Modulenumeric-prelude-0.4.4Haskell98

MathObj.RootSet

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 .

Contents

Conversions
Show
Additive
Ring
Field.C
Algebra

Synopsis

newtype T
value lift0
value lift1
value lift2
value const
value toPolynomial
value fromPolynomial
value toPowerSums
value fromPowerSums
value addRoot
value fromRoots
value liftPowerSum1Gen
value liftPowerSum2Gen
value liftPowerSum1
value liftPowerSum2
value liftPowerSumInt1
value liftPowerSumInt2
value appPrec
value add
value addInt
value mul
value mulInt
value pow
value powInt
value approxPolynomial

Packagenumeric-prelude-0.4.4
Exports25
LanguageHaskell98
LicenceBSD-3-Clause
SourceRootSet.hs

newtypenewtype T a

Constructors

Cons
- coeffs :: [a]

Instances5Show, C

Show a => Show (T a)Defined in numeric-prelude-0.4.4 · MathObj.RootSet
(C a, C a) => C (T a)Defined in numeric-prelude-0.4.4 · MathObj.RootSet
(C a, C a) => C (T a)Defined in numeric-prelude-0.4.4 · MathObj.RootSet
(C a, C a) => C (T a)Defined in numeric-prelude-0.4.4 · MathObj.RootSet
(C a, C a) => C (T a)Defined in numeric-prelude-0.4.4 · MathObj.RootSet

Conversions

valuelift0 :: [a] -> T a

valuelift1 :: ([a] -> [a]) -> T a -> T a

valuelift2 :: ([a] -> [a] -> [a]) -> T a -> T a -> T a

valueconst :: C a => a -> T a

valuetoPolynomial :: T a -> T a

valuefromPolynomial :: T a -> T a

valuetoPowerSums :: (C a, C a) => [a] -> [a]

valuefromPowerSums :: (C a, C a) => [a] -> [a]

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

Source#

cf. MathObj.Polynomial.mulLinearFactor

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

valueliftPowerSum1Gen

:: [a] -> [a]
-> [a] -> [a]
-> [a] -> [a]
-> [a]
-> [a]

valueliftPowerSum2Gen

:: [a] -> [a]
-> [a] -> [a]
-> [a] -> [a] -> [a]
-> [a]
-> [a]
-> [a]

valueliftPowerSum1 :: (C a, C a) => ([a] -> [a]) -> [a] -> [a]

valueliftPowerSum2 :: (C a, C a) => ([a] -> [a] -> [a]) -> [a] -> [a] -> [a]

valueliftPowerSumInt1 :: (C a, Eq a, C a) => ([a] -> [a]) -> [a] -> [a]

valueliftPowerSumInt2

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

Show

valueappPrec :: Int

Additive

valueadd :: (C a, C a) => [a] -> [a] -> [a]

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

Ring

valuemul :: (C a, C a) => [a] -> [a] -> [a]

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

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

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

Field.C

Algebra

valueapproxPolynomial :: 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.