Related papers: The Virtual Resolutions Package for Macaulay2
In this paper we discuss the design and implementation of a plasma display panel for a wide field of view desktop virtual reality environment. Present commercial plasma displays are not designed with virtual reality in mind, leading to…
A new method for solving systems of linear algebraic equations of a special type arising in solving problems of image reconstruction has been proposed. This method, due to a certain symmetry of the matrix and the choice of the voxel…
In the present work we generalize the curvilinear Virtual Element technology, introduced for a simple linear scalar problem in a previous work, to generic 2D solid mechanic problems in small deformations. Such generalization also includes…
We present a virtual reality display that is capable of generating a dense collection of depth/focal planes. This is achieved by driving a focus-tunable lens to sweep a range of focal lengths at a high frequency and, subsequently, tracking…
The ability to rapidly test a variety of algorithms for an arbitrary state estimation task is valuable in the prototyping phase of navigation systems. Lie group theory is now mainstream in the robotics community, and hence estimation…
We have developed a graphical user interface (GUI) based package $\mu$2mech to perform phase-field simulation for predicting microstructure evolution. The package can take inputs from ab initio calculations and CALPHAD (Calculation of Phase…
A toolbox for creation and rendering of dynamic virtual acoustic environments (TASCAR) that allows direct user interaction was developed for application in hearing aid research and audiology. This technical paper describes the general…
Visualization researchers and visualization professionals seek appropriate abstractions of visualization requirements that permit considering visualization solutions independently from specific problems. Abstractions can help us design,…
The aim of this article is to give a method to construct bimodule resolutions of associative algebras, generalizing Bardzell's well-known resolution of monomial algebras. We stress that this method leads to concrete computations, providing…
CP2K is a versatile open-source software package for simulations across a wide range of atomistic systems, from isolated molecules in the gas phase to low-dimensional functional materials and interfaces, as well as highly symmetric…
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…
This article introduces Globular, an online proof assistant for the formalization and verification of proofs in higher-dimensional category theory. The tool produces graphical visualizations of higher-dimensional proofs, assists in their…
The computation of microlensing light curves represents a bottleneck for the modeling of planetary events, making broad searches in the vast parameter space of microlensing extremely time-consuming. The release of the first version of…
Virtual Reality has become an important educational tool, due to the pandemic and increasing globalization of education. This paper presents a framework for teaching Virtual Anatomy at the university level. Virtual classes have become a…
In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…
In this paper we provide a description of the package \textit{PolyominoIdeals} for \textit{Macaulay2} that allows to deal with collections of cells, polyominoes and related binomial ideals.
In this paper, some real-world motivated examples are provided illustrating the power of linear algebra tools as the product of matrices, determinants, eigenvalues and eigenvectors. In this sense, some practical applications related to…
XMDS2 is a cross-platform, GPL-licensed, open source package for numerically integrating initial value problems that range from a single ordinary differential equation up to systems of coupled stochastic partial differential equations. The…
Alignment between real and virtual objects is a challenging task required for the deployment of Mixed Reality (MR) into manufacturing, medical, and construction applications. To face this challenge, a series of methods have been proposed.…
These notes survey some basic results in toric varieties over a field with examples and applications. A computer algebra package (written by the second author) is described which deals with both affine and projective toric varieties in any…