numeric-prelude-0.4.3.1: An experimental alternative hierarchy of numeric type classes

Copyright (c) Henning Thielemann 2004-2005 numericprelude@henning-thielemann.de provisional requires multi-parameter type classes None Haskell98

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 Fieldssums :: [a]
Instances
 (C a v, C v) => C a (T v) Source # Instance detailsDefined in MathObj.PowerSum Methods(*>) :: a -> T v -> T v Source # (C a v, C v) => C a (T v) Source # Instance detailsDefined in MathObj.PowerSum Show a => Show (T a) Source # Instance detailsDefined in MathObj.PowerSum MethodsshowsPrec :: Int -> T a -> ShowS #show :: T a -> String #showList :: [T a] -> ShowS # C a => C (T a) Source # Instance detailsDefined in MathObj.PowerSum Methodszero :: T a Source #(+) :: T a -> T a -> T a Source #(-) :: T a -> T a -> T a Source #negate :: T a -> T a Source # C a => C (T a) Source # Instance detailsDefined in MathObj.PowerSum Methods(*) :: T a -> T a -> T a Source #one :: T a Source #(^) :: T a -> Integer -> T a Source # (C a, C a) => C (T a) Source # Instance detailsDefined in MathObj.PowerSum Methods(/) :: T a -> T a -> T a Source #recip :: T a -> T a Source #(^-) :: T a -> Integer -> T a Source # (C a, C a) => C (T a) Source # Instance detailsDefined in MathObj.PowerSum Methodssqrt :: T a -> T a Source #root :: Integer -> T a -> T a Source #(^/) :: T a -> Rational -> T a Source #

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

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

Ring

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

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

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 #