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