FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2003, VOLUME 9, NUMBER 3, PAGES 199-212

Pair analysis of involutive divisions

A. S. Semenov

Abstract

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The main goal of this work is to describe a new approach to the study of involutive divisions using the pairwise property. The paper presents a simple and intuitive method for constructing the Janet division and reveals the deep intrinsic relationship between Janet division and $Lex$-ordering. A method for constructing some analogues of the Janet division for other orders is described. An example of pairwise, continuous, and nonconstructive involutive division is given.

Location: http://mech.math.msu.su/~fpm/eng/k03/k033/k03314h.htm.
Last modified: September 24, 2004.