Mathematica question-solving systems

Zeta-Flux · 2005-09-21, 18:13

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_10-k_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.)

R.D. Silverman · 2005-09-21, 18:59

Quote:

Originally Posted by Zeta-Flux

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_10-k_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.)

Does Mathematica have a capability or external package to handle
a Grobner Basis? You might approach the problem that way. Sorry,
but I know very little about the methodology.

Primeinator · 2005-09-21, 23:28

Zeta-Flux, 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 1-2 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

akruppa · 2005-09-21, 23:44

>(For example, k_20 k_10-k_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

Zeta-Flux · 2005-09-22, 02:05

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 non-zero 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

jinydu · 2005-09-22, 05:29

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 user-friendly.

Zeta-Flux · 2005-09-22, 21:47

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.

2005-09-21, 18:13	#1
Zeta-Flux May 2003 7×13×17 Posts	Mathematica question-solving 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_10-k_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.)

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2005-09-21, 23:28	#3
Primeinator "Kyle" Feb 2005 Somewhere near M52.. 393₁₆ Posts	Zeta-Flux, 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 1-2 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

2005-09-21, 23:44	#4
akruppa "Nancy" Aug 2002 Alexandria 4643₈ Posts	>(For example, k_20 k_10-k_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

2005-09-22, 02:05	#5
Zeta-Flux May 2003 11000001011₂ 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 non-zero 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

2005-09-22, 05:29	#6
jinydu 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 user-friendly.

2005-09-22, 21:47	#7
Zeta-Flux May 2003 7×13×17 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.