相关论文: Geometric Reasoning with polymake

Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…

We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…

We describe a Maple package that serves at least four purposes. First, one can use it to compute whether or not a given polyhedral structure is Zometool constructible. Second, one can use it to manipulate Zometool objects, for example to…

Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This…

We exhibit a class of classical or tropical posynomial systems which can be solved by reduction to linear or convex programming problems. This relies on a notion of colorful vectors with respect to a collection of Newton polytopes. This…

In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic…

Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials. These include: tightly containing a cloud of points (e.g., representing an…

We present two exact implementations of efficient output-sensitive algorithms that compute Minkowski sums of two convex polyhedra in 3D. We do not assume general position. Namely, we handle degenerate input, and produce exact results. We…

We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of…

Hyperplane arrangements form the latest addition to the zoo of combinatorial objects dealt with by polymake. We report on their implementation and on a algorithm to compute the associated cell decomposition. The implemented algorithm…

We present recent computer algebra methods that support the calculations of (multivariate) series solutions for (certain coupled systems of partial) linear differential equations. The summand of the series solutions may be built by…

This document is a companion for the Maple program \textbf{Summing a polynomial function over integral points of a polygon}. It contains two parts. First, we see what this programs does. In the second part, we briefly recall the…

simpcomp is an extension (a so called package) to GAP, the well known system for computational discrete algebra. The package enables the user to compute numerous properties of (abstract) simplicial complexes, provides functions to construct…

This paper presents an alternative approach to simplify the proofs of some important results related to polynomial mappings in Computational Algebraic Geometry such as Polynomial Implicitization, Image Closure and some properties of the…

Symmetric edge polytopes are a recent and well-studied family of centrally symmetric polytopes arising from graphs. In this paper, we introduce a generalization of this family to arbitrary simplicial complexes. We show how topological…

Polytope complexes are the generalisation of polygon meshes in geo-information systems (GIS) to arbitrary dimension, and a natural concept for accessing spatio-temporal information. Complexes of each dimension have a straight-forward…

PESummary is a Python software package for processing and visualising data from any parameter estimation code. The easy to use Python executable scripts and extensive online documentation has resulted in PESummary becoming a key component…

We develop a collection of numerical algorithms which connect ideas from polyhedral geometry and algebraic geometry. The first algorithm we develop functions as a numerical oracle for the Newton polytope of a hypersurface and is based on…

We strengthen the classical approximation theorems of Weierstrass, Runge and Mergelyan by showing the polynomial and rational approximants can be taken to have a simple geometric structure. In particular, when approximating a function $f$…

In this article, we propose a geometric programming method in order to compute lower bounds for real polynomials. We provide new sufficient conditions for polynomials to be nonnegative as well as to have a sum of binomial squares…