Trac #29524: bug with rational input in IntegerVectors

As reported on [[https://ask.sagemath.org/question/50814/error-with-
rational-input-in-integervectors/|ask]], we have the following
unexpected behavior of !IntegerVectors:
{{{
sage: IntegerVectors(2,3).list()
[[2, 0, 0], [1, 1, 0], [1, 0, 1], [0, 2, 0], [0, 1, 1], [0, 0, 2]]
sage: IntegerVectors(2,3/1).list()
[[2, 0, 0], [1, 1, 0]]
}}}
The relevant code block in the implementation of !IntegerVectors seems
to be the following:
{{{
    try:
        return IntegerVectors_nnondescents(n, tuple(k))
    except TypeError:
        pass

    return IntegerVectors_nk(n, k)
}}}
For k=3/1 one has that tuple(k) does not give a !TypeError (as opposed
to tuple(3)) and thus the code never tries to interpret k as an integer.
{{{
sage: tuple(3/1)
(3,)
sage: tuple(3)
------------------------------------------------------------------------
---
TypeError                                 Traceback (most recent call
last)
<ipython-input-2-35e4067a6e17> in <module>()
----> 1 tuple(Integer(3))

TypeError: 'sage.rings.integer.Integer' object is not iterable
}}}

URL: https://trac.sagemath.org/29524
Reported by: vdelecroix
Ticket author(s): Vincent Delecroix
Reviewer(s): Frédéric Chapoton

Author: Release Manager

src/sage/combinat/integer_vector.py

@@ -33,6 +33,7 @@
 
 from sage.combinat.integer_lists import IntegerListsLex
 from itertools import product
+import numbers
 
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
@@ -592,6 +593,13 @@ def __classcall_private__(cls, n=None, k=None, **kwargs):
             Traceback (most recent call last):
             ...
             ValueError: k and length both specified
+
+        :trac:`29524`::
+
+            sage: IntegerVectors(3, 3/1)
+            Traceback (most recent call last):
+            ...
+            TypeError: 'k' must be an integer or a tuple, got Rational
         """
         if 'length' in kwargs:
             if k is not None:
@@ -607,12 +615,12 @@ def __classcall_private__(cls, n=None, k=None, **kwargs):
         if n is None:
             return IntegerVectors_k(k)
 
-        try:
+        if isinstance(k, numbers.Integral):
+            return IntegerVectors_nk(n, k)
+        elif isinstance(k, (tuple, list)):
             return IntegerVectors_nnondescents(n, tuple(k))
-        except TypeError:
-            pass
-
-        return IntegerVectors_nk(n, k)
+        else:
+            raise TypeError("'k' must be an integer or a tuple, got {}".format(type(k).__name__))
 
     def __init__(self, category=None):
         """

src/sage/combinat/tableau.py

@@ -6500,9 +6500,9 @@ def random_element(self):
         from sage.rings.all import ZZ
         from sage.matrix.constructor import diagonal_matrix
         from sage.combinat.rsk import RSK
-        kchoose2m1 = self.max_entry * (self.max_entry - 1) / 2 - 1
+        kchoose2m1 = self.max_entry * (self.max_entry - 1) // 2 - 1
         km1 = self.max_entry - 1
-        weights = [binomial(self.size - i + km1, km1) * binomial((i/2) + kchoose2m1, kchoose2m1)
+        weights = [binomial(self.size - i + km1, km1) * binomial((i//2) + kchoose2m1, kchoose2m1)
                    for i in range(0, self.size + 1, 2)]
         randpos = ZZ.random_element(sum(weights))
         tot = weights[0]