Related papers: Symbolic computations in differential geometry
This paper presents an experimental performance study of implementations of three symbolic algorithms for solving band matrix systems of linear algebraic equations with heptadiagonal, pentadiagonal, and tridiagonal coefficient matrices. The…
We provide a survey of results from symbolic dynamics and algebraic topology relating to Grout, a new user-friendly program developed to calculate combinatorial properties and topological invariants of a large class of symbolic…
Data-driven deep learning has been successfully applied to various computed tomographic reconstruction problems. The deep inference models may outperform existing analytical and iterative algorithms, especially in ill-posed CT…
We introduce the Bandicoot C++ library for linear algebra and scientific computing on GPUs, overviewing its user interface and performance characteristics, as well as the technical details of its internal design. Bandicoot is the…
Most computer algebra systems (CAS) support symbolic integration as core functionality. The majority of the integration packages use a combination of heuristic algebraic and rule-based (integration table) methods. In this paper, we present…
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…
Cylindrical Algebraic Decomposition (CAD) is an important tool within computational real algebraic geometry, capable of solving many problems for polynomial systems over the reals. It has long been studied by the Symbolic Computation…
A Mathematica based program has been elaborated in order to determine the symmetry group of a finite difference equation, by means of its differential representation. The package provides functions which enable us to solve the determining…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
We contemplate this article to help the teachers of programming in his aspiration for giving some appropriate and interesting examples. The work will be especially useful for students-future programmers, and for their lecturers. Some of the…
Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…
Object-oriented programming languages such as Java and Objective C have become popular for implementing agent-based and other object-based simulations since objects in those languages can {\em reflect} (i.e. make runtime queries of an…
Visibility is a fundamental concept in computational geometry, with numerous applications in surveillance, robotics, and games. This software paper presents T\v{r}iVis, a C++ library developed by the authors for computing numerous…
Symbolic regression is a machine learning technique that can learn the governing formulas of data and thus has the potential to transform scientific discovery. However, symbolic regression is still limited in the complexity and…
We survey the application of computer algebra in the context of gravitational theories. After some general remarks, we show of how to check the second Bianchi-identity by means of the Reduce package Excalc. Subsequently we list some…
This paper presents the SPARE C++ library, an open source software tool conceived to build pattern recognition and soft computing systems. The library follows the requirement of the generality: most of the implemented algorithms are able to…
Interpretable regression models are important for many application domains, as they allow experts to understand relations between variables from sparse data. Symbolic regression addresses this issue by searching the space of all possible…
Hybrid systems are increasingly used in critical applications such as medical devices, infrastructure systems, and autonomous vehicles. Lince is an academic tool for specifying and simulating such systems using a C-like language with…
We exhibit differential geometric structures that arise in numerical methods, based on the construction of Cauchy sequences, that are currently used to prove explicitly the existence of weak solutions to functional equations. We describe…
Differentiable programming allows for derivatives of functions implemented via computer code to be calculated automatically. These derivatives are calculated using automatic differentiation (AD). This thesis explores two applications of…