The authors describe their package MARS for solving nonlinear polynomial systems of equations, the theoretical basis behind it and implementation issues. The polynomial system is reduced to a sparse eigenvalue problem, using Sylvester/Macaulay and Bézout type matrices. In the implementation, the symbolic part of the computation is performed by MAPLE, and the numerical linear algebra and general programming tasks by MATLAB and C. The paper gives some details, on how the theoretical concepts were implemented and concludes with some examples.