Trac #34019: minor code details in combinat

URL: https://trac.sagemath.org/34019
Reported by: chapoton
Ticket author(s): Frédéric Chapoton
Reviewer(s): David Coudert

Author: Release Manager

src/sage/arith/misc.py

@@ -967,7 +967,7 @@ def primes(start, stop=None, proof=None):
     argument proof controls whether the numbers returned are
     guaranteed to be prime or not.
 
-    This command is like the Python 2 ``xrange`` command, except it only iterates
+    This command is like the Python 3 ``range`` command, except it only iterates
     over primes. In some cases it is better to use primes than
     ``prime_range``, because primes does not build a list of all primes in
     the range in memory all at once. However, it is potentially much

src/sage/combinat/binary_recurrence_sequences.py

@@ -415,9 +415,7 @@ def period(self, m):
             #the identity mod p is of order (p^{e-1})^4.  So we compute the period mod p^e by successively
             #multiplying the period mod p by powers of p.
 
-            for i in Fac:
-                p = i[0]
-                e = i[1]
+            for p, e in Fac:
                 #first compute the period mod p
                 if p in self._period_dict:
                     perp = self._period_dict[p]

src/sage/combinat/cluster_algebra_quiver/cluster_seed.py

@@ -2074,39 +2074,34 @@ def highest_degree_denominator(self, filter=None):
             5
         """
         if filter is None:
-            filter = list(range(len(self.cluster())))
+            filter = range(len(self.cluster()))
         degree = 0
         vertex_to_mutate = []
 
         # if we have d vectors use those, else see if we have clusters
         if self._use_d_vec:
-            for i in list(enumerate(self.d_matrix().columns())):
-                if i[0] not in filter:
+            for vertex, col in enumerate(self.d_matrix().columns()):
+                if vertex not in filter:
                     continue
-                col = i[1]
-                vertex = i[0]
                 cur_vertex_degree = sum(col)
                 if degree == cur_vertex_degree:
                     vertex_to_mutate.append(vertex)
-                if degree < cur_vertex_degree:
+                elif degree < cur_vertex_degree:
                     degree = cur_vertex_degree
                     vertex_to_mutate = [vertex]
         elif self._use_fpolys:
-            for i in list(enumerate(self.cluster())):
-                if i[0] not in filter:
+            for vertex, vari in enumerate(self.cluster()):
+                if vertex not in filter:
                     continue
-                vari = i[1]
-                vertex = i[0]
                 denom = vari.denominator()
                 cur_vertex_degree = denom.degree()
                 if degree == cur_vertex_degree:
                     vertex_to_mutate.append(vertex)
-                if degree < cur_vertex_degree:
+                elif degree < cur_vertex_degree:
                     degree = cur_vertex_degree
                     vertex_to_mutate = [vertex]
 
-
-        return_key = randint(0,len(vertex_to_mutate) - 1)
+        return_key = randint(0, len(vertex_to_mutate) - 1)
         return vertex_to_mutate[return_key]
 
     def smallest_c_vector(self):
@@ -2848,14 +2843,11 @@ def mutation_analysis(self, options=['all'], filter=None):
               'sources_diff': {'added': [], 'removed': [5]},
               'urban_renewals': [],
               'urban_renewals_diff': {'added': [], 'removed': []}}}
-
         """
-
-        V = list(range(self._n))
-
+        V = range(self._n)
         if filter is None:
             filter = V
-        if filter in V:
+        elif filter in V:
             filter = [filter]
 
         # setup our initial information for differences later on

src/sage/combinat/crystals/letters.pyx

@@ -187,12 +187,12 @@ class ClassicalCrystalOfLetters(UniqueRepresentation, Parent):
                               self._element_constructor_(-1)]
             else:
                 self._list = [self._element_constructor_(i)
-                              for i in xrange(1, cartan_type.rank() + 1)]
+                              for i in range(1, cartan_type.rank() + 1)]
                 if cartan_type.type() == 'B':
                     self._list.append(self._element_constructor_(0))
                 if cartan_type.type() != 'A':
                     self._list += [self._element_constructor_(-i)
-                                   for i in xrange(cartan_type.rank(), 0, -1)]
+                                   for i in range(cartan_type.rank(), 0, -1)]
                 else:
                     self._list.append(self._element_constructor_(cartan_type.rank() + 1))
         self._element_print_style = element_print_style

