SOS! Are really "math bugs" an integral part of computer algebra systems?
Vladimir Bondarenko
Had I not have gross nerves, I'd get running scared.
Right now before my eyes a couple of CASs are running...
many of you have access to most of them... Simplest
convergent integrals diverge... trivial, obviously
finite limits yield something like "undefined result"...
not formidable taylors are looped... crashes... and
almost always, zombie bugs...
Massive loss of cattle...
(By the way, if someone have acquired Maple 11, it
would be great had you report about this stuff
http://groups.google.com/group/sci.math.symbolic/search?hl=en&group=sci.math.symbolic&q=Maple+bugs
http://groups.google.com/group/comp.soft-sys.math.maple/search?hl=en&group=comp.soft-sys.math.maple&q=Maple+bug
http://www.mapleprimes.com/search/node/bug
http://www.math.rwth-aachen.de/mapleAnswers/html/index.html#0
http://maple.bug-list.org/maple-crisis.php )
Again and again, I ask myself, SHOULD this be going
this way? Are really mathematically wrong results
an integral part of computer algebra systems?
(My honest opinion, Hell no. But, for a moment, let's
we forget about my viewpoint.)
This said, I know in person many developers of these
CASs, and almost invariably they are really intelligent
and knowledgeable and dedicated persons, many of them
also agreeable and easy to communicate to.
Consider, devilishly powerful hardware is coming, along
with a new phenomenon, mathematization of business. Now
it looks like we are not ready for this...
Any vision about WHAT's exactly happening and, if this
is medicable, HOW to treat, or better, cure this?
Unwillingness to design the things carefully?
Ridiculously insignificant regression testing?
What?
Best wishes,
Vladimir Bondarenko
VM and GEMM architect
Co-founder, CEO, Mathematical Director
http://www.cybertester.com/ Cyber Tester, LLC
http://maple.bug-list.org/ Maple Bugs Encyclopaedia
http://www.CAS-testing.org/ CAS Testing
........................................................
To have peace with this peculiar life; to accept what
we do not understand; to wait calmly for what awaits
us, you have to be wiser than I am.
-- Maurits Escher
........................................................
Roman Pearce
> Simplest convergent integrals diverge...
> Again and again, I ask myself, SHOULD this be going
> this way? Are really mathematically wrong results
> an integral part of computer algebra systems?
That depends on what you want the system to do. If it is just a
matter of implementing or fixing algorithms which are proven to work,
then I would say no. But if you are trying to make the system solve
problems when you don't have a general algorithm, then I would expect
lots of nonsense.
I will confess my ignorance here. What algorithms do CAS systems
implement to compute real and complex limits ? What about finding
discontinuities ?
The limit help page in Maple references this algorithm:
"A New Algorithm for Computing Symbolic Limits Using Hierarchical
Series."
Geddes, K. O., and Gonnet, G. H.
In Proceedings of ISSAC '88, pp. 490-495.
but the harder problems seem to use Dominik Gruntz's algorithm.
Vladimir, you probably have the most experience testing these things.
Do you have any insight into why these algorithms might be failing, or
what could be done to correct it ? Is it a problem where the
algorithms are being used in a more general setting than what is
guaranteed to work, or are there are "bad cases" where something
wasn't implemented properly ?
I would appreciate anyone's insight or suggestions, even just
references to papers.
> Consider, devilishly powerful hardware is coming, along
> with a new phenomenon, mathematization of business. Now
> it looks like we are not ready for this...
The powerful hardware is here today, and it is cheap and ubiquitous.
If your large computation does not max out a quad processor Opteron,
then you have some work to do. If you can't use a dual processor
effectively, then you have a problem. Here is a good tutorial on
pthreads:
http://www.morris.umn.edu/~gaoj/Teaching/Spring2007/CSci3401ModelsofComputingSystems/pthreadTutorial.pdf
> Unwillingness to design the things carefully?
> Ridiculously insignificant regression testing?
Regression testing does not help you fix a faulty design. It really
only helps you catch careless mistakes. Of course, developers (not
us!) make plenty of those :)
Roman Pearce
CECM/SFU
Vladimir Bondarenko
On Mar 4, 2:30 am, "Roman Pearce" <rpear...@gmail.com> writes:
RP> Vladimir, you probably have the most experience testing
RP> these things.
It looks like, in terms of the total distinct bugs discovered
in Analytic, Axiom, Derive, DoCon, Giac/xCAS, Maple, MathCAD,
Mathematica, Maxima, MuPAD, Pari/GP, Reduce, SAC, TI-Nspire,
yes.
Mostly, Cyber Tester's knowledge is based on an avalanche of
the bug results identified by the VM machine automatically a
tiny bit of which can be found on the fairly obsolete version
of our Maple Bugs Encyclopaedia available publicly
Now and then (not so rare as we'd want this) an accidental
piece of manual testing reveals extra bugs in computer algebra
systems.
RP> Do you have any insight into why these algorithms might
RP> be failing, or what could be done to correct it ? Is it
RP> a problem where the algorithms are being used in a more
RP> general setting than what is guaranteed to work, or are
RP> there are "bad cases" where something wasn't implemented
RP> properly ?
You have a rare gift of bringing up very nice issues. These
points you asked are, up to a wording, a part of our attempts
to understand is it possible and if yes, how to build a high-
performance almost zero-defect new generation CAS.
Some insights are already here, but I'd much prefer to drill
down to the roots deeper before speaking about them publicly.
At the same time in a reasonably near future (say, not in 5
years) Cyber Tester plans to touch this.
> pthreads:http://www.morris.umn.edu/~gaoj/Teaching/Spring2007/CSci3401ModelsofC...