2010/01/08 by Xiaoying Wang, Wang, Xiaoying, Shugong Zhang +3
Computer Science · Engineering · #12Y05 #13P10 #65D05 #Advanced Numerical Analysis Techniques #Commutative Algebra (math.AC) #Cryptography and Residue Arithmetic #FOS: Mathematics #Numerical Analysis (math.NA) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1001.1186
openalex publication_date 2010/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For the last almost three decades, since the famous Buchberger-Möller(BM) algorithm emerged, there has been wide interest in vanishing ideals of points and associated interpolation polynomials. Our paradigm is based on the theory of bivariate polynomial interpolation on cartesian point sets that gives us related degree reducing interpolation monomial and Newton bases directly. Since the bases are involved in the computation process as well as contained in the final output of BM algorithm, our paradigm obviously simplifies the computation and accelerates the BM process. The experiments show that the paradigm is best suited for the computation over finite prime fields that have many applications.