# 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.

HTML originally written by Reid M. Pinchback

Copyright 1996, Massachusetts Institute of Technology

Last modified: 96/09/25
*(reidmp@mit.edu)*