Copyright | (c) Henning Thielemann 2004-2005 |
---|---|

Maintainer | numericprelude@henning-thielemann.de |

Stability | provisional |

Portability | requires multi-parameter type classes |

Safe Haskell | None |

Language | Haskell98 |

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

# Conversions

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 #

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

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

# Show

# Additive

# Ring

# Module

# Field.C

# Algebra

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