numeric-prelude-0.1.1: An experimental alternative hierarchy of numeric type classesSource codeContentsIndex
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 :: a -> a
log :: a -> a
logBase :: a -> a -> a
(**) :: a -> a -> a
sin :: a -> a
tan :: a -> a
cos :: a -> a
asin :: a -> a
atan :: a -> a
acos :: a -> a
sinh :: a -> a
tanh :: a -> a
cosh :: a -> a
asinh :: a -> a
atanh :: a -> a
acosh :: 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 whereSource

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, sin, cos, asin, acos, atan

Methods
pi :: aSource
exp :: a -> aSource
log :: a -> aSource
logBase :: a -> a -> aSource
(**) :: a -> a -> aSource
sin :: a -> aSource
tan :: a -> aSource
cos :: a -> aSource
asin :: a -> aSource
atan :: a -> aSource
acos :: a -> aSource
sinh :: a -> aSource
tanh :: a -> aSource
cosh :: a -> aSource
asinh :: a -> aSource
atanh :: a -> aSource
acosh :: a -> aSource
show/hide Instances
C Double
C Float
C T
C T
(Ord a, C a) => C (T a)
C a => C (T a)
(C a, C a, Power a) => C (T a)
(C a, Eq 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 -> aSource
Transcendental laws, will only hold approximately on floating point numbers
propExpLog :: (Eq a, C a) => a -> BoolSource
propLogExp :: (Eq a, C a) => a -> BoolSource
propExpNeg :: (Eq a, C a) => a -> BoolSource
propLogRecip :: (Eq a, C a) => a -> BoolSource
propExpProduct :: (Eq a, C a) => a -> a -> BoolSource
propExpLogPower :: (Eq a, C a) => a -> a -> BoolSource
propLogSum :: (Eq a, C a) => a -> a -> BoolSource
propPowerCascade :: (Eq a, C a) => a -> a -> a -> BoolSource
propPowerProduct :: (Eq a, C a) => a -> a -> a -> BoolSource
propPowerDistributive :: (Eq a, C a) => a -> a -> a -> BoolSource
Trigonometric laws, addition theorems
propTrigonometricPythagoras :: (Eq a, C a) => a -> BoolSource
propSinPeriod :: (Eq a, C a) => a -> BoolSource
propCosPeriod :: (Eq a, C a) => a -> BoolSource
propTanPeriod :: (Eq a, C a) => a -> BoolSource
propSinAngleSum :: (Eq a, C a) => a -> a -> BoolSource
propCosAngleSum :: (Eq a, C a) => a -> a -> BoolSource
propSinDoubleAngle :: (Eq a, C a) => a -> BoolSource
propCosDoubleAngle :: (Eq a, C a) => a -> BoolSource
propSinSquare :: (Eq a, C a) => a -> BoolSource
propCosSquare :: (Eq a, C a) => a -> BoolSource
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