src/sage/combinat/designs/orthogonal_arrays_find_recursive.pyx

@@ -231,16 +231,17 @@ cpdef find_wilson_decomposition_with_two_truncated_groups(int k,int n):
         sage: _ = f(*args)
     """
     cdef int r,m_min,m_max,m,r1_min,r1_max,r1,r2,r1_p_r2
-    for r in [1] + list(xrange(k+1, n-2)): # as r*1+1+1 <= n and because we need
-                                   # an OA(k+2,r), necessarily r=1 or r >= k+1
+    for r in [1] + list(range(k+1, n-2)):
+        # as r*1+1+1 <= n and because we need
+        # an OA(k+2,r), necessarily r=1 or r >= k+1
         if not is_available(k+2,r):
             continue
         m_min = (n - (2*r-2))/r
         m_max = (n - 2)/r
         if m_min > 1:
-            m_values = list(xrange(max(m_min, k - 1), m_max + 1))
+            m_values = list(range(max(m_min, k - 1), m_max + 1))
         else:
-            m_values = [1] + list(xrange(k - 1, m_max + 1))
+            m_values = [1] + list(range(k - 1, m_max + 1))
         for m in m_values:
             r1_p_r2 = n-r*m # the sum of r1+r2
                             # it is automatically >= 2 since m <= m_max
@@ -253,9 +254,9 @@ cpdef find_wilson_decomposition_with_two_truncated_groups(int k,int n):
             r1_min = r1_p_r2 - (r-1)
             r1_max = min(r-1, r1_p_r2)
             if r1_min > 1:
-                r1_values = list(xrange(max(k - 1, r1_min), r1_max + 1))
+                r1_values = range(max(k - 1, r1_min), r1_max + 1)
             else:
-                r1_values = [1] + list(xrange(k-1, r1_max + 1))
+                r1_values = [1] + list(range(k-1, r1_max + 1))
             for r1 in r1_values:
                 if not is_available(k,r1):
                     continue
@@ -589,7 +590,8 @@ cpdef find_thwart_lemma_3_5(int k,int N):
                 continue
 
             NN = N - n*m
-            for a in range(max(0, (NN-n+2)/3), min(n, NN)+1): # (NN-n+2)/3 <==> ceil((NN-n)/3)
+            for a in range(max(0, (NN-n+2)/3), min(n, NN)+1):
+                # (NN-n+2)/3 <==> ceil((NN-n)/3)
                 if not is_available(k,a):
                     continue
                 na = n-a

src/sage/combinat/permutation_cython.pyx

@@ -248,7 +248,7 @@ cpdef bint next_perm(array l):
     #mset_list = mset_list[:two] + [x for x in reversed(mset_list[two:])]
     n -= 1 # In the loop, we only need n-1, so just do it once here
     cdef Py_ssize_t i
-    for i in xrange((n+1 - two) // 2 - 1, -1, -1):
+    for i in range((n + 1 - two) // 2 - 1, -1, -1):
         t = l.data.as_uints[i + two]
         l.data.as_uints[i + two] = l.data.as_uints[n - i]
         l.data.as_uints[n - i] = t

src/sage/combinat/root_system/reflection_group_element.pyx

@@ -657,7 +657,7 @@ cdef class ComplexReflectionGroupElement(PermutationGroupElement):
         cdef list M_gals = [x.galois_conjugates(m) if hasattr(x,"galois_conjugates") else [x] for x in M]
         cdef list conjugates = []
         cdef int i
-        for i in xrange(len(M_gals[0])):
+        for i in range(len(M_gals[0])):
             conjugates.append(Matrix(rk, [X[i] for X in M_gals]))
         return conjugates
 
@@ -977,12 +977,12 @@ cdef class RealReflectionGroupElement(ComplexReflectionGroupElement):
         cdef int j
         ret = Phi[0].parent().zero()
         if on_space == "primal":
-            for j in xrange(n):
+            for j in range(n):
                 ret += vec[j] * Phi[w.perm[j]]
             return ret
         elif on_space == "dual":
             w = <RealReflectionGroupElement>(~w)
-            for j in xrange(n):
+            for j in range(n):
                 ret += Phi[w.perm[j]] * vec[j]
             return ret
         else:
@@ -1122,7 +1122,8 @@ cdef class RealReflectionGroupElement(ComplexReflectionGroupElement):
             self = <RealReflectionGroupElement>(~self)
         elif side != "right":
             raise ValueError('side must be "left" or "right"')
-        return [Phi[i] for i in xrange(N) if self.perm[i] >= N]
+        return [Phi[i] for i in range(N) if self.perm[i] >= N]
+
 
