# [Maxima] Linearity of sum

Stavros Macrakis macrakis at alum.mit.edu
Sun Oct 17 17:48:26 CDT 2010

```Declaring f linear in Maxima is not just an assertion of a
mathematical property -- it means that f(a+b) automatically simplifies
to f(a)+f(b).  In many cases users want more control than this.

In the case of sum in particular, *infinite* sum is not linear in
general and Maxima can't know whether sum(...,n) is going to have
n->inf later in a calculation.

-s

On 2010-10-17, dlakelan <dlakelan at street-artists.org> wrote:
> On 10/17/2010 02:17 PM, Rupert Swarbrick wrote:
>> Robert Dodier<robert.dodier at gmail.com>  writes:
>> (snip)
>>> By default, Maxima doesn't assume sum is linear.
>>> Try declare(sum, linear).
>>
>> Just out of interest, why isn't sum assumed to be linear? ...
>
>> So, as I said, I'm sure there's a good reason and I'm being an idiot,
>> but could someone explain?
>
> Yes, especially because this might explain why some series solutions of
> equations that I've tried have failed. Does integrate know that sum is
> linear? If I remember correctly, I've asked it to integrate certain
> things before and it fails even though it knows how to integrate each
> term in the sum. That was a fairly obnoxious situation that I spent some
> time trying to figure out but now suspect is simply due to sum not being
> declared "linear"
>
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