Algebra.Transcendental
 Contents Transcendental laws, will only hold approximately on floating point numbers Trigonometric laws, addition theorems
Synopsis
class C a => C a where
 pi :: a exp :: a -> a log :: a -> a logBase :: a -> a -> a (**) :: a -> a -> a sin :: a -> a tan :: a -> a cos :: a -> a asin :: a -> a atan :: a -> a acos :: a -> a sinh :: a -> a tanh :: a -> a cosh :: a -> a asinh :: a -> a atanh :: a -> a acosh :: a -> a
(^?) :: C a => a -> a -> a
propExpLog :: (Eq a, C a) => a -> Bool
propLogExp :: (Eq a, C a) => a -> Bool
propExpNeg :: (Eq a, C a) => a -> Bool
propLogRecip :: (Eq a, C a) => a -> Bool
propExpProduct :: (Eq a, C a) => a -> a -> Bool
propExpLogPower :: (Eq a, C a) => a -> a -> Bool
propLogSum :: (Eq a, C a) => a -> a -> Bool
propPowerCascade :: (Eq a, C a) => a -> a -> a -> Bool
propPowerProduct :: (Eq a, C a) => a -> a -> a -> Bool
propPowerDistributive :: (Eq a, C a) => a -> a -> a -> Bool
propTrigonometricPythagoras :: (Eq a, C a) => a -> Bool
propSinPeriod :: (Eq a, C a) => a -> Bool
propCosPeriod :: (Eq a, C a) => a -> Bool
propTanPeriod :: (Eq a, C a) => a -> Bool
propSinAngleSum :: (Eq a, C a) => a -> a -> Bool
propCosAngleSum :: (Eq a, C a) => a -> a -> Bool
propSinDoubleAngle :: (Eq a, C a) => a -> Bool
propCosDoubleAngle :: (Eq a, C a) => a -> Bool
propSinSquare :: (Eq a, C a) => a -> Bool
propCosSquare :: (Eq a, C a) => a -> Bool
Documentation
 class C a => C a where Source

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 :: a Source
 exp :: a -> a Source
 log :: a -> a Source
 logBase :: a -> a -> a Source
 (**) :: a -> a -> a Source
 sin :: a -> a Source
 tan :: a -> a Source
 cos :: a -> a Source
 asin :: a -> a Source
 atan :: a -> a Source
 acos :: a -> a Source
 sinh :: a -> a Source
 tanh :: a -> a Source
 cosh :: a -> a Source
 asinh :: a -> a Source
 atanh :: a -> a Source
 acosh :: a -> a Source Instances
 C Double C Float C T C T (Ord a, C a) => C (T a) C a => C (T a) (C a, C a, Power a) => C (T a) (C a, Eq 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 -> a Source
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
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