From e65a63e5cc7fda873d9ed34ded4d8c72d3a666f5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Sun, 27 Aug 2017 09:14:25 +0200
Subject: [PATCH] py3: future division in matrix2

---
 src/sage/matrix/matrix2.pyx | 23 ++++++++++++-----------
 1 file changed, 12 insertions(+), 11 deletions(-)

diff --git a/src/sage/matrix/matrix2.pyx b/src/sage/matrix/matrix2.pyx
index f2f09095486..0e3787a103d 100644
--- a/src/sage/matrix/matrix2.pyx
+++ b/src/sage/matrix/matrix2.pyx
@@ -39,7 +39,7 @@ bug, see :trac:`17527`)::
 #  the License, or (at your option) any later version.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
-from __future__ import print_function, absolute_import
+from __future__ import print_function, absolute_import, division
 
 from cpython cimport *
 from cysignals.signals cimport sig_check
@@ -1348,22 +1348,23 @@ cdef class Matrix(Matrix1):
             B = self.new_matrix()
             for i in range(m):
                 for j in range(n):
-                    B.set_unsafe(i,j, one-self.get_unsafe(i,j))
+                    B.set_unsafe(i, j, one-self.get_unsafe(i, j))
             b = B.rook_vector(algorithm=algorithm, use_complement=False)
             complement = not complement
 
         elif algorithm == "Ryser":
-            b = [self.permanental_minor(k,algorithm="Ryser") for k in range(mn+1)]
+            b = [self.permanental_minor(k,algorithm="Ryser")
+                 for k in range(mn + 1)]
 
         elif algorithm == "ButeraPernici":
             p = permanental_minor_polynomial(self)
-            b = [p[k] for k in range(mn+1)]
+            b = [p[k] for k in range(mn + 1)]
 
         elif algorithm == "Godsil":
             from sage.graphs.bipartite_graph import BipartiteGraph
             p = BipartiteGraph(self).matching_polynomial()
             d = p.degree()
-            b = [p[i]*(-1)**((d - i)/2) for i in range(d, d-2*mn-1, -2)]
+            b = [p[i] * (-1)**((d - i)//2) for i in range(d, d-2*mn-1, -2)]
 
         else:
             raise ValueError('algorithm must be one of "Ryser", "ButeraPernici" or "Godsil".')
@@ -1371,7 +1372,7 @@ cdef class Matrix(Matrix1):
         # now compute the permanental minor of the complement matrix if needed
         if complement:
             a = [one]
-            c1 = 1
+            c1 = QQ.one()
             for k in range(1, mn + 1):
                 c1 = c1*(m-k+1)*(n-k+1)/k
                 c = c1
@@ -15013,17 +15014,17 @@ def _binomial(Py_ssize_t n, Py_ssize_t k):
     """
     cdef Py_ssize_t i
 
-    if k > (n/2):
-        k = n-k
+    if 2 * k > n:
+        k = n - k
     if k == 0:
         return 1
 
     result = n
-    n, k = n-1, k-1
+    n, k = n - 1, k - 1
     i = 2
     while k > 0:
-        result = (result*n)/i
-        i, n, k = i+1, n-1, k-1
+        result = (result * n) // i
+        i, n, k = i + 1, n - 1, k - 1
     return result
 
 def _jordan_form_vector_in_difference(V, W):