Comment #28 on issue 3128 by someb...@bluewin.ch: Sum and Product
manipulations
http://code.google.com/p/sympy/issues/detail?id=3128
However, the Karr convention imposes a directionality on the sum
In the very same way as for integrals:
\int_a^b f(x) dx is NOT equal to \int_b^a f(x) dx
In the summation case we have to shift limits due to the
discrete nature of "dx".
such that sometimes this will give the wrong answer now.
No, it does not.
The main reason for this definition is that the following holds:
\sum_{m <= i < n} f(i) = \sum_{m <= i < k} + \sum_{k <= i < n}
*independent* on the relative ordering of m, n and k.
This is what we have for integrals too.
Well, you could also make the *definition* that:
\int_a^b f(x) dx == \int_b^a f(x) dx
but that would not feel natural although it might be useful sometimes.
In the same way, defining that:
\sum_{i=a}^b f(i) == \sum_{i=b}^a f(i)
is "wrong".
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