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TitleAn Algorithm for Finding the Basis Elements in the Residue Class Ring Modulo a Zero Dimensional Polynomial Ideal
Author(s) Bruno Buchberger
TypePhD Theses
AbstractThe residue class ring of a zero dimensional polynomial ideal in K[x1, . . . , xn] has the structure of an algebra with finitely many basis elements. In the present work, an algorithm for enabling the computation of these basis elements from the generating polynomials of a polynomial ideal, which was provided by Professor Wolfgang Gröbner during his research seminar in the spring of 1964, will be studied more closely. The goal of studying this algorithm has is to find a termination criterion for the algorithm (Sections 4 and 8), and to sufficiently systematize it so that it is suitable for implementation on an electronic computer (Sections 4, 6, and 9). Certain inherent properties will also be presented, which suggest an application to the calculation of the Hilbert function of an arbitrary polynomial ideal (Sections 5 and 7).
JournalJournal of Symbolic Computation
SeriesSpecial Issue on Logic, Mathematics, and Computer Science: Interactions
EditorD. Kapur
Translation Yes
Refereed No
Organization Johannes Kepler University Linz
Institution RISC (Research Institute for Symbolic Computation)