Compact representation of polynomials for algorithms for computing Gröbner and involutive bases

In the computation of involutive and Gröbner bases with rational coefficients, the major part of the memory is occupied by precision numbers; however, in the case of modular operations (especially, in the computation of Gröbner bases), of most importance is the problem of compact representation of monomials composing polynomials of the system. For this purpose, for example, ZDD diagrams and other structures are used, which make execution of typical operations—multiplication by a monomial and reduction of polynomials—more complicated. In this paper, an attempt is made to develop convenient (in the sense of computation of bases) and compact representation of polynomials that is based on hash-tables. Results of test runs are presented.