Related papers: FinInG: a package for Finite Incidence Geometry

We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…

We present recent computer algebra methods that support the calculations of (multivariate) series solutions for (certain coupled systems of partial) linear differential equations. The summand of the series solutions may be built by…

We prove a characterization of profinite algebras, i.e., topological algebras that are isomorphic to a projective limit of finite discrete algebras. In general profiniteness concerns both the topological and algebraic characteristics of a…

Finite frame theory has become a powerful tool for many applications of mathematics. In this paper we introduce a new area of research in frame theory: Integer frames. These are frames having all integer coordinates with respect to a fixed…

This article introduces a benchmark application for seismic modeling using finite difference method, which is namedMiniMod, a mini application for seismic modeling. The purpose is to provide a benchmark suite that is, on one hand easy to…

We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness…

Semantic inpainting or image completion alludes to the task of inferring arbitrary large missing regions in images based on image semantics. Since the prediction of image pixels requires an indication of high-level context, this makes it…

Computer based techniques for recognizing finitely presented groups are quite powerful. Tools available for this purpose are outlined. They are available both in stand-alone programs and in more comprehensive systems. A general…

We introduce Infinigen, a procedural generator of photorealistic 3D scenes of the natural world. Infinigen is entirely procedural: every asset, from shape to texture, is generated from scratch via randomized mathematical rules, using no…

We demonstrate a construction method based on a gain function that is defined on the incidence graph of an incidence geometry. Restricting to when the incidence geometry is a linear space, we show that the construction yields a generalized…

A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…

Finite automata are used to encode geometric figures, functions and can be used for image compression and processing. The original approach is to represent each point of a figure in $\mathbb{R}^n$ as a convolution of its $n$ coordinates…

Algebraic multigrid (AMG) is conventionally applied in a black-box fashion, agnostic to the underlying geometry. In this work, we propose that using geometric information -- when available -- to assist with setting up the AMG hierarchy is…

Convolutional Neural Networks have rapidly become the most successful machine learning algorithm, enabling ubiquitous machine vision and intelligent decisions on even embedded computing-systems. While the underlying arithmetic is…

Over the past few years, neural network methods have evolved in various directions for approximating partial differential equations (PDEs). A promising new development is the integration of neural networks with classical numerical…

The design and implementation of parallel algorithms is a fundamental task in computer algebra. Combining the computer algebra system Singular and the workflow management system GPI-Space, we have developed an infrastructure for massively…

Geometric methods proposed by Stallings for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups. In the present paper we employ the…

With the help of link diagrams with decorated crossings, I explain computations in emergent algebras, introduced in arXiv:0907.1520, as the kind of computations done in the front end visual system.

Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…

T-IFISS is a finite element software package for studying finite element solution algorithms for deterministic and parametric elliptic partial differential equations. The emphasis is on self-adaptive algorithms with rigorous error control…