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.Comparison

Contents

Description

Comparison operations on convergent sequences.

Synopsis

Documentation

type SeqBool = SeqBoolA (->) Source #

data SequenceAtAccuracy a Source #

SequenceAtAccuracy exists only so that we can QuickCheck that Sequence satisfies properties whose statement relies on an instance of HasEqCertainly. Sequence is not an instance but SequenceAtAccuracy is.

Instances

Show a => Show (SequenceAtAccuracy a) Source # 
(HasOrderAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (OrderCompareType a b)) => HasOrderAsymmetric (SequenceAtAccuracy a) (SequenceAtAccuracy b) Source # 
(HasEqAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (EqCompareType a b)) => HasEqAsymmetric (SequenceAtAccuracy a) (SequenceAtAccuracy b) Source # 
type OrderCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) Source # 
type EqCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) Source # 

Orphan instances

(CanMinMaxAsymmetric MPBall b, SuitableForSeq b, CanSetPrecision (MinMaxType MPBall b)) => CanMinMaxAsymmetric MPBall (Sequence b) Source # 

Associated Types

type MinMaxType MPBall (Sequence b) :: * #

(QAArrow to0, CanMinMaxAsymmetric Int b0, SuitableForSeq b0, SuitableForSeq (MinMaxType Int b0)) => CanMinMaxAsymmetric Int (SequenceA to0 b0) Source # 

Associated Types

type MinMaxType Int (SequenceA to0 b0) :: * #

Methods

min :: Int -> SequenceA to0 b0 -> MinMaxType Int (SequenceA to0 b0) #

max :: Int -> SequenceA to0 b0 -> MinMaxType Int (SequenceA to0 b0) #

(QAArrow to0, CanMinMaxAsymmetric Integer b0, SuitableForSeq b0, SuitableForSeq (MinMaxType Integer b0)) => CanMinMaxAsymmetric Integer (SequenceA to0 b0) Source # 

Associated Types

type MinMaxType Integer (SequenceA to0 b0) :: * #

Methods

min :: Integer -> SequenceA to0 b0 -> MinMaxType Integer (SequenceA to0 b0) #

max :: Integer -> SequenceA to0 b0 -> MinMaxType Integer (SequenceA to0 b0) #

(QAArrow to0, CanMinMaxAsymmetric Rational b0, SuitableForSeq b0, SuitableForSeq (MinMaxType Rational b0)) => CanMinMaxAsymmetric Rational (SequenceA to0 b0) Source # 

Associated Types

type MinMaxType Rational (SequenceA to0 b0) :: * #

Methods

min :: Rational -> SequenceA to0 b0 -> MinMaxType Rational (SequenceA to0 b0) #

max :: Rational -> SequenceA to0 b0 -> MinMaxType Rational (SequenceA to0 b0) #

(QAArrow to0, CanMinMaxAsymmetric Dyadic b0, SuitableForSeq b0, SuitableForSeq (MinMaxType Dyadic b0)) => CanMinMaxAsymmetric Dyadic (SequenceA to0 b0) Source # 

Associated Types

type MinMaxType Dyadic (SequenceA to0 b0) :: * #

Methods

min :: Dyadic -> SequenceA to0 b0 -> MinMaxType Dyadic (SequenceA to0 b0) #

max :: Dyadic -> SequenceA to0 b0 -> MinMaxType Dyadic (SequenceA to0 b0) #

(QAArrow to0, HasOrderAsymmetric Int a0, SuitableForSeq a0, SuitableForSeq (OrderCompareType Int a0)) => HasOrderAsymmetric Int (SequenceA to0 a0) Source # 

