[Maxima] is maxima suitable for multiprocessor computations?
Richard Fateman
fateman at EECS.Berkeley.EDU
Wed Nov 14 08:30:47 CST 2007
Well, you get the same result if you do the computation in parallel, we hope. So there are no "interesting" results other than the possibility of getting the result faster...
There are a few areas of application in which large problems (in fact, potentially parallel) exist. Celestial mechanics is one; Poisson series in Maxima were written for support of celestial mechanics, though the way pois2 and pois3 are loaded into Maxima destroys one of the sets of routines. But no one uses Maxima for c.m. because the astronomers have written their own programs.
Another is Grobner basis reduction, where there have been a number of attempts to improve performance by parallelism; it seems a factor of 3 or 4 in speedup for some algorithms, by using maybe 6 or more processors; I don't know if the best serial algorithms can be sped up by parallelism.
If Grobner basis reduction is the only way to solve a problem, it is likely to take more time than you would like, and so speeding it up would be of some interest. Often G.B. is used when other methods, more efficient, can be used, but there is a large class of researchers who think that GB should be used for everything, and are therefore keen to make this faster. There is a relatively large percentage of research papers on GB in J. Symbolic Computing and ISSAC conferences; in my view a kind of feeding frenzy where people write papers on this because it must be important because people write papers about it. But you can accuse me of just being grumpy...
Anyway, parallel GB is out there. There was also a conference on parallelism in computer algebra, and in fact I supervised a PhD student at Berkeley doing research on this topic.. (Carl Ponder).
If you search on Google for parallel computer algebra you will get a bunch of references to papers and conferences, most of which are theoretically oriented, but one might suspect that they are theoretical because parallel computer hardware was non-existent, too expensive, or not really fast when the papers were written. That might be it, or it might be that the authors were not interested in doing the work necessary for demonstrating their ideas, or were (rightfully) fearful that their theoretical ideas were, practically speaking, of modest or zero value.
There has been a big upsurge in interest in parallel algorithms, but a lot of work was done in the mid 1980s when motorola 68000 computers were lashed together into parallel computers, and systems (including lisp) were implemented for them. Ponder's thesis has some comparative data on running symbolic programs.
RJF
----- Original Message -----
From: "Raymond Toy (RT/EUS)" <raymond.toy at ericsson.com>
Date: Tuesday, November 13, 2007 2:51 pm
Subject: Re: [Maxima] is maxima suitable for multiprocessor computations?
> Richard Fateman wrote:
> > I disagree. Some algorithms like polynomial multiplication, can
> be mapped to multiple processors fairly easily. Some lisps support
> parallelism with various levels of cost (OS process vs light-weight
> threads).>
>
> Are there interesting symbolic problems that would really benefit
> from
> parallelism? So what if I can do parallel polynomial
> multiplication
> really fast? Does that lead to some interesting result?
>
> I think I have some understanding of numerical problems that would
> benefit from parallelism, but I don't know anything about symbolic
> problems.
>
> Ray
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