Why cannot Maxima calculate some simple sums


On Sat, 5 Jun 2010, John Lapeyre wrote:

< maxima's behavior is a little puzzling with sums.
< 
< (%i2) integrate(1/n^2,n,1,inf);
< (%o2) 1
< 
< (%i3) sum(1/n^2,n,1,inf);
< (%o3) 'sum(1/n^2,n,1,inf)
<   ? search the manual
< 
< (%i4) sum(1/n^2,n,1,inf),simpsum;  /* why not simpintegrate ? */
< (%o4) %pi^2/6
< 
< (%i5) sum(1/n!,n,0,inf),simpsum;
< (%o5) 'sum(1/n!,n,0,inf)
< 
<  (Now the user assumes that maxima can't do this sum because the manual is clear about
<  simpsum and seems to imply that this is all there is to simplifying sums)
< 
<  Maybe no one got around to fixing this inconsistency... or maybe its hard to
<  change without breaking something.


I guess there are two responses. First, the Maxima online help system
needs to be improved. In comparison to Octave's, for example, it lacks
cross-referencing. However, and second,  users often forget that

?? sum

will list all topics which contain the 3 characters s u m.
In particular, you will find 'simplify_sum'.

I can't answer your question about the difference between simplification
flags for sum and integrate.

Leo

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