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So far, the scope of computer algebra has been needlessly restricted to exact algebraic methods. Its possible extension to approximate analytical methods is discussed. The entangled roles of functional analysis and symbolic programming,…
Mathematical software and graph-theoretical algorithmic packages to efficiently model, analyze and query graphs are crucial in an era where large-scale spatial, societal and economic network data are abundantly available. One such package…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
In this paper we will present SDeval, a software project that contains tools for creating and running benchmarks with a focus on problems in computer algebra. It is built on top of the Symbolic Data project, able to translate problems in…
Reflective systems allow their own structures to be altered from within. Here we are concerned with a style of reflection, called linguistic reflection, which is the ability of a running program to generate new program fragments and to…
We present an open source computational framework geared towards the efficient numerical investigation of open quantum systems written in the Julia programming language. Built exclusively in Julia and based on standard quantum optics…
Stochastic Programming is a framework for modelling and solving problems of decision making under uncertainty. Stochastic Dynamic Programming is a branch of Stochastic Programming that takes a "functional equation" approach to the discovery…
Recently Java programming environment has become so popular. Java programming language is a language that is designed to be portable enough to be executed in wide range of computers ranging from cell phones to supercomputers. Computer…
Safety-Critical Java (SCJ) introduces a new programming paradigm for applications that must be certified. The SCJ specification (JSR 302) is an Open Group Standard, but it does not include verification techniques. Previous work has…
This article reviews recent progress in the development of the computing framework vector symbolic architectures (VSA) (also known as hyperdimensional computing). This framework is well suited for implementation in stochastic, emerging…
We introduce the notion of a robust parameterized arithmetic circuit for the evaluation of algebraic families of multivariate polynomials. Based on this notion, we present a computation model, adapted to Scientific Computing, which captures…
Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…
Symbolic computation systems suffer from memory inefficiencies due to redundant storage of structurally identical subexpressions, commonly known as expression swell, which degrades performance in both classical computer algebra and emerging…
A prototype for an extensible interactive graphical term manipulation system is presented that combines pattern matching and nondeterministic evaluation to provide a convenient framework for doing tedious algebraic manipulations that so far…
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…
In the present paper, we describe some experiences in using programming, commands and graphical interfaces based on computer algebra systems, as tools for learning Physics and Mathematics.
The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference…
This paper describes a new modelling language for the effective design of Java annotations. Since their inclusion in the 5th edition of Java, annotations have grown from a useful tool for the addition of meta-data to play a central role in…
We describe a graph visualization tool for visualizing Java bytecode. Our tool, which we call J-Viz, visualizes connected directed graphs according to a canonical node ordering, which we call the sibling-first recursive (SFR) numbering. The…