numeric-prelude-0.4.4: An experimental alternative hierarchy of numeric type classes
Safe HaskellNone
LanguageHaskell98

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

Instances details
C Double Source # 
Instance details

Defined in Algebra.Transcendental

C Float Source # 
Instance details

Defined in Algebra.Transcendental

C T Source # 
Instance details

Defined in Number.FixedPoint.Check

Methods

pi :: T Source #

exp :: 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 #

C T Source # 
Instance details

Defined in Number.Positional.Check

Methods

pi :: T Source #

exp :: 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 details

Defined in Number.NonNegative

Methods

pi :: 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 details

Defined in MathObj.Wrapper.Haskell98

Methods

pi :: 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 details

Defined in Number.PartiallyTranscendental

Methods

pi :: 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 details

Defined in MathObj.PowerSeries

Methods

pi :: 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 details

Defined in Number.Complex

Methods

pi :: 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 details

Defined in MathObj.Wrapper.NumericPrelude

Methods

pi :: 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 details

Defined in Number.OccasionallyScalarExpression

Methods

pi :: 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 details

Defined in Number.Physical

Methods

pi :: 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 details

Defined in Number.SI

Methods

pi :: 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 #