Well, it is the simpsum bug, because on my patched version maxima does the
right thing -- and it shows exactly the behaviour of the bug: sum
unpatched fails if one part of a sum can be summed while another can't, in
this case sum unpatched returns only the summed stuff.
maxima patched: (instructions how to patch can be found in the bug report)
(C1) exp:2^(-i-1)*(i+1)+2^(-i-1);
- i - 1 - i - 1
(D1) (i + 1) 2 + 2
(C2) sum(exp,i,0,n);
n
====
\ - i - 1 - i - 1
(D2) > ((i + 1) 2 + 2 )
/
====
i = 0
(C3) sum(exp,i,0,n),simpsum;
n
====
- n - 1 \ - i - 1
(D3) - 2 + > (i + 1) 2 + 1
/
====
i = 0
(C4) sum(exp,i,0,n),simpsum,expand;
n
====
- n - 1 \ - i - 1
(D4) - 2 2 + > i 2 + 2
/
====
i = 0
(C5) nusum(exp,i,0,n);
n + 4
(D5) 3 - -----
n
2 2
Martin
On 24 Jan 2003, Wolfgang Jenkner wrote:
> Mathieu Avila <mavila@irisa.fr> writes:
>
> > In the dump following, the same expression "expt" is evaluated in two
> > different manners, and the result is different (whereas it
> > shoulnd't). The EV with the expand flag gives the right result.
> [...]
> > (C1) exp:2^(-INDICE-1)*(INDICE+1)+2^(-INDICE-1);
> > - INDICE - 1 - INDICE - 1
> > (D1) (INDICE + 1) 2 + 2
> > (C2) expt:sum( exp , indice,0,final);
> > FINAL
> > ====
> > \ - INDICE - 1 - INDICE - 1
> > (D2) > ((INDICE + 1) 2 + 2 )
> > /
> > ====
> > INDICE = 0
> > (C3) ev(expt,simpsum);
> > - FINAL - 1
> > (D3) 1 - 2
> > (C4) ev(expt,simpsum,expand);
> >
> > - FINAL - 1
> > (D4) 2 - 2 2
>
>
> I think that both results are wrong.
>
>
> (C1) expt:2^(-i-1)*(i+1)+2^(-i-1);
> - i - 1 - i - 1
> (D1) (i + 1) 2 + 2
> (C2) testsum(f):=apply('sum,[expt,i,0,f]);
> (D2) testsum(f) := APPLY('SUM, [EXPT, i, 0, f])
> (C3) testsum(1);
> 7
> (D3) -
> 4
>
> wheras the two results you got give 3/4 resp. 3/2.
>
> I suggest instead
>
> (C4) closed_form(f):=3-2^(-f-1)*(f+4);
> - f - 1
> (D4) closed_form(f) := 3 - 2 (f + 4)
> (C5) for f from 0 thru 10 do sprint(testsum(f));
> 1 7/4 9/4 41/16 11/4 183/64 187/64 757/256 381/128 3059/1024 3065/1024
> (D5) DONE
> (C6) for f from 0 thru 10 do sprint(closed_form(f));
> 1 7/4 9/4 41/16 11/4 183/64 187/64 757/256 381/128 3059/1024 3065/1024
> (D6) DONE
> (C7)
>
> Wolfgang
>
> _______________________________________________
> Maxima mailing list
> Maxima@www.math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima
>