
MathObj.RootSet  Portability  requires multiparameter type classes  Stability  provisional  Maintainer  numericprelude@henningthielemann.de 





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 {}   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 


Constructors   Instances  


Conversions




lift1 :: ([a] > [a]) > T a > T a  Source 


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




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 






Field.C


Algebra


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