numeric-prelude-0.4.3: 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 # Methods(*>) :: a -> T v -> T v Source # (C a v, C v) => C a (T v) Source # Show a => Show (T a) Source # MethodsshowsPrec :: Int -> T a -> ShowS #show :: T a -> String #showList :: [T a] -> ShowS # C a => C (T a) Source # 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 # 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 # 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 # 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 #

# Additive

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 #