On 2013-08-14, andre maute <andre.maute at gmx.de> wrote:
> On 08/14/2013 01:29 AM, Richard Fateman wrote:
>> On 8/13/2013 1:57 PM, andre maute wrote:
>>> Hi list,
>>>
>>> I am not really satisfied with algsys for solving/simplifying
>>> polynomial equations.
>>> I have a set of polynomial equations (40 variables, 70 equations,
>>> degree 4).
this is usually rather hopeless to attempt solving nonlinear systems
with 40 variables. You got lucky here: a good groebner basis
implementation was able to derive a contradiction from your equations
quickly, without chocking.
>>> I canceled Maxima after 10 hours of computation.
>>> This was on a recent machine, with 16 Gb given for the heap to sbcl.
>>> Then I extracted the polynomial set of equations, put it in a script
>>> for Macaulay2,
>>> and the dim command of Macaulay told me, within some seconds, that
>>> there were no solutions.
>>>
>>> Question:
>>> Does somebody know, if there is some functionality available,
>>> for calling Macaulay or e.g. Singular within Maxima?
>>
>> There seem to be several possibilities here:
>>
>> 1. The algorithm used by Singular could used by Maxima by recoding in
>> the Maxima language
>> or in Lisp. (It could be that the data structures etc are so foreign
>> to Lisp that it can't be done,
>> but that seems somewhat unlikely.) A difference of more than 10 hours
>> vs. some seconds
>> suggests they are just doing different computations entirely.
Singular has a C library API. Sage uses this.
Coding this stuff in Lisp or Maxima langauge (or any language) is not easy.
>>
>> 2. There could be a linkage to Macaulay2, if it can be called via a
>> foreign function (FF) call
>> (possible from SBCL if there is a suitable connection into
>> Macaulay2). Most lisps though
>> not GCL support FF).
>>
>> I think there is the functionality but taking advantage of it requires
>> finding someone
>> who knows more about SBCL and Macaulay and FF . Maybe you??
> I only know how to set the ring and the ideal in Macaulay and how to
> call some commands,
> I believe this should be done by someone, who is more trained in
> algebraic/arithmetic geometry.
there is also option 3:
use Sage, where you can easily go between Maxima and Singular.
(although Macaulay2 is sometimes more efficient than Singular).
>
> Andre