diff --git a/src/sage/categories/crystals.py b/src/sage/categories/crystals.py
index 5367ba52083..d44a0daf353 100644
--- a/src/sage/categories/crystals.py
+++ b/src/sage/categories/crystals.py
@@ -441,12 +441,12 @@ def morphism(b):
                 # - images contains all known morphism(x)
                 # - known contains all elements x for which we know morphism(x)
                 # - todo  contains all elements x for which we haven't propagated to each child
-                while todo <> set( [] ):
+                while todo != set( [] ):
                     x = todo.pop()
                     for i in index_set:
                         eix  = getattr(x, f_string)([i for k in range(similarity_factor_domain[i])])
                         eigx = getattr(morphism[x], f_string)([automorphism(i) for k in range(similarity_factor[i])])
-                        if bool(eix is None) <> bool(eigx is None):
+                        if bool(eix is None) != bool(eigx is None):
                             # This is not a crystal morphism!
                             raise ValueError, "This is not a morphism!" #, print("x="x,"g(x)="g(x),"i="i)
                         if (eix is not None) and (eix not in known):
diff --git a/src/sage/coding/code_constructions.py b/src/sage/coding/code_constructions.py
index bc004135dd5..892c7344500 100644
--- a/src/sage/coding/code_constructions.py
+++ b/src/sage/coding/code_constructions.py
@@ -221,13 +221,13 @@ def cyclotomic_cosets(q, n, t = None):
     the cosets are in ZZ/nZZ and 2 = 0 in ZZ/2ZZ.
     """
     from sage.misc.misc import srange
-    if not(t==None) and type(t)<>Integer:
+    if t is not None and not isinstance(t, Integer):
         raise TypeError,  "Optional input %s must None or an integer."%t
     if q<2 or n<2:
         raise TypeError,  "Inputs %s and %s must be > 1."%(q,n)
-    if GCD(q,n) <> 1:
+    if GCD(q,n) != 1:
         raise TypeError,  "Inputs %s and %s must be relative prime."%(q,n)
-    if t<>None and type(t)==Integer:
+    if t is not None and isinstance(t, Integer):
         S = Set([t*q**i%n for i in srange(n)])
         L = list(S)
         L.sort()
@@ -302,7 +302,7 @@ def is_a_splitting(S1,S2,n):
 
     This is a special case of Theorem 6.4.3 in [HP]_.
     """
-    if Set(S1).union(Set(S2)) <> Set(range(1,n)):
+    if Set(S1).union(Set(S2)) != Set(range(1,n)):
         raise TypeError, "Lists must partition [1,2,...,n-1]."
     if n<3:
         raise TypeError,  "Input %s must be > 2."%n
diff --git a/src/sage/coding/linear_code.py b/src/sage/coding/linear_code.py
index e762b669cce..09990c5d356 100644
--- a/src/sage/coding/linear_code.py
+++ b/src/sage/coding/linear_code.py
@@ -2919,9 +2919,9 @@ def standard_form(self):
         for i in range(1,k+1):
             r = M.rows()[i-1]
             j = r.nonzero_positions()[0]
-            if (j < d and i <> j+1):
+            if j < d and i != j+1:
                 perm = perm *G([(i,j+1)])
-        if perm <> G([()]):
+        if perm != G([()]):
             for i in range(k):
                 r = M.rows()[i]
                 A.append(perm_action(perm,r))
diff --git a/src/sage/combinat/integer_vector.py b/src/sage/combinat/integer_vector.py
index 22c4695cb01..7fc5cc90f27 100644
--- a/src/sage/combinat/integer_vector.py
+++ b/src/sage/combinat/integer_vector.py
@@ -393,7 +393,7 @@ def gale_ryser_theorem(p1, p2, algorithm="gale"):
 
             for k in range(1,n+1):
                 goodcols = [i for i in range(n) if s[i]==sum(A0.column(i))]
-                if sum(A0.column(n-k))<>s[n-k]:
+                if sum(A0.column(n-k)) != s[n-k]:
                     A0 = _slider01(A0,s[n-k],n-k, p1, p2, goodcols)
 
             # If we need to add empty rows/columns
diff --git a/src/sage/combinat/sf/monomial.py b/src/sage/combinat/sf/monomial.py
index f0a8433dfc2..cf73a5a371a 100644
--- a/src/sage/combinat/sf/monomial.py
+++ b/src/sage/combinat/sf/monomial.py
@@ -173,7 +173,7 @@ def from_polynomial(self, f, check=True):
         out = self.sum_of_terms((Partition(e), c)
                                 for (e,c) in f.dict().iteritems()
                                 if tuple(sorted(e)) == tuple(reversed(e)))
-        if check and out.expand(f.parent().ngens(),f.parent().gens()) <> f:
+        if check and out.expand(f.parent().ngens(),f.parent().gens()) != f:
             raise ValueError, "%s is not a symmetric polynomial"%f
         return out
 
