#11990: infinite sums that are infinite produce errors
------------------------+---------------------------------------------------
Reporter: dkrenn | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone: sage-4.8
Component: calculus | Keywords: infinite sums, infinite, maxima
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Changes (by kcrisman):
* cc: kcrisman (added)
Old description:
> Look at the following code:
> {{{
> sage: m = var('m')
> sage: sum(m, m, 0, oo)
> Traceback (most recent call last):
> ...
> ValueError: Computation failed since Maxima requested additional
> constraints; using the 'assume' command before summation *may* help
> (example of legal syntax is 'assume(m>0)', see `assume?` for more
> details)
> Is m positive or zero?
> }}}
> But inside the sum, it should be clear what `m` is. Using one of or both
> of the commands
> {{{
> sage: assume(m>=0)
> sage: assume(m, 'integer')
> }}}
> does not change the result. Execution of
> {{{
> sage: maxima.sum(m, m, 0, oo)
> }}}
> results in the same (except that a `TypeError` is thrown).
>
> A different behaviour brings the following example
> {{{
> sage: m = var('m')
> sage: sum(2^m, m, 0, oo)
> Traceback (most recent call last):
> ...
> ValueError: Sum is divergent.
> }}}
> Whereas
> {{{
> sage: maxima.sum(2^m, m, 0, oo)
> inf
> }}}
New description:
Look at the following code:
{{{
sage: m = var('m')
sage: sum(m, m, 0, oo)
Traceback (most recent call last):
...
ValueError: Computation failed since Maxima requested additional
constraints; using the 'assume' command before summation *may* help
(example of legal syntax is 'assume(m>0)', see `assume?` for more
details)
Is m positive or zero?
}}}
But inside the sum, it should be clear what `m` is. Using one of or both
of the commands
{{{
sage: assume(m>=0)
sage: assume(m, 'integer')
}}}
does not change the result. Execution of
{{{
sage: maxima.sum(m, m, 0, oo)
}}}
results in the same (except that a `TypeError` is thrown).
--
Comment:
Short story is that there are many things like this in Maxima. See #3732,
for example. This is a good ticket, but to be fair, it is nearly
impossible to guarantee that these interactions will never happen - the
Maxima devs would rightly point out that figuring out when all forms will
be equivalent is not decidable in polynomial time or something like that.
I'm moving the other one to #11987, as it's almost certainly the same
problem.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11990#comment:1>
Sage <http://www.sagemath.org>
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