119 citations · 638 across the 44 of their papers we have counts for
21 papers · 1 filter
Algorithms yield upper bounds in differential algebra
Wei Li, Alexey Ovchinnikov, Gleb Pogudin +1
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic o…
Elimination of unknowns for systems of algebraic differential-difference equations
Wei Li, Alexey Ovchinnikov, Gleb Pogudin +1
We establish effective elimination theorems for differential-difference equations. Specifically, we find a computable function of the natural number parameters and …
Corrigendum: 'On bounds for the effective differential Nullstellensatz, arXiv:1508.07508'
Omar Leon Sanchez, Alexey Ovchinnikov
We correct a small gap found in the authors' paper 'On bounds for the effective differential Nullstellensatz' (J Algebra 449:1-21, 2016). This gap is due to an inequality that does…
Bounds for elimination of unknowns in systems of differential-algebraic equations
Alexey Ovchinnikov, Gleb Pogudin, N. Thieu Vo
Elimination of unknowns in systems of equations, starting with Gaussian elimination, is a problem of general interest. The problem of finding an a priori upper bound for the number…
New order bounds in differential elimination algorithms
Richard Gustavson, Alexey Ovchinnikov, Gleb Pogudin
We present a new upper bound for the orders of derivatives in the Rosenfeld-Groebner algorithm. This algorithm computes a regular decomposition of a radical differential ideal in t…
On bounds for the effective differential Nullstellensatz
Omar León Sánchez, Alexey Ovchinnikov
Understanding bounds for the effective differential Nullstellensatz is a central problem in differential algebraic geometry. Recently, several bounds have been obtained using Dicks…