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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Structure of Gröbner bases with respect to block orders
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by M’Hammed El Kahoui and Said Rakrak PDF
Math. Comp. 76 (2007), 2181-2187 Request permission

Abstract:

In this paper we study the structure of Gröbner bases with respect to block orders. We extend Lazard’s theorem and the Gianni-Kalkbrenner theorem to the case of a zero-dimensional ideal whose trace in the ring generated by the first block of variables is radical. We then show that they do not hold for general zero-dimensional ideals.
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Additional Information
  • M’Hammed El Kahoui
  • Affiliation: Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany
  • Address at time of publication: Department of Mathematics, Faculty of Sciences Semlalie, Cadi Ayyad University, P.O. Box 2390, Marrakech, Morocco
  • Email: elkahoui@mpi-sb.mpg.de
  • Said Rakrak
  • Affiliation: Department of Mathematics and Computer Science, Faculty of Sciences and Techniques, Cadi Ayyad University, P.O. Box 549 Marrakech, Morocco
  • Email: rakrak@fstg-marrakech.ac.ma
  • Received by editor(s): October 28, 2004
  • Received by editor(s) in revised form: March 22, 2006
  • Published electronically: April 17, 2007
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 76 (2007), 2181-2187
  • MSC (2000): Primary 13P10, 12Y05
  • DOI: https://doi.org/10.1090/S0025-5718-07-01972-2
  • MathSciNet review: 2336290