Name
Abstract | ||
|---|---|---|
An ideal in a polynomial ring encodes a system of linear partial differential equations with constant coefficients. Primary decomposition organizes the solutions to the PDE. This paper develops a novel structure theory for primary ideals in a polynomial ring. We characterize primary ideals in terms of PDE, punctual Hilbert schemes, relative Weyl algebras, and the join construction. Solving the PDE described by a primary ideal amounts to computing Noetherian operators in the sense of Ehrenpreis and Palamodov. We develop new algorithms for this task, and we present efficient implementations. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1007/s10208-020-09485-6 | FOUNDATIONS OF COMPUTATIONAL MATHEMATICS |
Keywords | DocType | Volume |
Primary ideals, Linear partial differential equations, Noetherian operators, Differential operators, Punctual Hilbert scheme, Weyl algebra, Join of ideals, Symbolic powers | Journal | 21 |
Issue | ISSN | Citations |
5 | 1615-3375 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yairon Cid-Ruiz | 1 | 1 | 0.75 |
| Homs Roser | 2 | 0 | 0.34 |
| Bernd Sturmfels | 3 | 926 | 136.85 |