Copyright	(c) Michal Konecny
License	BSD3
Maintainer	[email protected]
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010

AERN2.MP.Ball.Field

Contents

Orphan instances

Description

Field operations on arbitrary precision dyadic balls

Documentation

mulBalls :: MPBall -> MPBall -> MPBall Source #

mulByEndpoints :: MPBall -> MPBall -> MPBall Source #

Orphan instances

CanAddAsymmetric MPBall MPBall Source #

Instance details

Associated Types

type AddType MPBall MPBall
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall MPBall = MPBall

Methods

add :: MPBall -> MPBall -> AddType MPBall MPBall #

CanAddAsymmetric MPBall Dyadic Source #

Instance details

Associated Types

type AddType MPBall Dyadic
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall Dyadic = MPBall

Methods

add :: MPBall -> Dyadic -> AddType MPBall Dyadic #

CanAddAsymmetric MPBall Rational Source #

Instance details

Associated Types

type AddType MPBall Rational
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall Rational = MPBall

Methods

add :: MPBall -> Rational -> AddType MPBall Rational #

CanAddAsymmetric MPBall Integer Source #

Instance details

Associated Types

type AddType MPBall Integer
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall Integer = MPBall

Methods

add :: MPBall -> Integer -> AddType MPBall Integer #

CanAddAsymmetric MPBall Int Source #

Instance details

Associated Types

type AddType MPBall Int
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall Int = MPBall

Methods

add :: MPBall -> Int -> AddType MPBall Int #

CanAddAsymmetric Dyadic MPBall Source #

Instance details

Associated Types

type AddType Dyadic MPBall
Instance details Defined in AERN2.MP.Ball.Field type AddType Dyadic MPBall = MPBall

Methods

add :: Dyadic -> MPBall -> AddType Dyadic MPBall #

CanAddAsymmetric Rational MPBall Source #

Instance details

Associated Types

type AddType Rational MPBall
Instance details Defined in AERN2.MP.Ball.Field type AddType Rational MPBall = MPBall

Methods

add :: Rational -> MPBall -> AddType Rational MPBall #

CanAddAsymmetric Integer MPBall Source #

Instance details

Associated Types

type AddType Integer MPBall
Instance details Defined in AERN2.MP.Ball.Field type AddType Integer MPBall = MPBall

Methods

add :: Integer -> MPBall -> AddType Integer MPBall #

CanAddAsymmetric Int MPBall Source #

Instance details

Associated Types

type AddType Int MPBall
Instance details Defined in AERN2.MP.Ball.Field type AddType Int MPBall = MPBall

Methods

add :: Int -> MPBall -> AddType Int MPBall #

CanSub MPBall MPBall Source #

Instance details

Associated Types

type SubType MPBall MPBall
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall MPBall = AddType MPBall (NegType MPBall)

Methods

sub :: MPBall -> MPBall -> SubType MPBall MPBall #

CanSub MPBall Dyadic Source #

Instance details

Associated Types

type SubType MPBall Dyadic
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall Dyadic = AddType MPBall (NegType Dyadic)

Methods

sub :: MPBall -> Dyadic -> SubType MPBall Dyadic #

CanSub MPBall Rational Source #

Instance details

Associated Types

type SubType MPBall Rational
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall Rational = AddType MPBall (NegType Rational)

Methods

sub :: MPBall -> Rational -> SubType MPBall Rational #

CanSub MPBall Integer Source #

Instance details

Associated Types

type SubType MPBall Integer
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall Integer = AddType MPBall (NegType Integer)

Methods

sub :: MPBall -> Integer -> SubType MPBall Integer #

CanSub MPBall Int Source #

Instance details

Associated Types

type SubType MPBall Int
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall Int = AddType MPBall (NegType Int)

Methods

sub :: MPBall -> Int -> SubType MPBall Int #

CanSub Dyadic MPBall Source #

Instance details

Associated Types

type SubType Dyadic MPBall
Instance details Defined in AERN2.MP.Ball.Field type SubType Dyadic MPBall = AddType Dyadic (NegType MPBall)

Methods

sub :: Dyadic -> MPBall -> SubType Dyadic MPBall #

CanSub Rational MPBall Source #

Instance details

Associated Types

type SubType Rational MPBall
Instance details Defined in AERN2.MP.Ball.Field type SubType Rational MPBall = AddType Rational (NegType MPBall)

Methods

sub :: Rational -> MPBall -> SubType Rational MPBall #

CanSub Integer MPBall Source #

Instance details

Associated Types

type SubType Integer MPBall
Instance details Defined in AERN2.MP.Ball.Field type SubType Integer MPBall = AddType Integer (NegType MPBall)

Methods

sub :: Integer -> MPBall -> SubType Integer MPBall #

CanSub Int MPBall Source #

Instance details

Associated Types

type SubType Int MPBall
Instance details Defined in AERN2.MP.Ball.Field type SubType Int MPBall = AddType Int (NegType MPBall)

