Modulenumeric-prelude-0.4.4Haskell98

Algebra.Transcendental

1 class
21 values

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

10 declarations

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

10 declarations

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