Effective differential Lüroth's theorem

This paper focuses on effectivity aspects of the Lüroth's theorem in differential fields. Let F be an ordinary differential field of characteristic 0 and F〈u〉 be the field of differential rational functions generated by a single indeterminate u. Let be given non-constant rational functions v1,v...

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Detalles Bibliográficos
Autores principales:	Jeronimo, Gabriela Tali, Solerno, Pablo Luis
Publicado:	2014
Materias:	12H05 12Y05 Differential algebra Differentiation index Lüroth's theorem
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v406_n_p1_DAlfonso http://hdl.handle.net/20.500.12110/paper_00218693_v406_n_p1_DAlfonso
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_00218693_v406_n_p1_DAlfonso
record_format	dspace
spelling	paper:paper_00218693_v406_n_p1_DAlfonso2023-06-08T14:42:27Z Effective differential Lüroth's theorem Jeronimo, Gabriela Tali Solerno, Pablo Luis 12H05 12Y05 Differential algebra Differentiation index Lüroth's theorem This paper focuses on effectivity aspects of the Lüroth's theorem in differential fields. Let F be an ordinary differential field of characteristic 0 and F〈u〉 be the field of differential rational functions generated by a single indeterminate u. Let be given non-constant rational functions v1,vn∈F〈u〉 generating a differential subfield G⊆F〈u〉. The differential Lüroth's theorem proved by Ritt in 1932 states that there exists v∈G such that G=F〈v〉. Here we prove that the total order and degree of a generator v are bounded by minjord(vj) and (n d(e +1) +1)2e +1, respectively, where e:=maxjord(vj) and d:=maxjdeg(vj). As a byproduct, our techniques enable us to compute a Lüroth generator by dealing with a polynomial ideal in a polynomial ring in finitely many variables. © 2014 Elsevier Inc. Fil:Jeronimo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Solernó, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v406_n_p1_DAlfonso http://hdl.handle.net/20.500.12110/paper_00218693_v406_n_p1_DAlfonso
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	12H05 12Y05 Differential algebra Differentiation index Lüroth's theorem
spellingShingle	12H05 12Y05 Differential algebra Differentiation index Lüroth's theorem Jeronimo, Gabriela Tali Solerno, Pablo Luis Effective differential Lüroth's theorem
topic_facet	12H05 12Y05 Differential algebra Differentiation index Lüroth's theorem
description	This paper focuses on effectivity aspects of the Lüroth's theorem in differential fields. Let F be an ordinary differential field of characteristic 0 and F〈u〉 be the field of differential rational functions generated by a single indeterminate u. Let be given non-constant rational functions v1,vn∈F〈u〉 generating a differential subfield G⊆F〈u〉. The differential Lüroth's theorem proved by Ritt in 1932 states that there exists v∈G such that G=F〈v〉. Here we prove that the total order and degree of a generator v are bounded by minjord(vj) and (n d(e +1) +1)2e +1, respectively, where e:=maxjord(vj) and d:=maxjdeg(vj). As a byproduct, our techniques enable us to compute a Lüroth generator by dealing with a polynomial ideal in a polynomial ring in finitely many variables. © 2014 Elsevier Inc.
author	Jeronimo, Gabriela Tali Solerno, Pablo Luis
author_facet	Jeronimo, Gabriela Tali Solerno, Pablo Luis
author_sort	Jeronimo, Gabriela Tali
title	Effective differential Lüroth's theorem
title_short	Effective differential Lüroth's theorem
title_full	Effective differential Lüroth's theorem
title_fullStr	Effective differential Lüroth's theorem
title_full_unstemmed	Effective differential Lüroth's theorem
title_sort	effective differential lüroth's theorem
publishDate	2014
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v406_n_p1_DAlfonso http://hdl.handle.net/20.500.12110/paper_00218693_v406_n_p1_DAlfonso
work_keys_str_mv	AT jeronimogabrielatali effectivedifferentiallurothstheorem AT solernopabloluis effectivedifferentiallurothstheorem
_version_	1768542019285680128

Effective differential Lüroth's theorem

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