numeric-prelude-0.2: An experimental alternative hierarchy of numeric type classes

Algebra.Transcendental

Contents

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 :: a -> aSource

log :: a -> aSource

logBase :: a -> a -> aSource

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

sin :: a -> aSource

tan :: a -> aSource

cos :: a -> aSource

asin :: a -> aSource

atan :: a -> aSource

acos :: a -> aSource

sinh :: a -> aSource

tanh :: a -> aSource

cosh :: a -> aSource

asinh :: a -> aSource

atanh :: a -> aSource

acosh :: a -> aSource

Instances

C Double 
C Float 
C T 
C T 
(Ord a, C a) => C (T a) 
C a => C (T a) 
(C a, Eq a) => C (T a) 
(C a, C a, Power 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

Trigonometric laws, addition theorems

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