[Maxima] Wrong limits
phhs80 at gmail.com
Fri Nov 2 12:31:27 CDT 2007
On 11/2/07, Stavros Macrakis <macrakis at alum.mit.edu> wrote:
> Thanks for bringing this particular bug to our attention.
> Alas, Maxima is not perfect, so bug reports like this are valuable.
> Subjectively, limit and definite integration seem to be among the weaker
> modules of Maxima; as a general rule, tlimit (which uses taylor) seems to be
> better in those cases it handles, but it doesn't handle as many cases as
> limit. As it happens, tlimit gets your problem right.
> As for trusting Maxima for limits ... or anything else ... Maxima is
> admittedly a fallible tool. We and our users regularly find bugs in many
> parts of the system, some of which are corrected rapidly, others of which
> have persisted for years. I do not know how Maxima's bug frequency,
> severity, and time-to-fix compares with the commercial CASs, but I do hear
> that bugs are not unknown in them, either. The commercial Macsyma did
> repair many of the older bugs in Maxima, as it received full-time
> development resources for many years; but it is apparently no longer
> I would not trust any CAS blindly, for anything. If a cross-check is
> possible with other techniques, I would always perform it when the answer is
> critical (as opposed to when I'm exploring solution methods): after
> factoring, expand the result (but this doesn't tell you if the factorization
> was complete); after integrating, differentiate; after inverting a matrix,
> multiply out; do sanity checks with specific numerical values; etc. For
> that matter, you might want to use high-precision arithmetic (bfloat) to
> check numerical calculations where rounding errors might be an issue. And
> having a colleague review math done on paper can be a good idea...!
I am an enthusiast of free software, and I am happy that with my bug
reports I am helping Maxima to become better. According to Richard
Fateman, also Mathematics fails regarding this particular limit.
Yesterday, I found a bug in Maple also regarding the calculation of a
Should I report this bug in some bugzilla site?
> On 11/2/07, Paul Smith < phhs80 at gmail.com> wrote:
> > (%i1)
> > (%i2) limit(h,k,1/3,plus);...
> > Both limits are wrong: the first one is +oo and the second one is -oo.
> > Can one really trust Maxima regarding the calculation of limits?...
More information about the Maxima