Trac #16781: Implementation of floordiv is incorrect for polynomials …

…over finite fields

As reported on sage-devel, the following is incorrect:
{{{
sage: F = GF(47)
sage: x = polygen(F)
sage: u = F(1)
sage: x//u
0
}}}
since {{{x//u}}} should give the quotient after dividing x by u.

This is fixed by #2034, so this ticket just adds a doctest.

URL: http://trac.sagemath.org/16781
Reported by: cremona
Ticket author(s): Jeroen Demeyer
Reviewer(s): Vincent Delecroix

src/sage/rings/polynomial/polynomial_template.pxi

@@ -1,11 +1,15 @@
 """
 Polynomial Template for C/C++ Library Interfaces
 """
+
 #*****************************************************************************
 #       Copyright (C) 2008 Martin Albrecht <M.R.Albrecht@rhul.ac.uk>
 #       Copyright (C) 2008 Robert Bradshaw
 #
-#  Distributed under the terms of the GNU General Public License (GPL)
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 2 of the License, or
+# (at your option) any later version.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
@@ -410,13 +414,25 @@ cdef class Polynomial_template(Polynomial):
 
     cpdef RingElement _floordiv_(self, RingElement right):
         """
-        EXAMPLE::
+        EXAMPLES::
 
             sage: P.<x> = GF(2)[]
             sage: x//(x + 1)
             1
             sage: (x + 1)//x
             1
+            sage: F = GF(47)
+            sage: R.<x> = F[]
+            sage: x // 1
+            x
+            sage: x // F(1)
+            x
+            sage: 1 // x
+            0
+            sage: parent(x // 1)
+            Univariate Polynomial Ring in x over Finite Field of size 47
+            sage: parent(1 // x)
+            Univariate Polynomial Ring in x over Finite Field of size 47
         """
         cdef Polynomial_template _right = <Polynomial_template>right