numeric-prelude-0.4.3.1: An experimental alternative hierarchy of numeric type classes

Algebra.Transcendental

Synopsis

# Documentation

class C a => C a where Source #

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 Source #

exp :: a -> a Source #

log :: a -> a Source #

logBase :: a -> a -> a Source #

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

sin :: a -> a Source #

cos :: a -> a Source #

tan :: a -> a Source #

asin :: a -> a Source #

acos :: a -> a Source #

atan :: a -> a Source #

sinh :: a -> a Source #

cosh :: a -> a Source #

tanh :: a -> a Source #

asinh :: a -> a Source #

acosh :: a -> a Source #

atanh :: a -> a Source #

Instances
 Source # Instance detailsDefined in Algebra.Transcendental Methods Source # Instance detailsDefined in Algebra.Transcendental Methods Source # Instance detailsDefined in Number.FixedPoint.Check Methodsexp :: T -> T Source #log :: T -> T Source #logBase :: T -> T -> T Source #(**) :: T -> T -> T Source #sin :: T -> T Source #cos :: T -> T Source #tan :: T -> T Source #asin :: T -> T Source #acos :: T -> T Source #atan :: T -> T Source #sinh :: T -> T Source #cosh :: T -> T Source #tanh :: T -> T Source #asinh :: T -> T Source #acosh :: T -> T Source #atanh :: T -> T Source # Source # Instance detailsDefined in Number.Positional.Check Methodsexp :: T -> T Source #log :: T -> T Source #logBase :: T -> T -> T Source #(**) :: T -> T -> T Source #sin :: T -> T Source #cos :: T -> T Source #tan :: T -> T Source #asin :: T -> T Source #acos :: T -> T Source #atan :: T -> T Source #sinh :: T -> T Source #cosh :: T -> T Source #tanh :: T -> T Source #asinh :: T -> T Source #acosh :: T -> T Source #atanh :: T -> T Source # (Ord a, C a) => C (T a) Source # Instance detailsDefined in Number.NonNegative Methodspi :: T a Source #exp :: T a -> T a Source #log :: T a -> T a Source #logBase :: T a -> T a -> T a Source #(**) :: T a -> T a -> T a Source #sin :: T a -> T a Source #cos :: T a -> T a Source #tan :: T a -> T a Source #asin :: T a -> T a Source #acos :: T a -> T a Source #atan :: T a -> T a Source #sinh :: T a -> T a Source #cosh :: T a -> T a Source #tanh :: T a -> T a Source #asinh :: T a -> T a Source #acosh :: T a -> T a Source #atanh :: T a -> T a Source # Floating a => C (T a) Source # Instance detailsDefined in MathObj.Wrapper.Haskell98 Methodspi :: T a Source #exp :: T a -> T a Source #log :: T a -> T a Source #logBase :: T a -> T a -> T a Source #(**) :: T a -> T a -> T a Source #sin :: T a -> T a Source #cos :: T a -> T a Source #tan :: T a -> T a Source #asin :: T a -> T a Source #acos :: T a -> T a Source #atan :: T a -> T a Source #sinh :: T a -> T a Source #cosh :: T a -> T a Source #tanh :: T a -> T a Source #asinh :: T a -> T a Source #acosh :: T a -> T a Source #atanh :: T a -> T a Source # (C a, Eq a) => C (T a) Source # Instance detailsDefined in Number.PartiallyTranscendental Methodspi :: T a Source #exp :: T a -> T a Source #log :: T a -> T a Source #logBase :: T a -> T a -> T a Source #(**) :: T a -> T a -> T a Source #sin :: T a -> T a Source #cos :: T a -> T a Source #tan :: T a -> T a Source #asin :: T a -> T a Source #acos :: T a -> T a Source #atan :: T a -> T a Source #sinh :: T a -> T a Source #cosh :: T a -> T a Source #tanh :: T a -> T a Source #asinh :: T a -> T a Source #acosh :: T a -> T a Source #atanh :: T a -> T a Source # C a => C (T a) Source # Instance detailsDefined in MathObj.PowerSeries Methodspi :: T a Source #exp :: T a -> T a Source #log :: T a -> T a Source #logBase :: T a -> T a -> T a Source #(**) :: T a -> T a -> T a Source #sin :: T a -> T a Source #cos :: T a -> T a Source #tan :: T a -> T a Source #asin :: T a -> T a Source #acos :: T a -> T a Source #atan :: T a -> T a Source #sinh :: T a -> T a Source #cosh :: T a -> T a Source #tanh :: T a -> T a Source #asinh :: T a -> T a Source #acosh :: T a -> T a Source #atanh :: T a -> T a Source # (C a, C a, C a, Power a) => C (T a) Source # Instance detailsDefined in Number.Complex Methodspi :: T a Source #exp :: T a -> T a Source #log :: T a -> T a Source #logBase :: T a -> T a -> T a Source #(**) :: T a -> T a -> T a Source #sin :: T a -> T a Source #cos :: T a -> T a Source #tan :: T a -> T a Source #asin :: T a -> T a Source #acos :: T a -> T a Source #atan :: T a -> T a Source #sinh :: T a -> T a Source #cosh :: T a -> T a Source #tanh :: T a -> T a Source #asinh :: T a -> T a Source #acosh :: T a -> T a Source #atanh :: T a -> T a Source # C a => C (T a) Source # Instance detailsDefined in MathObj.Wrapper.NumericPrelude Methodspi :: T a Source #exp :: T a -> T a Source #log :: T a -> T a Source #logBase :: T a -> T a -> T a Source #(**) :: T a -> T a -> T a Source #sin :: T a -> T a Source #cos :: T a -> T a Source #tan :: T a -> T a Source #asin :: T a -> T a Source #acos :: T a -> T a Source #atan :: T a -> T a Source #sinh :: T a -> T a Source #cosh :: T a -> T a Source #tanh :: T a -> T a Source #asinh :: T a -> T a Source #acosh :: T a -> T a Source #atanh :: T a -> T a Source # (C a, C v, Show v, C a v) => C (T a v) Source # Instance detailsDefined in Number.OccasionallyScalarExpression Methodspi :: T a v Source #exp :: T a v -> T a v Source #log :: T a v -> T a v Source #logBase :: T a v -> T a v -> T a v Source #(**) :: T a v -> T a v -> T a v Source #sin :: T a v -> T a v Source #cos :: T a v -> T a v Source #tan :: T a v -> T a v Source #asin :: T a v -> T a v Source #acos :: T a v -> T a v Source #atan :: T a v -> T a v Source #sinh :: T a v -> T a v Source #cosh :: T a v -> T a v Source #tanh :: T a v -> T a v Source #asinh :: T a v -> T a v Source #acosh :: T a v -> T a v Source #atanh :: T a v -> T a v Source # (Ord i, C a) => C (T i a) Source # Instance detailsDefined in Number.Physical Methodspi :: T i a Source #exp :: T i a -> T i a Source #log :: T i a -> T i a Source #logBase :: T i a -> T i a -> T i a Source #(**) :: T i a -> T i a -> T i a Source #sin :: T i a -> T i a Source #cos :: T i a -> T i a Source #tan :: T i a -> T i a Source #asin :: T i a -> T i a Source #acos :: T i a -> T i a Source #atan :: T i a -> T i a Source #sinh :: T i a -> T i a Source #cosh :: T i a -> T i a Source #tanh :: T i a -> T i a Source #asinh :: T i a -> T i a Source #acosh :: T i a -> T i a Source #atanh :: T i a -> T i a Source # C v => C (T a v) Source # Instance detailsDefined in Number.SI Methodspi :: T a v Source #exp :: T a v -> T a v Source #log :: T a v -> T a v Source #logBase :: T a v -> T a v -> T a v Source #(**) :: T a v -> T a v -> T a v Source #sin :: T a v -> T a v Source #cos :: T a v -> T a v Source #tan :: T a v -> T a v Source #asin :: T a v -> T a v Source #acos :: T a v -> T a v Source #atan :: T a v -> T a v Source #sinh :: T a v -> T a v Source #cosh :: T a v -> T a v Source #tanh :: T a v -> T a v Source #asinh :: T a v -> T a v Source #acosh :: T a v -> T a v Source #atanh :: T a v -> T a v Source #

