aern2-real-0.2.4.2: Real numbers as sequences of MPBalls
Copyright(c) Michal Konecny
LicenseBSD3
Maintainermikkonecny@gmail.com
Stabilityexperimental
Portabilityportable
Safe HaskellNone
LanguageHaskell2010

AERN2.Real.Type

Description

The type of constructive real numbers using convergent sequences of intervals.

Synopsis

Documentation

newtype CSequence t Source #

Constructors

CSequence [CN t] 

Instances

Instances details
Floating CReal Source # 
Instance details

Defined in AERN2.Real.Elementary

Fractional CReal Source # 
Instance details

Defined in AERN2.Real.Field

Num CReal Source # 
Instance details

Defined in AERN2.Real.Field

Arbitrary CReal Source # 
Instance details

Defined in AERN2.Real.Tests

Methods

arbitrary :: Gen CReal #

shrink :: CReal -> [CReal] #

CanSqrt CReal Source # 
Instance details

Defined in AERN2.Real.Elementary

Associated Types

type SqrtType CReal #

Methods

sqrt :: CReal -> SqrtType CReal #

CanExp CReal Source # 
Instance details

Defined in AERN2.Real.Elementary

Associated Types

type ExpType CReal #

Methods

exp :: CReal -> ExpType CReal #

CanLog CReal Source # 
Instance details

Defined in AERN2.Real.Elementary

Associated Types

type LogType CReal #

Methods

log :: CReal -> LogType CReal #

CanSinCos CReal Source # 
Instance details

Defined in AERN2.Real.Elementary

Associated Types

type SinCosType CReal #

Field CReal Source # 
Instance details

Defined in AERN2.Real.Field

OrderedField CReal Source # 
Instance details

Defined in AERN2.Real.Field

Ring CReal Source # 
Instance details

Defined in AERN2.Real.Field

OrderedRing CReal Source # 
Instance details

Defined in AERN2.Real.Field

CanSelect CKleenean Source # 
Instance details

Defined in AERN2.Real.CKleenean

Associated Types

type SelectType CKleenean Source #

HasLimits Int CReal Source # 
Instance details

Defined in AERN2.Real.Limit

Associated Types

type LimitType Int CReal #

Methods

limit :: (Int -> CReal) -> LimitType Int CReal #

HasLimits Integer CReal Source # 
Instance details

Defined in AERN2.Real.Limit

Associated Types

type LimitType Integer CReal #

HasLimits Rational CReal Source # 
Instance details

Defined in AERN2.Real.Limit

Associated Types

type LimitType Rational CReal #

ConvertibleExactly Int CReal Source # 
Instance details

Defined in AERN2.Real.Type

ConvertibleExactly Integer CReal Source # 
Instance details

Defined in AERN2.Real.Type

ConvertibleExactly Rational CReal Source # 
Instance details

Defined in AERN2.Real.Type

ConvertibleExactly t Kleenean => ConvertibleExactly t CKleenean Source # 
Instance details

Defined in AERN2.Real.CKleenean

ConvertibleExactly Dyadic CReal Source # 
Instance details

Defined in AERN2.Real.Type

ConvertibleExactly CReal CReal Source # 
Instance details

Defined in AERN2.Real.Type

ConvertibleWithPrecision CReal (CN MPBall) Source # 
Instance details

Defined in AERN2.Real.Type

CanTakeErrors NumErrors (CSequence t) Source # 
Instance details

Defined in AERN2.Real.Type

(CanPow Int e, HasOrderCertainly e Integer, CanTestInteger e) => CanPow Int (CSequence e) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type PowType Int (CSequence e) #

Methods

pow :: Int -> CSequence e -> PowType Int (CSequence e) #

(CanPow Integer e, HasOrderCertainly e Integer, CanTestInteger e) => CanPow Integer (CSequence e) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type PowType Integer (CSequence e) #

(CanPow Rational e, HasOrderCertainly e Integer, CanTestInteger e) => CanPow Rational (CSequence e) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type PowType Rational (CSequence e) #

(CanDiv Int a, CanTestZero a) => CanDiv Int (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType Int (CSequence a) #

Methods

divide :: Int -> CSequence a -> DivType Int (CSequence a) #

(CanDiv Integer a, CanTestZero a) => CanDiv Integer (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType Integer (CSequence a) #

(CanDiv Rational a, CanTestZero a) => CanDiv Rational (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType Rational (CSequence a) #

(CanDiv MPBall b, CanTestZero b) => CanDiv MPBall (CSequence b) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType MPBall (CSequence b) #

(CanDiv Dyadic a, CanTestZero a) => CanDiv Dyadic (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType Dyadic (CSequence a) #

(CanMulAsymmetric Int a, CanGiveUpIfVeryInaccurate (MulType Int a)) => CanMulAsymmetric Int (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType Int (CSequence a) #

Methods

mul :: Int -> CSequence a -> MulType Int (CSequence a) #

(CanMulAsymmetric Integer a, CanGiveUpIfVeryInaccurate (MulType Integer a)) => CanMulAsymmetric Integer (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType Integer (CSequence a) #

(CanMulAsymmetric Rational a, CanGiveUpIfVeryInaccurate (MulType Rational a)) => CanMulAsymmetric Rational (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType Rational (CSequence a) #

CanMulAsymmetric MPBall b => CanMulAsymmetric MPBall (CSequence b) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType MPBall (CSequence b) #

Methods

mul :: MPBall -> CSequence b -> MulType MPBall (CSequence b) #

(CanMulAsymmetric Dyadic a, CanGiveUpIfVeryInaccurate (MulType Dyadic a)) => CanMulAsymmetric Dyadic (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType Dyadic (CSequence a) #

Methods

mul :: Dyadic -> CSequence a -> MulType Dyadic (CSequence a) #

CanAddAsymmetric Int a => CanAddAsymmetric Int (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType Int (CSequence a) #

Methods

add :: Int -> CSequence a -> AddType Int (CSequence a) #

CanAddAsymmetric Integer a => CanAddAsymmetric Integer (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType Integer (CSequence a) #

CanAddAsymmetric Rational a => CanAddAsymmetric Rational (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType Rational (CSequence a) #

