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Abstract:

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.

Registro:

Documento: Artículo
Título:Effective differential Lüroth's theorem
Autor:D'Alfonso, L.; Jeronimo, G.; Solernó, P.
Filiación:Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428, Buenos Aires, Argentina
Departamento de Matemática and IMAS, UBA-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428, Buenos Aires, Argentina
Palabras clave:12H05; 12Y05; Differential algebra; Differentiation index; Lüroth's theorem
Año:2014
Volumen:406
Página de inicio:1
Página de fin:19
DOI: http://dx.doi.org/10.1016/j.jalgebra.2014.02.022
Título revista:Journal of Algebra
Título revista abreviado:J. Algebra
ISSN:00218693
CODEN:JALGA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v406_n_p1_DAlfonso

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Citas:

---------- APA ----------
D'Alfonso, L., Jeronimo, G. & Solernó, P. (2014) . Effective differential Lüroth's theorem. Journal of Algebra, 406, 1-19.
http://dx.doi.org/10.1016/j.jalgebra.2014.02.022
---------- CHICAGO ----------
D'Alfonso, L., Jeronimo, G., Solernó, P. "Effective differential Lüroth's theorem" . Journal of Algebra 406 (2014) : 1-19.
http://dx.doi.org/10.1016/j.jalgebra.2014.02.022
---------- MLA ----------
D'Alfonso, L., Jeronimo, G., Solernó, P. "Effective differential Lüroth's theorem" . Journal of Algebra, vol. 406, 2014, pp. 1-19.
http://dx.doi.org/10.1016/j.jalgebra.2014.02.022
---------- VANCOUVER ----------
D'Alfonso, L., Jeronimo, G., Solernó, P. Effective differential Lüroth's theorem. J. Algebra. 2014;406:1-19.
http://dx.doi.org/10.1016/j.jalgebra.2014.02.022