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:

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 <robert.dodier@gmail.com>:

On 2014-04-14, 本田康晃 <yasuaki.honda@gmail.com> wrote:Yasuaki san, thank you so much! That is really terrific. We should

> Qepmax package, an extension to Maxima to interface with Qepcad B, is

> available from Github at:

>

> https://github.com/YasuakiHonda/qepmax

probably talk about including it in Maxima.

best

Robert Dodier

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