diff --git a/src/sage/games/hexad.py b/src/sage/games/hexad.py
index 81b74c8f7a8..06f94c323f9 100644
--- a/src/sage/games/hexad.py
+++ b/src/sage/games/hexad.py
@@ -535,29 +535,29 @@ def find_hexad(self, pts):
                 if list(L2)[0] == MINIMOG[2][1]:
                           L1 = LL - L2
                           H,WHAT = self.find_hexad3(L1,MINIMOG[0][0],MINIMOG[2][1])
-                          if H <> []:
+                          if H != []:
                               return list(H),WHAT
                           L1 = LL - L2
                           H,WHAT = self.find_hexad3(L1,MINIMOG[0][2],MINIMOG[2][1])
-                          if H <> []:
+                          if H != []:
                               return list(H),WHAT
                 if list(L2)[0] == MINIMOG[0][0]:
                           L1 = (LL - L2)
                           H,WHAT = self.find_hexad3(L1,MINIMOG[0][0],MINIMOG[2][1])
-                          if H <> []:
+                          if H != []:
                               return list(H),WHAT
                           L1 = (LL - L2)
                           H,WHAT = self.find_hexad3(L1,MINIMOG[0][0],MINIMOG[0][2])
-                          if H <> []:
+                          if H != []:
                               return list(H),WHAT
                 if list(L2)[0] == MINIMOG[0][2]:
                           L1 = (LL - L2)
                           H,WHAT = self.find_hexad3(L1,MINIMOG[0][0],MINIMOG[0][2])
-                          if H <> []:
+                          if H != []:
                               return list(H),WHAT
                           L1 = (LL - L2)
                           H,WHAT = self.find_hexad3(L1,MINIMOG[2][1],MINIMOG[0][2])
-                          if H <> []:
+                          if H != []:
                               return list(H),WHAT
             return list(H),WHAT
             ## a cross in a pic at infty
diff --git a/src/sage/matrix/operation_table.py b/src/sage/matrix/operation_table.py
index 49267458511..c1d55fe9db6 100644
--- a/src/sage/matrix/operation_table.py
+++ b/src/sage/matrix/operation_table.py
@@ -476,7 +476,7 @@ def _name_maker(self, names):
             sage: T._name_maker(['x'])
             Traceback (most recent call last):
             ...
-            ValueError: list of element names must be the same size as the set, 1 <> 3
+            ValueError: list of element names must be the same size as the set, 1 != 3
             sage: T._name_maker(['x', 'y', 4])
             Traceback (most recent call last):
             ...
@@ -516,7 +516,7 @@ def _name_maker(self, names):
                 name_list.append(estr)
         elif isinstance(names, list):
             if len(names) != self._n:
-                raise ValueError('list of element names must be the same size as the set, %s <> %s'%(len(names), self._n))
+                raise ValueError('list of element names must be the same size as the set, %s != %s'%(len(names), self._n))
             width = 0
             for str in names:
                 if not isinstance(str, basestring):
diff --git a/src/sage/quadratic_forms/ternary.pyx b/src/sage/quadratic_forms/ternary.pyx
index 14496ebf828..a14e41955bc 100644
--- a/src/sage/quadratic_forms/ternary.pyx
+++ b/src/sage/quadratic_forms/ternary.pyx
@@ -122,19 +122,19 @@ def _reduced_ternary_form_eisenstein_with_matrix(a1, a2, a3, a23, a13, a12):
         a23+=a12*m
 
         # order 12
-        if ((a1>a2) or ((a1==a2) & (abs(a23)>abs(a13)))):
+        if a1 > a2 or (a1 == a2 and abs(a23) > abs(a13)):
             M*=matrix(ZZ,3,[0,-1,0,-1,0,0,0,0,-1])
             [a1,a2]=[a2,a1]
             [a13,a23]=[a23,a13]
 
         # order 23
-        if ((a2>a3) or ((a2==a3) & (abs(a13)>abs(a12)))):
+        if a2 > a3 or (a2 == a3 and abs(a13) > abs(a12)):
             M*=matrix(ZZ,3,[-1,0,0,0,0,-1,0,-1,0])
             [a2,a3]=[a3,a2]
             [a13,a12]=[a12,a13]
 
         # order 12
-        if ((a1>a2) or ((a1==a2) & (abs(a23)>abs(a13)))):
+        if a1 > a2 or (a1 == a2 and abs(a23) > abs(a13)):
             M*=matrix(ZZ,3,[0,-1,0,-1,0,0,0,0,-1])
             [a1,a2]=[a2,a1]
             [a13,a23]=[a23,a13]
@@ -176,7 +176,7 @@ def _reduced_ternary_form_eisenstein_with_matrix(a1, a2, a3, a23, a13, a12):
                   M*=diagonal_matrix([1,1,-1])
                   a12=-a12
 
-        loop=(not ((abs(a23)<=a2) & (abs(a13)<=a1) & (abs(a12)<=a1) & (a1+a2+a23+a13+a12>=0)))
+        loop = not (abs(a23) <= a2 and abs(a13) <= a1 and abs(a12) <= a1 and a1+a2+a23+a13+a12>=0)
 
 
 ################
@@ -185,14 +185,14 @@ def _reduced_ternary_form_eisenstein_with_matrix(a1, a2, a3, a23, a13, a12):
 
