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...
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00218693_v507_n_p547_DAlfonso |
| Aporte de: |
| id |
todo:paper_00218693_v507_n_p547_DAlfonso |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_00218693_v507_n_p547_DAlfonso2023-10-03T14:21:37Z Quantitative aspects of the generalized differential Lüroth's Theorem D'Alfonso, L. Jeronimo, G. Solernó, P. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 D'Alfonso, L. Jeronimo, G. Solernó, P. 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. |
| format |
JOUR |
| author |
D'Alfonso, L. Jeronimo, G. Solernó, P. |
| author_facet |
D'Alfonso, L. Jeronimo, G. Solernó, P. |
| author_sort |
D'Alfonso, L. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00218693_v507_n_p547_DAlfonso |
| work_keys_str_mv |
AT dalfonsol quantitativeaspectsofthegeneralizeddifferentiallurothstheorem AT jeronimog quantitativeaspectsofthegeneralizeddifferentiallurothstheorem AT solernop quantitativeaspectsofthegeneralizeddifferentiallurothstheorem |
| _version_ |
1807314823147421696 |