Maple Functionality:

Tips and Techniques

by Michael Monagan

In this month's column we look at three problems that users have had and then we take up the discussion we initiated last issue, namely: ``what simplifications are done by Maple automatically?, and, ``can I change those simplifications?''

Infinity Structures in Maple

by Dominik Gruntz

This article discusses how to represent and manipulate ``infinite structures'', e.g.  infinite streams and infinite power series expansions. The techniques used are ``lazy'' evaluation, self referential data structures and fixed point operations. The key idea is, that objects are constructed when they are needed rather than when they are defined.  This method has also been used in the "PS" package in the share library.

MathEdge: The Application Development Toolkit for Maple

by David Pintur

This article demonstrates how the symbolic engine of Maple can be integrated into your own software application using the MathEdge Developer's Toolkit.  Its capabilities are presented through working examples ranging from a symbolic calculator to a mechanism design application. The intended audience is not only application developers, but anyone who has wished that they could access Maple in ways other than through the Maple V Release 3 product.

Maple Applications:

Modeling and Simulating Robots in Maple

by Dieter Kraft

This article shows that Maple is a good environment for modeling and simulating multibody systems. This type of symbolic programming gives much deeper insight into dynamic models than pure numeric equations.

Maple as an Interface for Numerically Solving Chemical Kinetic Equations

by J. W. Stayman and Mark H. Holmes

This article  describes how Maple can be integrated with a C program to be able to construct a graphical interface for solving differential equations that arise in the study of chemical kinetics. This is a sequel to the article written by Holmes and Bell and shown in volume no. 0, issue no. 7 of this Newsletter (see mtn[0_7]).

``Quantum Mechanics and Maple: The rotation matrix functions

by Dennis Isbister

This article shows how Maple can be easily used to generate the matrix elements for the reduced rotation matrix elements which are pivotal to the theory of linear angular momentum in quantum mechanics. In addition, the Wigner 3j and 6j symbols(which are important in the addition of angular momenta) are also presented.  This code is available in the share library.

Using Maple in the selection of glasses or telescope objectives

by Richard Ditteon

This is an interesting application in optical lens design, namely on the optimization of achromatic aplanatic telescope objectives using Maple.

Maple in Education:

Thermodynamics with Maple: III Thermodynamic Property Relations and the Maxwell Equations

by Steve Adams and Ross Taylor

This is an expository article on the use of maple in thermodynamics. This article can be most useful to people in the area of chemical engineering.

Isomers, Groups, and Combinatorics

by Shalom Feigelstock

This article makes use of Maple's ``group'' and ``combinat'' packages in explaining Polya's theorem which involves the problem of enumerating "isomers" (molecules that differ only in the way their component atoms are bonded).  This could be of use to people interested in group theoretic approaches applied to molecules.

Generating Problems in Linear Algebra

by Jurgen Hausen

This article presents a method for creating exercises in linear algebra by making use of Maple's random number generator. The main tool for doing that is a Maple procedure which generates unimodular integral matrices.  The presentation also considers standard exercises for basic topics such as linear independence, bases and the rank of a matrix.