numeric-prelude-0.4.2: An experimental alternative hierarchy of numeric type classes

Copyright(c) Henning Thielemann 2004-2005
Maintainernumericprelude@henning-thielemann.de
Stabilityprovisional
Portabilityrequires multi-parameter type classes
Safe HaskellNone
LanguageHaskell98

MathObj.PowerSum

Contents

Description

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.

Synopsis

Documentation

newtype T a Source

Constructors

Cons 

Fields

sums :: [a]
 

Instances

(C a v, C v) => C a (T v) 
(C a v, C v) => C a (T v) 
Show a => Show (T a) 
C a => C (T 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

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

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

fromElemSymDenormalized :: (C a, C a) => [a] -> [a] Source

toElemSym :: (C a, C a) => [a] -> [a] Source

toElemSymInt :: (C a, C a) => [a] -> [a] Source

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

elemSymFromPolynomial :: C a => T a -> [a] Source

binomials :: C a => [[a]] Source

Show

appPrec :: Int Source

Additive

add :: C a => [a] -> [a] -> [a] Source

Ring

mul :: C a => [a] -> [a] -> [a] Source

pow :: Integer -> [a] -> [a] Source

Module

Field.C

Algebra

root :: C a => Integer -> [a] -> [a] Source

approxSeries :: C a b => [b] -> [a] -> [b] Source

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