2013/12/02 by Abhishek Dubey, Dubey, Abhishek, Ambedkar Dukkipati +1
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Commutative Algebra and Its Applications #Polynomial and algebraic computation #cs.SC
paper · pdf · doi:10.48550/arxiv.1312.0453
15 pages, 8 sections and 3 algorithms
arxiv created 2013/12/28 · arxiv updated 2013/12/31
In this paper, we extend the idea of comprehensive Gröbner bases given by Weispfenning (1992) to border bases for zero dimensional parametric polynomial ideals. For this, we introduce a notion of comprehensive border bases and border system, and prove their existence even in the cases where they do not correspond to any term order. We further present algorithms to compute comprehensive border bases and border system. Finally, we study the relation between comprehensive Gröbner bases and comprehensive border bases w.r.t. a term order and give an algorithm to compute such comprehensive border bases from comprehensive Gröbner bases.