Related papers: Minimal Canonical Comprehensive Groebner Systems
A Maple package for computing Groebner bases of linear difference ideals is described. The underlying algorithm is based on Janet and Janet-like monomial divisions associated with finite difference operators. The package can be used, for…
We establish the minimal model theory for normal pairs along log canonical locus in the complex analytic setting. This is the complex analytic analog of the previous result by the author.
Given a finite set of arbitrarily distributed points in affine space with arbitrary multiplicity structures, we present an algorithm to compute the reduced Groebner basis of the vanishing ideal under the lexicographic ordering. Our method…
We develop the theory of Gr\"obner bases for ideals in a polynomial ring with countably infinite variables over a field. As an application we reconstruct some of the one-one correspondences among various sets of partitions by using division…
Using techniques coming from the theory of marked bases, we develop new computational methods for detection and construction of Cohen-Macaulay, Gorenstein and complete intersection homogeneous polynomial ideals. Thanks to the functorial…
This paper is concerned with structures of general graphs with perfect matchings. We first reveal a partially ordered structure among factor-components of general graphs with perfect matchings. Our second result is a generalization of…
Left-right and conjugation actions on matrix tuples have received considerable attention in theoretical computer science due to their connections with polynomial identity testing, group isomorphism, and tensor isomorphism. In this paper, we…
In complicated/nonlinear parametric models, it is generally hard to know whether the model parameters are point identified. We provide computationally attractive procedures to construct confidence sets (CSs) for identified sets of full…
Subject of this paper is an implementation of a well-known Motzkin-Burger algorithm, which solves the problem of finding the full set of solutions of a system of linear homogeneous inequalities. There exist a number of implementations of…
We prove that one can run the log minimal model program for log canonical $3$-fold pairs in characteristic $p>5$. In particular we prove the Cone Theorem, Contraction Theorem, the existence of flips and the existence of log minimal models…
The complexity of computing the solutions of a system of multivariate polynomial equations by means of Groebner bases computations is upper bounded by a function of the solving degree. In this paper, we discuss how to rigorously estimate…
We consider the time evolution of a one dimensional $n$-gradient continuum. Our aim is to construct and analyze discrete approximations in terms of physically realizable mechanical systems, called microscopic because they are living on a…
In the MINIMUM CONVEX COVER (MCC) problem, we are given a simple polygon $\mathcal P$ and an integer $k$, and the question is if there exist $k$ convex polygons whose union is $\mathcal P$. It is known that MCC is $\mathsf{NP}$-hard…
In the work are defined the concepts semi-canonical and canonical binary matrix. What is described is an algorithm solving the combinatorial problem for finding the semi-canonical matrices in the set \Lambda_n^k consisting of all n\times n…
Polynomial system solving arises in many application areas to model non-linear geometric properties. In such settings, polynomial systems may come with degeneration which the end-user wants to exclude from the solution set. The…
A set of polynomials G in a polynomial ring S over a field is said to be a universal Groebner basis, if G is a Groebner basis with respect to every term order on S. Twenty years ago Bernstein, Sturmfels, and Zelevinsky proved that the set…
This paper describes a Buchberger-style algorithm to compute a Groebner basis of a polynomial ideal, allowing for a selection strategy based on "signatures". We explain how three recent algorithms can be viewed as different strategies for…
The problem of simplifying tensor expressions is addressed in two parts. The first part presents an algorithm designed to put tensor expressions into a canonical form, taking into account the symmetries with respect to index permutations…
In this work we introduce the concept of a sub-space decomposition, subject to a partition of the coordinates. Considering metrics determined by partial orders in the set of coordinates, the so called poset metrics, we show the existence of…
In this paper, we present an algorithm for computing a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in several variables. This algorithm is a generalization of a method developed for…