starting over

1 files changed, 46 insertions, 46 deletions

diff --git a/lib/zmod.py b/lib/zmod.py
index 3b38df9..d7f06db 100644
--- a/lib/zmod.py
+++ b/lib/zmod.py
@@ -1,7 +1,7 @@
 # module 'zmod'
 
 # Compute properties of mathematical "fields" formed by taking
-# Z/n (the whole numbers modulo some whole number n) and an
+# Z/n (the whole numbers modulo some whole number n) and an 
 # irreducible polynomial (i.e., a polynomial with only complex zeros),
 # e.g., Z/5 and X**2 + 2.
 #
@@ -10,11 +10,11 @@
 #
 # Note that this procedure doesn't yield a field for all combinations
 # of n and p: it may well be that some numbers have more than one
-# inverse and others have none. This is what we check.
+# inverse and others have none.  This is what we check.
 #
 # Remember that a field is a ring where each element has an inverse.
 # A ring has commutative addition and multiplication, a zero and a one:
-# 0*x = x*0 = 0, 0+x = x+0 = x, 1*x = x*1 = x. Also, the distributive
+# 0*x = x*0 = 0, 0+x = x+0 = x, 1*x = x*1 = x.  Also, the distributive
 # property holds: a*(b+c) = a*b + b*c.
 # (XXX I forget if this is an axiom or follows from the rules.)
 
@@ -27,68 +27,68 @@ N = 5
 P = poly.plus(poly.one(0, 2), poly.one(2, 1)) # 2 + x**2
 
 
-# Return x modulo y. Returns >= 0 even if x < 0.
+# Return x modulo y.  Returns >= 0 even if x < 0.
 
 def mod(x, y):
- return divmod(x, y)[1]
+	return divmod(x, y)[1]
 
 
 # Normalize a polynomial modulo n and modulo p.
 
 def norm(a, n, p):
- a = poly.modulo(a, p)
- a = a[:]
- for i in range(len(a)): a[i] = mod(a[i], n)
- a = poly.normalize(a)
- return a
+	a = poly.modulo(a, p)
+	a = a[:]
+	for i in range(len(a)): a[i] = mod(a[i], n)
+	a = poly.normalize(a)
+	return a
 
 
 # Make a list of all n^d elements of the proposed field.
 
 def make_all(mat):
- all = []
- for row in mat:
- for a in row:
- all.append(a)
- return all
+	all = []
+	for row in mat:
+		for a in row:
+			all.append(a)
+	return all
 
 def make_elements(n, d):
- if d = 0: return [poly.one(0, 0)]
- sub = make_elements(n, d-1)
- all = []
- for a in sub:
- for i in range(n):
- all.append(poly.plus(a, poly.one(d-1, i)))
- return all
+	if d = 0: return [poly.one(0, 0)]
+	sub = make_elements(n, d-1)
+	all = []
+	for a in sub:
+		for i in range(n):
+			all.append(poly.plus(a, poly.one(d-1, i)))
+	return all
 
 def make_inv(all, n, p):
- x = poly.one(1, 1)
- inv = []
- for a in all:
- inv.append(norm(poly.times(a, x), n, p))
- return inv
+	x = poly.one(1, 1)
+	inv = []
+	for a in all:
+		inv.append(norm(poly.times(a, x), n, p))
+	return inv
 
 def checkfield(n, p):
- all = make_elements(n, len(p)-1)
- inv = make_inv(all, n, p)
- all1 = all[:]
- inv1 = inv[:]
- all1.sort()
- inv1.sort()
- if all1 = inv1: print 'BINGO!'
- else:
- print 'Sorry:', n, p
- print all
- print inv
+	all = make_elements(n, len(p)-1)
+	inv = make_inv(all, n, p)
+	all1 = all[:]
+	inv1 = inv[:]
+	all1.sort()
+	inv1.sort()
+	if all1 = inv1: print 'BINGO!'
+	else:
+		print 'Sorry:', n, p
+		print all
+		print inv
 
 def rj(s, width):
- if type(s) <> type(''): s = `s`
- n = len(s)
- if n >= width: return s
- return ' '*(width - n) + s
+	if type(s) <> type(''): s = `s`
+	n = len(s)
+	if n >= width: return s
+	return ' '*(width - n) + s
 
 def lj(s, width):
- if type(s) <> type(''): s = `s`
- n = len(s)
- if n >= width: return s
- return s + ' '*(width - n)
+	if type(s) <> type(''): s = `s`
+	n = len(s)
+	if n >= width: return s
+	return s + ' '*(width - n)