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:
- There are $m^2$ variables.
- Every variable appears in exactly 7 equation.
- Every equation contains at most 3 variables.
- The coefficient of the variables is always 1.
- 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).
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.