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Open problems from the 15th Annual ACM Symposium on Computational Geometry.
Software engineering research benefited for decades from openly available tools, accessible systems, and problems that could be studied at modest scale. Today, many of the most relevant software systems are large, proprietary, and embedded…
Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of…
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…
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
This article presents some aspects and experience in the use of algebraic manipulation software applied to general relativity. Some years ago certain results were reported using computer algebra platforms, but the growing popularity of…
What is the best representation for doing euclidean geometry on computers? These notes from a SIGGRAPH 2019 short course entitled "Geometric algebra for computer graphics" introduce projective geometric algebra (PGA) as a modern framework…
Various fields of science and engineering rely on linear algebra for large scale data analysis, modeling and simulation, machine learning, and other applied problems. Linear algebra computations often dominate the execution time of such…
The Art Gallery Problem is one of the most well-known problems in Computational Geometry, with a rich history in the study of algorithms, complexity, and variants. Recently there has been a surge in experimental work on the problem. In this…
This list of problems arose as a collaborative effort among the participants of the Arbeitsgemeinschaft on Mathematical Quasicrystals, which was held at the Mathematisches Forschungsinstitut Oberwolfach in October 2015. The purpose of our…
Applications integrating analysis components require a programmable interface which defines statistical operations independently of any programming language. By separating concerns of scientific computing from application and implementation…
The reproduction and replication of novel results has become a major issue for a number of scientific disciplines. In computer science and related computational disciplines such as systems biology, the issues closely revolve around the…
Given a parametric polynomial ideal I, the algorithm DISPGB, introduced by the author in 2002, builds up a binary tree describing a dichotomic discussion of the different reduced Groebner bases depending on the values of the parameters,…
Orientation of modern software systems towards data-intensive processing raises new difficulties in software engineering on how to build and maintain such systems. Some of the important challenges concern the design of software…
Context: Advancements in machine learning (ML) lead to a shift from the traditional view of software development, where algorithms are hard-coded by humans, to ML systems materialized through learning from data. Therefore, we need to…
This is a user guide for the first version of our developed Maple library, named Singularity. The first version here is designed for the qualitative study of local real zeros of scalar smooth maps. This library will be extended for symbolic…
The article highlights the promising ways of providing access to the mathematical software in higher educational institutions. It is emphasized that the cloud computing services implementation is the actual trend of modern ICT pedagogical…
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
This is the list of open problems in topological algebra posed on the conference dedicated to the 20th anniversary of the Chair of Algebra and Topology of Lviv National University, that was held on 28 September 2001.