# MTN Issue 9, Spring 1993

## Extended Functionality (Maple V Release 2)

Lambert's W Function in Maple
R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey
This article presents the mathematics of the `W` function in Maple, the solution to the equation w*exp(w)=x for w. The article gives several applications and concludes with a set of integral exercies which involve Lambert's W function.
Introduction to Gauss
D. Gruntz and M. Monagan
This article describes a new model for programming mathematical algorithms in Maple based on ideas from the axiom system. The primary idea is "domains and categories". In computer science we don't use this terminology, we use instead "parameterized types and parameterized abstract types" respectively and in the object-oriented programming community we could call them "parameterized classes and parameterized meta classes."
Grobner Bases in Gauss
D. Gruntz
An implementation of Buchbergers algorithm for Grobner bases in `Gauss` illustrating the flexibility and power of `Gauss`.

## Applications

Harmonic Analysis of Phase Controlled Waveforms
A.D. Rough and J. Richardson
This is an article for engineers and scientists which presents Maple programs to investigate the harmonic structure of single-phase and 3-phase waveforms of thyristor circuits.
Engineering Applications of Maple V Release 2: Analysis and Design of Machines
J. Argent and T. Lee
An application of Maple in mechanical engineering. Two design problems for a machine element to solve equilibrium equations to obtain general solutions for shear and normal stresses.
Using Computer Algebra to Help Understand the Nature of Eigenvalues and Eigenvectors
M. Monagan
This worksheet shows a worked example of how symbolic computation can be used in linear algebra to analyse the eigenvalues and eigenvectors of a matrix containing a parameter, in particular to study what happens to the eigenvectors when the eigenvalues coincide.
Solving the Congruence x^2 == a mod n
M.O. Vahle
Presents a complete description of the mathematics and algorithms needed to solve this well known problem in number theory. The article is intended for use in education.