic (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type SubType Dyadic (SequenceA to b) :: * # Methods sub :: Dyadic -> SequenceA to b -> SubType Dyadic (SequenceA to b) #
(QAArrow to, CanMinMaxAsymmetric Int b, SuitableForSeq b, SuitableForSeq (MinMaxType Int b)) => CanMinMaxAsymmetric Int (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type MinMaxType Int (SequenceA to b) :: * # Methods min :: Int -> SequenceA to b -> MinMaxType Int (SequenceA to b) # max :: Int -> SequenceA to b -> MinMaxType Int (SequenceA to b) #
(QAArrow to, CanMinMaxAsymmetric Integer b, SuitableForSeq b, SuitableForSeq (MinMaxType Integer b)) => CanMinMaxAsymmetric Integer (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type MinMaxType Integer (SequenceA to b) :: * # Methods min :: Integer -> SequenceA to b -> MinMaxType Integer (SequenceA to b) # max :: Integer -> SequenceA to b -> MinMaxType Integer (SequenceA to b) #
(QAArrow to, CanMinMaxAsymmetric Rational b, SuitableForSeq b, SuitableForSeq (MinMaxType Rational b)) => CanMinMaxAsymmetric Rational (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type MinMaxType Rational (SequenceA to b) :: * # Methods min :: Rational -> SequenceA to b -> MinMaxType Rational (SequenceA to b) # max :: Rational -> SequenceA to b -> MinMaxType Rational (SequenceA to b) #
(QAArrow to, CanMinMaxAsymmetric Dyadic b, SuitableForSeq b, SuitableForSeq (MinMaxType Dyadic b)) => CanMinMaxAsymmetric Dyadic (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type MinMaxType Dyadic (SequenceA to b) :: * # Methods min :: Dyadic -> SequenceA to b -> MinMaxType Dyadic (SequenceA to b) # max :: Dyadic -> SequenceA to b -> MinMaxType Dyadic (SequenceA to b) #
(QAArrow to, HasEqAsymmetric Int a, SuitableForSeq a, SuitableForSeq (EqCompareType Int a)) => HasEqAsymmetric Int (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type EqCompareType Int (SequenceA to a) :: * # Methods equalTo :: Int -> SequenceA to a -> EqCompareType Int (SequenceA to a) # notEqualTo :: Int -> SequenceA to a -> EqCompareType Int (SequenceA to a) #
(QAArrow to, HasEqAsymmetric Integer a, SuitableForSeq a, SuitableForSeq (EqCompareType Integer a)) => HasEqAsymmetric Integer (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type EqCompareType Integer (SequenceA to a) :: * # Methods equalTo :: Integer -> SequenceA to a -> EqCompareType Integer (SequenceA to a) # notEqualTo :: Integer -> SequenceA to a -> EqCompareType Integer (SequenceA to a) #
(QAArrow to, HasEqAsymmetric Rational a, SuitableForSeq a, SuitableForSeq (EqCompareType Rational a)) => HasEqAsymmetric Rational (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type EqCompareType Rational (SequenceA to a) :: * # Methods equalTo :: Rational -> SequenceA to a -> EqCompareType Rational (SequenceA to a) # notEqualTo :: Rational -> SequenceA to a -> EqCompareType Rational (SequenceA to a) #
(QAArrow to, HasEqAsymmetric Dyadic a, SuitableForSeq a, SuitableForSeq (EqCompareType Dyadic a)) => HasEqAsymmetric Dyadic (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type EqCompareType Dyadic (SequenceA to a) :: * # Methods equalTo :: Dyadic -> SequenceA to a -> EqCompareType Dyadic (SequenceA to a) # notEqualTo :: Dyadic -> SequenceA to a -> EqCompareType Dyadic (SequenceA to a) #
(QAArrow to, HasOrderAsymmetric Int a, SuitableForSeq a, SuitableForSeq (OrderCompareType Int a)) => HasOrderAsymmetric Int (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type OrderCompareType Int (SequenceA to a) :: * # Methods lessThan :: Int -> SequenceA to a -> OrderCompareType Int (SequenceA to a) # greaterThan :: Int -> SequenceA to a -> OrderCompareType Int (SequenceA to a) # leq :: Int -> SequenceA to a -> OrderCompareType Int (SequenceA to a) # geq :: Int -> SequenceA to a -> OrderCompareType Int (SequenceA to a) #
(QAArrow to, HasOrderAsymmetric Integer a, SuitableForSeq a, SuitableForSeq (OrderCompareType Integer a)) => HasOrderAsymmetric Integer (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type OrderCompareType Integer (SequenceA to a) :: * # Methods lessThan :: Integer -> SequenceA to a -> OrderCompareType Integer (SequenceA to a) # greaterThan :: Integer -> SequenceA to a -> OrderCompareType Integer (SequenceA to a) # leq :: Integer -> SequenceA to a -> OrderCompareType Integer (SequenceA to a) # geq :: Integer -> SequenceA to a -> OrderCompareType Integer (SequenceA to a) #
(QAArrow to, HasOrderAsymmetric Rational a, SuitableForSeq a, SuitableForSeq (OrderCompareType Rational a)) => HasOrderAsymmetric Rational (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type OrderCompareType Rational (SequenceA to a) :: * # Methods lessThan :: Rational -> SequenceA to a -> OrderCompareType Rational (SequenceA to a) # greaterThan :: Rational -> SequenceA to a -> OrderCompareType Rational (SequenceA to a) # leq :: Rational -> SequenceA to a -> OrderCompareType Rational (SequenceA to a) # geq :: Rational -> SequenceA to a -> OrderCompareType Rational (SequenceA to a) #
(QAArrow to, HasOrderAsymmetric Dyadic a, SuitableForSeq a, SuitableForSeq (OrderCompareType Dyadic a)) => HasOrderAsymmetric Dyadic (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type OrderCompareType Dyadic (SequenceA to a) :: * # Methods lessThan :: Dyadic -> SequenceA to a -> OrderCompareType Dyadic (SequenceA to a) # greaterThan :: Dyadic -> SequenceA to a -> OrderCompareType Dyadic (SequenceA to a) # leq :: Dyadic -> SequenceA to a -> OrderCompareType Dyadic (SequenceA to a) # geq :: Dyadic -> SequenceA to a -> OrderCompareType Dyadic (SequenceA to a) #
(QAArrow to, HasBools b, SuitableForSeq b) => ConvertibleExactly Bool (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison Methods safeConvertExactly :: Bool -> ConvertResult (SequenceA to b) #
(QAArrow to, ConvertibleExactly Int a, CanSetPrecision a, SuitableForSeq a) => ConvertibleExactly Int (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Type Methods safeConvertExactly :: Int -> ConvertResult (SequenceA to a) #
(QAArrow to, ConvertibleExactly Integer a, CanSetPrecision a, SuitableForSeq a) => ConvertibleExactly Integer (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Type Methods safeConvertExactly :: Integer -> ConvertResult (SequenceA to a) #
(QAArrow to, ConvertibleWithPrecision Rational a, CanSetPrecision a, SuitableForSeq a) => ConvertibleExactly Rational (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Type Methods safeConvertExactly :: Rational -> ConvertResult (SequenceA to a) #
(QAArrow to, ConvertibleExactly Dyadic a, CanSetPrecision a, SuitableForSeq a) => ConvertibleExactly Dyadic (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Type Methods safeConvertExactly :: Dyadic -> ConvertResult (SequenceA to a) #
(Arrow to, SuitableForCE es, CanEnsureCE es a) => CanEnsureCE es (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Type Associated Types type EnsureCE es (SequenceA to a) :: * # type EnsureNoCE es (SequenceA to a) :: * # Methods ensureCE :: Maybe es -> SequenceA to a -> EnsureCE es (SequenceA to a) # deEnsureCE :: Maybe es -> EnsureCE es (SequenceA to a) -> Either es (SequenceA to a) # ensureNoCE :: Maybe es -> SequenceA to a -> (Maybe (EnsureNoCE es (SequenceA to a)), es) # noValueECE :: Maybe (SequenceA to a) -> es -> EnsureCE es (SequenceA to a) # prependErrorsECE :: Maybe (SequenceA to a) -> es -> EnsureCE es (SequenceA to a) -> EnsureCE es (SequenceA to a) #
HasLimits Rational (CauchyReal -> CauchyRealCN) #
Instance details Defined in AERN2.Limit Associated Types type LimitType Rational (CauchyReal -> CauchyRealCN) :: * # Methods limit :: (Rational -> CauchyReal -> CauchyRealCN) -> LimitType Rational (CauchyReal -> CauchyRealCN) #
HasEqCertainly a a => Eq (Sequence a) #
Instance details Defined in AERN2.Sequence.PreludeOps Methods (==) :: Sequence a -> Sequence a -> Bool # (/=) :: Sequence a -> Sequence a -> Bool #
(Field a, CanAbsSameType a, ConvertibleWithPrecision Rational a, SuitableForSeq a, SuitableForSeq (EnsureCN a), CanSetPrecision a, HasNorm (EnsureNoCN a), CanEnsureCN a, CanIntersectCNSameType a) => Fractional (Sequence a) #
Instance details Defined in AERN2.Sequence.PreludeOps Methods (/) :: Sequence a -> Sequence a -> Sequence a # recip :: Sequence a -> Sequence a # fromRational :: Rational -> Sequence a #
(Ring a, CanAbsSameType a, SuitableForSeq a, CanSetPrecision a, HasNorm (EnsureNoCN a), CanEnsureCN a) => Num (Sequence a) #
Instance details Defined in AERN2.Sequence.PreludeOps Methods (+) :: Sequence a -> Sequence a -> Sequence a # (-) :: Sequence a -> Sequence a -> Sequence a # (*) :: Sequence a -> Sequence a -> Sequence a # negate :: Sequence a -> Sequence a # abs :: Sequence a -> Sequence a # signum :: Sequence a -> Sequence a # fromInteger :: Integer -> Sequence a #
(HasEqCertainly a a, HasOrderCertainly a a) => Ord (Sequence a) #
Instance details Defined in AERN2.Sequence.PreludeOps Methods compare :: Sequence a -> Sequence a -> Ordering # (<) :: Sequence a -> Sequence a -> Bool # (<=) :: Sequence a -> Sequence a -> Bool # (>) :: Sequence a -> Sequence a -> Bool # (>=) :: Sequence a -> Sequence a -> Bool # max :: Sequence a -> Sequence a -> Sequence a # min :: Sequence a -> Sequence a -> Sequence a #
Show a => Show (Sequence a) #
Instance details Defined in AERN2.Sequence.Type Methods showsPrec :: Int -> Sequence a -> ShowS # show :: Sequence a -> String # showList :: [Sequence a] -> ShowS #
Show a => Show (SequenceP a) #
Instance details Defined in AERN2.Sequence.Type Methods showsPrec :: Int -> SequenceP a -> ShowS # show :: SequenceP a -> String # showList :: [SequenceP a] -> ShowS #
QAArrow to => Field (CauchyRealA to) #
Instance details Defined in AERN2.Real.Arithmetic
QAArrow to => OrderedField (CauchyRealA to) #
Instance details Defined in AERN2.Real.Arithmetic
QAArrow to => Ring (CauchyRealA to) #
Instance details Defined in AERN2.Real.Arithmetic
QAArrow to => OrderedRing (CauchyRealA to) #
