José Miguel Serradilla Merinero | UNIR (International University of La Rioja (Spain) (original) (raw)
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Graduate Center of the City University of New York
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Papers by José Miguel Serradilla Merinero
Proceedings of the 2006 international symposium on Symbolic and algebraic computation, 2006
ABSTRACT In this paper we present a method to compute an implicitization of a rational parametriz... more ABSTRACT In this paper we present a method to compute an implicitization of a rational parametrized curve in an affine space over an algebraically closed field. This method is the natural generalization of the resultant method for planar curves. For this purpose we need some normality assumptions on the parametrization of the curve. Furthermore, we provide a test to decide whether a parametrization is normal and if not, we compute a normal parametrization.
Journal of Symbolic Computation, 2009
In this paper we give an algorithm that detects real singularities, including singularities at in... more In this paper we give an algorithm that detects real singularities, including singularities at infinity, and counts local branches and multiplicities of real rational curves in the affine n-space without knowing an implicitization. The main idea behind this is a generalization of the D-resultant (see [van den Essen, A., Yu, J.-T., 1997. The D-resultant, singularities and the degree of unfaithfulness. Proc. Amer. Math. Soc. 25 (3), 689-695]) to n rational functions. This allows us to find all real parameters corresponding to the real singularities between the solutions of a system of polynomials in one variable.
We introduce the quasi-ordinarization transform of a numerical semigroup. This transform will all... more We introduce the quasi-ordinarization transform of a numerical semigroup. This transform will allow to organize all the semigroups of a given genus in a forest rooted at all quasi-ordinary semigroups with the given genus. This construction provides an alternative approach to the conjecture on the increasingness of the number of numerical semigroups for each given genus. We elaborate on the number of nodes at each tree depth in the forest and present a few new conjectures that can be developed in the future. We prove some properties of the quasi-ordinarization transform, its relations with the ordinarization transform, and we also present an alternative approach to the conjecture that the number of numerical semigroups of each given genus is increasing.
Proceedings of the 2006 international symposium on Symbolic and algebraic computation, 2006
ABSTRACT In this paper we present a method to compute an implicitization of a rational parametriz... more ABSTRACT In this paper we present a method to compute an implicitization of a rational parametrized curve in an affine space over an algebraically closed field. This method is the natural generalization of the resultant method for planar curves. For this purpose we need some normality assumptions on the parametrization of the curve. Furthermore, we provide a test to decide whether a parametrization is normal and if not, we compute a normal parametrization.
Journal of Symbolic Computation, 2009
In this paper we give an algorithm that detects real singularities, including singularities at in... more In this paper we give an algorithm that detects real singularities, including singularities at infinity, and counts local branches and multiplicities of real rational curves in the affine n-space without knowing an implicitization. The main idea behind this is a generalization of the D-resultant (see [van den Essen, A., Yu, J.-T., 1997. The D-resultant, singularities and the degree of unfaithfulness. Proc. Amer. Math. Soc. 25 (3), 689-695]) to n rational functions. This allows us to find all real parameters corresponding to the real singularities between the solutions of a system of polynomials in one variable.
We introduce the quasi-ordinarization transform of a numerical semigroup. This transform will all... more We introduce the quasi-ordinarization transform of a numerical semigroup. This transform will allow to organize all the semigroups of a given genus in a forest rooted at all quasi-ordinary semigroups with the given genus. This construction provides an alternative approach to the conjecture on the increasingness of the number of numerical semigroups for each given genus. We elaborate on the number of nodes at each tree depth in the forest and present a few new conjectures that can be developed in the future. We prove some properties of the quasi-ordinarization transform, its relations with the ordinarization transform, and we also present an alternative approach to the conjecture that the number of numerical semigroups of each given genus is increasing.