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- Janet_basis abstract "In mathematics, a Janet basis is a normal form for systems of linear homogeneous partial differential equations (PDEs) that removes the inherent arbitrariness of any such system. It was introduced in 1920 by Maurice Janet. It was first called the Janet basis by F. Schwarz in 1998.The left hand sides of such systems of equations may be considered as differential polynomials of a ring, and Janet's normal form as a special basis of the ideal that they generate. By abuse of language, this terminology will be applied both to the original system and the ideal of differential polynomials generated by the left hand sides. A Janet basis is the predecessor of a Groebner basis introduced by Bruno Buchberger for polynomial ideals. In order to generate a Janet basis for any given system of linear pde's a ranking of its derivatives must be provided; then the corresponding Janet basis is unique. If a system of linear pde's is given in terms of a Janet basis its differential dimension may easily be determined; it is a measure for the degree of indeterminacy of its general solution. In order to generate a Loewy decomposition of a system of linear pde's its Janet basis must be determined first.".
- Janet_basis wikiPageID "41553887".
- Janet_basis wikiPageLength "11036".
- Janet_basis wikiPageOutDegree "8".
- Janet_basis wikiPageRevisionID "632036448".
- Janet_basis wikiPageWikiLink Bruno_Buchberger.
- Janet_basis wikiPageWikiLink Canonical_form.
- Janet_basis wikiPageWikiLink Category:Computer_algebra.
- Janet_basis wikiPageWikiLink Category:Differential_algebra.
- Janet_basis wikiPageWikiLink Groebner_basis.
- Janet_basis wikiPageWikiLink Gröbner_basis.
- Janet_basis wikiPageWikiLink Loewy_decomposition.
- Janet_basis wikiPageWikiLink Maurice_Janet.
- Janet_basis wikiPageWikiLink Partial_differential_equation.
- Janet_basis wikiPageWikiLinkText "Janet basis".
- Janet_basis hasPhotoCollection Janet_basis.
- Janet_basis wikiPageUsesTemplate Template:Reflist.
- Janet_basis subject Category:Computer_algebra.
- Janet_basis subject Category:Differential_algebra.
- Janet_basis hypernym Form.
- Janet_basis comment "In mathematics, a Janet basis is a normal form for systems of linear homogeneous partial differential equations (PDEs) that removes the inherent arbitrariness of any such system. It was introduced in 1920 by Maurice Janet. It was first called the Janet basis by F. Schwarz in 1998.The left hand sides of such systems of equations may be considered as differential polynomials of a ring, and Janet's normal form as a special basis of the ideal that they generate.".
- Janet_basis label "Janet basis".
- Janet_basis sameAs m.0_95vch.
- Janet_basis sameAs Q17092828.
- Janet_basis sameAs Q17092828.
- Janet_basis wasDerivedFrom Janet_basis?oldid=632036448.
- Janet_basis isPrimaryTopicOf Janet_basis.