should bound symbols gain limit assumptions at instantiation?

[smichr]

I noticed that the condition k >= 1 is unevaluated in the first case:

>>> var('k',positive=True)
k
>>> Sum(Piecewise((1, k >= 1), (0, True)), (k, 1, 10))
Sum(Piecewise((1, k >= 1), (0, True)), (k, 1, 10))

but not in this case -- even though the context of the Sum warrants the change:

>>> var('k',positive=True, integer=True)
k
>>> Sum(Piecewise((1, k >= 1), (0, True)), (k, 1, 10))
Sum(1, (k, 1, 10))

Inheritance of the attributes of the range is only done during doit. Would it make sense to do so at instantiation if evaluate is not False? Instantiation could happen in two steps: obj.xreplace({bound:bound_with_assumptions}).xreplace({bound_with_assumptions: bound}). The first step would allow anything to evaluate based on assumptions; the second step would allow the user to still access that symbol.

[smichr]

It might be good to include a check for assumptions that the integration variable has that a limit expression does not have, e.g. the summation variable has been declared as a positive integer in the following:

>>> lim = [var('i',integer=1,positive=1),0, var('n',integer=True)]
>>> Sum(Piecewise((1, n>=0),(0,True)),lim)
Sum(Piecewise((1, n >= 0), (0, True)), (i, 0, n))

but two issues

1. it should be nonnegative since the lower limit is 0 (or else an error should be raised)
2. the upper limit appears in the Piecewise because it was not conveyed that it was a nonnegative value