Related papers: The Virtual Resolutions Package for Macaulay2
This paper introduces soliton_solver, an open-source GPU-accelerated software package for the simulation and real-time visualization of topological solitons in two-dimensional non-linear field theories. The software is structured around a…
We discuss an algorithm computing the push-forward to projective space of several classes associated to a (possibly singular, reducible, nonreduced) projective scheme. For example, the algorithm yields the topological Euler characteristic…
Twistronics is an emerging and captivating field in condensed matter physics and material science. However, accurately and efficiently calculating the electronic structures of twisted systems remains a significant challenge. To address…
We present an algorithm for computing curves and families of curves of prescribed degree and geometric genus on real rational surfaces.
Quantum computer provides new opportunities for quantum chemistry. In this article, we present a versatile, extensible, and efficient software package, named Q$^2$Chemistry, for developing quantum algorithms and quantum inspired classical…
We describe an algorithm for computing Macaulay dual spaces for multi-graded ideals. For homogeneous ideals, the natural grading is inherited by the Macaulay dual space which has been leveraged to develop algorithms to compute the Macaulay…
Quadratic hypersurfaces are a natural generalization of affine subspaces, and projections are elementary blocks of algorithms in optimization and machine learning. It is therefore intriguing that no proper studies and tools have been…
We give an introduction to the Mathematica package Lambda, designed for calculating $\lambda$-brackets in both vertex algebras, and in SUSY vertex algebras. This is equivalent to calculating operator product expansions in two-dimensional…
A process of extending sets which can be used as foundation for an alternative organization for Differential and Integral Calculus is presented.
We present OGRe, a modern Mathematica package for tensor calculus, designed to be both powerful and user-friendly. The package can be used in a variety of contexts where tensor calculations are needed, in both mathematics and physics, but…
Analog Quantum Computers are promising tools for improving performance on applications such as modeling behavior of quantum materials, providing fast heuristic solutions to optimization problems, and simulating quantum systems. Due to the…
We survey some general-purpose symbolic software packages that implement algorithms from enumerative and analytic combinatorics. Software for the following areas is covered: basic combinatorial objects, symbolic combinatorics, P\'olya…
For simulation studies of (macro) molecular liquids it would be of significant interest to be able to adjust or increase the level of resolution within one region of space, while allowing for the free exchange of molecules between open…
The CompModels package for R provides a suite of computer model test functions that can be used for computer model prediction/emulation, uncertainty quantification, and calibration, but in particular, the sequential optimization of computer…
Engineers and computational scientists often study the behavior of their simulations by repeated solutions with variations in their parameters, which can be for instance boundary values or initial conditions. Through such simulation…
Mayavi is an open-source, general-purpose, 3D scientific visualization package. It seeks to provide easy and interactive tools for data visualization that fit with the scientific user's workflow. For this purpose, Mayavi provides several…
In this paper we report on an application of computer algebra in which mathematical puzzles are generated of a type that had been widely used in mathematics contests by a large number of participants worldwide. The algorithmic aspect of our…
We describe a significant update to the Macaulay2 package A1BrouwerDegrees. We extend several methods in the previous version of the package to the setting of finite \'{e}tale algebras, allowing the computation of transfers along finite…
The virtual reality (VR) provides us a three-dimensional, immersive, and fully interactive visualization environment. To make the best use of the VR's potential in scientific visualization, a VR visualization software named VFIVE has been…
The minimal free resolution of the coordinate ring of a complete intersection in projective space is a Koszul complex on a regular sequence. In the product of projective spaces $\mathbb{P}^1 \times \mathbb{P}^1$, we investigate which sets…