Re: [Maxima-discuss] Qepmax package: interface to Qepcad

[Richard F. <fa...@be...>]

I don't know much about the implementation of Qepcad B, except from a
brief peek at the github web site.

It seems to me that it is based on an entirely different computer 
algebra system, SAC-2,
and so to use it one ends up loading another parser, a polynomial 
arithmetic package,
an arbitrary-precision arithmetic package, a display package,  and who 
knows what else.

It may be that SAC-2 is much more efficient in all of these things than 
Maxima, but that is
not at all guaranteed.   It could be that the essential part of QEPcad B 
can be coded
in Maxima's language,  or coded in Lisp, in a few pages, given that 
Maxima already
has most of the major components.  These include exact evaluation of a 
polynomial,
realroots()   which determines  root isolation intervals (using Sturm 
sequences)
and resultant().

I have personally avoided looking too closely at qe/ cad because it 
seemed to me
to be computing something I thought I didn't need, and algorithmically 
guaranteed
to be slow, and the program implementations
were being refined mostly by George Collins' students in a very 
deliberative way.

It may be, however, that there are applications appearing in tasks
involving systems of  polynomial inequalities, and that justifies the 
possibly long
computation time.

Note for example, solving  x^2-1>0  for x  is a (univariate) cylindrical 
decomposition
yielding   x<-1  or  x> 1.

We already do this with to_poly_solve(x^2-1<0,x)   which
gives %union({1<x], [x<-1])

but we  are not so clever with something like

solve( x^2+y^2>4  and x>0, [x,y])     for example.

Anyway, the thought is that some ambitious person might wish to go through
the current best practice for CAD implementation and do it in Maxima.
Assuming the underlying lisp has excellent bignum arithmetic, and the
rest of the stuff is more-or-less OK,

  I don't know if  there is any reason to believe
that SAC-2 would be a better basis than Maxima itself. I vaguely recall 
doing
some timing on SAC-2 vs. Macsyma and was surprised that SAC-2 was
not faster.  But that was probably 25 or 30 years ago.

RJF






On 4/15/2014 8:43 AM, 本田康晃 wrote:
> Hi Robert san,
> Thanks for your words.
>
> It would be great if you can try it and share with me if it works or not.
>
> Anyway, thanks and best regards,
> Yasuaki Honda
>
>
> 2014-04-15 4:52 GMT+09:00 Robert Dodier <rob...@gm... 
> <mailto:rob...@gm...>>:
>
>     On 2014-04-14, 本田康晃 <yas...@gm...
>     <mailto:yas...@gm...>> wrote:
>
>     > Qepmax package, an extension to Maxima to interface with Qepcad
>     B, is
>     > available from Github at:
>     >
>     > https://github.com/YasuakiHonda/qepmax
>
>     Yasuaki san, thank you so much! That is really terrific. We should
>     probably talk about including it in Maxima.
>
>     best
>
>     Robert Dodier
>
>
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