Details:
Title  An Algorithm for Finding the Basis Elements in the Residue Class Ring Modulo a Zero Dimensional Polynomial Ideal  Author(s)  Bruno Buchberger  Type  PhD Theses  Abstract  The 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).  Length  36 
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 Language  English  Journal  Journal of Symbolic Computation  Series  Special Issue on Logic, Mathematics, and Computer Science: Interactions  Volume  41  Number  34  Pages  475511  Year  2006  Month  March  Editor  D. Kapur  Translation 
Yes  Refereed 
No  Organization 
Johannes Kepler University Linz  Institution 
RISC (Research Institute for Symbolic Computation) 