CanAddAsymmetric MPBall b => CanAddAsymmetric MPBall (CSequence b) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType MPBall (CSequence b) #

Methods

add :: MPBall -> CSequence b -> AddType MPBall (CSequence b) #

CanAddAsymmetric Dyadic a => CanAddAsymmetric Dyadic (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType Dyadic (CSequence a) #

Methods

add :: Dyadic -> CSequence a -> AddType Dyadic (CSequence a) #

CanSub Int a => CanSub Int (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType Int (CSequence a) #

Methods

sub :: Int -> CSequence a -> SubType Int (CSequence a) #

CanSub Integer a => CanSub Integer (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType Integer (CSequence a) #

CanSub Rational a => CanSub Rational (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType Rational (CSequence a) #

CanSub MPBall b => CanSub MPBall (CSequence b) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType MPBall (CSequence b) #

Methods

sub :: MPBall -> CSequence b -> SubType MPBall (CSequence b) #

CanSub Dyadic a => CanSub Dyadic (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType Dyadic (CSequence a) #

Methods

sub :: Dyadic -> CSequence a -> SubType Dyadic (CSequence a) #

CanMinMaxAsymmetric Int a => CanMinMaxAsymmetric Int (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType Int (CSequence a) #

CanMinMaxAsymmetric Integer a => CanMinMaxAsymmetric Integer (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType Integer (CSequence a) #

CanMinMaxAsymmetric Rational a => CanMinMaxAsymmetric Rational (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType Rational (CSequence a) #

CanMinMaxAsymmetric MPBall a => CanMinMaxAsymmetric MPBall (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType MPBall (CSequence a) #

CanMinMaxAsymmetric Dyadic a => CanMinMaxAsymmetric Dyadic (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType Dyadic (CSequence a) #

(HasEqAsymmetric Int a, IsBool (CSequence (EqCompareType Int a))) => HasEqAsymmetric Int (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType Int (CSequence a) #

(HasEqAsymmetric Integer a, IsBool (CSequence (EqCompareType Integer a))) => HasEqAsymmetric Integer (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType Integer (CSequence a) #

(HasEqAsymmetric Rational a, IsBool (CSequence (EqCompareType Rational a))) => HasEqAsymmetric Rational (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType Rational (CSequence a) #

HasEqAsymmetric MPBall b => HasEqAsymmetric MPBall (CSequence b) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType MPBall (CSequence b) #

(HasEqAsymmetric Dyadic a, IsBool (CSequence (EqCompareType Dyadic a))) => HasEqAsymmetric Dyadic (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType Dyadic (CSequence a) #

(HasOrderAsymmetric Int a, IsBool (CSequence (OrderCompareType Int a))) => HasOrderAsymmetric Int (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType Int (CSequence a) #

(HasOrderAsymmetric Integer a, IsBool (CSequence (OrderCompareType Integer a))) => HasOrderAsymmetric Integer (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType Integer (CSequence a) #

(HasOrderAsymmetric Rational a, IsBool (CSequence (OrderCompareType Rational a))) => HasOrderAsymmetric Rational (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType Rational (CSequence a) #

HasOrderAsymmetric MPBall b => HasOrderAsymmetric MPBall (CSequence b) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType MPBall (CSequence b) #

(HasOrderAsymmetric Dyadic a, IsBool (CSequence (OrderCompareType Dyadic a))) => HasOrderAsymmetric Dyadic (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType Dyadic (CSequence a) #

CanUnionCNSameType t => HasIfThenElse CKleenean (CSequence t) Source # 
Instance details

Defined in AERN2.Real.CKleenean

Associated Types

type IfThenElseType CKleenean (CSequence t) #

(HasCReals t, HasIntegers t) => ConvertibleExactly CReal (Complex t) Source # 
Instance details

Defined in AERN2.Complex

HasLimits Rational (CReal -> CReal) Source # 
Instance details

Defined in AERN2.Real.Limit

Associated Types

type LimitType Rational (CReal -> CReal) #

Methods

limit :: (Rational -> CReal -> CReal) -> LimitType Rational (CReal -> CReal) #

HasEqCertainly a a => Eq (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Methods

(==) :: CSequence a -> CSequence a -> Bool #

(/=) :: CSequence a -> CSequence a -> Bool #

(HasEqCertainly a a, HasOrderCertainly a a) => Ord (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Show t => Show (CSequence t) Source # 
Instance details

Defined in AERN2.Real.Type

CanClearPotentialErrors (CSequence t) Source # 
Instance details

Defined in AERN2.Real.Type

CanAbs t1 => CanAbs (CSequence t1) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type AbsType (CSequence t1) #

Methods

abs :: CSequence t1 -> AbsType (CSequence t1) #

CanNeg t => CanNeg (CSequence t) Source # 
Instance details

Defined in AERN2.Real.CKleenean

Associated Types

type NegType (CSequence t) #

Methods

negate :: CSequence t -> NegType (CSequence t) #

(CanPow b Integer, HasOrderCertainly b Integer, HasEqCertainly b Integer) => CanPow (CSequence b) Integer Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type PowType (CSequence b) Integer #

(CanPow b Int, HasOrderCertainly b Integer, HasEqCertainly b Integer) => CanPow (CSequence b) Int Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type PowType (CSequence b) Int #

Methods

pow :: CSequence b -> Int -> PowType (CSequence b) Int #

(CanPow b Rational, HasOrderCertainly b Integer, HasEqCertainly b Integer) => CanPow (CSequence b) Rational Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type PowType (CSequence b) Rational #

CanDiv b MPBall => CanDiv (CSequence b) MPBall Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType (CSequence b) MPBall #

CanDiv a Integer => CanDiv (CSequence a) Integer Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType (CSequence a) Integer #

CanDiv a Int => CanDiv (CSequence a) Int Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType (CSequence a) Int #

Methods

divide :: CSequence a -> Int -> DivType (CSequence a) Int #

CanDiv a Rational => CanDiv (CSequence a) Rational Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType (CSequence a) Rational #

CanDiv a Dyadic => CanDiv (CSequence a) Dyadic Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType (CSequence a) Dyadic #

