AERN2.Sequence.Ring

Ring operations on convergent sequences

Documentation

mulGetInitAC :: (HasNorm (EnsureNoCN other), CanEnsureCN other) => other -> AccuracySG -> AccuracySG

Orphan instances

(CanMulAsymmetric MPBall b, SuitableForSeq b, CanSetPrecision (MulType MPBall b)) => CanMulAsymmetric MPBall (Sequence b)

Associated Types

type MulType MPBall (Sequence b) :: *

Methods

mul :: MPBall -> Sequence b -> MulType MPBall (Sequence b)

(CanAddAsymmetric MPBall b, SuitableForSeq b, CanSetPrecision (AddType MPBall b)) => CanAddAsymmetric MPBall (Sequence b)

Associated Types

type AddType MPBall (Sequence b) :: *

Methods

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

(CanSub MPBall b, SuitableForSeq b, CanSetPrecision (SubType MPBall b)) => CanSub MPBall (Sequence b)

Associated Types

type SubType MPBall (Sequence b) :: *

Methods

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

(QAArrow to0, CanMulAsymmetric Int b0, SuitableForSeq b0, SuitableForSeq (MulType Int b0)) => CanMulAsymmetric Int (SequenceA to0 b0)

Associated Types

type MulType Int (SequenceA to0 b0) :: *

Methods

mul :: Int -> SequenceA to0 b0 -> MulType Int (SequenceA to0 b0)

(QAArrow to0, CanMulAsymmetric Integer b0, SuitableForSeq b0, SuitableForSeq (MulType Integer b0)) => CanMulAsymmetric Integer (SequenceA to0 b0)

Associated Types

type MulType Integer (SequenceA to0 b0) :: *

Methods

mul :: Integer -> SequenceA to0 b0 -> MulType Integer (SequenceA to0 b0)

(QAArrow to0, CanMulAsymmetric Rational b0, SuitableForSeq b0, SuitableForSeq (MulType Rational b0)) => CanMulAsymmetric Rational (SequenceA to0 b0)

Associated Types

type MulType Rational (SequenceA to0 b0) :: *

Methods

mul :: Rational -> SequenceA to0 b0 -> MulType Rational (SequenceA to0 b0)

(QAArrow to0, CanMulAsymmetric Dyadic b0, SuitableForSeq b0, SuitableForSeq (MulType Dyadic b0)) => CanMulAsymmetric Dyadic (SequenceA to0 b0)

Associated Types

type MulType Dyadic (SequenceA to0 b0) :: *

Methods

mul :: Dyadic -> SequenceA to0 b0 -> MulType Dyadic (SequenceA to0 b0)

(QAArrow to0, CanAddAsymmetric Int b0, SuitableForSeq b0, SuitableForSeq (AddType Int b0)) => CanAddAsymmetric Int (SequenceA to0 b0)

Associated Types

type AddType Int (SequenceA to0 b0) :: *

Methods

add :: Int -> SequenceA to0 b0 -> AddType Int (SequenceA to0 b0)

(QAArrow to0, CanAddAsymmetric Integer b0, SuitableForSeq b0, SuitableForSeq (AddType Integer b0)) => CanAddAsymmetric Integer (SequenceA to0 b0)

Associated Types

type AddType Integer (SequenceA to0 b0) :: *

Methods

add :: Integer -> SequenceA to0 b0 -> AddType Integer (SequenceA to0 b0)

(QAArrow to0, CanAddAsymmetric Rational b0, SuitableForSeq b0, SuitableForSeq (AddType Rational b0)) => CanAddAsymmetric Rational (SequenceA to0 b0)

Associated Types

type AddType Rational (SequenceA to0 b0) :: *

Methods

add :: Rational -> SequenceA to0 b0 -> AddType Rational (SequenceA to0 b0)

(QAArrow to0, CanAddAsymmetric Dyadic b0, SuitableForSeq b0, SuitableForSeq (AddType Dyadic b0)) => CanAddAsymmetric Dyadic (SequenceA to0 b0)

Associated Types

type AddType Dyadic (SequenceA to0 b0) :: *

Methods

add :: Dyadic -> SequenceA to0 b0 -> AddType Dyadic (SequenceA to0 b0)

(QAArrow to0, CanSub Int b0, SuitableForSeq b0, SuitableForSeq (SubType Int b0)) => CanSub Int (SequenceA to0 b0)

Associated Types

type SubType Int (SequenceA to0 b0) :: *

Methods

sub :: Int -> SequenceA to0 b0 -> SubType Int (SequenceA to0 b0)

(QAArrow to0, CanSub Integer b0, SuitableForSeq b0, SuitableForSeq (SubType Integer b0)) => CanSub Integer (SequenceA to0 b0)

Associated Types

type SubType Integer (SequenceA to0 b0) :: *

Methods

sub :: Integer -> SequenceA to0 b0 -> SubType Integer (SequenceA to0 b0)

