#11990: infinite sums that are infinite produce errors
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Reporter: dkrenn | Owner: burcin
Type: defect | Status:
needs_review
Priority: major | Milestone: sage-5.6
Component: calculus | Resolution:
Keywords: infinite sums, infinite, maxima | Work issues:
Report Upstream: N/A | Reviewers: Burcin
Erocal
Authors: | Merged in:
Dependencies: | Stopgaps:
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Comment (by kcrisman):
> Exactly. The behavior of the `sum()` function in Sage is consistent.
`maxima.sum()` is just a wrapper to call Maxima. That is also consistent
with Maxima behavior.
Yes.
> The expression `sum(m, m, 0, oo)` is divergent if `m != 0` and `0` if
`m=0`. So the best we can do without the assumption Maxima is asking for
is to leave it unevaluated.
Well, I don't know about this. In some sense, this should be a "dummy
variable" in which case the sum is clearly 0+1+2+... but for consistency
perhaps this is okay in our case. Otherwise I do agree with dkrenn that
`sum(2^m, m, 0, oo)` should also be asking a question. But this would be
an upstream issue, more or less.
> On the question of shall we raise an error or return `oo`: Leaving aside
the problem that it is usually not that easy to decide which type of
infinity to return, I would like to get an error as soon as a divergent
sum is encountered. If this expression was part of a larger one, and we
decide that its divergent after a substitution, there isn't much point in
carrying on evaluating the expression.
> Since we already have a ticket about handling interactive prompts from
Maxima, I suggest we close this ticket.
I guess I would be interested in whether Maxima considers the discrepancy
between `sum(2^m, m, 0, oo)` and `sum(m, m, 0, oo)` behavior is a bug.
After all, `m` should really be a dummy variable! I've actually sent an
email and so request to not close this ticket, since this is a (slightly)
different issue than the overall issue of Maxima giving interactive
prompts. After all, Maxima's `integrate(m,m,0,inf)` doesn't ask such a
question, but says it's divergent.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11990#comment:8>
Sage <http://www.sagemath.org>
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