Instance details Defined in AERN2.Real.Arithmetic
CanPickNonZero a => CanPickNonZero (Sequence a) #
Instance details Defined in AERN2.Sequence.Branching Methods pickNonZero :: [(Sequence a, s)] -> Maybe (Sequence a, s) #
SuitableForSeq a => QAProtocolCacheable (SequenceP a) #
Instance details Defined in AERN2.Sequence.Type Associated Types type QACache (SequenceP a) :: * # Methods newQACache :: SequenceP a -> QACache (SequenceP a) # lookupQACache :: SequenceP a -> QACache (SequenceP a) -> Q (SequenceP a) -> (Maybe (A (SequenceP a)), Maybe String) # updateQACache :: SequenceP a -> Q (SequenceP a) -> A (SequenceP a) -> QACache (SequenceP a) -> QACache (SequenceP a) #
Show a => QAProtocol (SequenceP a) #
Instance details Defined in AERN2.Sequence.Type Associated Types type Q (SequenceP a) :: * # type A (SequenceP a) :: * #
(CanDiv a MPBall, SuitableForSeq a, CanSetPrecision (DivType a MPBall), CanSetPrecision (DivTypeNoCN a MPBall)) => CanDiv (Sequence a) MPBall #
Instance details Defined in AERN2.Sequence.Field Associated Types type DivTypeNoCN (Sequence a) MPBall :: * # type DivType (Sequence a) MPBall :: * # Methods divideNoCN :: Sequence a -> MPBall -> DivTypeNoCN (Sequence a) MPBall # divide :: Sequence a -> MPBall -> DivType (Sequence a) MPBall #
(CanMulAsymmetric a MPBall, SuitableForSeq a, CanSetPrecision (MulType a MPBall)) => CanMulAsymmetric (Sequence a) MPBall #
Instance details Defined in AERN2.Sequence.Ring Associated Types type MulType (Sequence a) MPBall :: * # Methods mul :: Sequence a -> MPBall -> MulType (Sequence a) MPBall #
(CanPow a MPBall, SuitableForSeq a, HasNorm (EnsureNoCN a), CanEnsureCN a, CanSetPrecision (PowTypeNoCN a MPBall), CanSetPrecision (PowType a MPBall)) => CanPow (Sequence a) MPBall #
Instance details Defined in AERN2.Sequence.Elementary Associated Types type PowTypeNoCN (Sequence a) MPBall :: * # type PowType (Sequence a) MPBall :: * # Methods powNoCN :: Sequence a -> MPBall -> PowTypeNoCN (Sequence a) MPBall # pow :: Sequence a -> MPBall -> PowType (Sequence a) MPBall #
(CanAddAsymmetric a MPBall, SuitableForSeq a, CanSetPrecision (AddType a MPBall)) => CanAddAsymmetric (Sequence a) MPBall #
Instance details Defined in AERN2.Sequence.Ring Associated Types type AddType (Sequence a) MPBall :: * # Methods add :: Sequence a -> MPBall -> AddType (Sequence a) MPBall #
(CanSub a MPBall, SuitableForSeq a, CanSetPrecision (SubType a MPBall)) => CanSub (Sequence a) MPBall #
Instance details Defined in AERN2.Sequence.Ring Associated Types type SubType (Sequence a) MPBall :: * # Methods sub :: Sequence a -> MPBall -> SubType (Sequence a) MPBall #
(CanMinMaxAsymmetric a MPBall, SuitableForSeq a, CanSetPrecision (MinMaxType a MPBall)) => CanMinMaxAsymmetric (Sequence a) MPBall #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type MinMaxType (Sequence a) MPBall :: * # Methods min :: Sequence a -> MPBall -> MinMaxType (Sequence a) MPBall # max :: Sequence a -> MPBall -> MinMaxType (Sequence a) MPBall #
CanMulAsymmetric t (CauchyRealA to) => CanMulAsymmetric (Complex t) (CauchyRealA to) #
Instance details Defined in AERN2.Real.Arithmetic Associated Types type MulType (Complex t) (CauchyRealA to) :: * # Methods mul :: Complex t -> CauchyRealA to -> MulType (Complex t) (CauchyRealA to) #
CanMulAsymmetric (CauchyRealA to) t => CanMulAsymmetric (CauchyRealA to) (Complex t) #
Instance details Defined in AERN2.Real.Arithmetic Associated Types type MulType (CauchyRealA to) (Complex t) :: * # Methods mul :: CauchyRealA to -> Complex t -> MulType (CauchyRealA to) (Complex t) #
(QAArrow to, CanAddAsymmetric t (CauchyRealA to)) => CanAddAsymmetric (Complex t) (CauchyRealA to) #
Instance details Defined in AERN2.Real.Arithmetic Associated Types type AddType (Complex t) (CauchyRealA to) :: * # Methods add :: Complex t -> CauchyRealA to -> AddType (Complex t) (CauchyRealA to) #
(QAArrow to, CanAddAsymmetric (CauchyRealA to) t) => CanAddAsymmetric (CauchyRealA to) (Complex t) #
Instance details Defined in AERN2.Real.Arithmetic Associated Types type AddType (CauchyRealA to) (Complex t) :: * # Methods add :: CauchyRealA to -> Complex t -> AddType (CauchyRealA to) (Complex t) #
(QAArrow to, CanAdd t (CauchyRealA to)) => CanSub (Complex t) (CauchyRealA to) #
Instance details Defined in AERN2.Real.Arithmetic Associated Types type SubType (Complex t) (CauchyRealA to) :: * # Methods sub :: Complex t -> CauchyRealA to -> SubType (Complex t) (CauchyRealA to) #
(QAArrow to, CanAdd (CauchyRealA to) t, CanNegSameType t) => CanSub (CauchyRealA to) (Complex t) #
Instance details Defined in AERN2.Real.Arithmetic Associated Types type SubType (CauchyRealA to) (Complex t) :: * # Methods sub :: CauchyRealA to -> Complex t -> SubType (CauchyRealA to) (Complex t) #
(QAArrow to, CanSqrt a, CanMinMaxThis a Integer, CanEnsureCN (SqrtType a), HasNorm (EnsureNoCN (SqrtType a)), SuitableForSeq a, SuitableForSeq (SqrtType a)) => CanSqrt (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary Associated Types type SqrtType (SequenceA to a) :: * # Methods sqrt :: SequenceA to a -> SqrtType (SequenceA to a) #
(QAArrow to, CanExp a, CanEnsureCN (ExpType a), HasNorm (EnsureNoCN (ExpType a)), SuitableForSeq a, SuitableForSeq (ExpType a)) => CanExp (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary Associated Types type ExpType (SequenceA to a) :: * # Methods exp :: SequenceA to a -> ExpType (SequenceA to a) #
(QAArrow to, CanLog a, CanSetPrecision a, CanEnsureCN a, HasNorm (EnsureNoCN a), SuitableForSeq a, SuitableForSeq (LogType a)) => CanLog (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary Associated Types type LogType (SequenceA to a) :: * # Methods log :: SequenceA to a -> LogType (SequenceA to a) #
(QAArrow to, CanSinCos a, CanEnsureCN (SinCosType a), HasNorm (EnsureNoCN (SinCosType a)), SuitableForSeq a, SuitableForSeq (SinCosType a)) => CanSinCos (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary Associated Types type SinCosType (SequenceA to a) :: * # Methods cos :: SequenceA to a -> SinCosType (SequenceA to a) # sin :: SequenceA to a -> SinCosType (SequenceA to a) #
(QAArrow to, CanAbs a, SuitableForSeq a, SuitableForSeq (AbsType a)) => CanAbs (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type AbsType (SequenceA to a) :: * # Methods abs :: SequenceA to a -> AbsType (SequenceA to a) #
(QAArrow to, CanNeg a, SuitableForSeq a, SuitableForSeq (NegType a)) => CanNeg (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type NegType (SequenceA to a) :: * # Methods negate :: SequenceA to a -> NegType (SequenceA to a) #
(QAArrow to, CanDiv a Integer, SuitableForSeq a, SuitableForSeq (DivType a Integer), SuitableForSeq (DivTypeNoCN a Integer)) => CanDiv (SequenceA to a) Integer #
Instance details Defined in AERN2.Sequence.Field Associated Types type DivTypeNoCN (SequenceA to a) Integer :: * # type DivType (SequenceA to a) Integer :: * # Methods divideNoCN :: SequenceA to a -> Integer -> DivTypeNoCN (SequenceA to a) Integer # divide :: SequenceA to a -> Integer -> DivType (SequenceA to a) Integer #
(QAArrow to, CanDiv a Int, SuitableForSeq a, SuitableForSeq (DivType a Int), SuitableForSeq (DivTypeNoCN a Int)) => CanDiv (SequenceA to a) Int #
Instance details Defined in AERN2.Sequence.Field Associated Types type DivTypeNoCN (SequenceA to a) Int :: * # type DivType (SequenceA to a) Int :: * # Methods divideNoCN :: SequenceA to a -> Int -> DivTypeNoCN (SequenceA to a) Int # divide :: SequenceA to a -> Int -> DivType (SequenceA to a) Int #
(QAArrow to, CanDiv a Rational, SuitableForSeq a, SuitableForSeq (DivType a Rational), SuitableForSeq (DivTypeNoCN a Rational)) => CanDiv (SequenceA to a) Rational #
Instance details Defined in AERN2.Sequence.Field Associated Types type DivTypeNoCN (SequenceA to a) Rational :: * # type DivType (SequenceA to a) Rational :: * # Methods divideNoCN :: SequenceA to a -> Rational -> DivTypeNoCN (SequenceA to a) Rational # divide :: SequenceA to a -> Rational -> DivType (SequenceA to a) Rational #
(QAArrow to, CanDiv a Dyadic, SuitableForSeq a, SuitableForSeq (DivType a Dyadic), SuitableForSeq (DivTypeNoCN a Dyadic)) => CanDiv (SequenceA to a) Dyadic #
Instance details Defined in AERN2.Sequence.Field Associated Types type DivTypeNoCN (SequenceA to a) Dyadic :: * # type DivType (SequenceA to a) Dyadic :: * # Methods divideNoCN :: SequenceA to a -> Dyadic -> DivTypeNoCN (SequenceA to a) Dyadic # divide :: SequenceA to a -> Dyadic -> DivType (SequenceA to a) Dyadic #
(QAArrow to, CanMulAsymmetric a Integer, SuitableForSeq a, SuitableForSeq (MulType a Integer)) => CanMulAsymmetric (SequenceA to a) Integer #
Instance details Defined in AERN2.Sequence.Ring Associated Types type MulType (SequenceA to a) Integer :: * # Methods mul :: SequenceA to a -> Integer -> MulType (SequenceA to a) Integer #
(QAArrow to, CanMulAsymmetric a Int, SuitableForSeq a, SuitableForSeq (MulType a Int)) => CanMulAsymmetric (SequenceA to a) Int #
Instance details Defined in AERN2.Sequence.Ring Associated Types type MulType (SequenceA to a) Int :: * # Methods mul :: SequenceA to a -> Int -> MulType (SequenceA to a) Int #
(QAArrow to, CanMulAsymmetric a Rational, SuitableForSeq a, SuitableForSeq (MulType a Rational)) => CanMulAsymmetric (SequenceA to a) Rational #
Instance details Defined in AERN2.Sequence.Ring Associated Types type MulType (SequenceA to a) Rational :: * # Methods mul :: SequenceA to a -> Rational -> MulType (SequenceA to a) Rational #
(QAArrow to, CanMulAsymmetric a Dyadic, SuitableForSeq a, SuitableForSeq (MulType a Dyadic)) => CanMulAsymmetric (SequenceA to a) Dyadic #
Instance details Defined in AERN2.Sequence.Ring Associated Types type MulType (SequenceA to a) Dyadic :: * # Methods mul :: SequenceA to a -> Dyadic -> MulType (SequenceA to a) Dyadic #
(QAArrow to, CanPow a Integer, CanSetPrecision a, CanEnsureCN a, HasNorm (EnsureNoCN a), SuitableForSeq a, SuitableForSeq (PowTypeNoCN a Integer), SuitableForSeq (PowType a Integer)) => CanPow (SequenceA to a) Integer #
