Comment #6 on issue 3657 by prasoon9...@gmail.com: Summation over
non-integers
http://code.google.com/p/sympy/issues/detail?id=3657
Hmm.. The idea to implement a set here would be good. But, as I see it,
elements of the set must have some recognizable pattern in them so that we
can transform f appropriately . Then, it can be passed to the usual
summation process.
For example, if we want to sum f over {1/n : n belongs to Naturals}, then
we need to be able to identify what transform we need to do to f (in this
case f(x) -> f(1/x) and then sum over positive integers). Similarly, to sum
over {1/n^2: n belongs to Natural}, we need to find out the exact transform.
My point is, if we are provided a general set where the elements vary
according to some rule, we will need to know what rule that is. If
TransformationSet is used with Lambda, then it's a trivial matter to find
this relation but if we are to support user generated list(say), then this
will not work.
Also, if we use Lambda, we are asking the user to provide the
transformation on f by himself, as well the scaled limits. For example, if
we want to sum f from 0 to 1 with a step of 0.2, we are asking the user to
provide us the transformed function, namely f(x) -> f(x/0.2), _and_ the
scaled range, (0, 5). This, I believe, isn't good functionality from user
POV.
So, for now, I am implementing a function like python range() with start,
stop and step with support for non-integer step. For the ideal case, as you
put it, it will require writing a new summation, with probably heuristic
support for identifying transformation to use for any given set. This seems
to be quite a bit of work and my midsems start in a few days, so I can't do
it just yet. Will put in a #TODO for extending this.
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