Singular

 Page 1 of 1 [ 3 posts ]
 Print view | E-mail friend Previous topic | Next topic
Author Message
 Post subject: Gröbner complexity.Posted: Mon Mar 13, 2017 8:21 am
I have a question. I am aware that the complexity of Gröbner bases is not very well understood in practice, theoretical results apart.

I have this ideal with 21 polynomials, 16 variables. Degrees are: 5, 7, 7, 8, 10, 11, 14, 14, 15, 15, 18, 19, 19, 19, 23, 23, 23, 27, 27, 31, 31.

I have 10 nodes, 128 GB of RAM each, available to me. How much time should it take to calculate the Gröbner basis with modStd ? I need only an approximate idea. Gave it 7,000 hours of computer time. Will that be enough? The system is 14.1 MB in size. It comes from quantum chemistry.

Top

 Post subject: Re: Gröbner complexity.Posted: Mon Mar 13, 2017 3:25 pm

Joined: Thu Mar 04, 2010 1:29 pm
Posts: 14
You can first try to compute a Gröbner basis in positive characteristic, using a ring definition like
Code:
ring r = 32003, x(1..16), dp;

or something similar. You can also switch on
Code:
option(prot);

see http://www.singular.uni-kl.de/Manual/latest/sing_307.htm.

If this computation doesn't finish, then trying modStd() will be hopeless. If it finishes, then you have good chances that modStd() will finish as well.

Given the data you mentioned (21 polynomials in 16 variables of degree up to 31 and size 14.1 MB), the system seems to be quite complicated, but you can still try.

Top

 Post subject: Re: Gröbner complexity.Posted: Thu Mar 16, 2017 2:26 am
14.1 MB was the size of the system after interred(). I inserted 12 more relations and 12 new variables, did interred(again), and the size of the system became "only" 422 KB. That gives me hope. I have given 7,000 hours to the calculation, in a computer of 10 nodes, 128 GB RAM each, so I hope for the best.

The system comes, as I said, from quantum chemistry. Turned one single differential equation into a system of polynomial equations.

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 3 posts ]

 You can post new topics in this forumYou can reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

 It is currently Sun Oct 21, 2018 10:54 am
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group