119 citations · 269 across the 38 of their papers we have counts for
8 papers · 1 filter
Wronskians form the inverse system of the arcs of a double point
Rida Ait El Manssour, Gleb Pogudin
The ideal of the arc scheme of a double point or, equivalently, the differential ideal generated by the ideal of a double point is a primary ideal in an infinite-dimensional polyno…
From algebra to analysis: new proofs of theorems by Ritt and Seidenberg
Dmitrii Pavlov, Gleb Pogudin, Yury Razmyslov
Ritt's theorem of zeroes and Seidenberg's embedding theorem are classical results in differential algebra allowing to connect algebraic and model-theoretic results on nonlinear PDE…
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 …
Primitive Element Theorem for Fields with Commuting Derivations and Automorphisms
Gleb Pogudin
We establish a Primitive Element Theorem for fields equipped with several commuting operators such that each of the operators is either a derivation or an automorphism. More precis…
Products of Ideals and Jet Schemes
Gleb Pogudin
In the present paper, we give a full description of the jet schemes of the polynomial ideal over a field of zero characterist…
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…