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 :: a -> a

log :: a -> a

logBase :: a -> a -> a

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

sin :: a -> a

cos :: a -> a

tan :: a -> a

asin :: a -> a

acos :: a -> a

atan :: a -> a

sinh :: a -> a

cosh :: a -> a

tanh :: a -> a

asinh :: a -> a

acosh :: a -> a

atanh :: a -> a

Instances

C Double

Methods

pi :: Double

exp :: Double -> Double

log :: Double -> Double

logBase :: Double -> Double -> Double

(**) :: Double -> Double -> Double

sin :: Double -> Double

cos :: Double -> Double

tan :: Double -> Double

asin :: Double -> Double

acos :: Double -> Double

atan :: Double -> Double

sinh :: Double -> Double

cosh :: Double -> Double

tanh :: Double -> Double

asinh :: Double -> Double

acosh :: Double -> Double

atanh :: Double -> Double

C Float

Methods

pi :: Float

exp :: Float -> Float

log :: Float -> Float

logBase :: Float -> Float -> Float

(**) :: Float -> Float -> Float

sin :: Float -> Float

cos :: Float -> Float

tan :: Float -> Float

asin :: Float -> Float

acos :: Float -> Float

atan :: Float -> Float

sinh :: Float -> Float

cosh :: Float -> Float

tanh :: Float -> Float

asinh :: Float -> Float

acosh :: Float -> Float

atanh :: Float -> Float

C T

Methods

pi :: T

exp :: T -> T

log :: T -> T

logBase :: T -> T -> T

(**) :: T -> T -> T

sin :: T -> T

cos :: T -> T

tan :: T -> T

asin :: T -> T

acos :: T -> T

atan :: T -> T

sinh :: T -> T

cosh :: T -> T

tanh :: T -> T

asinh :: T -> T

acosh :: T -> T

atanh :: T -> T

C T

Methods

pi :: T

exp :: T -> T

log :: T -> T

logBase :: T -> T -> T

(**) :: T -> T -> T

sin :: T -> T

cos :: T -> T

tan :: T -> T

asin :: T -> T

acos :: T -> T

atan :: T -> T

sinh :: T -> T

cosh :: T -> T

tanh :: T -> T

asinh :: T -> T

acosh :: T -> T

atanh :: T -> T

Floating a => C (T a)

Methods

pi :: T a

exp :: T a -> T a

log :: T a -> T a

logBase :: T a -> T a -> T a

(**) :: T a -> T a -> T a

sin :: T a -> T a

cos :: T a -> T a

tan :: T a -> T a

asin :: T a -> T a

acos :: T a -> T a

atan :: T a -> T a

sinh :: T a -> T a

cosh :: T a -> T a

tanh :: T a -> T a

asinh :: T a -> T a

acosh :: T a -> T a

atanh :: T a -> T a

(C a, Eq a) => C (T a)

Methods

pi :: T a

exp :: T a -> T a

log :: T a -> T a

logBase :: T a -> T a -> T a

(**) :: T a -> T a -> T a

sin :: T a -> T a

cos :: T a -> T a

tan :: T a -> T a

asin :: T a -> T a

acos :: T a -> T a

atan :: T a -> T a

sinh :: T a -> T a

cosh :: T a -> T a

tanh :: T a -> T a

asinh :: T a -> T a

acosh :: T a -> T a

atanh :: T a -> T a

C a => C (T a)

Methods

pi :: T a

exp :: T a -> T a

log :: T a -> T a

logBase :: T a -> T a -> T a

(**) :: T a -> T a -> T a

sin :: T a -> T a

cos :: T a -> T a

tan :: T a -> T a

asin :: T a -> T a

acos :: T a -> T a

atan :: T a -> T a

sinh :: T a -> T a

cosh :: T a -> T a

tanh :: T a -> T a

asinh :: T a -> T a

acosh :: T a -> T a

atanh :: T a -> T a

(C a, C a, C a, Power a) => C (T a)

Methods

pi :: T a

exp :: T a -> T a

log :: T a -> T a

logBase :: T a -> T a -> T a

(**) :: T a -> T a -> T a

sin :: T a -> T a

cos :: T a -> T a

tan :: T a -> T a

asin :: T a -> T a

acos :: T a -> T a

atan :: T a -> T a

sinh :: T a -> T a

cosh :: T a -> T a

tanh :: T a -> T a

asinh :: T a -> T a

acosh :: T a -> T a

atanh :: T a -> T a

C a => C (T a)

Methods

pi :: T a

exp :: T a -> T a

log :: T a -> T a

logBase :: T a -> T a -> T a

(**) :: T a -> T a -> T a

sin :: T a -> T a

cos :: T a -> T a

tan :: T a -> T a

asin :: T a -> T a

acos :: T a -> T a

atan :: T a -> T a

sinh :: T a -> T a

cosh :: T a -> T a

tanh :: T a -> T a

asinh :: T a -> T a

acosh :: T a -> T a

atanh :: T a -> T a

(C a, C v, Show v, C a v) => C (T a v)

Methods

pi :: T a v

exp :: T a v -> T a v

log :: T a v -> T a v

logBase :: T a v -> T a v -> T a v

(**) :: T a v -> T a v -> T a v

sin :: T a v -> T a v

cos :: T a v -> T a v

tan :: T a v -> T a v

asin :: T a v -> T a v

acos :: T a v -> T a v

atan :: T a v -> T a v

sinh :: T a v -> T a v

cosh :: T a v -> T a v

tanh :: T a v -> T a v

asinh :: T a v -> T a v

acosh :: T a v -> T a v

atanh :: T a v -> T a v

(Ord i, C a) => C (T i a)

Methods

pi :: T i a

exp :: T i a -> T i a

log :: T i a -> T i a

logBase :: T i a -> T i a -> T i a

(**) :: T i a -> T i a -> T i a

sin :: T i a -> T i a

cos :: T i a -> T i a

tan :: T i a -> T i a

asin :: T i a -> T i a

acos :: T i a -> T i a

atan :: T i a -> T i a

sinh :: T i a -> T i a

cosh :: T i a -> T i a

tanh :: T i a -> T i a

asinh :: T i a -> T i a

acosh :: T i a -> T i a

atanh :: T i a -> T i a

C v => C (T a v)

Methods

pi :: T a v

exp :: T a v -> T a v

log :: T a v -> T a v

logBase :: T a v -> T a v -> T a v

(**) :: T a v -> T a v -> T a v

sin :: T a v -> T a v

cos :: T a v -> T a v

tan :: T a v -> T a v

asin :: T a v -> T a v

acos :: T a v -> T a v

atan :: T a v -> T a v

sinh :: T a v -> T a v

cosh :: T a v -> T a v

tanh :: T a v -> T a v

asinh :: T a v -> T a v

acosh :: T a v -> T a v

atanh :: T a v -> 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