Related papers: Groebner Bases for Everyone with CoCoA-5 and CoCoA…
In this paper we show how to combine different techniques from Commutative Algebra and a systematic use of a Computer Algebra System (in our case mainly CoCoA) in order to explicitly construct Cohen-Macaulay domains, which are standard…
Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the last years. However, the polynomial case has not been…
Despite the successes of pretrained language models, there are still few high-quality, general-purpose QA systems that are freely available. In response, we present Macaw, a versatile, generative question-answering (QA) system that we are…
Computing Gr\"obner bases is known to have a very high upper bound on computation time with respect to input length. Due to the connection between polyhedral geometry and Gr\"obner bases through the Gr\"obner fan, one can attempt an…
Designing flexible graph kernels that can run well on various platforms is a crucial research problem due to the frequent usage of graphs for modeling data and recent architectural advances and variety. In this work, we propose a novel…
The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. In this contribution, we develop a solution based upon Gaussian belief propagation…
The famous F5 algorithm for computing \gr basis was presented by Faug\`ere in 2002. The original version of F5 is given in programming codes, so it is a bit difficult to understand. In this paper, the F5 algorithm is simplified as F5B in a…
Distributed Constraint Optimization Problems (DCOPs) have been widely used to coordinate interactions (i.e. constraints) in cooperative multi-agent systems. The traditional DCOP model assumes that variables owned by the agents can take only…
The so called generalized down-up algebras are revisited from a viewpoint of Gr\"obner basis theory. Particularly it is shown explicitly that generalized down-up algebras are solvable polynomial algebras (provided $\lambda\omega\ne 0$), and…
Recently, Large Language Models (LLMs) have undergone a significant transformation, marked by a rapid rise in both their popularity and capabilities. Leading this evolution are proprietary LLMs like GPT-4 and GPT-o1, which have captured…
In this paper we introduce a binomial ideal derived from a binary linear code. We present some applications of a Gr\"obner basis of this ideal with respect to a total degree ordering. In the first application we give a decoding method for…
General AI Agents are increasingly recognized as foundational frameworks for the next generation of artificial intelligence, enabling complex reasoning, web interaction, coding, and autonomous research capabilities. However, current agent…
The article surveys a little of the history of the technology, sets out the main current theoretical approaches in brief, and discusses the on-going opposition between theoretical and empirical approaches. It illustrates the situation with…
GitHub Copilot is an artificial intelligence model for automatically generating source code from natural language problem descriptions. Since June 2022, Copilot has officially been available for free to all students as a plug-in to…
Semantic code search, which aims to retrieve code snippets relevant to a given natural language query, has attracted many research efforts with the purpose of accelerating software development. The huge amount of online publicly available…
To broaden participation, competitive programming contests may include beginner-level problems that do not require knowledge of advanced Computer Science concepts (e.g., algorithms and data structures). However, since most participants have…
This dissertation focuses on the design and the implementation of domain-specific compilers for linear algebra matrix equations. The development of efficient libraries for such equations, which lie at the heart of most software for…
Gr\"obner bases can be used for computing the Hilbert basis of a numerical submonoid. By using these techniques, we provide an algorithm that calculates a basis of a subspace of a finite-dimensional vector space over a finite prime field…
We introduce the package \textbf{arrangements} for the software CoCoA. This package provides a data structure and the necessary methods for working with hyperplane arrangements. In particular, the package implements methods to enumerate…
To the best of our knowledge, there are no general well-founded robust methods for statistical unsupervised learning. Most of the unsupervised methods explicitly or implicitly depend on the kernel covariance operator (kernel CO) or kernel…