2,069 research outputs found
Basic Module Theory over Non-Commutative Rings with Computational Aspects of Operator Algebras
The present text surveys some relevant situations and results where basic
Module Theory interacts with computational aspects of operator algebras. We
tried to keep a balance between constructive and algebraic aspects.Comment: To appear in the Proceedings of the AADIOS 2012 conference, to be
published in Lecture Notes in Computer Scienc
Computational Methods for the Construction of a Class of Noetherian Operators
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
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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