Related papers: Drinfeld modules in SageMath
In this paper we describe the compactification of the Drinfeld modular curve. This compactification is analogous to the compactification of the classical modular curve given by Katz and Mazur. We show how the Weil pairing on Drinfeld…
When travelling from the number fields theory to the function fields theory, one cannot miss the deep analogy between rank 1 Drinfeld modules and the group of root of unity and the analogy between rank 2 Drinfeld modules and elliptic…
The article describes the advisable ways of the cloud-based systems use to support students collaboration in the process of math disciplines learning. The SageMathCloud-based component that aggregates electronic resources for several math…
We give a global description of the Frobenius elements in the division fields of Drinfeld modules of rank $2$. We apply this description to derive a criterion for the splitting modulo primes of a class of non-solvable polynomials, and to…
We study the structure of the vector space of Drinfeld quasi-modular forms for congruence subgroups. We provide representations as polynomials in the false Eisenstein series with coefficients in the space of Drinfeld modular forms (the…
In-situ small- and wide-angle scattering experiments at synchrotrons often result in massive amounts of data within seconds only. Especially during such beamtimes, processing of the acquired data online, so without mentionable delay, is key…
We provide a direct proof of the Drinfeld realization for the quantum affine algebras.
Let $\mathbb{F}_q[T]$ be the polynomial ring over a finite field $\mathbb{F}_q$. We study the endomorphism rings of Drinfeld $\mathbb{F}_q[T]$-modules of arbitrary rank over finite fields. We compare the endomorphism rings to their subrings…
A braided tensor category $FM_{\kappa}$ of `factorizable D-modules' over configuration spaces is introduced, analogous to the category $FS_q$ of factorizable sheaves from q-alg/9604001. This category is equivalent to the category of finite…
We provide an explicit construction of skew cell modules for diagram algebras.
Motivated by finding analogues of elliptic curve point counting techniques, we introduce one deterministic and two new Monte Carlo randomized algorithms to compute the characteristic polynomial of a finite rank-two Drinfeld module. We…
This paper presents the basic concepts and the module structure of the Distributed and Unified Numerics Environment and reflects on recent developments and general changes that happened since the release of the first Dune version in 2007…
The construction and classification of super-modular categories is an ongoing project, of interest in algebra, topology and physics. In a recent paper, Cho, Kim, Seo and You produced two mysterious families of super-modular data, with no…
Inclusion preserving maps from modules over an Artin algebra to complete partially ordered sets are studied. This yields a filtration of the Ziegler spectrum which is indexed by all Gabriel-Roiter measures. Another application is a…
We prove a uniqueness theorem for irreducible non-critical Gelfand-Tsetlin modules. The uniqueness result leads to a complete classification of the irreducible Gelfand-Tsetlin modules with 1-singularity. An explicit construction of such…
Developing new functionality for underwater robots and testing them in the real world is time-consuming and resource-intensive. Simulation environments allow for rapid testing before field deployment. However, existing tools lack certain…
We propose and rigorously analyze two randomized algorithms to factor univariate polynomials over finite fields using rank $2$ Drinfeld modules. The first algorithm estimates the degree of an irreducible factor of a polynomial from…
The question we propose to answer throughout this paper is the following: Given an isogeny class of Drinfeld modules over a finite field, what are the orders of the corresponding endomorphism algebra (which is an isogeny invariant) that…
SrRietveld is a highly automated software toolkit for Rietveld refinement. Compared to traditional refinement programs, it is more efficient to use and easier to learn. It is designed for modern high throughput diffractometers and capable…
Recently, with the advent of deep convolutional neural networks (DCNN), the improvements in visual saliency prediction research are impressive. One possible direction to approach the next improvement is to fully characterize the multi-scale…