Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Given $m=385$, I have a linear equation system over a field $\mathbb{F}_p$ with $p$ a small prime (could be 5,7,11, something like this) with the following properties:

  1. There are $m^2$ variables.
  2. Every variable appears in exactly 7 equation.
  3. Every equation contains at most 3 variables.
  4. The coefficient of the variables is always 1.
  5. The free term in the equations are always 0, with one specific equation (an equation of the form $3x=1$ for a specific variable $x$).

I am currently using SAGE. It solved nicely smaller equation systems, but this one killed it, even when constructing the matrix as sparse ("Error allocating matrix"). The question is - should I simply try a better (and less convenient) sparse matrix handling package, or is there a better way to deal with such sparse systems of equations? (I can do a little programming myself if needed).

share|cite|improve this question
You will get more comprehensive replies for such questions @ – Inquest Feb 8 '12 at 15:45

Since you have constant number of non-zero entries per row, your system is fit for iterative methods, namely in finite fields case: Wiedemann's algorithm. Check out LinBox library. As for convenience, AFAIK LinBox is included in SAGE.

share|cite|improve this answer
Thank you! This seems very promising. – Gadi A Jan 9 '12 at 16:17
It seems there are two problems here. First, the algorithm is for square matrices, and mine isn't; second, the algorithm is not supposed to work well in small finite fields, which is exactly the case I'm dealing with. – Gadi A Jan 10 '12 at 9:56
(1) Squarizer can handle rectangular matrices (2) IIRC LinBox supports small finite field through the field type <Modular>. To find out more, you should post your problem to LinBox users group. – user2468 Jan 10 '12 at 14:20

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.