(QAArrow to0, CanSub Rational b0, SuitableForSeq b0, SuitableForSeq (SubType Rational b0)) => CanSub Rational (SequenceA to0 b0)

Associated Types

type SubType Rational (SequenceA to0 b0) :: *

Methods

sub :: Rational -> SequenceA to0 b0 -> SubType Rational (SequenceA to0 b0)

(QAArrow to0, CanSub Dyadic b0, SuitableForSeq b0, SuitableForSeq (SubType Dyadic b0)) => CanSub Dyadic (SequenceA to0 b0)

Associated Types

type SubType Dyadic (SequenceA to0 b0) :: *

Methods

sub :: Dyadic -> SequenceA to0 b0 -> SubType Dyadic (SequenceA to0 b0)

(CanMulAsymmetric a MPBall, SuitableForSeq a, CanSetPrecision (MulType a MPBall)) => CanMulAsymmetric (Sequence a) MPBall

Associated Types

type MulType (Sequence a) MPBall :: *

Methods

mul :: Sequence a -> MPBall -> MulType (Sequence a) MPBall

(CanAddAsymmetric a MPBall, SuitableForSeq a, CanSetPrecision (AddType a MPBall)) => CanAddAsymmetric (Sequence a) MPBall

Associated Types

type AddType (Sequence a) MPBall :: *

Methods

add :: Sequence a -> MPBall -> AddType (Sequence a) MPBall

(CanSub a MPBall, SuitableForSeq a, CanSetPrecision (SubType a MPBall)) => CanSub (Sequence a) MPBall

Associated Types

type SubType (Sequence a) MPBall :: *

Methods

sub :: Sequence a -> MPBall -> SubType (Sequence a) MPBall

(QAArrow to0, CanMulAsymmetric a0 Dyadic, SuitableForSeq a0, SuitableForSeq (MulType a0 Dyadic)) => CanMulAsymmetric (SequenceA to0 a0) Dyadic

Associated Types

type MulType (SequenceA to0 a0) Dyadic :: *

Methods

mul :: SequenceA to0 a0 -> Dyadic -> MulType (SequenceA to0 a0) Dyadic

(QAArrow to0, CanMulAsymmetric a0 Rational, SuitableForSeq a0, SuitableForSeq (MulType a0 Rational)) => CanMulAsymmetric (SequenceA to0 a0) Rational

Associated Types

type MulType (SequenceA to0 a0) Rational :: *

Methods

mul :: SequenceA to0 a0 -> Rational -> MulType (SequenceA to0 a0) Rational

(QAArrow to0, CanMulAsymmetric a0 Int, SuitableForSeq a0, SuitableForSeq (MulType a0 Int)) => CanMulAsymmetric (SequenceA to0 a0) Int

Associated Types

type MulType (SequenceA to0 a0) Int :: *

Methods

mul :: SequenceA to0 a0 -> Int -> MulType (SequenceA to0 a0) Int

(QAArrow to0, CanMulAsymmetric a0 Integer, SuitableForSeq a0, SuitableForSeq (MulType a0 Integer)) => CanMulAsymmetric (SequenceA to0 a0) Integer

Associated Types

type MulType (SequenceA to0 a0) Integer :: *

Methods

mul :: SequenceA to0 a0 -> Integer -> MulType (SequenceA to0 a0) Integer

(QAArrow to0, CanAddAsymmetric a0 Dyadic, SuitableForSeq a0, SuitableForSeq (AddType a0 Dyadic)) => CanAddAsymmetric (SequenceA to0 a0) Dyadic

Associated Types

type AddType (SequenceA to0 a0) Dyadic :: *

Methods

add :: SequenceA to0 a0 -> Dyadic -> AddType (SequenceA to0 a0) Dyadic

(QAArrow to0, CanAddAsymmetric a0 Rational, SuitableForSeq a0, SuitableForSeq (AddType a0 Rational)) => CanAddAsymmetric (SequenceA to0 a0) Rational

Associated Types

type AddType (SequenceA to0 a0) Rational :: *

Methods

add :: SequenceA to0 a0 -> Rational -> AddType (SequenceA to0 a0) Rational

(QAArrow to0, CanAddAsymmetric a0 Int, SuitableForSeq a0, SuitableForSeq (AddType a0 Int)) => CanAddAsymmetric (SequenceA to0 a0) Int

Associated Types

type AddType (SequenceA to0 a0) Int :: *

Methods

add :: SequenceA to0 a0 -> Int -> AddType (SequenceA to0 a0) Int

(QAArrow to0, CanAddAsymmetric a0 Integer, SuitableForSeq a0, SuitableForSeq (AddType a0 Integer)) => CanAddAsymmetric (SequenceA to0 a0) Integer

