aern2-real-0.2.16.1: Real numbers as convergent sequences of intervals
Copyright(c) Michal Konecny
LicenseBSD3
Maintainermikkonecny@gmail.com
Stabilityexperimental
Portabilityportable
Safe HaskellSafe-Inferred
LanguageHaskell2010

AERN2.Real.Comparisons

Description

Comparison relations over Cauchy Real numbers.

Orphan instances

(HasEqAsymmetric MPBall b, CanTestCertainly (EqCompareType MPBall b)) => HasEqAsymmetric MPBall (CSequence b) Source # 
Instance details

Associated Types

type EqCompareType MPBall (CSequence b) #

(HasEqAsymmetric Dyadic a, IsBool (CSequence (EqCompareType Dyadic a)), CanTestCertainly (EqCompareType Dyadic a)) => HasEqAsymmetric Dyadic (CSequence a) Source # 
Instance details

Associated Types

type EqCompareType Dyadic (CSequence a) #

(HasEqAsymmetric Rational a, IsBool (CSequence (EqCompareType Rational a)), CanTestCertainly (EqCompareType Rational a)) => HasEqAsymmetric Rational (CSequence a) Source # 
Instance details

Associated Types

type EqCompareType Rational (CSequence a) #

(HasEqAsymmetric Integer a, IsBool (CSequence (EqCompareType Integer a)), CanTestCertainly (EqCompareType Integer a)) => HasEqAsymmetric Integer (CSequence a) Source # 
Instance details

Associated Types

type EqCompareType Integer (CSequence a) #

(HasEqAsymmetric Int a, IsBool (CSequence (EqCompareType Int a)), CanTestCertainly (EqCompareType Int a)) => HasEqAsymmetric Int (CSequence a) Source # 
Instance details

Associated Types

type EqCompareType Int (CSequence a) #

CanMinMaxAsymmetric MPBall a => CanMinMaxAsymmetric MPBall (CSequence a) Source # 
Instance details

Associated Types

type MinMaxType MPBall (CSequence a) #

CanMinMaxAsymmetric Dyadic a => CanMinMaxAsymmetric Dyadic (CSequence a) Source # 
Instance details

Associated Types

type MinMaxType Dyadic (CSequence a) #

CanMinMaxAsymmetric Rational a => CanMinMaxAsymmetric Rational (CSequence a) Source # 
Instance details

Associated Types

type MinMaxType Rational (CSequence a) #

CanMinMaxAsymmetric Integer a => CanMinMaxAsymmetric Integer (CSequence a) Source # 
Instance details

Associated Types

type MinMaxType Integer (CSequence a) #

CanMinMaxAsymmetric Int a => CanMinMaxAsymmetric Int (CSequence a) Source # 
Instance details

Associated Types

type MinMaxType Int (CSequence a) #

(HasOrderAsymmetric MPBall b, CanTestCertainly (OrderCompareType MPBall b)) => HasOrderAsymmetric MPBall (CSequence b) Source # 
Instance details

Associated Types

type OrderCompareType MPBall (CSequence b) #

(HasOrderAsymmetric Dyadic a, IsBool (CSequence (OrderCompareType Dyadic a)), CanTestCertainly (OrderCompareType Dyadic a)) => HasOrderAsymmetric Dyadic (CSequence a) Source # 
Instance details

Associated Types

type OrderCompareType Dyadic (CSequence a) #

(HasOrderAsymmetric Rational a, IsBool (CSequence (OrderCompareType Rational a)), CanTestCertainly (OrderCompareType Rational a)) => HasOrderAsymmetric Rational (CSequence a) Source # 
Instance details

Associated Types

type OrderCompareType Rational (CSequence a) #

(HasOrderAsymmetric Integer a, IsBool (CSequence (OrderCompareType Integer a)), CanTestCertainly (OrderCompareType Integer a)) => HasOrderAsymmetric Integer (CSequence a) Source # 
Instance details

Associated Types

type OrderCompareType Integer (CSequence a) #

(HasOrderAsymmetric Int a, IsBool (CSequence (OrderCompareType Int a)), CanTestCertainly (OrderCompareType Int a)) => HasOrderAsymmetric Int (CSequence a) Source # 
Instance details

Associated Types

type OrderCompareType Int (CSequence a) #

HasEqCertainly a a => Eq (CSequence a) Source # 
Instance details

Methods

(==) :: CSequence a -> CSequence a -> Bool #

(/=) :: CSequence a -> CSequence a -> Bool #

(HasEqCertainly a a, HasOrderCertainly a a) => Ord (CSequence a) Source # 
Instance details

