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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| Autores principales: | , , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00218693_v507_n_p547_DAlfonso |
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| Sumario: | 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. |
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