AERN2.Real.Type

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

Documentation

newtype CSequence t

Constructors

CSequence [CN t]

Instances

Floating CReal

Defined in AERN2.Real.Elementary

Methods

pi :: CReal

exp :: CReal -> CReal

log :: CReal -> CReal

sqrt :: CReal -> CReal

(**) :: CReal -> CReal -> CReal

logBase :: CReal -> CReal -> CReal

sin :: CReal -> CReal

cos :: CReal -> CReal

tan :: CReal -> CReal

asin :: CReal -> CReal

acos :: CReal -> CReal

atan :: CReal -> CReal

sinh :: CReal -> CReal

cosh :: CReal -> CReal

tanh :: CReal -> CReal

asinh :: CReal -> CReal

acosh :: CReal -> CReal

atanh :: CReal -> CReal

log1p :: CReal -> CReal

expm1 :: CReal -> CReal

log1pexp :: CReal -> CReal

log1mexp :: CReal -> CReal

Fractional CReal

Defined in AERN2.Real.Field

Methods

(/) :: CReal -> CReal -> CReal

recip :: CReal -> CReal

fromRational :: Rational -> CReal

Num CReal

Defined in AERN2.Real.Field

Methods

(+) :: CReal -> CReal -> CReal

(-) :: CReal -> CReal -> CReal

(*) :: CReal -> CReal -> CReal

negate :: CReal -> CReal

abs :: CReal -> CReal

signum :: CReal -> CReal

fromInteger :: Integer -> CReal

Arbitrary CReal

Defined in AERN2.Real.Tests

Methods

arbitrary :: Gen CReal

shrink :: CReal -> [CReal]

CanSelect CKleenean

Defined in AERN2.Real.CKleenean

Associated Types

type SelectType CKleenean

Methods

select :: CKleenean -> CKleenean -> SelectType CKleenean

CanSqrt CReal

Defined in AERN2.Real.Elementary

Associated Types

type SqrtType CReal

Methods

sqrt :: CReal -> SqrtType CReal

CanExp CReal

Defined in AERN2.Real.Elementary

Associated Types

type ExpType CReal

Methods

exp :: CReal -> ExpType CReal

CanLog CReal

Defined in AERN2.Real.Elementary

Associated Types

type LogType CReal

Methods

log :: CReal -> LogType CReal

CanSinCos CReal

Defined in AERN2.Real.Elementary

Associated Types

type SinCosType CReal

Methods

cos :: CReal -> SinCosType CReal

sin :: CReal -> SinCosType CReal

Field CReal

Defined in AERN2.Real.Field

OrderedField CReal

Defined in AERN2.Real.Field

Ring CReal

Defined in AERN2.Real.Field

OrderedRing CReal

Defined in AERN2.Real.Field

RealNumber CReal

Defined in AERN2.Real

HasLimits Int CReal

Defined in AERN2.Real.Limit

Associated Types

type LimitType Int CReal

Methods

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

HasLimits Integer CReal

Defined in AERN2.Real.Limit

Associated Types

type LimitType Integer CReal

Methods

limit :: (Integer -> CReal) -> LimitType Integer CReal

HasLimits Rational CReal

Defined in AERN2.Real.Limit

Associated Types

type LimitType Rational CReal

Methods

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

ConvertibleExactly Int CReal

Defined in AERN2.Real.Type

Methods

safeConvertExactly :: Int -> ConvertResult CReal

ConvertibleExactly Integer CReal

Defined in AERN2.Real.Type

Methods

safeConvertExactly :: Integer -> ConvertResult CReal

ConvertibleExactly Rational CReal

Defined in AERN2.Real.Type

Methods

safeConvertExactly :: Rational -> ConvertResult CReal

ConvertibleExactly t Kleenean => ConvertibleExactly t CKleenean

Defined in AERN2.Real.CKleenean

Methods

safeConvertExactly :: t -> ConvertResult CKleenean

ConvertibleExactly Dyadic CReal

Defined in AERN2.Real.Type

Methods

safeConvertExactly :: Dyadic -> ConvertResult CReal

ConvertibleExactly CReal CReal

Defined in AERN2.Real.Type

Methods

safeConvertExactly :: CReal -> ConvertResult CReal

ConvertibleWithPrecision CReal (CN MPBall)

Defined in AERN2.Real.Type

Methods

safeConvertP :: Precision -> CReal -> ConvertResult (CN MPBall)

CanTakeErrors NumErrors (CSequence t)

Defined in AERN2.Real.Type

Methods

takeErrors :: NumErrors -> CSequence t -> CSequence t

takeErrorsNoValue :: NumErrors -> CSequence t

(CanDiv Int a, CanTestZero a) => CanDiv Int (CSequence a)

Defined in AERN2.Real.FieldTH

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)

Defined in AERN2.Real.FieldTH

Associated Types

type DivType Integer (CSequence a)

Methods

divide :: Integer -> CSequence a -> DivType Integer (CSequence a)

(CanDiv Rational a, CanTestZero a) => CanDiv Rational (CSequence a)

Defined in AERN2.Real.FieldTH

Associated Types

type DivType Rational (CSequence a)

Methods

divide :: Rational -> CSequence a -> DivType Rational (CSequence a)

(CanDiv MPBall b, CanTestZero b) => CanDiv MPBall (CSequence b)

Defined in AERN2.Real.Field

Associated Types

type DivType MPBall (CSequence b)

Methods

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

(CanDiv Dyadic a, CanTestZero a) => CanDiv Dyadic (CSequence a)

Defined in AERN2.Real.FieldTH

Associated Types

type DivType Dyadic (CSequence a)

Methods

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

(CanPow Int e, HasOrderCertainly e Integer, CanTestIsIntegerType e, CanTestInteger e) => CanPow Int (CSequence e)

Defined in AERN2.Real.FieldTH

Associated Types

type PowType Int (CSequence e)

type PPowType Int (CSequence e)

Methods

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

ppow :: Int -> CSequence e -> PPowType Int (CSequence e)

(CanPow Integer e, HasOrderCertainly e Integer, CanTestIsIntegerType e, CanTestInteger e) => CanPow Integer (CSequence e)

Defined in AERN2.Real.FieldTH

Associated Types

type PowType Integer (CSequence e)

type PPowType Integer (CSequence e)

Methods

pow :: Integer -> CSequence e -> PowType Integer (CSequence e)

ppow :: Integer -> CSequence e -> PPowType Integer (CSequence e)

(CanPow Rational e, HasOrderCertainly e Integer, CanTestIsIntegerType e, CanTestInteger e) => CanPow Rational (CSequence e)

Defined in AERN2.Real.FieldTH

Associated Types

type PowType Rational (CSequence e)

type PPowType Rational (CSequence e)

Methods

pow :: Rational -> CSequence e -> PowType Rational (CSequence e)

ppow :: Rational -> CSequence e -> PPowType Rational (CSequence e)

(CanMulAsymmetric Int a, CanGiveUpIfVeryInaccurate (MulType Int a)) => CanMulAsymmetric Int (CSequence a)

Defined in AERN2.Real.FieldTH

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)

Defined in AERN2.Real.FieldTH

Associated Types

type MulType Integer (CSequence a)

Methods

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

(CanMulAsymmetric Rational a, CanGiveUpIfVeryInaccurate (MulType Rational a)) => CanMulAsymmetric Rational (CSequence a)

Defined in AERN2.Real.FieldTH

Associated Types

type MulType Rational (CSequence a)

Methods

mul :: Rational -> CSequence a -> MulType Rational (CSequence a)

CanMulAsymmetric MPBall b => CanMulAsymmetric MPBall (CSequence b)

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)

Defined in AERN2.Real.FieldTH

Associated Types

type MulType Dyadic (CSequence a)

Methods

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

CanAddAsymmetric Int a => CanAddAsymmetric Int (CSequence a)

Defined in AERN2.Real.FieldTH

Associated Types

type AddType Int (CSequence a)

Methods

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

CanAddAsymmetric Integer a => CanAddAsymmetric Integer (CSequence a)

Defined in AERN2.Real.FieldTH

Associated Types

type AddType Integer (CSequence a)

Methods

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

CanAddAsymmetric Rational a => CanAddAsymmetric Rational (CSequence a)

Defined in AERN2.Real.FieldTH

Associated Types

type AddType Rational (CSequence a)

Methods

add :: Rational -> CSequence a -> AddType Rational (CSequence a)

CanAddAsymmetric MPBall b => CanAddAsymmetric MPBall (CSequence b)

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)

Defined in AERN2.Real.FieldTH

Associated Types

type AddType Dyadic (CSequence a)

Methods

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

CanSub Int a => CanSub Int (CSequence a)

Defined in AERN2.Real.FieldTH

Associated Types

type SubType Int (CSequence a)

Methods

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

CanSub Integer a => CanSub Integer (CSequence a)

Defined in AERN2.Real.FieldTH

Associated Types

type SubType Integer (CSequence a)

Methods

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

CanSub Rational a => CanSub Rational (CSequence a)

Defined in AERN2.Real.FieldTH

Associated Types

type SubType Rational (CSequence a)

Methods

sub :: Rational -> CSequence a -> SubType Rational (CSequence a)

CanSub MPBall b => CanSub MPBall (CSequence b)

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)

Defined in AERN2.Real.FieldTH

Associated Types

type SubType Dyadic (CSequence a)

Methods

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

CanMinMaxAsymmetric Int a => CanMinMaxAsymmetric Int (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType Int (CSequence a)

Methods

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

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

CanMinMaxAsymmetric Integer a => CanMinMaxAsymmetric Integer (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType Integer (CSequence a)

Methods

min :: Integer -> CSequence a -> MinMaxType Integer (CSequence a)

max :: Integer -> CSequence a -> MinMaxType Integer (CSequence a)

CanMinMaxAsymmetric Rational a => CanMinMaxAsymmetric Rational (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType Rational (CSequence a)

Methods

min :: Rational -> CSequence a -> MinMaxType Rational (CSequence a)

max :: Rational -> CSequence a -> MinMaxType Rational (CSequence a)

CanMinMaxAsymmetric MPBall a => CanMinMaxAsymmetric MPBall (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType MPBall (CSequence a)

