Alexandros Droseltis wrote:
> Hello!
>
> [Using Maxima 5.17.0 provided by the rpm 5.17.0-1.3 for openSuSE]
>
> Please, have a look at this.
>
> These sums are correct:
>
> (%i27) sum(k, k, 1, 4);
> (%o27) 10
> (%i28) sum(-k, k, -4, -1);
> (%o28) 10
>
> Now check these two sums:
>
> (%i1) simpsum: true;
> (%o1) true
> (%i2) sum(k, k, 1, a);
> 2
> a + a
> (%o2) ------
> 2
> (%i3) sum(-k, k, -a, -1);
> Is a positive, negative, or zero?
>
> p;
> 2
> a - a
> (%o3) ------
> 2
> (%i4) sum(-k, k, -a, -1);
> Is a positive, negative, or zero?
>
> n;
> 2
> - a + (- a - 1) - 1
> (%o4) --------------------
> 2
> (%i5) ratsimp(%);
> 2
> a + a
> (%o5) ------
> 2
>
>
> Should n't a positive "a" create the same result as %o2 and a negative
> the empty sum, thus 0? Do I miss something?
>
> Best Regards
>
> Alexandros
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> Maxima at math.utexas.edu
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>
First of all, convince yourself that
sum(f(i),i,a,b) = -sum(f(i),i,b+1,a-1) when a>b, NOT zero.
This is a consequence of
sum(f(i),i,a,b) + sum(f(i),i,b+1,c) = sum(f(i),i,a,c)
where a<=b<c
being extended to all b.
Commercial Macsyma has a flag "sumhack" that makes this true.
A "negative sum" is not zero if you maintain this identity.
I think what you are seeing is that one part of Maxima believes this
identity and another one doesn't.
Two people can disagree on which part of Maxima is in error.