Comment #22 on issue 3128 by trel...@psu.edu: Sum and Product manipulations
http://code.google.com/p/sympy/issues/detail?id=3128
I've posted my edits to subs, expand, and factor for Sum.
See https://github.com/sympy/sympy/pull/2198
It seems summation notation in it's classical form is not up
to the demands we place on it these days. I know I'm late to
the conversation, but I think the choice of the Karr
convention is a bad idea (#1696).
1) Given that there isn't an excepted convention, I think
the default should be the thing that's easiest to
understand. Pre-calc students in high-school, who do not yet
understand integration, will be really confused by sum(
f(x), (x,3,0)) != f(3) + f(2) + f(1) + f(0).
2) We don't always want Sum(f(x),(x,a,b)) +
Sum(f(x),(x,b,c)) == Sum(f(x),(x,a,c)). It depends on
context.
3) Notation should make everything explicit, avoid
ambiguity, and should not rely on implicit assumptions that
are not easily discovered by a naive reader. Examples of bad
notation are einstein summation notation (not uniquely
parsable) and stochastic differential equation notation
(depends on the specific definition of stochastic
integration used). Summation notation is not a perfect
parallel with integration -- there is no infinitessimal (dx)
term that explicitly communicates some type of orientation
is the summation.
I'd like to just be able to specify a summation in the form
Sum(f(i) for i in W(n)) where W is an rather general
collection of sets of integers parameterized by n, and not
have to worry about the algebra system trying to tell me
what the signs of f(i) should be.
A systematic survey of users would and popular opinion
on what " Sum(x,x=3..1) " means would go a long way to
justifying the choice, 1 way or the other.
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