doit() method *sometimes* ignores floor and ceiling within Sum

[rajkk1]

Summary of problem: the doit() method will sometimes (depending on the expression) ignore any floor or ceiling that is located inside a Sum.

Example detailing the bug

The following code sets up the problem:

from sympy import floor, Sum, Symbol
i = Symbol('i')
a = Sum(floor(2*2**(-i)), (i, 1, 2))
b = floor(2*2**(-1)) + floor(2*2**(-2))

Note that these two expressions a and b are the same, just a is written with the summation notation and b is written out explicitly. They both equal 1.

Printing these variables give us the expected results:

However, if we run the doit() method on them we see a discrepancy:

where we see that the floor function inside the summation has been ignored. The same issue also arises when using the ceiling method (i.e. the doit() method ignores it when it is in a summation).

However it seems like this problem is not consistent, e.g. if you remove the 2* from the expression it works fine. More precisely if you run

from sympy import floor, Sum, Symbol
i = Symbol('i')
a = Sum(floor(2**(-i)), (i, 1, 2))
b = floor(2**(-1)) + floor(2**(-2))
print(a.doit())
print(b.doit())

you get the exptected results (this works for ceiling too)

(bug discovered on sympy version 1.8 on python 3.7.3)

[oscargus]

The problem arises since

k = Symbol('k', positive=True, integer=True)
floor(2*2**(-k))

returns 2/2**k so for some reason the floor is missing there.

(Summation replaces the original variable with a dummy variable with additional assumptions, such as integer, and in this case, positive.)

[oscargus]

This doesn't happen for the equivalent floor(2**(-k+1)).