Form is really slow and fast for me. What could this mean?

[Richard Fateman]

Thanks for this data.  Your timings look like mine for the
ones that overlap.  The difference between 1Gh and 933Mhz
is not that great, and I guess the other parameters are
close too. It is odd that Maple 7 is so much slower than Maple4 etc.
Maybe the change to longer forms slowed it down.


I tried downloading form3.0, and I find it mysterious.  Maybe I am not using
it correctly.  My first version took 101.23 seconds. I repeated it and 
it took 97 seconds

This is what I did:

C:\form>form sample3.frm
form sample3.frm
FORM by J.Vermaseren,version 3.0(Jan 28 2001) Run at: Thu Mar 28 
10:26:41 2002
     Symbols x,y,z;
     Local q=(1+x+y+z)^20;
     Local q1=q+1;
     Local res=q*q1;
     .end
.....
This changed program however took only
0.98 second:

C:\form>form sample7.frm
form sample7.frm
FORM by J.Vermaseren,version 3.0(Jan 28 2001) Run at: Thu Mar 28 
10:50:53 2002
     Symbols x,y,z;
     Local q2=(1+x+y+z)^20*(1+(1+x+y+z)^20);
     .end


Time =       1.04 sec    Generated terms =      14112

                q2        Terms in output =      12341

                          Bytes used      =     305378


Richard B. Kreckel wrote:

> Hi,
> 
> On Sun, 24 Mar 2002, Richard Fateman wrote:
> 
>>This seems to me to be a design that should be revisited.  For
>>the univariate case it is particularly bad since multiplying polynomials
>>of degree u and v gives you only degree u+v,  and you will have
>>allocated (u+1)*(v+1) cells.
>>
> 
> Sure.  Done now.
> 
> 
>>When this problem works on GiNaC I'd like to know its speed!
>>
> 
> Here are timings on a P-III, 1GHz, 512kB cache, running Linux, with
> approximate memory usage:
> 
> System                                               time     Memory
> --------------------------------------------------+--------+---------
> GiNaC-1.0.8 (from CVS), using GCC-3.1 prerelease:    57.3s       8MB
> MuPAD 1.4.2:                                        119.2s      25MB
> MuPAD 2.0:                                          117.0s      30MB
> Form 3.0:                                             0.5s       6MB
> Maxima 5.6 (GCL 2.4.0):                              51.0s       8MB
> MapleVR3:                                            16.7s       7MB
> MapleVR4:                                            17.9s       8MB
> MapleVR5:                                            18.4s       8MB
> Mathematica 4.1:                                     80.5s      11MB
> Reduce 3.6:                                       Segmentation Fault
> Yacas 1.0.48:            N/A (smaller examples fail to expand fully)
> 
> Richard, I noticed a mistake in the printed version of the Mathematica
> program (missing Expand[]) and the MockMMA doesn't seem right to me
> either.  Note that Form can really only do ring operations like in this
> test, but its speed there should come as no surprise.  You probably just
> cannot beat it with any more general system.
> 
> Regards
>     -richy.
>