Involutive divisions and monomial orderings
A. S. Semenov, P. A. Zyuzikov · Programming and Computer Software · 2007
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.