NumericPrelude-0.0: An experimental alternative hierarchy of numeric type classes Contents Index

MathObj.PowerSum Portability requires multi-parameter type classes Stability provisional Maintainer numericprelude@henning-thielemann.de

Contents Conversions Show Additive Ring Module Field.C Algebra

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

newtype T a = Cons { sums :: [a] } lift0 :: [a] -> T a lift1 :: ([a] -> [a]) -> T a -> T a lift2 :: ([a] -> [a] -> [a]) -> T a -> T a -> T a const :: C a => a -> T a fromElemSym :: (Eq a, C a) => [a] -> [a] divOneFlip :: (Eq a, C a) => [a] -> [a] -> [a] fromElemSymDenormalized :: (C a, C a) => [a] -> [a] toElemSym :: (C a, C a) => [a] -> [a] toElemSymInt :: (C a, C a) => [a] -> [a] fromPolynomial :: (C a, C a) => T a -> [a] elemSymFromPolynomial :: C a => T a -> [a] binomials :: C a => [[a]] appPrec :: Int add :: C a => [a] -> [a] -> [a] mul :: C a => [a] -> [a] -> [a] pow :: Integer -> [a] -> [a] root :: C a => Integer -> [a] -> [a] approxSeries :: C a b => [b] -> [a] -> [b] propOp :: (Eq a, C a, C a) => ([a] -> [a] -> [a]) -> (a -> a -> a) -> [a] -> [a] -> [Bool]

Documentation

newtype T a

Constructors Cons sums :: [a] Instances (C a v, C v) => C a (T v) (C a v, C v) => C a (T v) C a => C (T a) C a => C (T a) (C a, C a) => C (T a) (C a, C a) => C (T a) Show a => Show (T a)

Conversions

lift0 :: [a] -> T a

lift1 :: ([a] -> [a]) -> T a -> T a

lift2 :: ([a] -> [a] -> [a]) -> T a -> T a -> T a

const :: C a => a -> T a

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

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

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

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

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

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

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

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

Show

appPrec :: Int

Additive

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

Ring

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

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

Module

Field.C

Algebra

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

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

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

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