I think your citing of Karr's paper is OK; the more modern notation seems
to be
sum (i in the set{M} of f(i)) which avoids the order of enumeration of
elements of M.
As far as the best known algorithm, what about
Bill Gosper's?
e.g.
http://mathworld.wolfram.com/GospersAlgorithm.html
and the umpteen related papers some of which are in the references there?
(which don't mention Karr;
in fact, it seems mathematica ignores him!)
While I have not recently read Karr's paper (the one in J. ACM) I recall
it being quite lengthy and not contributing
anything new that could be programmed in Macsyma. At least not programmed
by me.
Not to say that anything in it is wrong. Just not helpful.
Other work, Zeilberger, Wilf. .. has been put into Maxima, I think.
RJF
On Monday, November 3, 2014 4:43:43 PM UTC-8, Aaron Meurer wrote:
>
> We've been calling it the Karr convention because Karr outlines it in
> detail in his paper, "Summation in Finite Terms" and explains in detail why
> it is necessary. To quote from Section 1.4.
>
> Consider Sum_m<=i<n f(i). If m < n, this has an obvious meaning. If m =>
>> n, this is summation over the null set, *which is customarily defined to
>> be zero*.
>
>
> (emphasis mine)
>
> I think the fact that Karr indicates that this convention is not
> customary, the fact that he outlines why it is necessary in detail (at
> least relative detail considering the rest of the paper), and the fact that
> he is the author of the best known algorithm for doing summation in finite
> terms (to my knowledge) justifies calling it that. He may not be the first
> person to consider this, but it would hardly be the first time something in
> mathematics is named after someone who wasn't the first person to discover
> it (nor in computer algebra; consider Groebner bases).
>
> At any rate, the way the convention is described in the documentation does
> not necessarily predicate that this is the standard term for the
> convention. It is introduced as "for finite sums (and sums with symbolic
> limits assumed to be finite) we follow the summation convention described
> by Karr [1], especially definition 3 of section 1.4." Karr's paper is the
> best reference for why this convention is necessary that we have found, so
> referencing is and calling it thereafter "the Karr convention" or "Karr's
> convention" seems fine to me.
>
> Aaron Meurer
>
>
> On Mon, Nov 3, 2014 at 4:59 PM, Sergey B Kirpichev <[email protected]
> <javascript:>> wrote:
>
>> On Mon, Nov 03, 2014 at 02:39:41PM -0800, Richard Fateman wrote:
>> > I checked with Gradshteyn and Rhyzik (1960, revised various times
>> later),
>> > and they define sum if n<m to be zero.
>>
>> Yes, that's a different convention (Mathematica uses that, as well as
>> Maxima).
>>
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