About: Loewy decomposition

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Loewy decomposition Goto Sponge NotDistinct Permalink

An Entity of Type : yago:WikicatDifferentialEquations, within Data Space : dbpedia.org associated with source document(s)
QRcode icon

In the study of differential equations, the Loewy decomposition breaks every linear ordinary differential equation (ODE) into what are called largest completely reducible components. It was introduced by Alfred Loewy. Loewy's results have been extended to linear partial differential equations (PDEs) in two independent variables. In this way, algorithmic methods for solving large classes of linear PDEs have become available.

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Communication100033020 yago:DifferentialEquation106670521 yago:Equation106669864 yago:MathematicalStatement106732169 yago:Message106598915 yago:Statement106722453 yago:WikicatDifferentialEquations
rdfs:label	Loewy decomposition (en)
rdfs:comment	In the study of differential equations, the Loewy decomposition breaks every linear ordinary differential equation (ODE) into what are called largest completely reducible components. It was introduced by Alfred Loewy. Loewy's results have been extended to linear partial differential equations (PDEs) in two independent variables. In this way, algorithmic methods for solving large classes of linear PDEs have become available. (en)
name	Theorem 1 (en)
dcterms:subject	Differential equations
Wikipage page ID	41390065 (xsd:integer)
Wikipage revision ID	1117655201 (xsd:integer)
Link from a Wikipage to another Wikipage	Monomial Bessel function Derivative Alfred Loewy Algorithm Indeterminate (variable) Lexicography Mathematics Quotient Corollary Theorem Legendre function Closed-form expression Commutative algebra Function space Partial derivative Bruno Buchberger Janet basis Algebraic number Factorization Parameter Partial differential equation Differential equation Differential operator Differential equations Coefficient Differential algebra Polynomial Gröbner bases Ordinary differential equation Riccati equation
sameAs	Loewy decomposition Loewy decomposition Loewy decomposition Loewy decomposition
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:Math_theorem
has abstract	In the study of differential equations, the Loewy decomposition breaks every linear ordinary differential equation (ODE) into what are called largest completely reducible components. It was introduced by Alfred Loewy. Solving differential equations is one of the most important subfields in mathematics. Of particular interest are solutions in closed form. Breaking ODEs into largest irreducible components, reduces the process of solving the original equation to solving irreducible equations of lowest possible order. This procedure is algorithmic, so that the best possible answer for solving a reducible equation is guaranteed. A detailed discussion may be found in. Loewy's results have been extended to linear partial differential equations (PDEs) in two independent variables. In this way, algorithmic methods for solving large classes of linear PDEs have become available. (en)
math statement	Let be a derivative and . A differential operator of order may be written uniquely as the product of completely reducible factors of maximal order over in the form with . The factors are unique. Any factor , may be written as with ; for , denotes an irreducible operator of order over . (en)
prov:wasDerivedFrom	wikipedia-en:Loewy_decomposition?oldid=1117655201&ns=0
page length (characters) of wiki page	34415 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Loewy_decomposition
is Link from a Wikipage to another Wikipage of	List of dynamical systems and differential equations topics Alfred Loewy Janet basis Loewy Decomposition
is Wikipage redirect of	Loewy Decomposition
is foaf:primaryTopic of	wikipedia-en:Loewy_decomposition

Faceted Search & Find service v1.17_git147 as of Sep 06 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3332 as of Dec 5 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 67 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2025 OpenLink Software