CanMulAsymmetric b MPBall => CanMulAsymmetric (CSequence b) MPBall Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType (CSequence b) MPBall #

Methods

mul :: CSequence b -> MPBall -> MulType (CSequence b) MPBall #

(CanMulAsymmetric a Integer, CanGiveUpIfVeryInaccurate (MulType a Integer)) => CanMulAsymmetric (CSequence a) Integer Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType (CSequence a) Integer #

(CanMulAsymmetric a Int, CanGiveUpIfVeryInaccurate (MulType a Int)) => CanMulAsymmetric (CSequence a) Int Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType (CSequence a) Int #

Methods

mul :: CSequence a -> Int -> MulType (CSequence a) Int #

(CanMulAsymmetric a Rational, CanGiveUpIfVeryInaccurate (MulType a Rational)) => CanMulAsymmetric (CSequence a) Rational Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType (CSequence a) Rational #

(CanMulAsymmetric a Dyadic, CanGiveUpIfVeryInaccurate (MulType a Dyadic)) => CanMulAsymmetric (CSequence a) Dyadic Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType (CSequence a) Dyadic #

Methods

mul :: CSequence a -> Dyadic -> MulType (CSequence a) Dyadic #

CanAddAsymmetric b MPBall => CanAddAsymmetric (CSequence b) MPBall Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType (CSequence b) MPBall #

Methods

add :: CSequence b -> MPBall -> AddType (CSequence b) MPBall #

CanAddAsymmetric a Integer => CanAddAsymmetric (CSequence a) Integer Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType (CSequence a) Integer #

CanAddAsymmetric a Int => CanAddAsymmetric (CSequence a) Int Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType (CSequence a) Int #

Methods

add :: CSequence a -> Int -> AddType (CSequence a) Int #

CanAddAsymmetric a Rational => CanAddAsymmetric (CSequence a) Rational Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType (CSequence a) Rational #

CanAddAsymmetric a Dyadic => CanAddAsymmetric (CSequence a) Dyadic Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType (CSequence a) Dyadic #

Methods

add :: CSequence a -> Dyadic -> AddType (CSequence a) Dyadic #

CanSub b MPBall => CanSub (CSequence b) MPBall Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType (CSequence b) MPBall #

Methods

sub :: CSequence b -> MPBall -> SubType (CSequence b) MPBall #

CanSub a Integer => CanSub (CSequence a) Integer Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType (CSequence a) Integer #

CanSub a Int => CanSub (CSequence a) Int Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType (CSequence a) Int #

Methods

sub :: CSequence a -> Int -> SubType (CSequence a) Int #

CanSub a Rational => CanSub (CSequence a) Rational Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType (CSequence a) Rational #

CanSub a Dyadic => CanSub (CSequence a) Dyadic Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType (CSequence a) Dyadic #

Methods

sub :: CSequence a -> Dyadic -> SubType (CSequence a) Dyadic #

CanMinMaxAsymmetric a MPBall => CanMinMaxAsymmetric (CSequence a) MPBall Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) MPBall #

CanMinMaxAsymmetric a Integer => CanMinMaxAsymmetric (CSequence a) Integer Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) Integer #

CanMinMaxAsymmetric a Int => CanMinMaxAsymmetric (CSequence a) Int Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) Int #

CanMinMaxAsymmetric a Rational => CanMinMaxAsymmetric (CSequence a) Rational Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) Rational #

CanMinMaxAsymmetric a Dyadic => CanMinMaxAsymmetric (CSequence a) Dyadic Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) Dyadic #

HasEqAsymmetric a MPBall => HasEqAsymmetric (CSequence a) MPBall Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) MPBall #

(HasEqAsymmetric a Integer, IsBool (CSequence (EqCompareType a Integer))) => HasEqAsymmetric (CSequence a) Integer Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) Integer #

(HasEqAsymmetric a Int, IsBool (CSequence (EqCompareType a Int))) => HasEqAsymmetric (CSequence a) Int Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) Int #

(HasEqAsymmetric a Rational, IsBool (CSequence (EqCompareType a Rational))) => HasEqAsymmetric (CSequence a) Rational Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) Rational #

(HasEqAsymmetric a Dyadic, IsBool (CSequence (EqCompareType a Dyadic))) => HasEqAsymmetric (CSequence a) Dyadic Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) Dyadic #

HasOrderAsymmetric a MPBall => HasOrderAsymmetric (CSequence a) MPBall Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) MPBall #

(HasOrderAsymmetric a Integer, IsBool (CSequence (OrderCompareType a Integer))) => HasOrderAsymmetric (CSequence a) Integer Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) Integer #

(HasOrderAsymmetric a Int, IsBool (CSequence (OrderCompareType a Int))) => HasOrderAsymmetric (CSequence a) Int Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) Int #

(HasOrderAsymmetric a Rational, IsBool (CSequence (OrderCompareType a Rational))) => HasOrderAsymmetric (CSequence a) Rational Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) Rational #

(HasOrderAsymmetric a Dyadic, IsBool (CSequence (OrderCompareType a Dyadic))) => HasOrderAsymmetric (CSequence a) Dyadic Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) Dyadic #

ConvertibleExactly (WithAnyPrec (CN MPBall)) CReal Source # 
Instance details

Defined in AERN2.Real.Type

CanExtractApproximation (CSequence t) Precision Source # 
Instance details

Defined in AERN2.Real.Type

HasAccuracy t => CanExtractApproximation (CSequence t) Accuracy Source # 
Instance details

Defined in AERN2.Real.Type

(CanPow b e, HasOrderCertainly b Integer, HasOrderCertainly e Integer, HasEqCertainly b Integer, CanTestInteger e) => CanPow (CSequence b) (CSequence e) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type PowType (CSequence b) (CSequence e) #

Methods

pow :: CSequence b -> CSequence e -> PowType (CSequence b) (CSequence e) #

(CanDiv Int a, CanTestZero a) => CanDiv (CN Int) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType (CN Int) (CSequence a) #

Methods

divide :: CN Int -> CSequence a -> DivType (CN Int) (CSequence a) #

(CanDiv Integer a, CanTestZero a) => CanDiv (CN Integer) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType (CN Integer) (CSequence a) #

