Related papers: Drinfeld modules in SageMath
In this paper, we investigate properties of modules introduced by Kra\'skiewicz and Pragacz which realize Schubert polynomials as their characters. In particular, we give some characterizations of modules having a filtration by…
We continue the study of projective module wavelet frames corresponding to diagonal dilation matrices on $\mathbb R^n$ with integer entries, focusing on the construction of a projective multi-resolution analysis corresponding to dilations…
We introduce the formalism of Coleman's power series for rank 1 Drinfeld modules and apply it to formulate and prove the analogue of Wiles' explicit reciprocity law in this setting.
Advances in robotic automation, high-performance computing (HPC), and artificial intelligence (AI) encourage us to conceive of science factories: large, general-purpose computation- and AI-enabled self-driving laboratories (SDLs) with the…
We present a new plug-in for the ARGoS swarm robotic simulator to implement the Crazyflie drone, including its controllers, sensors, and some expansion decks. We have based our development on the former Spiri drone, upgrading the position…
The perception module of self-driving vehicles relies on a multi-sensor system to understand its environment. Recent advancements in deep learning have led to the rapid development of approaches that integrate multi-sensory measurements to…
In this paper we study the robustness of dynamically gradient multivalued semiflows. As an application, we describe the dynamical properties of a family of Chafee-Infante problems approximating a differential inclusion studied in [3],…
The notion of singular reduction modules, i.e., of singular modules of nonclassical (conditional) symmetry, of differential equations is introduced. It is shown that the derivation of nonclassical symmetries for differential equations can…
Over fields of characteristic zero, we determine all absolutely irreducible Yetter-Drinfeld modules over groups that have prime dimension and yield a finite-dimensional Nichols algebra. To achieve our goal, we introduce orders of braided…
We state and prove a formula for a certain value of the Goss L-function of a Drinfeld module. This gives characteristic-p-valued function field analogues of the class number formula and of the Birch and Swinnerton-Dyer conjecture. The…
We develop tools for constructing rigid analytic trivializations for Drinfeld modules as infinite products of Frobenius twists of matrices, from which we recover the rigid analytic trivialization given by Pellarin in terms of Anderson…
In the arithmetic of function fields Drinfeld modules play the role that elliptic curves take on in the arithmetic of number fields. As higher dimensional generalizations of Drinfeld modules, and as the appropriate analogues of abelian…
In previous work we have studied how an explicit representation of background knowledge associated with a specific spreadsheet can be exploited to alleviate usability problems with spreadsheet-based applications. We have implemented this…
Recent work showed that hybrid networks, which combine predefined and learnt filters within a single architecture, are more amenable to theoretical analysis and less prone to overfitting in data-limited scenarios. However, their performance…
A Drinfeld module has a $\mathfrak{p}$-adic Tate module not only for every finite place $\mathfrak{p}$ of the coefficient ring but also for $\mathfrak{p} = \infty$. This was discovered by J.-K. Yu in the form of a representation of the Weil…
In this paper, we study the ramification of extensions of a function field generated by division points of rank 2 Drinfeld modules. Also conductors of certain rank 2 Drinfeld modules are defined as analogues of those for elliptic curves. A…
We calculate the category of D-modules on the loop space of the affine line in coherent terms. Specifically, we find that this category is derived equivalent to the category of ind-coherent sheaves on the moduli space of rank one de Rham…
We describe Lagrangian algebras in twisted Drinfeld centres for finite groups. Using the full centre construction, we establish a 1-1 correspondence between Lagrangian algebras and module categories over pointed fusion categories.
Nowadays interactive digital scientific environments have become an integral part of scientific computing in solving various scientific tasks in research, but also STEM education. We introduce SageMath or shortly Sage -- a free open…
A review of the present status, recent enhancements, and applicability of the SIESTA program is presented. Since its debut in the mid-nineties, SIESTA's flexibility, efficiency and free distribution has given advanced materials simulation…