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The large data volumes expected from the High Luminosity LHC (HL-LHC) present challenges to existing paradigms and facilities for end-user data analysis. Modern cyberinfrastructure tools provide a diverse set of services that can be…
In this note, we extend modular techniques for computing Gr\"obner bases from the commutative setting to the vast class of noncommutative $G$-algebras. As in the commutative case, an effective verification test is only known to us in the…
Computation nowadays is becoming inherently concurrent, either because of characteristics of the hardware (with multicore processors becoming omnipresent) or due to the ubiquitous presence of distributed systems (incarnated in the…
This note is based on the plenary talk given by the second author at MACIS 2015, the Sixth International Conference on Mathematical Aspects of Computer and Information Sciences. Motivated by some of the work done within the Priority…
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…
Generalized quasi-cyclic (GQC) codes form a wide and useful class of linear codes that includes thoroughly quasi-cyclic codes, finite geometry (FG) low density parity check (LDPC) codes, and Hermitian codes. Although it is known that the…
Hilbert schemes of zero-dimensional ideals in a polynomial ring can be covered with suitable affine open subschemes whose construction is achieved using border bases. Moreover, border bases have proved to be an excellent tool for describing…
Question answering over knowledge bases (KBQA) has become a popular approach to help users extract information from knowledge bases. Although several systems exist, choosing one suitable for a particular application scenario is difficult.…
Let $(f\_1,\dots, f\_s) \in \mathbb{Q}\_p [X\_1,\dots, X\_n]^s$ be a sequence of homogeneous polynomials with $p$-adic coefficients. Such system may happen, for example, in arithmetic geometry. Yet, since $\mathbb{Q}\_p$ is not an effective…
The complexity of Gr\"{o}bner computations has inspired many improvements to Buchberger's algorithm over the years. Looking for further insights into the algorithm's performance, we offer a threaded implementation of classical Buchberger's…
Covalent Organic Frameworks (COFs) have gained significant popularity in recent years due to their unique ability to provide a high surface area and customizable pore geometry and chemistry. These traits make COFs a highly promising choice…
In mobile network research, the integration of real-world components such as User Equipment (UE) with open-source network infrastructure is essential yet challenging. To address these issues, we introduce open5Gcube, a modular framework…
This paper is a survey on the study of the behaviour of the composition of polynomials on the computation of Gr\"obner bases. This survey brings together some works published between 1995 and 2007. The authors of these papers gave answers…
Prior to the public release of Kubernetes it was difficult to conduct joint development of elaborate analysis facilities due to the highly non-homogeneous nature of hardware and network topology across compute facilities. However, since the…
What is Sequence Algebra? This is a question that any teacher or student of mathematics or computer science can engage with. Sequences are in Calculus, Combinatorics, Statistics and Computation. They are foundational, a step up from number…
The Coq Platform is a continuously developed distribution of the Coq proof assistant together with commonly used libraries, plugins, and external tools useful in Coq-based formal verification projects. The Coq Platform enables reproducing…
Conventional coded computing frameworks are predominantly tailored for structured computations, such as matrix multiplication and polynomial evaluation. Such tasks allow the reuse of tools and techniques from algebraic coding theory to…
Ihe first author presented an efficient algorithm for computing involutive (and reduced Groebner) bases. In this paper, we consider a modification of this algorithm which simplifies matters to understand it and to implement. We prove…
Given a parametric polynomial ideal I, the algorithm DISPGB, introduced by the author in 2002, builds up a binary tree describing a dichotomic discussion of the different reduced Groebner bases depending on the values of the parameters,…
List decoding of Hermitian codes is reformulated to allow an efficient and simple algorithm for the interpolation step. The algorithm is developed using the theory of Groebner bases of modules. The computational complexity of the algorithm…