Title：Characteristic Decomposition: Connecting Lexicographic Groebner Bases and Triangular Sets
Speaker： Chenqi Mou（Beihang University）
Time&Venue： 2021.11.15 13:30-14:30，N420
Abstract： Lexicographic Groebner bases and triangular sets are standard tools in computational elimination theory. In this talk, I will first present new results on the intrinsic structures of lexicographic Greobner bases and the relations between lexicographic Groenber bases and the minimal triangular sets contained in them called W-characteristic sets. Then I introduce the concept of characteristic pair consisting of a reduced lexicographic Groebner basis and its W-characteristic set. The decomposition from any polynomial set into finitely many characteristic pairs with associated ideal and zero relations is called characteristic decomposition, and it provides representations of the ideal generated by the polynomial set in terms of Groebner bases and triangular sets simultaneously. Basic properties of the decomposition and the resulting characteristic pairs, in particular the relationships between the Groebner basis and W-characterisitic set in each pair, will also be presented. This talk is based on the joint work with Dongming Wang and Rina Dong.