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I would say that it is because
type(d)
does not return the same thing in the two cases. There are different forms of integers in Sage, and it can be tricky from time to time : there are for instance "python" integers (i.e. int(6)) and Sage integers (i.e. Integer(6)).
The range function, in particular, only returns Python integers
sage: int(9)/int(4)
2
While you probably want to use Sage integers instead, which knows when they should consider themselves as rational numbers
sage: Integer(9)/Integer(4)
9/4
Sooooooo if you want to change your code a bit, I would say that you can fix it by replacing {{{range(something)}}} by {{{srange(something)}}}. srange returns Sage integers :-)
sage: map(type,range(4))
[int, int, int, int]
sage: map(type,srange(4))
[sage.rings.integer.Integer,
sage.rings.integer.Integer,
sage.rings.integer.Integer,
sage.rings.integer.Integer]
Nathann
