Factorial generalizado

8 Comentarios

1. Haskell

   import Test.QuickCheck factGen :: Integer -> Integer -> Integer -> Integer factGen x y z = product [x,x-z..x-(y-1)*z] fact :: Integer -> Integer fact 0 = 1 fact x = product [1..x] prop :: (Positive Integer) -> Bool prop (Positive x) = fact x == factGen x x 1 -- λ> quickCheck prop -- +++ OK, passed 100 tests.

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   import Test.QuickCheck   factGen :: Integer -> Integer -> Integer -> Integer factGen x y z = product [x,x-z..x-(y-1)*z]   fact :: Integer -> Integer fact 0 = 1 fact x = product [1..x]   prop :: (Positive Integer) -> Bool prop (Positive x) = fact x == factGen x x 1   -- λ> quickCheck prop -- +++ OK, passed 100 tests.

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   1. En realidad, la ecuación fact 0 = 1 es innecesaria. Podría simplificarse.

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2. Haskell

   import Test.QuickCheck factGen :: Integer -> Integer -> Integer -> Integer factGen x y z = product [ x-(m*z) | m <- [0..y-1] ] prop_factGen :: Positive Integer -> Bool prop_factGen (Positive x) = factGen x x 1 == fact x fact :: (Enum a, Num a) => a -> a fact x = product [1..x] -- *Main> quickCheck prop_factGen -- +++ OK, passed 100 tests.

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   import Test.QuickCheck   factGen :: Integer -> Integer -> Integer -> Integer factGen x y z = product [ x-(m*z) | m <- [0..y-1] ]   prop_factGen :: Positive Integer -> Bool prop_factGen (Positive x) = factGen x x 1 == fact x   fact :: (Enum a, Num a) => a -> a fact x = product [1..x]   -- *Main> quickCheck prop_factGen -- +++ OK, passed 100 tests.

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3. Haskell

   import Test.QuickCheck factGen :: Integer -> Integer -> Integer -> Integer factGen x y z = product $ take (fromIntegral y) (iterate (+(-z)) x) prop_factGen :: Positive Integer -> Bool prop_factGen (Positive x) = factGen x x 1 == product [1..x] -- *Main> quickCheck prop_factGen -- +++ OK, passed 100 tests.

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   import Test.QuickCheck   factGen :: Integer -> Integer -> Integer -> Integer factGen x y z = product $ take (fromIntegral y) (iterate (+(-z)) x)   prop_factGen :: Positive Integer -> Bool prop_factGen (Positive x) = factGen x x 1 == product [1..x]   -- *Main> quickCheck prop_factGen -- +++ OK, passed 100 tests.

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4. Haskell

   import Test.QuickCheck factGen :: Integer -> Integer -> Integer -> Integer factGen x y z = product $ map (\k -> x-k*z) [0..y-1] prop_factGen :: Positive Integer -> Bool prop_factGen (Positive x) = factGen x x 1 == product [1..x] -- *Main> quickCheck prop_factGen -- +++ OK, passed 100 tests.

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   import Test.QuickCheck   factGen :: Integer -> Integer -> Integer -> Integer factGen x y z = product $ map (\k -> x-k*z) [0..y-1]   prop_factGen :: Positive Integer -> Bool prop_factGen (Positive x) = factGen x x 1 == product [1..x] -- *Main> quickCheck prop_factGen -- +++ OK, passed 100 tests.

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5. Haskell

   import Test.QuickCheck factGen :: Integer -> Integer -> Integer -> Integer factGen x y z = product [x, x-z..(x-(y-1)*z)] prop_factGen :: Positive Integer -> Bool prop_factGen (Positive x) = factGen x x 1 == product [1..x]

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   import Test.QuickCheck   factGen :: Integer -> Integer -> Integer -> Integer factGen x y z = product [x, x-z..(x-(y-1)*z)]   prop_factGen :: Positive Integer -> Bool prop_factGen (Positive x) = factGen x x 1 == product [1..x]

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6. factGen (x,y,z) := block (lreduce("*",create_list(x-(m*z),m,makelist(k,k,0,y-1))))$

   1	factGen (x,y,z) := block (lreduce("*",create_list(x-(m*z),m,makelist(k,k,0,y-1))))$

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7. En Maxima está predefinido

   factGen (x,y,z) := genfact (x,y,z)$

   1	factGen (x,y,z) := genfact (x,y,z)$

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