Elementary differentals, their graphs and codes

Many tens or hundreds of elementary differentials must be taken into account in constructing one-step numerical methods for solving ODE (like Runge–Kutta methods, Rosenbrock methods, ABC-schemes) of high order accuracy. Their graphical representation in use nowadays does not allow to computerize the huge amount of manual labor. We propose a simple and intuitive way for digital encoding of them and algorithms for generation, analysis and synthesis of these codes. These algorithms are implemented in a computer program that computes tables of codes for elementary differentials up to arbitrary order, together with their multiplicities and gamma-factors.