Loading...
El problema de pertenencia a ideales de Z[x]
López Gallo, Silvia María
López Gallo, Silvia María
Citations
Altmetric:
Abstract
El problema de pertenencia a un ideal consiste en determinar si un elemento de un anillo pertenece o no a un ideal dado del anillo. En anillos de polinomios, el problema de pertenencia a un ideal es un problema algorítmico con importantes aplicaciones en sistemas de álgebra computacional y, por ende, algoritmos para este problema son ampliamente estudiados. De hecho, para anillos de polinomios sobre campos, el problema de pertenencia a un ideal se puede resolver efectivamente gracias a la teoría de las bases de Gröbner. En esta tesis estudiamos, en particular, el problema de pertenencia a ideales del anillo de polinomios en una variable con coeficientes enteros. Para ello, presentamos un recorrido histórico que muestra cómo se desarrolló, a través de diversos autores, una teoría análoga a la teoría de las bases de Gröbner, que permite abordar efectivamente el problema de pertenencia a ideales del anillo de polinomios en una variable con coeficientes enteros.
The ideal membership problem consists of determining whether or not an element of a ring belongs to a given ideal of the ring. In polynomial rings, the ideal membership problem is an algorithmic problem with important applications in computer algebra systems, and thus algorithms for this problem are widely studied. In fact, for polynomial rings over fields, the ideal membership problem can be effectively solved thanks to the theory of Gröbner basis. In this thesis, we focus on the study of the ideal membership problem in the polynomial ring in one variable with integer coefficients. To do this, we present a historical review that shows how a theory analogous to the theory of Gröbner basis was developed through various authors, which allows to effectively solve the ideal membership problem in the polynomial ring in one variable with integer coefficients.
The ideal membership problem consists of determining whether or not an element of a ring belongs to a given ideal of the ring. In polynomial rings, the ideal membership problem is an algorithmic problem with important applications in computer algebra systems, and thus algorithms for this problem are widely studied. In fact, for polynomial rings over fields, the ideal membership problem can be effectively solved thanks to the theory of Gröbner basis. In this thesis, we focus on the study of the ideal membership problem in the polynomial ring in one variable with integer coefficients. To do this, we present a historical review that shows how a theory analogous to the theory of Gröbner basis was developed through various authors, which allows to effectively solve the ideal membership problem in the polynomial ring in one variable with integer coefficients.
Description
Date
2023-05-12
Journal Title
Journal ISSN
Volume Title
Publisher
Collections
Keywords
Anillo de polinomios, Problema de pertenencia, Bases de Gröbner, Números enteros