Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Number.Flint.Acb.ComplexField

Contents

Polar form
Conjugate

Synopsis

newtype CF (n :: Nat) = CF Acb
class RF' a where
- euler :: a
- glaisher :: a
- catalan :: a
- khinchin :: a
- polylog :: a -> a -> a
- midPoint :: a -> a
class Special a where
- gamma :: a -> a
- digamma :: a -> a
- lgamma :: a -> a
- zeta :: a -> a
- erf :: a -> a
- airy :: a -> (a, a, a, a)
- airyZeros :: Fmpz -> (a, a, a, a)
- besselJ :: a -> a -> a
- besselY :: a -> a -> a
- besselI :: a -> a -> a
- besselK :: a -> a -> a
- modj :: a -> a
- modjq :: a -> a
- modeta :: a -> a
- modetaq :: a -> a
- modlambda :: a -> a
- modlambdaq :: a -> a
- ellipp :: a -> a -> a
- ellipzeta :: a -> a -> a
- ellipsigma :: a -> a -> a
- barnesg :: a -> a
- agm :: a -> a -> a
- fresnels :: a -> a
- fresnelc :: a -> a
realPart :: forall n. KnownNat n => CF n -> RF n
imagPart :: forall n. KnownNat n => CF n -> RF n
mkPolar :: forall n. KnownNat n => RF n -> RF n -> CF n
cis :: forall n. KnownNat n => RF n -> CF n
polar :: forall n. KnownNat n => CF n -> (RF n, RF n)
magnitude :: forall n. KnownNat n => CF n -> RF n
phase :: forall n. KnownNat n => CF n -> RF n
conjugate :: forall n. KnownNat n => CF n -> CF n

Documentation

newtype CF (n :: Nat) Source #

Constructors

CF Acb

Instances

Instances details

KnownNat n => RF' (CF n) Source #
Instance details Defined in Data.Number.Flint.Acb.ComplexField Methods euler :: CF n Source # glaisher :: CF n Source # catalan :: CF n Source # khinchin :: CF n Source # polylog :: CF n -> CF n -> CF n Source # midPoint :: CF n -> CF n Source #
KnownNat n => Special (CF n) Source #
Instance details Defined in Data.Number.Flint.Acb.ComplexField Methods gamma :: CF n -> CF n Source # digamma :: CF n -> CF n Source # lgamma :: CF n -> CF n Source # zeta :: CF n -> CF n Source # erf :: CF n -> CF n Source # airy :: CF n -> (CF n, CF n, CF n, CF n) Source # airyZeros :: Fmpz -> (CF n, CF n, CF n, CF n) Source # besselJ :: CF n -> CF n -> CF n Source # besselY :: CF n -> CF n -> CF n Source # besselI :: CF n -> CF n -> CF n Source # besselK :: CF n -> CF n -> CF n Source # modj :: CF n -> CF n Source # modjq :: CF n -> CF n Source # modeta :: CF n -> CF n Source # modetaq :: CF n -> CF n Source # modlambda :: CF n -> CF n Source # modlambdaq :: CF n -> CF n Source # ellipp :: CF n -> CF n -> CF n Source # ellipzeta :: CF n -> CF n -> CF n Source # ellipsigma :: CF n -> CF n -> CF n Source # barnesg :: CF n -> CF n Source # agm :: CF n -> CF n -> CF n Source # fresnels :: CF n -> CF n Source # fresnelc :: CF n -> CF n Source #
KnownNat n => Floating (CF n) Source #
Instance details Defined in Data.Number.Flint.Acb.ComplexField Methods pi :: CF n # exp :: CF n -> CF n # log :: CF n -> CF n # sqrt :: CF n -> CF n # (**) :: CF n -> CF n -> CF n # logBase :: CF n -> CF n -> CF n # sin :: CF n -> CF n # cos :: CF n -> CF n # tan :: CF n -> CF n # asin :: CF n -> CF n # acos :: CF n -> CF n # atan :: CF n -> CF n # sinh :: CF n -> CF n # cosh :: CF n -> CF n # tanh :: CF n -> CF n # asinh :: CF n -> CF n # acosh :: CF n -> CF n # atanh :: CF n -> CF n # log1p :: CF n -> CF n # expm1 :: CF n -> CF n # log1pexp :: CF n -> CF n # log1mexp :: CF n -> CF n #
KnownNat n => Num (CF n) Source #
Instance details Defined in Data.Number.Flint.Acb.ComplexField Methods (+) :: CF n -> CF n -> CF n # (-) :: CF n -> CF n -> CF n # (*) :: CF n -> CF n -> CF n # negate :: CF n -> CF n # abs :: CF n -> CF n # signum :: CF n -> CF n # fromInteger :: Integer -> CF n #
KnownNat n => Fractional (CF n) Source #
Instance details Defined in Data.Number.Flint.Acb.ComplexField Methods (/) :: CF n -> CF n -> CF n # recip :: CF n -> CF n # fromRational :: Rational -> CF n #
KnownNat n => Real (CF n) Source #
Instance details Defined in Data.Number.Flint.Acb.ComplexField Methods toRational :: CF n -> Rational #
KnownNat n => RealFrac (CF n) Source #
Instance details Defined in Data.Number.Flint.Acb.ComplexField Methods properFraction :: Integral b => CF n -> (b, CF n) # truncate :: Integral b => CF n -> b # round :: Integral b => CF n -> b # ceiling :: Integral b => CF n -> b # floor :: Integral b => CF n -> b #
KnownNat n => Show (CF n) Source #
Instance details Defined in Data.Number.Flint.Acb.ComplexField Methods showsPrec :: Int -> CF n -> ShowS # show :: CF n -> String # showList :: [CF n] -> ShowS #
KnownNat n => Eq (CF n) Source #
Instance details Defined in Data.Number.Flint.Acb.ComplexField Methods (==) :: CF n -> CF n -> Bool # (/=) :: CF n -> CF n -> Bool #
KnownNat n => Ord (CF n) Source #
Instance details Defined in Data.Number.Flint.Acb.ComplexField Methods compare :: CF n -> CF n -> Ordering # (<) :: CF n -> CF n -> Bool # (<=) :: CF n -> CF n -> Bool # (>) :: CF n -> CF n -> Bool # (>=) :: CF n -> CF n -> Bool # max :: CF n -> CF n -> CF n # min :: CF n -> CF n -> CF n #

