MathObj.RootSet
 Portability requires multi-parameter type classes Stability provisional Maintainer numericprelude@henning-thielemann.de
 Contents Conversions Show Additive Ring Field.C Algebra
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
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]
Documentation
 newtype T a Source
Constructors
Cons
 coeffs :: [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
 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. 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
 appPrec :: Int Source