Journal of Formalized Mathematics
Volume 14, 2002
University of Bialystok
Copyright (c) 2002 Association of Mizar Users

Term Orders


Christoph Schwarzweller
University of Tuebingen

Summary.

We continue the formalization of [5] towards Gr\"obner Bases. Here we deal with term orders, that is with orders on bags. We introduce the notions of head term, head coefficient, and head monomial necessary to define reduction for polynomials.

MML Identifier: TERMORD

The terminology and notation used in this paper have been introduced in the following articles [18] [16] [22] [23] [1] [10] [24] [7] [8] [3] [2] [12] [20] [17] [4] [6] [9] [11] [25] [14] [13] [19] [21] [15]

Contents (PDF format)

  1. Preliminaries
  2. Term Orders
  3. Head Terms, Head Monomials, and Head Coefficients
  4. Reductum of a Polynomial

Acknowledgments

I'd like to thank Piotr Rudnicki for valuable discussions on how to represent term orders in Mizar.

Bibliography

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Received December 20, 2002

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