NumericPrelude-0.0: An experimental alternative hierarchy of numeric type classes Contents Index

MathObj.LaurentPolynomial Portability requires multi-parameter type classes Stability provisional Maintainer numericprelude@henning-thielemann.de

Contents Basic Operations Show Additive Module Ring Field.C Comparisons Transformations of arguments

Description

Polynomials with negative and positive exponents.

Synopsis

data T a = Cons { expon :: Int coeffs :: [a] } const :: a -> T a (!) :: C a => T a -> Int -> a fromList :: [a] -> T a fromPolynomial :: T a -> T a fromPowerSeries :: T a -> T a bounds :: T a -> (Int, Int) translate :: Int -> T a -> T a appPrec :: Int add :: C a => T a -> T a -> T a series :: C a => [T a] -> T a addShiftedMany :: C a => [Int] -> [[a]] -> [a] addShifted :: C a => Int -> [a] -> [a] -> [a] negate :: C a => T a -> T a sub :: C a => T a -> T a -> T a scale :: C a => a -> [a] -> [a] mul :: C a => T a -> T a -> T a div :: (C a, C a) => T a -> T a -> T a divExample :: T Rational equivalent :: (Eq a, C a) => T a -> T a -> Bool identical :: Eq a => T a -> T a -> Bool isAbsolute :: C a => T a -> Bool alternate :: C a => T a -> T a reverse :: T a -> T a

Documentation

data T a

Polynomial including negative exponents Constructors Cons expon :: Int coeffs :: [a] Instances C T Functor T C a b => C a (T b) (C a, C a b) => C a (T b) C a => C (T a) C a => C (T a) (C a, C a) => C (T a) (Eq a, C a) => Eq (T a) Show a => Show (T a)

Basic Operations

const :: a -> T a

(!) :: C a => T a -> Int -> a

fromList :: [a] -> T a

fromPolynomial :: T a -> T a

fromPowerSeries :: T a -> T a

bounds :: T a -> (Int, Int)

translate :: Int -> T a -> T a

Show

appPrec :: Int

Additive

add :: C a => T a -> T a -> T a

series :: C a => [T a] -> T a

addShiftedMany :: C a => [Int] -> [[a]] -> [a]

The list of relative shifts is one element shorter than the list of summands.

addShifted :: C a => Int -> [a] -> [a] -> [a]

negate :: C a => T a -> T a

sub :: C a => T a -> T a -> T a

Module

scale :: C a => a -> [a] -> [a]

Ring

mul :: C a => T a -> T a -> T a

Field.C

div :: (C a, C a) => T a -> T a -> T a

divExample :: T Rational

Comparisons

equivalent :: (Eq a, C a) => T a -> T a -> Bool

Two signals may be different in structure but represent the same infinite signal. This function checks whether two signals represent the same infinite signal.

identical :: Eq a => T a -> T a -> Bool

isAbsolute :: C a => T a -> Bool

Check whether a signal is an impulse at time zero.

Transformations of arguments

alternate :: C a => T a -> T a

p(z) -> p(-z)

reverse :: T a -> T a

p(z) -> p(1/z)

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