numeric-prelude-0.4: An experimental alternative hierarchy of numeric type classes

Algebra.Transcendental

Synopsis

# Documentation

class C a => C a whereSource

Transcendental is the type of numbers supporting the elementary transcendental functions. Examples include real numbers, complex numbers, and computable reals represented as a lazy list of rational approximations.

Note the default declaration for a superclass. See the comments below, under Instance declaractions for superclasses.

The semantics of these operations are rather ill-defined because of branch cuts, etc.

Minimal complete definition: pi, exp, log, sin, cos, asin, acos, atan

Methods

pi :: aSource

exp, log :: a -> aSource

logBase, (**) :: a -> a -> aSource

sin, tan, cos :: a -> aSource

asin, atan, acos :: a -> aSource

sinh, tanh, cosh :: a -> aSource

asinh, atanh, acosh :: a -> aSource

Instances

 C Double C Float C T C T (Ord a, C a) => C (T a) C a => C (T a) Floating a => C (T a) (C a, C a, C a, Power a) => C (T a) (C a, Eq a) => C (T a) C a => C (T a) (C a, C v, Show v, C a v) => C (T a v) (Ord i, C a) => C (T i a) C v => C (T a v)

(^?) :: C a => a -> a -> aSource

# Transcendental laws, will only hold approximately on floating point numbers

propExpLog :: (Eq a, C a) => a -> BoolSource

propLogExp :: (Eq a, C a) => a -> BoolSource

propExpNeg :: (Eq a, C a) => a -> BoolSource

propLogRecip :: (Eq a, C a) => a -> BoolSource

propExpProduct :: (Eq a, C a) => a -> a -> BoolSource

propExpLogPower :: (Eq a, C a) => a -> a -> BoolSource

propLogSum :: (Eq a, C a) => a -> a -> BoolSource

propPowerCascade :: (Eq a, C a) => a -> a -> a -> BoolSource

propPowerProduct :: (Eq a, C a) => a -> a -> a -> BoolSource

propPowerDistributive :: (Eq a, C a) => a -> a -> a -> BoolSource

propSinPeriod :: (Eq a, C a) => a -> BoolSource

propCosPeriod :: (Eq a, C a) => a -> BoolSource

propTanPeriod :: (Eq a, C a) => a -> BoolSource

propSinAngleSum :: (Eq a, C a) => a -> a -> BoolSource

propCosAngleSum :: (Eq a, C a) => a -> a -> BoolSource

propSinDoubleAngle :: (Eq a, C a) => a -> BoolSource

propCosDoubleAngle :: (Eq a, C a) => a -> BoolSource

propSinSquare :: (Eq a, C a) => a -> BoolSource

propCosSquare :: (Eq a, C a) => a -> BoolSource