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Capítulo de Libro
Nouvelle Cuisine for the Computation of the Annihilating Ideal of $f^s$
(2005)
Let $f_1,\ldots, f_p$ be polynomials in ${\bf C}[x_1,\ldots, x_n]$ and let $D = D_n$ be the $n$-th Weyl algebra. The annihilating ideal of $f^s=f_1^{s_1}\cdots f_p^{s_p}$ in $D[s]=D[s_1,\ldots,s_p]$ is a necessary step ...
Artículo
Bases for Projective modules in An(k)
(2003-12)
Let $A_n(k)$ be the Weyl algebra, with $k$ a field of characteristic zero. It is known that every projective finitely generated left module is free or isomorphic to a left ideal. Let $M$ be a left submodule of a free module. ...
Ponencia
The Chemist's Cabinet Puzzle: a polynomial approach
(Universidad de Granada. Departamento de Álgebra, 2008-09)
Realizamos un análisis del juego conocido por el herbolario. Se modeliza su solución mediante un sistema polinómico, y deducimos el número de soluciones a partir de herramientas de Álgebra Conmutativa.
Artículo
Constructions in R[x_1, ..., x_n]. Applications to K-Theory
(2002-06-25)
A classical result in K-Theory about polynomial rings like the Quillen-Suslin theorem admits an algorithmic approach when the ring of coefficients has some computational properties, associated with Gröbner bases. There ...
Artículo
Comparison of theoretical complexities of two methods for computing annihilating ideals of polynomials
(2005)
Let f1, . . . , fp be polynomials in C[x1, . . . , xn] and let D = Dn be the n-th Weyl algebra. We provide upper bounds for the complexity of computing the annihilating ideal of f s = f s1 1 · · · f sp p in D[s] = D[s1, . ...
Capítulo de Libro
Algorithmic Invariants for Alexander Modules
(2006)
Let $G$ be a group given by generators and relations. It is possible to compute a presentation matrix of a module over a ring through Fox's differential calculus. We show how to use Gröbner bases as an algorithmic tool ...
Capítulo de Libro
Sudokus and Gröbner Bases: not only a Divertimento
(2006)
Sudoku is a logic-based placement puzzle. We recall how to translate this puzzle into a 9-colouring problem which is equivalent to a (big) algebraic system of polynomial equations. We study how far Gröbner bases techniques ...