Programming and Computer Software

, Volume 33, Issue 3, pp 139–146 | Cite as

Involutive divisions and monomial orderings

  • A. S. Semenov
  • P. A. Zyuzikov


In the paper, two classes of involutive divisions related to admissible monomial orderings—≻-divisions and ≺-divisions—are considered. The latter may be viewed as an improvement of the class of induced divisions introduced in [1]. The continuity and constructivity of the ≺-divisions, as well as a number of additional properties of the ≻-divisions, are proved. Taking into account that the Janet division is a ≻-division associated with the lexicographical order, its “antipode”—a ≺-division associated with the same order—is separated in the class of the ≺-divisions.


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Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  • A. S. Semenov
    • 1
  • P. A. Zyuzikov
    • 1
  1. 1.Department of Mechanics and MathematicsMoscow State UniversityLeninskie gory, MoscowRussia

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