Related papers: Groebner Bases for Everyone with CoCoA-5 and CoCoA…

Humans gather information by engaging in conversations involving a series of interconnected questions and answers. For machines to assist in information gathering, it is therefore essential to enable them to answer conversational questions.…

Many years ago, Rota proposed a program on determining algebraic identities that can be satisfied by linear operators. After an extended period of dormant, progress on this program picked up speed in recent years, thanks to perspectives…

Interpreting the internal behavior of large language models trained on code remains a critical challenge, particularly for applications demanding trust, transparency, and semantic robustness. We propose Code Concept Analysis (CoCoA): a…

The traditional split-up into a low level language and a high level language in the design of computer algebra systems may become obsolete with the advent of more versatile computer languages. We describe GiNaC, a special-purpose system…

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…

Multipersistence homology modules were introduced by G.Carlsson and A.Zomorodian which gave, together with G.Singh, an algorithm to compute their Groebner bases. Although their algorithm has polynomial complexity when the chain modules are…

We present a revived version of CERNLIB, the basis for software ecosystems of most of the pre-LHC HEP experiments. The efforts to consolidate CERNLIB are part of the activities of the Data Preservation for High Energy Physics collaboration…

This paper considers parallel Gr\"obner bases algorithms on distributed memory parallel computers with multi-core compute nodes. We summarize three different Gr\"obner bases implementations: shared memory parallel, pure distributed memory…

The main results of this paper establish a partial correspondence between two previously-studied analogues of Groebner bases in the setting of algebras: namely, subalgebra (aka SAGBI) bases for quotients of polynomial rings and Khovanskii…

Vision-language models have demonstrated impressive capabilities as computer-use agents (CUAs) capable of automating diverse computer tasks. As their commercial potential grows, critical details of the most capable CUA systems remain…

This example of Clifford algebras calculations uses GiNaC (http://www.ginac.de/) library, which includes a support for generic Clifford algebra starting from version~1.3.0. Both symbolic and numeric calculation are possible and can be…

G-algebras, or Groebner bases algebras, were considered by Levandovsky, these algebras include very important families of algebras, like the Weyl algebras and the universal enveloping algebra of a finite dimensional Lie algebra. These…

This paper introduces QOperAv v1.5, a Java application available for free. (Source code included in the distribution.) QOperAv is a "code generator" for generating quantum circuits. The quantum circuits generated by QOperAv can be used to…

Implementing large software, as software analyzers which aim to be used in industrial settings, requires a well-engineered software architecture in order to ease its daily development and its maintenance process during its lifecycle. If the…

In 1992, V. Weispfenning proved the existence of Comprehensive Groebner Bases (CGB) and gave an algorithm to compute one. That algorithm was not very efficient and not canonical. Using his suggestions, A. Montes obtained in 2002 a more…

We investigate the use of noncommutative Groebner bases in solving partially prescribed matrix inverse completion problems. The types of problems considered here are similar to those in [BLJW]. There the authors gave necessary and…

We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu's method and the Groebner bases method), their implementation and integration in educational tools. The project includes formal…

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…

Quaternionic polynomials occur naturally in applications of quaternions in science and engineering, and normalization of quaternionic polynomials is a basic manipulation. Once a Groebner basis is certified for the defining ideal I of the…

Recently, we have developed an efficient generic partition refinement algorithm, which computes behavioural equivalence on a state-based system given as an encoded coalgebra, and implemented it in the tool CoPaR. Here we extend this to a…