The various non-linear transformations incurred by the rays in an optical system can be modelled by matrix products up to any desired order of approximation. Mathematica software has been used to find the appropriate matrix coefficients for the straight path transformation and for the transformations induced by conical surfaces, both direction change and position offset. The same software packa...

Abst ract The functional approach to scientiic computing is illustrated using various random walk models and the Mathematica programming language.

Dyson-Schwinger equations are important tools for non-perturbative analyses of quantum field theories. For example, they are very useful for investigations in quantum chromodynamics and related theories. However, sometimes progress is impeded by the complexity of the equations. Thus automating parts of the calculations will certainly be helpful in future investigations. In this article we prese...

There are many ways of representing piecewise functions inMathematica c . We study three different methods. One is by using the function Piecewise. Another is by using a difference of two HeavisideTheta functions for each piece. And a third way is by using product to two HeavisideTheta functions for each piece. If efficiency in integration is a criterion, which of these is the best way to do so...

We give a simple tutorial introduction to the Mathematica package STRINGVACUA, which is designed to find vacua of string-derived or inspired four-dimensional N = 1 supergravities. The package uses powerful algebro-geometric methods, as implemented in the free computer algebra system Singular, but requires no knowledge of the mathematics upon which it is based. A series of easy-to-use Mathematic...

We present extensions to the computer algebra and multimedia environmentMathematica to enable students to investigate signal processing theory. Students interact with the extensions at two levels. The lower level is a set of Mathematica programs called the Signal Processing Packages (SPP) that implement signals and systems not found in the core of Mathematica. The higher level is a set of inter...

This article discusses an object-oriented approach to industrial software development using Mathematica. We present the package Elements for structured representation of physical, engineering, and mathematical objects. This package introduces object-oriented paradigms into Mathematica and is used to develop a modeling environment built on a knowledge base where class and object properties and r...

This paper analyzes some graph issues by using the symbolic program Mathematica and its version for theWeb, webMathematica. In particular, we consider the problem of graph coloring: the assignment of colors to the vertices/edges of the graph such that adjacent vertices/edges are colored differently. In addition, we address the problem of obtaining the tenacity of binomial trees with Mathematica...

A project is being developed with the main goal of creating an application of web server which allows students to use Mathematica software from their computers without the necessity of installing this software and of programming the necessary algorithms. The project consists of a set of mathematical models programmed with Mathematica and stored in a web server, which has been installed in a com...