 
     # adj 3
-    if ((a1+a2+a23+a13+a12==0) & (2*a1+2*a13+a12>0)):
+    if a1+a2+a23+a13+a12 == 0 and 2*a1+2*a13+a12 > 0:
         M*=matrix(ZZ,3,[-1,0,1,0,-1,1,0,0,1])
         # a3 += a1+a2+a23+a13+a12
         a23=-2*a2-a23-a12
         a13=-2*a1-a13-a12
 
     # adj 5.12
-    if ((a1==-a12) & (a13!=0)):
+    if a1 == -a12 and a13 != 0:
         M*=matrix(ZZ,3,[-1,-1,0,0,-1,0,0,0,1])
         #a2 += a1+a12
         a23=-a23-a13
@@ -200,7 +200,7 @@ def _reduced_ternary_form_eisenstein_with_matrix(a1, a2, a3, a23, a13, a12):
         a12=-a12  # = 2*a1+a12
 
     # adj 5.13
-    if ((a1==-a13) & (a12!=0)):
+    if a1 == -a13 and a12 != 0:
         M*=matrix(ZZ,3,[-1,0,-1,0,1,0,0,0,-1])
         # a3 += a1+a13
         a23=-a23-a12
@@ -208,7 +208,7 @@ def _reduced_ternary_form_eisenstein_with_matrix(a1, a2, a3, a23, a13, a12):
         a12=-a12
 
     # adj 5.23
-    if ((a2==-a23) & (a12!=0)):
+    if a2 == -a23 and a12 != 0:
         M*=matrix(ZZ,3,[1,0,0,0,-1,-1,0,0,-1])
         # a3 += a2+a23
         a23=-a23  # = 2*a2+a23
@@ -216,39 +216,39 @@ def _reduced_ternary_form_eisenstein_with_matrix(a1, a2, a3, a23, a13, a12):
         a12=-a12
 
     # adj 4.12
-    if ((a1==a12) & (a13>2*a23)):
+    if a1 == a12 and a13 > 2*a23:
         M*=matrix(ZZ,3,[-1,-1,0,0,1,0,0,0,-1])
         # a 2 += a1-a12
         a23 = -a23 + a13
         # a12 = 2*a1 - a12
 
     # adj 4.13
-    if ((a1==a13) & (a12>2*a23)):
+    if a1 == a13 and a12 > 2*a23:
         M*=matrix(ZZ,3,[-1,0,-1,0,-1,0,0,0,1])
         # a3 += a1-a13
         a23 = -a23 + a12
         # a13 = 2*a1 - a13
 
     # adj 4.23
-    if ((a2==a23) & (a12>2*a13)):
+    if a2 == a23 and a12 > 2*a13:
         M*=matrix(ZZ,3,[-1,0,0,0,-1,-1,0,0,1])
         # a3 += a2-a23
         # a23 = 2*a2 - a23
         a13 = -a13 + a12
 
     # order 12
-    if (a1==a2) & (abs(a23)>abs(a13)):
+    if a1 == a2 and abs(a23) > abs(a13):
         M*=matrix(ZZ,3,[0,-1,0,-1,0,0,0,0,-1])
         [a1,a2]=[a2,a1]
         [a13,a23]=[a23,a13]
 
     # order 23
-    if (a2==a3) & (abs(a13)>abs(a12)):
+    if a2 == a3 and abs(a13) > abs(a12):
         M*=matrix(ZZ,3,[-1,0,0,0,0,-1,0,-1,0])
         [a13,a12]=[a12,a13]
 
     # order 12
-    if (a1==a2) & (abs(a23)>abs(a13)):
+    if a1 == a2 and abs(a23) > abs(a13):
         M*=matrix(ZZ,3,[0,-1,0,-1,0,0,0,0,-1])
         [a13,a23]=[a23,a13]
 
@@ -309,22 +309,22 @@ def _reduced_ternary_form_eisenstein_without_matrix(a1, a2, a3, a23, a13, a12):
         a23+=a12*m
 
         # order 12
-        if ((a1>a2) or ((a1==a2) & (abs(a23)>abs(a13)))):
+        if a1 > a2 or (a1 == a2 and abs(a23) > abs(a13)):
             [a1,a2]=[a2,a1]
             [a13,a23]=[a23,a13]
 
         # order 23
-        if ((a2>a3) or ((a2==a3) & (abs(a13)>abs(a12)))):
+        if a2 > a3 or (a2 == a3 and abs(a13) > abs(a12)):
             [a2,a3]=[a3,a2]
             [a13,a12]=[a12,a13]
 
         # order 12
-        if ((a1>a2) or ((a1==a2) & (abs(a23)>abs(a13)))):
+        if a1 > a2 or (a1 == a2 and abs(a23) > abs(a13)):
             [a1,a2]=[a2,a1]
             [a13,a23]=[a23,a13]
 
         # signs
-        if (a23*a13*a12>0):
+        if a23*a13*a12 > 0:
             # a23, a13, a12 positive
 
             if (a23<0):
@@ -354,7 +354,7 @@ def _reduced_ternary_form_eisenstein_without_matrix(a1, a2, a3, a23, a13, a12):
             if s3:
                   a12=-a12
 
-        loop=(not ((abs(a23)<=a2) & (abs(a13)<=a1) & (abs(a12)<=a1) & (a1+a2+a23+a13+a12>=0)))
+        loop = not (abs(a23) <= a2 and abs(a13) <= a1 and abs(a12) <= a1 and a1+a2+a23+a13+a12 >= 0)
 
