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Comment #4 on issue 2723 by asmeurer: What should summation() do with
non-integer limits?
http://code.google.com/p/sympy/issues/detail?id=2723
As Mathematica or Maple have no problems with this why should it be
forbidden or not working nicely in Sympy?
Maples gives me:
sum(exp(a*x), x=-1/2..1/2);
1
which I think means it is only summing over the integers in the range
[-1/2, 1/2], which is just 0. WolframAlpha does give your result:
http://www.wolframalpha.com/input/?i=sum(exp(a*x)%2C+x%3D-1%2F2..1%2F2)
The problem is that the summation is not well-defined in the way that you
want it to be. SymPy computes the sum by first computing the indefinite
sum and then plugging in the limits (similar to the fundamental theorem of
calculus for integration). Doing that gives the result that SymPy returns,
as I showed in comment 1.
My guess (and I could be completely wrong here), is that for spin
variables, they use a convenient notation that the summation takes place on
integers offset by 1/2 (or whatever). Maybe one of our physicists will
know. If this is indeed the case, then you can perhaps add a function to
the physics module (or maybe one already exists) that does this for you.
I'd also like to see if Mateusz or anyone else knows more about this from a
mathematical standpoint as I really haven't encountered summations with
non-integer limits before.
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