Safe Haskell	None
Language	Haskell98

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, log :: a -> a
- logBase, (**) :: a -> a -> a
- sin, cos, tan :: a -> a
- asin, acos, atan :: a -> a
- sinh, cosh, tanh :: a -> a
- asinh, acosh, atanh :: 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 #

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 #
Instance details Defined in Algebra.Transcendental 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 #
Instance details Defined in Algebra.Transcendental 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 #
Instance details Defined in Number.FixedPoint.Check 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 #
Instance details Defined in Number.Positional.Check 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 #
(Ord a, C a) => C (T a) #
Instance details Defined in Number.NonNegative 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 #
Floating a => C (T a) #
Instance details Defined in MathObj.Wrapper.Haskell98 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) #
Instance details Defined in Number.PartiallyTranscendental 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) #
Instance details Defined in MathObj.PowerSeries 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) #
Instance details Defined in Number.Complex 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) #
Instance details Defined in MathObj.Wrapper.NumericPrelude 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) #
Instance details Defined in Number.OccasionallyScalarExpression 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) #
Instance details Defined in Number.Physical 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) #
Instance details Defined in Number.SI 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 #