相关论文: Automatic Generation of Polynomial Symmetry Breaki…

An algorithm to generate a minimal comprehensive Gr\"obner\, basis of a parametric polynomial system from an arbitrary faithful comprehensive Gr\"obner\, system is presented. A basis of a parametric polynomial ideal is a comprehensive…

In this paper we study the problem of deciding whether two disjoint semialgebraic sets of an algebraic variety over R are separable by a polynomial. For that we isolate a dense subfamily of Spaces of Orderings, named Geometric, which…

We present a systematic computational framework for generating positive quadrature rules in multiple dimensions on general geometries. A direct moment-matching formulation that enforces exact integration on polynomial subspaces yields…

We develop a method for generating pseudorandom binary sequences using the Bernoulli map on cubic algebraic integers. The distinguishing characteristic of our generator is that it generates chaotic true orbits of the Bernoulli map by exact…

This paper presents a program analysis method that generates program summaries involving polynomial arithmetic. Our approach builds on prior techniques that use solvable polynomial maps for summarizing loops. These techniques are able to…

Reductions combine collections of input values with an associative and often commutative operator to produce collections of results. When the same input value contributes to multiple outputs, there is an opportunity to reuse partial…

We perform a systematic symmetry classification of the Markov generators of classical stochastic processes. Our classification scheme is based on the action of involutive symmetry transformations of a real Markov generator, extending the…

We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by…

This article presents uniform random generators of plane partitions according to the size (the number of cubes in the 3D interpretation). Combining a bijection of Pak with the method of Boltzmann sampling, we obtain random samplers that are…

It is a classical problem to compute a minimal set of invariant polynomial generating the invariant ring of a finite group as an algebra. We present here an algorithm for the computation of minimal generating sets in the non-modular case.…

It is well-known that the graph isomorphism problem can be posed as an equivalent problem of determining whether an auxiliary graph structure contains a clique of specific order. However, the algorithms that have been developed so far for…

Computing the real solutions to a system of polynomial equations is a challenging problem, particularly verifying that all solutions have been computed. We describe an approach that combines numerical algebraic geometry and sums of squares…

Symmetry breaking is a widely popular approach to enhance solvers in constraint programming, such as those for SAT or MIP. Symmetry breaking predicates (SBPs) typically impose an order on variables and single out the lexicographic leader…

In this paper, we present a novel approach to synthesize invariant clusters for polynomial programs. An invariant cluster is a set of program invariants that share a common structure, which could, for example, be used to save the needs for…

Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for computing integrals and sampling from distributions on algebraic…

The Galois/monodromy group of a family of geometric problems or equations is a subtle invariant that encodes the structure of the solutions. Computing monodromy permutations using numerical algebraic geometry gives information about the…

The topic of this paper are integer programming models in which a subset of 0/1-variables encode a partitioning of a set of objects into disjoint subsets. Such models can be surprisingly hard to solve by branch-and-cut algorithms if the…

A polynomial-time algorithm for 0-1 integer linear programmings has been proposed. This method continues the classic idea of solving ILP with its LP relaxation. The innovation is that every constraint in the LP is reconstructed into a…

Linear algebra is a major field of numerical computation and is widely applied. Most linear algebra libraries (in most programming languages) do not statically guarantee consistency of the dimensions of vectors and matrices, causing runtime…

In many applications, we need algorithms which can align partially overlapping point sets and are invariant to the corresponding transformations. In this work, a method possessing such properties is realized by minimizing the objective of…