Related papers: Rota's program on algebraic operators, rewriting s…

Linear spaces with an Euclidean metric are ubiquitous in mathematics, arising both from quadratic forms and inner products. Operators on such spaces also occur naturally. In recent years, the study of multivariate operator theory has made…

This paper presents an algebraic approach to characterizing higher-order differential operators. While the foundational Leibniz rule addresses first-order derivatives, its extension to higher orders typically involves identities relating…

In this article we continue to explore the notion of Rota-Baxter algebras in the context of the Hopf algebraic approach to renormalization theory in perturbative quantum field theory. We show in very simple algebraic terms that the…

In this paper, we extend the concept of Lie superalgebras to a more generalized framework called Super-Lie superalgebras. In addition, they seem to be exploring various supergeneralizations of other algebraic structures, such as…

Introduced by Tate in [Ta71], Tate algebras play a major role in the context of analytic geometry over the-adics, where they act as a counterpart to the use of polynomial algebras in classical algebraic geometry. In [CVV19] the formalism of…

Motivated by better understanding the bideterminant (=product of minors) basis on the polynomial ring in $n \times m$ variables, we develop theory \& algorithms for Gr\"obner bases in not only algebras with straightening law (ASLs or Hodge…

We describe several technical tools that prove to be efficient for investigating the rewrite systems associated with a family of algebraic laws, and might be useful for more general rewrite systems. These tools consist in introducing a…

This paper is concerned with linear algebra based methods for solving exactly polynomial systems through so-called Gr\"obner bases, which allow one to compute modulo the polynomial ideal generated by the input equations. This is a topical…

This note surveys the historical background of the Gr\"obner basis theory for D-modules and linear rewriting theory. The objective is to present a deep interaction of these two fields largely developed in algebra throughout the twentieth…

A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and…

This work revisits operator learning from a spectral perspective by introducing Polar Linear Algebra, a structured framework based on polar geometry that combines a linear radial component with a periodic angular component. Starting from…

In this paper, we tackle the problem of automatically generating algorithms for linear algebra operations by taking advantage of problem-specific knowledge. In most situations, users possess much more information about the problem at hand…

Recent research in extensions of Answer Set Programming has included a renewed interest in the language of Epistemic Specifications, which adds modal operators K ("known") and M ("may be true") to provide for more powerful introspective…

Tate introduced in [Ta71] the notion of Tate algebras to serve, in the context of analytic geometry over the-adics, as a counterpart of polynomial algebras in classical algebraic geometry. In [CVV19, CVV20] the formalism of Gr{\"o}bner…

The notion of commutative integro-differential algebra was introduced for the algebraic study of boundary problems for linear ordinary differential equations. Its noncommutative analog achieves a similar purpose for linear systems of such…

We consider the problem of determining Gr\"obner bases of binomial ideals associated with linear error correcting codes. Computation of Gr\"obner bases of linear codes have become a topic of interest to many researchers in coding theory…

Recent advances in stochastic PDEs, Hopf algebras of typed trees and integral equations have inspired the study of algebraic structures with replicating operations. To understand their algebraic and combinatorial nature, we first use rooted…

In this paper, by using Gr\"obner-Shirshov bases, we show that in the following classes, each (resp. countably generated) algebra can be embedded into a simple (resp. two-generated) algebra: associative differential algebras, associative…

This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…

Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…