aern2-real-0.1.1.0: Exact real numbers via Cauchy sequences and MPFR

Copyright(c) Michal Konecny
LicenseBSD3
Maintainermikkonecny@gmail.com
Stabilityexperimental
Portabilityportable
Safe HaskellNone
LanguageHaskell98

AERN2.Sequence.Field

Contents

Description

Field operations on convergent sequences.

Orphan instances

(CanDiv MPBall b, SuitableForSeq b, HasNorm (EnsureNoCN b), CanEnsureCN b, CanSetPrecision (DivType MPBall b), CanSetPrecision (DivTypeNoCN MPBall b)) => CanDiv MPBall (Sequence b) # 
Instance details

Associated Types

type DivTypeNoCN MPBall (Sequence b) :: * #

type DivType MPBall (Sequence b) :: * #

(QAArrow to, CanDiv Int b, SuitableForSeq b, SuitableForSeq (DivType Int b), SuitableForSeq (DivTypeNoCN Int b), HasNorm (EnsureNoCN b)) => CanDiv Int (SequenceA to b) # 
Instance details

Associated Types

type DivTypeNoCN Int (SequenceA to b) :: * #

type DivType Int (SequenceA to b) :: * #

Methods

divideNoCN :: Int -> SequenceA to b -> DivTypeNoCN Int (SequenceA to b) #

divide :: Int -> SequenceA to b -> DivType Int (SequenceA to b) #

(QAArrow to, CanDiv Integer b, SuitableForSeq b, SuitableForSeq (DivType Integer b), SuitableForSeq (DivTypeNoCN Integer b), HasNorm (EnsureNoCN b)) => CanDiv Integer (SequenceA to b) # 
Instance details

Associated Types

type DivTypeNoCN Integer (SequenceA to b) :: * #

type DivType Integer (SequenceA to b) :: * #

(QAArrow to, CanDiv Rational b, SuitableForSeq b, SuitableForSeq (DivType Rational b), SuitableForSeq (DivTypeNoCN Rational b), HasNorm (EnsureNoCN b)) => CanDiv Rational (SequenceA to b) # 
Instance details

Associated Types

type DivTypeNoCN Rational (SequenceA to b) :: * #

type DivType Rational (SequenceA to b) :: * #

(QAArrow to, CanDiv Dyadic b, SuitableForSeq b, SuitableForSeq (DivType Dyadic b), SuitableForSeq (DivTypeNoCN Dyadic b), HasNorm (EnsureNoCN b)) => CanDiv Dyadic (SequenceA to b) # 
Instance details

Associated Types

type DivTypeNoCN Dyadic (SequenceA to b) :: * #

type DivType Dyadic (SequenceA to b) :: * #

(CanDiv a MPBall, SuitableForSeq a, CanSetPrecision (DivType a MPBall), CanSetPrecision (DivTypeNoCN a MPBall)) => CanDiv (Sequence a) MPBall # 
Instance details

Associated Types

type DivTypeNoCN (Sequence a) MPBall :: * #

type DivType (Sequence a) MPBall :: * #

(QAArrow to, CanDiv a Integer, SuitableForSeq a, SuitableForSeq (DivType a Integer), SuitableForSeq (DivTypeNoCN a Integer)) => CanDiv (SequenceA to a) Integer # 
Instance details

Associated Types

type DivTypeNoCN (SequenceA to a) Integer :: * #

type DivType (SequenceA to a) Integer :: * #

(QAArrow to, CanDiv a Int, SuitableForSeq a, SuitableForSeq (DivType a Int), SuitableForSeq (DivTypeNoCN a Int)) => CanDiv (SequenceA to a) Int # 
Instance details

Associated Types

type DivTypeNoCN (SequenceA to a) Int :: * #

type DivType (SequenceA to a) Int :: * #

Methods

divideNoCN :: SequenceA to a -> Int -> DivTypeNoCN (SequenceA to a) Int #

divide :: SequenceA to a -> Int -> DivType (SequenceA to a) Int #

(QAArrow to, CanDiv a Rational, SuitableForSeq a, SuitableForSeq (DivType a Rational), SuitableForSeq (DivTypeNoCN a Rational)) => CanDiv (SequenceA to a) Rational # 
Instance details

Associated Types

type DivTypeNoCN (SequenceA to a) Rational :: * #

type DivType (SequenceA to a) Rational :: * #

(QAArrow to, CanDiv a Dyadic, SuitableForSeq a, SuitableForSeq (DivType a Dyadic), SuitableForSeq (DivTypeNoCN a Dyadic)) => CanDiv (SequenceA to a) Dyadic # 
Instance details

Associated Types

type DivTypeNoCN (SequenceA to a) Dyadic :: * #

type DivType (SequenceA to a) Dyadic :: * #

(CanDiv a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (DivType a (SequenceA to b)), CanEnsureCE es (DivTypeNoCN a (SequenceA to b)), SuitableForCE es) => CanDiv (CollectErrors es a) (SequenceA to b) # 
Instance details

Associated Types

type DivTypeNoCN (CollectErrors es a) (SequenceA to b) :: * #

type DivType (CollectErrors es a) (SequenceA to b) :: * #

Methods

divideNoCN :: CollectErrors es a -> SequenceA to b -> DivTypeNoCN (CollectErrors es a) (SequenceA to b) #

divide :: CollectErrors es a -> SequenceA to b -> DivType (CollectErrors es a) (SequenceA to b) #

(CanDiv (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (DivType (SequenceA to a) b), CanEnsureCE es (DivTypeNoCN (SequenceA to a) b), SuitableForCE es) => CanDiv (SequenceA to a) (CollectErrors es b) # 
Instance details

Associated Types

type DivTypeNoCN (SequenceA to a) (CollectErrors es b) :: * #

type DivType (SequenceA to a) (CollectErrors es b) :: * #

Methods

divideNoCN :: SequenceA to a -> CollectErrors es b -> DivTypeNoCN (SequenceA to a) (CollectErrors es b) #

divide :: SequenceA to a -> CollectErrors es b -> DivType (SequenceA to a) (CollectErrors es b) #

(QAArrow to, CanDiv a b, HasNorm (EnsureNoCN a), HasNorm (EnsureNoCN b), SuitableForSeq a, SuitableForSeq b, SuitableForSeq (DivType a b), SuitableForSeq (DivTypeNoCN a b)) => CanDiv (SequenceA to a) (SequenceA to b) # 
Instance details

Associated Types

type DivTypeNoCN (SequenceA to a) (SequenceA to b) :: * #

type DivType (SequenceA to a) (SequenceA to b) :: * #

Methods

divideNoCN :: SequenceA to a -> SequenceA to b -> DivTypeNoCN (SequenceA to a) (SequenceA to b) #

divide :: SequenceA to a -> SequenceA to b -> DivType (SequenceA to a) (SequenceA to b) #