Related papers: On Computing Groebner Basis in the Rings of Differ…
First, we give a new proof for the Beals commutator criterion for non-magnetic Weyl pseudo-differential operators based on classical Gabor tight frames. Second, by introducing a modified 'magnetic' Gabor tight frame, we naturally derive the…
The paper aims to provide a full characterization of all operators $T\colon \mathscr{P}(\mathbb{C}) \to \mathscr{P}(\mathbb{C})$ acting on the space of all complex polynomials that satisfy the Leibniz rule \[ T(f\cdot g)= T(f)\cdot g+f\cdot…
We increase the scope of previous work on change of basis between finite bases of polynomials by defining ascending and descending bases and introducing three techniques for defining them from known ones. The minimum degrees of polynomials…
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…
The algebraic formulation of the derivation and integration related by the First Fundamental Theorem of Calculus (FFTC) gives rise to the notion of differential Rota-Baxter algebra. The notion has a remarkable list of categorical…
We present Groebner.jl, a Julia package for computing Groebner bases with the F4 algorithm. Groebner.jl is an efficient, portable, and open-source software. Groebner.jl works over integers modulo a prime and over the rationals, supports…
In this paper, we introduce novel concepts and establish a formal framework for twisted differential operators in the context of several variables. The focus is on twisted coordinates within Huber rings, which facilitate the construction of…
We aim to give a self-contained and detailed yet simplified account of the foundations of the theory of double operator integrals, in order to provide an accessible entry point to the theory. We make two new contributions to these…
Differential algebra approaches to structural identifiability analysis of a dynamic system model in many instances heavily depend upon Ritt's pseudodivision at an early step in analysis. The pseudodivision algorithm is used to find the…
Several algebro-geometric properties of commutative rings of partial differential operators as well as several geometric constructions are investigated. In particular, we show how to associate a geometric data by a commutative ring of…
In contrast with differential operators on modules over commutative and graded commutative rings, there is no satisfactory notion of a differential operator in noncommutative geometry.
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…
We give a new operator formula for Grothendieck polynomials that generalizes Magyar's Demazure operator formula for Schubert polynomials. Our proofs are purely combinatorial, contrasting with the geometric and representation theoretic tools…
A sequence $\{\delta_n^{(k)}\}$ associated to a Bochner differential operator is introduced as an effective tool to study this kind of operators. Some properties of this sequence are proven and used to deduce that a particular operator…
The structure of filtered algebras of Grothendieck's differential operators of truncated polynomials in one variable and graded Poisson algebras of their principal symbols is explicitly determined. A related infinitesimal-birational duality…
In this paper we describe how an idea centered on the concept of self-saturation allows several improvements in the computation of Groebner bases via Buchberger's Algorithm.
We consider an integral operator $\mathcal{I}$, special instances of which was studied in various contexts. Using an appropriate transformation we write this operator in terms of weighted composition operators. Then, we provide a…
The theme of symbolic computation in algebraic categories has become of utmost importance in the last decade since it enables the automatic modeling of modern algebra theories. On this theoretical background, the present paper reveals the…
In this paper, we give the first and second fundamental theorems of invariant theory for certain invariant rings whose generators are expressed by circulant determinants.
In the present paper the unconditional convergence and the invertibility of multipliers is investigated. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or…