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]> 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). > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/20141103225929.GA15940%40darkstar.order.hcn-strela.ru > . > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6KBJUGoCPURwvz14Ppm86E3nQe47zJERS99Qf2OEporDg%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
