1
$\begingroup$

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).

  • 0
    You will get more comprehensive replies for such questions @ scicomp.stackexchange.com.2012-02-08

1 Answers 1

1

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.

  • 0
    (1) [Squarizer](http://www.linalg.org/linbox-html/class_lin_box_1_1_squarize.html) can handle rectangular matrices (2) IIRC LinBox supports small finite field through the field type [](http://www.linalg.org/linbox-html/field_2modular_8h.html). To find out more, you should post your problem to [LinBox users group](http://groups.google.com/group/linbox-use).2012-01-10