February 3, 2005
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, especially the functional and transformational paradigms, are put forward. In the future, algebraic algorithms could constitute the core of extended symbolic manipulation systems including primitives for symbolic approximations.
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August 27, 2021
Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within the Julia framework as they work within the Python framework. There are libraries for Julia that cover the majority of scientific and engineering computations demands. The aim of this paper is to combine the usage of the Julia framework for numerical computations and for symbolic computations in ma...
December 26, 2017
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 design of such complex systems. It also provides means for characterization of all solutions and studying them before realizing a particular solution. This note provides a brief survey on some of the applications of symbolic computations in co...
February 29, 2000
In this survey I should like to introduce some concepts of algebraic geometry and try to demonstrate the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science. One of the aims of this article is to show, by means of examples, the usefulness of computer algebra to mathematical research.
November 14, 2018
In this note for the joint meeting of DMV and GDM we illustrate with examples the role of computer algebra in university mathematics education. We discuss its potential in teaching algebra, but also computer algebra as a subject in its own right, its value in the context of practical programming projects and its role as a research topic in student papers.
September 20, 2002
These lectures given to graduate students in theoretical particle physics, provide an introduction to the ``inner workings'' of computer algebra systems. Computer algebra has become an indispensable tool for precision calculations in particle physics. A good knowledge of the basics of computer algebra systems allows one to exploit these systems more efficiently.
December 17, 1994
Ich m\"ochte in diesem Bericht algorithmische Methoden vorstellen, die im wesentlichen in diesem Jahrzehnt Einzug in die Computeralgebra gefunden haben. Die haupts\"achlichen Ideen gehen auf Stanley \cite{Sta} und Zeilberger \cite{Zei1}--\cite{Zei4} zur\"uck, vgl.\ die Beschreibung \cite{Strehl1}, und haben ihre Wurzeln teilweise bereits im letzten Jahrhundert (siehe z.\ B.\ \cite{Beke1}--\cite{Beke2}), gerieten aber auf Grund der Komplexit\"at der auftretenden Algorithmen wi...
January 15, 1999
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 problem was not implemented in standard software packages like REDUCE, MATHEMATICA, etc. and if the using of internal programming languages of the packages looks not very efficient. Functional languages like LISP had some advantages and trad...
September 23, 2013
Symbolic integration is an important module of a typical Computer Algebra System. As for now, Mathematica, Matlab, Maple and Sage are all mainstream CAS. They share the same framework for symbolic integration at some points. In this book first we review the state of the art in the field of CAS. Then we focus on typical frameworks of the current symbolic integration systems and summarize the main mathematical theories behind these frameworks. Based on the open-source computer ...
October 18, 2013
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 the database into executable code for various computer algebra systems. The included tools are designed to be very flexible to use and to extend, such that they can be utilized even in contexts of other communities. With the presentation of S...
April 22, 2011
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.