فهرست مطالب abdolali basiri

In this paper, we address the problem of analyzing and computing all steady states of an overlapping generation (OLG) model with production and many generations. The characterization of steady states coincides with a geometrical representation of the algebraic variety of a polynomial ideal, and, in principle, one can apply computational algebraic geometry methods to solve the problem. However, it is infeasible for standard methods to solve problems with a large number of variables and parameters. Instead, we use the specific structure of the economic problem to develop a new algorithm that does not employ the usual steps for the computation of Grobner basis such as the computation of successive S-polynomial and expensive division.

Ideals of points are considered as a significant and efficient tools in modeling and computingscience, which is why algorithms computing these types of ideals are of crucial importance. This paperproposes an algorithm to compute order ideals for ideals of points. Then those order ideals are used formodeling gene regulatory networks.

Grobner basis with respect to several orderings is a powerful tool to compute multivariate difference dimension polynomials. In this paper, an algorithm for computing a Grobner basis of a difference module over a ground difference field with respect to several term orderings is presented. In this direction, a representation of an element of a difference module with respect to several term orderings is introduced. Based on such representation, we generalize the Buchberger theorem to the case of free modules over difference rings with several term orderings associated with a partition of the set of variables. Furthermore, the necessary and sufficient condition is given for the existence of a Grobner basis with respect to several term orderings. In the sequel, we present our implementation of the algorithm on Maple.

Lie’s theory of symmetry groups plays an important role in analyzing and solving differential equations; for instance, by decreasing the order of equation. Moreover, there are some analytic methods to find the infinitesimal generators that span the Lie algebra of symmetries. In this paper, we first converted the problem of finding infinitesimal generators in to the problem of solving a system of polynomial equations in the context of computational algebraic geometry. Then, we used Gröbner basis a novel computational tool to solve this problem. As far as we know, when a differential equation contains some parameters, there is no linear algebraic algorithm up to our knowledge to deal with these parameters; so, we must apply the algorithms, which are based on Gröbner basis.

In this paper, an efficient symbolic-numerical procedure based on the power series method is presented for solving a system of differential equations. The basic idea is to substitute power series into the differential equations and to find a polynomial system of coefficients, where a powerful symbolic computation technique (i.e., Grobner basis) is used to solve the system. In fact, the proposed method is an excellent bridge between symbolic and numeric computation and specially, enables us to find the solution of linear and non-linear stiff systems. Numerical experiments were performed to justify our new approach.

We present a new algorithm for computing a SAGBI basis up to an arbitrary degree for a subalgebra generated by a set of homogeneous polynomials. Our idea is based on linear algebra methods which cause a low level of complexity and computational cost. We then use it to solve the membership problem in subalgebras.

In this paper, a new  algorithm for computing secondary invariants of  invariant rings of monomial groups is presented. The main idea is to compute simultaneously a truncated SAGBI-G basis and the standard invariants of the ideal generated by the set of primary invariants.  The advantage of the presented algorithm lies in the fact that it is well-suited to complexity analysis and very easy to implement.