Instance details Defined in AERN2.Sequence.Elementary Associated Types type PowTypeNoCN (SequenceA to a) Integer :: * # type PowType (SequenceA to a) Integer :: * # Methods powNoCN :: SequenceA to a -> Integer -> PowTypeNoCN (SequenceA to a) Integer # pow :: SequenceA to a -> Integer -> PowType (SequenceA to a) Integer #
(QAArrow to, CanPow a Int, CanSetPrecision a, CanEnsureCN a, HasNorm (EnsureNoCN a), SuitableForSeq a, SuitableForSeq (PowTypeNoCN a Int), SuitableForSeq (PowType a Int)) => CanPow (SequenceA to a) Int #
Instance details Defined in AERN2.Sequence.Elementary Associated Types type PowTypeNoCN (SequenceA to a) Int :: * # type PowType (SequenceA to a) Int :: * # Methods powNoCN :: SequenceA to a -> Int -> PowTypeNoCN (SequenceA to a) Int # pow :: SequenceA to a -> Int -> PowType (SequenceA to a) Int #
(QAArrow to, CanPow a Dyadic, CanSetPrecision a, CanEnsureCN a, HasNorm (EnsureNoCN a), SuitableForSeq a, SuitableForSeq (PowTypeNoCN a Dyadic), SuitableForSeq (PowType a Dyadic)) => CanPow (SequenceA to a) Dyadic #
Instance details Defined in AERN2.Sequence.Elementary Associated Types type PowTypeNoCN (SequenceA to a) Dyadic :: * # type PowType (SequenceA to a) Dyadic :: * # Methods powNoCN :: SequenceA to a -> Dyadic -> PowTypeNoCN (SequenceA to a) Dyadic # pow :: SequenceA to a -> Dyadic -> PowType (SequenceA to a) Dyadic #
(QAArrow to, CanPow a Rational, CanSetPrecision a, CanEnsureCN a, HasNorm (EnsureNoCN a), SuitableForSeq a, SuitableForSeq (PowTypeNoCN a Rational), SuitableForSeq (PowType a Rational)) => CanPow (SequenceA to a) Rational #
Instance details Defined in AERN2.Sequence.Elementary Associated Types type PowTypeNoCN (SequenceA to a) Rational :: * # type PowType (SequenceA to a) Rational :: * # Methods powNoCN :: SequenceA to a -> Rational -> PowTypeNoCN (SequenceA to a) Rational # pow :: SequenceA to a -> Rational -> PowType (SequenceA to a) Rational #
(QAArrow to, CanAddAsymmetric a Integer, SuitableForSeq a, SuitableForSeq (AddType a Integer)) => CanAddAsymmetric (SequenceA to a) Integer #
Instance details Defined in AERN2.Sequence.Ring Associated Types type AddType (SequenceA to a) Integer :: * # Methods add :: SequenceA to a -> Integer -> AddType (SequenceA to a) Integer #
(QAArrow to, CanAddAsymmetric a Int, SuitableForSeq a, SuitableForSeq (AddType a Int)) => CanAddAsymmetric (SequenceA to a) Int #
Instance details Defined in AERN2.Sequence.Ring Associated Types type AddType (SequenceA to a) Int :: * # Methods add :: SequenceA to a -> Int -> AddType (SequenceA to a) Int #
(QAArrow to, CanAddAsymmetric a Rational, SuitableForSeq a, SuitableForSeq (AddType a Rational)) => CanAddAsymmetric (SequenceA to a) Rational #
Instance details Defined in AERN2.Sequence.Ring Associated Types type AddType (SequenceA to a) Rational :: * # Methods add :: SequenceA to a -> Rational -> AddType (SequenceA to a) Rational #
(QAArrow to, CanAddAsymmetric a Dyadic, SuitableForSeq a, SuitableForSeq (AddType a Dyadic)) => CanAddAsymmetric (SequenceA to a) Dyadic #
Instance details Defined in AERN2.Sequence.Ring Associated Types type AddType (SequenceA to a) Dyadic :: * # Methods add :: SequenceA to a -> Dyadic -> AddType (SequenceA to a) Dyadic #
(QAArrow to, CanSub a Integer, SuitableForSeq a, SuitableForSeq (SubType a Integer)) => CanSub (SequenceA to a) Integer #
Instance details Defined in AERN2.Sequence.Ring Associated Types type SubType (SequenceA to a) Integer :: * # Methods sub :: SequenceA to a -> Integer -> SubType (SequenceA to a) Integer #
(QAArrow to, CanSub a Int, SuitableForSeq a, SuitableForSeq (SubType a Int)) => CanSub (SequenceA to a) Int #
Instance details Defined in AERN2.Sequence.Ring Associated Types type SubType (SequenceA to a) Int :: * # Methods sub :: SequenceA to a -> Int -> SubType (SequenceA to a) Int #
(QAArrow to, CanSub a Rational, SuitableForSeq a, SuitableForSeq (SubType a Rational)) => CanSub (SequenceA to a) Rational #
Instance details Defined in AERN2.Sequence.Ring Associated Types type SubType (SequenceA to a) Rational :: * # Methods sub :: SequenceA to a -> Rational -> SubType (SequenceA to a) Rational #
(QAArrow to, CanSub a Dyadic, SuitableForSeq a, SuitableForSeq (SubType a Dyadic)) => CanSub (SequenceA to a) Dyadic #
Instance details Defined in AERN2.Sequence.Ring Associated Types type SubType (SequenceA to a) Dyadic :: * # Methods sub :: SequenceA to a -> Dyadic -> SubType (SequenceA to a) Dyadic #
(QAArrow to, CanMinMaxAsymmetric a Integer, SuitableForSeq a, SuitableForSeq (MinMaxType a Integer)) => CanMinMaxAsymmetric (SequenceA to a) Integer #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type MinMaxType (SequenceA to a) Integer :: * # Methods min :: SequenceA to a -> Integer -> MinMaxType (SequenceA to a) Integer # max :: SequenceA to a -> Integer -> MinMaxType (SequenceA to a) Integer #
(QAArrow to, CanMinMaxAsymmetric a Int, SuitableForSeq a, SuitableForSeq (MinMaxType a Int)) => CanMinMaxAsymmetric (SequenceA to a) Int #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type MinMaxType (SequenceA to a) Int :: * # Methods min :: SequenceA to a -> Int -> MinMaxType (SequenceA to a) Int # max :: SequenceA to a -> Int -> MinMaxType (SequenceA to a) Int #
(QAArrow to, CanMinMaxAsymmetric a Rational, SuitableForSeq a, SuitableForSeq (MinMaxType a Rational)) => CanMinMaxAsymmetric (SequenceA to a) Rational #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type MinMaxType (SequenceA to a) Rational :: * # Methods min :: SequenceA to a -> Rational -> MinMaxType (SequenceA to a) Rational # max :: SequenceA to a -> Rational -> MinMaxType (SequenceA to a) Rational #
(QAArrow to, CanMinMaxAsymmetric a Dyadic, SuitableForSeq a, SuitableForSeq (MinMaxType a Dyadic)) => CanMinMaxAsymmetric (SequenceA to a) Dyadic #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type MinMaxType (SequenceA to a) Dyadic :: * # Methods min :: SequenceA to a -> Dyadic -> MinMaxType (SequenceA to a) Dyadic # max :: SequenceA to a -> Dyadic -> MinMaxType (SequenceA to a) Dyadic #
(QAArrow to, HasEqAsymmetric a Integer, SuitableForSeq a, SuitableForSeq (EqCompareType a Integer)) => HasEqAsymmetric (SequenceA to a) Integer #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type EqCompareType (SequenceA to a) Integer :: * # Methods equalTo :: SequenceA to a -> Integer -> EqCompareType (SequenceA to a) Integer # notEqualTo :: SequenceA to a -> Integer -> EqCompareType (SequenceA to a) Integer #
(QAArrow to, HasEqAsymmetric a Int, SuitableForSeq a, SuitableForSeq (EqCompareType a Int)) => HasEqAsymmetric (SequenceA to a) Int #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type EqCompareType (SequenceA to a) Int :: * # Methods equalTo :: SequenceA to a -> Int -> EqCompareType (SequenceA to a) Int # notEqualTo :: SequenceA to a -> Int -> EqCompareType (SequenceA to a) Int #
(QAArrow to, HasEqAsymmetric a Rational, SuitableForSeq a, SuitableForSeq (EqCompareType a Rational)) => HasEqAsymmetric (SequenceA to a) Rational #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type EqCompareType (SequenceA to a) Rational :: * # Methods equalTo :: SequenceA to a -> Rational -> EqCompareType (SequenceA to a) Rational # notEqualTo :: SequenceA to a -> Rational -> EqCompareType (SequenceA to a) Rational #
(QAArrow to, HasEqAsymmetric a Dyadic, SuitableForSeq a, SuitableForSeq (EqCompareType a Dyadic)) => HasEqAsymmetric (SequenceA to a) Dyadic #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type EqCompareType (SequenceA to a) Dyadic :: * # Methods equalTo :: SequenceA to a -> Dyadic -> EqCompareType (SequenceA to a) Dyadic # notEqualTo :: SequenceA to a -> Dyadic -> EqCompareType (SequenceA to a) Dyadic #
(QAArrow to, HasOrderAsymmetric a Integer, SuitableForSeq a, SuitableForSeq (OrderCompareType a Integer)) => HasOrderAsymmetric (SequenceA to a) Integer #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type OrderCompareType (SequenceA to a) Integer :: * # Methods lessThan :: SequenceA to a -> Integer -> OrderCompareType (SequenceA to a) Integer # greaterThan :: SequenceA to a -> Integer -> OrderCompareType (SequenceA to a) Integer # leq :: SequenceA to a -> Integer -> OrderCompareType (SequenceA to a) Integer # geq :: SequenceA to a -> Integer -> OrderCompareType (SequenceA to a) Integer #
(QAArrow to, HasOrderAsymmetric a Int, SuitableForSeq a, SuitableForSeq (OrderCompareType a Int)) => HasOrderAsymmetric (SequenceA to a) Int #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type OrderCompareType (SequenceA to a) Int :: * # Methods lessThan :: SequenceA to a -> Int -> OrderCompareType (SequenceA to a) Int # greaterThan :: SequenceA to a -> Int -> OrderCompareType (SequenceA to a) Int # leq :: SequenceA to a -> Int -> OrderCompareType (SequenceA to a) Int # geq :: SequenceA to a -> Int -> OrderCompareType (SequenceA to a) Int #
(QAArrow to, HasOrderAsymmetric a Rational, SuitableForSeq a, SuitableForSeq (OrderCompareType a Rational)) => HasOrderAsymmetric (SequenceA to a) Rational #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type OrderCompareType (SequenceA to a) Rational :: * # Methods lessThan :: SequenceA to a -> Rational -> OrderCompareType (SequenceA to a) Rational # greaterThan :: SequenceA to a -> Rational -> OrderCompareType (SequenceA to a) Rational # leq :: SequenceA to a -> Rational -> OrderCompareType (SequenceA to a) Rational # geq :: SequenceA to a -> Rational -> OrderCompareType (SequenceA to a) Rational #
(QAArrow to, HasOrderAsymmetric a Dyadic, SuitableForSeq a, SuitableForSeq (OrderCompareType a Dyadic)) => HasOrderAsymmetric (SequenceA to a) Dyadic #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type OrderCompareType (SequenceA to a) Dyadic :: * # Methods lessThan :: SequenceA to a -> Dyadic -> OrderCompareType (SequenceA to a) Dyadic # greaterThan :: SequenceA to a -> Dyadic -> OrderCompareType (SequenceA to a) Dyadic # leq :: SequenceA to a -> Dyadic -> OrderCompareType (SequenceA to a) Dyadic # geq :: SequenceA to a -> Dyadic -> OrderCompareType (SequenceA to a) Dyadic #