 
 ################
@@ -363,61 +363,61 @@ def _reduced_ternary_form_eisenstein_without_matrix(a1, a2, a3, a23, a13, a12):
 
 
     # adj 3
-    if ((a1+a2+a23+a13+a12==0) & (2*a1+2*a13+a12>0)):
+    if a1+a2+a23+a13+a12 == 0 and 2*a1+2*a13+a12 > 0:
         # a3 += a1+a2+a23+a13+a12
         a23=-2*a2-a23-a12
         a13=-2*a1-a13-a12
 
     # adj 5.12
-    if ((a1==-a12) & (a13!=0)):
+    if a1 == -a12 and a13 != 0:
         #a2 += a1+a12
         a23=-a23-a13
         a13=-a13
         a12=-a12  # = 2*a1+a12
 
     # adj 5.13
-    if ((a1==-a13) & (a12!=0)):
+    if a1 == -a13 and a12 != 0:
         # a3 += a1+a13
         a23=-a23-a12
         a13=-a13  # = 2*a1+a13
         a12=-a12
 
     # adj 5.23
-    if ((a2==-a23) & (a12!=0)):
+    if a2 == -a23 and a12 != 0:
         # a3 += a2+a23
         a23=-a23  # = 2*a2+a23
         a13=-a13-a12
         a12=-a12
 
     # adj 4.12
-    if ((a1==a12) & (a13>2*a23)):
+    if a1 == a12 and a13 > 2*a23:
         # a 2 += a1-a12
         a23 = -a23 + a13
         # a12 = 2*a1 - a12
 
     # adj 4.13
-    if ((a1==a13) & (a12>2*a23)):
+    if a1 == a13 and a12 > 2*a23:
         # a3 += a1-a13
         a23 = -a23 + a12
         # a13 = 2*a1 - a13
 
     # adj 4.23
-    if ((a2==a23) & (a12>2*a13)):
+    if a2 == a23 and a12 > 2*a13:
         # a3 += a2-a23
         # a23 = 2*a2 - a23
         a13 = -a13 + a12
 
     # order 12
-    if (a1==a2) & (abs(a23)>abs(a13)):
+    if a1 == a2 and abs(a23) > abs(a13):
         [a1,a2]=[a2,a1]
         [a13,a23]=[a23,a13]
 
     # order 23
-    if (a2==a3) & (abs(a13)>abs(a12)):
+    if a2 == a3 and abs(a13) > abs(a12):
         [a13,a12]=[a12,a13]
 
     # order 12
-    if (a1==a2) & (abs(a23)>abs(a13)):
+    if a1 == a2 and abs(a23) > abs(a13):
         [a13,a23]=[a23,a13]
 
     return((a1,a2,a3,a23,a13,a12))
@@ -727,44 +727,44 @@ def _find_all_ternary_qf_by_level_disc(long long N, long long d):
                         if (d-r*s*t+a*r*r+b*s*s)%(4*a*b-t**2)==0:
 
                             c=(d-r*s*t+a*r*r+b*s*s)//(4*a*b-t**2)
-                            if r<=0:
-                                is_reduced=True
-                                if r<-b:
-                                    is_reduced=False
-                                elif not ((b<=c) & (0<=a+b+r-s-t)):
-                                    is_reduced=False
-                                elif ((a==b) & (abs(r) > abs(s))):
-                                    is_reduced=False
-                                elif ((b==c) & (abs(s) > abs(t))):
-                                    is_reduced=False
-                                elif ((a+b+r-s-t==0) & (2*a-2*s-t>0)):
-                                    is_reduced=False
-                                elif ((a==t) & (s<>0)):
-                                    is_reduced=False
-                                elif ((a==s) & (t<>0)):
-                                    is_reduced=False
-                                elif ((b==-r) & (t<>0)):
-                                    is_reduced=False
+                            if r <= 0:
+                                is_reduced = True
+                                if r < -b:
+                                    is_reduced = False
+                                elif not (b <= c and 0 <= a+b+r-s-t):
+                                    is_reduced = False
+                                elif a == b and abs(r) > abs(s):
+                                    is_reduced = False
+                                elif b == c and abs(s) > abs(t):
+                                    is_reduced = False
+                                elif a+b+r-s-t == 0 and 2*a-2*s-t > 0:
+                                    is_reduced = False
+                                elif a == t and s != 0:
+                                    is_reduced = False
+                                elif a == s and t != 0:
+                                    is_reduced = False
+                                elif b == -r and t != 0:
+                                    is_reduced = False
                                 if is_reduced:
                                     m_q=gcd((4*b*c-r**2, 4*a*c-s**2, 4*a*b-t**2, 2*s*t-4*a*r, -2*r*t+4*b*s, -2*r*s+4*c*t))
                                     if m_q==m:
                                         l.append((ZZ(a), ZZ(b), ZZ(c), ZZ(r), ZZ(-s), ZZ(-t)))
                             else:
                                 is_reduced=True
-                                if not ((b<=c) & (0<=a+b+r+s+t)):
-                                    is_reduced=False
-                                elif ((a==b) & (abs(r) > abs(s))):
-                                    is_reduced=False
-                                elif ((b==c) & (abs(s) > abs(t))):
-                                    is_reduced=False
-                                elif ((a+b+r+s+t==0) & (2*a+2*s+t>0)):
-                                    is_reduced=False
-                                elif ((a==t) & (s>2*r)):
-                                    is_reduced=False
-                                elif ((a==s) & (t>2*r)):
-                                    is_reduced=False
-                                elif ((b==r) & (t>2*s)):
-                                    is_reduced=False
+                                if not (b <= c and 0 <= a+b+r+s+t):
+                                    is_reduced = False
+                                elif a == b and abs(r) > abs(s):
+                                    is_reduced = False
+                                elif b == c and abs(s) > abs(t):
+                                    is_reduced = False
+                                elif a+b+r+s+t == 0 and 2*a+2*s+t > 0:
+                                    is_reduced = False
+                                elif a == t and s > 2*r:
+                                    is_reduced = False
+                                elif a == s and t > 2*r:
+                                    is_reduced = False
+                                elif b == r and t > 2*s:
+                                    is_reduced = False
                                 if is_reduced:
                                     m_q=gcd((4*b*c-r**2, 4*a*c-s**2, 4*a*b-t**2, 2*s*t-4*a*r, 2*r*t-4*b*s, 2*r*s-4*c*t))
                                     if m_q==m:
@@ -868,44 +868,44 @@ def _find_a_ternary_qf_by_level_disc(long long N, long long d):
                         if (d-r*s*t+a*r*r+b*s*s)%(4*a*b-t**2)==0:
 
