numeric-prelude-0.1.3: An experimental alternative hierarchy of numeric type classesSource codeContentsIndex
MathObj.RootSet
Portabilityrequires multi-parameter type classes
Stabilityprovisional
Maintainernumericprelude@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]
show/hide 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
toPolynomial :: T a -> T aSource
fromPolynomial :: T 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
appPrec :: IntSource
Additive
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
Field.C
Algebra
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