20050921, 18:13  #1 
May 2003
7×13×17 Posts 
Mathematica questionsolving systems
I'm working on a problem that involves 60 variables. In these variables, I have tons and tons of polynomial equations. (For example, k_20 k_10k_30 k_1=0.) I'd like to use Mathematica to simultaneously solve them, but just due to the sheer number of equations I have it would take more than the lifetime of the universe if I try to do it using "Solve". Is there anything else I could try, or is this intractable? (Note: I'm only interested in integer solutions to these equations.)

20050921, 18:59  #2  
Nov 2003
16444_{8} Posts 
Quote:
a Grobner Basis? You might approach the problem that way. Sorry, but I know very little about the methodology. 

20050921, 23:28  #3 
"Kyle"
Feb 2005
Somewhere near M52..
915_{10} Posts 
ZetaFlux, I would try emailing Dr. Math. He and his staff are extremely knowledgeable on a wide range of math fields and can probably answer your question. Their service is free, however you will have to wait 12 weeks for a reply (if you get one at all) since they operate on their free time. If a method to solve your problem more effeciently exists, they'll probably be able to tell you. Before you send an email however I would check the FAQ on their site to see if someone else has posed a similar question previously. Here is the site if you're interested.
http://mathforum.org/dr.math/ Good luck. Primeinator 
20050921, 23:44  #4 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
>(For example, k_20 k_10k_30 k_1=0.)
Out of curiosity (sadly, it's not like I knew anything about how to solve this problem), are all the coefficients of your polynomials +1 or 0? Is the constant term always 0? Alex 
20050922, 02:05  #5 
May 2003
7·13·17 Posts 
akruppa,
If only! I do realize that if all the constant terms were 0 then there would be a trivial solution and life would be dandy. :) HOWEVER, in fact only ONE of the equations has a nonzero constant term (and the constant is 1). The coefficients are limited to 0,1,2,1, and 2 (however, it might be the case that the 2's can be factored out...I haven't looked at that yet).  R.D. Silverman, I actually don't have to use Mathematica. That's just the only program I have. I'm willing to send the equations to someone who has a program that can solve them for me. I don't know if Mathematica handles Grobner bases.  Primeinator, Time until a response isn't an issue. But neither is understanding HOW to solve the system. What I need is some program to do it for me in an efficient way. Cheers, Pace 
20050922, 05:29  #6 
Dec 2003
Hopefully Near M48
2·3·293 Posts 
I have found that Mathematica is far slower than some other computer programs, probably because it's a "high level language" and is designed to handle a very broad variety of calculations. (You can see my thread in the Programming forum). You could probably get several orders of magnitude improvement by using languages like C++, but that is of course far less userfriendly.

20050922, 21:47  #7 
May 2003
11000001011_{2} Posts 
Okay, slightly different question. Is there a way to have Mathematica look for solutions only in F_2 (i.e. the finite field with two elements)? For the problem I'm looking at, this should actually work for me.

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