Thanks Richard but I would like to solve this one :) Thanks for your
valuable comments :)
Ahmet Alper Parker
On 5/19/07, Richard Fateman <fateman at cs.berkeley.edu> wrote:
>
> 1. Your problem is to solve a set of non-linear equations. A program
> which is claimed to be efficient for this is Singular.
> Unless there is some special structure to the solution, it will probably
> not be possible to find it in closed form, regardless of the computer
> language or hardware you use.
> 2. Exploiting parallel computing on a supercomputer is probably
> irrelevant. There are papers (indeed, whole conferences) about parallel
> algebraic computation, and parallel Grobner basis computations. There are
> some lisps that support parallel computation, but Maxima does not make
> particular use of these features because Maxima operates largely in a common
> subset of Lisp (i.e. essentially ANSI Common Lisp). But your problems
> probably take exponentially more time and space, e.g. doubling when you go
> from 28 to 29 variables; doubling again when you go from 29 to 30 ...
> 3. MockMMA will not be especially more useful than Maxima.
> 4. Translating Lisp to C++ by hand is probably pointless, since compiling
> Lisp converts it to ASSEMBLER.
>
> What's left to do? (a) discover additional structure in your problem that
> enables you to solve it. (b) choose a different problem :)
>
> RJF
>
>
> ------------------------------
> *From:* maxima-bounces at math.utexas.edu [mailto:
> maxima-bounces at math.utexas.edu] *On Behalf Of *ahmet alper parker
> *Sent:* Saturday, May 19, 2007 10:18 AM
> *To:* maxima at math.utexas.edu
> *Subject:* Re: [Maxima] ram problem
>
> Dear Richard,
> I saw MMA at your web site. I want to inform you that I have downloaded a
> copy of it. Can this be a solution to my problem? Also in future I may have
> to solve more equations than the belows like 48 unknowns in a similar
> formulation. In my university we have a supercomputer that can handle
> parallel computations, can maxima or mma or other software (instead of the
> commercial ones like mathematica, maple etc.) be compiled to do parallel
> computation? I saw that lisp is the main programming language in this field.
> If there is no parallel lisp compiler, is it possible to translate lisp code
> to c++ or equivalent to parallelize it?
> Thanks a lot all of you...
> Ahmet Alper Parker
>
>
> On 5/19/07, ahmet alper parker <aaparker at gmail.com> wrote:
> >
> > Dear Richard and Robert
> > Thanks for the wise solution. I am sending you the command I have tried
> > to solve. On cygwin I succesfully compiled maxima with clisp and it stoped
> > because of the lack of memory I do not have instead of the programs own
> > limitations. Here is the problem:
> >
> > ***************************************************************************************************************
> > algsys([
> > t/(4*A)*(b1^2*D11+a1^2*D33)=k11-k71^2/k77,
> > t/(4*A)*(b1*b2*D11+a1*a2*D33)=k21-(k72*k71)/k77,
> > t/(4*A)*(b2^2*D11+a2^2*D33)=k22-k72^2/k77,
> > t/(4*A)*(b1*b3*D11+a1*a3*D33)=k31-(k71*k73)/k77,
> > t/(4*A)*(b2*b3*D11+a2*a3*D33)=k32-(k72*k73)/k77,
> > t/(4*A)*(b3^2*D11+a3^2*D33)=k33-k73^2/k77,
> > t/(4*A)*(a1*b1*D12+a1*b1*D33)=k41-(k71*k74)/k77,
> > t/(4*A)*(a1*b2*D12+a2*b1*D33)=k42-(k72*k74)/k77,
> > t/(4*A)*(a1*b3*D12+a3*b1*D33)=k43-(k73*k74)/k77,
> > t/(4*A)*(a1^2*D22+b1^2*D33)=k44-k74^2/k77,
> > t/(4*A)*(a2*b1*D12+a1*b2*D33)=k51-(k71*k75)/k77,
> > t/(4*A)*(a2*b2*D12+a2*b2*D33)=k52-(k72*k75)/k77,
> > t/(4*A)*(a2*b3*D12+a3*b2*D33)=k53-(k73*k75)/k77,
> > t/(4*A)*(a1*a2*D22+b1*b2*D33)=k54-(k74*k75)/k77,
> > t/(4*A)*(a2^2*D22+b2^2*D33)=k55-k75^2/k77,
> > t/(4*A)*(a3*b1*D12+b3*a1*D33)=k61-(k71*k76)/k77,
> > t/(4*A)*(a3*b2*D12+b3*a2*D33)=k62-(k72*k76)/k77,
> > t/(4*A)*(a3*b3*D12+b3*a3*D33)=k63-(k73*k76)/k77,
> > t/(4*A)*(a1*a3*D22+b1*b3*D33)=k64-(k74*k76)/k77,
> > t/(4*A)*(a2*a3*D22+b2*b3*D33)=k65-(k75*k76)/k77,
> > t/(4*A)*(a3^2*D22+b3^2*D33)=k66-k76^2/k77,
> > b3*k21-b2*k31+a3*k51-a2*k61=(-k71),
> > b3*k22-b2*k32+a3*k52-a2*k62=(-k72),
> > b3*k23-b2*k33+a3*k53-a2*k63=(-k73),
> > b3*k24-b2*k34+a3*k54-a2*k64=(-k74),
> > b3*k25-b2*k35+a3*k55-a2*k65=(-k75),
> > b3*k26-b2*k36+a3*k56-a2*k66=(-k76),
> > b3*k27-b2*k37+a3*k57-a2*k67=(-k77)
> > ],[
> >
> > k11,k21,k22,k31,k32,k33,k41,k42,k43,k44,k51,k52,k53,k54,k55,k61,k62,k63,k64,k65,k66,k71,k72,k73,k74,k75,k76,k77
> > ])
> > ***************************************************************************************************************
> >
> > How should I approach the solution? What should I do in this case? If
> > there is a reading about efficient computation of the same problem on
> > maxima, can you drop a link?
> > Thanks a lot :)
> > Ahmet Alper Parker
> >
> >
> > On 5/19/07, Robert Dodier <robert.dodier at gmail.com > wrote:
> > >
> > > On 5/19/07, Richard Fateman <fateman at cs.berkeley.edu> wrote:
> > >
> > > > Without further analysis, it is hard to know, but it may simply be
> > > the case
> > > > that having 2X or 4X the RAM available will not be enough
> > > either. The wrong
> > > > approach can put you on a path where the solution takes exponential
> > > memory
> > > > in the size of the input.
> > >
> > > Agreed 100% here. Just increasing the memory may very well
> > > mean it just takes more time before running into the same error.
> > >
> > > It would help a lot to know more about the details of the problem.
> > >
> > > Robert
> > >
> >
> >
>