Quantitative aspects of the generalized differential Lüroth's Theorem

Let F be a differential field of characteristic 0, t=t1,…,tm a finite set of differential indeterminates over F and G⊂F〈t〉 a differential field extension of F, generated by nonconstant rational functions α1,…,αn of total degree and order bounded by d and e≥1 respectively. The generalized differentia...

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Detalles Bibliográficos
Publicado: 2018
Materias:
Differential algebra
Differentiation index
Lüroth's Theorem
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v507_n_p547_DAlfonso
http://hdl.handle.net/20.500.12110/paper_00218693_v507_n_p547_DAlfonso
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00218693_v507_n_p547_DAlfonso
record_format dspace
spelling paper:paper_00218693_v507_n_p547_DAlfonso2023-06-08T14:42:31Z Quantitative aspects of the generalized differential Lüroth's Theorem Differential algebra Differentiation index Lüroth's Theorem Let F be a differential field of characteristic 0, t=t1,…,tm a finite set of differential indeterminates over F and G⊂F〈t〉 a differential field extension of F, generated by nonconstant rational functions α1,…,αn of total degree and order bounded by d and e≥1 respectively. The generalized differential Lüroth's Theorem states that if the differential transcendence degree of G over F is 1, there exists v∈G such that G=F〈v〉. We prove a new explicit upper bound for the degree of v in terms of n,m,d and e. Further, we exhibit an effective procedure to compute v. © 2018 Elsevier Inc. 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v507_n_p547_DAlfonso http://hdl.handle.net/20.500.12110/paper_00218693_v507_n_p547_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 Differential algebra
Differentiation index
Lüroth's Theorem
spellingShingle Differential algebra
Differentiation index
Lüroth's Theorem
Quantitative aspects of the generalized differential Lüroth's Theorem
topic_facet Differential algebra
Differentiation index
Lüroth's Theorem
description Let F be a differential field of characteristic 0, t=t1,…,tm a finite set of differential indeterminates over F and G⊂F〈t〉 a differential field extension of F, generated by nonconstant rational functions α1,…,αn of total degree and order bounded by d and e≥1 respectively. The generalized differential Lüroth's Theorem states that if the differential transcendence degree of G over F is 1, there exists v∈G such that G=F〈v〉. We prove a new explicit upper bound for the degree of v in terms of n,m,d and e. Further, we exhibit an effective procedure to compute v. © 2018 Elsevier Inc.
title Quantitative aspects of the generalized differential Lüroth's Theorem
title_short Quantitative aspects of the generalized differential Lüroth's Theorem
title_full Quantitative aspects of the generalized differential Lüroth's Theorem
title_fullStr Quantitative aspects of the generalized differential Lüroth's Theorem
title_full_unstemmed Quantitative aspects of the generalized differential Lüroth's Theorem
title_sort quantitative aspects of the generalized differential lüroth's theorem
publishDate 2018
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v507_n_p547_DAlfonso
http://hdl.handle.net/20.500.12110/paper_00218693_v507_n_p547_DAlfonso
_version_ 1768545450219012096

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