Symmetric group arithmetic

sym.py

# Computes ab in the symmetric group S_n, where a and b are given in cyclic
# notation.
def compose(a, b, n):
  i   = 1
  out = []
  
  while not i in out:
    out.append(i)
    i = apply(a, apply(b, i))
  
  if out == [1]:
    return []
  
  return out
  
# Computes a(x) for a in S_n and 1 <= x <= n.
def apply(a, x):
  if x in a:
    return a[(a.index(x) + 1) % len(a)]
  else:
    return x