Polynomials.hs

module Polynomials

where

difs :: [Integer] -> [Integer]
difs [] = []
difs [n] = []
difs (n:m:ks) = m-n : difs (m:ks)

difLists :: [[Integer]]->[[Integer]]
difLists [] = []
difLists lists@(xs:xss) =
    if constant xs then lists else difLists ((difs xs):lists)
    where
      constant (n:m:ms) = all (==n) (m:ms)
      constant _ = error "lack of data or not a polynomial fct"

genDifs :: [Integer] -> [Integer]
genDifs xs = map last (difLists [xs])

nextD :: [Integer] -> [Integer]
nextD [] = error "no data"
nextD [n] = [n]
nextD (n:m:ks) = n : nextD (n+m : ks)

next :: [Integer] -> Integer
next = last . nextD . genDifs

continue :: [Integer] -> [Integer]
continue xs = map last (iterate nextD differences)
    where
      differences = nextD (genDifs xs)

degree :: [Integer] -> Int
degree xs = length (difLists [xs]) - 1