(CanDiv a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (DivType a (SequenceA to b)), CanEnsureCE es (DivTypeNoCN a (SequenceA to b)), SuitableForCE es) => CanDiv (CollectErrors es a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Field Associated Types type DivTypeNoCN (CollectErrors es a) (SequenceA to b) :: * # type DivType (CollectErrors es a) (SequenceA to b) :: * # Methods divideNoCN :: CollectErrors es a -> SequenceA to b -> DivTypeNoCN (CollectErrors es a) (SequenceA to b) # divide :: CollectErrors es a -> SequenceA to b -> DivType (CollectErrors es a) (SequenceA to b) #
(CanDiv (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (DivType (SequenceA to a) b), CanEnsureCE es (DivTypeNoCN (SequenceA to a) b), SuitableForCE es) => CanDiv (SequenceA to a) (CollectErrors es b) #
Instance details Defined in AERN2.Sequence.Field Associated Types type DivTypeNoCN (SequenceA to a) (CollectErrors es b) :: * # type DivType (SequenceA to a) (CollectErrors es b) :: * # Methods divideNoCN :: SequenceA to a -> CollectErrors es b -> DivTypeNoCN (SequenceA to a) (CollectErrors es b) # divide :: SequenceA to a -> CollectErrors es b -> DivType (SequenceA to a) (CollectErrors es b) #
(QAArrow to, CanDiv a b, HasNorm (EnsureNoCN a), HasNorm (EnsureNoCN b), SuitableForSeq a, SuitableForSeq b, SuitableForSeq (DivType a b), SuitableForSeq (DivTypeNoCN a b)) => CanDiv (SequenceA to a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Field Associated Types type DivTypeNoCN (SequenceA to a) (SequenceA to b) :: * # type DivType (SequenceA to a) (SequenceA to b) :: * # Methods divideNoCN :: SequenceA to a -> SequenceA to b -> DivTypeNoCN (SequenceA to a) (SequenceA to b) # divide :: SequenceA to a -> SequenceA to b -> DivType (SequenceA to a) (SequenceA to b) #
(CanMulAsymmetric a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (MulType a (SequenceA to b)), SuitableForCE es) => CanMulAsymmetric (CollectErrors es a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type MulType (CollectErrors es a) (SequenceA to b) :: * # Methods mul :: CollectErrors es a -> SequenceA to b -> MulType (CollectErrors es a) (SequenceA to b) #
(CanMulAsymmetric (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (MulType (SequenceA to a) b), SuitableForCE es) => CanMulAsymmetric (SequenceA to a) (CollectErrors es b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type MulType (SequenceA to a) (CollectErrors es b) :: * # Methods mul :: SequenceA to a -> CollectErrors es b -> MulType (SequenceA to a) (CollectErrors es b) #
(QAArrow to, CanMulAsymmetric a b, HasNorm (EnsureNoCN a), HasNorm (EnsureNoCN b), SuitableForSeq a, SuitableForSeq b, SuitableForSeq (MulType a b)) => CanMulAsymmetric (SequenceA to a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type MulType (SequenceA to a) (SequenceA to b) :: * # Methods mul :: SequenceA to a -> SequenceA to b -> MulType (SequenceA to a) (SequenceA to b) #
(CanPow a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (PowType a (SequenceA to b)), CanEnsureCE es (PowTypeNoCN a (SequenceA to b)), SuitableForCE es) => CanPow (CollectErrors es a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Elementary Associated Types type PowTypeNoCN (CollectErrors es a) (SequenceA to b) :: * # type PowType (CollectErrors es a) (SequenceA to b) :: * # Methods powNoCN :: CollectErrors es a -> SequenceA to b -> PowTypeNoCN (CollectErrors es a) (SequenceA to b) # pow :: CollectErrors es a -> SequenceA to b -> PowType (CollectErrors es a) (SequenceA to b) #
(CanPow (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (PowTypeNoCN (SequenceA to a) b), CanEnsureCE es (PowType (SequenceA to a) b), SuitableForCE es) => CanPow (SequenceA to a) (CollectErrors es b) #
Instance details Defined in AERN2.Sequence.Elementary Associated Types type PowTypeNoCN (SequenceA to a) (CollectErrors es b) :: * # type PowType (SequenceA to a) (CollectErrors es b) :: * # Methods powNoCN :: SequenceA to a -> CollectErrors es b -> PowTypeNoCN (SequenceA to a) (CollectErrors es b) # pow :: SequenceA to a -> CollectErrors es b -> PowType (SequenceA to a) (CollectErrors es b) #
(QAArrow to, CanPow a e, CanEnsureCN a, HasNorm (EnsureNoCN a), HasIntegerBounds e, SuitableForSeq a, SuitableForSeq e, SuitableForSeq (PowTypeNoCN a e), SuitableForSeq (PowType a e)) => CanPow (SequenceA to a) (SequenceA to e) #
Instance details Defined in AERN2.Sequence.Elementary Associated Types type PowTypeNoCN (SequenceA to a) (SequenceA to e) :: * # type PowType (SequenceA to a) (SequenceA to e) :: * # Methods powNoCN :: SequenceA to a -> SequenceA to e -> PowTypeNoCN (SequenceA to a) (SequenceA to e) # pow :: SequenceA to a -> SequenceA to e -> PowType (SequenceA to a) (SequenceA to e) #
(CanAddAsymmetric a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (AddType a (SequenceA to b)), SuitableForCE es) => CanAddAsymmetric (CollectErrors es a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type AddType (CollectErrors es a) (SequenceA to b) :: * # Methods add :: CollectErrors es a -> SequenceA to b -> AddType (CollectErrors es a) (SequenceA to b) #
(QAArrow to, CanAddAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (AddType a b)) => CanAddAsymmetric (SequenceA to a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type AddType (SequenceA to a) (SequenceA to b) :: * # Methods add :: SequenceA to a -> SequenceA to b -> AddType (SequenceA to a) (SequenceA to b) #
(CanAddAsymmetric (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (AddType (SequenceA to a) b), SuitableForCE es) => CanAddAsymmetric (SequenceA to a) (CollectErrors es b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type AddType (SequenceA to a) (CollectErrors es b) :: * # Methods add :: SequenceA to a -> CollectErrors es b -> AddType (SequenceA to a) (CollectErrors es b) #
(CanSub a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (SubType a (SequenceA to b)), SuitableForCE es) => CanSub (CollectErrors es a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type SubType (CollectErrors es a) (SequenceA to b) :: * # Methods sub :: CollectErrors es a -> SequenceA to b -> SubType (CollectErrors es a) (SequenceA to b) #
(QAArrow to, CanSub a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (SubType a b)) => CanSub (SequenceA to a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type SubType (SequenceA to a) (SequenceA to b) :: * # Methods sub :: SequenceA to a -> SequenceA to b -> SubType (SequenceA to a) (SequenceA to b) #
(CanSub (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (SubType (SequenceA to a) b), SuitableForCE es) => CanSub (SequenceA to a) (CollectErrors es b) #
Instance details Defined in AERN2.Sequence.Ring Associated Types type SubType (SequenceA to a) (CollectErrors es b) :: * # Methods sub :: SequenceA to a -> CollectErrors es b -> SubType (SequenceA to a) (CollectErrors es b) #
(CanMinMaxAsymmetric a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (MinMaxType a (SequenceA to b)), SuitableForCE es) => CanMinMaxAsymmetric (CollectErrors es a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type MinMaxType (CollectErrors es a) (SequenceA to b) :: * # Methods min :: CollectErrors es a -> SequenceA to b -> MinMaxType (CollectErrors es a) (SequenceA to b) # max :: CollectErrors es a -> SequenceA to b -> MinMaxType (CollectErrors es a) (SequenceA to b) #
(CanMinMaxAsymmetric (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (MinMaxType (SequenceA to a) b), SuitableForCE es) => CanMinMaxAsymmetric (SequenceA to a) (CollectErrors es b) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type MinMaxType (SequenceA to a) (CollectErrors es b) :: * # Methods min :: SequenceA to a -> CollectErrors es b -> MinMaxType (SequenceA to a) (CollectErrors es b) # max :: SequenceA to a -> CollectErrors es b -> MinMaxType (SequenceA to a) (CollectErrors es b) #
(QAArrow to, CanMinMaxAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (MinMaxType a b)) => CanMinMaxAsymmetric (SequenceA to a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type MinMaxType (SequenceA to a) (SequenceA to b) :: * # Methods min :: SequenceA to a -> SequenceA to b -> MinMaxType (SequenceA to a) (SequenceA to b) # max :: SequenceA to a -> SequenceA to b -> MinMaxType (SequenceA to a) (SequenceA to b) #
(HasEqAsymmetric a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (EqCompareType a (SequenceA to b)), IsBool (EnsureCE es (EqCompareType a (SequenceA to b))), SuitableForCE es) => HasEqAsymmetric (CollectErrors es a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type EqCompareType (CollectErrors es a) (SequenceA to b) :: * # Methods equalTo :: CollectErrors es a -> SequenceA to b -> EqCompareType (CollectErrors es a) (SequenceA to b) # notEqualTo :: CollectErrors es a -> SequenceA to b -> EqCompareType (CollectErrors es a) (SequenceA to b) #
(HasEqAsymmetric (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (EqCompareType (SequenceA to a) b), IsBool (EnsureCE es (EqCompareType (SequenceA to a) b)), SuitableForCE es) => HasEqAsymmetric (SequenceA to a) (CollectErrors es b) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type EqCompareType (SequenceA to a) (CollectErrors es b) :: * # Methods equalTo :: SequenceA to a -> CollectErrors es b -> EqCompareType (SequenceA to a) (CollectErrors es b) # notEqualTo :: SequenceA to a -> CollectErrors es b -> EqCompareType (SequenceA to a) (CollectErrors es b) #
(QAArrow to, HasEqAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (EqCompareType a b)) => HasEqAsymmetric (SequenceA to a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type EqCompareType (SequenceA to a) (SequenceA to b) :: * # Methods equalTo :: SequenceA to a -> SequenceA to b -> EqCompareType (SequenceA to a) (SequenceA to b) # notEqualTo :: SequenceA to a -> SequenceA to b -> EqCompareType (SequenceA to a) (SequenceA to b) #