(CanDiv Rational a, CanTestZero a) => CanDiv (CN Rational) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType (CN Rational) (CSequence a) #

(CanDiv MPBall b, CanTestZero b) => CanDiv (CN MPBall) (CSequence b) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType (CN MPBall) (CSequence b) #

Methods

divide :: CN MPBall -> CSequence b -> DivType (CN MPBall) (CSequence b) #

(CanDiv Dyadic a, CanTestZero a) => CanDiv (CN Dyadic) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType (CN Dyadic) (CSequence a) #

Methods

divide :: CN Dyadic -> CSequence a -> DivType (CN Dyadic) (CSequence a) #

(CanDiv t1 t2, CanTestZero t2) => CanDiv (CSequence t1) (CSequence t2) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType (CSequence t1) (CSequence t2) #

Methods

divide :: CSequence t1 -> CSequence t2 -> DivType (CSequence t1) (CSequence t2) #

CanDiv b MPBall => CanDiv (CSequence b) (CN MPBall) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType (CSequence b) (CN MPBall) #

Methods

divide :: CSequence b -> CN MPBall -> DivType (CSequence b) (CN MPBall) #

CanDiv a Integer => CanDiv (CSequence a) (CN Integer) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType (CSequence a) (CN Integer) #

CanDiv a Int => CanDiv (CSequence a) (CN Int) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType (CSequence a) (CN Int) #

Methods

divide :: CSequence a -> CN Int -> DivType (CSequence a) (CN Int) #

CanDiv a Rational => CanDiv (CSequence a) (CN Rational) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType (CSequence a) (CN Rational) #

CanDiv a Dyadic => CanDiv (CSequence a) (CN Dyadic) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type DivType (CSequence a) (CN Dyadic) #

Methods

divide :: CSequence a -> CN Dyadic -> DivType (CSequence a) (CN Dyadic) #

(CanMulAsymmetric Int a, CanGiveUpIfVeryInaccurate (MulType Int a)) => CanMulAsymmetric (CN Int) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType (CN Int) (CSequence a) #

Methods

mul :: CN Int -> CSequence a -> MulType (CN Int) (CSequence a) #

(CanMulAsymmetric Integer a, CanGiveUpIfVeryInaccurate (MulType Integer a)) => CanMulAsymmetric (CN Integer) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType (CN Integer) (CSequence a) #

Methods

mul :: CN Integer -> CSequence a -> MulType (CN Integer) (CSequence a) #

(CanMulAsymmetric Rational a, CanGiveUpIfVeryInaccurate (MulType Rational a)) => CanMulAsymmetric (CN Rational) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType (CN Rational) (CSequence a) #

(CanMulAsymmetric MPBall b, CanGiveUpIfVeryInaccurate (MulType MPBall b)) => CanMulAsymmetric (CN MPBall) (CSequence b) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType (CN MPBall) (CSequence b) #

Methods

mul :: CN MPBall -> CSequence b -> MulType (CN MPBall) (CSequence b) #

(CanMulAsymmetric Dyadic a, CanGiveUpIfVeryInaccurate (MulType Dyadic a)) => CanMulAsymmetric (CN Dyadic) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType (CN Dyadic) (CSequence a) #

Methods

mul :: CN Dyadic -> CSequence a -> MulType (CN Dyadic) (CSequence a) #

(CanMulAsymmetric t1 t2, CanGiveUpIfVeryInaccurate (MulType t1 t2)) => CanMulAsymmetric (CSequence t1) (CSequence t2) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType (CSequence t1) (CSequence t2) #

Methods

mul :: CSequence t1 -> CSequence t2 -> MulType (CSequence t1) (CSequence t2) #

(CanMulAsymmetric b MPBall, CanGiveUpIfVeryInaccurate (MulType b MPBall)) => CanMulAsymmetric (CSequence b) (CN MPBall) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType (CSequence b) (CN MPBall) #

Methods

mul :: CSequence b -> CN MPBall -> MulType (CSequence b) (CN MPBall) #

(CanMulAsymmetric a Integer, CanGiveUpIfVeryInaccurate (MulType a Integer)) => CanMulAsymmetric (CSequence a) (CN Integer) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType (CSequence a) (CN Integer) #

Methods

mul :: CSequence a -> CN Integer -> MulType (CSequence a) (CN Integer) #

(CanMulAsymmetric a Int, CanGiveUpIfVeryInaccurate (MulType a Int)) => CanMulAsymmetric (CSequence a) (CN Int) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType (CSequence a) (CN Int) #

Methods

mul :: CSequence a -> CN Int -> MulType (CSequence a) (CN Int) #

(CanMulAsymmetric a Rational, CanGiveUpIfVeryInaccurate (MulType a Rational)) => CanMulAsymmetric (CSequence a) (CN Rational) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType (CSequence a) (CN Rational) #

(CanMulAsymmetric a Dyadic, CanGiveUpIfVeryInaccurate (MulType a Dyadic)) => CanMulAsymmetric (CSequence a) (CN Dyadic) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type MulType (CSequence a) (CN Dyadic) #

Methods

mul :: CSequence a -> CN Dyadic -> MulType (CSequence a) (CN Dyadic) #

CanAddAsymmetric Int a => CanAddAsymmetric (CN Int) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType (CN Int) (CSequence a) #

Methods

add :: CN Int -> CSequence a -> AddType (CN Int) (CSequence a) #

CanAddAsymmetric Integer a => CanAddAsymmetric (CN Integer) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType (CN Integer) (CSequence a) #

Methods

add :: CN Integer -> CSequence a -> AddType (CN Integer) (CSequence a) #

CanAddAsymmetric Rational a => CanAddAsymmetric (CN Rational) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType (CN Rational) (CSequence a) #

CanAddAsymmetric MPBall b => CanAddAsymmetric (CN MPBall) (CSequence b) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType (CN MPBall) (CSequence b) #

Methods

add :: CN MPBall -> CSequence b -> AddType (CN MPBall) (CSequence b) #

CanAddAsymmetric Dyadic a => CanAddAsymmetric (CN Dyadic) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType (CN Dyadic) (CSequence a) #

