Involutive bases of ideals in the ring of polynomials

Involutive bases of ideals in the ring of polynomials

This paper continues the study of the relationship between Gröbner bases and involutive bases of polynomial ideals started in [1, 5]. Involutive bases are considered as Gröbner bases with some fixed normal form algorithms. It is shown that once the search order of critical pairs is coordinated, the...

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Veröffentlicht in:Programming and computer software 2000-01, Vol.26 (1), p.31-35
Hauptverfasser: Astrelin, A. V., Golubitsky, O. D., Pankratiev, E. V.
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Canonical forms
Polynomials
Rings (mathematics)
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Zusammenfassung:This paper continues the study of the relationship between Gröbner bases and involutive bases of polynomial ideals started in [1, 5]. Involutive bases are considered as Gröbner bases with some fixed normal form algorithms. It is shown that once the search order of critical pairs is coordinated, the sameS-elements and their reductions appear in the same order in the process of the construction of Gröbner bases and involutive bases.
ISSN:0361-7688
1608-3261
DOI:10.1007/BF02759177