I. Made Sulandra, Gamal Abdul Aziz
The strong Grabner bases over principal ideal ring R can be calculated efficiently using the factoring method with canonical projections R → R/nR, n ≠ 0 and ring isomorphism R → R1 × R2. This paper presents a modification of the method by using the F4 algorithm as the semi-core calculation and its comparison with the original method written by Eder and Hofmann, to see that the use of the F4 algorithm as the semi-core calculation is more efficient in the case of calculating strong Grabner bases on polynomial-large polynomial. Experimental data show that the implementation of the F4 algorithm has a much shorter computation time in the large ideal case, but this is inversely proportional to the implementation of the Buchberger algorithm, where in calculating the Grabner basis strong on small ideals, this algorithm runs with shorter computation times. © 2024 Author(s).
Departement of Mathematics, Mathematics and Natural Science Faculty, Universitas Negeri Malang, Malang, Indonesia