Related papers: Exploiting Symmetries in Polyhedral Computations
Some differential equations are considered in the context of Synthetic Differential Geometry. Here, this means that not only nilpotent infinitesimals, but also the formation of function spaces, is exploited. In particular, we utilize…
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…
Nowadays, we have seen that dual quaternion algorithms are used in 3D coordinate transformation problems due to their advantages. 3D coordinate transformation problem is one of the important problems in geodesy. This transformation problem…
Symmetry, a central concept in understanding the laws of nature, has been used for centuries in physics, mathematics, and chemistry, to help make mathematical models tractable. Yet, despite its power, symmetry has not been used extensively…
We show some of the mathematics that is being developed for the computation of deep inelastic structure functions to three loops. These include harmonic sums, harmonic polylogarithms and a class of difference equations that can be solved…
The geometric kernel (or simply the kernel) of a polyhedron is the set of points from which the whole polyhedron is visible. Whilst the computation of the kernel for a polygon has been largely addressed in the literature, fewer methods have…
In this paper, we present a review of three widely-used practical square root algorithms. We then describe a unifying framework where each of these well-known algorithms can be seen as a special case of it. The framework with singular…
In this paper I present several novel, efficient, algorithmic techniques for solving some multidimensional geometric data management and analysis problems. The techniques are based on several data structures from computational geometry…
Polypolyhedra are edge-transitive compounds of polyhedra. In this paper we use group theory to determine the number of distinct polypolyhedra whose symmetry group is any given finite irreducible Coxeter group. We apply this result in order…
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…
We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…
We give an overview of recently implemented polymake features for computations in tropical geometry. The main focus is on explicit examples rather than technical explanations. Our computations employ tropical hypersurfaces, moduli of…
A key problem in multiobjective linear programming is to find the set of all efficient extreme points in objective space. In this paper we introduce oriented projective geometry as an efficient and effective framework for solving this…
The relaxation complexity rc(X) of the set of integer points X contained in a polyhedron is the minimal number of inequalities needed to formulate a linear optimization problem over X without using auxiliary variables. Besides its relevance…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…
An algorithmic method to exploit a general class of infinitesimal symmetries for reducing stochastic differential equations is presented and a natural definition of reconstruction, inspired by the classical reconstruction by quadratures, is…
In the last quarter of a century, algebraic statistics has established itself as an expanding field which uses multilinear algebra, commutative algebra, computational algebra, geometry, and combinatorics to tackle problems in mathematical…
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…
Using semi-tensor product of matrices, the structures of several kinds of symmetric games are investigated via the linear representation of symmetric group in the structure vector of games as its representation space. First of all, the…