Polynomial now returns a correct string representation of itself.

lfsr.py

@@ -4,7 +4,7 @@
 # @author Michael Foukarakis
 # @version 1.0
 # @date Created: Thu Feb 03, 2011 08:19 GTB Standard Time
-# Last Update: Tue Mar 26, 2013 12:41 GTB Standard Time
+# Last Update: Wed Aug 28, 2013 10:22 BST
 #------------------------------------------------------------------------
 # Description: Implementation of a Galois LFSR
 # The bitstream is provided by the generator function
@@ -47,7 +47,7 @@ def states(self, repeat=False):
 One = Polynomial([1])
 
 def bm(seq):
- '''Implementation of the Berlekamp-Massey algorithm, the purpose
+ """Implementation of the Berlekamp-Massey algorithm, the purpose
  of which is to find a LFSR with the smallest possible length
  that generates a given sequence.
 
@@ -66,7 +66,7 @@ def bm(seq):
  The generating function G(x) = s_0 + s_1 * x^1 + s_2 * x^2 + ...
  of a LFSR is rational and (when written in lowest terms) the
  denominator f(x) is called the characteristic polynomial of the
- LFSR. Here we have f(x) = c0 * x^m + c1 * x^{m-1} +...+ c{m-1} * x + 1.'''
+ LFSR. Here we have f(x) = c0 * x^m + c1 * x^{m-1} +...+ c{m-1} * x + 1."""
  # Allow for an input string along with a list or tuple
  if type(S)==type("string"):
  S = map(int,tuple(S))

polynomial.py

@@ -3,7 +3,7 @@
 # @author Michael Foukarakis
 # @version 0.1
 # @date Created: Sun Jul 10, 2011 03:03 PDT
-# Last Update: Mon Jan 24, 2011 14:54 GTB Standard Time
+# Last Update: Wed Aug 28, 2013 10:23 BST
 #------------------------------------------------------------------------
 # Description: A class representing polynomials over GF(2).
 # The coefficients are stored in a list.
@@ -14,9 +14,8 @@
 
 class Polynomial(list):
  def __str__(self):
- L = ['x^{}'.format(k) for k in enumerate(self[::-1]) if x == 1]
- L.reverse()
- return '+'.join(L)
+ L = ['{}*x^{}'.format(e, i) for i,e in enumerate(self)]
+ return ' + '.join(L)
 
  def __add__(self, other):
  if len(self) < len(other):
@@ -57,5 +56,5 @@ def __pow__(self,ex):
 
 
 def dot(x, y):
- '''Returns the dot product of two lists.'''
+ """Returns the dot product of two lists."""
  return reduce(xor, [a&b for (a,b) in zip(x,y)], 0)