Related papers: GAPS: Generator for Automatic Polynomial Solvers

This paper presents an algorithm for computing Groebner bases based upon labeled polynomials and ideas from the algorithm F5. The main highlights of this algorithm compared with analogues are simplicity both of the algorithm and of the its…

One of the biggest open problems in computational algebra is the design of efficient algorithms for Gr{\"o}bner basis computations that take into account the sparsity of the input polynomials. We can perform such computations in the case of…

In many numerical schemes, the computational complexity scales non-linearly with the problem size. Solving a linear system of equations using direct methods or most iterative methods is a typical example. Algebraic multi-grid (AMG) methods…

In this paper we describe an efficient involutive algorithm for constructing Groebner bases of polynomial ideals. The algorithm is based on the concept of involutive monomial division which restricts the conventional division in a certain…

Signature-based algorithms are a popular kind of algorithms for computing Groebner basis, including the famous F5 algorithm, F5C, extended F5, G2V and the GVW algorithm. In this paper, an efficient method is proposed to solve the…

Linear solvers for large and sparse systems are a key element of scientific applications, and their efficient implementation is necessary to harness the computational power of current computers. Algebraic MultiGrid (AMG) preconditioners are…

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…

The computation of Gr\"obner bases is an established hard problem. By contrast with many other problems, however, there has been little investigation of whether this hardness is robust. In this paper, we frame and present results on the…

We present an efficient algorithm for computing the leading monomials of a minimal Groebner basis of a generic sequence of homogeneous polynomials. Our approach bypasses costly polynomial reductions by exploiting structural properties…

In this paper we consider systems of partial (multidimensional) linear difference equations. Specifically, such systems arise in scientific computing under discretization of linear partial differential equations and in computational high…

Modular algorithm are widely used in computer algebra systems (CAS), for example to compute efficiently the gcd of multivariate polynomials. It is known to work to compute Groebner basis over $\Q$, but it does not seem to be popular among…

Graph neural networks (GNNs) have proven their efficacy in a variety of real-world applications, but their underlying mechanisms remain a mystery. To address this challenge and enable reliable decision-making, many GNN explainers have been…

Graph neural network (GNN) inference faces significant bottlenecks in preprocessing, which often dominate overall inference latency. We introduce AutoGNN, an FPGA-based accelerator designed to address these challenges by leveraging FPGA's…

This article focuses on automatically generating polynomial equations that are inductive loop invariants of computer programs. We propose a new algorithm for this task, which is based on polynomial interpolation. Though the proposed…

The exponential growth of complex data demands fully automatic clustering. Gaussian mixture models (GMMs) provide uncertainty-aware grouping but often require expertise to specify hyperparameters, e.g., component count and covariance…

Standard Gibbs sampling applied to a multivariate normal distribution with a specified precision matrix is equivalent in fundamental ways to the Gauss-Seidel iterative solution of linear equations in the precision matrix. Specifically, the…

In this paper we present a novel algorithm for automatic performance testing that uses an online variant of the Generative Adversarial Network (GAN) to optimize the test generation process. The objective of the proposed approach is to…

In April 2025 GMV announced a competition for finding the best method to solve a particular polynomial system over a finite field. In this paper we provide a method for solving the given equation system significantly faster than what is…

The generalized eigenvalue problem (GEP) serves as a cornerstone in a wide range of applications in numerical linear algebra and scientific computing. However, traditional approaches that aim to maximize the classical Rayleigh quotient…

We propose a new approach to train the Generative Adversarial Nets (GANs) with a mixture of generators to overcome the mode collapsing problem. The main intuition is to employ multiple generators, instead of using a single one as in the…