polynomials systems eat memory

roman_pearce — Fri, 15 Feb 2013 11:48:01 Z

Unfortunately solving polynomial systems tends to produce exactly this kind of blowup, and there is often little anyone can do. The algorithms generally have to conserve as much memory as possible in order to produce any solution at all

If you post the system we can try to solve it, but it could also be the case that your problem is too hard at present.

This is an area of active research so I encourage you to post the system.

Actually it is a semi-algebraic system ...

Sergio Parreiras — Thu, 21 Feb 2013 10:34:30 Z

Roman thanks a lot for your answer. First let me apologize: the Groebner package does work fine (unlike I posted previously) in the Linux cluster -- but not on my laptop :-)

The problem was with the package RegularChains that I have to use since my ultimate goal is to prove the existence of an unique real solution in the interior of (0,1)^16 (in the 16 x 16 example/case) - we economists always have to deal with constraints so localization and isolation are very important to us.

My first attempt was to generate a lex Groeber basis for the system (it takes few secs in the Linux cluster) and then fed the solution to RealRootCounting of RegularChains/SemiAlgebraicSetTools package but RealRootCounting's algorithm is very slow for my problem. After 5 days running I killed the process. Skipping second attempt story... In my final attempt, I fed the lex Grobner basis but with its first equation simplified (the solution of the 12 x 12 case tells me what roots of the 16 x 16 case are not in (0,1)^16 -- due to the specifics of the problem) to IsolateRealRoots also in the RegularChains package. It took a total of 29 secs and I got the output, which is just one box. If I understood correctly the description of the command,

"The RealRootIsolate command returns a list of boxes. Each box isolates exactly one real root of the regular chain rc or semi-algebraic system S whose polynomial equations, non-negative polynomial inequalities, (strictly) positive polynomial inequalities and polynomial inequations are given respectively by F, N, P, and H. Moreover, it is guaranteed that all real solutions are found."

having just one box means the solution exists and is unique. In the end of the story I was puzzled with the performance of RealRootCounting, with RealRootIsolate I used method='Discoverer'. RealRootCounting does not support a method option.

Thanks again!

my system

Sergio Parreiras — Sun, 17 Mar 2013 08:20:46 Z

Sometimes Maple solves a smaller version i:=4 very fast (2000 or 5000 seconds) but sometimes even the smaller version runs forever and ever - even if I askf or the same amount of resources: memory, CPU time, swap memory, processors! I am starting to suspect that are some gremlins at work...

G3.txt

MaplePrimes - answers and comments on Question, Can I trade time for memory in Maple?

polynomials systems eat memory

Actually it is a semi-algebraic system ...

my system