                             c=(d-r*s*t+a*r*r+b*s*s)//(4*a*b-t**2)
-                            if r<=0:
-                                is_reduced=True
-                                if r<-b:
-                                    is_reduced=False
-                                elif not ((b<=c) & (0<=a+b+r-s-t)):
-                                    is_reduced=False
-                                elif ((a==b) & (abs(r) > abs(s))):
-                                    is_reduced=False
-                                elif ((b==c) & (abs(s) > abs(t))):
-                                    is_reduced=False
-                                elif ((a+b+r-s-t==0) & (2*a-2*s-t>0)):
-                                    is_reduced=False
-                                elif ((a==t) & (s<>0)):
-                                    is_reduced=False
-                                elif ((a==s) & (t<>0)):
-                                    is_reduced=False
-                                elif ((b==-r) & (t<>0)):
-                                    is_reduced=False
+                            if r <= 0:
+                                is_reduced = True
+                                if r < -b:
+                                    is_reduced = False
+                                elif not (b <= c and 0 <= a+b+r-s-t):
+                                    is_reduced = False
+                                elif a == b and abs(r) > abs(s):
+                                    is_reduced = False
+                                elif b == c and abs(s) > abs(t):
+                                    is_reduced = False
+                                elif a+b+r-s-t == 0 and 2*a-2*s-t > 0:
+                                    is_reduced = False
+                                elif a == t and s != 0:
+                                    is_reduced = False
+                                elif a == s and t != 0:
+                                    is_reduced = False
+                                elif b == -r and t != 0:
+                                    is_reduced = False
                                 if is_reduced:
                                     m_q=gcd((4*b*c-r**2, 4*a*c-s**2, 4*a*b-t**2, 2*s*t-4*a*r, -2*r*t+4*b*s, -2*r*s+4*c*t))
                                     if m_q==m:
                                         return ZZ(a), ZZ(b), ZZ(c), ZZ(r), ZZ(-s), ZZ(-t)
                             else:
-                                is_reduced=True
-                                if not ((b<=c) & (0<=a+b+r+s+t)):
-                                    is_reduced=False
-                                elif ((a==b) & (abs(r) > abs(s))):
-                                    is_reduced=False
-                                elif ((b==c) & (abs(s) > abs(t))):
-                                    is_reduced=False
-                                elif ((a+b+r+s+t==0) & (2*a+2*s+t>0)):
-                                    is_reduced=False
-                                elif ((a==t) & (s>2*r)):
-                                    is_reduced=False
-                                elif ((a==s) & (t>2*r)):
-                                    is_reduced=False
-                                elif ((b==r) & (t>2*s)):
-                                    is_reduced=False
+                                is_reduced = True
+                                if not (b <= c and 0 <= a+b+r+s+t):
+                                    is_reduced = False
+                                elif a == b and abs(r) > abs(s):
+                                    is_reduced = False
+                                elif b == c and abs(s) > abs(t):
+                                    is_reduced = False
+                                elif a+b+r+s+t == 0 and 2*a+2*s+t > 0:
+                                    is_reduced = False
+                                elif a==t and s > 2*r:
+                                    is_reduced = False
+                                elif a == s and t>2*r:
+                                    is_reduced = False
+                                elif b == r and t > 2*s:
+                                    is_reduced = False
                                 if is_reduced:
                                     m_q=gcd((4*b*c-r**2, 4*a*c-s**2, 4*a*b-t**2, 2*s*t-4*a*r, 2*r*t-4*b*s, 2*r*s-4*c*t))
                                     if m_q==m:
diff --git a/src/sage/quadratic_forms/ternary_qf.py b/src/sage/quadratic_forms/ternary_qf.py
index 003309759d1..9548e646aae 100644
--- a/src/sage/quadratic_forms/ternary_qf.py
+++ b/src/sage/quadratic_forms/ternary_qf.py
@@ -760,43 +760,43 @@ def is_eisenstein_reduced(self):
         [a,b,c,r,s,t]=[self._a,self._b,self._c,self._r,self._s,self._t]
 