Methods

add :: CN Dyadic -> CSequence a -> AddType (CN Dyadic) (CSequence a) #

CanAddAsymmetric t1 t2 => CanAddAsymmetric (CSequence t1) (CSequence t2) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType (CSequence t1) (CSequence t2) #

Methods

add :: CSequence t1 -> CSequence t2 -> AddType (CSequence t1) (CSequence t2) #

CanAddAsymmetric b MPBall => CanAddAsymmetric (CSequence b) (CN MPBall) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType (CSequence b) (CN MPBall) #

Methods

add :: CSequence b -> CN MPBall -> AddType (CSequence b) (CN MPBall) #

CanAddAsymmetric a Integer => CanAddAsymmetric (CSequence a) (CN Integer) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType (CSequence a) (CN Integer) #

Methods

add :: CSequence a -> CN Integer -> AddType (CSequence a) (CN Integer) #

CanAddAsymmetric a Int => CanAddAsymmetric (CSequence a) (CN Int) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType (CSequence a) (CN Int) #

Methods

add :: CSequence a -> CN Int -> AddType (CSequence a) (CN Int) #

CanAddAsymmetric a Rational => CanAddAsymmetric (CSequence a) (CN Rational) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType (CSequence a) (CN Rational) #

CanAddAsymmetric a Dyadic => CanAddAsymmetric (CSequence a) (CN Dyadic) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type AddType (CSequence a) (CN Dyadic) #

Methods

add :: CSequence a -> CN Dyadic -> AddType (CSequence a) (CN Dyadic) #

CanSub Int a => CanSub (CN Int) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType (CN Int) (CSequence a) #

Methods

sub :: CN Int -> CSequence a -> SubType (CN Int) (CSequence a) #

CanSub Integer a => CanSub (CN Integer) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType (CN Integer) (CSequence a) #

Methods

sub :: CN Integer -> CSequence a -> SubType (CN Integer) (CSequence a) #

CanSub Rational a => CanSub (CN Rational) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType (CN Rational) (CSequence a) #

CanSub MPBall b => CanSub (CN MPBall) (CSequence b) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType (CN MPBall) (CSequence b) #

Methods

sub :: CN MPBall -> CSequence b -> SubType (CN MPBall) (CSequence b) #

CanSub Dyadic a => CanSub (CN Dyadic) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType (CN Dyadic) (CSequence a) #

Methods

sub :: CN Dyadic -> CSequence a -> SubType (CN Dyadic) (CSequence a) #

CanSub t1 t2 => CanSub (CSequence t1) (CSequence t2) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType (CSequence t1) (CSequence t2) #

Methods

sub :: CSequence t1 -> CSequence t2 -> SubType (CSequence t1) (CSequence t2) #

CanSub b MPBall => CanSub (CSequence b) (CN MPBall) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType (CSequence b) (CN MPBall) #

Methods

sub :: CSequence b -> CN MPBall -> SubType (CSequence b) (CN MPBall) #

CanSub a Integer => CanSub (CSequence a) (CN Integer) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType (CSequence a) (CN Integer) #

Methods

sub :: CSequence a -> CN Integer -> SubType (CSequence a) (CN Integer) #

CanSub a Int => CanSub (CSequence a) (CN Int) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType (CSequence a) (CN Int) #

Methods

sub :: CSequence a -> CN Int -> SubType (CSequence a) (CN Int) #

CanSub a Rational => CanSub (CSequence a) (CN Rational) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType (CSequence a) (CN Rational) #

CanSub a Dyadic => CanSub (CSequence a) (CN Dyadic) Source # 
Instance details

Defined in AERN2.Real.Field

Associated Types

type SubType (CSequence a) (CN Dyadic) #

Methods

sub :: CSequence a -> CN Dyadic -> SubType (CSequence a) (CN Dyadic) #

CanMinMaxAsymmetric Int a => CanMinMaxAsymmetric (CN Int) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CN Int) (CSequence a) #

Methods

min :: CN Int -> CSequence a -> MinMaxType (CN Int) (CSequence a) #

max :: CN Int -> CSequence a -> MinMaxType (CN Int) (CSequence a) #

CanMinMaxAsymmetric Integer a => CanMinMaxAsymmetric (CN Integer) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CN Integer) (CSequence a) #

CanMinMaxAsymmetric Rational a => CanMinMaxAsymmetric (CN Rational) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CN Rational) (CSequence a) #

CanMinMaxAsymmetric MPBall a => CanMinMaxAsymmetric (CN MPBall) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CN MPBall) (CSequence a) #

CanMinMaxAsymmetric Dyadic a => CanMinMaxAsymmetric (CN Dyadic) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CN Dyadic) (CSequence a) #

CanMinMaxAsymmetric a MPBall => CanMinMaxAsymmetric (CSequence a) (CN MPBall) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) (CN MPBall) #

CanMinMaxAsymmetric t1 t2 => CanMinMaxAsymmetric (CSequence t1) (CSequence t2) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence t1) (CSequence t2) #

Methods

min :: CSequence t1 -> CSequence t2 -> MinMaxType (CSequence t1) (CSequence t2) #

max :: CSequence t1 -> CSequence t2 -> MinMaxType (CSequence t1) (CSequence t2) #

CanMinMaxAsymmetric a Integer => CanMinMaxAsymmetric (CSequence a) (CN Integer) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) (CN Integer) #

CanMinMaxAsymmetric a Int => CanMinMaxAsymmetric (CSequence a) (CN Int) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) (CN Int) #

Methods

min :: CSequence a -> CN Int -> MinMaxType (CSequence a) (CN Int) #

max :: CSequence a -> CN Int -> MinMaxType (CSequence a) (CN Int) #

CanMinMaxAsymmetric a Rational => CanMinMaxAsymmetric (CSequence a) (CN Rational) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) (CN Rational) #

CanMinMaxAsymmetric a Dyadic => CanMinMaxAsymmetric (CSequence a) (CN Dyadic) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) (CN Dyadic) #

(HasEqAsymmetric Int a, IsBool (CSequence (EqCompareType Int a))) => HasEqAsymmetric (CN Int) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CN Int) (CSequence a) #

