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alogic0/GirardNewton.hs

Created January 19, 2021 03:13
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Solution for math problem
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GirardNewton.hs
-- Haskell version of formulae from
-- https://youtu.be/4FNCIYD8HdA
import Control.Monad (join)
import Data.Ratio
oneS :: [Rational]
oneS = join $ repeat [1, (-1)]
pSum :: Int -> Rational
pSum 1 = 1
pSum 2 = 2
pSum 3 = 3
pSum n = sum (zipWith (*) oneS (map (\k -> pSum (n - k) * eSum k) [1 .. (n - 1)])) + fromIntegral n * (oneS !! n) * eSum n
eSum :: Int -> Rational
eSum 0 = 1
eSum 1 = 1
eSum n | n > 3 = 0
eSum n = sum (zipWith (*) oneS (map (\k -> pSum k * eSum (n - k)) [1 .. n])) / fromIntegral n
-- now try
-- pSum 4
-- pSum 5
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