(HasOrderAsymmetric a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (OrderCompareType a (SequenceA to b)), IsBool (EnsureCE es (OrderCompareType a (SequenceA to b))), SuitableForCE es) => HasOrderAsymmetric (CollectErrors es a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type OrderCompareType (CollectErrors es a) (SequenceA to b) :: * # Methods lessThan :: CollectErrors es a -> SequenceA to b -> OrderCompareType (CollectErrors es a) (SequenceA to b) # greaterThan :: CollectErrors es a -> SequenceA to b -> OrderCompareType (CollectErrors es a) (SequenceA to b) # leq :: CollectErrors es a -> SequenceA to b -> OrderCompareType (CollectErrors es a) (SequenceA to b) # geq :: CollectErrors es a -> SequenceA to b -> OrderCompareType (CollectErrors es a) (SequenceA to b) #
(HasOrderAsymmetric (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (OrderCompareType (SequenceA to a) b), IsBool (EnsureCE es (OrderCompareType (SequenceA to a) b)), SuitableForCE es) => HasOrderAsymmetric (SequenceA to a) (CollectErrors es b) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type OrderCompareType (SequenceA to a) (CollectErrors es b) :: * # Methods lessThan :: SequenceA to a -> CollectErrors es b -> OrderCompareType (SequenceA to a) (CollectErrors es b) # greaterThan :: SequenceA to a -> CollectErrors es b -> OrderCompareType (SequenceA to a) (CollectErrors es b) # leq :: SequenceA to a -> CollectErrors es b -> OrderCompareType (SequenceA to a) (CollectErrors es b) # geq :: SequenceA to a -> CollectErrors es b -> OrderCompareType (SequenceA to a) (CollectErrors es b) #
(QAArrow to, HasOrderAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (OrderCompareType a b)) => HasOrderAsymmetric (SequenceA to a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type OrderCompareType (SequenceA to a) (SequenceA to b) :: * # Methods lessThan :: SequenceA to a -> SequenceA to b -> OrderCompareType (SequenceA to a) (SequenceA to b) # greaterThan :: SequenceA to a -> SequenceA to b -> OrderCompareType (SequenceA to a) (SequenceA to b) # leq :: SequenceA to a -> SequenceA to b -> OrderCompareType (SequenceA to a) (SequenceA to b) # geq :: SequenceA to a -> SequenceA to b -> OrderCompareType (SequenceA to a) (SequenceA to b) #
(QAArrow to, CanAndOrAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (AndOrType a b)) => CanAndOrAsymmetric (SequenceA to a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type AndOrType (SequenceA to a) (SequenceA to b) :: * # Methods and2 :: SequenceA to a -> SequenceA to b -> AndOrType (SequenceA to a) (SequenceA to b) # or2 :: SequenceA to a -> SequenceA to b -> AndOrType (SequenceA to a) (SequenceA to b) #
(QAArrow to, ArrowApply to, HasIfThenElse b t, HasIfThenElse b (to AccuracySG t), IfThenElseType b (to AccuracySG t) ~ to AccuracySG (IfThenElseType b t), SuitableForSeq b, SuitableForSeq t, SuitableForSeq (IfThenElseType b t)) => HasIfThenElse (SequenceA to b) (SequenceA to t) #	"parallel if"
Instance details Defined in AERN2.Sequence.Branching Associated Types type IfThenElseType (SequenceA to b) (SequenceA to t) :: * # Methods ifThenElse :: SequenceA to b -> SequenceA to t -> SequenceA to t -> IfThenElseType (SequenceA to b) (SequenceA to t) #
type DivType Double CauchyReal #
Instance details Defined in AERN2.Real.Arithmetic type DivType Double CauchyReal = Double
type DivType CauchyReal Double #
Instance details Defined in AERN2.Real.Arithmetic type DivType CauchyReal Double = Double
type DivTypeNoCN Double CauchyReal #
Instance details Defined in AERN2.Real.Arithmetic type DivTypeNoCN Double CauchyReal = Double
type DivTypeNoCN CauchyReal Double #
Instance details Defined in AERN2.Real.Arithmetic type DivTypeNoCN CauchyReal Double = Double
type MulType Double CauchyReal #
Instance details Defined in AERN2.Real.Arithmetic type MulType Double CauchyReal = Double
type MulType CauchyReal Double #
Instance details Defined in AERN2.Real.Arithmetic type MulType CauchyReal Double = Double
type PowType Double CauchyReal #
Instance details Defined in AERN2.Real.Arithmetic type PowType Double CauchyReal = Double
type PowType CauchyReal Double #
Instance details Defined in AERN2.Real.Arithmetic type PowType CauchyReal Double = Double
type PowTypeNoCN Double CauchyReal #
Instance details Defined in AERN2.Real.Arithmetic type PowTypeNoCN Double CauchyReal = Double
type PowTypeNoCN CauchyReal Double #
Instance details Defined in AERN2.Real.Arithmetic type PowTypeNoCN CauchyReal Double = Double
type AddType Double CauchyReal #
Instance details Defined in AERN2.Real.Arithmetic type AddType Double CauchyReal = Double
type AddType CauchyReal Double #
Instance details Defined in AERN2.Real.Arithmetic type AddType CauchyReal Double = Double
type SubType Double CauchyReal #
Instance details Defined in AERN2.Real.Arithmetic type SubType Double CauchyReal = Double
type SubType CauchyReal Double #
Instance details Defined in AERN2.Real.Arithmetic type SubType CauchyReal Double = Double
type LimitType Rational CauchyReal #
Instance details Defined in AERN2.Limit type LimitType Rational CauchyReal = CauchyReal
type DivType MPBall (Sequence b) #
Instance details Defined in AERN2.Sequence.Field type DivType MPBall (Sequence b) = DivType MPBall b
type DivTypeNoCN MPBall (Sequence b) #
Instance details Defined in AERN2.Sequence.Field type DivTypeNoCN MPBall (Sequence b) = DivTypeNoCN MPBall b
type MulType MPBall (Sequence b) #
Instance details Defined in AERN2.Sequence.Ring type MulType MPBall (Sequence b) = MulType MPBall b
type PowType MPBall (Sequence e) #
Instance details Defined in AERN2.Sequence.Elementary type PowType MPBall (Sequence e) = PowType MPBall e
type PowTypeNoCN MPBall (Sequence e) #
Instance details Defined in AERN2.Sequence.Elementary type PowTypeNoCN MPBall (Sequence e) = PowTypeNoCN MPBall e
type AddType MPBall (Sequence b) #
Instance details Defined in AERN2.Sequence.Ring type AddType MPBall (Sequence b) = AddType MPBall b
type SubType MPBall (Sequence b) #
Instance details Defined in AERN2.Sequence.Ring type SubType MPBall (Sequence b) = SubType MPBall b
type MinMaxType MPBall (Sequence b) #
Instance details Defined in AERN2.Sequence.Comparison type MinMaxType MPBall (Sequence b) = MinMaxType MPBall b
type EnsureNoCE es (SequenceP a) #
Instance details Defined in AERN2.Sequence.Type type EnsureNoCE es (SequenceP a) = SequenceP (EnsureNoCE es a)
type EnsureCE es (SequenceP a) #
Instance details Defined in AERN2.Sequence.Type type EnsureCE es (SequenceP a) = SequenceP (EnsureCE es a)
type LimitType Rational (WithLipschitz (CauchyReal -> CauchyRealCN)) #
Instance details Defined in AERN2.Limit type LimitType Rational (WithLipschitz (CauchyReal -> CauchyRealCN)) = CauchyReal -> CauchyRealCN
type DivType Int (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Field type DivType Int (SequenceA to b) = SequenceA to (DivType Int b)
type DivType Integer (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Field type DivType Integer (SequenceA to b) = SequenceA to (DivType Integer b)
type DivType Rational (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Field type DivType Rational (SequenceA to b) = SequenceA to (DivType Rational b)
type DivType Dyadic (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Field type DivType Dyadic (SequenceA to b) = SequenceA to (DivType Dyadic b)
type DivTypeNoCN Int (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Field type DivTypeNoCN Int (SequenceA to b) = SequenceA to (DivTypeNoCN Int b)
type DivTypeNoCN Integer (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Field type DivTypeNoCN Integer (SequenceA to b) = SequenceA to (DivTypeNoCN Integer b)
type DivTypeNoCN Rational (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Field type DivTypeNoCN Rational (SequenceA to b) = SequenceA to (DivTypeNoCN Rational b)
type DivTypeNoCN Dyadic (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Field type DivTypeNoCN Dyadic (SequenceA to b) = SequenceA to (DivTypeNoCN Dyadic b)
type MulType Int (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring type MulType Int (SequenceA to b) = SequenceA to (MulType Int b)
type MulType Integer (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring type MulType Integer (SequenceA to b) = SequenceA to (MulType Integer b)
type MulType Rational (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring type MulType Rational (SequenceA to b) = SequenceA to (MulType Rational b)
type MulType Dyadic (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring type MulType Dyadic (SequenceA to b) = SequenceA to (MulType Dyadic b)
type PowType Int (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary type PowType Int (SequenceA to a) = SequenceA to (PowType Int a)
type PowType Integer (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary type PowType Integer (SequenceA to a) = SequenceA to (PowType Integer a)
type PowType Rational (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary type PowType Rational (SequenceA to a) = SequenceA to (PowType Rational a)
type PowType Dyadic (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary type PowType Dyadic (SequenceA to a) = SequenceA to (PowType Dyadic a)
type PowTypeNoCN Int (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary type PowTypeNoCN Int (SequenceA to a) = SequenceA to (PowTypeNoCN Int a)
type PowTypeNoCN Integer (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary type PowTypeNoCN Integer (SequenceA to a) = SequenceA to (PowTypeNoCN Integer a)
type PowTypeNoCN Rational (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary type PowTypeNoCN Rational (SequenceA to a) = SequenceA to (PowTypeNoCN Rational a)
type PowTypeNoCN Dyadic (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary type PowTypeNoCN Dyadic (SequenceA to a) = SequenceA to (PowTypeNoCN Dyadic a)
