Related papers: Computer algebra in Julia
We present the Julia interface Polymake.jl to polymake, a software for research in polyhedral geometry. We describe the technical design and how the integration into Julia makes it possible to combine polymake with state-of-the-art…
In this paper we present an introduction to the area of computability in dynamical systems. This is a fairly new field which has received quite some attention in recent years. One of the central questions in this area is if relevant…
As the twin movements of open science and open source bring an ever greater share of the scientific process into the digital realm, new opportunities arise for the meta-scientific study of science itself, including of data science and…
This paper proposes integrating Aspect-oriented Programming (AOP) into Julia, a language widely used in scientific and High-Performance Computing (HPC). AOP enhances software modularity by encapsulating cross-cutting concerns, such as…
The universal object oriented languages made programming more simple and efficient. In the article is considered possibilities of using similar methods in computer algebra. A clear and powerful universal language is useful if particular…
This is a proposal of an algebra which aims at distributed array processing. The focus lies on re-arranging and distributing array data, which may be multi-dimensional. The context of the work is scientific processing; thus, the core…
We show that under the definition of computability which is natural from the point of view of applications, there exist non-computable quadratic Julia sets.
As the main theoretical support of quantum metrology, quantum parameter estimation must follow the steps of quantum metrology towards the applied science and industry. Hence, optimal scheme design will soon be a crucial and core task for…
The rapid and widespread adoption of Java has created a demand for reliable and reusable mathematical software components to support the growing number of compute-intensive applications now under development, particularly in science and…
As developers of libraries implementing interval arithmetic, we faced the same difficulties when it comes to testing our libraries. What must be tested? How can we devise relevant test cases for unit testing? How can we ensure a high (and…
The julia package integrates the Julia programming language into Stata. Users can transfer data between Stata and Julia, issue Julia commands to analyze and plot, and pass results back to Stata. Julia's econometric ecosystem is not as…
This article proposes an artistic approach to increase and enrich the understanding of Julia Sets. This approach includes the mathematical, the playful, the artistic and the computational dimensions. It is argued that these four dimensions…
We present a Julia package HypersurfaceRegions.jl for computing all connected components in the complement of an arrangement of real algebraic hypersurfaces in $\mathbb{R}^n$.
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…
Program synthesis -- the automatic generation of code given a specification -- is one of the most fundamental tasks in artificial intelligence (AI) and the dream of many programmers. Numerous synthesizers have been developed for program…
NetworkDynamics.jl is an easy-to-use and computationally efficient package for working with heterogeneous dynamical systems on complex networks, written in Julia, a high-level, high-performance, dynamic programming language. By combining…
The study of dynamical systems involves analyzing how functions behave under iteration in different mathematical spaces. In the context of complex dynamics, tools such as Julia sets and filled Julia sets are used to understand the long-term…
We report on the computer implementation for toric geometry in the computer algebra system $\texttt{OSCAR}$. The main architectural feature of $\texttt{OSCAR}$ is that its four fundamental tools $\texttt{Antic}$ (Hecke, Nemo),…
We present graph-based modeling abstractions to represent cyber-physical dependencies arising in complex systems. Specifically, we propose an algebraic graph abstraction to capture physical connectivity in complex optimization models and a…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…