#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-5.4
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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Changes (by burcin):
* status: new => needs_review
* reviewer: => Burcin Erocal
Comment:
Replying to [comment:6 kcrisman]:
> > The reason I open the ticket is, that all sums above have the same
behavior, but the output is always different, which should not be.
> Well, `maxima.sum` is not really applicable, because that is a Maxima
element. That's sort of like complaining that mpmath returns `mpf`
numbers - you aren't asking for a Sage element. So it still sort of
reverts to the big question.
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.
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.
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.
In Sage there is one exception to this rule, we return different types of
infinity from special functions if you hit a pole. For example `gamma(-1)
-> Infinity`. This is compatible with MMA, although it contradicts Maple
or GiNaC. This allows us to do `(1/gamma(n)).subs(n=-1) -> 0` instead of
raising an error. Compared to what goes on when evaluating `sum()`,
`gamma()` is a fundamental operation. This convenience to avoid special
casing potential poles of `gamma()` is well worth the bug hunting after a
complex expression ends up evaluating to `oo`.
Since we already have a ticket about handling interactive prompts from
Maxima, I suggest we close this ticket.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11990#comment:7>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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