polynomial arithmetic over ginac

[Richard B. Kreckel]

On Sat, 19 Aug 2000, Parisse Bernard <parisse at mozart.ujf-grenoble.fr> wrote:
> On Sat, 19 Aug 2000, Ayal Pinkus <apinkus at xs4all.nl> wrote:
> > I am a bit curious as to how you plan to use GiNaC as a CAS for PDAs? GiNaC
> > is meant to be
> > used  on a workstation with a c++ compiler, something I'm sure
> > you will have a hard time getting to run on a PDA given the memory limits.
> > Also, that would
> > require a text editor etc. PDAs are notoriously hard to use for programming
> > purposes, given
> > they have a small keyboard (if they have one at all) and small screen. A
> > completely different
> > experience from working on a workstation, I can assure you.
> > In fact, to make it useful on a PDA, the most important thing is actually a
> > good user interface.
> > And you will have a hard time designing a user interface that is different
> > from the calculator
> > metaphor. A calculator is not very suited for the more elaborate
> > calculations, where you actually
> > have to write a little program to solve the problem.
> 
> I disagree with this. I'm the main programmer of the HP49G and HP40G
> calculators CAS and I believe that a calculator is well suited for
> little programs, that's not much different from writing a small program
> in a CAS 
> like Maple or MuPAD. 
> The main problem with graphing calculators (especially the HP4xG) is the
> processor speed (about 1000* slower than my laptop), not the programming
> environment (e.g. you have a debugger, you can put breakpoints and exec
> your program step by step, and view the current stack).
> If we want to replace one day the proprietary CAS with GPL'ed CAS, we
> must 
> start by providing a good solution for the educationnal market and the
> non-mathematician users.

Hmm, just don't know whether I'm kicking a dead horse here.  It's an old
thread.  But really, I've been hacking on CLN/GiNaC support for ARM
lately and they seems to fit well into quite old ARM computers.  Many
PDAs are running on such things.  So, the portability is there and the
machines are getting faster than what we see here:

timing commutative expansion and substitution.... passed
        size:   25      50      100     200
        time/s: 1.57    6.5     27.08   113.19
timing Laurent series expansion of Gamma function.... passed
        order:  10      15      20      25
        time/s: 4.49    25.33   113.37  431.3
timing determinant of univariate symbolic Vandermonde matrices.... passed
        dim:    4x4     6x6     8x8     10x10
        time/s: 0.13    1.26    13.63   125.07
timing determinant of polyvariate symbolic Toeplitz matrices.... passed
        dim:    5x5     6x6     7x7     8x8
        time/s: 1.56    7.46    33.21   134.36
timing Lewis-Wester test A (divide factorials). passed 1.64s
timing Lewis-Wester test B (sum of rational numbers). passed 0.28s
timing Lewis-Wester test C (gcd of big integers). passed 1.56s
timing Lewis-Wester test D (normalized sum of rational fcns). passed 30.24s
timing Lewis-Wester test E (normalized sum of rational fcns). passed 26.44s
timing Lewis-Wester test F (gcd of 2-var polys). passed 3.75s
timing Lewis-Wester test G (gcd of 3-var polys). passed 81.24s
timing Lewis-Wester test H (det of 80x80 Hilbert). passed 291.67s
timing Lewis-Wester test I (invert rank 40 Hilbert). passed 104.21s
timing Lewis-Wester test J (check rank 40 Hilbert). passed 68.17s
timing Lewis-Wester test K (invert rank 70 Hilbert). passed 603.7s
timing Lewis-Wester test L (check rank 70 Hilbert). passed 369.04s
timing Lewis-Wester test M1 (26x26 sparse, det). passed 21.8s
timing Lewis-Wester test M2 (101x101 sparse, det) disabled
timing Lewis-Wester test N (poly at rational fcns) disabled
timing Lewis-Wester test O1 (three 15x15 dets) disabled
timing Lewis-Wester test P (det of sparse rank 101). passed 63.5s
timing Lewis-Wester test P' (det of less sparse rank 101). passed 198.2s
timing Lewis-Wester test Q (charpoly(P)) disabled
timing Lewis-Wester test Q' (charpoly(P')) disabled
timing computation of an antipode in Yukawa theory. passed 6261.38s

Isn't it lovely?  Almost 100 times slower than our workstations but
still useful.

Regards
     -richy.
-- 
Richard Kreckel
<Richard.Kreckel at Uni-Mainz.DE>
<http://wwwthep.physik.uni-mainz.de/~kreckel/>