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Historical background to Gröbner's paper

Historical background to Gröbner's paper ACM Communications in Computer Algebra, Issue 168, Vol. 43, No. 2, June 2009 Historical Background to Gr bner ™s Paper o Michael P. Abramson In his 1965 Ph.D. thesis [2], Bruno Buchberger invented the algebraic object known today as a Gr bner basis. o The thesis problem that Buchberger was given by his advisor, Wolfgang Gr bner, was that of nding a basis of the o residue class ring of a zero-dimensional polynomial ideal. It is clear that Gr bner knew generally of a method for computing this [1], and indeed the last paragraph of o Gr bner ™s 1950 paper [3] reads (in translation) o For about 17 years, I have applied and tested these methods in the most varied and complicated cases, and I believe I can say, on the basis of my experiences, that they in fact represent a useful and valuable tool for the solution of these and similar ideal theoretic tasks in every case. Because I have often been asked how one can most easily nd the reduced representation of a polynomial ideal, I have now decided to publish the essential features of these methods, omitting the details. The paper appearing here in http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM SIGSAM Bulletin Association for Computing Machinery

Historical background to Gröbner's paper

Abramson, Michael P.
ACM SIGSAM Bulletin , Volume 43 (1/2) – Sep 9, 2009
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References (5)

Publisher
Association for Computing Machinery
Copyright
The ACM Portal is published by the Association for Computing Machinery. Copyright © 2010 ACM, Inc.
Subject
Theory
ISSN
0163-5824
DOI
10.1145/1610296.1610301
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Abstract

ACM Communications in Computer Algebra, Issue 168, Vol. 43, No. 2, June 2009 Historical Background to Gr bner ™s Paper o Michael P. Abramson In his 1965 Ph.D. thesis [2], Bruno Buchberger invented the algebraic object known today as a Gr bner basis. o The thesis problem that Buchberger was given by his advisor, Wolfgang Gr bner, was that of nding a basis of the o residue class ring of a zero-dimensional polynomial ideal. It is clear that Gr bner knew generally of a method for computing this [1], and indeed the last paragraph of o Gr bner ™s 1950 paper [3] reads (in translation) o For about 17 years, I have applied and tested these methods in the most varied and complicated cases, and I believe I can say, on the basis of my experiences, that they in fact represent a useful and valuable tool for the solution of these and similar ideal theoretic tasks in every case. Because I have often been asked how one can most easily nd the reduced representation of a polynomial ideal, I have now decided to publish the essential features of these methods, omitting the details. The paper appearing here in

Journal

ACM SIGSAM Bulletin – Association for Computing Machinery

Published: Sep 9, 2009

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