CanAbs t1 => CanAbs (CSequence t1) Source # 
Instance details

Associated Types

type AbsType (CSequence t1) #

Methods

abs :: CSequence t1 -> AbsType (CSequence t1) #

(HasEqAsymmetric a MPBall, CanTestCertainly (EqCompareType a MPBall)) => HasEqAsymmetric (CSequence a) MPBall Source # 
Instance details

Associated Types

type EqCompareType (CSequence a) MPBall #

(HasEqAsymmetric a Dyadic, IsBool (CSequence (EqCompareType a Dyadic)), CanTestCertainly (EqCompareType a Dyadic)) => HasEqAsymmetric (CSequence a) Dyadic Source # 
Instance details

Associated Types

type EqCompareType (CSequence a) Dyadic #

(HasEqAsymmetric a Rational, IsBool (CSequence (EqCompareType a Rational)), CanTestCertainly (EqCompareType a Rational)) => HasEqAsymmetric (CSequence a) Rational Source # 
Instance details

Associated Types

type EqCompareType (CSequence a) Rational #

(HasEqAsymmetric a Integer, IsBool (CSequence (EqCompareType a Integer)), CanTestCertainly (EqCompareType a Integer)) => HasEqAsymmetric (CSequence a) Integer Source # 
Instance details

Associated Types

type EqCompareType (CSequence a) Integer #

(HasEqAsymmetric a Int, IsBool (CSequence (EqCompareType a Int)), CanTestCertainly (EqCompareType a Int)) => HasEqAsymmetric (CSequence a) Int Source # 
Instance details

Associated Types

type EqCompareType (CSequence a) Int #

CanMinMaxAsymmetric a MPBall => CanMinMaxAsymmetric (CSequence a) MPBall Source # 
Instance details

Associated Types

type MinMaxType (CSequence a) MPBall #

CanMinMaxAsymmetric a Dyadic => CanMinMaxAsymmetric (CSequence a) Dyadic Source # 
Instance details

Associated Types

type MinMaxType (CSequence a) Dyadic #

CanMinMaxAsymmetric a Rational => CanMinMaxAsymmetric (CSequence a) Rational Source # 
Instance details

Associated Types

type MinMaxType (CSequence a) Rational #

CanMinMaxAsymmetric a Integer => CanMinMaxAsymmetric (CSequence a) Integer Source # 
Instance details

Associated Types

type MinMaxType (CSequence a) Integer #

CanMinMaxAsymmetric a Int => CanMinMaxAsymmetric (CSequence a) Int Source # 
Instance details

Associated Types

type MinMaxType (CSequence a) Int #

(HasOrderAsymmetric a MPBall, CanTestCertainly (OrderCompareType a MPBall)) => HasOrderAsymmetric (CSequence a) MPBall Source # 
Instance details

Associated Types

type OrderCompareType (CSequence a) MPBall #

(HasOrderAsymmetric a Dyadic, IsBool (CSequence (OrderCompareType a Dyadic)), CanTestCertainly (OrderCompareType a Dyadic)) => HasOrderAsymmetric (CSequence a) Dyadic Source # 
Instance details

Associated Types

type OrderCompareType (CSequence a) Dyadic #

(HasOrderAsymmetric a Rational, IsBool (CSequence (OrderCompareType a Rational)), CanTestCertainly (OrderCompareType a Rational)) => HasOrderAsymmetric (CSequence a) Rational Source # 
Instance details

Associated Types

type OrderCompareType (CSequence a) Rational #

(HasOrderAsymmetric a Integer, IsBool (CSequence (OrderCompareType a Integer)), CanTestCertainly (OrderCompareType a Integer)) => HasOrderAsymmetric (CSequence a) Integer Source # 
Instance details

Associated Types

type OrderCompareType (CSequence a) Integer #

(HasOrderAsymmetric a Int, IsBool (CSequence (OrderCompareType a Int)), CanTestCertainly (OrderCompareType a Int)) => HasOrderAsymmetric (CSequence a) Int Source # 
Instance details

Associated Types

type OrderCompareType (CSequence a) Int #

(HasEqAsymmetric a MPBall, CanTestCertainly (EqCompareType a MPBall)) => HasEqAsymmetric (CSequence a) (CN MPBall) Source # 
Instance details

Associated Types

type EqCompareType (CSequence a) (CN MPBall) #

(HasEqAsymmetric t1 t2, IsBool (CSequence (EqCompareType t1 t2)), CanTestCertainly (EqCompareType t1 t2)) => HasEqAsymmetric (CSequence t1) (CSequence t2) Source # 
Instance details

