What4.Utils.Complex

This module provides complex numbers without the RealFloat constraints that Data.Complex has. This is useful for representing various intermediate symbolic representations of complex numbers that are not literally number representations.

Documentation

data Complex a

A complex pair over an arbitrary type.

Constructors

!a :+ !a infix 6

Instances

Functor Complex

Defined in What4.Utils.Complex

Methods

fmap :: (a -> b) -> Complex a -> Complex b

(<$) :: a -> Complex b -> Complex a

Foldable Complex

Defined in What4.Utils.Complex

Methods

fold :: Monoid m => Complex m -> m

foldMap :: Monoid m => (a -> m) -> Complex a -> m

foldMap' :: Monoid m => (a -> m) -> Complex a -> m

foldr :: (a -> b -> b) -> b -> Complex a -> b

foldr' :: (a -> b -> b) -> b -> Complex a -> b

foldl :: (b -> a -> b) -> b -> Complex a -> b

foldl' :: (b -> a -> b) -> b -> Complex a -> b

foldr1 :: (a -> a -> a) -> Complex a -> a

foldl1 :: (a -> a -> a) -> Complex a -> a

toList :: Complex a -> [a]

null :: Complex a -> Bool

length :: Complex a -> Int

elem :: Eq a => a -> Complex a -> Bool

maximum :: Ord a => Complex a -> a

minimum :: Ord a => Complex a -> a

sum :: Num a => Complex a -> a

product :: Num a => Complex a -> a

Traversable Complex

Defined in What4.Utils.Complex

Methods

traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b)

sequenceA :: Applicative f => Complex (f a) -> f (Complex a)

mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b)

sequence :: Monad m => Complex (m a) -> m (Complex a)

Eq a => Eq (Complex a)

Defined in What4.Utils.Complex

Methods

(==) :: Complex a -> Complex a -> Bool

(/=) :: Complex a -> Complex a -> Bool

RealFloat a => Floating (Complex a)

Defined in What4.Utils.Complex

Methods

pi :: Complex a

exp :: Complex a -> Complex a

log :: Complex a -> Complex a

sqrt :: Complex a -> Complex a

(**) :: Complex a -> Complex a -> Complex a

logBase :: Complex a -> Complex a -> Complex a

sin :: Complex a -> Complex a

cos :: Complex a -> Complex a

tan :: Complex a -> Complex a

asin :: Complex a -> Complex a

acos :: Complex a -> Complex a

atan :: Complex a -> Complex a

sinh :: Complex a -> Complex a

cosh :: Complex a -> Complex a

tanh :: Complex a -> Complex a

asinh :: Complex a -> Complex a

acosh :: Complex a -> Complex a

atanh :: Complex a -> Complex a

log1p :: Complex a -> Complex a

expm1 :: Complex a -> Complex a

log1pexp :: Complex a -> Complex a

log1mexp :: Complex a -> Complex a

Floating a => Fractional (Complex a)

Defined in What4.Utils.Complex

Methods

(/) :: Complex a -> Complex a -> Complex a

recip :: Complex a -> Complex a

fromRational :: Rational -> Complex a

Floating a => Num (Complex a)

Defined in What4.Utils.Complex

Methods

(+) :: Complex a -> Complex a -> Complex a

(-) :: Complex a -> Complex a -> Complex a

(*) :: Complex a -> Complex a -> Complex a

negate :: Complex a -> Complex a

abs :: Complex a -> Complex a

signum :: Complex a -> Complex a

fromInteger :: Integer -> Complex a

Ord a => Ord (Complex a)

Defined in What4.Utils.Complex

Methods

compare :: Complex a -> Complex a -> Ordering

(<) :: Complex a -> Complex a -> Bool

(<=) :: Complex a -> Complex a -> Bool

(>) :: Complex a -> Complex a -> Bool

(>=) :: Complex a -> Complex a -> Bool

max :: Complex a -> Complex a -> Complex a

min :: Complex a -> Complex a -> Complex a

(Ord a, Floating a) => Real (Complex a)

Defined in What4.Utils.Complex

Methods

toRational :: Complex a -> Rational

(Ord a, Floating a) => RealFrac (Complex a)

Defined in What4.Utils.Complex

Methods

properFraction :: Integral b => Complex a -> (b, Complex a)

truncate :: Integral b => Complex a -> b

round :: Integral b => Complex a -> b

ceiling :: Integral b => Complex a -> b

floor :: Integral b => Complex a -> b

(Eq a, Num a, Show a) => Show (Complex a)

Defined in What4.Utils.Complex

Methods

showsPrec :: Int -> Complex a -> ShowS

show :: Complex a -> String

showList :: [Complex a] -> ShowS

Generic (Complex a)

Defined in What4.Utils.Complex

Associated Types

type Rep (Complex a) :: Type -> Type

Methods

from :: Complex a -> Rep (Complex a) x

to :: Rep (Complex a) x -> Complex a

Hashable a => Hashable (Complex a)

Defined in What4.Utils.Complex

Methods

hashWithSalt :: Int -> Complex a -> Int

hash :: Complex a -> Int

PolyEq x y => PolyEq (Complex x) (Complex y)

Defined in What4.Utils.Complex

Methods

polyEqF :: Complex x -> Complex y -> Maybe (Complex x :~: Complex y)

polyEq :: Complex x -> Complex y -> Bool

type Rep (Complex a)

Defined in What4.Utils.Complex

type Rep (Complex a) = D1 ('MetaData "Complex" "What4.Utils.Complex" "what4-1.1-F6JmVDCUG2e4tsAmUzrLc2" 'False) (C1 ('MetaCons ":+" ('InfixI 'NotAssociative 6) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)))

realPart :: Complex a -> a

imagPart :: Complex a -> a

magnitude :: Floating a => Complex a -> a

magnitudeSq :: Num a => Complex a -> a

Returns square of magnitude.

complexNegate :: Num a => Complex a -> Complex a

complexAdd :: Num a => Complex a -> Complex a -> Complex a

complexSub :: Num a => Complex a -> Complex a -> Complex a

complexMul :: Num a => Complex a -> Complex a -> Complex a

complexDiv :: Fractional a => Complex a -> Complex a -> Complex a

complexRecip :: Fractional a => Complex a -> Complex a

tryComplexSqrt

Arguments

:: (Ord a, Fractional a, Monad m)

=> (a -> m a)

Square-root function defined for non-negative values a.

-> Complex a

-> m (Complex a)

tryMagnitude

Arguments

:: Num a

=> (a -> b)

Sqrt function

-> Complex a

-> b

complexAsRational :: Complex Rational -> Maybe Rational