- Make sure the files main.sing, procedures.sing and sums.exe are in the same directory. - Open a DOS command prompt and go to the directory containing the files. > cd directory_name - Execute main.sing with Singular and observe the output generation. > singular main.sing - Execute sums.exe and observe the output generation. > sums - The program sums.exe assumes that $k=3$ and that the characteristic exponents are complex numbers whose real part has modulus less than or equal to $2$. See section 5 of the paper "On homogenous minimal involutive varieties" by L. C. O Almeida and S. C. Coutinho, published in the LMS Journal of Computation and Mathematics.