Related papers: A user guide for Singularity
Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets, with applications within algebraic geometry and beyond. We recently reported on a new implementation of CAD in Maple which…
We present the first public release of ShapePipe, an open-source and modular weak-lensing measurement, analysis, and validation pipeline written in Python. We describe the design of the software and justify the choices made. We provide a…
The Lean mathematical library mathlib is developed by a community of users with very different backgrounds and levels of experience. To lower the barrier of entry for contributors and to lessen the burden of reviewing contributions, we have…
We give a brief historical overview of the development of the Computer Algebra System SINGULAR: why it came about and how the development was related to the attempt to refute Zariski's multiplicity conjecture.
Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets. Originally introduced by Collins in the 1970s for use in quantifier elimination it has since found numerous applications within…
We develop a new symbolic-numeric algorithm for the certification of singular isolated points, using their associated local ring structure and certified numerical computations. An improvement of an existing method to compute inverse systems…
In this work, we investigate the optimal map-making technique for the linear system $d=Ax+n$ while carefully taking into account singularities that may come from either the covariance matrix $C = \langle nn^t \rangle$ or the main matrix…
We present the package SADE (Symmetry Analysis of Differential Equations) for the determination of symmetries and related properties of systems of differential equations. The main methods implemented are: Lie, nonclassical, Lie-B\"acklund…
As machine learning is applied more widely, data scientists often struggle to find or create end-to-end machine learning systems for specific tasks. The proliferation of libraries and frameworks and the complexity of the tasks have led to…
We present Mirror, an open-source platform for data exploration and analysis powered by large language models. Mirror offers an intuitive natural language interface for querying databases, and automatically generates executable SQL commands…
Open science is a fundamental pillar to promote scientific progress and collaboration, based on the principles of open data, open source and open access. However, the requirements for publishing and sharing open data are in many cases…
Developing a 21st Century Global Library for Mathematics Research discusses how information about what the mathematical literature contains can be formalized and made easier to express, encode, and explore. Many of the tools necessary to…
Machine learning (ML) models rely heavily on consistent and accurate performance metrics to evaluate and compare their effectiveness. However, existing libraries often suffer from fragmentation, inconsistent implementations, and…
Monocular Re-Localization (MRL) is a critical component in autonomous applications, estimating 6 degree-of-freedom ego poses w.r.t. the scene map based on monocular images. In recent decades, significant progress has been made in the…
With the expansion of scientific research, the number of scientific research is increasing. A new urgent problem is raised that how to keep these researches in a proper way. Therefore, knowledge mapping methods come into being, providing a…
In this article, we discuss formal invariants of singularly-perturbed linear differential systems in neighborhood of turning points and give algorithms which allow their computation. The algorithms proposed are implemented in the computer…
Systematic literature studies have received much attention in empirical software engineering in recent years. They have become a powerful tool to collect and structure reported knowledge in a systematic and reproducible way. We distinguish…
Many computer science disciplines (e.g., combinatorial optimization, natural language processing, and information retrieval) use standard or established test suites for evaluating algorithms. In visualization, similar approaches have been…
A classical approach for surface classification is to find a compact algebraic representation for each surface that would be similar for objects within the same class and preserve dissimilarities between classes. We introduce Self…
This is the first of a series of papers studying real algebraic threefolds using the minimal model program. The main results are outlined in Part II. The present part I. contains the necessary preliminary work concerning terminal…