numeric-prelude-0.4.3.1: 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

Instances
(C a v, C v) => C a (T v) Source # 
Instance details

Defined in MathObj.PowerSum

Methods

(*>) :: a -> T v -> T v Source #

(C a v, C v) => C a (T v) Source # 
Instance details

Defined in MathObj.PowerSum

Show a => Show (T a) Source # 
Instance details

Defined in MathObj.PowerSum

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

C a => C (T a) Source # 
Instance details

Defined in MathObj.PowerSum

Methods

zero :: 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 details

Defined in MathObj.PowerSum

Methods

(*) :: T a -> T a -> T a Source #

one :: T a Source #

fromInteger :: Integer -> T a Source #

(^) :: T a -> Integer -> T a Source #

(C a, C a) => C (T a) Source # 
Instance details

Defined in MathObj.PowerSum

Methods

(/) :: T a -> T a -> T a Source #

recip :: T a -> T a Source #

fromRational' :: Rational -> T a Source #

(^-) :: T a -> Integer -> T a Source #

(C a, C a) => C (T a) Source # 
Instance details

Defined in MathObj.PowerSum

Methods

sqrt :: 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

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 #