相关论文: Geometric Reasoning with polymake
Convex polyhedra are the basis for several abstractions used in static analysis and computer-aided verification of complex and sometimes mission critical systems. For such applications, the identification of an appropriate…
In this paper we study algorithmic aspects of tropical intersection theory. We analyse how divisors and intersection products on tropical cycles can actually be computed using polyhedral geometry. The main focus of this paper is the study…
This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of…
This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The…
Computing mixed volume of convex polytopes is an important problem in computational algebraic geometry. This paper establishes sufficient conditions under which the mixed volume of several convex polytopes exactly equals the normalized…
A programming tactic involving polyhedra is reported that has been widely applied in the polyhedral analysis of (constraint) logic programs. The method enables the computations of convex hulls that are required for polyhedral analysis to be…
The article deals with operations defined on convex polyhedra or polyhedral convex functions. Given two convex polyhedra, operations like Minkowski sum, intersection and closed convex hull of the union are considered. Basic operations for…
Geometric programming problem is a powerful tool for solving some special type non-linear programming problems. It has a wide range of applications in optimization and engineering for solving some complex optimization problems. Many…
The purpose of this thesis is to study classical combinatorial objects, such as polytopes, polytopal complexes, and subspace arrangements, using tools that have been developed in combinatorial topology, especially those tools developed in…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…
Metric spaces defined within convex polygons, such as the Thompson, Funk, reverse Funk, and Hilbert metrics, are subjects of recent exploration and study in computational geometry. This paper contributes an educational piece of software for…
In the last decade major steps towards an algorithmic treatment of orthogonal polynomials and special functions (OP & SF) have been made, notably Zeilberger's brilliant extension of Gosper's algorithm on algorithmic definite hypergeometric…
The computation of Feynman integrals often involves square roots. One way to obtain a solution in terms of multiple polylogarithms is to rationalize these square roots by a suitable variable change. We present a program that can be used to…
Multiple elliptic polylogarithms can be written as (multiple) integrals of products of basic hypergeometric functions. The latter are computable, to arbitrary precision, using a q-difference equation and q-contiguous relations.
Geometric modeling of multivariate reliability polynomials is based on algebraic hypersurfaces, constant level sets, rulings etc. The solved basic problems are: (i) find the reliability polynomial using the Maple and Matlab software…
A Geometric programming (GP) is a type of mathematical problem characterized by objective and constraint functions that have a special form. Many methods have been developed to solve large scale engineering design GP problems. In this paper…
Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…
The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…