Primary Ideals and Their Differential Equations

Autor: Roser Homs, Yairon Cid-Ruiz, Bernd Sturmfels
Rok vydání: 2021
Předmět:
Pure mathematics
Constant coefficients
Differential equation
Polynomial ring
MathematicsofComputing_NUMERICALANALYSIS
010103 numerical & computational mathematics
Symbolic powers
Join of ideals
Commutative Algebra (math.AC)
01 natural sciences
Punctual Hilbert scheme
Mathematics - Algebraic Geometry
Mathematics - Analysis of PDEs
Primary ideals
Primary ideal
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
FOS: Mathematics
Weyl algebra
0101 mathematics
Differential operators
Algebraic Geometry (math.AG)
Mathematics
Linear partial differential equations
Ideal (set theory)
CONSTRUCTION
Mathematics::Commutative Algebra
Applied Mathematics
Mathematics - Commutative Algebra
Differential operator
Noetherian operators
Primary decomposition
Computational Mathematics
Mathematics and Statistics
Computational Theory and Mathematics
Analysis
Analysis of PDEs (math.AP)
Zdroj: FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
ISSN: 1615-3383
1615-3375
DOI: 10.1007/s10208-020-09485-6
Popis: 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.
Comment: 32 pages. To appear in Foundations of Computational Mathematics
Databáze: OpenAIRE
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