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 .

Documentation

newtype T a

Constructors

Cons

Fields

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

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]

cf. MathObj.Polynomial.mulLinearFactor

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]

Show

appPrec :: Int

Additive

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

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

Ring

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]

Field.C

Algebra