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Distributed optimization algorithms are essential for training machine learning models on very large-scale datasets. However, they often suffer from communication bottlenecks. Confronting this issue, a communication-efficient primal-dual…
Legacy programming languages such as COBOL (Common Business-Oriented Language) remain critical in business computing. However, maintaining legacy COBOL systems is increasingly challenging due to a declining pool of skilled developers and…
In this expository style of writing I will give an introduction of Gr\"{o}bner bases and compute it for some algebras and then show how to use it to compute Hilbert series for algebras from chains.
We introduce the theory of monoidal Groebner bases, a concept which generalizes the familiar notion in a polynomial ring and allows for a description of Groebner bases of ideals that are stable under the action of a monoid. The main…
There are several efficient methods to solve linear interval polynomial systems in the context of interval computations, however, the general case of interval polynomial systems is not yet covered as well. In this paper we introduce a new…
Designing software systems for Geometric Computing applications can be a challenging task. Software engineers typically use software abstractions to hide and manage the high complexity of such systems. Without the presence of a unifying…
To integer programming problems, computational algebraic approaches using Grobner bases or standard pairs via the discreteness of toric ideals have been studied in recent years. Although these approaches have not given improved time…
This paper is a survey on the area of signature-based Gr\"obner basis algorithms that was initiated by Faug\`ere's F5 algorithm in 2002. We explain the general ideas behind the usage of signatures. We show how to classify the various known…
It has been discovered that linear codes may be described by binomial ideals. This makes it possible to study linear codes by commutative algebra and algebraic geometry methods. In this paper, we give a decoding algorithm for binary linear…
The BeyondPlanck and Cosmoglobe collaborations have implemented the first integrated Bayesian end-to-end analysis pipeline for CMB experiments. The primary long-term motivation for this work is to develop a common analysis platform that…
Gr{\"o}bner bases is one the most powerful tools in algorithmic non-linear algebra. Their computation is an intrinsically hard problem with a complexity at least single exponential in the number of variables. However, in most of the cases,…
The characteristic feature of 5G is the diversity of its services for different user needs. However, the requirements for these services are competing in nature, which impresses the necessity of a coordinated and flexible network…
Designing project-based learning (PBL) demands managing highly interdependent components, a task that both traditional linear tools and purely conversational AI struggle with. Traditional tools fail to capture the non-linear nature of…
In this paper we present an algorithm for computing all algebraic intermediate subfields in a separably generated unirational field extension (which in particular includes the zero characteristic case). One of the main tools is Groebner…
We present a generic and executable formalization of signature-based algorithms (such as Faug\`ere's $F_5$) for computing Gr\"obner bases, as well as their mathematical background, in the Isabelle/HOL proof assistant. Said algorithms are…
We describe jsCcoq, a new platform and user environment for the Coq interactive proof assistant. The jsCoq system targets the HTML5-ECMAScript 2015 specification, and it is typically run inside a standards-compliant browser, without the…
We study the complexity of Gr\"obner bases computation, in particular in the generic situation where the variables are in simultaneous Noether position with respect to the system. We give a bound on the number of polynomials of degree $d$…
In recent years, the research community has raised serious questions about the reproducibility of scientific work. In particular, since many studies include some kind of computing work, reproducibility is also a technological challenge, not…
We present the CosmoBolognaLib, a large set of Open Source C++ numerical libraries for cosmological calculations. CosmoBolognaLib is a living project aimed at defining a common numerical environment for cosmological investigations of the…
We generalize the list decoding algorithm for Hermitian codes proposed by Lee and O'Sullivan based on Gr\"obner bases to general one-point AG codes, under an assumption weaker than one used by Beelen and Brander. By using the same…