Methods

min :: MPBall -> CSequence a -> MinMaxType MPBall (CSequence a)

max :: MPBall -> CSequence a -> MinMaxType MPBall (CSequence a)

CanMinMaxAsymmetric Dyadic a => CanMinMaxAsymmetric Dyadic (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType Dyadic (CSequence a)

Methods

min :: Dyadic -> CSequence a -> MinMaxType Dyadic (CSequence a)

max :: Dyadic -> CSequence a -> MinMaxType Dyadic (CSequence a)

(HasEqAsymmetric Int a, IsBool (CSequence (EqCompareType Int a))) => HasEqAsymmetric Int (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType Int (CSequence a)

Methods

equalTo :: Int -> CSequence a -> EqCompareType Int (CSequence a)

notEqualTo :: Int -> CSequence a -> EqCompareType Int (CSequence a)

(HasEqAsymmetric Integer a, IsBool (CSequence (EqCompareType Integer a))) => HasEqAsymmetric Integer (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType Integer (CSequence a)

Methods

equalTo :: Integer -> CSequence a -> EqCompareType Integer (CSequence a)

notEqualTo :: Integer -> CSequence a -> EqCompareType Integer (CSequence a)

(HasEqAsymmetric Rational a, IsBool (CSequence (EqCompareType Rational a))) => HasEqAsymmetric Rational (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType Rational (CSequence a)

Methods

equalTo :: Rational -> CSequence a -> EqCompareType Rational (CSequence a)

notEqualTo :: Rational -> CSequence a -> EqCompareType Rational (CSequence a)

HasEqAsymmetric MPBall b => HasEqAsymmetric MPBall (CSequence b)

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType MPBall (CSequence b)

Methods

equalTo :: MPBall -> CSequence b -> EqCompareType MPBall (CSequence b)

notEqualTo :: MPBall -> CSequence b -> EqCompareType MPBall (CSequence b)

(HasEqAsymmetric Dyadic a, IsBool (CSequence (EqCompareType Dyadic a))) => HasEqAsymmetric Dyadic (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType Dyadic (CSequence a)

Methods

equalTo :: Dyadic -> CSequence a -> EqCompareType Dyadic (CSequence a)

notEqualTo :: Dyadic -> CSequence a -> EqCompareType Dyadic (CSequence a)

(HasOrderAsymmetric Int a, IsBool (CSequence (OrderCompareType Int a))) => HasOrderAsymmetric Int (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType Int (CSequence a)

Methods

lessThan :: Int -> CSequence a -> OrderCompareType Int (CSequence a)

greaterThan :: Int -> CSequence a -> OrderCompareType Int (CSequence a)

leq :: Int -> CSequence a -> OrderCompareType Int (CSequence a)

geq :: Int -> CSequence a -> OrderCompareType Int (CSequence a)

(HasOrderAsymmetric Integer a, IsBool (CSequence (OrderCompareType Integer a))) => HasOrderAsymmetric Integer (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType Integer (CSequence a)

Methods

lessThan :: Integer -> CSequence a -> OrderCompareType Integer (CSequence a)

greaterThan :: Integer -> CSequence a -> OrderCompareType Integer (CSequence a)

leq :: Integer -> CSequence a -> OrderCompareType Integer (CSequence a)

geq :: Integer -> CSequence a -> OrderCompareType Integer (CSequence a)

(HasOrderAsymmetric Rational a, IsBool (CSequence (OrderCompareType Rational a))) => HasOrderAsymmetric Rational (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType Rational (CSequence a)

Methods

lessThan :: Rational -> CSequence a -> OrderCompareType Rational (CSequence a)

greaterThan :: Rational -> CSequence a -> OrderCompareType Rational (CSequence a)

leq :: Rational -> CSequence a -> OrderCompareType Rational (CSequence a)

geq :: Rational -> CSequence a -> OrderCompareType Rational (CSequence a)

HasOrderAsymmetric MPBall b => HasOrderAsymmetric MPBall (CSequence b)

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType MPBall (CSequence b)

Methods

lessThan :: MPBall -> CSequence b -> OrderCompareType MPBall (CSequence b)

greaterThan :: MPBall -> CSequence b -> OrderCompareType MPBall (CSequence b)

leq :: MPBall -> CSequence b -> OrderCompareType MPBall (CSequence b)

geq :: MPBall -> CSequence b -> OrderCompareType MPBall (CSequence b)

(HasOrderAsymmetric Dyadic a, IsBool (CSequence (OrderCompareType Dyadic a))) => HasOrderAsymmetric Dyadic (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType Dyadic (CSequence a)

Methods

lessThan :: Dyadic -> CSequence a -> OrderCompareType Dyadic (CSequence a)

greaterThan :: Dyadic -> CSequence a -> OrderCompareType Dyadic (CSequence a)

leq :: Dyadic -> CSequence a -> OrderCompareType Dyadic (CSequence a)

geq :: Dyadic -> CSequence a -> OrderCompareType Dyadic (CSequence a)

CanUnionCNSameType t => HasIfThenElse CKleenean (CSequence t)

Defined in AERN2.Real.CKleenean

Associated Types

type IfThenElseType CKleenean (CSequence t)

Methods

ifThenElse :: CKleenean -> CSequence t -> CSequence t -> IfThenElseType CKleenean (CSequence t)

(HasCReals t, HasIntegers t) => ConvertibleExactly CReal (Complex t)

Defined in AERN2.Complex

Methods

safeConvertExactly :: CReal -> ConvertResult (Complex t)

HasLimits Rational (CReal -> CReal)

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)

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)

Defined in AERN2.Real.Comparisons

Methods

compare :: CSequence a -> CSequence a -> Ordering

(<) :: CSequence a -> CSequence a -> Bool

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

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

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

max :: CSequence a -> CSequence a -> CSequence a

min :: CSequence a -> CSequence a -> CSequence a

Show t => Show (CSequence t)

Defined in AERN2.Real.Type

Methods

showsPrec :: Int -> CSequence t -> ShowS

show :: CSequence t -> String

showList :: [CSequence t] -> ShowS

CanClearPotentialErrors (CSequence t)

Defined in AERN2.Real.Type

Methods

clearPotentialErrors :: CSequence t -> CSequence t

CanTestIsIntegerType t => CanTestIsIntegerType (CSequence t)

Defined in AERN2.Real.Type

Methods

isIntegerType :: CSequence t -> Bool

CanAbs t1 => CanAbs (CSequence t1)

Defined in AERN2.Real.Comparisons

Associated Types

type AbsType (CSequence t1)

Methods

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

CanNeg t => CanNeg (CSequence t)

Defined in AERN2.Real.CKleenean

Associated Types

type NegType (CSequence t)

Methods

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

CanDiv a Integer => CanDiv (CSequence a) Integer

Defined in AERN2.Real.FieldTH

Associated Types

type DivType (CSequence a) Integer

Methods

divide :: CSequence a -> Integer -> DivType (CSequence a) Integer

CanDiv a Int => CanDiv (CSequence a) Int

Defined in AERN2.Real.FieldTH

Associated Types

type DivType (CSequence a) Int

Methods

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

CanDiv a Rational => CanDiv (CSequence a) Rational

Defined in AERN2.Real.FieldTH

Associated Types

type DivType (CSequence a) Rational

Methods

divide :: CSequence a -> Rational -> DivType (CSequence a) Rational

CanDiv a Dyadic => CanDiv (CSequence a) Dyadic

Defined in AERN2.Real.FieldTH

Associated Types

type DivType (CSequence a) Dyadic

Methods

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

CanDiv b MPBall => CanDiv (CSequence b) MPBall

Defined in AERN2.Real.Field

Associated Types

type DivType (CSequence b) MPBall

Methods

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

(CanPow b Integer, HasOrderCertainly b Integer, HasEqCertainly b Integer, CanTestIsIntegerType b) => CanPow (CSequence b) Integer

Defined in AERN2.Real.FieldTH

Associated Types

type PowType (CSequence b) Integer

type PPowType (CSequence b) Integer

Methods

pow :: CSequence b -> Integer -> PowType (CSequence b) Integer

ppow :: CSequence b -> Integer -> PPowType (CSequence b) Integer

(CanPow b Int, HasOrderCertainly b Integer, HasEqCertainly b Integer, CanTestIsIntegerType b) => CanPow (CSequence b) Int

Defined in AERN2.Real.FieldTH

Associated Types

type PowType (CSequence b) Int

type PPowType (CSequence b) Int

Methods

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

ppow :: CSequence b -> Int -> PPowType (CSequence b) Int

(CanPow b Rational, HasOrderCertainly b Integer, HasEqCertainly b Integer, CanTestIsIntegerType b) => CanPow (CSequence b) Rational

Defined in AERN2.Real.FieldTH

Associated Types

type PowType (CSequence b) Rational

type PPowType (CSequence b) Rational

Methods

pow :: CSequence b -> Rational -> PowType (CSequence b) Rational

ppow :: CSequence b -> Rational -> PPowType (CSequence b) Rational

(CanMulAsymmetric a Integer, CanGiveUpIfVeryInaccurate (MulType a Integer)) => CanMulAsymmetric (CSequence a) Integer

Defined in AERN2.Real.FieldTH

Associated Types

type MulType (CSequence a) Integer

Methods

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

(CanMulAsymmetric a Int, CanGiveUpIfVeryInaccurate (MulType a Int)) => CanMulAsymmetric (CSequence a) Int

Defined in AERN2.Real.FieldTH

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

Defined in AERN2.Real.FieldTH

Associated Types

type MulType (CSequence a) Rational

Methods

mul :: CSequence a -> Rational -> MulType (CSequence a) Rational

(CanMulAsymmetric a Dyadic, CanGiveUpIfVeryInaccurate (MulType a Dyadic)) => CanMulAsymmetric (CSequence a) Dyadic