Methods

sub :: Int -> MPBall -> SubType Int MPBall #

CanDiv MPBall MPBall Source #

Instance details

Associated Types

type DivType MPBall MPBall
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall MPBall = MPBall

Methods

divide :: MPBall -> MPBall -> DivType MPBall MPBall #

CanDiv MPBall Dyadic Source #

Instance details

Associated Types

type DivType MPBall Dyadic
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall Dyadic = MPBall

Methods

divide :: MPBall -> Dyadic -> DivType MPBall Dyadic #

CanDiv MPBall Rational Source #

Instance details

Associated Types

type DivType MPBall Rational
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall Rational = MPBall

Methods

divide :: MPBall -> Rational -> DivType MPBall Rational #

CanDiv MPBall Integer Source #

Instance details

Associated Types

type DivType MPBall Integer
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall Integer = MPBall

Methods

divide :: MPBall -> Integer -> DivType MPBall Integer #

CanDiv MPBall Int Source #

Instance details

Associated Types

type DivType MPBall Int
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall Int = MPBall

Methods

divide :: MPBall -> Int -> DivType MPBall Int #

CanDiv Dyadic MPBall Source #

Instance details

Associated Types

type DivType Dyadic MPBall
Instance details Defined in AERN2.MP.Ball.Field type DivType Dyadic MPBall = MPBall

Methods

divide :: Dyadic -> MPBall -> DivType Dyadic MPBall #

CanDiv Dyadic Dyadic Source #

Instance details

Associated Types

type DivType Dyadic Dyadic
Instance details Defined in AERN2.MP.Ball.Field type DivType Dyadic Dyadic = MPBall

Methods

divide :: Dyadic -> Dyadic -> DivType Dyadic Dyadic #

CanDiv Rational MPBall Source #

Instance details

Associated Types

type DivType Rational MPBall
Instance details Defined in AERN2.MP.Ball.Field type DivType Rational MPBall = MPBall

Methods

divide :: Rational -> MPBall -> DivType Rational MPBall #

CanDiv Integer MPBall Source #

Instance details

Associated Types

type DivType Integer MPBall
Instance details Defined in AERN2.MP.Ball.Field type DivType Integer MPBall = MPBall

Methods

divide :: Integer -> MPBall -> DivType Integer MPBall #

CanDiv Int MPBall Source #

Instance details

Associated Types

type DivType Int MPBall
Instance details Defined in AERN2.MP.Ball.Field type DivType Int MPBall = MPBall

Methods

divide :: Int -> MPBall -> DivType Int MPBall #

CanMulAsymmetric MPBall MPBall Source #

Instance details

Associated Types

type MulType MPBall MPBall
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall MPBall = MPBall

Methods

mul :: MPBall -> MPBall -> MulType MPBall MPBall #

CanMulAsymmetric MPBall Dyadic Source #

Instance details

Associated Types

type MulType MPBall Dyadic
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall Dyadic = MPBall

Methods

mul :: MPBall -> Dyadic -> MulType MPBall Dyadic #

CanMulAsymmetric MPBall Rational Source #

Instance details

Associated Types

type MulType MPBall Rational
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall Rational = MPBall

Methods

mul :: MPBall -> Rational -> MulType MPBall Rational #

CanMulAsymmetric MPBall Integer Source #

Instance details

Associated Types

type MulType MPBall Integer
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall Integer = MPBall

Methods

mul :: MPBall -> Integer -> MulType MPBall Integer #

CanMulAsymmetric MPBall Int Source #

Instance details

Associated Types

type MulType MPBall Int
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall Int = MPBall

Methods

mul :: MPBall -> Int -> MulType MPBall Int #

CanMulAsymmetric Dyadic MPBall Source #

Instance details

Associated Types

type MulType Dyadic MPBall
Instance details Defined in AERN2.MP.Ball.Field type MulType Dyadic MPBall = MPBall

Methods

mul :: Dyadic -> MPBall -> MulType Dyadic MPBall #

CanMulAsymmetric Rational MPBall Source #

Instance details

Associated Types

type MulType Rational MPBall
Instance details Defined in AERN2.MP.Ball.Field type MulType Rational MPBall = MPBall

Methods

mul :: Rational -> MPBall -> MulType Rational MPBall #

CanMulAsymmetric Integer MPBall Source #

Instance details

Associated Types

type MulType Integer MPBall
Instance details Defined in AERN2.MP.Ball.Field type MulType Integer MPBall = MPBall

Methods

mul :: Integer -> MPBall -> MulType Integer MPBall #

CanMulAsymmetric Int MPBall Source #

Instance details

Associated Types

type MulType Int MPBall
Instance details Defined in AERN2.MP.Ball.Field type MulType Int MPBall = MPBall

Methods

mul :: Int -> MPBall -> MulType Int MPBall #

CanPow MPBall Integer Source #

Instance details

Associated Types

type PowType MPBall Integer
Instance details Defined in AERN2.MP.Ball.Field type PowType MPBall Integer = MPBall
type PPowType MPBall Integer
Instance details Defined in AERN2.MP.Ball.Field type PPowType MPBall Integer = PowType MPBall Integer

