compatibility among big number of (linear) equations

[Davide Alessio <lists4davide@gmail.com>]

Hi,
I have a (quite big) set of variables and their values (generated randomly).
I need to know if they respect few conditions.

a_{i,j} \in {0,1};  for i \in {0, ..., 80}
                    for j \in {0, ..., 32}

the same for b, ..., f.

and some conditions as b_{31,3} \neq 0 and so on.

I would like to use libpari. I tought about matsolve (gauss()) function, but I 
would need a invertible matrix...

Any suggestion?