The algorithm for distributed calculating Gr¨obner or involutive bases of polynomial ideals

In this paper, a new distributed computing method is proposed for finding Gr¨obner and involutive bases. A key innovation is the adaptation of a peerto-peer network to distribute computing between multiple nodes, which allows to use a set of less powerful computers instead of high-performance servers or cloud services. This approach is especially valuable for researchers who do not have access to supercomputers. The distribution of the process, in which each node processes a certain polynomial and its combinations, effectively prevents duplication of calculations. Although the effectiveness of the proposed system requires further analysis, it already demonstrates significant potential in simplifying the calculation of bases. In addition, our work highlights the advantages of the involutive division method implemented in the GInv system, which showed higher speed in tests compared to traditional algorithms.