Defined in AERN2.Real.FieldTH

Associated Types

type MulType (CSequence a) Dyadic

Methods

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

CanMulAsymmetric b MPBall => CanMulAsymmetric (CSequence b) MPBall

Defined in AERN2.Real.Field

Associated Types

type MulType (CSequence b) MPBall

Methods

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

CanAddAsymmetric a Integer => CanAddAsymmetric (CSequence a) Integer

Defined in AERN2.Real.FieldTH

Associated Types

type AddType (CSequence a) Integer

Methods

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

CanAddAsymmetric a Int => CanAddAsymmetric (CSequence a) Int

Defined in AERN2.Real.FieldTH

Associated Types

type AddType (CSequence a) Int

Methods

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

CanAddAsymmetric a Rational => CanAddAsymmetric (CSequence a) Rational

Defined in AERN2.Real.FieldTH

Associated Types

type AddType (CSequence a) Rational

Methods

add :: CSequence a -> Rational -> AddType (CSequence a) Rational

CanAddAsymmetric a Dyadic => CanAddAsymmetric (CSequence a) Dyadic

Defined in AERN2.Real.FieldTH

Associated Types

type AddType (CSequence a) Dyadic

Methods

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

CanAddAsymmetric b MPBall => CanAddAsymmetric (CSequence b) MPBall

Defined in AERN2.Real.Field

Associated Types

type AddType (CSequence b) MPBall

Methods

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

CanSub a Integer => CanSub (CSequence a) Integer

Defined in AERN2.Real.FieldTH

Associated Types

type SubType (CSequence a) Integer

Methods

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

CanSub a Int => CanSub (CSequence a) Int

Defined in AERN2.Real.FieldTH

Associated Types

type SubType (CSequence a) Int

Methods

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

CanSub a Rational => CanSub (CSequence a) Rational

Defined in AERN2.Real.FieldTH

Associated Types

type SubType (CSequence a) Rational

Methods

sub :: CSequence a -> Rational -> SubType (CSequence a) Rational

CanSub a Dyadic => CanSub (CSequence a) Dyadic

Defined in AERN2.Real.FieldTH

Associated Types

type SubType (CSequence a) Dyadic

Methods

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

CanSub b MPBall => CanSub (CSequence b) MPBall

Defined in AERN2.Real.Field

Associated Types

type SubType (CSequence b) MPBall

Methods

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

CanMinMaxAsymmetric a MPBall => CanMinMaxAsymmetric (CSequence a) MPBall

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) MPBall

Methods

min :: CSequence a -> MPBall -> MinMaxType (CSequence a) MPBall

max :: CSequence a -> MPBall -> MinMaxType (CSequence a) MPBall

CanMinMaxAsymmetric a Integer => CanMinMaxAsymmetric (CSequence a) Integer

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) Integer

Methods

min :: CSequence a -> Integer -> MinMaxType (CSequence a) Integer

max :: CSequence a -> Integer -> MinMaxType (CSequence a) Integer

CanMinMaxAsymmetric a Int => CanMinMaxAsymmetric (CSequence a) Int

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) Int

Methods

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

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

CanMinMaxAsymmetric a Rational => CanMinMaxAsymmetric (CSequence a) Rational

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) Rational

Methods

min :: CSequence a -> Rational -> MinMaxType (CSequence a) Rational

max :: CSequence a -> Rational -> MinMaxType (CSequence a) Rational

CanMinMaxAsymmetric a Dyadic => CanMinMaxAsymmetric (CSequence a) Dyadic

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) Dyadic

Methods

min :: CSequence a -> Dyadic -> MinMaxType (CSequence a) Dyadic

max :: CSequence a -> Dyadic -> MinMaxType (CSequence a) Dyadic

HasEqAsymmetric a MPBall => HasEqAsymmetric (CSequence a) MPBall

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) MPBall

Methods

equalTo :: CSequence a -> MPBall -> EqCompareType (CSequence a) MPBall

notEqualTo :: CSequence a -> MPBall -> EqCompareType (CSequence a) MPBall

(HasEqAsymmetric a Integer, IsBool (CSequence (EqCompareType a Integer))) => HasEqAsymmetric (CSequence a) Integer

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) Integer

Methods

equalTo :: CSequence a -> Integer -> EqCompareType (CSequence a) Integer

notEqualTo :: CSequence a -> Integer -> EqCompareType (CSequence a) Integer

(HasEqAsymmetric a Int, IsBool (CSequence (EqCompareType a Int))) => HasEqAsymmetric (CSequence a) Int

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) Int

Methods

equalTo :: CSequence a -> Int -> EqCompareType (CSequence a) Int

notEqualTo :: CSequence a -> Int -> EqCompareType (CSequence a) Int

(HasEqAsymmetric a Rational, IsBool (CSequence (EqCompareType a Rational))) => HasEqAsymmetric (CSequence a) Rational

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) Rational

Methods

equalTo :: CSequence a -> Rational -> EqCompareType (CSequence a) Rational

notEqualTo :: CSequence a -> Rational -> EqCompareType (CSequence a) Rational

(HasEqAsymmetric a Dyadic, IsBool (CSequence (EqCompareType a Dyadic))) => HasEqAsymmetric (CSequence a) Dyadic

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) Dyadic

Methods

equalTo :: CSequence a -> Dyadic -> EqCompareType (CSequence a) Dyadic

notEqualTo :: CSequence a -> Dyadic -> EqCompareType (CSequence a) Dyadic

HasOrderAsymmetric a MPBall => HasOrderAsymmetric (CSequence a) MPBall

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) MPBall

Methods

lessThan :: CSequence a -> MPBall -> OrderCompareType (CSequence a) MPBall

greaterThan :: CSequence a -> MPBall -> OrderCompareType (CSequence a) MPBall

leq :: CSequence a -> MPBall -> OrderCompareType (CSequence a) MPBall

geq :: CSequence a -> MPBall -> OrderCompareType (CSequence a) MPBall

(HasOrderAsymmetric a Integer, IsBool (CSequence (OrderCompareType a Integer))) => HasOrderAsymmetric (CSequence a) Integer

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) Integer

Methods

lessThan :: CSequence a -> Integer -> OrderCompareType (CSequence a) Integer

greaterThan :: CSequence a -> Integer -> OrderCompareType (CSequence a) Integer

leq :: CSequence a -> Integer -> OrderCompareType (CSequence a) Integer

geq :: CSequence a -> Integer -> OrderCompareType (CSequence a) Integer

(HasOrderAsymmetric a Int, IsBool (CSequence (OrderCompareType a Int))) => HasOrderAsymmetric (CSequence a) Int

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) Int

Methods

lessThan :: CSequence a -> Int -> OrderCompareType (CSequence a) Int

greaterThan :: CSequence a -> Int -> OrderCompareType (CSequence a) Int

leq :: CSequence a -> Int -> OrderCompareType (CSequence a) Int

geq :: CSequence a -> Int -> OrderCompareType (CSequence a) Int

(HasOrderAsymmetric a Rational, IsBool (CSequence (OrderCompareType a Rational))) => HasOrderAsymmetric (CSequence a) Rational

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) Rational

Methods

lessThan :: CSequence a -> Rational -> OrderCompareType (CSequence a) Rational

greaterThan :: CSequence a -> Rational -> OrderCompareType (CSequence a) Rational

leq :: CSequence a -> Rational -> OrderCompareType (CSequence a) Rational

geq :: CSequence a -> Rational -> OrderCompareType (CSequence a) Rational

(HasOrderAsymmetric a Dyadic, IsBool (CSequence (OrderCompareType a Dyadic))) => HasOrderAsymmetric (CSequence a) Dyadic

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) Dyadic

Methods

lessThan :: CSequence a -> Dyadic -> OrderCompareType (CSequence a) Dyadic

greaterThan :: CSequence a -> Dyadic -> OrderCompareType (CSequence a) Dyadic

leq :: CSequence a -> Dyadic -> OrderCompareType (CSequence a) Dyadic

geq :: CSequence a -> Dyadic -> OrderCompareType (CSequence a) Dyadic

ConvertibleExactly (WithAnyPrec (CN MPBall)) CReal

Defined in AERN2.Real.Type

Methods

safeConvertExactly :: WithAnyPrec (CN MPBall) -> ConvertResult CReal

CanExtractApproximation (CSequence t) Precision

Defined in AERN2.Real.Type

Associated Types

type ExtractedApproximation (CSequence t) Precision

Methods

extractApproximation :: CSequence t -> Precision -> ExtractedApproximation (CSequence t) Precision

HasAccuracy t => CanExtractApproximation (CSequence t) Accuracy

Defined in AERN2.Real.Type

Associated Types

type ExtractedApproximation (CSequence t) Accuracy

Methods

extractApproximation :: CSequence t -> Accuracy -> ExtractedApproximation (CSequence t) Accuracy

(CanDiv Int a, CanTestZero a) => CanDiv (CN Int) (CSequence a)

Defined in AERN2.Real.FieldTH

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)

Defined in AERN2.Real.FieldTH

Associated Types

type DivType (CN Integer) (CSequence a)

Methods

divide :: CN Integer -> CSequence a -> DivType (CN Integer) (CSequence a)

(CanDiv Rational a, CanTestZero a) => CanDiv (CN Rational) (CSequence a)

Defined in AERN2.Real.FieldTH

Associated Types

type DivType (CN Rational) (CSequence a)

Methods

divide :: CN Rational -> CSequence a -> DivType (CN Rational) (CSequence a)

(CanDiv MPBall b, CanTestZero b) => CanDiv (CN MPBall) (CSequence b)

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)

Defined in AERN2.Real.FieldTH

Associated Types

type DivType (CN Dyadic) (CSequence a)

Methods

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

CanDiv a Integer => CanDiv (CSequence a) (CN Integer)

Defined in AERN2.Real.FieldTH

Associated Types

type DivType (CSequence a) (CN Integer)

Methods

divide :: CSequence a -> CN Integer -> DivType (CSequence a) (CN Integer)

CanDiv a Int => CanDiv (CSequence a) (CN Int)

Defined in AERN2.Real.FieldTH

Associated Types

type DivType (CSequence a) (CN Int)

Methods

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

CanDiv a Rational => CanDiv (CSequence a) (CN Rational)

Defined in AERN2.Real.FieldTH

Associated Types

type DivType (CSequence a) (CN Rational)

Methods

divide :: CSequence a -> CN Rational -> DivType (CSequence a) (CN Rational)

CanDiv a Dyadic => CanDiv (CSequence a) (CN Dyadic)

Defined in AERN2.Real.FieldTH

Associated Types

type DivType (CSequence a) (CN Dyadic)

Methods

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

CanDiv b MPBall => CanDiv (CSequence b) (CN MPBall)

Defined in AERN2.Real.Field

Associated Types

type DivType (CSequence b) (CN MPBall)

