5.2 polynomials

polynomials.ex

defmodule Chapter5 do
  def polynomial2(as, x) do
    Stream.iterate(1, &(&1 * x))
      |> Enum.zip(as)
      |> Enum.map(fn {x, a} -> x * a end)
      |> Enum.sum
  end

  def polynomial3(as, x) do
    Enum.reverse(as) |> Enum.reduce(&(&2 * x + &1))
  end
end

polynomials.hs

polynomial1 :: [Double] -> Double -> Double
polynomial1 as x = poly as x 0
  where
    poly [] x i = 0
    poly (b:bs) x i = b * (x**i) + (poly bs x (i + 1))

polynomial2 :: [Double] -> Double -> Double
polynomial2 as x = sum $ zipWith (*) as xs
  where
    xs = 1:zipWith (*) xs [x, x..]

polynomial3 :: [Double] -> Double -> Double
polynomial3 as x = foldr1 (\a p -> x * p + a) as

polynomials.rb

# as: [a0, a1, a2, a3, ..., an]

def polynomial1(as, x, i = 0)
  if as.empty?
    0
  else
    as.first * (x**i) + polynomial1(as.drop(1), x, i + 1)
  end
end

def polynomial2(as, x)
  as.reduce([0, 1]) {|(t, xe), a| [t + a * xe, xe * x] }.first
end

def polynomial3(as, x)
  as.reverse.reduce {|p, a| p * x + a }
end


def polynomial_all(as, x)
  (1..3).map do |n|
    send :"polynomial#{n}", as, x
  end
end

examples = [
  [[4,3,2,1], 5],
  [[1.2, 9.8, -7.3], 12.9]
]

examples.each do |(as, x)|
  puts '=' * 80
  puts "as = #{as}, x = #{x}"
  puts polynomial_all(as, x)
end