Flint2-0.1.0.5: Haskell bindings for the flint library for number theory

Data.Number.Flint.Acb.ComplexField

Contents

Synopsis

# Documentation

newtype CF (n :: Nat) Source #

Constructors

 CF Acb

#### Instances

Instances details
 KnownNat n => RF' (CF n) Source # Instance detailsDefined in Data.Number.Flint.Acb.ComplexField Methodspolylog :: CF n -> CF n -> CF n Source #midPoint :: CF n -> CF n Source # KnownNat n => Special (CF n) Source # Instance detailsDefined in Data.Number.Flint.Acb.ComplexField Methodsgamma :: 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 detailsDefined in Data.Number.Flint.Acb.ComplexField Methodspi :: 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 detailsDefined 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 # KnownNat n => Fractional (CF n) Source # Instance detailsDefined in Data.Number.Flint.Acb.ComplexField Methods(/) :: CF n -> CF n -> CF n #recip :: CF n -> CF n # KnownNat n => Real (CF n) Source # Instance detailsDefined in Data.Number.Flint.Acb.ComplexField MethodstoRational :: CF n -> Rational # KnownNat n => RealFrac (CF n) Source # Instance detailsDefined in Data.Number.Flint.Acb.ComplexField MethodsproperFraction :: 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 detailsDefined in Data.Number.Flint.Acb.ComplexField MethodsshowsPrec :: Int -> CF n -> ShowS #show :: CF n -> String #showList :: [CF n] -> ShowS # KnownNat n => Eq (CF n) Source # Instance detailsDefined in Data.Number.Flint.Acb.ComplexField Methods(==) :: CF n -> CF n -> Bool #(/=) :: CF n -> CF n -> Bool # KnownNat n => Ord (CF n) Source # Instance detailsDefined in Data.Number.Flint.Acb.ComplexField Methodscompare :: 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 detailsDefined in Data.Number.Flint.Acb.ComplexField Methodspolylog :: CF n -> CF n -> CF n Source #midPoint :: CF n -> CF n Source # KnownNat n => RF' (RF n) Source # Instance detailsDefined in Data.Number.Flint.Arb.RealField Methodspolylog :: 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 detailsDefined in Data.Number.Flint.Acb.ComplexField Methodsgamma :: 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 detailsDefined in Data.Number.Flint.Arb.RealField Methodsgamma :: 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 #