AERN2.Sequence.Elementary

Elementary functions on fast converging sequences.

Orphan instances

(CanPow MPBall e, SuitableForSeq e, HasIntegerBounds e, CanSetPrecision (PowTypeNoCN MPBall e), CanSetPrecision (PowType MPBall e)) => CanPow MPBall (Sequence e)

Associated Types

type PowTypeNoCN MPBall (Sequence e) :: *

type PowType MPBall (Sequence e) :: *

Methods

powNoCN :: MPBall -> Sequence e -> PowTypeNoCN MPBall (Sequence e)

pow :: MPBall -> Sequence e -> PowType MPBall (Sequence e)

(QAArrow to0, CanPow Int a0, CanSetPrecision a0, HasIntegerBounds a0, SuitableForSeq a0, SuitableForSeq (PowType Int a0), SuitableForSeq (PowTypeNoCN Int a0)) => CanPow Int (SequenceA to0 a0)

Associated Types

type PowTypeNoCN Int (SequenceA to0 a0) :: *

type PowType Int (SequenceA to0 a0) :: *

Methods

powNoCN :: Int -> SequenceA to0 a0 -> PowTypeNoCN Int (SequenceA to0 a0)

pow :: Int -> SequenceA to0 a0 -> PowType Int (SequenceA to0 a0)

(QAArrow to0, CanPow Integer a0, CanSetPrecision a0, HasIntegerBounds a0, SuitableForSeq a0, SuitableForSeq (PowType Integer a0), SuitableForSeq (PowTypeNoCN Integer a0)) => CanPow Integer (SequenceA to0 a0)

Associated Types

type PowTypeNoCN Integer (SequenceA to0 a0) :: *

type PowType Integer (SequenceA to0 a0) :: *

Methods

powNoCN :: Integer -> SequenceA to0 a0 -> PowTypeNoCN Integer (SequenceA to0 a0)

pow :: Integer -> SequenceA to0 a0 -> PowType Integer (SequenceA to0 a0)

(QAArrow to0, CanPow Rational a0, CanSetPrecision a0, HasIntegerBounds a0, SuitableForSeq a0, SuitableForSeq (PowType Rational a0), SuitableForSeq (PowTypeNoCN Rational a0)) => CanPow Rational (SequenceA to0 a0)

Associated Types

type PowTypeNoCN Rational (SequenceA to0 a0) :: *

type PowType Rational (SequenceA to0 a0) :: *

Methods

powNoCN :: Rational -> SequenceA to0 a0 -> PowTypeNoCN Rational (SequenceA to0 a0)

pow :: Rational -> SequenceA to0 a0 -> PowType Rational (SequenceA to0 a0)

(QAArrow to0, CanPow Dyadic a0, CanSetPrecision a0, HasIntegerBounds a0, SuitableForSeq a0, SuitableForSeq (PowType Dyadic a0), SuitableForSeq (PowTypeNoCN Dyadic a0)) => CanPow Dyadic (SequenceA to0 a0)

Associated Types

type PowTypeNoCN Dyadic (SequenceA to0 a0) :: *

type PowType Dyadic (SequenceA to0 a0) :: *

Methods

powNoCN :: Dyadic -> SequenceA to0 a0 -> PowTypeNoCN Dyadic (SequenceA to0 a0)

pow :: Dyadic -> SequenceA to0 a0 -> PowType Dyadic (SequenceA to0 a0)

(CanPow a MPBall, SuitableForSeq a, HasNorm (EnsureNoCN a), CanEnsureCN a, CanSetPrecision (PowTypeNoCN a MPBall), CanSetPrecision (PowType a MPBall)) => CanPow (Sequence a) MPBall

Associated Types

type PowTypeNoCN (Sequence a) MPBall :: *

type PowType (Sequence a) MPBall :: *

Methods

powNoCN :: Sequence a -> MPBall -> PowTypeNoCN (Sequence a) MPBall

pow :: Sequence a -> MPBall -> PowType (Sequence a) MPBall

(QAArrow to, CanSqrt a, CanMinMaxThis a Integer, CanEnsureCN (SqrtType a), HasNorm (EnsureNoCN (SqrtType a)), SuitableForSeq a, SuitableForSeq (SqrtType a)) => CanSqrt (SequenceA to a)

Associated Types

type SqrtType (SequenceA to a) :: *

Methods

sqrt :: SequenceA to a -> SqrtType (SequenceA to a)

(QAArrow to, CanExp a, CanEnsureCN (ExpType a), HasNorm (EnsureNoCN (ExpType a)), SuitableForSeq a, SuitableForSeq (ExpType a)) => CanExp (SequenceA to a)

Associated Types

type ExpType (SequenceA to a) :: *

Methods

exp :: SequenceA to a -> ExpType (SequenceA to a)

(QAArrow to, CanLog a, CanSetPrecision a, CanEnsureCN a, HasNorm (EnsureNoCN a), SuitableForSeq a, SuitableForSeq (LogType a)) => CanLog (SequenceA to a)

Associated Types

type LogType (SequenceA to a) :: *

Methods

log :: SequenceA to a -> LogType (SequenceA to a)

