Babbage's Difference Engine in Python

diff_engine.py

def diff(seq):
  """ [1,4,9] => [3,5] """
  return map(lambda x,y: x-y, seq[1:], seq[:-1])
 
def triangle(seq):
  """ [1,4,9] => [[1,4,9],[3,5],[2]] """
  diffs=[seq]
  for i in range(1, len(seq)):
    diffs.append(diff(diffs[i-1]))
  return diffs
 
def reductions(seq):
  """ [1,4,9] => [1,5,14] """
  l = [seq[0]]
  for i in range(1, len(seq)):
    l.append(seq[i]+l[i-1])
  return l
 
def infer(pattern, n):
  """ infer([1,4,9], 10) => [1,4,9,16,25 ... 100] """
  gen_seq = [seq[-1] for seq in triangle(pattern)]
  gen_seq.reverse()
  
  elements = pattern[:-1]
  for count in range(len(pattern)-1, n):
    elements.append(gen_seq[-1])
    gen_seq = reductions(gen_seq)
  
  return elements

This is a Python port of some Clojure code that I wrote about some time back in a blog post .