33 citations · 74 across the 6 of their papers we have counts for
6 papers
A bound for a typical differential dimension of system of linear differential equations
Marina Kondratieva
We prove upper and lower bounds for leading coefficient of Kolchin dimension polynomial of systems of partial linear differential equations in codimension two.
New effective differential Nullstellensatz
Richard Gustavson, Marina Kondratieva, Alexey Ovchinnikov
We show new upper and lower bounds for the effective differential Nullstellensatz for differential fields of characteristic zero with several commuting derivations. Seidenberg was…
On the generalised Ritt problem as a computational problem
Oleg Golubitsky, Marina Kondratieva, Alexey Ovchinnikov
The Ritt problem asks if there is an algorithm that tells whether one prime differential ideal is contained in another one if both are given by their characteristic sets. We give s…
A Bound for Orders in Differential Nullstellensatz
Oleg Golubitsky, Marina Kondratieva, Alexey Ovchinnikov +1
We give the first known bound for orders of differentiations in differential Nullstellensatz for both partial and ordinary algebraic differential equations. This problem was previo…
Bounds for algorithms in differential algebra
Oleg Golubitsky, Marina Kondratieva, Marc Moreno Maza +1
We consider the Rosenfeld-Groebner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n inde…
On Computation of Kolchin Characteristic Sets: Ordinary and Partial Cases
Marina Kondratieva, Alexey Ovchinnikov
In this paper we study the problem of computing a Kolchin characteristic set of a radical differential ideal. The central part of the article is the presentation of algorithms solv…