Solve set of modular equations in C++

Question

I am working on Quadratic Sieve algorithm in c++. And after Gaussian elimination I need to solve set of modular equations such as, for example :

(1) b + c = 0 mod 2
(2) a + c = 0 mod 2

Here the symbol = is used to mean "is congruent to". I am processing matrix as shown here:https://math.stackexchange.com/questions/289348/matrix-processing-in-the-quadratic-sieve?rq=1. If anyone has any ideas how to implement such a function that will solve these equations I would appreciate it.

Answer 1

You can rewrite this system in matrix notation:

   M   . X  =  S 

|0 1 1|.|a| = |0|
|1 0 1| |b|   |0|
        |c|   

Then you solve it as usual using Gaussian elimination. The small difference is that you only work with the values 0 and 1 and that substracting a row is the same as adding the row (in Z/2Z, -a = a)