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Projecting dynamical systems via a support bound
Yulia Mukhina, Gleb Pogudin
For a polynomial dynamical system, we study the problem of computing the minimal differential equation satisfied by a chosen coordinate (in other words, projecting the system on th…
Simple generators of rational function fields
Alexander Demin, Gleb Pogudin
Consider a subfield of the field of rational functions in several indeterminates. We present an algorithm that, given a set of generators of such a subfield, finds a simple generat…
Quadratization of Autonomous Partial Differential Equations: Theory and Algorithms
Albani Olivieri, Gleb Pogudin, Boris Kramer
Quadratization for partial differential equations (PDEs) is a process that transforms a nonquadratic PDE into a quadratic form by introducing auxiliary variables. This symbolic tra…
Support bound for differential elimination in polynomial dynamical systems
Yulia Mukhina, Gleb Pogudin
We study an important special case of the differential elimination problem: given a polynomial parametric dynamical system and…
Discovering Polynomial and Quadratic Structure in Nonlinear Ordinary Differential Equations
Boris Kramer, Gleb Pogudin
Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, an…
Persistent components in Canny's Generalized Characteristic Polynomial
Gleb Pogudin
When using resultants for elimination, one standard issue is that the resultant vanishes if the variety contains components of dimension larger than the expected dimension. J. Cann…