| Copyright | (c) Henning Thielemann 2004-2006 |
|---|---|
| Maintainer | numericprelude@henning-thielemann.de |
| Stability | provisional |
| Portability | requires multi-parameter type classes |
| Safe Haskell | None |
| Language | Haskell98 |
MathObj.LaurentPolynomial
Description
Polynomials with negative and positive exponents.
Synopsis
- data T a = Cons {}
- const :: a -> T a
- (!) :: C a => T a -> Int -> a
- fromCoeffs :: [a] -> T a
- fromShiftCoeffs :: Int -> [a] -> T a
- fromPolynomial :: T a -> T a
- fromPowerSeries :: T a -> T a
- bounds :: T a -> (Int, Int)
- shift :: Int -> T a -> T a
- 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
- 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
- adjoint :: C a => T (T a) -> T (T a)
Documentation
Polynomial including negative exponents
Basic Operations
fromCoeffs :: [a] -> T a Source #
fromShiftCoeffs :: Int -> [a] -> T a Source #
fromPolynomial :: T a -> T a Source #
fromPowerSeries :: T a -> T a Source #
translate :: Int -> T a -> T a Source #
Deprecated: In order to avoid confusion with Polynomial.translate, use shift instead
Show
Additive
addShiftedMany :: C a => [Int] -> [[a]] -> [a] Source #
Add lists of numbers respecting a relative shift between the starts of the lists. The shifts must be non-negative. The list of relative shifts is one element shorter than the list of summands. Infinitely many summands are permitted, provided that runs of zero shifts are all finite.
We could add the lists either with foldl or with foldr,
foldl would be straightforward, but more time consuming (quadratic time)
whereas foldr is not so obvious but needs only linear time.
(stars denote the coefficients,
frames denote what is contained in the interim results)
foldl sums this way:
| | | ******************************* | | +-------------------------------- | | ************************ | +---------------------------------- | ************ +------------------------------------
I.e. foldl would use much time find the time differences
by successive subtraction 1.
foldr mixes this way:
+--------------------------------
| *******************************
| +-------------------------
| | ************************
| | +-------------
| | | ************addShifted :: C a => Int -> [a] -> [a] -> [a] Source #
Module
Ring
Field.C
divExample :: T Rational Source #
Comparisons
equivalent :: (Eq a, C a) => T a -> T a -> Bool Source #
Two polynomials may be stored differently.
This function checks whether two values of type LaurentPolynomial
actually represent the same polynomial.
isAbsolute :: C a => T a -> Bool Source #
Check whether a Laurent polynomial has only the absolute term, that is, it represents the constant polynomial.