Methods

pow :: MPBall -> Integer -> PowType MPBall Integer #

ppow :: MPBall -> Integer -> PPowType MPBall Integer #

CanPow MPBall Int Source #

Instance details

Associated Types

type PowType MPBall Int
Instance details Defined in AERN2.MP.Ball.Field type PowType MPBall Int = MPBall
type PPowType MPBall Int
Instance details Defined in AERN2.MP.Ball.Field type PPowType MPBall Int = PowType MPBall Int

Methods

pow :: MPBall -> Int -> PowType MPBall Int #

ppow :: MPBall -> Int -> PPowType MPBall Int #

CanDivIMod MPBall MPBall Source #

Instance details

Associated Types

type DivIType MPBall MPBall
Instance details Defined in AERN2.MP.Ball.Field type DivIType MPBall MPBall = Integer
type ModType MPBall MPBall
Instance details Defined in AERN2.MP.Ball.Field type ModType MPBall MPBall = MPBall

Methods

divIMod :: MPBall -> MPBall -> (DivIType MPBall MPBall, ModType MPBall MPBall) #

mod :: MPBall -> MPBall -> ModType MPBall MPBall #

divI :: MPBall -> MPBall -> DivIType MPBall MPBall #

CanAddAsymmetric MPBall b => CanAddAsymmetric MPBall (CN b) Source #

Instance details

Associated Types

type AddType MPBall (CN b)
Instance details Defined in AERN2.MP.Ball.Field type AddType MPBall (CN b) = CN (AddType MPBall b)

Methods

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

CanSub MPBall b => CanSub MPBall (CN b) Source #

Instance details

Associated Types

type SubType MPBall (CN b)
Instance details Defined in AERN2.MP.Ball.Field type SubType MPBall (CN b) = CN (SubType MPBall b)

Methods

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

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

Instance details

Associated Types

type DivType MPBall (CN b)
Instance details Defined in AERN2.MP.Ball.Field type DivType MPBall (CN b) = CN (DivType MPBall b)

Methods

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

CanMulAsymmetric MPBall b => CanMulAsymmetric MPBall (CN b) Source #

Instance details

Associated Types

type MulType MPBall (CN b)
Instance details Defined in AERN2.MP.Ball.Field type MulType MPBall (CN b) = CN (MulType MPBall b)

Methods

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

CanPow MPBall b => CanPow MPBall (CN b) Source #

Instance details

Associated Types

type PowType MPBall (CN b)
Instance details Defined in AERN2.MP.Ball.Field type PowType MPBall (CN b) = CN (PowType MPBall b)
type PPowType MPBall (CN b)
Instance details Defined in AERN2.MP.Ball.Field type PPowType MPBall (CN b) = PowType MPBall (CN b)

Methods

pow :: MPBall -> CN b -> PowType MPBall (CN b) #

ppow :: MPBall -> CN b -> PPowType MPBall (CN b) #

CanAddAsymmetric a MPBall => CanAddAsymmetric (CN a) MPBall Source #

Instance details

Associated Types

type AddType (CN a) MPBall
Instance details Defined in AERN2.MP.Ball.Field type AddType (CN a) MPBall = CN (AddType a MPBall)

Methods

add :: CN a -> MPBall -> AddType (CN a) MPBall #

CanSub a MPBall => CanSub (CN a) MPBall Source #

Instance details

Associated Types

type SubType (CN a) MPBall
Instance details Defined in AERN2.MP.Ball.Field type SubType (CN a) MPBall = CN (SubType a MPBall)

Methods

sub :: CN a -> MPBall -> SubType (CN a) MPBall #

CanDiv a MPBall => CanDiv (CN a) MPBall Source #

Instance details

Associated Types

type DivType (CN a) MPBall
Instance details Defined in AERN2.MP.Ball.Field type DivType (CN a) MPBall = CN (DivType a MPBall)

Methods

divide :: CN a -> MPBall -> DivType (CN a) MPBall #

CanMulAsymmetric a MPBall => CanMulAsymmetric (CN a) MPBall Source #

Instance details

Associated Types

type MulType (CN a) MPBall
Instance details Defined in AERN2.MP.Ball.Field type MulType (CN a) MPBall = CN (MulType a MPBall)

Methods

mul :: CN a -> MPBall -> MulType (CN a) MPBall #

CanPow a MPBall => CanPow (CN a) MPBall Source #

Instance details

Associated Types

type PowType (CN a) MPBall
Instance details Defined in AERN2.MP.Ball.Field type PowType (CN a) MPBall = CN (PowType a MPBall)
type PPowType (CN a) MPBall
Instance details Defined in AERN2.MP.Ball.Field type PPowType (CN a) MPBall = PowType (CN a) MPBall

Methods

pow :: CN a -> MPBall -> PowType (CN a) MPBall #

ppow :: CN a -> MPBall -> PPowType (CN a) MPBall #