Built into Maxima, there are rules for simplifying pochhammer and
binomial expressions that are special cases of the sumhack / prodhack
identities; for example:
(%i2) pochhammer(a,-2);
(%o2) 1/((a-2)*(a-1))
>From the perspective of consistency with these (well-known)
simplifications, I would say that the default should be for sum and
product to use the sumhack / prodhack identities.
Of course, lsum cannot sumhack. If lsum were extended somewhat and we
had a simple way to represent subsets of the integers, we could make
lsum the non-sumhack sum. Something like lsum(1/k,k, 1 .. 10^7), where
1 .. 10^7 = set(1,2,3,..., 10^7, or 1 .. -1 = empty set.
Barton
-----maxima-bounces at math.utexas.edu wrote: -----
>My?opinions:
>1.?Sumhack?is?a?respectable?and?useful?feature.
>
>2.??Loops?and?Sums?should?be?different?when?they?are?different.