FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 4, PAGES 121-135

One-element differential standard bases with respect to inverse lexicographical orderings

A. I. Zobnin

Abstract

View as HTML     View as gif image

We give a simplified proof of the following fact: for all nonnegative integers $n$ and $d$ the monomial $y$_n^d forms a differential standard basis of the ideal $[y$_n^d]. In contrast to Levi's combinatorial proof, in this proof we use the Gröbner bases technique. Under some assumptions we prove the converse result: if an isobaric polynomial $f$ forms a differential standard basis of $[f]$, then $f=y$_n^d.

Location: http://mech.math.msu.su/~fpm/eng/k08/k084/k08407h.htm
Last modified: February 26, 2009