numerics; was: ECL? was ..Re: Runtime determination of share directories?

Robert Dodier wrote:
> On Fri, Jan 23, 2009 at 6:17 PM, Raymond Toy <toy.raymond at gmail.com> wrote:
> 
>> Numeric speed is not the reason to use maxima; there are many other
>> things that would be better suited.
> 
> Well, at the risk of prolonging this discussion, my $0.02 on this
> is that symbolic problems very often lead to numeric ones,
> and it would be really nice to be able to solve such problems
> all in one environment.
> 
> My pet example, not related to LAPACK or GMP or anything else,
> is the computation of marginal probability distributions; typically
> one can make some headway with symbolic calculations, but in
> many cases it is necessary to resort to numerical approximations
> (some variety of numerical integration).

I am sorry, but I could not resist this one: Many algorithms for exact 
linear algebra problems can be reduced to multimodular problems that 
then in turn are solved using BLAS since operations in F_p can be done 
via floats or doubles assuming p is lower than some bound. I.e. the 
reason a determinant in Sage over ZZ for example blows Maxima out of the 
water because exactly that implementation is used (yes, even with the 
RAT trick). We are talking about significantly better asymptotic 
complexity coupled with much faster finite field arithmetic.  The same 
applied to HNF, charpoly, solving linear systems and on and on. And 
those building blocks are used to implement more high level algorithms 
which very much benefit from the fast low level implementations. Now you 
might not care about any of this since the problems you solve have 
little to do with exact linear algebra problems of any significant size, 
but your competitors, commercial as well as Open Source do. When your 
basic operations are slow you cannot really have fast high level code. 
Obviously clever algorithms can compensate for that to some extend.

> FWIW
> 
> Robert Dodier

Cheers,

Michael

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