Modulenumeric-prelude-0.4.4Haskell98

Algebra.Transcendental

Contents

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

Synopsis

class C
value ^?
value propExpLog
value propLogExp
value propExpNeg
value propLogRecip
value propExpProduct
value propExpLogPower
value propLogSum
value propPowerCascade
value propPowerProduct
value propPowerDistributive
value propTrigonometricPythagoras
value propSinPeriod
value propCosPeriod
value propTanPeriod
value propSinAngleSum
value propCosAngleSum
value propSinDoubleAngle
value propCosDoubleAngle
value propSinSquare
value propCosSquare

Packagenumeric-prelude-0.4.4
Exports22
LanguageHaskell98
LicenceBSD-3-Clause
SourceTranscendental.hs

classclass 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

Methods

pi :: a
exp :: a -> a
log :: a -> a
logBase :: a -> a -> a
(**) :: a -> a -> ainfixr 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

Instances13C, …

C DoubleDefined in numeric-prelude-0.4.4 · Algebra.Transcendental
C FloatDefined in numeric-prelude-0.4.4 · Algebra.Transcendental
C TDefined in numeric-prelude-0.4.4 · Number.FixedPoint.Check
C TDefined in numeric-prelude-0.4.4 · Number.Positional.Check
Floating a => C (T a)Defined in numeric-prelude-0.4.4 · MathObj.Wrapper.Haskell98
C a => C (T a)Defined in numeric-prelude-0.4.4 · MathObj.PowerSeries
C a => C (T a)Defined in numeric-prelude-0.4.4 · MathObj.Wrapper.NumericPrelude
(Ord a, C a) => C (T a)Defined in numeric-prelude-0.4.4 · Number.NonNegative · orphan
(C a, Eq a) => C (T a)Defined in numeric-prelude-0.4.4 · Number.PartiallyTranscendental
(C a, C a, C a, Power a) => C (T a)Defined in numeric-prelude-0.4.4 · Number.Complex
C v => C (T a v)Defined in numeric-prelude-0.4.4 · Number.SI
(Ord i, C a) => C (T i a)Defined in numeric-prelude-0.4.4 · Number.Physical
(C a, C v, Show v, C a v) => C (T a v)Defined in numeric-prelude-0.4.4 · Number.OccasionallyScalarExpression

value(^?) :: C a => a -> a -> a

Transcendental laws, will only hold approximately on floating point numbers

valuepropExpLog :: (Eq a, C a) => a -> Bool

valuepropLogExp :: (Eq a, C a) => a -> Bool

valuepropExpNeg :: (Eq a, C a) => a -> Bool

valuepropLogRecip :: (Eq a, C a) => a -> Bool

valuepropExpProduct :: (Eq a, C a) => a -> a -> Bool

valuepropExpLogPower :: (Eq a, C a) => a -> a -> Bool

valuepropLogSum :: (Eq a, C a) => a -> a -> Bool

valuepropPowerCascade :: (Eq a, C a) => a -> a -> a -> Bool

valuepropPowerProduct :: (Eq a, C a) => a -> a -> a -> Bool

valuepropPowerDistributive :: (Eq a, C a) => a -> a -> a -> Bool

Trigonometric laws, addition theorems

valuepropTrigonometricPythagoras :: (Eq a, C a) => a -> Bool

valuepropSinPeriod :: (Eq a, C a) => a -> Bool

valuepropCosPeriod :: (Eq a, C a) => a -> Bool

valuepropTanPeriod :: (Eq a, C a) => a -> Bool

valuepropSinAngleSum :: (Eq a, C a) => a -> a -> Bool

valuepropCosAngleSum :: (Eq a, C a) => a -> a -> Bool

valuepropSinDoubleAngle :: (Eq a, C a) => a -> Bool

valuepropCosDoubleAngle :: (Eq a, C a) => a -> Bool

valuepropSinSquare :: (Eq a, C a) => a -> Bool

valuepropCosSquare :: (Eq a, C a) => a -> Bool