Nouvelle Cuisine for the Computation of the Annihilating Ideal of fs

• Published in: Computer Algebra in Scientific Computing pp. 162 - 173
• Main Authors: Gago-Vargas, J., Hartillo-Hermoso, M. I., Ucha-Enríquez, J. M.
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg
• Series: Lecture Notes in Computer Science
• Subjects: Compositio Math; Computer Algebra; Diagonal Form; Fourier Integral Operator; Weyl Algebra
• ISBN: 9783540289661; 3540289666
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11555964_14

Let f1,..., fp be polynomials in C[x1,..., xn] and let D = Dn be the n-th Weyl algebra. The annihilating ideal of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$f^{s}=f_{1}^{s1}...f_{p}^{sp}$\end{document} in D[s]=D[s1,...,sp] is a necessary step for the computation of the Bernstein-Sato ideals of f1,..., fp. We point out experimental differences among the efficiency of the available methods to obtain this annihilating ideal and provide some upper bounds for the complexity of its computation.