Associated Types

type OrderCompareType Int (SequenceA to0 a0) :: * #

Methods

lessThan :: Int -> SequenceA to0 a0 -> OrderCompareType Int (SequenceA to0 a0) #

greaterThan :: Int -> SequenceA to0 a0 -> OrderCompareType Int (SequenceA to0 a0) #

leq :: Int -> SequenceA to0 a0 -> OrderCompareType Int (SequenceA to0 a0) #

geq :: Int -> SequenceA to0 a0 -> OrderCompareType Int (SequenceA to0 a0) #

(QAArrow to0, HasOrderAsymmetric Integer a0, SuitableForSeq a0, SuitableForSeq (OrderCompareType Integer a0)) => HasOrderAsymmetric Integer (SequenceA to0 a0) Source # 
(QAArrow to0, HasOrderAsymmetric Rational a0, SuitableForSeq a0, SuitableForSeq (OrderCompareType Rational a0)) => HasOrderAsymmetric Rational (SequenceA to0 a0) Source # 
(QAArrow to0, HasOrderAsymmetric Dyadic a0, SuitableForSeq a0, SuitableForSeq (OrderCompareType Dyadic a0)) => HasOrderAsymmetric Dyadic (SequenceA to0 a0) Source # 

Associated Types

type OrderCompareType Dyadic (SequenceA to0 a0) :: * #

(QAArrow to0, HasEqAsymmetric Int a0, SuitableForSeq a0, SuitableForSeq (EqCompareType Int a0)) => HasEqAsymmetric Int (SequenceA to0 a0) Source # 

Associated Types

type EqCompareType Int (SequenceA to0 a0) :: * #

Methods

equalTo :: Int -> SequenceA to0 a0 -> EqCompareType Int (SequenceA to0 a0) #

notEqualTo :: Int -> SequenceA to0 a0 -> EqCompareType Int (SequenceA to0 a0) #

(QAArrow to0, HasEqAsymmetric Integer a0, SuitableForSeq a0, SuitableForSeq (EqCompareType Integer a0)) => HasEqAsymmetric Integer (SequenceA to0 a0) Source # 

Associated Types

type EqCompareType Integer (SequenceA to0 a0) :: * #

(QAArrow to0, HasEqAsymmetric Rational a0, SuitableForSeq a0, SuitableForSeq (EqCompareType Rational a0)) => HasEqAsymmetric Rational (SequenceA to0 a0) Source # 

Associated Types

type EqCompareType Rational (SequenceA to0 a0) :: * #

(QAArrow to0, HasEqAsymmetric Dyadic a0, SuitableForSeq a0, SuitableForSeq (EqCompareType Dyadic a0)) => HasEqAsymmetric Dyadic (SequenceA to0 a0) Source # 

Associated Types

type EqCompareType Dyadic (SequenceA to0 a0) :: * #

(QAArrow to, HasBools b, SuitableForSeq b) => ConvertibleExactly Bool (SequenceA to b) Source # 
(CanMinMaxAsymmetric a MPBall, SuitableForSeq a, CanSetPrecision (MinMaxType a MPBall)) => CanMinMaxAsymmetric (Sequence a) MPBall Source # 

Associated Types

type MinMaxType (Sequence a) MPBall :: * #

(QAArrow to, CanAbs a, SuitableForSeq a, SuitableForSeq (AbsType a)) => CanAbs (SequenceA to a) Source # 

Associated Types

type AbsType (SequenceA to a) :: * #

Methods

abs :: SequenceA to a -> AbsType (SequenceA to a) #

(QAArrow to, CanNeg a, SuitableForSeq a, SuitableForSeq (NegType a)) => CanNeg (SequenceA to a) Source # 

Associated Types

type NegType (SequenceA to a) :: * #

Methods

negate :: SequenceA to a -> NegType (SequenceA to a) #

(QAArrow to0, CanMinMaxAsymmetric a0 Dyadic, SuitableForSeq a0, SuitableForSeq (MinMaxType a0 Dyadic)) => CanMinMaxAsymmetric (SequenceA to0 a0) Dyadic Source # 

Associated Types

type MinMaxType (SequenceA to0 a0) Dyadic :: * #

Methods

min :: SequenceA to0 a0 -> Dyadic -> MinMaxType (SequenceA to0 a0) Dyadic #

max :: SequenceA to0 a0 -> Dyadic -> MinMaxType (SequenceA to0 a0) Dyadic #

(QAArrow to0, CanMinMaxAsymmetric a0 Rational, SuitableForSeq a0, SuitableForSeq (MinMaxType a0 Rational)) => CanMinMaxAsymmetric (SequenceA to0 a0) Rational Source # 