type AddType Int (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring type AddType Int (SequenceA to b) = SequenceA to (AddType Int b)
type AddType Integer (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring type AddType Integer (SequenceA to b) = SequenceA to (AddType Integer b)
type AddType Rational (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring type AddType Rational (SequenceA to b) = SequenceA to (AddType Rational b)
type AddType Dyadic (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring type AddType Dyadic (SequenceA to b) = SequenceA to (AddType Dyadic b)
type SubType Int (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring type SubType Int (SequenceA to b) = SequenceA to (SubType Int b)
type SubType Integer (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring type SubType Integer (SequenceA to b) = SequenceA to (SubType Integer b)
type SubType Rational (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring type SubType Rational (SequenceA to b) = SequenceA to (SubType Rational b)
type SubType Dyadic (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring type SubType Dyadic (SequenceA to b) = SequenceA to (SubType Dyadic b)
type MinMaxType Int (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison type MinMaxType Int (SequenceA to b) = SequenceA to (MinMaxType Int b)
type MinMaxType Integer (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison type MinMaxType Integer (SequenceA to b) = SequenceA to (MinMaxType Integer b)
type MinMaxType Rational (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison type MinMaxType Rational (SequenceA to b) = SequenceA to (MinMaxType Rational b)
type MinMaxType Dyadic (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison type MinMaxType Dyadic (SequenceA to b) = SequenceA to (MinMaxType Dyadic b)
type EqCompareType Int (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison type EqCompareType Int (SequenceA to a) = SequenceA to (EqCompareType Int a)
type EqCompareType Integer (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison type EqCompareType Integer (SequenceA to a) = SequenceA to (EqCompareType Integer a)
type EqCompareType Rational (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison type EqCompareType Rational (SequenceA to a) = SequenceA to (EqCompareType Rational a)
type EqCompareType Dyadic (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison type EqCompareType Dyadic (SequenceA to a) = SequenceA to (EqCompareType Dyadic a)
type OrderCompareType Int (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison type OrderCompareType Int (SequenceA to a) = SequenceA to (OrderCompareType Int a)
type OrderCompareType Integer (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison type OrderCompareType Integer (SequenceA to a) = SequenceA to (OrderCompareType Integer a)
type OrderCompareType Rational (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison type OrderCompareType Rational (SequenceA to a) = SequenceA to (OrderCompareType Rational a)
type OrderCompareType Dyadic (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison type OrderCompareType Dyadic (SequenceA to a) = SequenceA to (OrderCompareType Dyadic a)
type EnsureNoCE es (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Type type EnsureNoCE es (SequenceA to a) = SequenceA to (EnsureNoCE es a)
type EnsureCE es (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Type type EnsureCE es (SequenceA to a) = SequenceA to (EnsureCE es a)
type LimitType Rational (CauchyReal -> CauchyRealCN) #
Instance details Defined in AERN2.Limit type LimitType Rational (CauchyReal -> CauchyRealCN) = CauchyReal -> CauchyRealCN
type QACache (SequenceP a) #
Instance details Defined in AERN2.Sequence.Type type QACache (SequenceP a) = Maybe (a, AccuracySG)
type Q (SequenceP a) #
Instance details Defined in AERN2.Sequence.Type type Q (SequenceP a) = AccuracySG
type A (SequenceP a) #
Instance details Defined in AERN2.Sequence.Type type A (SequenceP a) = a
type DivType (Sequence a) MPBall #
Instance details Defined in AERN2.Sequence.Field type DivType (Sequence a) MPBall = DivType a MPBall
type DivTypeNoCN (Sequence a) MPBall #
Instance details Defined in AERN2.Sequence.Field type DivTypeNoCN (Sequence a) MPBall = DivTypeNoCN a MPBall
type MulType (Sequence a) MPBall #
Instance details Defined in AERN2.Sequence.Ring type MulType (Sequence a) MPBall = MulType a MPBall
type PowType (Sequence a) MPBall #
Instance details Defined in AERN2.Sequence.Elementary type PowType (Sequence a) MPBall = PowType a MPBall
type PowTypeNoCN (Sequence a) MPBall #
Instance details Defined in AERN2.Sequence.Elementary type PowTypeNoCN (Sequence a) MPBall = PowTypeNoCN a MPBall
type AddType (Sequence a) MPBall #
Instance details Defined in AERN2.Sequence.Ring type AddType (Sequence a) MPBall = AddType a MPBall
type SubType (Sequence a) MPBall #
Instance details Defined in AERN2.Sequence.Ring type SubType (Sequence a) MPBall = SubType a MPBall
type MinMaxType (Sequence a) MPBall #
Instance details Defined in AERN2.Sequence.Comparison type MinMaxType (Sequence a) MPBall = MinMaxType a MPBall
type MulType (Complex t) (CauchyRealA to) #
Instance details Defined in AERN2.Real.Arithmetic type MulType (Complex t) (CauchyRealA to) = Complex (MulType t (CauchyRealA to))
type MulType (CauchyRealA to) (Complex t) #
Instance details Defined in AERN2.Real.Arithmetic type MulType (CauchyRealA to) (Complex t) = Complex (MulType (CauchyRealA to) t)
type AddType (Complex t) (CauchyRealA to) #
Instance details Defined in AERN2.Real.Arithmetic type AddType (Complex t) (CauchyRealA to) = Complex (AddType t (CauchyRealA to))
type AddType (CauchyRealA to) (Complex t) #
Instance details Defined in AERN2.Real.Arithmetic type AddType (CauchyRealA to) (Complex t) = Complex (AddType (CauchyRealA to) t)
type SubType (Complex t) (CauchyRealA to) #
Instance details Defined in AERN2.Real.Arithmetic type SubType (Complex t) (CauchyRealA to) = AddType (Complex t) (NegType (CauchyRealA to))
type SubType (CauchyRealA to) (Complex t) #
Instance details Defined in AERN2.Real.Arithmetic type SubType (CauchyRealA to) (Complex t) = AddType (CauchyRealA to) (NegType (Complex t))
type SqrtType (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary type SqrtType (SequenceA to a) = SequenceA to (SqrtType a)
type ExpType (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary type ExpType (SequenceA to a) = SequenceA to (ExpType a)
type LogType (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary type LogType (SequenceA to a) = SequenceA to (LogType a)
type SinCosType (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Elementary type SinCosType (SequenceA to a) = SequenceA to (SinCosType a)
type AbsType (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison type AbsType (SequenceA to a) = SequenceA to (AbsType a)
type NegType (SequenceA to a) #
Instance details Defined in AERN2.Sequence.Comparison type NegType (SequenceA to a) = SequenceA to (NegType a)
type DivType (SequenceA to a) Dyadic #
Instance details Defined in AERN2.Sequence.Field type DivType (SequenceA to a) Dyadic = SequenceA to (DivType a Dyadic)
type DivType (SequenceA to a) Rational #
Instance details Defined in AERN2.Sequence.Field type DivType (SequenceA to a) Rational = SequenceA to (DivType a Rational)
type DivType (SequenceA to a) Int #
Instance details Defined in AERN2.Sequence.Field type DivType (SequenceA to a) Int = SequenceA to (DivType a Int)
type DivType (SequenceA to a) Integer #
Instance details Defined in AERN2.Sequence.Field type DivType (SequenceA to a) Integer = SequenceA to (DivType a Integer)
type DivTypeNoCN (SequenceA to a) Dyadic #
Instance details Defined in AERN2.Sequence.Field type DivTypeNoCN (SequenceA to a) Dyadic = SequenceA to (DivTypeNoCN a Dyadic)
type DivTypeNoCN (SequenceA to a) Rational #
Instance details Defined in AERN2.Sequence.Field type DivTypeNoCN (SequenceA to a) Rational = SequenceA to (DivTypeNoCN a Rational)
type DivTypeNoCN (SequenceA to a) Int #
Instance details Defined in AERN2.Sequence.Field type DivTypeNoCN (SequenceA to a) Int = SequenceA to (DivTypeNoCN a Int)
type DivTypeNoCN (SequenceA to a) Integer #
Instance details Defined in AERN2.Sequence.Field type DivTypeNoCN (SequenceA to a) Integer = SequenceA to (DivTypeNoCN a Integer)
type MulType (SequenceA to a) Dyadic #
Instance details Defined in AERN2.Sequence.Ring type MulType (SequenceA to a) Dyadic = SequenceA to (MulType a Dyadic)
type MulType (SequenceA to a) Rational #
Instance details Defined in AERN2.Sequence.Ring type MulType (SequenceA to a) Rational = SequenceA to (MulType a Rational)
type MulType (SequenceA to a) Int #
Instance details Defined in AERN2.Sequence.Ring type MulType (SequenceA to a) Int = SequenceA to (MulType a Int)
type MulType (SequenceA to a) Integer #
Instance details Defined in AERN2.Sequence.Ring type MulType (SequenceA to a) Integer = SequenceA to (MulType a Integer)
type PowType (SequenceA to a) Rational #
Instance details Defined in AERN2.Sequence.Elementary type PowType (SequenceA to a) Rational = SequenceA to (PowType a Rational)
type PowType (SequenceA to a) Dyadic #
Instance details Defined in AERN2.Sequence.Elementary type PowType (SequenceA to a) Dyadic = SequenceA to (PowType a Dyadic)
type PowType (SequenceA to a) Int #
Instance details Defined in AERN2.Sequence.Elementary type PowType (SequenceA to a) Int = SequenceA to (PowType a Int)
type PowType (SequenceA to a) Integer #
Instance details Defined in AERN2.Sequence.Elementary type PowType (SequenceA to a) Integer = SequenceA to (PowType a Integer)
type PowTypeNoCN (SequenceA to a) Rational #
Instance details Defined in AERN2.Sequence.Elementary type PowTypeNoCN (SequenceA to a) Rational = SequenceA to (PowTypeNoCN a Rational)
type PowTypeNoCN (SequenceA to a) Dyadic #
Instance details Defined in AERN2.Sequence.Elementary type PowTypeNoCN (SequenceA to a) Dyadic = SequenceA to (PowTypeNoCN a Dyadic)
