example
{
   "EXAMPLE:";
   echo=2;
   ring r=0,(x),lp;
   matrix A[3][4]=1,2,3,4,5,6,7,8,9,10,11,12;
   print(A);
   print(gauss_reduction(A,0));   
   print(gauss_reduction(A,1));
   matrix B[4][3]=2,3,4,-4,-6,-8,1,4,5,-3,-2,-3;
   print(B);
   print(gauss_reduction(B,0));
   print(gauss_reduction(B,1));
   matrix C[4][3]=0,0,0,0,0,0,0,0,0,0,0,0;
   print(C);
   print(gauss_reduction(C,0));
   print(gauss_reduction(C,1));
   matrix D[1][3]=0,2,3;
   print(D);
   print(gauss_reduction(D,0));
   print(gauss_reduction(D,1));
   matrix E[2][3]=0,0,1,0,1,0;
   print(E);
   print(gauss_reduction(E,0));
   print(gauss_reduction(E,1));
   matrix F[3][4]=1,0,2,3,1,0,3,4,2,0,5,3;
   print(F);
   print(gauss_reduction(F,0));
   print(gauss_reduction(F,1));
   matrix G[3][6]=1,1,0,-1,0,0,0,1,1,0,-1,0,1,0,1,0,0,-1;
   print(gauss_reduction(G,0));
   print(gauss_reduction(G,1));
   matrix H[4][8]=2,1,0,1,-1,0,0,0,3,1,1,1,0,-1,0,0,2,0,1,1,0,0,-1,0,2,1,0,1,0,0,0,-1;
   print(H);
   print(gauss_reduction(H,0));
   print(gauss_reduction(H,1));   
}