Associated Types

type MinMaxType (SequenceA to0 a0) Rational :: * #

Methods

min :: SequenceA to0 a0 -> Rational -> MinMaxType (SequenceA to0 a0) Rational #

max :: SequenceA to0 a0 -> Rational -> MinMaxType (SequenceA to0 a0) Rational #

(QAArrow to0, CanMinMaxAsymmetric a0 Int, SuitableForSeq a0, SuitableForSeq (MinMaxType a0 Int)) => CanMinMaxAsymmetric (SequenceA to0 a0) Int Source # 

Associated Types

type MinMaxType (SequenceA to0 a0) Int :: * #

Methods

min :: SequenceA to0 a0 -> Int -> MinMaxType (SequenceA to0 a0) Int #

max :: SequenceA to0 a0 -> Int -> MinMaxType (SequenceA to0 a0) Int #

(QAArrow to0, CanMinMaxAsymmetric a0 Integer, SuitableForSeq a0, SuitableForSeq (MinMaxType a0 Integer)) => CanMinMaxAsymmetric (SequenceA to0 a0) Integer Source # 

Associated Types

type MinMaxType (SequenceA to0 a0) Integer :: * #

Methods

min :: SequenceA to0 a0 -> Integer -> MinMaxType (SequenceA to0 a0) Integer #

max :: SequenceA to0 a0 -> Integer -> MinMaxType (SequenceA to0 a0) Integer #

(QAArrow to0, HasOrderAsymmetric a0 Dyadic, SuitableForSeq a0, SuitableForSeq (OrderCompareType a0 Dyadic)) => HasOrderAsymmetric (SequenceA to0 a0) Dyadic Source # 

Associated Types

type OrderCompareType (SequenceA to0 a0) Dyadic :: * #

(QAArrow to0, HasOrderAsymmetric a0 Rational, SuitableForSeq a0, SuitableForSeq (OrderCompareType a0 Rational)) => HasOrderAsymmetric (SequenceA to0 a0) Rational Source # 
(QAArrow to0, HasOrderAsymmetric a0 Int, SuitableForSeq a0, SuitableForSeq (OrderCompareType a0 Int)) => HasOrderAsymmetric (SequenceA to0 a0) Int Source # 

Associated Types

type OrderCompareType (SequenceA to0 a0) Int :: * #

Methods

lessThan :: SequenceA to0 a0 -> Int -> OrderCompareType (SequenceA to0 a0) Int #

greaterThan :: SequenceA to0 a0 -> Int -> OrderCompareType (SequenceA to0 a0) Int #

leq :: SequenceA to0 a0 -> Int -> OrderCompareType (SequenceA to0 a0) Int #

geq :: SequenceA to0 a0 -> Int -> OrderCompareType (SequenceA to0 a0) Int #

(QAArrow to0, HasOrderAsymmetric a0 Integer, SuitableForSeq a0, SuitableForSeq (OrderCompareType a0 Integer)) => HasOrderAsymmetric (SequenceA to0 a0) Integer Source # 
(QAArrow to0, HasEqAsymmetric a0 Dyadic, SuitableForSeq a0, SuitableForSeq (EqCompareType a0 Dyadic)) => HasEqAsymmetric (SequenceA to0 a0) Dyadic Source # 

Associated Types

type EqCompareType (SequenceA to0 a0) Dyadic :: * #

(QAArrow to0, HasEqAsymmetric a0 Rational, SuitableForSeq a0, SuitableForSeq (EqCompareType a0 Rational)) => HasEqAsymmetric (SequenceA to0 a0) Rational Source # 

Associated Types

type EqCompareType (SequenceA to0 a0) Rational :: * #

(QAArrow to0, HasEqAsymmetric a0 Int, SuitableForSeq a0, SuitableForSeq (EqCompareType a0 Int)) => HasEqAsymmetric (SequenceA to0 a0) Int Source # 

Associated Types

type EqCompareType (SequenceA to0 a0) Int :: * #

Methods

equalTo :: SequenceA to0 a0 -> Int -> EqCompareType (SequenceA to0 a0) Int #

notEqualTo :: SequenceA to0 a0 -> Int -> EqCompareType (SequenceA to0 a0) Int #

(QAArrow to0, HasEqAsymmetric a0 Integer, SuitableForSeq a0, SuitableForSeq (EqCompareType a0 Integer)) => HasEqAsymmetric (SequenceA to0 a0) Integer Source # 

