> < ^ Date: Wed, 19 Jul 2000 15:00:10 -0600
> < ^ From: Nicolas Thiery <nthiery@icare.mines.edu >
< ^ Subject: Re: Series expansions

Dear GAP Forum,

Not as far as I know. A very, very quick and crude test, suggests
that MuPAD is much faster for polynomials over the integers (or
rationals) but that GAP is much faster for polynomials over small
finite fields. I don't use MuPAD at all regularly though, so I may
have been doing something stupid.

Could you send me your test anyway ? That's always a basis to
elaborate on. Your results seems to suggest that the difference
between MuPAD and GAP comes from a speed difference in the arithmetic
of the "base field" (integer/rational/mod p integers). MuPAD uses Pari
for this. What about GAP ?

No, neither of these functions is implemented at present, nor ae
there data structures for potentially infinite series expansions
(although there are concepts such as potentially infinite virtual
lists, on which they could be implemented).

Actually I just would need to compute the first n coefficients of the
series expansion of a rational fraction. Something like:

series(1/(1-x),x,5)  ->  1+x+x^2+x^3+x^4

So, even if a real data structure for series/series expansions would
be nicer, it's not really necessary.

Do keep us posted with the progress of your project, if you go
ahead, and please consider the possibility of eventually
"publishing" the software as a GAP share package (see
http://www-groups.dcs.st-and.ac.uk/~gap/Info4/share.html ).

I will. My current plan is to first finish to clean up my version for
MuPAD, which should take a few weeks. Then, I will have to decide if I
just adapt it for MuPAD 2 (which should be straightforward), or if I
go for GAP for further development.

Thanks for your answers,

Best regards,
Nicolas M. Thiéry "Isil", 412 Washington Avenue, 80403 Golden Colorado (USA)
Mél: nthiery@mines.edu, Tél: (303)273-5492, Fax: (303)273-3875
WWW: <URL:http://www.mines.edu/~nthiery/>

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