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    Computational Methods for the Construction of a Class of Noetherian Operators

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    This paper presents some algorithmic techniques to compute explicitly the noetherian operators associated to a class of ideals and modules over a polynomial ring. The procedures we include in this work can be easily encoded in computer algebra packages such as CoCoA and Singular

    Uniqueness of limit cycles for quadratic vector fields

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    Producción CientíficaThis article deals with the study of the number of limit cycles surrounding a critical point of a quadratic planar vector field, which, in normal form, can be written as x ′ = a1x − y − a3x 2 + (2a2 + a5)xy+a6y 2 , y ′ = x+a1y+a2x 2+(2a3+a4)xy−a2y 2 . In particular, we study the semi-varieties defined in terms of the parameters a1, a2, . . . , a6 where some classical criteria for the associated Abel equation apply. The proofs will combine classical ideas with tools from computational algebraic geometry.Agencia Estatal de Investigación - Fondo Europeo de Desarrollo Regional (grant MTM 2011-22751)Junta de Extremadura (grant GR15055)Ministerio de Economía, Industria y Competitividad - Fondo Europeo de Desarrollo Regional (grant MTM2015-65764-C3-1-P
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