(QAArrow to, CanSinCos a, CanEnsureCN (SinCosType a), HasNorm (EnsureNoCN (SinCosType a)), SuitableForSeq a, SuitableForSeq (SinCosType a)) => CanSinCos (SequenceA to a)

Associated Types

type SinCosType (SequenceA to a) :: *

Methods

cos :: SequenceA to a -> SinCosType (SequenceA to a)

sin :: SequenceA to a -> SinCosType (SequenceA to a)

(QAArrow to0, CanPow a0 Rational, CanSetPrecision a0, CanEnsureCN a0, HasNorm (EnsureNoCN a0), SuitableForSeq a0, SuitableForSeq (PowTypeNoCN a0 Rational), SuitableForSeq (PowType a0 Rational)) => CanPow (SequenceA to0 a0) Rational

Associated Types

type PowTypeNoCN (SequenceA to0 a0) Rational :: *

type PowType (SequenceA to0 a0) Rational :: *

Methods

powNoCN :: SequenceA to0 a0 -> Rational -> PowTypeNoCN (SequenceA to0 a0) Rational

pow :: SequenceA to0 a0 -> Rational -> PowType (SequenceA to0 a0) Rational

(QAArrow to0, CanPow a0 Dyadic, CanSetPrecision a0, CanEnsureCN a0, HasNorm (EnsureNoCN a0), SuitableForSeq a0, SuitableForSeq (PowTypeNoCN a0 Dyadic), SuitableForSeq (PowType a0 Dyadic)) => CanPow (SequenceA to0 a0) Dyadic

Associated Types

type PowTypeNoCN (SequenceA to0 a0) Dyadic :: *

type PowType (SequenceA to0 a0) Dyadic :: *

Methods

powNoCN :: SequenceA to0 a0 -> Dyadic -> PowTypeNoCN (SequenceA to0 a0) Dyadic

pow :: SequenceA to0 a0 -> Dyadic -> PowType (SequenceA to0 a0) Dyadic

(QAArrow to0, CanPow a0 Int, CanSetPrecision a0, CanEnsureCN a0, HasNorm (EnsureNoCN a0), SuitableForSeq a0, SuitableForSeq (PowTypeNoCN a0 Int), SuitableForSeq (PowType a0 Int)) => CanPow (SequenceA to0 a0) Int

Associated Types

type PowTypeNoCN (SequenceA to0 a0) Int :: *

type PowType (SequenceA to0 a0) Int :: *

Methods

powNoCN :: SequenceA to0 a0 -> Int -> PowTypeNoCN (SequenceA to0 a0) Int

pow :: SequenceA to0 a0 -> Int -> PowType (SequenceA to0 a0) Int

(QAArrow to0, CanPow a0 Integer, CanSetPrecision a0, CanEnsureCN a0, HasNorm (EnsureNoCN a0), SuitableForSeq a0, SuitableForSeq (PowTypeNoCN a0 Integer), SuitableForSeq (PowType a0 Integer)) => CanPow (SequenceA to0 a0) Integer

Associated Types

type PowTypeNoCN (SequenceA to0 a0) Integer :: *

type PowType (SequenceA to0 a0) Integer :: *

Methods

powNoCN :: SequenceA to0 a0 -> Integer -> PowTypeNoCN (SequenceA to0 a0) Integer

pow :: SequenceA to0 a0 -> Integer -> PowType (SequenceA to0 a0) Integer

(CanPow a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (PowType a (SequenceA to b)), CanEnsureCE es (PowTypeNoCN a (SequenceA to b)), SuitableForCE es) => CanPow (CollectErrors es a) (SequenceA to b)

Associated Types

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

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

Methods

powNoCN :: CollectErrors es a -> SequenceA to b -> PowTypeNoCN (CollectErrors es a) (SequenceA to b)

pow :: CollectErrors es a -> SequenceA to b -> PowType (CollectErrors es a) (SequenceA to b)

(CanPow (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (PowTypeNoCN (SequenceA to a) b), CanEnsureCE es (PowType (SequenceA to a) b), SuitableForCE es) => CanPow (SequenceA to a) (CollectErrors es b)

Associated Types

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

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

Methods

powNoCN :: SequenceA to a -> CollectErrors es b -> PowTypeNoCN (SequenceA to a) (CollectErrors es b)

pow :: SequenceA to a -> CollectErrors es b -> PowType (SequenceA to a) (CollectErrors es b)

(QAArrow to, CanPow a e, CanEnsureCN a, HasNorm (EnsureNoCN a), HasIntegerBounds e, SuitableForSeq a, SuitableForSeq e, SuitableForSeq (PowTypeNoCN a e), SuitableForSeq (PowType a e)) => CanPow (SequenceA to a) (SequenceA to e)

Associated Types

type PowTypeNoCN (SequenceA to a) (SequenceA to e) :: *

type PowType (SequenceA to a) (SequenceA to e) :: *

Methods

powNoCN :: SequenceA to a -> SequenceA to e -> PowTypeNoCN (SequenceA to a) (SequenceA to e)

pow :: SequenceA to a -> SequenceA to e -> PowType (SequenceA to a) (SequenceA to e)