Associated Types

type EqCompareType (CSequence t1) (CSequence t2) #

(HasEqAsymmetric a Dyadic, IsBool (CSequence (EqCompareType a Dyadic)), CanTestCertainly (EqCompareType a Dyadic)) => HasEqAsymmetric (CSequence a) (CN Dyadic) Source # 
Instance details

Associated Types

type EqCompareType (CSequence a) (CN Dyadic) #

(HasEqAsymmetric a Rational, IsBool (CSequence (EqCompareType a Rational)), CanTestCertainly (EqCompareType a Rational)) => HasEqAsymmetric (CSequence a) (CN Rational) Source # 
Instance details

Associated Types

type EqCompareType (CSequence a) (CN Rational) #

(HasEqAsymmetric a Integer, IsBool (CSequence (EqCompareType a Integer)), CanTestCertainly (EqCompareType a Integer)) => HasEqAsymmetric (CSequence a) (CN Integer) Source # 
Instance details

Associated Types

type EqCompareType (CSequence a) (CN Integer) #

(HasEqAsymmetric a Int, IsBool (CSequence (EqCompareType a Int)), CanTestCertainly (EqCompareType a Int)) => HasEqAsymmetric (CSequence a) (CN Int) Source # 
Instance details

Associated Types

type EqCompareType (CSequence a) (CN Int) #

(HasEqAsymmetric MPBall b, CanTestCertainly (EqCompareType MPBall b)) => HasEqAsymmetric (CN MPBall) (CSequence b) Source # 
Instance details

Associated Types

type EqCompareType (CN MPBall) (CSequence b) #

(HasEqAsymmetric Dyadic a, IsBool (CSequence (EqCompareType Dyadic a)), CanTestCertainly (EqCompareType Dyadic a)) => HasEqAsymmetric (CN Dyadic) (CSequence a) Source # 
Instance details

Associated Types

type EqCompareType (CN Dyadic) (CSequence a) #

(HasEqAsymmetric Rational a, IsBool (CSequence (EqCompareType Rational a)), CanTestCertainly (EqCompareType Rational a)) => HasEqAsymmetric (CN Rational) (CSequence a) Source # 
Instance details

Associated Types

type EqCompareType (CN Rational) (CSequence a) #

(HasEqAsymmetric Integer a, IsBool (CSequence (EqCompareType Integer a)), CanTestCertainly (EqCompareType Integer a)) => HasEqAsymmetric (CN Integer) (CSequence a) Source # 
Instance details

Associated Types

type EqCompareType (CN Integer) (CSequence a) #

(HasEqAsymmetric Int a, IsBool (CSequence (EqCompareType Int a)), CanTestCertainly (EqCompareType Int a)) => HasEqAsymmetric (CN Int) (CSequence a) Source # 
Instance details

Associated Types

type EqCompareType (CN Int) (CSequence a) #

CanMinMaxAsymmetric a MPBall => CanMinMaxAsymmetric (CSequence a) (CN MPBall) Source # 
Instance details

Associated Types

type MinMaxType (CSequence a) (CN MPBall) #

CanMinMaxAsymmetric t1 t2 => CanMinMaxAsymmetric (CSequence t1) (CSequence t2) Source # 
Instance details

Associated Types

type MinMaxType (CSequence t1) (CSequence t2) #

Methods

min :: CSequence t1 -> CSequence t2 -> MinMaxType (CSequence t1) (CSequence t2) #

max :: CSequence t1 -> CSequence t2 -> MinMaxType (CSequence t1) (CSequence t2) #

CanMinMaxAsymmetric a Dyadic => CanMinMaxAsymmetric (CSequence a) (CN Dyadic) Source # 
Instance details

Associated Types

type MinMaxType (CSequence a) (CN Dyadic) #

CanMinMaxAsymmetric a Rational => CanMinMaxAsymmetric (CSequence a) (CN Rational) Source # 
Instance details

Associated Types

type MinMaxType (CSequence a) (CN Rational) #

CanMinMaxAsymmetric a Integer => CanMinMaxAsymmetric (CSequence a) (CN Integer) Source # 
Instance details

Associated Types

type MinMaxType (CSequence a) (CN Integer) #

CanMinMaxAsymmetric a Int => CanMinMaxAsymmetric (CSequence a) (CN Int) Source # 
Instance details

Associated Types

type MinMaxType (CSequence a) (CN Int) #

Methods

min :: CSequence a -> CN Int -> MinMaxType (CSequence a) (CN Int) #

max :: CSequence a -> CN Int -> MinMaxType (CSequence a) (CN Int) #

CanMinMaxAsymmetric MPBall a => CanMinMaxAsymmetric (CN MPBall) (CSequence a) Source # 
Instance details

