Related papers: A user guide for Singularity
While functionality and correctness of code has traditionally been the main focus of computing educators, quality aspects of code are getting increasingly more attention. High-quality code contributes to the maintainability of software…
Fold maps are higher dimensional versions of Morse functions, which play important roles in the studies of smooth manifolds, and such general maps also have been fundamental tools in the studies of smooth manifolds by using generic maps. In…
Optimizing parallel programs for distributed systems is a complex task, often requiring significant code modifications. Task-based programming systems improve modularity by separating performance decisions from application logic, but their…
Correctness is one of the more important criteria of qualitative software. However, it is often taught in isolation and most students consider it only as an afterthought. They also do not receive sufficient feedback on code quality and…
We report on our experience formalizing differential geometry with mathlib, the Lean mathematical library. Our account is geared towards geometers with no knowledge of type theory, but eager to learn more about the formalization of…
The rise of multi-paradigm languages challenges traditional classification methods, leading to practical software engineering issues like interoperability defects. This systematic literature review (SLR) maps the formal foundations of…
There have been some effective tools for solving (constant/parametric) semi-algebraic systems in Maple's library RegularChains since Maple 13. By using the functions of the library, e.g., RealRootClassfication, one can prove and discover…
This paper introduces a novel paradigm for the analysis and verification of concurrent programs -- the Singularity Theory. We model the execution space of a concurrent program as a branched topological space, where program states are points…
Scientific software is one of the key elements for reproducible research. However, classic publications and related scientific software are typically not (sufficiently) linked, and it lacks tools to jointly explore these artefacts. In this…
We study the long-standing open problem of efficiently testing rectilinear planarity of series-parallel graphs (SP-graphs) in the variable embedding setting. A key ingredient behind the design of a linear-time testing algorithm for…
simpcomp is an extension (a so called package) to GAP, the well known system for computational discrete algebra. The package enables the user to compute numerous properties of (abstract) simplicial complexes, provides functions to construct…
In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also exercises at the end of each chapter above to let students…
Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet…
A new system of library code is proposed and initiated. It is emphasized that the same terminologies as we find in our textbooks should be used for class names in the library code. The language C# invented by Microsoft is adopted in this…
Self-organising maps are a powerful tool for cluster analysis in a wide range of data contexts. From the pioneer work of Kohonen, many variants and improvements have been proposed. This review focuses on the last decade, in order to provide…
We discuss a problem on singularity theory of differentiable (smooth) or real algebraic maps which is different from knowing existence and has been difficult: constructing explcit real algebraic functions. We discuss construction of real…
Protocol for a Systematic Mapping of the Literature, which aims to identify and classify the estimations techniques used in software development agile methodologies based on the results found, and to compare their estimation accuracies…
preCICE is a free/open-source coupling library. It enables creating partitioned multi-physics simulations by gluing together separate software packages. This paper summarizes the development efforts in preCICE of the past five years. During…
Mathematical educational soft explore, investigating in a dynamical way, some algebraically, geometrically problems, the expected results being used to involve a lot of mathematical results. One such software soft is GeoGebra. The software…
Somoclu is a massively parallel tool for training self-organizing maps on large data sets written in C++. It builds on OpenMP for multicore execution, and on MPI for distributing the workload across the nodes in a cluster. It is also able…