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

Algebra.Transcendental

Contents

Transcendental laws, will only hold approximately on floating point numbers
Trigonometric laws, addition theorems

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

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 -> Bool Source

propLogExp :: (Eq a, C a) => a -> Bool Source

propExpNeg :: (Eq a, C a) => a -> Bool Source

propLogRecip :: (Eq a, C a) => a -> Bool Source

propExpProduct :: (Eq a, C a) => a -> a -> Bool Source

propExpLogPower :: (Eq a, C a) => a -> a -> Bool Source

propLogSum :: (Eq a, C a) => a -> a -> Bool Source

propPowerCascade :: (Eq a, C a) => a -> a -> a -> Bool Source

propPowerProduct :: (Eq a, C a) => a -> a -> a -> Bool Source

propPowerDistributive :: (Eq a, C a) => a -> a -> a -> Bool Source

Trigonometric laws, addition theorems

propTrigonometricPythagoras :: (Eq a, C a) => a -> Bool Source

propSinPeriod :: (Eq a, C a) => a -> Bool Source

propCosPeriod :: (Eq a, C a) => a -> Bool Source

propTanPeriod :: (Eq a, C a) => a -> Bool Source

propSinAngleSum :: (Eq a, C a) => a -> a -> Bool Source

propCosAngleSum :: (Eq a, C a) => a -> a -> Bool Source

propSinDoubleAngle :: (Eq a, C a) => a -> Bool Source

propCosDoubleAngle :: (Eq a, C a) => a -> Bool Source

propSinSquare :: (Eq a, C a) => a -> Bool Source

propCosSquare :: (Eq a, C a) => a -> Bool Source