33 lines
979 B
Haskell
33 lines
979 B
Haskell
import Control.Monad (forM_)
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import Data.List (intercalate)
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import Data.List.Split (chunksOf)
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import Math.NumberTheory.Primes (factorise, unPrime)
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import Text.Printf (printf)
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-- The arithmetic derivative of a number, which is assumed to be non-negative.
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arithderiv_ :: Integer -> Integer
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arithderiv_ 0 = 0
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arithderiv_ n = foldr step 0 $ factorise n
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where step (p, v) s = s + n `quot` unPrime p * fromIntegral v
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-- The arithmetic derivative of any integer.
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arithderiv :: Integer -> Integer
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arithderiv n | n < 0 = negate $ arithderiv_ (negate n)
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| otherwise = arithderiv_ n
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printTable :: [Integer] -> IO ()
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printTable = putStrLn
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. intercalate "\n"
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. map unwords
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. chunksOf 10
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. map (printf "%5d")
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main :: IO ()
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main = do
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printTable [arithderiv n | n <- [-99..100]]
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putStrLn ""
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forM_ [1..20 :: Integer] $ \i ->
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let q = 7
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n = arithderiv (10^i) `quot` q
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in printf "D(10^%-2d) / %d = %d\n" i q n
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