Associated Types

type MinMaxType (CN MPBall) (CSequence a) #

CanMinMaxAsymmetric Dyadic a => CanMinMaxAsymmetric (CN Dyadic) (CSequence a) Source # 
Instance details

Associated Types

type MinMaxType (CN Dyadic) (CSequence a) #

CanMinMaxAsymmetric Rational a => CanMinMaxAsymmetric (CN Rational) (CSequence a) Source # 
Instance details

Associated Types

type MinMaxType (CN Rational) (CSequence a) #

CanMinMaxAsymmetric Integer a => CanMinMaxAsymmetric (CN Integer) (CSequence a) Source # 
Instance details

Associated Types

type MinMaxType (CN Integer) (CSequence a) #

CanMinMaxAsymmetric Int a => CanMinMaxAsymmetric (CN Int) (CSequence a) Source # 
Instance details

Associated Types

type MinMaxType (CN Int) (CSequence a) #

Methods

min :: CN Int -> CSequence a -> MinMaxType (CN Int) (CSequence a) #

max :: CN Int -> CSequence a -> MinMaxType (CN Int) (CSequence a) #

(HasOrderAsymmetric a MPBall, CanTestCertainly (OrderCompareType a MPBall)) => HasOrderAsymmetric (CSequence a) (CN MPBall) Source # 
Instance details

Associated Types

type OrderCompareType (CSequence a) (CN MPBall) #

(HasOrderAsymmetric t1 t2, IsBool (CSequence (OrderCompareType t1 t2)), CanTestCertainly (OrderCompareType t1 t2)) => HasOrderAsymmetric (CSequence t1) (CSequence t2) Source # 
Instance details

Associated Types

type OrderCompareType (CSequence t1) (CSequence t2) #

(HasOrderAsymmetric a Dyadic, IsBool (CSequence (OrderCompareType a Dyadic)), CanTestCertainly (OrderCompareType a Dyadic)) => HasOrderAsymmetric (CSequence a) (CN Dyadic) Source # 
Instance details

Associated Types

type OrderCompareType (CSequence a) (CN Dyadic) #

(HasOrderAsymmetric a Rational, IsBool (CSequence (OrderCompareType a Rational)), CanTestCertainly (OrderCompareType a Rational)) => HasOrderAsymmetric (CSequence a) (CN Rational) Source # 
Instance details

Associated Types

type OrderCompareType (CSequence a) (CN Rational) #

(HasOrderAsymmetric a Integer, IsBool (CSequence (OrderCompareType a Integer)), CanTestCertainly (OrderCompareType a Integer)) => HasOrderAsymmetric (CSequence a) (CN Integer) Source # 
Instance details

Associated Types

type OrderCompareType (CSequence a) (CN Integer) #

(HasOrderAsymmetric a Int, IsBool (CSequence (OrderCompareType a Int)), CanTestCertainly (OrderCompareType a Int)) => HasOrderAsymmetric (CSequence a) (CN Int) Source # 
Instance details

Associated Types

type OrderCompareType (CSequence a) (CN Int) #

(HasOrderAsymmetric MPBall b, CanTestCertainly (OrderCompareType MPBall b)) => HasOrderAsymmetric (CN MPBall) (CSequence b) Source # 
Instance details

Associated Types

type OrderCompareType (CN MPBall) (CSequence b) #

(HasOrderAsymmetric Dyadic a, IsBool (CSequence (OrderCompareType Dyadic a)), CanTestCertainly (OrderCompareType Dyadic a)) => HasOrderAsymmetric (CN Dyadic) (CSequence a) Source # 
Instance details

Associated Types

type OrderCompareType (CN Dyadic) (CSequence a) #

(HasOrderAsymmetric Rational a, IsBool (CSequence (OrderCompareType Rational a)), CanTestCertainly (OrderCompareType Rational a)) => HasOrderAsymmetric (CN Rational) (CSequence a) Source # 
Instance details

Associated Types

type OrderCompareType (CN Rational) (CSequence a) #

(HasOrderAsymmetric Integer a, IsBool (CSequence (OrderCompareType Integer a)), CanTestCertainly (OrderCompareType Integer a)) => HasOrderAsymmetric (CN Integer) (CSequence a) Source # 
Instance details

Associated Types

type OrderCompareType (CN Integer) (CSequence a) #

(HasOrderAsymmetric Int a, IsBool (CSequence (OrderCompareType Int a)), CanTestCertainly (OrderCompareType Int a)) => HasOrderAsymmetric (CN Int) (CSequence a) Source # 
Instance details

Associated Types

type OrderCompareType (CN Int) (CSequence a) #