(^?) :: C a => a -> a -> a infixr 8 Source #

# Transcendental laws, will only hold approximately on floating point numbers

propExpLog :: (Eq a, C a) => a -> Bool Source #

propLogExp :: (Eq a, C a) => a -> Bool Source #

propExpNeg :: (Eq a, C a) => a -> Bool Source #

propLogRecip :: (Eq a, C a) => a -> Bool Source #

propExpProduct :: (Eq a, C a) => a -> a -> Bool Source #

propExpLogPower :: (Eq a, C a) => a -> a -> Bool Source #

propLogSum :: (Eq a, C a) => a -> a -> Bool Source #

propPowerCascade :: (Eq a, C a) => a -> a -> a -> Bool Source #

propPowerProduct :: (Eq a, C a) => a -> a -> a -> Bool Source #

propPowerDistributive :: (Eq a, C a) => a -> a -> a -> Bool Source #

# Trigonometric laws, addition theorems

propSinPeriod :: (Eq a, C a) => a -> Bool Source #

propCosPeriod :: (Eq a, C a) => a -> Bool Source #

propTanPeriod :: (Eq a, C a) => a -> Bool Source #

propSinAngleSum :: (Eq a, C a) => a -> a -> Bool Source #

propCosAngleSum :: (Eq a, C a) => a -> a -> Bool Source #

propSinDoubleAngle :: (Eq a, C a) => a -> Bool Source #

propCosDoubleAngle :: (Eq a, C a) => a -> Bool Source #

propSinSquare :: (Eq a, C a) => a -> Bool Source #

propCosSquare :: (Eq a, C a) => a -> Bool Source #