(HasEqAsymmetric Integer a, IsBool (CSequence (EqCompareType Integer a))) => HasEqAsymmetric (CN Integer) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CN Integer) (CSequence a) #

(HasEqAsymmetric Rational a, IsBool (CSequence (EqCompareType Rational a))) => HasEqAsymmetric (CN Rational) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CN Rational) (CSequence a) #

HasEqAsymmetric MPBall b => HasEqAsymmetric (CN MPBall) (CSequence b) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CN MPBall) (CSequence b) #

(HasEqAsymmetric Dyadic a, IsBool (CSequence (EqCompareType Dyadic a))) => HasEqAsymmetric (CN Dyadic) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CN Dyadic) (CSequence a) #

HasEqAsymmetric a MPBall => HasEqAsymmetric (CSequence a) (CN MPBall) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) (CN MPBall) #

(HasEqAsymmetric t1 t2, IsBool (CSequence (EqCompareType t1 t2))) => HasEqAsymmetric (CSequence t1) (CSequence t2) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence t1) (CSequence t2) #

(HasEqAsymmetric a Integer, IsBool (CSequence (EqCompareType a Integer))) => HasEqAsymmetric (CSequence a) (CN Integer) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) (CN Integer) #

(HasEqAsymmetric a Int, IsBool (CSequence (EqCompareType a Int))) => HasEqAsymmetric (CSequence a) (CN Int) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) (CN Int) #

(HasEqAsymmetric a Rational, IsBool (CSequence (EqCompareType a Rational))) => HasEqAsymmetric (CSequence a) (CN Rational) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) (CN Rational) #

(HasEqAsymmetric a Dyadic, IsBool (CSequence (EqCompareType a Dyadic))) => HasEqAsymmetric (CSequence a) (CN Dyadic) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) (CN Dyadic) #

(HasOrderAsymmetric Int a, IsBool (CSequence (OrderCompareType Int a))) => HasOrderAsymmetric (CN Int) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CN Int) (CSequence a) #

(HasOrderAsymmetric Integer a, IsBool (CSequence (OrderCompareType Integer a))) => HasOrderAsymmetric (CN Integer) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CN Integer) (CSequence a) #

(HasOrderAsymmetric Rational a, IsBool (CSequence (OrderCompareType Rational a))) => HasOrderAsymmetric (CN Rational) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CN Rational) (CSequence a) #

HasOrderAsymmetric MPBall b => HasOrderAsymmetric (CN MPBall) (CSequence b) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CN MPBall) (CSequence b) #

(HasOrderAsymmetric Dyadic a, IsBool (CSequence (OrderCompareType Dyadic a))) => HasOrderAsymmetric (CN Dyadic) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CN Dyadic) (CSequence a) #

HasOrderAsymmetric a MPBall => HasOrderAsymmetric (CSequence a) (CN MPBall) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) (CN MPBall) #

(HasOrderAsymmetric t1 t2, IsBool (CSequence (OrderCompareType t1 t2))) => HasOrderAsymmetric (CSequence t1) (CSequence t2) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence t1) (CSequence t2) #

(HasOrderAsymmetric a Integer, IsBool (CSequence (OrderCompareType a Integer))) => HasOrderAsymmetric (CSequence a) (CN Integer) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) (CN Integer) #

(HasOrderAsymmetric a Int, IsBool (CSequence (OrderCompareType a Int))) => HasOrderAsymmetric (CSequence a) (CN Int) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) (CN Int) #

(HasOrderAsymmetric a Rational, IsBool (CSequence (OrderCompareType a Rational))) => HasOrderAsymmetric (CSequence a) (CN Rational) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) (CN Rational) #

(HasOrderAsymmetric a Dyadic, IsBool (CSequence (OrderCompareType a Dyadic))) => HasOrderAsymmetric (CSequence a) (CN Dyadic) Source # 
Instance details

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) (CN Dyadic) #

CanAndOrAsymmetric t1 t2 => CanAndOrAsymmetric (CSequence t1) (CSequence t2) Source # 
Instance details

Defined in AERN2.Real.CKleenean

Associated Types

type AndOrType (CSequence t1) (CSequence t2) #

Methods

and2 :: CSequence t1 -> CSequence t2 -> AndOrType (CSequence t1) (CSequence t2) #

or2 :: CSequence t1 -> CSequence t2 -> AndOrType (CSequence t1) (CSequence t2) #

type SqrtType CReal Source # 
Instance details

Defined in AERN2.Real.Elementary

type ExpType CReal Source # 
Instance details

Defined in AERN2.Real.Elementary

type LogType CReal Source # 
Instance details

Defined in AERN2.Real.Elementary

type SinCosType CReal Source # 
Instance details

Defined in AERN2.Real.Elementary

type SelectType CKleenean Source # 
Instance details

Defined in AERN2.Real.CKleenean

type LimitType Int CReal Source # 
Instance details

Defined in AERN2.Real.Limit

type LimitType Integer CReal Source # 
Instance details

Defined in AERN2.Real.Limit

type LimitType Rational CReal Source # 
Instance details

Defined in AERN2.Real.Limit

type PowType Int (CSequence e) Source # 
Instance details

Defined in AERN2.Real.Field

type PowType Integer (CSequence e) Source # 
Instance details

Defined in AERN2.Real.Field

type PowType Rational (CSequence e) Source # 
Instance details

Defined in AERN2.Real.Field

type DivType Int (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

type DivType Integer (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

type DivType Rational (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

type DivType MPBall (CSequence b) Source # 
Instance details

Defined in AERN2.Real.Field

type DivType Dyadic (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

type MulType Int (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

type MulType Integer (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

type MulType Rational (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

type MulType MPBall (CSequence b) Source # 
Instance details

Defined in AERN2.Real.Field

type MulType Dyadic (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

type AddType Int (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

type AddType Integer (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

type AddType Rational (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

type AddType MPBall (CSequence b) Source # 
Instance details

Defined in AERN2.Real.Field

type AddType Dyadic (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

type SubType Int (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

type SubType Integer (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

type SubType Rational (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

type SubType MPBall (CSequence b) Source # 
Instance details

Defined in AERN2.Real.Field

type SubType Dyadic (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Field

type MinMaxType Int (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

type MinMaxType Integer (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

type MinMaxType Rational (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

type MinMaxType MPBall (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

type MinMaxType Dyadic (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

type EqCompareType Int (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

type EqCompareType Integer (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

