Copyright | (c) Henning Thielemann 2004-2005 |
---|---|

Maintainer | numericprelude@henning-thielemann.de |

Stability | provisional |

Portability | requires multi-parameter type classes |

Safe Haskell | None |

Language | Haskell98 |

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

- newtype T a = Cons {
- coeffs :: [a]

- lift0 :: [a] -> T a
- lift1 :: ([a] -> [a]) -> T a -> T a
- lift2 :: ([a] -> [a] -> [a]) -> T a -> T a -> T a
- const :: C a => a -> T a
- toPolynomial :: T a -> T a
- fromPolynomial :: T a -> T a
- toPowerSums :: (C a, C a) => [a] -> [a]
- fromPowerSums :: (C a, C a) => [a] -> [a]
- addRoot :: C a => a -> [a] -> [a]
- fromRoots :: C a => [a] -> [a]
- liftPowerSum1Gen :: ([a] -> [a]) -> ([a] -> [a]) -> ([a] -> [a]) -> [a] -> [a]
- liftPowerSum2Gen :: ([a] -> [a]) -> ([a] -> [a]) -> ([a] -> [a] -> [a]) -> [a] -> [a] -> [a]
- liftPowerSum1 :: (C a, C a) => ([a] -> [a]) -> [a] -> [a]
- liftPowerSum2 :: (C a, C a) => ([a] -> [a] -> [a]) -> [a] -> [a] -> [a]
- liftPowerSumInt1 :: (C a, Eq a, C a) => ([a] -> [a]) -> [a] -> [a]
- liftPowerSumInt2 :: (C a, Eq a, C a) => ([a] -> [a] -> [a]) -> [a] -> [a] -> [a]
- appPrec :: Int
- add :: (C a, C a) => [a] -> [a] -> [a]
- addInt :: (C a, Eq a, C a) => [a] -> [a] -> [a]
- mul :: (C a, C a) => [a] -> [a] -> [a]
- mulInt :: (C a, Eq a, C a) => [a] -> [a] -> [a]
- pow :: (C a, C a) => Integer -> [a] -> [a]
- powInt :: (C a, Eq a, C a) => Integer -> [a] -> [a]
- approxPolynomial :: C a => Int -> Integer -> a -> (a, T a)

# Documentation

# Conversions

toPolynomial :: T a -> T a Source #

fromPolynomial :: T 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`

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 #

# Show

# Additive

# Ring

# Field.C

# 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.