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

Fractional CReal

Methods

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

recip :: CReal -> CReal

fromRational :: Rational -> CReal

Num CReal

Methods

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

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

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

negate :: CReal -> CReal

abs :: CReal -> CReal

signum :: CReal -> CReal

fromInteger :: Integer -> CReal

Field CReal

OrderedField CReal

Ring CReal

OrderedRing CReal

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

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)

Associated Types

type PowType Integer (CSequence e)

Methods

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

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

Associated Types

type PowType Rational (CSequence e)

Methods

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

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

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)

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)

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)

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)

Associated Types

type DivType Dyadic (CSequence a)

Methods

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

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

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)

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)

Associated Types

type MulType Rational (CSequence a)

Methods

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

CanMulAsymmetric MPBall b => CanMulAsymmetric MPBall (CSequence b)

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)

Associated Types

type MulType Dyadic (CSequence a)

Methods

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

CanAddAsymmetric Int a => CanAddAsymmetric Int (CSequence a)

Associated Types

type AddType Int (CSequence a)

Methods

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

CanAddAsymmetric Integer a => CanAddAsymmetric Integer (CSequence a)

Associated Types

type AddType Integer (CSequence a)

Methods

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

CanAddAsymmetric Rational a => CanAddAsymmetric Rational (CSequence a)

Associated Types

type AddType Rational (CSequence a)

Methods

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

CanAddAsymmetric MPBall b => CanAddAsymmetric MPBall (CSequence b)

Associated Types

type AddType MPBall (CSequence b)

Methods

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

CanAddAsymmetric Dyadic a => CanAddAsymmetric Dyadic (CSequence a)

Associated Types

type AddType Dyadic (CSequence a)

Methods

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

CanSub Int a => CanSub Int (CSequence a)

Associated Types

type SubType Int (CSequence a)

Methods

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

CanSub Integer a => CanSub Integer (CSequence a)

Associated Types

type SubType Integer (CSequence a)

Methods

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

CanSub Rational a => CanSub Rational (CSequence a)

Associated Types

type SubType Rational (CSequence a)

Methods

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

CanSub MPBall b => CanSub MPBall (CSequence b)

Associated Types

type SubType MPBall (CSequence b)

Methods

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

CanSub Dyadic a => CanSub Dyadic (CSequence a)

Associated Types

type SubType Dyadic (CSequence a)

Methods

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

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

Associated Types

type PowType (CSequence b) Integer

Methods

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

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

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

Associated Types

type PowType (CSequence b) Rational

Methods

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

CanDiv b MPBall => CanDiv (CSequence b) MPBall

Associated Types

type DivType (CSequence b) MPBall

Methods

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

CanDiv a Integer => CanDiv (CSequence a) Integer

Associated Types

type DivType (CSequence a) Integer

Methods

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

CanDiv a Int => CanDiv (CSequence a) Int

Associated Types

type DivType (CSequence a) Int

Methods

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

CanDiv a Rational => CanDiv (CSequence a) Rational

Associated Types

type DivType (CSequence a) Rational

Methods

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

CanDiv a Dyadic => CanDiv (CSequence a) Dyadic

Associated Types

type DivType (CSequence a) Dyadic

Methods

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

CanMulAsymmetric b MPBall => CanMulAsymmetric (CSequence b) MPBall

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

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

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

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

Associated Types

type MulType (CSequence a) Dyadic

Methods

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

CanAddAsymmetric b MPBall => CanAddAsymmetric (CSequence b) MPBall

Associated Types

type AddType (CSequence b) MPBall

Methods

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

CanAddAsymmetric a Integer => CanAddAsymmetric (CSequence a) Integer

Associated Types

type AddType (CSequence a) Integer

Methods

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

CanAddAsymmetric a Int => CanAddAsymmetric (CSequence a) Int

Associated Types

type AddType (CSequence a) Int

Methods

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

CanAddAsymmetric a Rational => CanAddAsymmetric (CSequence a) Rational

Associated Types

type AddType (CSequence a) Rational

Methods

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

CanAddAsymmetric a Dyadic => CanAddAsymmetric (CSequence a) Dyadic

Associated Types

type AddType (CSequence a) Dyadic

Methods

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

CanSub b MPBall => CanSub (CSequence b) MPBall

Associated Types

type SubType (CSequence b) MPBall

Methods

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

CanSub a Integer => CanSub (CSequence a) Integer

Associated Types

type SubType (CSequence a) Integer

Methods

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

CanSub a Int => CanSub (CSequence a) Int

Associated Types

type SubType (CSequence a) Int

Methods

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

CanSub a Rational => CanSub (CSequence a) Rational

Associated Types

type SubType (CSequence a) Rational

Methods

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

CanSub a Dyadic => CanSub (CSequence a) Dyadic

Associated Types

type SubType (CSequence a) Dyadic

Methods

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

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

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

Associated Types

type SubType (CSequence a) (CN Dyadic)

Methods

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