Data.Number.Flint.Acb.ComplexField

Documentation

newtype CF (n :: Nat)

Constructors

CF Acb

Instances

KnownNat n => RF' (CF n)

Defined in Data.Number.Flint.Acb.ComplexField

Methods

euler :: CF n

glaisher :: CF n

catalan :: CF n

khinchin :: CF n

polylog :: CF n -> CF n -> CF n

midPoint :: CF n -> CF n

KnownNat n => Special (CF n)

Defined in Data.Number.Flint.Acb.ComplexField

Methods

gamma :: CF n -> CF n

digamma :: CF n -> CF n

lgamma :: CF n -> CF n

zeta :: CF n -> CF n

erf :: CF n -> CF n

airy :: CF n -> (CF n, CF n, CF n, CF n)

airyZeros :: Fmpz -> (CF n, CF n, CF n, CF n)

besselJ :: CF n -> CF n -> CF n

besselY :: CF n -> CF n -> CF n

besselI :: CF n -> CF n -> CF n

besselK :: CF n -> CF n -> CF n

modj :: CF n -> CF n

modjq :: CF n -> CF n

modeta :: CF n -> CF n

modetaq :: CF n -> CF n

modlambda :: CF n -> CF n

modlambdaq :: CF n -> CF n

ellipp :: CF n -> CF n -> CF n

ellipzeta :: CF n -> CF n -> CF n

ellipsigma :: CF n -> CF n -> CF n

barnesg :: CF n -> CF n

agm :: CF n -> CF n -> CF n

fresnels :: CF n -> CF n

fresnelc :: CF n -> CF n

KnownNat n => Floating (CF n)

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)

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)

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)

Defined in Data.Number.Flint.Acb.ComplexField

Methods

toRational :: CF n -> Rational

KnownNat n => RealFrac (CF n)

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)

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)

Defined in Data.Number.Flint.Acb.ComplexField

Methods

(==) :: CF n -> CF n -> Bool

(/=) :: CF n -> CF n -> Bool

KnownNat n => Ord (CF n)

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

Methods

euler :: a

glaisher :: a

catalan :: a

khinchin :: a

polylog :: a -> a -> a

midPoint :: a -> a

Instances

KnownNat n => RF' (CF n)

Defined in Data.Number.Flint.Acb.ComplexField

Methods

euler :: CF n

glaisher :: CF n

catalan :: CF n

khinchin :: CF n

polylog :: CF n -> CF n -> CF n

midPoint :: CF n -> CF n

KnownNat n => RF' (RF n)

Defined in Data.Number.Flint.Arb.RealField

Methods

euler :: RF n

glaisher :: RF n

catalan :: RF n

khinchin :: RF n

polylog :: RF n -> RF n -> RF n

midPoint :: RF n -> RF n

class Special a where

Methods

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

Instances

KnownNat n => Special (CF n)

Defined in Data.Number.Flint.Acb.ComplexField

Methods

gamma :: CF n -> CF n

digamma :: CF n -> CF n

lgamma :: CF n -> CF n

zeta :: CF n -> CF n

erf :: CF n -> CF n

airy :: CF n -> (CF n, CF n, CF n, CF n)

airyZeros :: Fmpz -> (CF n, CF n, CF n, CF n)

besselJ :: CF n -> CF n -> CF n

besselY :: CF n -> CF n -> CF n

besselI :: CF n -> CF n -> CF n

besselK :: CF n -> CF n -> CF n

modj :: CF n -> CF n

modjq :: CF n -> CF n

modeta :: CF n -> CF n

modetaq :: CF n -> CF n

modlambda :: CF n -> CF n

modlambdaq :: CF n -> CF n

ellipp :: CF n -> CF n -> CF n

ellipzeta :: CF n -> CF n -> CF n

ellipsigma :: CF n -> CF n -> CF n

barnesg :: CF n -> CF n

agm :: CF n -> CF n -> CF n

fresnels :: CF n -> CF n

fresnelc :: CF n -> CF n

KnownNat n => Special (RF n)

Defined in Data.Number.Flint.Arb.RealField

Methods

gamma :: RF n -> RF n

digamma :: RF n -> RF n

lgamma :: RF n -> RF n

zeta :: RF n -> RF n

erf :: RF n -> RF n

airy :: RF n -> (RF n, RF n, RF n, RF n)

airyZeros :: Fmpz -> (RF n, RF n, RF n, RF n)

besselJ :: RF n -> RF n -> RF n

besselY :: RF n -> RF n -> RF n

besselI :: RF n -> RF n -> RF n

besselK :: RF n -> RF n -> RF n

modj :: RF n -> RF n

modjq :: RF n -> RF n

modeta :: RF n -> RF n

modetaq :: RF n -> RF n

modlambda :: RF n -> RF n

modlambdaq :: RF n -> RF n

ellipp :: RF n -> RF n -> RF n

ellipzeta :: RF n -> RF n -> RF n

ellipsigma :: RF n -> RF n -> RF n

barnesg :: RF n -> RF n

agm :: RF n -> RF n -> RF n

fresnels :: RF n -> RF n

fresnelc :: RF n -> RF n

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

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

Polar form

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

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