         # cond 2
-        if not ((r>0) & (t>0) & (s>0)):
-            if not ((r<=0) & (s<=0) & (t<=0)):
+        if not (r > 0 and t > 0 and s > 0):
+            if not (r <= 0 and s <= 0 and t <= 0):
                 return False
 
         # cond 1 & 4
-        if not ((a<=b<=c) & (0<=a+b+r+s+t)):
+        if not (a <= b <= c and 0 <= a+b+r+s+t):
             return False
 
         # cond 3
-        if not ((a>=abs(s)) & (a>=abs(t)) & (b>=abs(r))):
+        if not (a >= abs(s) and a >= abs(t) and b >= abs(r)):
             return False
 
         # cond 8
-        if ((a==b) & (abs(r)>abs(s))):
+        if a == b and abs(r) > abs(s):
             return False
-        if ((b==c) & (abs(s)>abs(t))):
+        if b == c and abs(s) > abs(t):
             return False
-        if ((a+b+r+s+t==0) & (2*a+2*s+t>0)):
+        if a+b+r+s+t == 0 and 2*a+2*s+t > 0:
             return False
 
         # cond 6
         # r, s, t <= 0
         if r<=0:
-            if ((a==-t) & (s<>0)):
+            if a == -t and s != 0:
                 return False
-            if ((a==-s) & (t<>0)):
+            if a == -s and t != 0:
                 return False
-            if ((b==-r) & (t<>0)):
+            if b == -r and t != 0:
                 return False
 
         # cond 7
         # r, s, t > 0
-        if ((a==t) & (s>2*r)):
+        if a == t and s > 2*r:
             return False
-        if ((a==s) & (t>2*r)):
+        if a == s and t > 2*r:
             return False
-        if ((b==r) & (t>2*s)):
+        if b == r and t > 2*s:
             return False
 
         return True
@@ -1477,7 +1477,7 @@ def _automorphisms_reduced_fast(self):
                         (-1, 0, 0, 0, 1, -1, 0, 0, -1)]
 
         if self._border(7):
-            if self._border(8) & self._border(15):
+            if self._border(8) and self._border(15):
                 if self._border(16):
                     if self._border(9):
                         # borders 7, 8, 9, 15, 16
@@ -1537,7 +1537,7 @@ def _automorphisms_reduced_fast(self):
 
         if self._border(8):
             if self._border(9):
-                if self._border(10) & self._border(11) & self._border(12):
+                if self._border(10) and self._border(11) and self._border(12):
                     # borders 8, 9, 10, 11, 12
                     return [(1, 0, 0, 0, 1, 0, 0, 0, 1),
                             (-1, 0, 0, 0, -1, 0, 0, 0, 1),
@@ -1563,7 +1563,7 @@ def _automorphisms_reduced_fast(self):
                             (1, 0, 0, 0, -1, 0, 0, 0, -1),
                             (1, 0, 0, 0, 0, -1, 0, 1, 0),
                             (1, 0, 0, 0, 0, 1, 0, -1, 0)]
-                elif self._border(13) & self._border(14):
+                elif self._border(13) and self._border(14):
                     # borders 8, 9, 13, 14
                     return [(1, 0, 0, 0, 1, 0, 0, 0, 1),
                             (-1, -1, -1, 0, 0, 1, 0, 1, 0),
@@ -1598,7 +1598,7 @@ def _automorphisms_reduced_fast(self):
                             (0, 0, 1, 1, 0, 0, 0, 1, 0),
                             (0, 1, 0, 0, 0, 1, 1, 0, 0)]
             elif self._border(10):
-                if self._border(11) & self._border(12):
+                if self._border(11) and self._border(12):
                     # borders 8, 10, 11, 12
                     return [(1, 0, 0, 0, 1, 0, 0, 0, 1),
                             (-1, 0, 0, 0, -1, 0, 0, 0, 1),
@@ -1629,7 +1629,7 @@ def _automorphisms_reduced_fast(self):
 
         if self._border(9):
             if self._border(12):
-                if self._border(10) & self._border(11):
+                if self._border(10) and self._border(11):
                     # borders 9, 10, 11, 12
                     return [(1, 0, 0, 0, 1, 0, 0, 0, 1),
                             (-1, 0, 0, 0, -1, 0, 0, 0, 1),
@@ -1674,7 +1674,7 @@ def _automorphisms_reduced_fast(self):
                         (-1, 0, 0, 0, 0, -1, 0, -1, 0)]
 
         if self._border(10):
-            if self._border(11) & self._border(12):
+            if self._border(11) and self._border(12):
                 # borders 10, 11, 12
                 return [(1, 0, 0, 0, 1, 0, 0, 0, 1),
                         (-1, 0, 0, 0, -1, 0, 0, 0, 1),
@@ -1695,7 +1695,7 @@ def _automorphisms_reduced_fast(self):
             return [(1, 0, 0, 0, 1, 0, 0, 0, 1),
                     (1, 0, 0, 0, -1, 0, 0, 0, -1)]
 
