Related papers: Computing Arrangements of Hypersurfaces
We introduce the VirtualResolution package for the computer algebra system Macaulay2. This package has tools to construct, display, and study virtual resolutions for products of projective spaces. The package also has tools for generating…
A program to calculate the three-particle hyperspherical brackets is presented. Test results are listed and it is seen that the program is well applicable up to very high values of the hypermomentum and orbital momenta. The listed runs show…
We present the mathematical background of a software package that computes triangulations of mapping tori of surface homeomorphisms, suitable for Jeff Weeks's program SnapPea. It consists of two programs. jmt computes triangulations and…
We devise some differential forms after Chern to compute a family of formulas for comparing total mean curvatures of nested hypersurfaces in Riemannian manifolds. This yields a quicker proof of a recent result of the author with Joel…
Increasing emphasis on data and quantitative methods in the biomedical sciences is making biological research more computational. Collecting, curating, processing, and analysing large genomic and imaging data sets poses major computational…
This paper introduces the TulipaProfileFitting.jl package, a tool developed in Julia for generating renewable energy profiles that fit a specified capacity factor. It addresses the limitations of naive methods in adjusting existing profiles…
For an arrangement $\mathcal{H}$ of hyperplanes in $\mathbb{R}^n$ through the origin, a region is a connected subset of $\mathbb{R}^n\setminus\mathcal{H}$. The graph of regions $G(\mathcal{H})$ has a vertex for every region, and an edge…
We introduce ACEpotentials.jl, a Julia-language software package that constructs interatomic potentials from quantum mechanical reference data using the Atomic Cluster Expansion (Drautz, 2019). As the latter provides a complete description…
Any finite union of disjoint, mutually exterior Jordan curves in the complex plane can be approximated arbitrarily well in the Hausdorff topology by polynomial Julia sets. Furthermore, the proof is constructive.
There are plenty of excellent plotting libraries. Each excels at a different use case: one is good for printed 2D publication figures, the other at interactive 3D graphics, a third has excellent L A TEX integration or is good for creating…
Motivated by problems arising in the complex analysis of perturbative quantum field theory, we investigate the homology of finite unions of certain non-degenerate quadratic affine hypersurfaces of complex dimension $n$ in general position.…
This paper is devoted to the bounding and computation of the dimension of deformation spaces of tropical curves and hypersurfaces. This characteristic is interesting in light of the fact that it often coincides with the dimension of…
We introduce tessellation of the filled Julia sets for hyperbolic and parabolic quadratic maps. Then the dynamics inside their Julia sets are organized by tiles which work like external rays outside. We also construct continuous families of…
Using the mathematical framework of information geometry, we introduce a novel method which allows one to efficiently determine the exact shape of simultaneous confidence regions for non-linearly parametrised models. Furthermore, we show…
We report on the computation of invariants, covariants, and contravariants of cubic surfaces. All algorithms are implemented in the computer algebra system magma.
For a finite separable field extension K/k, all subfields can be obtained by intersecting so-called principal subfields of K/k. In this work we present a way to quickly compute these intersections. If the number of subfields is high, then…
The set theory relations \in, \backslash, \Delta, \cap, and \cup have corollaries in subspace relations. Geometric Algebra is introduced as the ideal framework to explore these subspace operations. The relations \in, \backslash, and \Delta…
Tropical geometry is a piecewise linear "shadow" of algebraic geometry. It allows for the computation of several cohomological invariants of an algebraic variety. In particular, its application to enumerative algebraic geometry led to…
We introduce two new packages, Nemo and Hecke, written in the Julia programming language for computer algebra and number theory. We demonstrate that high performance generic algorithms can be implemented in Julia, without the need to resort…
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…