Calcolo del conduttore di curve algebriche e ideali di punti
Canonical bases for subalgebras on two generators in the univariate polynomial ring.
Castelnuovo-Mumford regularity of products of ideals.
The Castelnuovo-Mumford regularity reg(M) is one of the most important invariants of a finitely generated graded module M over a polynomial ring R. For instance, it measures the amount of computational resources that working with M requires. In general one knows that the regularity of a module can be doubly exponential in the degrees of the minimal generators and in the number of the variables. On the other hand, in many situations one has or one conjectures a much better behavior. One may ask,...
Classification of solvable Lie algebras.
Cohen-Macaulay modifications of the vertex cover ideal of a graph
We study when the modifications of the Cohen-Macaulay vertex cover ideal of a graph are Cohen-Macaulay.
Combinatorial-algebraic techniques in Gröbner bases theory.
Complex centers of polynomial differential equations.
Complexity bound of absolute factoring of parametric polynomials.
Composition-diamond lemma for modules
We investigate the relationship between the Gröbner-Shirshov bases in free associative algebras, free left modules and “double-free” left modules (that is, free modules over a free algebra). We first give Chibrikov’s Composition-Diamond lemma for modules and then we show that Kang-Lee’s Composition-Diamond lemma follows from it. We give the Gröbner-Shirshov bases for the following modules: the highest weight module over a Lie algebra , the Verma module over a Kac-Moody algebra, the Verma module...
Computations with Frobenius powers.
Computing Gröbner fans of toric ideals.
Computing Hilbert-Kunz functions of 1-dimensional graded rings.
Computing versal deformations.
Constructing invariants for finite groups.
Construction of a controller with a generalized linear immersion
Gröbner bases for modules are used to calculate a generalized linear immersion for a plant whose solutions to its regulation equations are polynomials or pseudo-polynomials. After calculating the generalized linear immersion, we build the controller which gives the robust regulation.
Counting equivalence classes of irreducible representations.