type EqCompareType Rational (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

type EqCompareType MPBall (CSequence b) Source # 
Instance details

Defined in AERN2.Real.Comparisons

type EqCompareType Dyadic (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

type OrderCompareType Int (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

type OrderCompareType Integer (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

type OrderCompareType Rational (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

type OrderCompareType MPBall (CSequence b) Source # 
Instance details

Defined in AERN2.Real.Comparisons

type OrderCompareType Dyadic (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

type IfThenElseType CKleenean (CSequence t) Source # 
Instance details

Defined in AERN2.Real.CKleenean

type LimitType Rational (CReal -> CReal) Source # 
Instance details

Defined in AERN2.Real.Limit

type AbsType (CSequence t1) Source # 
Instance details

Defined in AERN2.Real.Comparisons

type NegType (CSequence t) Source # 
Instance details

Defined in AERN2.Real.CKleenean

type PowType (CSequence b) Rational Source # 
Instance details

Defined in AERN2.Real.Field

type PowType (CSequence b) Int Source # 
Instance details

Defined in AERN2.Real.Field

type PowType (CSequence b) Integer Source # 
Instance details

Defined in AERN2.Real.Field

type DivType (CSequence b) MPBall Source # 
Instance details

Defined in AERN2.Real.Field

type DivType (CSequence a) Dyadic Source # 
Instance details

Defined in AERN2.Real.Field

type DivType (CSequence a) Rational Source # 
Instance details

Defined in AERN2.Real.Field

type DivType (CSequence a) Int Source # 
Instance details

Defined in AERN2.Real.Field

type DivType (CSequence a) Integer Source # 
Instance details

Defined in AERN2.Real.Field

type MulType (CSequence b) MPBall Source # 
Instance details

Defined in AERN2.Real.Field

type MulType (CSequence a) Dyadic Source # 
Instance details

Defined in AERN2.Real.Field

type MulType (CSequence a) Rational Source # 
Instance details

Defined in AERN2.Real.Field

type MulType (CSequence a) Int Source # 
Instance details

Defined in AERN2.Real.Field

type MulType (CSequence a) Integer Source # 
Instance details

Defined in AERN2.Real.Field

type AddType (CSequence b) MPBall Source # 
Instance details

Defined in AERN2.Real.Field

type AddType (CSequence a) Dyadic Source # 
Instance details

Defined in AERN2.Real.Field

type AddType (CSequence a) Rational Source # 
Instance details

Defined in AERN2.Real.Field

type AddType (CSequence a) Int Source # 
Instance details

Defined in AERN2.Real.Field

type AddType (CSequence a) Integer Source # 
Instance details

Defined in AERN2.Real.Field

type SubType (CSequence b) MPBall Source # 
Instance details

Defined in AERN2.Real.Field

type SubType (CSequence a) Dyadic Source # 
Instance details

Defined in AERN2.Real.Field

type SubType (CSequence a) Rational Source # 
Instance details

Defined in AERN2.Real.Field

type SubType (CSequence a) Int Source # 
Instance details

Defined in AERN2.Real.Field

type SubType (CSequence a) Integer Source # 
Instance details

Defined in AERN2.Real.Field

type MinMaxType (CSequence a) MPBall Source # 
Instance details

Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) Dyadic Source # 
Instance details

Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) Rational Source # 
Instance details

Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) Int Source # 
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Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) Integer Source # 
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Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) MPBall Source # 
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Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) Dyadic Source # 
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Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) Rational Source # 
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Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) Int Source # 
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Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) Integer Source # 
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Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) MPBall Source # 
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Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) Dyadic Source # 
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Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) Rational Source # 
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Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) Int Source # 
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Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) Integer Source # 
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Defined in AERN2.Real.Comparisons

type ExtractedApproximation (CSequence t) Precision Source # 
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Defined in AERN2.Real.Type

type ExtractedApproximation (CSequence t) Accuracy Source # 
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Defined in AERN2.Real.Type

type PowType (CSequence b) (CSequence e) Source # 
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Defined in AERN2.Real.Field

type DivType (CN Int) (CSequence a) Source # 
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Defined in AERN2.Real.Field

type DivType (CN Integer) (CSequence a) Source # 
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Defined in AERN2.Real.Field

type DivType (CN Rational) (CSequence a) Source # 
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Defined in AERN2.Real.Field

type DivType (CN MPBall) (CSequence b) Source # 
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Defined in AERN2.Real.Field

type DivType (CN Dyadic) (CSequence a) Source # 
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Defined in AERN2.Real.Field

type DivType (CSequence t1) (CSequence t2) Source # 
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Defined in AERN2.Real.Field

type DivType (CSequence t1) (CSequence t2) = CSequence (DivType t1 t2)
type DivType (CSequence b) (CN MPBall) Source # 
Instance details

Defined in AERN2.Real.Field

type DivType (CSequence a) (CN Dyadic) Source # 
Instance details

Defined in AERN2.Real.Field

type DivType (CSequence a) (CN Rational) Source # 
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Defined in AERN2.Real.Field

type DivType (CSequence a) (CN Int) Source # 
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Defined in AERN2.Real.Field

type DivType (CSequence a) (CN Integer) Source # 
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Defined in AERN2.Real.Field

type MulType (CN Int) (CSequence a) Source # 
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Defined in AERN2.Real.Field

type MulType (CN Integer) (CSequence a) Source # 
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Defined in AERN2.Real.Field

type MulType (CN Rational) (CSequence a) Source # 
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Defined in AERN2.Real.Field

type MulType (CN MPBall) (CSequence b) Source # 
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Defined in AERN2.Real.Field

type MulType (CN Dyadic) (CSequence a) Source # 
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Defined in AERN2.Real.Field

type MulType (CSequence t1) (CSequence t2) Source # 
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Defined in AERN2.Real.Field

type MulType (CSequence t1) (CSequence t2) = CSequence (MulType t1 t2)
type MulType (CSequence b) (CN MPBall) Source # 
Instance details

