Related papers: Detecting Binomiality
We discuss the problem of determining reduction number of a polynomial ideal I in n variables. We present two algorithms based on parametric computations. The first one determines the absolute reduction number of I and requires computation…
An algorithm is presented here, for discovering Hopf-Bifurcation varieties of polynomial dynamical systems. It is based on the expression of specific polynomials, as sums of products of first degree polynomials, with parametrical…
Motivated by recent best case analyses for some sorting algorithms and based on the type of complexity we partition the algorithms into two classes: homogeneous and non homogeneous algorithms. Although both classes contain algorithms with…
An ideal of polynomials is symmetric if it is closed under permutations of variables. We relate general symmetric ideals to the so called Specht ideals generated by all Specht polynomials of a given shape. We show a connection between the…
We determine simplicity criteria in characteristics 0 and $p$ for a ubiquitous class of iterated skew polynomial rings in two indeterminates over a base ring. One obstruction to simplicity is the possible existence of a canonical normal…
We give necessary and sufficient existence criteria, and methods for finding, continuous solutions of linear equations whose coefficients are polynomials.
Ideals generated by adjacent 2-minors are studied. First, the problem when such an ideal is a prime ideal as well as the problem when such an ideal possesses a quadratic Gr\"obner basis is solved. Second, we describe explicitly a primary…
We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of monomial ideals is finite. Then we investigate ordinal…
In the context of modeling biological systems, it is of interest to generate ideals of points with a unique reduced Groebner basis, and the first main goal of this paper is to identify classes of ideals in polynomial rings which share this…
Consider a binary decision making process where a single machine learning classifier replaces a multitude of humans. We raise questions about the resulting loss of diversity in the decision making process. We study the potential benefits of…
We investigate the computational problem of determining whether a bivariate polynomial with non-negative coefficients and no constant term can attain a prime value. While classical conjectures such as Bouniakowsky's provide necessary…
Let $k$ be an infinite field and $I\subset k [x_1, \ldots ,x_n]$ be an ideal such that dim $V(I)=q$. Denote by $(f_1, \ldots, f_s)$ a set of generators of $I$. One can see that in the set $I\cap k [x_{1},...,x_{q+1}]$ there exist non-zero…
We study linear systems of equations with coefficients in a generic partially ordered ring $R$ and a unique solution, and seek conditions for the solution to be nonnegative, that is, every component of the solution is a quotient of two…
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…
We introduce a detection algorithm for SAGBI basis in polynomial rings, analogous to a Gr\"obner basis detection algorithm previously proposed by Gritzmann and Sturmfels. We also present two accompanying software packages named…
Normal ideals on regular uncountable cardinals are familiar objects. We investigate ideals that are pleasant--while a normal ideal is closed under arbitrary diagonal unions, a pleasant ideal is closed only under diagonal unions indexed by…
We give a strongly polynomial time algorithm which determines whether or not a bivariate polynomial is real stable. As a corollary, this implies an algorithm for testing whether a given linear transformation on univariate polynomials…
Scattered over the past few years have been several occurrences of simplicial complexes whose topological behavior characterize the Cohen-Macaulay property for quotients of polynomial rings by arbitrary (not necessarily squarefree) monomial…
This short paper presents saturation-based algorithms for homogenization and elimination. This algorithm can compute elimination ideals by using syzygies and ideal membership test, hence it works with any} monomial order, in particular…
We give a complete characterization of graphs whose binomial edge ideal is licci. An important tool is a new general upper bound for the regularity of binomial edge ideals.