Some Improvements on Algebraic Representation of PDE Systems

Rosenfeld-Gröbner algorithm is a novel computational tool in the context of differential algebra which gives a full decomposition on the solution space of a partially differential equation (PDE) system. Although this algorithm has some efficiencies, there are some parts yet which need to be improved. In this paper, we figure out some crucial parts of this algorithm which need to be modified and give a new structure to this algorithm making it possible to give some improvements. Then we compare the our result by the primitive version of the algorithm to evaluate the performance of our improvements.