Modulenumeric-prelude-0.4.4Haskell98

MathObj.PowerSum

For a multi-set of numbers, we describe a sequence of the sums of powers of the numbers in the set. These can be easily converted to polynomials and back. Thus they provide an easy way for computations on the roots of a polynomial.

Contents

Conversions
Show
Additive
Ring
Module
Field.C
Algebra

Synopsis

newtype T
value lift0
value lift1
value lift2
value const
value fromElemSym
value divOneFlip
value fromElemSymDenormalized
value toElemSym
value toElemSymInt
value fromPolynomial
value elemSymFromPolynomial
value binomials
value appPrec
value add
value mul
value pow
value root
value approxSeries
value propOp

Packagenumeric-prelude-0.4.4
Exports20
LanguageHaskell98
LicenceBSD-3-Clause
SourcePowerSum.hs

newtypenewtype T a

Constructors

Cons
- sums :: [a]

Instances7Show, C, …

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

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

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

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

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

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

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

valuefromPolynomial :: (C a, C a) => T a -> [a]

valueelemSymFromPolynomial :: C a => T a -> [a]

valuebinomials :: C a => [[a]]

Show

valueappPrec :: Int

Additive

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

Ring

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

valuepow :: Integer -> [a] -> [a]

Module

Field.C

Algebra

valueroot :: C a => Integer -> [a] -> [a]

valueapproxSeries :: C a b => [b] -> [a] -> [b]

valuepropOp

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