The solving degrees for computing Gr\"{o}bner bases of affine semi-regular polynomial sequences

arXiv:2404.03530v1 Announce Type: cross
Abstract: Determining the complexity of computing Gr\"{o}bner bases is an important problem both in theory and in practice, and for that the solving degree plays a key role. In this paper, we study the solving degrees of affine semi-regular sequences and their homogenized sequences. Some of our results are considered to give mathematically rigorous proofs of the correctness of methods for computing Gr\"{o}bner bases of the ideal generated by an affine semi-regular sequence. This paper is …

arxiv complexity computing cs.cr cs.sc important key math.ag practice problem regular role semi study theory