numeric-prelude-0.4.2: An experimental alternative hierarchy of numeric type classes

Copyright (c) Henning Thielemann 2004-2005 numericprelude@henning-thielemann.de provisional requires multi-parameter type classes None Haskell98

MathObj.RootSet

Contents

Description

Computations on the set of roots of a polynomial. These are represented as the list of their elementar symmetric terms. The difference between a polynomial and the list of elementar symmetric terms is the reversed order and the alternated signs.

Cf. MathObj.PowerSum .

Synopsis

# Documentation

newtype T a Source

Constructors

 Cons Fieldscoeffs :: [a]

Instances

 Show a => Show (T a) (C a, C a) => C (T a) (C a, C a) => C (T a) (C a, C a) => C (T a) (C a, C a) => C (T a)

# Conversions

lift0 :: [a] -> T a Source

lift1 :: ([a] -> [a]) -> T a -> T a Source

lift2 :: ([a] -> [a] -> [a]) -> T a -> T a -> T a Source

const :: C a => a -> T a Source

toPowerSums :: (C a, C a) => [a] -> [a] Source

fromPowerSums :: (C a, C a) => [a] -> [a] Source

addRoot :: C a => a -> [a] -> [a] Source

cf. `mulLinearFactor`

fromRoots :: C a => [a] -> [a] Source

liftPowerSum1Gen :: ([a] -> [a]) -> ([a] -> [a]) -> ([a] -> [a]) -> [a] -> [a] Source

liftPowerSum2Gen :: ([a] -> [a]) -> ([a] -> [a]) -> ([a] -> [a] -> [a]) -> [a] -> [a] -> [a] Source

liftPowerSum1 :: (C a, C a) => ([a] -> [a]) -> [a] -> [a] Source

liftPowerSum2 :: (C a, C a) => ([a] -> [a] -> [a]) -> [a] -> [a] -> [a] Source

liftPowerSumInt1 :: (C a, Eq a, C a) => ([a] -> [a]) -> [a] -> [a] Source

liftPowerSumInt2 :: (C a, Eq a, C a) => ([a] -> [a] -> [a]) -> [a] -> [a] -> [a] Source

# Show

add :: (C a, C a) => [a] -> [a] -> [a] Source

addInt :: (C a, Eq a, C a) => [a] -> [a] -> [a] Source

# Ring

mul :: (C a, C a) => [a] -> [a] -> [a] Source

mulInt :: (C a, Eq a, C a) => [a] -> [a] -> [a] Source

pow :: (C a, C a) => Integer -> [a] -> [a] Source

powInt :: (C a, Eq a, C a) => Integer -> [a] -> [a] Source

# Algebra

approxPolynomial :: C a => Int -> Integer -> a -> (a, T a) Source

Given an approximation of a root, the degree of the polynomial and maximum value of coefficients, find candidates of polynomials that have approximately this root and show the actual value of the polynomial at the given root approximation.

This algorithm runs easily into a stack overflow, I do not know why. We may also employ a more sophisticated integer relation algorithm, like PSLQ and friends.