Associated Types

type EqCompareType (SequenceA to0 a0) Integer :: * #

(CanMinMaxAsymmetric a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (MinMaxType a (SequenceA to b)), SuitableForCE es) => CanMinMaxAsymmetric (CollectErrors es a) (SequenceA to b) Source # 

Associated Types

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

Methods

min :: CollectErrors es a -> SequenceA to b -> MinMaxType (CollectErrors es a) (SequenceA to b) #

max :: CollectErrors es a -> SequenceA to b -> MinMaxType (CollectErrors es a) (SequenceA to b) #

(CanMinMaxAsymmetric (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (MinMaxType (SequenceA to a) b), SuitableForCE es) => CanMinMaxAsymmetric (SequenceA to a) (CollectErrors es b) Source # 

Associated Types

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

Methods

min :: SequenceA to a -> CollectErrors es b -> MinMaxType (SequenceA to a) (CollectErrors es b) #

max :: SequenceA to a -> CollectErrors es b -> MinMaxType (SequenceA to a) (CollectErrors es b) #

(QAArrow to, CanMinMaxAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (MinMaxType a b)) => CanMinMaxAsymmetric (SequenceA to a) (SequenceA to b) Source # 

Associated Types

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

Methods

min :: SequenceA to a -> SequenceA to b -> MinMaxType (SequenceA to a) (SequenceA to b) #

max :: SequenceA to a -> SequenceA to b -> MinMaxType (SequenceA to a) (SequenceA to b) #

(HasOrderAsymmetric a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (OrderCompareType a (SequenceA to b)), IsBool (EnsureCE es (OrderCompareType a (SequenceA to b))), SuitableForCE es) => HasOrderAsymmetric (CollectErrors es a) (SequenceA to b) Source # 

Associated Types

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

(HasOrderAsymmetric (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (OrderCompareType (SequenceA to a) b), IsBool (EnsureCE es (OrderCompareType (SequenceA to a) b)), SuitableForCE es) => HasOrderAsymmetric (SequenceA to a) (CollectErrors es b) Source # 

Associated Types

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

(QAArrow to, HasOrderAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (OrderCompareType a b)) => HasOrderAsymmetric (SequenceA to a) (SequenceA to b) Source # 

Associated Types

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

Methods

lessThan :: SequenceA to a -> SequenceA to b -> OrderCompareType (SequenceA to a) (SequenceA to b) #

greaterThan :: SequenceA to a -> SequenceA to b -> OrderCompareType (SequenceA to a) (SequenceA to b) #

leq :: SequenceA to a -> SequenceA to b -> OrderCompareType (SequenceA to a) (SequenceA to b) #

geq :: SequenceA to a -> SequenceA to b -> OrderCompareType (SequenceA to a) (SequenceA to b) #

(HasEqAsymmetric a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (EqCompareType a (SequenceA to b)), IsBool (EnsureCE es (EqCompareType a (SequenceA to b))), SuitableForCE es) => HasEqAsymmetric (CollectErrors es a) (SequenceA to b) Source # 

Associated Types

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

(HasEqAsymmetric (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (EqCompareType (SequenceA to a) b), IsBool (EnsureCE es (EqCompareType (SequenceA to a) b)), SuitableForCE es) => HasEqAsymmetric (SequenceA to a) (CollectErrors es b) Source # 

Associated Types

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

(QAArrow to, HasEqAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (EqCompareType a b)) => HasEqAsymmetric (SequenceA to a) (SequenceA to b) Source # 

Associated Types

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

Methods

equalTo :: SequenceA to a -> SequenceA to b -> EqCompareType (SequenceA to a) (SequenceA to b) #

notEqualTo :: SequenceA to a -> SequenceA to b -> EqCompareType (SequenceA to a) (SequenceA to b) #

(QAArrow to, CanAndOrAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (AndOrType a b)) => CanAndOrAsymmetric (SequenceA to a) (SequenceA to b) Source # 

Associated Types

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

Methods

and2 :: SequenceA to a -> SequenceA to b -> AndOrType (SequenceA to a) (SequenceA to b) #

or2 :: SequenceA to a -> SequenceA to b -> AndOrType (SequenceA to a) (SequenceA to b) #