class RF' a where Source #

Methods

euler :: a Source #

glaisher :: a Source #

catalan :: a Source #

khinchin :: a Source #

polylog :: a -> a -> a Source #

midPoint :: a -> a Source #

Instances

Instances details

KnownNat n => RF' (CF n) Source #
Instance details Defined in Data.Number.Flint.Acb.ComplexField Methods euler :: CF n Source # glaisher :: CF n Source # catalan :: CF n Source # khinchin :: CF n Source # polylog :: CF n -> CF n -> CF n Source # midPoint :: CF n -> CF n Source #
KnownNat n => RF' (RF n) Source #
Instance details Defined in Data.Number.Flint.Arb.RealField Methods euler :: RF n Source # glaisher :: RF n Source # catalan :: RF n Source # khinchin :: RF n Source # polylog :: RF n -> RF n -> RF n Source # midPoint :: RF n -> RF n Source #

class Special a where Source #

Methods

gamma :: a -> a Source #

digamma :: a -> a Source #

lgamma :: a -> a Source #

zeta :: a -> a Source #

erf :: a -> a Source #

airy :: a -> (a, a, a, a) Source #

airyZeros :: Fmpz -> (a, a, a, a) Source #

besselJ :: a -> a -> a Source #

besselY :: a -> a -> a Source #

besselI :: a -> a -> a Source #

besselK :: a -> a -> a Source #

modj :: a -> a Source #

modjq :: a -> a Source #

modeta :: a -> a Source #

modetaq :: a -> a Source #

modlambda :: a -> a Source #

modlambdaq :: a -> a Source #

ellipp :: a -> a -> a Source #

ellipzeta :: a -> a -> a Source #

ellipsigma :: a -> a -> a Source #

barnesg :: a -> a Source #

agm :: a -> a -> a Source #

fresnels :: a -> a Source #

fresnelc :: a -> a Source #

Instances

Instances details

KnownNat n => Special (CF n) Source #
Instance details Defined in Data.Number.Flint.Acb.ComplexField Methods gamma :: CF n -> CF n Source # digamma :: CF n -> CF n Source # lgamma :: CF n -> CF n Source # zeta :: CF n -> CF n Source # erf :: CF n -> CF n Source # airy :: CF n -> (CF n, CF n, CF n, CF n) Source # airyZeros :: Fmpz -> (CF n, CF n, CF n, CF n) Source # besselJ :: CF n -> CF n -> CF n Source # besselY :: CF n -> CF n -> CF n Source # besselI :: CF n -> CF n -> CF n Source # besselK :: CF n -> CF n -> CF n Source # modj :: CF n -> CF n Source # modjq :: CF n -> CF n Source # modeta :: CF n -> CF n Source # modetaq :: CF n -> CF n Source # modlambda :: CF n -> CF n Source # modlambdaq :: CF n -> CF n Source # ellipp :: CF n -> CF n -> CF n Source # ellipzeta :: CF n -> CF n -> CF n Source # ellipsigma :: CF n -> CF n -> CF n Source # barnesg :: CF n -> CF n Source # agm :: CF n -> CF n -> CF n Source # fresnels :: CF n -> CF n Source # fresnelc :: CF n -> CF n Source #
KnownNat n => Special (RF n) Source #
Instance details Defined in Data.Number.Flint.Arb.RealField Methods gamma :: RF n -> RF n Source # digamma :: RF n -> RF n Source # lgamma :: RF n -> RF n Source # zeta :: RF n -> RF n Source # erf :: RF n -> RF n Source # airy :: RF n -> (RF n, RF n, RF n, RF n) Source # airyZeros :: Fmpz -> (RF n, RF n, RF n, RF n) Source # besselJ :: RF n -> RF n -> RF n Source # besselY :: RF n -> RF n -> RF n Source # besselI :: RF n -> RF n -> RF n Source # besselK :: RF n -> RF n -> RF n Source # modj :: RF n -> RF n Source # modjq :: RF n -> RF n Source # modeta :: RF n -> RF n Source # modetaq :: RF n -> RF n Source # modlambda :: RF n -> RF n Source # modlambdaq :: RF n -> RF n Source # ellipp :: RF n -> RF n -> RF n Source # ellipzeta :: RF n -> RF n -> RF n Source # ellipsigma :: RF n -> RF n -> RF n Source # barnesg :: RF n -> RF n Source # agm :: RF n -> RF n -> RF n Source # fresnels :: RF n -> RF n Source # fresnelc :: RF n -> RF n Source #

realPart :: forall n. KnownNat n => CF n -> RF n Source #

imagPart :: forall n. KnownNat n => CF n -> RF n Source #

Polar form

mkPolar :: forall n. KnownNat n => RF n -> RF n -> CF n Source #

cis :: forall n. KnownNat n => RF n -> CF n Source #

polar :: forall n. KnownNat n => CF n -> (RF n, RF n) Source #

magnitude :: forall n. KnownNat n => CF n -> RF n Source #

phase :: forall n. KnownNat n => CF n -> RF n Source #

Conjugate

conjugate :: forall n. KnownNat n => CF n -> CF n Source #