AERN2.Real.Field

Field operations on Cauchy Real numbers.

field ops (add, sub, mul, div) for `CReal -> CReal -> CReal`

field ops for `CReal -> t -> CReal` and `t -> CReal -> CReal` where t is Int, Integer, Rational, Dyadic

field ops for `CReal -> MPBall -> MPBall` and `CReal -> CN MPBall -> CN MPBall`

Orphan instances

Num CReal

Methods

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

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

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

negate :: CReal -> CReal

abs :: CReal -> CReal

signum :: CReal -> CReal

fromInteger :: Integer -> CReal

Fractional CReal

Methods

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

recip :: CReal -> CReal

fromRational :: Rational -> CReal

Field CReal

OrderedField CReal

OrderedRing CReal

Ring CReal

CanAddAsymmetric MPBall b => CanAddAsymmetric MPBall (CSequence b)

Associated Types

type AddType MPBall (CSequence b)

Methods

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

CanSub MPBall b => CanSub MPBall (CSequence b)

Associated Types

type SubType MPBall (CSequence b)

Methods

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

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

Associated Types

type DivType MPBall (CSequence b)

Methods

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

CanMulAsymmetric MPBall b => CanMulAsymmetric MPBall (CSequence b)

Associated Types

type MulType MPBall (CSequence b)

Methods

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

CanAddAsymmetric b MPBall => CanAddAsymmetric (CSequence b) MPBall

Associated Types

type AddType (CSequence b) MPBall

Methods

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

CanSub b MPBall => CanSub (CSequence b) MPBall

Associated Types

type SubType (CSequence b) MPBall

Methods

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

CanDiv b MPBall => CanDiv (CSequence b) MPBall

Associated Types

type DivType (CSequence b) MPBall

Methods

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

CanMulAsymmetric b MPBall => CanMulAsymmetric (CSequence b) MPBall

Associated Types

type MulType (CSequence b) MPBall

Methods

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

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

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)

Associated Types

type AddType (CSequence t1) (CSequence t2)

Methods

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

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

Associated Types

type AddType (CN MPBall) (CSequence b)

Methods

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

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

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)

Associated Types

type SubType (CSequence t1) (CSequence t2)

Methods

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

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

Associated Types

type SubType (CN MPBall) (CSequence b)

Methods

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

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

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)

Associated Types

type DivType (CSequence t1) (CSequence t2)

Methods

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

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

Associated Types

type DivType (CN MPBall) (CSequence b)

Methods

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

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

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)

Associated Types

type MulType (CSequence t1) (CSequence t2)

Methods

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

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

Associated Types

type MulType (CN MPBall) (CSequence b)

Methods

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

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

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)