numeric-prelude-0.2.2.1: An experimental alternative hierarchy of numeric type classes

Portability requires multi-parameter type classes provisional numericprelude@henning-thielemann.de

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 aSource

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

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

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

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

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

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

cf. `MathObj.Polynomial.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