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Sudokus and Gröbner Bases: not only a Divertimento [Chapter of Book]
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 ...
Algorithmic Invariants for Alexander Modules [Chapter of Book]
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 ...
Bases for Projective modules in An(k) [Article]
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. ...
Constructions in R[x_1, ..., x_n]. Applications to K-Theory [Article]
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 ...