Defined in AERN2.Real.Field

type MulType (CSequence a) (CN Dyadic) Source # 
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Defined in AERN2.Real.Field

type MulType (CSequence a) (CN Rational) Source # 
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Defined in AERN2.Real.Field

type MulType (CSequence a) (CN Int) Source # 
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Defined in AERN2.Real.Field

type MulType (CSequence a) (CN Integer) Source # 
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Defined in AERN2.Real.Field

type AddType (CN Int) (CSequence a) Source # 
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Defined in AERN2.Real.Field

type AddType (CN Integer) (CSequence a) Source # 
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Defined in AERN2.Real.Field

type AddType (CN Rational) (CSequence a) Source # 
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Defined in AERN2.Real.Field

type AddType (CN MPBall) (CSequence b) Source # 
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Defined in AERN2.Real.Field

type AddType (CN Dyadic) (CSequence a) Source # 
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Defined in AERN2.Real.Field

type AddType (CSequence t1) (CSequence t2) Source # 
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Defined in AERN2.Real.Field

type AddType (CSequence t1) (CSequence t2) = CSequence (AddType t1 t2)
type AddType (CSequence b) (CN MPBall) Source # 
Instance details

Defined in AERN2.Real.Field

type AddType (CSequence a) (CN Dyadic) Source # 
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Defined in AERN2.Real.Field

type AddType (CSequence a) (CN Rational) Source # 
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Defined in AERN2.Real.Field

type AddType (CSequence a) (CN Int) Source # 
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Defined in AERN2.Real.Field

type AddType (CSequence a) (CN Integer) Source # 
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Defined in AERN2.Real.Field

type SubType (CN Int) (CSequence a) Source # 
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Defined in AERN2.Real.Field

type SubType (CN Integer) (CSequence a) Source # 
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Defined in AERN2.Real.Field

type SubType (CN Rational) (CSequence a) Source # 
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Defined in AERN2.Real.Field

type SubType (CN MPBall) (CSequence b) Source # 
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Defined in AERN2.Real.Field

type SubType (CN Dyadic) (CSequence a) Source # 
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Defined in AERN2.Real.Field

type SubType (CSequence t1) (CSequence t2) Source # 
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Defined in AERN2.Real.Field

type SubType (CSequence t1) (CSequence t2) = CSequence (SubType t1 t2)
type SubType (CSequence b) (CN MPBall) Source # 
Instance details

Defined in AERN2.Real.Field

type SubType (CSequence a) (CN Dyadic) Source # 
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Defined in AERN2.Real.Field

type SubType (CSequence a) (CN Rational) Source # 
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Defined in AERN2.Real.Field

type SubType (CSequence a) (CN Int) Source # 
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Defined in AERN2.Real.Field

type SubType (CSequence a) (CN Integer) Source # 
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Defined in AERN2.Real.Field

type MinMaxType (CN Int) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

type MinMaxType (CN Integer) (CSequence a) Source # 
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Defined in AERN2.Real.Comparisons

type MinMaxType (CN Rational) (CSequence a) Source # 
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Defined in AERN2.Real.Comparisons

type MinMaxType (CN MPBall) (CSequence a) Source # 
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Defined in AERN2.Real.Comparisons

type MinMaxType (CN Dyadic) (CSequence a) Source # 
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Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) (CN MPBall) Source # 
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Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence t1) (CSequence t2) Source # 
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Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) (CN Dyadic) Source # 
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Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) (CN Rational) Source # 
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Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) (CN Int) Source # 
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Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) (CN Integer) Source # 
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Defined in AERN2.Real.Comparisons

type EqCompareType (CN Int) (CSequence a) Source # 
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Defined in AERN2.Real.Comparisons

type EqCompareType (CN Integer) (CSequence a) Source # 
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Defined in AERN2.Real.Comparisons

type EqCompareType (CN Rational) (CSequence a) Source # 
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Defined in AERN2.Real.Comparisons

type EqCompareType (CN MPBall) (CSequence b) Source # 
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Defined in AERN2.Real.Comparisons

type EqCompareType (CN Dyadic) (CSequence a) Source # 
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Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) (CN MPBall) Source # 
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Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence t1) (CSequence t2) Source # 
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Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) (CN Dyadic) Source # 
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Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) (CN Rational) Source # 
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Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) (CN Int) Source # 
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Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) (CN Integer) Source # 
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Defined in AERN2.Real.Comparisons

type OrderCompareType (CN Int) (CSequence a) Source # 
Instance details

Defined in AERN2.Real.Comparisons

type OrderCompareType (CN Integer) (CSequence a) Source # 
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Defined in AERN2.Real.Comparisons

type OrderCompareType (CN Rational) (CSequence a) Source # 
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Defined in AERN2.Real.Comparisons

type OrderCompareType (CN MPBall) (CSequence b) Source # 
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Defined in AERN2.Real.Comparisons

type OrderCompareType (CN Dyadic) (CSequence a) Source # 
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Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) (CN MPBall) Source # 
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Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence t1) (CSequence t2) Source # 
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Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) (CN Dyadic) Source # 
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Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) (CN Rational) Source # 
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Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) (CN Int) Source # 
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Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) (CN Integer) Source # 
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Defined in AERN2.Real.Comparisons

type AndOrType (CSequence t1) (CSequence t2) Source # 
Instance details

Defined in AERN2.Real.CKleenean

lift1 :: (CN t1 -> CN t2) -> CSequence t1 -> CSequence t2 Source #

lift2 :: (CN t1 -> CN t2 -> CN t3) -> CSequence t1 -> CSequence t2 -> CSequence t3 Source #

lift1T :: (CN t1 -> t2 -> CN t3) -> CSequence t1 -> t2 -> CSequence t3 Source #

liftT1 :: (t1 -> CN t2 -> CN t3) -> t1 -> CSequence t2 -> CSequence t3 Source #

class CanExtractApproximation e q where Source #

Associated Types

type ExtractedApproximation e q Source #

Methods

extractApproximation Source #

Arguments

:: e

exact value

-> q

query

-> ExtractedApproximation e q 

Get an approximation of an exact value using the given query

realWithAccuracy :: CReal -> Accuracy -> CN MPBall Source #

Get a ball approximation of the real number with at least the specified accuracy