TY - GEN
T1 - Support Bound for Differential Elimination in Polynomial Dynamical Systems
AU - Mukhina, Yulia
AU - Pogudin, Gleb
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.
PY - 2026/1/1
Y1 - 2026/1/1
N2 - We study an important special case of the differential elimination problem: given a polynomial parametric dynamical system x′=g(μ,x) and a polynomial observation function y=f(μ,x), find the minimal differential equation satisfied by y. In our previous work [29], for the case y=x1, we established a bound on the support of such a differential equation for the non-parametric case and showed that it can be turned into an algorithm via the evaluation-interpolation approach. The main contribution of the present paper is a generalization of the aforementioned result in two directions: to allow any polynomial function y=f(x), not just a single coordinate, and to allow g and f to depend on unknown symbolic parameters. We conduct computation experiments to evaluate the accuracy of our new bound and show that the approach allows to perform elimination for some cases out of reach for the state of the art software.
AB - We study an important special case of the differential elimination problem: given a polynomial parametric dynamical system x′=g(μ,x) and a polynomial observation function y=f(μ,x), find the minimal differential equation satisfied by y. In our previous work [29], for the case y=x1, we established a bound on the support of such a differential equation for the non-parametric case and showed that it can be turned into an algorithm via the evaluation-interpolation approach. The main contribution of the present paper is a generalization of the aforementioned result in two directions: to allow any polynomial function y=f(x), not just a single coordinate, and to allow g and f to depend on unknown symbolic parameters. We conduct computation experiments to evaluate the accuracy of our new bound and show that the approach allows to perform elimination for some cases out of reach for the state of the art software.
KW - Differential elimination
KW - Evaluation-interpolation
KW - Newton polytope
KW - Polynomial dynamical system
UR - https://www.scopus.com/pages/publications/105021804382
U2 - 10.1007/978-3-032-09645-6_15
DO - 10.1007/978-3-032-09645-6_15
M3 - Conference contribution
AN - SCOPUS:105021804382
SN - 9783032096449
T3 - Lecture Notes in Computer Science
SP - 265
EP - 285
BT - Computer Algebra in Scientific Computing - 27th International Workshop, CASC 2025, Proceedings
A2 - Boulier, François
A2 - Mou, Chenqi
A2 - Sadykov, Timur M.
A2 - Vorozhtsov, Evgenii V.
PB - Springer Science and Business Media Deutschland GmbH
T2 - 27th International Workshop on Computer Algebra in Scientific Computing, CASC 2025
Y2 - 24 November 2025 through 28 November 2025
ER -