Atribución-NoComercial 4.0 InternacionalVélez Caicedo, Juan Diego (Thesis advisor)Hernández Rodas, Juan Pablo2019-07-022019-07-022015https://repositorio.unal.edu.co/handle/unal/54927This thesis is divided in three main parts. In the first part we provide a theoretical method to determine the existence of the limit of a quotient of polynomial functions of three variables. An algorithm to compute such limits in the case where the polynomials have rational coeffcients, or more generally, coefficients in a real finite extension of the rational numbers is also described. In the second part, for any finite abelian group G, we present an exact formula to count the G graded twisted algebras satisfying certain symmetry condition. Finally, in the third part we describe an algorithm to compute the F-rational locus of an affine algebra over a field of prime characteristic p 0 by computing first its global test ideal. As a consequence we deduce the Openness of the F-rational locus, a result originally proved in [27]application/pdfspaDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/51 Matemáticas / MathematicsTrabajo de grado - Doctoradohttp://bdigital.unal.edu.co/50191/info:eu-repo/semantics/openAccessG-graded twisted algebrasLimits of rational functions of three variblesF-rational locus