1999/12/04 by Vladimir P. Gerdt, Gerdt, Vladimir P.
Computer Science · Engineering · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Commutative Algebra (math.AC) #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical Analysis (math.NA) #Polynomial and algebraic computation #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.math/9912030
openalex publication_date 1999/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, in addition to the earlier introduced involutive divisions, we consider a new class of divisions induced by admissible monomial orderings. We prove that these divisions are noetherian and constructive. Thereby each of them allows one to compute an involutive Groebner basis of a polynomial ideal by sequentially examining multiplicative reductions of nonmultiplicative prolongations. We study dependence of involutive algorithms on the completion ordering. Based on properties of particular involutive divisions two computational optimizations are suggested. One of them consists in a special choice of the completion ordering. Another optimization is related to recomputing multiplicative and nonmultiplicative variables in the course of the algorithm.