 def _gap_factorization(w, gens):
     r"""

src/sage/combinat/subword_complex.py

@@ -1242,7 +1242,8 @@ def __contains__(self, F):
         """
         W = self.group()
         Q = self.word()
-        if not all(i in list(range(len(Q))) for i in F):
+        r = range(len(Q))
+        if not all(i in r for i in F):
             return False
         return W.from_reduced_word(Qi for i, Qi in enumerate(Q) if i not in F) == self.pi()
 

src/sage/combinat/subword_complex_c.pyx

@@ -42,7 +42,7 @@ cpdef int _flip_c(W, set positions, list extended_root_conf_indices,
     nr_ref = W.number_of_reflections()
     r_minus = (r + nr_ref) % (2 * nr_ref)  # get the negative root -r
     j = i
-    for k in xrange(len(extended_root_conf_indices)):
+    for k in range(len(extended_root_conf_indices)):
         if extended_root_conf_indices[k] == r_minus and k not in positions and side != "positive":
             j = k
             break
@@ -54,7 +54,7 @@ cpdef int _flip_c(W, set positions, list extended_root_conf_indices,
     R = list(W.reflections())
     if j != i:
         t = R[min(r, r_minus)]
-        for k in xrange(min(i, j) + 1, max(i, j) + 1):
+        for k in range(min(i, j) + 1, max(i, j) + 1):
             extended_root_conf_indices[k] = t.action_on_root_indices(extended_root_conf_indices[k],side="left")
     return j
 
@@ -89,7 +89,7 @@ cpdef list _construct_facets_c(tuple Q, w, int n=-1, int pos=0, int l=-1):
         first = False
 
     if l == 0:
-        return [list(xrange(pos, n))]
+        return [list(range(pos, n))]
     elif n < l + pos:
         return []
 

src/sage/combinat/tutorial.py

@@ -1243,9 +1243,6 @@
 
     sage: import itertools
 
-The behaviour of this library has changed a lot between Python 2 and
-Python 3. What follows is mostly written for Python 2.
-
 We will demonstrate some applications, taking as a starting point the
 permutations of `3`::
 
@@ -1268,12 +1265,12 @@
 
 To apply a function to all the elements, one can do::
 
-    sage: list(z.cycle_type() for z in Permutations(3))
+    sage: [z.cycle_type() for z in Permutations(3)]
     [[1, 1, 1], [2, 1], [2, 1], [3], [3], [2, 1]]
 
 and similarly to select the elements satisfying a certain condition::
 
-    sage: list(z for z in Permutations(3) if z.has_pattern([1,2]))
+    sage: [z for z in Permutations(3) if z.has_pattern([1,2])]
     [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2]]
 
 Implementation of new iterators

src/sage/rings/polynomial/pbori/pbori.pyx

@@ -1851,7 +1851,7 @@ def get_var_mapping(ring, other):
     """
     my_names = list(ring._names)  # we need .index(.)
     if isinstance(other, (Parent, BooleanMonomialMonoid)):
-        indices = list(range(other.ngens()))
+        indices = range(other.ngens())
         ovar_names = other._names
     else:
         ovar_names = other.parent().variable_names()
@@ -1862,7 +1862,7 @@ def get_var_mapping(ring, other):
         else:
             t = other.variables()
             ovar_names = list(ovar_names)
-            indices = [ovar_names.index(str(var)) for var in t]
+            indices = (ovar_names.index(str(var)) for var in t)
 
     var_mapping = [None] * len(ovar_names)
     for idx in indices:

src/sage/rings/polynomial/weil/weil_polynomials.pyx

@@ -367,22 +367,6 @@ class WeilPolynomials_iter():
                 raise StopIteration
         return self.pol(self.ans.pop())
 
-    def next(self): # For Python2 backward compatibility
-        r"""
-        Step the iterator forward.
-
-        Included for Python2 backward compatibility.
-
-        EXAMPLES::
-
-            sage: from sage.rings.polynomial.weil.weil_polynomials import WeilPolynomials
-            sage: w = WeilPolynomials(10,1,sign=1,lead=[3,1,1])
-            sage: it = iter(w)
-            sage: next(it)
-            3*x^10 + x^9 + x^8 + 7*x^7 + 5*x^6 + 2*x^5 + 5*x^4 + 7*x^3 + x^2 + x + 3
-        """
-        return self.__next__()
-
     def node_count(self):
         r"""
         Return the number of terminal nodes found in the tree, excluding