Related papers: The software package SpectralSequences
We present a new package ZpL for the mathematical software system SM. It implements a sharp tracking of precision on p-adic numbers, following the theory of ultrametric precision introduced in [4]. The underlying algorithms are mostly based…
In this article we construct what we call a higher spectral sequence for any chain complex (or topological space) that is filtered in $n$ compatible ways. For this we extend the previous spectral system construction of the author, and we…
Specialized computational chemistry packages have permanently reshaped the landscape of chemical and materials science by providing tools to support and guide experimental efforts and for the prediction of atomistic and electronic…
The analysis of experimental results with Python often requires writing many code scripts which all need access to the same set of functions. In a common field of research, this set will be nearly the same for many users. The qspec Python…
This preprint contains a description of a package for Mathematica called EinS. This package allows one to perform various calculations with indexed objects.
stagedtrees is an R package which includes several algorithms for learning the structure of staged trees and chain event graphs from data. Score-based and clustering-based algorithms are implemented, as well as various functionalities to…
An R package SpatialPack that implements routines to compute point estimators and perform hypothesis testing of the spatial association between two stochastic sequences is introduced. These methods address the spatial association between…
In previous work we described how the process algebra based language PSF can be used in software engineering, using the ToolBus, a coordination architecture also based on process algebra, as implementation model. In this article we…
We present the Matlab toolbox MacaulayLab, which implements numerical linear algebra algorithms for solving multivariate polynomial systems and rectangular multiparameter eigenvalue problems. Its structure and functionality are the result…
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…
A computer-algebra aided method is carried out, for determining geometric objects associated to differential operators that satisfy the elliptic ansatz. This results in examples of Lame curves with double reduction and in the explicit…
Automated searches for strong gravitational lensing in optical imaging survey datasets often employ machine learning and deep learning approaches. These techniques require more example systems to train the algorithms than have presently…
We give a summary on spectral techniques for finite dimensional algebras and study its link to singularity theory. In particular, we offer a contribution to the categorification of the Milnor lattice of two-dimensional singularities through…
Spectral 3D computer vision examines both the geometric and spectral properties of objects. It provides a deeper understanding of an object's physical properties by providing information from narrow bands in various regions of the…
We present a method to compute the degrees of the Segre classes of a subscheme of complex projective space. The method is based on generic residuation and intersection theory. It has been implemented using the software system Macaulay2.
Computer algebra systems are complex software systems that cover a wide range of scientific and practical problems. However, the absolute coverage cannot be achieved. Often, it is required to create a user extension for an existing computer…
In this article, we describe the theoretical foundations of the Macaulay2 package ConnectionMatrices and explain how to use it. For a left ideal in the Weyl algebra that is of finite holonomic rank, we implement the computation of the…
Macaulay dual spaces provide a local description of an affine scheme and give rise to computational machinery that is compatible with the methods of numerical algebraic geometry. We introduce eliminating dual spaces, use them for computing…
We offer a Maple package {\tt Poincare\_Series} for calculating the Poincar\'e series for the algebras of invariants/covariants of binary forms, for the algebras of joint invariants/covariants of several binary forms, for the kernel of…
Speckle patterns are used in a broad range of applications including microscopy, imaging, and light-matter interactions. Tailoring speckles' statistics can dramatically enhance their performance in applications. We present an experimental…