type PowTypeNoCN (SequenceA to a) Int #
Instance details Defined in AERN2.Sequence.Elementary type PowTypeNoCN (SequenceA to a) Int = SequenceA to (PowTypeNoCN a Int)
type PowTypeNoCN (SequenceA to a) Integer #
Instance details Defined in AERN2.Sequence.Elementary type PowTypeNoCN (SequenceA to a) Integer = SequenceA to (PowTypeNoCN a Integer)
type AddType (SequenceA to a) Dyadic #
Instance details Defined in AERN2.Sequence.Ring type AddType (SequenceA to a) Dyadic = SequenceA to (AddType a Dyadic)
type AddType (SequenceA to a) Rational #
Instance details Defined in AERN2.Sequence.Ring type AddType (SequenceA to a) Rational = SequenceA to (AddType a Rational)
type AddType (SequenceA to a) Int #
Instance details Defined in AERN2.Sequence.Ring type AddType (SequenceA to a) Int = SequenceA to (AddType a Int)
type AddType (SequenceA to a) Integer #
Instance details Defined in AERN2.Sequence.Ring type AddType (SequenceA to a) Integer = SequenceA to (AddType a Integer)
type SubType (SequenceA to a) Dyadic #
Instance details Defined in AERN2.Sequence.Ring type SubType (SequenceA to a) Dyadic = SequenceA to (SubType a Dyadic)
type SubType (SequenceA to a) Rational #
Instance details Defined in AERN2.Sequence.Ring type SubType (SequenceA to a) Rational = SequenceA to (SubType a Rational)
type SubType (SequenceA to a) Int #
Instance details Defined in AERN2.Sequence.Ring type SubType (SequenceA to a) Int = SequenceA to (SubType a Int)
type SubType (SequenceA to a) Integer #
Instance details Defined in AERN2.Sequence.Ring type SubType (SequenceA to a) Integer = SequenceA to (SubType a Integer)
type MinMaxType (SequenceA to a) Dyadic #
Instance details Defined in AERN2.Sequence.Comparison type MinMaxType (SequenceA to a) Dyadic = SequenceA to (MinMaxType a Dyadic)
type MinMaxType (SequenceA to a) Rational #
Instance details Defined in AERN2.Sequence.Comparison type MinMaxType (SequenceA to a) Rational = SequenceA to (MinMaxType a Rational)
type MinMaxType (SequenceA to a) Int #
Instance details Defined in AERN2.Sequence.Comparison type MinMaxType (SequenceA to a) Int = SequenceA to (MinMaxType a Int)
type MinMaxType (SequenceA to a) Integer #
Instance details Defined in AERN2.Sequence.Comparison type MinMaxType (SequenceA to a) Integer = SequenceA to (MinMaxType a Integer)
type EqCompareType (SequenceA to a) Dyadic #
Instance details Defined in AERN2.Sequence.Comparison type EqCompareType (SequenceA to a) Dyadic = SequenceA to (EqCompareType a Dyadic)
type EqCompareType (SequenceA to a) Rational #
Instance details Defined in AERN2.Sequence.Comparison type EqCompareType (SequenceA to a) Rational = SequenceA to (EqCompareType a Rational)
type EqCompareType (SequenceA to a) Int #
Instance details Defined in AERN2.Sequence.Comparison type EqCompareType (SequenceA to a) Int = SequenceA to (EqCompareType a Int)
type EqCompareType (SequenceA to a) Integer #
Instance details Defined in AERN2.Sequence.Comparison type EqCompareType (SequenceA to a) Integer = SequenceA to (EqCompareType a Integer)
type OrderCompareType (SequenceA to a) Dyadic #
Instance details Defined in AERN2.Sequence.Comparison type OrderCompareType (SequenceA to a) Dyadic = SequenceA to (OrderCompareType a Dyadic)
type OrderCompareType (SequenceA to a) Rational #
Instance details Defined in AERN2.Sequence.Comparison type OrderCompareType (SequenceA to a) Rational = SequenceA to (OrderCompareType a Rational)
type OrderCompareType (SequenceA to a) Int #
Instance details Defined in AERN2.Sequence.Comparison type OrderCompareType (SequenceA to a) Int = SequenceA to (OrderCompareType a Int)
type OrderCompareType (SequenceA to a) Integer #
Instance details Defined in AERN2.Sequence.Comparison type OrderCompareType (SequenceA to a) Integer = SequenceA to (OrderCompareType a Integer)
type DivType (CollectErrors es a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Field type DivType (CollectErrors es a) (SequenceA to b) = EnsureCE es (DivType a (SequenceA to b))
type DivType (SequenceA to a) (CollectErrors es b) #
Instance details Defined in AERN2.Sequence.Field type DivType (SequenceA to a) (CollectErrors es b) = EnsureCE es (DivType (SequenceA to a) b)
type DivType (SequenceA to a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Field type DivType (SequenceA to a) (SequenceA to b) = SequenceA to (DivType a b)
type DivTypeNoCN (CollectErrors es a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Field type DivTypeNoCN (CollectErrors es a) (SequenceA to b) = EnsureCE es (DivTypeNoCN a (SequenceA to b))
type DivTypeNoCN (SequenceA to a) (CollectErrors es b) #
Instance details Defined in AERN2.Sequence.Field type DivTypeNoCN (SequenceA to a) (CollectErrors es b) = EnsureCE es (DivTypeNoCN (SequenceA to a) b)
type DivTypeNoCN (SequenceA to a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Field type DivTypeNoCN (SequenceA to a) (SequenceA to b) = SequenceA to (DivTypeNoCN a b)
type MulType (CollectErrors es a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring type MulType (CollectErrors es a) (SequenceA to b) = EnsureCE es (MulType a (SequenceA to b))
type MulType (SequenceA to a) (CollectErrors es b) #
Instance details Defined in AERN2.Sequence.Ring type MulType (SequenceA to a) (CollectErrors es b) = EnsureCE es (MulType (SequenceA to a) b)
type MulType (SequenceA to a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring type MulType (SequenceA to a) (SequenceA to b) = SequenceA to (MulType a b)
type PowType (CollectErrors es a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Elementary type PowType (CollectErrors es a) (SequenceA to b) = EnsureCE es (PowType a (SequenceA to b))
type PowType (SequenceA to a) (CollectErrors es b) #
Instance details Defined in AERN2.Sequence.Elementary type PowType (SequenceA to a) (CollectErrors es b) = EnsureCE es (PowType (SequenceA to a) b)
type PowType (SequenceA to a) (SequenceA to e) #
Instance details Defined in AERN2.Sequence.Elementary type PowType (SequenceA to a) (SequenceA to e) = SequenceA to (PowType a e)
type PowTypeNoCN (CollectErrors es a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Elementary type PowTypeNoCN (CollectErrors es a) (SequenceA to b) = EnsureCE es (PowTypeNoCN a (SequenceA to b))
type PowTypeNoCN (SequenceA to a) (CollectErrors es b) #
Instance details Defined in AERN2.Sequence.Elementary type PowTypeNoCN (SequenceA to a) (CollectErrors es b) = EnsureCE es (PowTypeNoCN (SequenceA to a) b)
type PowTypeNoCN (SequenceA to a) (SequenceA to e) #
Instance details Defined in AERN2.Sequence.Elementary type PowTypeNoCN (SequenceA to a) (SequenceA to e) = SequenceA to (PowTypeNoCN a e)
type AddType (CollectErrors es a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring type AddType (CollectErrors es a) (SequenceA to b) = EnsureCE es (AddType a (SequenceA to b))
type AddType (SequenceA to a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring type AddType (SequenceA to a) (SequenceA to b) = SequenceA to (AddType a b)
type AddType (SequenceA to a) (CollectErrors es b) #
Instance details Defined in AERN2.Sequence.Ring type AddType (SequenceA to a) (CollectErrors es b) = EnsureCE es (AddType (SequenceA to a) b)
type SubType (CollectErrors es a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring type SubType (CollectErrors es a) (SequenceA to b) = EnsureCE es (SubType a (SequenceA to b))
type SubType (SequenceA to a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Ring type SubType (SequenceA to a) (SequenceA to b) = SequenceA to (SubType a b)
type SubType (SequenceA to a) (CollectErrors es b) #
Instance details Defined in AERN2.Sequence.Ring type SubType (SequenceA to a) (CollectErrors es b) = EnsureCE es (SubType (SequenceA to a) b)
type MinMaxType (CollectErrors es a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison type MinMaxType (CollectErrors es a) (SequenceA to b) = EnsureCE es (MinMaxType a (SequenceA to b))
type MinMaxType (SequenceA to a) (CollectErrors es b) #
Instance details Defined in AERN2.Sequence.Comparison type MinMaxType (SequenceA to a) (CollectErrors es b) = EnsureCE es (MinMaxType (SequenceA to a) b)
type MinMaxType (SequenceA to a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison type MinMaxType (SequenceA to a) (SequenceA to b) = SequenceA to (MinMaxType a b)
type EqCompareType (CollectErrors es a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison type EqCompareType (CollectErrors es a) (SequenceA to b) = EnsureCE es (EqCompareType a (SequenceA to b))
type EqCompareType (SequenceA to a) (CollectErrors es b) #
Instance details Defined in AERN2.Sequence.Comparison type EqCompareType (SequenceA to a) (CollectErrors es b) = EnsureCE es (EqCompareType (SequenceA to a) b)
type EqCompareType (SequenceA to a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison type EqCompareType (SequenceA to a) (SequenceA to b) = SequenceA to (EqCompareType a b)
type OrderCompareType (CollectErrors es a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison type OrderCompareType (CollectErrors es a) (SequenceA to b) = EnsureCE es (OrderCompareType a (SequenceA to b))
type OrderCompareType (SequenceA to a) (CollectErrors es b) #
Instance details Defined in AERN2.Sequence.Comparison type OrderCompareType (SequenceA to a) (CollectErrors es b) = EnsureCE es (OrderCompareType (SequenceA to a) b)
type OrderCompareType (SequenceA to a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison type OrderCompareType (SequenceA to a) (SequenceA to b) = SequenceA to (OrderCompareType a b)
type AndOrType (SequenceA to a) (SequenceA to b) #
Instance details Defined in AERN2.Sequence.Comparison type AndOrType (SequenceA to a) (SequenceA to b) = SequenceA to (AndOrType a b)
type IfThenElseType (SequenceA to b) (SequenceA to t) #
Instance details Defined in AERN2.Sequence.Branching type IfThenElseType (SequenceA to b) (SequenceA to t) = SequenceA to (IfThenElseType b t)

