Can Computer Algebra be Liberated from its Algebraic Yoke ?

In this note, I develop my personal view on the scope and relevance of symbolic computation in software science. For this, I discuss the interaction and differences between symbolic computation, software science, automatic programming, mathematical knowledge management, artificial intelligence, algorithmic intelligence, numerical computation, and machine learning. In the discussion of these notions, I allow myself to refer also to papers (1982, 1985, 2001, 2003, 2013) of mine...

This article introduces and explains a computer algebra system (CAS) wxMaxima for Calculus teaching and learning at the tertiary level. The didactic reasoning behind this approach is the need to implement an element of technology into classrooms to enhance students' understanding of Calculus concepts. For many mathematics educators who have been using CAS, this material is of great interest, particularly for secondary teachers and university instructors who plan to introduce ...

Symbolic mathematical computing systems have served as a canary in the coal mine of software systems for more than sixty years. They have introduced or have been early adopters of programming language ideas such ideas as dynamic memory management, arbitrary precision arithmetic and dependent types. These systems have the feature of being highly complex while at the same time operating in a domain where results are well-defined and clearly verifiable. These software systems sp...

The 2025 ISSAC conference in Guanajuato, Mexico, marks the 50th event in this significant series, making it an ideal moment to reflect on the field's history. This paper reviews the formative years of symbolic computation up to 1975, fifty years ago. By revisiting a period unfamiliar to most current participants, this survey aims to shed light on once-pressing issues that are now largely resolved and to highlight how some of today's challenges were recognized earlier than exp...

Our Chapter in the upcoming Volume I: Computer Science and Software Engineering of Computing Handbook (Third edition), Allen Tucker, Teo Gonzales and Jorge L. Diaz-Herrera, editors, covers Algebraic Algorithms, both symbolic and numerical, for matrix computations and root-finding for polynomials and systems of polynomials equations. We cover part of these large subjects and include basic bibliography for further study. To meet space limitation we cite books, surveys, and comp...

The advantages of mixed approach with using different kinds of programming techniques for symbolic manipulation are discussed. The main purpose of approach offered is merge the methods of object oriented programming that convenient for presentation data and algorithms for user with advantages of functional languages for data manipulation, internal presentation, and portability of software.

The advent of computers has allowed mathematicians to do increasingly more difficult computations that used to be practically impossible. Peer reviewers will seldom look at any code attached to a math paper, however. In this article, we advocate for a software peer-reviewing process and will discuss some best practices for reviewers on how to peer review mathematical papers with code and providing guidelines for authors to improve the code that accompanies their mathematical ...

This article documents the free computer algebra system "gTybalt". The program is build on top of other packages, among others GiNaC, TeXmacs and Root. It offers the possibility of interactive symbolic calculations within the C++ programming language. Mathematical formulae are visualized using TeX fonts.

The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be approached from a computational viewpoint.

Almost all problems in applied mathematics, including the analysis of dynamical systems, deal with spaces of real-valued functions on Euclidean domains in their formulation and solution. In this paper, we describe the the tool Ariadne, which provides a rigorous calculus for working with Euclidean functions. We first introduce the Ariadne framework, which is based on a clean separation of objects as providing exact, effective, validated and approximate information. We then dis...