Associated Types

type AddType (SequenceA to0 a0) Integer :: *

Methods

add :: SequenceA to0 a0 -> Integer -> AddType (SequenceA to0 a0) Integer

(QAArrow to0, CanSub a0 Dyadic, SuitableForSeq a0, SuitableForSeq (SubType a0 Dyadic)) => CanSub (SequenceA to0 a0) Dyadic

Associated Types

type SubType (SequenceA to0 a0) Dyadic :: *

Methods

sub :: SequenceA to0 a0 -> Dyadic -> SubType (SequenceA to0 a0) Dyadic

(QAArrow to0, CanSub a0 Rational, SuitableForSeq a0, SuitableForSeq (SubType a0 Rational)) => CanSub (SequenceA to0 a0) Rational

Associated Types

type SubType (SequenceA to0 a0) Rational :: *

Methods

sub :: SequenceA to0 a0 -> Rational -> SubType (SequenceA to0 a0) Rational

(QAArrow to0, CanSub a0 Int, SuitableForSeq a0, SuitableForSeq (SubType a0 Int)) => CanSub (SequenceA to0 a0) Int

Associated Types

type SubType (SequenceA to0 a0) Int :: *

Methods

sub :: SequenceA to0 a0 -> Int -> SubType (SequenceA to0 a0) Int

(QAArrow to0, CanSub a0 Integer, SuitableForSeq a0, SuitableForSeq (SubType a0 Integer)) => CanSub (SequenceA to0 a0) Integer

Associated Types

type SubType (SequenceA to0 a0) Integer :: *

Methods

sub :: SequenceA to0 a0 -> Integer -> SubType (SequenceA to0 a0) Integer

(CanMulAsymmetric a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (MulType a (SequenceA to b)), SuitableForCE es) => CanMulAsymmetric (CollectErrors es a) (SequenceA to b)

Associated Types

type MulType (CollectErrors es a) (SequenceA to b) :: *

Methods

mul :: CollectErrors es a -> SequenceA to b -> MulType (CollectErrors es a) (SequenceA to b)

(CanMulAsymmetric (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (MulType (SequenceA to a) b), SuitableForCE es) => CanMulAsymmetric (SequenceA to a) (CollectErrors es b)

Associated Types

type MulType (SequenceA to a) (CollectErrors es b) :: *

Methods

mul :: SequenceA to a -> CollectErrors es b -> MulType (SequenceA to a) (CollectErrors es b)

(QAArrow to, CanMulAsymmetric a b, HasNorm (EnsureNoCN a), HasNorm (EnsureNoCN b), SuitableForSeq a, SuitableForSeq b, SuitableForSeq (MulType a b)) => CanMulAsymmetric (SequenceA to a) (SequenceA to b)

Associated Types

type MulType (SequenceA to a) (SequenceA to b) :: *

Methods

mul :: SequenceA to a -> SequenceA to b -> MulType (SequenceA to a) (SequenceA to b)

(CanAddAsymmetric a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (AddType a (SequenceA to b)), SuitableForCE es) => CanAddAsymmetric (CollectErrors es a) (SequenceA to b)

Associated Types

type AddType (CollectErrors es a) (SequenceA to b) :: *

Methods

add :: CollectErrors es a -> SequenceA to b -> AddType (CollectErrors es a) (SequenceA to b)

(QAArrow to, CanAddAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (AddType a b)) => CanAddAsymmetric (SequenceA to a) (SequenceA to b)

Associated Types

type AddType (SequenceA to a) (SequenceA to b) :: *

Methods

add :: SequenceA to a -> SequenceA to b -> AddType (SequenceA to a) (SequenceA to b)

(CanAddAsymmetric (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (AddType (SequenceA to a) b), SuitableForCE es) => CanAddAsymmetric (SequenceA to a) (CollectErrors es b)

Associated Types

type AddType (SequenceA to a) (CollectErrors es b) :: *

Methods

add :: SequenceA to a -> CollectErrors es b -> AddType (SequenceA to a) (CollectErrors es b)

(CanSub a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (SubType a (SequenceA to b)), SuitableForCE es) => CanSub (CollectErrors es a) (SequenceA to b)

Associated Types

type SubType (CollectErrors es a) (SequenceA to b) :: *

Methods

sub :: CollectErrors es a -> SequenceA to b -> SubType (CollectErrors es a) (SequenceA to b)

(QAArrow to, CanSub a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (SubType a b)) => CanSub (SequenceA to a) (SequenceA to b)

Associated Types

type SubType (SequenceA to a) (SequenceA to b) :: *

Methods

sub :: SequenceA to a -> SequenceA to b -> SubType (SequenceA to a) (SequenceA to b)

(CanSub (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (SubType (SequenceA to a) b), SuitableForCE es) => CanSub (SequenceA to a) (CollectErrors es b)

Associated Types

type SubType (SequenceA to a) (CollectErrors es b) :: *

Methods

sub :: SequenceA to a -> CollectErrors es b -> SubType (SequenceA to a) (CollectErrors es b)