pSeq :: a -> SequenceP a #

class (Show a, Show (EnsureNoCN a), Show (EnsureCN a), HasAccuracy a, CanAdjustToAccuracySG a, CanEnsureCN a, CanEnsureCN (EnsureCN a), HasAccuracy (EnsureNoCN a), CanIntersectCNSameType a) => SuitableForSeq a #

Instances

SuitableForSeq Bool #
Instance details Defined in AERN2.Sequence.Type
SuitableForSeq MPBall #
Instance details Defined in AERN2.Sequence.Type
SuitableForSeq t => SuitableForSeq (Maybe t) #
Instance details Defined in AERN2.Sequence.Type
SuitableForSeq (CN Bool) #
Instance details Defined in AERN2.Sequence.Type
SuitableForSeq (CN MPBall) #
Instance details Defined in AERN2.Sequence.Type

type SequenceA to a = QA to (SequenceP a) #

type Sequence a = SequenceA (->) a #

newSeq :: (QAArrow to, SuitableForSeq a) => a -> String -> [AnyProtocolQA to] -> ((Maybe (QAId to), Maybe (QAId to)) -> AccuracySG `to` a) -> SequenceA to a #

newSeqSimple :: (QAArrow to, SuitableForSeq a) => a -> ((Maybe (QAId to), Maybe (QAId to)) -> AccuracySG `to` a) -> SequenceA to a #

seqName :: SequenceA to a -> String #

seqId :: SequenceA to a -> Maybe (QAId to) #

seqSources :: SequenceA to a -> [QAId to] #

seqRename :: (String -> String) -> SequenceA to a -> SequenceA to a #

seqWithAccuracy :: QAArrow to => SequenceA to a -> Maybe (QAId to) -> AccuracySG `to` a #

Get an approximation of the limit with at least the specified accuracy. (A specialisation of qaMakeQuery for Cauchy sequences.)

(?) :: QAArrow to => QA to p -> Q p `to` A p infix 1 #

An infix synonym of qaMakeQuery with no source

seqWithAccuracyA :: QAArrow to => Maybe (QAId to) -> (SequenceA to a, AccuracySG) `to` a #

seqsWithAccuracyA :: QAArrow to => Maybe (QAId to) -> ([SequenceA to a], AccuracySG) `to` [a] #

(-:-) :: (QAArrow to, QAProtocolCacheable p) => QA to p `to` QA to p infix 0 #

An infix synonym of qaRegister

(-:-||) :: (QAArrow to, QAProtocolCacheable p) => QA to p `to` QA to p infix 0 #

An infix synonym of qaRegister

(-:-|) :: (QAArrow to, QAProtocolCacheable p) => QA to p `to` QA to p infix 0 #

An infix synonym of qaRegister

data SequenceAtAccuracy a #

SequenceAtAccuracy exists only so that we can QuickCheck that Sequence satisfies properties whose statement relies on an instance of HasEqCertainly. Sequence is not an instance but SequenceAtAccuracy is.

Constructors

SequenceAtAccuracy (Sequence a) AccuracySG

Instances

Arbitrary CauchyRealAtAccuracy #
Instance details Defined in AERN2.Real.Tests Methods arbitrary :: Gen CauchyRealAtAccuracy # shrink :: CauchyRealAtAccuracy -> [CauchyRealAtAccuracy] #
Show a => Show (SequenceAtAccuracy a) #
Instance details Defined in AERN2.Sequence.Comparison Methods showsPrec :: Int -> SequenceAtAccuracy a -> ShowS # show :: SequenceAtAccuracy a -> String # showList :: [SequenceAtAccuracy a] -> ShowS #
(HasEqAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (EqCompareType a b)) => HasEqAsymmetric (SequenceAtAccuracy a) (SequenceAtAccuracy b) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type EqCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) :: * # Methods equalTo :: SequenceAtAccuracy a -> SequenceAtAccuracy b -> EqCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) # notEqualTo :: SequenceAtAccuracy a -> SequenceAtAccuracy b -> EqCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) #
(HasOrderAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (OrderCompareType a b)) => HasOrderAsymmetric (SequenceAtAccuracy a) (SequenceAtAccuracy b) #
Instance details Defined in AERN2.Sequence.Comparison Associated Types type OrderCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) :: * # Methods lessThan :: SequenceAtAccuracy a -> SequenceAtAccuracy b -> OrderCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) # greaterThan :: SequenceAtAccuracy a -> SequenceAtAccuracy b -> OrderCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) # leq :: SequenceAtAccuracy a -> SequenceAtAccuracy b -> OrderCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) # geq :: SequenceAtAccuracy a -> SequenceAtAccuracy b -> OrderCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) #
type EqCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) #
Instance details Defined in AERN2.Sequence.Comparison type EqCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) = EqCompareType a b
type OrderCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) #
Instance details Defined in AERN2.Sequence.Comparison type OrderCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) = OrderCompareType a b

convergentList2SequenceA :: (QAArrow to, SuitableForSeq a) => String -> [a] -> SequenceA to a #

seqByPrecision2SequenceA :: (QAArrow to, SuitableForSeq a) => String -> (Precision -> a) -> SequenceA to a #

selecting one of several staged computations

pick :: QAArrow to => Maybe (QAId to) -> [SequenceA to (Maybe a)] `to` a #

auxiliary functions for making new sequence operations

unaryOp :: (QAArrow to, SuitableForSeq a, SuitableForSeq b) => String -> (a -> b) -> (Maybe (QAId to) -> SequenceA to a -> AccuracySG `to` (AccuracySG, Maybe a)) -> SequenceA to a -> SequenceA to b #

binaryOp :: (QAArrow to, SuitableForSeq a, SuitableForSeq b, SuitableForSeq c) => String -> (a -> b -> c) -> (Maybe (QAId to) -> SequenceA to a -> SequenceA to b -> AccuracySG `to` ((AccuracySG, Maybe a), (AccuracySG, Maybe b))) -> SequenceA to a -> SequenceA to b -> SequenceA to c #

binaryOpWithPureArg :: (QAArrow to, SuitableForSeq a, SuitableForSeq b) => String -> (a -> t -> b) -> (Maybe (QAId to) -> SequenceA to a -> t -> AccuracySG `to` (AccuracySG, Maybe a)) -> SequenceA to a -> t -> SequenceA to b #

getSeqFnNormLog :: (QAArrow to, CanEnsureCN v, HasNorm (EnsureNoCN v)) => Maybe (QAId to) -> SequenceA to a -> (a -> v) -> AccuracySG `to` (Maybe Integer, a) #

getInitQ1FromSimple #

Arguments

:: Arrow to
=> (AccuracySG `to` q)
-> Maybe (QAId to)	my id
-> r1
-> AccuracySG `to` (q, Maybe a)

getInitQ1TFromSimple #

Arguments

:: Arrow to
=> (AccuracySG `to` q)
-> Maybe (QAId to)	my id
-> r1
-> t
-> AccuracySG `to` (q, Maybe a)

getInitQ1Q2FromSimple #

Arguments

:: Arrow to
=> (AccuracySG `to` (q, q))
-> Maybe (QAId to)	my id
-> r1
-> r2
-> AccuracySG `to` ((q, Maybe a), (q, Maybe b))