相关论文: PySymmPol: Symmetric Polynomials in Python

The solutions of a system of polynomials in several variables are often needed, e.g.: in the design of mechanical systems, and in phase-space analyses of nonlinear biological dynamics. Reliable, accurate, and comprehensive numerical…

In an isomorphic copy of the ring of symmetric polynomials we study some families of polynomials which are indexed by rational weight vectors. These families include well known symmetric polynomials, such as the elementary, homogeneous, and…

Zernike polynomials serve as an orthogonal basis on the unit disc, and have proven to be effective in optics simulations, astrophysics, and more recently in plasma simulations. Unlike Bessel functions, Zernike polynomials are inherently…

Pattern matching is a powerful tool for symbolic computations. Applications include term rewriting systems, as well as the manipulation of symbolic expressions, abstract syntax trees, and XML and JSON data. It also allows for an intuitive…

We present PyMoosh, a Python-based simulation library designed to provide a comprehensive set of numerical tools allowing to compute essentially all optical characteristics of multilayered structures, ranging from reflectance and…

Motivation: Accurate detection of sequence similarity and homologous recombination are essential parts of many evolutionary analyses. Results: We have developed SimPlot++, an open-source multiplatform application implemented in Python,…

Molecular dynamics simulations play an increasingly important role in the rational design of (nano)-materials and in the study of biomacromolecules. However, generating input files and realistic starting coordinates for these simulations is…

Background and Objective: Deep learning enables tremendous progress in medical image analysis. One driving force of this progress are open-source frameworks like TensorFlow and PyTorch. However, these frameworks rarely address issues…

Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from…

Synchrotron processes, the radiative processes associated with the interaction of energetic charged particles with magnetic field, are of interest in many areas in astronomy, from the interstellar medium to extreme environments near compact…

The Macaulay2 package SumsOfSquares decomposes polynomials as sums of squares. It is based on methods to rationalize sum-of-squares decompositions due to Parrilo and Peyrl. The package features a data type for sums-of-squares polynomials,…

In this technical report, we describe a new version of SimpleSBML which provides an easier to use interface to python-libSBML allowing users of Python to more easily construct, edit, and inspect SBML based models. The most commonly used…

E-graphs have emerged as a versatile data structure with applications in synthesis, optimization, and verification through techniques such as equality saturation. This paper introduces Python bindings for the experimental egglog library…

Consider the algebra Q<<x_1,x_2,...>> of formal power series in countably many noncommuting variables over the rationals. The subalgebra Pi(x_1,x_2,...) of symmetric functions in noncommuting variables consists of all elements invariant…

One of the most attractive features of R is its linear modeling capabilities. We describe a Python package, salmon, that brings the best of R's linear modeling functionality to Python in a Pythonic way -- by providing composable objects for…

$clustertools$ is a Python package for analyzing star cluster simulations. The package is built around the $StarCluster$ class, which stores all data read in from the snapshot of a given model star cluster. The package contains functions…

Condensed matter compounds typically form crystals, which break the rotational and translational invariance of space but remain invariant under a discrete set of symmetry operations. Understanding the effects allowed by this symmetry…

We here specialize the standard matrix-valued polynomial interpolation to the case where on the imaginary axis the interpolating polynomials admit various symmetries: Positive semidefinite, Skew-Hermitian, $J$-Hermitian, Hamiltonian and…

We introduce hankl, a lightweight Python implementation of the FFTLog algorithm for Cosmology. The FFTLog algorithm is an extension of the Fast Fourier Transform (FFT) for logarithmically spaced periodic sequences. It can be used to…

The dynamic mode decomposition (DMD) is a simple and powerful data-driven modeling technique that is capable of revealing coherent spatiotemporal patterns from data. The method's linear algebra-based formulation additionally allows for a…