Algebra.Transcendental

Documentation

class C a => C a where

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 or logBase), sin, cos, atan

Minimal complete definition

pi, exp, (log | logBase), sin, cos, atan

Methods

pi :: a

exp, log :: a -> a

logBase, (**) :: a -> a -> a infixr 8

sin, tan, cos :: a -> a

asin, atan, acos :: a -> a

sinh, tanh, cosh :: a -> a

asinh, atanh, acosh :: a -> a

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)

Floating a => C (T a)

(C a, C a, C a, Power 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 -> a infixr 8

Transcendental laws, will only hold approximately on floating point numbers

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

Trigonometric laws, addition theorems

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