Use Of Computer Algebra Systems Research Articles

On the Use of Computer Algebra Systems in a Calculus Course for Thai Engineering Students — Developing and Testing Modules for Visualisation —

On the Use of Computer Algebra Systems in a Calculus Course for Thai Engineering Students — Developing and Testing Modules for Visualisation —

The use of computer algebra in the formulaic solving of complex algebraic problems

In the introduction to this paradigmatic article on computer‐aided mathematics teaching in schools, essential aspects of the solving of complex algebraic problems using computer algebra are discussed. The main part of the article puts general observations into concrete terms using the example of solid geometry problems which may be considered typical of the complex algebraic problems set to high school students. An initial didactic evaluation of the formulaic solving of complex algebraic problems using a modified Auto‐Solver is presented. The article concludes with some general hypotheses concerning the use of computer algebra systems in secondary education.

A Toolbox for Symbolic Nonlinear Feedback Design

Geometrical and algebraic analysis and design methods for non linear systems require the use of computer-algebra systems to carry out the extensive symbolic calculations. Based on the experience with a MACSYMA program for the analysis and design of nonlinear observers, the new concept of a toolbox for the design of nonlinear controllers using Mathematica is developed. The main focus is on the flatness based design of quasi-static state feedback for nonlinear tracking. The controller design for a nonlinear chemical reactor model illustrates the functionality of the program.

Application of computer algebra to the iterative solution of singular integral equations

The use of computer algebra systems in the approximate iterative solution of Cauchy-type singular integral equations (SIEs), appearing in crack problems of plane elasticity and in many additional branches of applied mechanics and engineering, is proposed. The resulting method, combining numerical and symbolic computations, is called a semi-analytical/numerical (SAN) method. The computer algebra system DERIVE is used in the present computations, where the problem of a periodic array of collinear cracks has been selected for the illustration of the present approach. Extensive SAN results are displayed and their convergence is shown, as well as their agreement (for the stress intensity factor) with the already available theoretical formula in this concrete application. Generalizations of the present SAN approach are completely possible.

Say It Again in Plain Algebra: The growing use of computer algebra systems has driven mathematicians to find ways of simplifying the horrendously complex expressions number crunchers sometimes spit out

On considere le probleme de la simplification d'expressions complexes, obtenues avec le calcul formel dans la resolution d'equations algebriques d'ordre superieur, notamment l'identification de racines emboitees comme nombres simples. L'auteur presente les principes des premiers algorithmes existants, qui font appel a la theorie des groupes