-        if self._border(13) & self._border(14):
+        if self._border(13) and self._border(14):
             # border 13, 14
             return [(1, 0, 0, 0, 1, 0, 0, 0, 1),
                     (1, 1, 1, 0, -1, 0, 0, 0, -1)]
@@ -1912,7 +1912,7 @@ def _number_of_automorphisms_reduced(self):
                 return 2
 
         if self._border(7):
-            if self._border(8) & self._border(15):
+            if self._border(8) and self._border(15):
                 if self._border(16):
                     if self._border(9):
                         # borders 7, 8, 9, 15, 16
@@ -1933,17 +1933,17 @@ def _number_of_automorphisms_reduced(self):
 
         if self._border(8):
             if self._border(9):
-                if self._border(10) & self._border(11) & self._border(12):
+                if self._border(10) and self._border(11) and self._border(12):
                     # borders 8, 9, 10, 11, 12
                     return 24
-                elif self._border(13) & self._border(14):
+                elif self._border(13) and self._border(14):
                     # borders 8, 9, 13, 14
                     return 24
                 else:
                     # borders 8, 9
                     return 6
             elif self._border(10):
-                if self._border(11) & self._border(12):
+                if self._border(11) and self._border(12):
                     # borders 8, 10, 11, 12
                     return 8
                 else:
@@ -1958,7 +1958,7 @@ def _number_of_automorphisms_reduced(self):
 
         if self._border(9):
             if self._border(12):
-                if self._border(10) & self._border(11):
+                if self._border(10) and self._border(11):
                     # borders 9, 10, 11, 12
                     return 8
                 else:
@@ -1979,7 +1979,7 @@ def _number_of_automorphisms_reduced(self):
                 return 2
 
         if self._border(10):
-            if self._border(11) & self._border(12):
+            if self._border(11) and self._border(12):
                 # borders 10, 11, 12
                 return 4
             else:
@@ -1994,7 +1994,7 @@ def _number_of_automorphisms_reduced(self):
             # border 12
             return 2
 
-        if self._border(13) & self._border(14):
+        if self._border(13) and self._border(14):
             # border 13, 14
             return 2
 
diff --git a/src/sage/rings/complex_mpc.pyx b/src/sage/rings/complex_mpc.pyx
index e405368a5ed..7150ebd99ad 100644
--- a/src/sage/rings/complex_mpc.pyx
+++ b/src/sage/rings/complex_mpc.pyx
@@ -1269,7 +1269,7 @@ cdef class MPComplexNumber(sage.structure.element.FieldElement):
             sage: C200(1+i).is_real()
             False
         """
-        return (mpfr_zero_p(self.value.im) <> 0)
+        return (mpfr_zero_p(self.value.im) != 0)
 
     def is_imaginary(self):
         """
@@ -1283,7 +1283,7 @@ cdef class MPComplexNumber(sage.structure.element.FieldElement):
             sage: C200(1+i).is_imaginary()
             False
         """
-        return (mpfr_zero_p(self.value.re) <> 0)
+        return (mpfr_zero_p(self.value.re) != 0)
 
     def algebraic_dependency(self, n, **kwds):
         """
diff --git a/src/sage/rings/complex_number.pyx b/src/sage/rings/complex_number.pyx
index 9f0a97cf666..5fb02097125 100644
--- a/src/sage/rings/complex_number.pyx
+++ b/src/sage/rings/complex_number.pyx
@@ -2249,7 +2249,7 @@ cdef class ComplexNumber(sage.structure.element.FieldElement):
             sage: CC(1+i).is_real()
             False
         """
-        return (mpfr_zero_p(self.__im) <> 0)
+        return (mpfr_zero_p(self.__im) != 0)
 
     def is_imaginary(self):
         """
@@ -2262,7 +2262,7 @@ cdef class ComplexNumber(sage.structure.element.FieldElement):
             sage: CC(1+i).is_imaginary()
             False
         """
-        return (mpfr_zero_p(self.__re) <> 0)
+        return (mpfr_zero_p(self.__re) != 0)
 
     def zeta(self):
         """
diff --git a/src/sage/rings/ideal.py b/src/sage/rings/ideal.py
index a0663314a2c..8c34becd67a 100644
--- a/src/sage/rings/ideal.py
+++ b/src/sage/rings/ideal.py
@@ -821,7 +821,7 @@ def is_prime(self):
             ass = self.associated_primes()
         except (NotImplementedError, ValueError):
             raise NotImplementedError
-        if len(ass) <> 1:
+        if len(ass) != 1:
             return False
         if self == ass[0]:
             return True
diff --git a/src/sage/rings/number_field/totallyreal_data.pyx b/src/sage/rings/number_field/totallyreal_data.pyx
index 216727bd69e..0804309e7bb 100644
--- a/src/sage/rings/number_field/totallyreal_data.pyx
+++ b/src/sage/rings/number_field/totallyreal_data.pyx
@@ -525,7 +525,7 @@ cdef class tr_data:
             # The value of k is the largest index of the coefficients of a which is
             # currently unknown; e.g., if k == -1, then we can iterate
             # over polynomials, and if k == n-1, then we have finished iterating.
-            if a[len(a)-1] <> 1:
+            if a[len(a)-1] != 1:
                 raise ValueError, "a[len(a)-1](=%s) must be 1 so polynomial is monic"%a[len(a)-1]
 