Methods

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

(CanDiv t1 t2, CanTestZero t2) => CanDiv (CSequence t1) (CSequence t2)

Defined in AERN2.Real.Field

Associated Types

type DivType (CSequence t1) (CSequence t2)

Methods

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

(CanPow b e, HasOrderCertainly b Integer, HasOrderCertainly e Integer, HasEqCertainly b Integer, CanTestInteger e, CanTestIsIntegerType b, CanTestIsIntegerType e) => CanPow (CSequence b) (CSequence e)

Defined in AERN2.Real.Field

Associated Types

type PowType (CSequence b) (CSequence e)

type PPowType (CSequence b) (CSequence e)

Methods

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

ppow :: CSequence b -> CSequence e -> PPowType (CSequence b) (CSequence e)

(CanMulAsymmetric Int a, CanGiveUpIfVeryInaccurate (MulType Int a)) => CanMulAsymmetric (CN Int) (CSequence a)

Defined in AERN2.Real.FieldTH

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)

Defined in AERN2.Real.FieldTH

Associated Types

type MulType (CN Integer) (CSequence a)

Methods

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

(CanMulAsymmetric Rational a, CanGiveUpIfVeryInaccurate (MulType Rational a)) => CanMulAsymmetric (CN Rational) (CSequence a)

Defined in AERN2.Real.FieldTH

Associated Types

type MulType (CN Rational) (CSequence a)

Methods

mul :: CN Rational -> CSequence a -> MulType (CN Rational) (CSequence a)

(CanMulAsymmetric MPBall b, CanGiveUpIfVeryInaccurate (MulType MPBall b)) => CanMulAsymmetric (CN MPBall) (CSequence b)

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)

Defined in AERN2.Real.FieldTH

Associated Types

type MulType (CN Dyadic) (CSequence a)

Methods

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

(CanMulAsymmetric a Integer, CanGiveUpIfVeryInaccurate (MulType a Integer)) => CanMulAsymmetric (CSequence a) (CN Integer)

Defined in AERN2.Real.FieldTH

Associated Types

type MulType (CSequence a) (CN Integer)

Methods

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

(CanMulAsymmetric a Int, CanGiveUpIfVeryInaccurate (MulType a Int)) => CanMulAsymmetric (CSequence a) (CN Int)

Defined in AERN2.Real.FieldTH

Associated Types

type MulType (CSequence a) (CN Int)

Methods

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

(CanMulAsymmetric a Rational, CanGiveUpIfVeryInaccurate (MulType a Rational)) => CanMulAsymmetric (CSequence a) (CN Rational)

Defined in AERN2.Real.FieldTH

Associated Types

type MulType (CSequence a) (CN Rational)

Methods

mul :: CSequence a -> CN Rational -> MulType (CSequence a) (CN Rational)

(CanMulAsymmetric a Dyadic, CanGiveUpIfVeryInaccurate (MulType a Dyadic)) => CanMulAsymmetric (CSequence a) (CN Dyadic)

Defined in AERN2.Real.FieldTH

Associated Types

type MulType (CSequence a) (CN Dyadic)

Methods

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

(CanMulAsymmetric b MPBall, CanGiveUpIfVeryInaccurate (MulType b MPBall)) => CanMulAsymmetric (CSequence b) (CN MPBall)

Defined in AERN2.Real.Field

Associated Types

type MulType (CSequence b) (CN MPBall)

Methods

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

(CanMulAsymmetric t1 t2, CanGiveUpIfVeryInaccurate (MulType t1 t2)) => CanMulAsymmetric (CSequence t1) (CSequence t2)

Defined in AERN2.Real.Field

Associated Types

type MulType (CSequence t1) (CSequence t2)

Methods

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

CanAddAsymmetric Int a => CanAddAsymmetric (CN Int) (CSequence a)

Defined in AERN2.Real.FieldTH

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)

Defined in AERN2.Real.FieldTH

Associated Types

type AddType (CN Integer) (CSequence a)

Methods

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

CanAddAsymmetric Rational a => CanAddAsymmetric (CN Rational) (CSequence a)

Defined in AERN2.Real.FieldTH

Associated Types

type AddType (CN Rational) (CSequence a)

Methods

add :: CN Rational -> CSequence a -> AddType (CN Rational) (CSequence a)

CanAddAsymmetric MPBall b => CanAddAsymmetric (CN MPBall) (CSequence b)

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)

Defined in AERN2.Real.FieldTH

Associated Types

type AddType (CN Dyadic) (CSequence a)

Methods

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

CanAddAsymmetric a Integer => CanAddAsymmetric (CSequence a) (CN Integer)

Defined in AERN2.Real.FieldTH

Associated Types

type AddType (CSequence a) (CN Integer)

Methods

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

CanAddAsymmetric a Int => CanAddAsymmetric (CSequence a) (CN Int)

Defined in AERN2.Real.FieldTH

Associated Types

type AddType (CSequence a) (CN Int)

Methods

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

CanAddAsymmetric a Rational => CanAddAsymmetric (CSequence a) (CN Rational)

Defined in AERN2.Real.FieldTH

Associated Types

type AddType (CSequence a) (CN Rational)

Methods

add :: CSequence a -> CN Rational -> AddType (CSequence a) (CN Rational)

CanAddAsymmetric a Dyadic => CanAddAsymmetric (CSequence a) (CN Dyadic)

Defined in AERN2.Real.FieldTH

Associated Types

type AddType (CSequence a) (CN Dyadic)

Methods

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

CanAddAsymmetric b MPBall => CanAddAsymmetric (CSequence b) (CN MPBall)

Defined in AERN2.Real.Field

Associated Types

type AddType (CSequence b) (CN MPBall)

Methods

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

CanAddAsymmetric t1 t2 => CanAddAsymmetric (CSequence t1) (CSequence t2)

Defined in AERN2.Real.Field

Associated Types

type AddType (CSequence t1) (CSequence t2)

Methods

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

CanSub Int a => CanSub (CN Int) (CSequence a)

Defined in AERN2.Real.FieldTH

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)

Defined in AERN2.Real.FieldTH

Associated Types

type SubType (CN Integer) (CSequence a)

Methods

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

CanSub Rational a => CanSub (CN Rational) (CSequence a)

Defined in AERN2.Real.FieldTH

Associated Types

type SubType (CN Rational) (CSequence a)

Methods

sub :: CN Rational -> CSequence a -> SubType (CN Rational) (CSequence a)

CanSub MPBall b => CanSub (CN MPBall) (CSequence b)

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)

Defined in AERN2.Real.FieldTH

Associated Types

type SubType (CN Dyadic) (CSequence a)

Methods

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

CanSub a Integer => CanSub (CSequence a) (CN Integer)

Defined in AERN2.Real.FieldTH

Associated Types

type SubType (CSequence a) (CN Integer)

Methods

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

CanSub a Int => CanSub (CSequence a) (CN Int)

Defined in AERN2.Real.FieldTH

Associated Types

type SubType (CSequence a) (CN Int)

Methods

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

CanSub a Rational => CanSub (CSequence a) (CN Rational)

Defined in AERN2.Real.FieldTH

Associated Types

type SubType (CSequence a) (CN Rational)

Methods

sub :: CSequence a -> CN Rational -> SubType (CSequence a) (CN Rational)

CanSub a Dyadic => CanSub (CSequence a) (CN Dyadic)

Defined in AERN2.Real.FieldTH

Associated Types

type SubType (CSequence a) (CN Dyadic)

Methods

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

CanSub b MPBall => CanSub (CSequence b) (CN MPBall)

Defined in AERN2.Real.Field

Associated Types

type SubType (CSequence b) (CN MPBall)

Methods

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

CanSub t1 t2 => CanSub (CSequence t1) (CSequence t2)

Defined in AERN2.Real.Field

Associated Types

type SubType (CSequence t1) (CSequence t2)

Methods

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

CanMinMaxAsymmetric Int a => CanMinMaxAsymmetric (CN Int) (CSequence a)

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)

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CN Integer) (CSequence a)

Methods

min :: CN Integer -> CSequence a -> MinMaxType (CN Integer) (CSequence a)

max :: CN Integer -> CSequence a -> MinMaxType (CN Integer) (CSequence a)

CanMinMaxAsymmetric Rational a => CanMinMaxAsymmetric (CN Rational) (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CN Rational) (CSequence a)

Methods

min :: CN Rational -> CSequence a -> MinMaxType (CN Rational) (CSequence a)

max :: CN Rational -> CSequence a -> MinMaxType (CN Rational) (CSequence a)

CanMinMaxAsymmetric MPBall a => CanMinMaxAsymmetric (CN MPBall) (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CN MPBall) (CSequence a)

Methods

min :: CN MPBall -> CSequence a -> MinMaxType (CN MPBall) (CSequence a)

max :: CN MPBall -> CSequence a -> MinMaxType (CN MPBall) (CSequence a)

CanMinMaxAsymmetric Dyadic a => CanMinMaxAsymmetric (CN Dyadic) (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CN Dyadic) (CSequence a)

Methods

min :: CN Dyadic -> CSequence a -> MinMaxType (CN Dyadic) (CSequence a)

max :: CN Dyadic -> CSequence a -> MinMaxType (CN Dyadic) (CSequence a)

CanMinMaxAsymmetric a MPBall => CanMinMaxAsymmetric (CSequence a) (CN MPBall)

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) (CN MPBall)

Methods

min :: CSequence a -> CN MPBall -> MinMaxType (CSequence a) (CN MPBall)

max :: CSequence a -> CN MPBall -> MinMaxType (CSequence a) (CN MPBall)

CanMinMaxAsymmetric t1 t2 => CanMinMaxAsymmetric (CSequence t1) (CSequence t2)

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)

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) (CN Integer)

Methods

min :: CSequence a -> CN Integer -> MinMaxType (CSequence a) (CN Integer)

max :: CSequence a -> CN Integer -> MinMaxType (CSequence a) (CN Integer)

CanMinMaxAsymmetric a Int => CanMinMaxAsymmetric (CSequence a) (CN Int)

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)

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) (CN Rational)

Methods

min :: CSequence a -> CN Rational -> MinMaxType (CSequence a) (CN Rational)

max :: CSequence a -> CN Rational -> MinMaxType (CSequence a) (CN Rational)

CanMinMaxAsymmetric a Dyadic => CanMinMaxAsymmetric (CSequence a) (CN Dyadic)

Defined in AERN2.Real.Comparisons

Associated Types

type MinMaxType (CSequence a) (CN Dyadic)

Methods

min :: CSequence a -> CN Dyadic -> MinMaxType (CSequence a) (CN Dyadic)

max :: CSequence a -> CN Dyadic -> MinMaxType (CSequence a) (CN Dyadic)

(HasEqAsymmetric Int a, IsBool (CSequence (EqCompareType Int a))) => HasEqAsymmetric (CN Int) (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CN Int) (CSequence a)

Methods

equalTo :: CN Int -> CSequence a -> EqCompareType (CN Int) (CSequence a)

notEqualTo :: CN Int -> CSequence a -> EqCompareType (CN Int) (CSequence a)

(HasEqAsymmetric Integer a, IsBool (CSequence (EqCompareType Integer a))) => HasEqAsymmetric (CN Integer) (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CN Integer) (CSequence a)

Methods

equalTo :: CN Integer -> CSequence a -> EqCompareType (CN Integer) (CSequence a)

notEqualTo :: CN Integer -> CSequence a -> EqCompareType (CN Integer) (CSequence a)

(HasEqAsymmetric Rational a, IsBool (CSequence (EqCompareType Rational a))) => HasEqAsymmetric (CN Rational) (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CN Rational) (CSequence a)

Methods

equalTo :: CN Rational -> CSequence a -> EqCompareType (CN Rational) (CSequence a)

notEqualTo :: CN Rational -> CSequence a -> EqCompareType (CN Rational) (CSequence a)

HasEqAsymmetric MPBall b => HasEqAsymmetric (CN MPBall) (CSequence b)

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CN MPBall) (CSequence b)

Methods

equalTo :: CN MPBall -> CSequence b -> EqCompareType (CN MPBall) (CSequence b)

notEqualTo :: CN MPBall -> CSequence b -> EqCompareType (CN MPBall) (CSequence b)

(HasEqAsymmetric Dyadic a, IsBool (CSequence (EqCompareType Dyadic a))) => HasEqAsymmetric (CN Dyadic) (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CN Dyadic) (CSequence a)

Methods

equalTo :: CN Dyadic -> CSequence a -> EqCompareType (CN Dyadic) (CSequence a)

notEqualTo :: CN Dyadic -> CSequence a -> EqCompareType (CN Dyadic) (CSequence a)

HasEqAsymmetric a MPBall => HasEqAsymmetric (CSequence a) (CN MPBall)

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) (CN MPBall)

Methods

equalTo :: CSequence a -> CN MPBall -> EqCompareType (CSequence a) (CN MPBall)

notEqualTo :: CSequence a -> CN MPBall -> EqCompareType (CSequence a) (CN MPBall)

(HasEqAsymmetric t1 t2, IsBool (CSequence (EqCompareType t1 t2))) => HasEqAsymmetric (CSequence t1) (CSequence t2)

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence t1) (CSequence t2)

Methods

equalTo :: CSequence t1 -> CSequence t2 -> EqCompareType (CSequence t1) (CSequence t2)

notEqualTo :: CSequence t1 -> CSequence t2 -> EqCompareType (CSequence t1) (CSequence t2)

(HasEqAsymmetric a Integer, IsBool (CSequence (EqCompareType a Integer))) => HasEqAsymmetric (CSequence a) (CN Integer)

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) (CN Integer)

Methods

equalTo :: CSequence a -> CN Integer -> EqCompareType (CSequence a) (CN Integer)

notEqualTo :: CSequence a -> CN Integer -> EqCompareType (CSequence a) (CN Integer)

(HasEqAsymmetric a Int, IsBool (CSequence (EqCompareType a Int))) => HasEqAsymmetric (CSequence a) (CN Int)

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) (CN Int)

Methods

equalTo :: CSequence a -> CN Int -> EqCompareType (CSequence a) (CN Int)

notEqualTo :: CSequence a -> CN Int -> EqCompareType (CSequence a) (CN Int)

(HasEqAsymmetric a Rational, IsBool (CSequence (EqCompareType a Rational))) => HasEqAsymmetric (CSequence a) (CN Rational)

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) (CN Rational)

Methods

equalTo :: CSequence a -> CN Rational -> EqCompareType (CSequence a) (CN Rational)

notEqualTo :: CSequence a -> CN Rational -> EqCompareType (CSequence a) (CN Rational)

(HasEqAsymmetric a Dyadic, IsBool (CSequence (EqCompareType a Dyadic))) => HasEqAsymmetric (CSequence a) (CN Dyadic)

Defined in AERN2.Real.Comparisons

Associated Types

type EqCompareType (CSequence a) (CN Dyadic)

Methods

equalTo :: CSequence a -> CN Dyadic -> EqCompareType (CSequence a) (CN Dyadic)

notEqualTo :: CSequence a -> CN Dyadic -> EqCompareType (CSequence a) (CN Dyadic)

(HasOrderAsymmetric Int a, IsBool (CSequence (OrderCompareType Int a))) => HasOrderAsymmetric (CN Int) (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CN Int) (CSequence a)

Methods

lessThan :: CN Int -> CSequence a -> OrderCompareType (CN Int) (CSequence a)

greaterThan :: CN Int -> CSequence a -> OrderCompareType (CN Int) (CSequence a)

leq :: CN Int -> CSequence a -> OrderCompareType (CN Int) (CSequence a)

geq :: CN Int -> CSequence a -> OrderCompareType (CN Int) (CSequence a)

(HasOrderAsymmetric Integer a, IsBool (CSequence (OrderCompareType Integer a))) => HasOrderAsymmetric (CN Integer) (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CN Integer) (CSequence a)

Methods

lessThan :: CN Integer -> CSequence a -> OrderCompareType (CN Integer) (CSequence a)

greaterThan :: CN Integer -> CSequence a -> OrderCompareType (CN Integer) (CSequence a)

leq :: CN Integer -> CSequence a -> OrderCompareType (CN Integer) (CSequence a)

geq :: CN Integer -> CSequence a -> OrderCompareType (CN Integer) (CSequence a)

(HasOrderAsymmetric Rational a, IsBool (CSequence (OrderCompareType Rational a))) => HasOrderAsymmetric (CN Rational) (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CN Rational) (CSequence a)

Methods

lessThan :: CN Rational -> CSequence a -> OrderCompareType (CN Rational) (CSequence a)

greaterThan :: CN Rational -> CSequence a -> OrderCompareType (CN Rational) (CSequence a)

leq :: CN Rational -> CSequence a -> OrderCompareType (CN Rational) (CSequence a)

geq :: CN Rational -> CSequence a -> OrderCompareType (CN Rational) (CSequence a)

HasOrderAsymmetric MPBall b => HasOrderAsymmetric (CN MPBall) (CSequence b)

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CN MPBall) (CSequence b)

Methods

lessThan :: CN MPBall -> CSequence b -> OrderCompareType (CN MPBall) (CSequence b)

greaterThan :: CN MPBall -> CSequence b -> OrderCompareType (CN MPBall) (CSequence b)

leq :: CN MPBall -> CSequence b -> OrderCompareType (CN MPBall) (CSequence b)

geq :: CN MPBall -> CSequence b -> OrderCompareType (CN MPBall) (CSequence b)

(HasOrderAsymmetric Dyadic a, IsBool (CSequence (OrderCompareType Dyadic a))) => HasOrderAsymmetric (CN Dyadic) (CSequence a)

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CN Dyadic) (CSequence a)

Methods

lessThan :: CN Dyadic -> CSequence a -> OrderCompareType (CN Dyadic) (CSequence a)

greaterThan :: CN Dyadic -> CSequence a -> OrderCompareType (CN Dyadic) (CSequence a)

leq :: CN Dyadic -> CSequence a -> OrderCompareType (CN Dyadic) (CSequence a)

geq :: CN Dyadic -> CSequence a -> OrderCompareType (CN Dyadic) (CSequence a)

HasOrderAsymmetric a MPBall => HasOrderAsymmetric (CSequence a) (CN MPBall)

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) (CN MPBall)

Methods

lessThan :: CSequence a -> CN MPBall -> OrderCompareType (CSequence a) (CN MPBall)

greaterThan :: CSequence a -> CN MPBall -> OrderCompareType (CSequence a) (CN MPBall)

leq :: CSequence a -> CN MPBall -> OrderCompareType (CSequence a) (CN MPBall)

geq :: CSequence a -> CN MPBall -> OrderCompareType (CSequence a) (CN MPBall)

(HasOrderAsymmetric t1 t2, IsBool (CSequence (OrderCompareType t1 t2))) => HasOrderAsymmetric (CSequence t1) (CSequence t2)

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence t1) (CSequence t2)

Methods

lessThan :: CSequence t1 -> CSequence t2 -> OrderCompareType (CSequence t1) (CSequence t2)

greaterThan :: CSequence t1 -> CSequence t2 -> OrderCompareType (CSequence t1) (CSequence t2)

leq :: CSequence t1 -> CSequence t2 -> OrderCompareType (CSequence t1) (CSequence t2)

geq :: CSequence t1 -> CSequence t2 -> OrderCompareType (CSequence t1) (CSequence t2)

(HasOrderAsymmetric a Integer, IsBool (CSequence (OrderCompareType a Integer))) => HasOrderAsymmetric (CSequence a) (CN Integer)

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) (CN Integer)

Methods

lessThan :: CSequence a -> CN Integer -> OrderCompareType (CSequence a) (CN Integer)

greaterThan :: CSequence a -> CN Integer -> OrderCompareType (CSequence a) (CN Integer)

leq :: CSequence a -> CN Integer -> OrderCompareType (CSequence a) (CN Integer)

geq :: CSequence a -> CN Integer -> OrderCompareType (CSequence a) (CN Integer)

(HasOrderAsymmetric a Int, IsBool (CSequence (OrderCompareType a Int))) => HasOrderAsymmetric (CSequence a) (CN Int)

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) (CN Int)

Methods

lessThan :: CSequence a -> CN Int -> OrderCompareType (CSequence a) (CN Int)

greaterThan :: CSequence a -> CN Int -> OrderCompareType (CSequence a) (CN Int)

leq :: CSequence a -> CN Int -> OrderCompareType (CSequence a) (CN Int)

geq :: CSequence a -> CN Int -> OrderCompareType (CSequence a) (CN Int)

(HasOrderAsymmetric a Rational, IsBool (CSequence (OrderCompareType a Rational))) => HasOrderAsymmetric (CSequence a) (CN Rational)

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) (CN Rational)

Methods

lessThan :: CSequence a -> CN Rational -> OrderCompareType (CSequence a) (CN Rational)

greaterThan :: CSequence a -> CN Rational -> OrderCompareType (CSequence a) (CN Rational)

leq :: CSequence a -> CN Rational -> OrderCompareType (CSequence a) (CN Rational)

geq :: CSequence a -> CN Rational -> OrderCompareType (CSequence a) (CN Rational)

(HasOrderAsymmetric a Dyadic, IsBool (CSequence (OrderCompareType a Dyadic))) => HasOrderAsymmetric (CSequence a) (CN Dyadic)

Defined in AERN2.Real.Comparisons

Associated Types

type OrderCompareType (CSequence a) (CN Dyadic)

Methods

lessThan :: CSequence a -> CN Dyadic -> OrderCompareType (CSequence a) (CN Dyadic)

greaterThan :: CSequence a -> CN Dyadic -> OrderCompareType (CSequence a) (CN Dyadic)

leq :: CSequence a -> CN Dyadic -> OrderCompareType (CSequence a) (CN Dyadic)

geq :: CSequence a -> CN Dyadic -> OrderCompareType (CSequence a) (CN Dyadic)

CanAndOrAsymmetric t1 t2 => CanAndOrAsymmetric (CSequence t1) (CSequence t2)

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 SelectType CKleenean

Defined in AERN2.Real.CKleenean

type SelectType CKleenean = Bool

type SqrtType CReal

Defined in AERN2.Real.Elementary

type SqrtType CReal = CReal

type ExpType CReal

Defined in AERN2.Real.Elementary

type ExpType CReal = CReal

type LogType CReal

Defined in AERN2.Real.Elementary

type LogType CReal = CReal

type SinCosType CReal

Defined in AERN2.Real.Elementary

type SinCosType CReal = CReal

type LimitType Int CReal

Defined in AERN2.Real.Limit

type LimitType Int CReal = CReal

type LimitType Integer CReal

Defined in AERN2.Real.Limit

type LimitType Integer CReal = CReal

type LimitType Rational CReal

Defined in AERN2.Real.Limit

type LimitType Rational CReal = CReal

type DivType Int (CSequence a)

Defined in AERN2.Real.FieldTH

type DivType Int (CSequence a) = CSequence (DivType Int a)

type DivType Integer (CSequence a)

Defined in AERN2.Real.FieldTH

type DivType Integer (CSequence a) = CSequence (DivType Integer a)

type DivType Rational (CSequence a)

Defined in AERN2.Real.FieldTH

type DivType Rational (CSequence a) = CSequence (DivType Rational a)

type DivType MPBall (CSequence b)

Defined in AERN2.Real.Field

type DivType MPBall (CSequence b) = DivType MPBall b

type DivType Dyadic (CSequence a)

Defined in AERN2.Real.FieldTH

type DivType Dyadic (CSequence a) = CSequence (DivType Dyadic a)

type PPowType Int (CSequence e)

Defined in AERN2.Real.FieldTH

type PPowType Int (CSequence e) = CSequence (PPowType Int e)

type PPowType Integer (CSequence e)

Defined in AERN2.Real.FieldTH

type PPowType Integer (CSequence e) = CSequence (PPowType Integer e)

type PPowType Rational (CSequence e)

Defined in AERN2.Real.FieldTH

type PPowType Rational (CSequence e) = CSequence (PPowType Rational e)

type PowType Int (CSequence e)

Defined in AERN2.Real.FieldTH

type PowType Int (CSequence e) = CSequence (PowType Int e)

type PowType Integer (CSequence e)

Defined in AERN2.Real.FieldTH

type PowType Integer (CSequence e) = CSequence (PowType Integer e)

type PowType Rational (CSequence e)

Defined in AERN2.Real.FieldTH

type PowType Rational (CSequence e) = CSequence (PowType Rational e)

type MulType Int (CSequence a)

Defined in AERN2.Real.FieldTH

type MulType Int (CSequence a) = CSequence (MulType Int a)

type MulType Integer (CSequence a)

Defined in AERN2.Real.FieldTH

type MulType Integer (CSequence a) = CSequence (MulType Integer a)

type MulType Rational (CSequence a)

Defined in AERN2.Real.FieldTH

type MulType Rational (CSequence a) = CSequence (MulType Rational a)

type MulType MPBall (CSequence b)

Defined in AERN2.Real.Field

type MulType MPBall (CSequence b) = MulType MPBall b

type MulType Dyadic (CSequence a)

Defined in AERN2.Real.FieldTH

type MulType Dyadic (CSequence a) = CSequence (MulType Dyadic a)

type AddType Int (CSequence a)

Defined in AERN2.Real.FieldTH

type AddType Int (CSequence a) = CSequence (AddType Int a)

type AddType Integer (CSequence a)

Defined in AERN2.Real.FieldTH

type AddType Integer (CSequence a) = CSequence (AddType Integer a)

type AddType Rational (CSequence a)

Defined in AERN2.Real.FieldTH

type AddType Rational (CSequence a) = CSequence (AddType Rational a)

type AddType MPBall (CSequence b)

Defined in AERN2.Real.Field

type AddType MPBall (CSequence b) = AddType MPBall b

type AddType Dyadic (CSequence a)

Defined in AERN2.Real.FieldTH

type AddType Dyadic (CSequence a) = CSequence (AddType Dyadic a)

type SubType Int (CSequence a)

Defined in AERN2.Real.FieldTH

type SubType Int (CSequence a) = CSequence (SubType Int a)

type SubType Integer (CSequence a)

Defined in AERN2.Real.FieldTH

type SubType Integer (CSequence a) = CSequence (SubType Integer a)

type SubType Rational (CSequence a)

Defined in AERN2.Real.FieldTH

type SubType Rational (CSequence a) = CSequence (SubType Rational a)

type SubType MPBall (CSequence b)

Defined in AERN2.Real.Field

type SubType MPBall (CSequence b) = SubType MPBall b

type SubType Dyadic (CSequence a)

Defined in AERN2.Real.FieldTH

type SubType Dyadic (CSequence a) = CSequence (SubType Dyadic a)

type MinMaxType Int (CSequence a)

Defined in AERN2.Real.Comparisons

type MinMaxType Int (CSequence a) = CSequence (MinMaxType Int a)

type MinMaxType Integer (CSequence a)

Defined in AERN2.Real.Comparisons

type MinMaxType Integer (CSequence a) = CSequence (MinMaxType Integer a)

type MinMaxType Rational (CSequence a)

Defined in AERN2.Real.Comparisons

type MinMaxType Rational (CSequence a) = CSequence (MinMaxType Rational a)

type MinMaxType MPBall (CSequence a)

Defined in AERN2.Real.Comparisons

type MinMaxType MPBall (CSequence a) = MinMaxType (CN MPBall) (CN a)

type MinMaxType Dyadic (CSequence a)

Defined in AERN2.Real.Comparisons

type MinMaxType Dyadic (CSequence a) = CSequence (MinMaxType Dyadic a)

type EqCompareType Int (CSequence a)

Defined in AERN2.Real.Comparisons

type EqCompareType Int (CSequence a) = CSequence (EqCompareType Int a)

type EqCompareType Integer (CSequence a)

Defined in AERN2.Real.Comparisons

type EqCompareType Integer (CSequence a) = CSequence (EqCompareType Integer a)

type EqCompareType Rational (CSequence a)

Defined in AERN2.Real.Comparisons

type EqCompareType Rational (CSequence a) = CSequence (EqCompareType Rational a)

type EqCompareType MPBall (CSequence b)

Defined in AERN2.Real.Comparisons

type EqCompareType MPBall (CSequence b) = EqCompareType (CN MPBall) (CN b)

type EqCompareType Dyadic (CSequence a)

Defined in AERN2.Real.Comparisons

type EqCompareType Dyadic (CSequence a) = CSequence (EqCompareType Dyadic a)

type OrderCompareType Int (CSequence a)

Defined in AERN2.Real.Comparisons

type OrderCompareType Int (CSequence a) = CSequence (OrderCompareType Int a)

type OrderCompareType Integer (CSequence a)

Defined in AERN2.Real.Comparisons

type OrderCompareType Integer (CSequence a) = CSequence (OrderCompareType Integer a)

type OrderCompareType Rational (CSequence a)

Defined in AERN2.Real.Comparisons

type OrderCompareType Rational (CSequence a) = CSequence (OrderCompareType Rational a)

type OrderCompareType MPBall (CSequence b)

Defined in AERN2.Real.Comparisons

type OrderCompareType MPBall (CSequence b) = OrderCompareType (CN MPBall) (CN b)

type OrderCompareType Dyadic (CSequence a)

Defined in AERN2.Real.Comparisons

type OrderCompareType Dyadic (CSequence a) = CSequence (OrderCompareType Dyadic a)

type IfThenElseType CKleenean (CSequence t)

Defined in AERN2.Real.CKleenean

type IfThenElseType CKleenean (CSequence t) = CSequence t

type LimitType Rational (CReal -> CReal)

Defined in AERN2.Real.Limit

type LimitType Rational (CReal -> CReal) = CReal -> CReal

type AbsType (CSequence t1)

Defined in AERN2.Real.Comparisons

type AbsType (CSequence t1) = CSequence (AbsType t1)

type NegType (CSequence t)

Defined in AERN2.Real.CKleenean

type NegType (CSequence t) = CSequence (NegType t)

type DivType (CSequence a) Dyadic

Defined in AERN2.Real.FieldTH

type DivType (CSequence a) Dyadic = CSequence (DivType a Dyadic)

type DivType (CSequence a) Rational

Defined in AERN2.Real.FieldTH

type DivType (CSequence a) Rational = CSequence (DivType a Rational)

type DivType (CSequence a) Int

Defined in AERN2.Real.FieldTH

type DivType (CSequence a) Int = CSequence (DivType a Int)

type DivType (CSequence a) Integer

Defined in AERN2.Real.FieldTH

type DivType (CSequence a) Integer = CSequence (DivType a Integer)

type DivType (CSequence b) MPBall

Defined in AERN2.Real.Field

type DivType (CSequence b) MPBall = DivType b MPBall

type PPowType (CSequence b) Rational

Defined in AERN2.Real.FieldTH

type PPowType (CSequence b) Rational = CSequence (PPowType b Rational)

type PPowType (CSequence b) Int

Defined in AERN2.Real.FieldTH

type PPowType (CSequence b) Int = CSequence (PPowType b Int)

type PPowType (CSequence b) Integer

Defined in AERN2.Real.FieldTH

type PPowType (CSequence b) Integer = CSequence (PPowType b Integer)

type PowType (CSequence b) Rational

Defined in AERN2.Real.FieldTH

type PowType (CSequence b) Rational = CSequence (PowType b Rational)

type PowType (CSequence b) Int

Defined in AERN2.Real.FieldTH

type PowType (CSequence b) Int = CSequence (PowType b Int)

type PowType (CSequence b) Integer

Defined in AERN2.Real.FieldTH

type PowType (CSequence b) Integer = CSequence (PowType b Integer)

type MulType (CSequence a) Dyadic

Defined in AERN2.Real.FieldTH

type MulType (CSequence a) Dyadic = CSequence (MulType a Dyadic)

type MulType (CSequence a) Rational

Defined in AERN2.Real.FieldTH

type MulType (CSequence a) Rational = CSequence (MulType a Rational)

type MulType (CSequence a) Int

Defined in AERN2.Real.FieldTH

type MulType (CSequence a) Int = CSequence (MulType a Int)

type MulType (CSequence a) Integer

Defined in AERN2.Real.FieldTH

type MulType (CSequence a) Integer = CSequence (MulType a Integer)

type MulType (CSequence b) MPBall

Defined in AERN2.Real.Field

type MulType (CSequence b) MPBall = MulType b MPBall

type AddType (CSequence a) Dyadic

Defined in AERN2.Real.FieldTH

type AddType (CSequence a) Dyadic = CSequence (AddType a Dyadic)

type AddType (CSequence a) Rational

Defined in AERN2.Real.FieldTH

type AddType (CSequence a) Rational = CSequence (AddType a Rational)

type AddType (CSequence a) Int

Defined in AERN2.Real.FieldTH

type AddType (CSequence a) Int = CSequence (AddType a Int)

type AddType (CSequence a) Integer

Defined in AERN2.Real.FieldTH

type AddType (CSequence a) Integer = CSequence (AddType a Integer)

type AddType (CSequence b) MPBall

Defined in AERN2.Real.Field

type AddType (CSequence b) MPBall = AddType b MPBall

type SubType (CSequence a) Dyadic

Defined in AERN2.Real.FieldTH

type SubType (CSequence a) Dyadic = CSequence (SubType a Dyadic)

type SubType (CSequence a) Rational

Defined in AERN2.Real.FieldTH

type SubType (CSequence a) Rational = CSequence (SubType a Rational)

type SubType (CSequence a) Int

Defined in AERN2.Real.FieldTH

type SubType (CSequence a) Int = CSequence (SubType a Int)

type SubType (CSequence a) Integer

Defined in AERN2.Real.FieldTH

type SubType (CSequence a) Integer = CSequence (SubType a Integer)

type SubType (CSequence b) MPBall

Defined in AERN2.Real.Field

type SubType (CSequence b) MPBall = SubType b MPBall

type MinMaxType (CSequence a) MPBall

Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) MPBall = MinMaxType (CN a) (CN MPBall)

type MinMaxType (CSequence a) Dyadic

Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) Dyadic = CSequence (MinMaxType a Dyadic)

type MinMaxType (CSequence a) Rational

Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) Rational = CSequence (MinMaxType a Rational)

type MinMaxType (CSequence a) Int

Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) Int = CSequence (MinMaxType a Int)

type MinMaxType (CSequence a) Integer

Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) Integer = CSequence (MinMaxType a Integer)

type EqCompareType (CSequence a) MPBall

Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) MPBall = EqCompareType (CN a) (CN MPBall)

type EqCompareType (CSequence a) Dyadic

Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) Dyadic = CSequence (EqCompareType a Dyadic)

type EqCompareType (CSequence a) Rational

Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) Rational = CSequence (EqCompareType a Rational)

type EqCompareType (CSequence a) Int

Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) Int = CSequence (EqCompareType a Int)

type EqCompareType (CSequence a) Integer

Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) Integer = CSequence (EqCompareType a Integer)

type OrderCompareType (CSequence a) MPBall

Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) MPBall = OrderCompareType (CN a) (CN MPBall)

type OrderCompareType (CSequence a) Dyadic

Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) Dyadic = CSequence (OrderCompareType a Dyadic)

type OrderCompareType (CSequence a) Rational

Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) Rational = CSequence (OrderCompareType a Rational)

type OrderCompareType (CSequence a) Int

Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) Int = CSequence (OrderCompareType a Int)

type OrderCompareType (CSequence a) Integer

Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) Integer = CSequence (OrderCompareType a Integer)

type ExtractedApproximation (CSequence t) Precision

Defined in AERN2.Real.Type

type ExtractedApproximation (CSequence t) Precision = CN t

type ExtractedApproximation (CSequence t) Accuracy

Defined in AERN2.Real.Type

type ExtractedApproximation (CSequence t) Accuracy = CN t

type DivType (CN Int) (CSequence a)

Defined in AERN2.Real.FieldTH

type DivType (CN Int) (CSequence a) = CSequence (DivType Int a)

type DivType (CN Integer) (CSequence a)

Defined in AERN2.Real.FieldTH

type DivType (CN Integer) (CSequence a) = CSequence (DivType Integer a)

type DivType (CN Rational) (CSequence a)

Defined in AERN2.Real.FieldTH

type DivType (CN Rational) (CSequence a) = CSequence (DivType Rational a)

type DivType (CN MPBall) (CSequence b)

Defined in AERN2.Real.Field

type DivType (CN MPBall) (CSequence b) = DivType (CN MPBall) (CN b)

type DivType (CN Dyadic) (CSequence a)

Defined in AERN2.Real.FieldTH

type DivType (CN Dyadic) (CSequence a) = CSequence (DivType Dyadic a)

type DivType (CSequence a) (CN Dyadic)

Defined in AERN2.Real.FieldTH

type DivType (CSequence a) (CN Dyadic) = CSequence (DivType a Dyadic)

type DivType (CSequence a) (CN Rational)

Defined in AERN2.Real.FieldTH

type DivType (CSequence a) (CN Rational) = CSequence (DivType a Rational)

type DivType (CSequence a) (CN Int)

Defined in AERN2.Real.FieldTH

type DivType (CSequence a) (CN Int) = CSequence (DivType a Int)

type DivType (CSequence a) (CN Integer)

Defined in AERN2.Real.FieldTH

type DivType (CSequence a) (CN Integer) = CSequence (DivType a Integer)

type DivType (CSequence b) (CN MPBall)

Defined in AERN2.Real.Field

type DivType (CSequence b) (CN MPBall) = DivType (CN b) (CN MPBall)

type DivType (CSequence t1) (CSequence t2)

Defined in AERN2.Real.Field

type DivType (CSequence t1) (CSequence t2) = CSequence (DivType t1 t2)

type PPowType (CSequence b) (CSequence e)

Defined in AERN2.Real.Field

type PPowType (CSequence b) (CSequence e) = CSequence (PPowType b e)

type PowType (CSequence b) (CSequence e)

Defined in AERN2.Real.Field

type PowType (CSequence b) (CSequence e) = CSequence (PowType b e)

type MulType (CN Int) (CSequence a)

Defined in AERN2.Real.FieldTH

type MulType (CN Int) (CSequence a) = CSequence (MulType Int a)

type MulType (CN Integer) (CSequence a)

Defined in AERN2.Real.FieldTH

type MulType (CN Integer) (CSequence a) = CSequence (MulType Integer a)

type MulType (CN Rational) (CSequence a)

Defined in AERN2.Real.FieldTH

type MulType (CN Rational) (CSequence a) = CSequence (MulType Rational a)

type MulType (CN MPBall) (CSequence b)

Defined in AERN2.Real.Field

type MulType (CN MPBall) (CSequence b) = MulType (CN MPBall) (CN b)

type MulType (CN Dyadic) (CSequence a)

Defined in AERN2.Real.FieldTH

type MulType (CN Dyadic) (CSequence a) = CSequence (MulType Dyadic a)

type MulType (CSequence a) (CN Dyadic)

Defined in AERN2.Real.FieldTH

type MulType (CSequence a) (CN Dyadic) = CSequence (MulType a Dyadic)

type MulType (CSequence a) (CN Rational)

Defined in AERN2.Real.FieldTH

type MulType (CSequence a) (CN Rational) = CSequence (MulType a Rational)

type MulType (CSequence a) (CN Int)

Defined in AERN2.Real.FieldTH

type MulType (CSequence a) (CN Int) = CSequence (MulType a Int)

type MulType (CSequence a) (CN Integer)

Defined in AERN2.Real.FieldTH

type MulType (CSequence a) (CN Integer) = CSequence (MulType a Integer)

type MulType (CSequence b) (CN MPBall)

Defined in AERN2.Real.Field

type MulType (CSequence b) (CN MPBall) = MulType (CN b) (CN MPBall)

type MulType (CSequence t1) (CSequence t2)

Defined in AERN2.Real.Field

type MulType (CSequence t1) (CSequence t2) = CSequence (MulType t1 t2)

type AddType (CN Int) (CSequence a)

Defined in AERN2.Real.FieldTH

type AddType (CN Int) (CSequence a) = CSequence (AddType Int a)

type AddType (CN Integer) (CSequence a)

Defined in AERN2.Real.FieldTH

type AddType (CN Integer) (CSequence a) = CSequence (AddType Integer a)

type AddType (CN Rational) (CSequence a)

Defined in AERN2.Real.FieldTH

type AddType (CN Rational) (CSequence a) = CSequence (AddType Rational a)

type AddType (CN MPBall) (CSequence b)

Defined in AERN2.Real.Field

type AddType (CN MPBall) (CSequence b) = AddType (CN MPBall) (CN b)

type AddType (CN Dyadic) (CSequence a)

Defined in AERN2.Real.FieldTH

type AddType (CN Dyadic) (CSequence a) = CSequence (AddType Dyadic a)

type AddType (CSequence a) (CN Dyadic)

Defined in AERN2.Real.FieldTH

type AddType (CSequence a) (CN Dyadic) = CSequence (AddType a Dyadic)

type AddType (CSequence a) (CN Rational)

Defined in AERN2.Real.FieldTH

type AddType (CSequence a) (CN Rational) = CSequence (AddType a Rational)

type AddType (CSequence a) (CN Int)

Defined in AERN2.Real.FieldTH

type AddType (CSequence a) (CN Int) = CSequence (AddType a Int)

type AddType (CSequence a) (CN Integer)

Defined in AERN2.Real.FieldTH

type AddType (CSequence a) (CN Integer) = CSequence (AddType a Integer)

type AddType (CSequence b) (CN MPBall)

Defined in AERN2.Real.Field

type AddType (CSequence b) (CN MPBall) = AddType (CN b) (CN MPBall)

type AddType (CSequence t1) (CSequence t2)

Defined in AERN2.Real.Field

type AddType (CSequence t1) (CSequence t2) = CSequence (AddType t1 t2)

type SubType (CN Int) (CSequence a)

Defined in AERN2.Real.FieldTH

type SubType (CN Int) (CSequence a) = CSequence (SubType Int a)

type SubType (CN Integer) (CSequence a)

Defined in AERN2.Real.FieldTH

type SubType (CN Integer) (CSequence a) = CSequence (SubType Integer a)

type SubType (CN Rational) (CSequence a)

Defined in AERN2.Real.FieldTH

type SubType (CN Rational) (CSequence a) = CSequence (SubType Rational a)

type SubType (CN MPBall) (CSequence b)

Defined in AERN2.Real.Field

type SubType (CN MPBall) (CSequence b) = SubType (CN MPBall) (CN b)

type SubType (CN Dyadic) (CSequence a)

Defined in AERN2.Real.FieldTH

type SubType (CN Dyadic) (CSequence a) = CSequence (SubType Dyadic a)

type SubType (CSequence a) (CN Dyadic)

Defined in AERN2.Real.FieldTH

type SubType (CSequence a) (CN Dyadic) = CSequence (SubType a Dyadic)

type SubType (CSequence a) (CN Rational)

Defined in AERN2.Real.FieldTH

type SubType (CSequence a) (CN Rational) = CSequence (SubType a Rational)

type SubType (CSequence a) (CN Int)

Defined in AERN2.Real.FieldTH

type SubType (CSequence a) (CN Int) = CSequence (SubType a Int)

type SubType (CSequence a) (CN Integer)

Defined in AERN2.Real.FieldTH

type SubType (CSequence a) (CN Integer) = CSequence (SubType a Integer)

type SubType (CSequence b) (CN MPBall)

Defined in AERN2.Real.Field

type SubType (CSequence b) (CN MPBall) = SubType (CN b) (CN MPBall)

type SubType (CSequence t1) (CSequence t2)

Defined in AERN2.Real.Field

type SubType (CSequence t1) (CSequence t2) = CSequence (SubType t1 t2)

type MinMaxType (CN Int) (CSequence a)

Defined in AERN2.Real.Comparisons

type MinMaxType (CN Int) (CSequence a) = CSequence (MinMaxType Int a)

type MinMaxType (CN Integer) (CSequence a)

Defined in AERN2.Real.Comparisons

type MinMaxType (CN Integer) (CSequence a) = CSequence (MinMaxType Integer a)

type MinMaxType (CN Rational) (CSequence a)

Defined in AERN2.Real.Comparisons

type MinMaxType (CN Rational) (CSequence a) = CSequence (MinMaxType Rational a)

type MinMaxType (CN MPBall) (CSequence a)

Defined in AERN2.Real.Comparisons

type MinMaxType (CN MPBall) (CSequence a) = MinMaxType (CN MPBall) (CN a)

type MinMaxType (CN Dyadic) (CSequence a)

Defined in AERN2.Real.Comparisons

type MinMaxType (CN Dyadic) (CSequence a) = CSequence (MinMaxType Dyadic a)

type MinMaxType (CSequence a) (CN MPBall)

Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) (CN MPBall) = MinMaxType (CN a) (CN MPBall)

type MinMaxType (CSequence t1) (CSequence t2)

Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence t1) (CSequence t2) = CSequence (MinMaxType t1 t2)

type MinMaxType (CSequence a) (CN Dyadic)

Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) (CN Dyadic) = CSequence (MinMaxType a Dyadic)

type MinMaxType (CSequence a) (CN Rational)

Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) (CN Rational) = CSequence (MinMaxType a Rational)

type MinMaxType (CSequence a) (CN Int)

Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) (CN Int) = CSequence (MinMaxType a Int)

type MinMaxType (CSequence a) (CN Integer)

Defined in AERN2.Real.Comparisons

type MinMaxType (CSequence a) (CN Integer) = CSequence (MinMaxType a Integer)

type EqCompareType (CN Int) (CSequence a)

Defined in AERN2.Real.Comparisons

type EqCompareType (CN Int) (CSequence a) = CSequence (EqCompareType Int a)

type EqCompareType (CN Integer) (CSequence a)

Defined in AERN2.Real.Comparisons

type EqCompareType (CN Integer) (CSequence a) = CSequence (EqCompareType Integer a)

type EqCompareType (CN Rational) (CSequence a)

Defined in AERN2.Real.Comparisons

type EqCompareType (CN Rational) (CSequence a) = CSequence (EqCompareType Rational a)

type EqCompareType (CN MPBall) (CSequence b)

Defined in AERN2.Real.Comparisons

type EqCompareType (CN MPBall) (CSequence b) = EqCompareType (CN MPBall) (CN b)

type EqCompareType (CN Dyadic) (CSequence a)

Defined in AERN2.Real.Comparisons

type EqCompareType (CN Dyadic) (CSequence a) = CSequence (EqCompareType Dyadic a)

type EqCompareType (CSequence a) (CN MPBall)

Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) (CN MPBall) = EqCompareType (CN a) (CN MPBall)

type EqCompareType (CSequence t1) (CSequence t2)

Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence t1) (CSequence t2) = CSequence (EqCompareType t1 t2)

type EqCompareType (CSequence a) (CN Dyadic)

Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) (CN Dyadic) = CSequence (EqCompareType a Dyadic)

type EqCompareType (CSequence a) (CN Rational)

Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) (CN Rational) = CSequence (EqCompareType a Rational)

type EqCompareType (CSequence a) (CN Int)

Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) (CN Int) = CSequence (EqCompareType a Int)

type EqCompareType (CSequence a) (CN Integer)

Defined in AERN2.Real.Comparisons

type EqCompareType (CSequence a) (CN Integer) = CSequence (EqCompareType a Integer)

type OrderCompareType (CN Int) (CSequence a)

Defined in AERN2.Real.Comparisons

type OrderCompareType (CN Int) (CSequence a) = CSequence (OrderCompareType Int a)

type OrderCompareType (CN Integer) (CSequence a)

Defined in AERN2.Real.Comparisons

type OrderCompareType (CN Integer) (CSequence a) = CSequence (OrderCompareType Integer a)

type OrderCompareType (CN Rational) (CSequence a)

Defined in AERN2.Real.Comparisons

type OrderCompareType (CN Rational) (CSequence a) = CSequence (OrderCompareType Rational a)

type OrderCompareType (CN MPBall) (CSequence b)

Defined in AERN2.Real.Comparisons

type OrderCompareType (CN MPBall) (CSequence b) = OrderCompareType (CN MPBall) (CN b)

type OrderCompareType (CN Dyadic) (CSequence a)

Defined in AERN2.Real.Comparisons

type OrderCompareType (CN Dyadic) (CSequence a) = CSequence (OrderCompareType Dyadic a)

type OrderCompareType (CSequence a) (CN MPBall)

Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) (CN MPBall) = OrderCompareType (CN a) (CN MPBall)

type OrderCompareType (CSequence t1) (CSequence t2)

Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence t1) (CSequence t2) = CSequence (OrderCompareType t1 t2)

type OrderCompareType (CSequence a) (CN Dyadic)

Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) (CN Dyadic) = CSequence (OrderCompareType a Dyadic)

type OrderCompareType (CSequence a) (CN Rational)

Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) (CN Rational) = CSequence (OrderCompareType a Rational)

type OrderCompareType (CSequence a) (CN Int)

Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) (CN Int) = CSequence (OrderCompareType a Int)

type OrderCompareType (CSequence a) (CN Integer)

Defined in AERN2.Real.Comparisons

type OrderCompareType (CSequence a) (CN Integer) = CSequence (OrderCompareType a Integer)

type AndOrType (CSequence t1) (CSequence t2)

Defined in AERN2.Real.CKleenean

type AndOrType (CSequence t1) (CSequence t2) = CSequence (AndOrType t1 t2)

cseqShowDefaultIndex :: Integer

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

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

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

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

cseqPrecisions :: [Precision]

cseqIndexForPrecision :: Precision -> Integer

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

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

type CReal = CSequence MPBall

type HasCReals t = ConvertibleExactly CReal t

type CanBeCReal t = ConvertibleExactly t CReal

creal :: CanBeCReal t => t -> CReal

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

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

class CanExtractApproximation e q where

Associated Types

type ExtractedApproximation e q

Methods

extractApproximation

Arguments

:: e

exact value

-> q

query

-> ExtractedApproximation e q

Get an approximation of an exact value using the given query

Instances

CanExtractApproximation (CSequence t) Precision

Defined in AERN2.Real.Type

Associated Types

type ExtractedApproximation (CSequence t) Precision

Methods

extractApproximation :: CSequence t -> Precision -> ExtractedApproximation (CSequence t) Precision

HasAccuracy t => CanExtractApproximation (CSequence t) Accuracy

Defined in AERN2.Real.Type

Associated Types

type ExtractedApproximation (CSequence t) Accuracy

Methods

extractApproximation :: CSequence t -> Accuracy -> ExtractedApproximation (CSequence t) Accuracy

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

_example1 :: CReal

_example2 :: CN MPBall

_example3 :: CN MPBall