Given m = 385, I have a linear equation system over a field 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 3 x = 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).

Question

Given   m  =  385, I have a linear equation system over a field             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   3  x  =  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 (&quot;Error allocating matrix&quot;). 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).

Giovani Hickman · Accepted Answer

Since you have constant number of non-zero entries per row, your system is fit for iterative methods, namely in finite fields case: Wiedemann&#039;s algorithm.

Given m = 385 , I have a linear equation system over a field <mrow class="MJX-T

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