             k = n-len(a)
@@ -774,7 +774,7 @@ cdef class tr_data:
                             f = ZZx([self.gnk[(k+1)*n+i] for i in range(n-(k+1)+1)])
                             # Could just take self.gnk(k+2)*n+i, but this may not be initialized...
                             df = ZZx([i*self.gnk[(k+1)*n+i] for i in range(1,n-(k+1)+1)])
-                            if gcd(f,df) <> 1:
+                            if gcd(f,df) != 1:
                                 if verbose:
                                     print "  gnk has multiple factor!"
                                 maxoutflag = 1
diff --git a/src/sage/rings/number_field/totallyreal_phc.py b/src/sage/rings/number_field/totallyreal_phc.py
index bbfa53a30d1..82c5d5c30e5 100644
--- a/src/sage/rings/number_field/totallyreal_phc.py
+++ b/src/sage/rings/number_field/totallyreal_phc.py
@@ -138,7 +138,7 @@ def __lagrange_bounds_phc(n, m, a, tmpfile=None):
         f_str = f.read()
         pos = f_str.find('= real ')
         crits = []
-        while pos <> -1:
+        while pos != -1:
             posl = f_str.rfind('xn', 0, pos)
             f_str_split = f_str[posl:pos].split()
             crits += [float(f_str_split[2])]
diff --git a/src/sage/rings/number_field/totallyreal_rel.py b/src/sage/rings/number_field/totallyreal_rel.py
index c5d5993d20a..0956c8482e8 100644
--- a/src/sage/rings/number_field/totallyreal_rel.py
+++ b/src/sage/rings/number_field/totallyreal_rel.py
@@ -311,7 +311,7 @@ def __init__(self, F, m, B, a=None):
             # The value of k is the largest index of the coefficients of a which is
             # currently unknown; e.g., if k == -1, then we can iterate
             # over polynomials, and if k == n-1, then we have finished iterating.
-            if a[len(a)-1] <> 1:
+            if a[len(a)-1] != 1:
                 raise ValueError, "a[len(a)-1](=%s) must be 1 so polynomial is monic"%a[len(a)-1]
 
             raise NotImplementedError, "These have not been checked."
@@ -518,7 +518,7 @@ def incr(self, f_out, verbose=False, haltk=0):
                             # the Python routine should be sufficiently fast...
                             f = self.Fx(self.gnk[k+1])
                             df = self.Fx(self.gnk[k+2])
-                            if gcd(f,df) <> 1:
+                            if gcd(f,df) != 1:
                                 if verbose:
                                     print "  gnk has multiple factor!"
                                 maxoutflag = True
@@ -725,7 +725,7 @@ def enumerate_totallyreal_fields_rel(F, m, B, a = [], verbose=0, return_seqs=Fal
     nfF = pari(str(F.defining_polynomial()).replace('x', str(F.primitive_element()) ) )
     parit = pari(str(F.primitive_element()))
 
-    while f_out[m] <> 0:
+    while f_out[m] != 0:
         counts[0] += 1
         if verbose:
             print "==>", f_out,
diff --git a/src/sage/symbolic/relation.py b/src/sage/symbolic/relation.py
index a3c57698782..707630e5b49 100644
--- a/src/sage/symbolic/relation.py
+++ b/src/sage/symbolic/relation.py
@@ -382,8 +382,6 @@ def test_relation_maxima(relation):
         True
         sage: test_relation_maxima(x!=1)
         False
-        sage: test_relation_maxima(x<>1) # alternate syntax for not equal
-        False
         sage: forget()
         sage: assume(x>0)
         sage: test_relation_maxima(x==0)
diff --git a/src/sage/tests/french_book/float_doctest.py b/src/sage/tests/french_book/float_doctest.py
index 666542c541f..b4d6afa4c6b 100644
--- a/src/sage/tests/french_book/float_doctest.py
+++ b/src/sage/tests/french_book/float_doctest.py
@@ -174,7 +174,7 @@
     sage: def sumharmo(P):
     ....:    RFP = RealField(P)
     ....:    y = RFP(1.); x = RFP(0.); n = 1
-    ....:    while x <> y:
+    ....:    while x != y:
     ....:        y = x; x += 1/n; n += 1
     ....:    return P, n, x
 
diff --git a/src/sage/tests/french_book/programmation_doctest.py b/src/sage/tests/french_book/programmation_doctest.py
index bb35e606904..ccb96770210 100644
--- a/src/sage/tests/french_book/programmation_doctest.py
+++ b/src/sage/tests/french_book/programmation_doctest.py
@@ -132,7 +132,7 @@
 Sage example in ./programmation.tex, line 807::
 
   sage: u = 6 ; n = 0
-  sage: while u != 1:    # test "différent de" <> aussi possible
+  sage: while u != 1:    # test "différent de"
   ....:   if u % 2 == 0: # l'opérateur % donne le reste euclidien
   ....:     u = u//2     # // : quotient de la division euclidienne
   ....:   else: