Mathematica Page

I will include on this page various notebooks and packages which may be of interest to the general Mathematica community. You will need the Mathematica program to utilize these notebooks. It can be obtained from Wolfram Research

As of April 2007 I am operating with a new computer on Windows Vista and broadband Internet service and everything is in better shape.

The Presentations/DrawGraphics, Cardano3 and ExtendUnits packages are being offered for purchase through the Kagi online store to whom I am a supplier. A number of the subpackages and associated application notebooks will be free.

Mathematica provides state-of-the-art core functionality for CAS operations. However, this functionality is not always organized for convenient use by students and researchers. There is a gap between Mathematica and ease of use in many fields. The packages offered here were developed over a number of years in working with mathematics and physics textbooks. They provide routines that fill the usage gaps. You can think more like a scientist or mathematician and less like a computer programmer. An example using all these packages together is presented in a 77 KB pdf file FullSpectrumPhysics.pdf or you can download the 25 KB Mathematica notebook FullSpectrumPhysics.nb, which requires the packages. There are additional pdf files showing examples of Tensorial and DrawGraphics at Renan Cabrera's Tensorial page Tensorial 4.0 Examples

The packages are well documented, with core Mathematica style Help pages and examples for every command and many other extended examples. They have been used in at least several courses at the University level. They blend naturally with regular Mathematica usage and style. They are economically priced compared to most Mathematica software.

The mechanics of purchase and installation of the packages are as follows. There is a single Kagi store site that can be accessed from any of the package pages below. Upon purchase of the package(s) you will receive within about 10 minutes or so a 'Thank you for your purchase' confirmation email from Kagi. I also receive a copy of this email. The email will contain links to download pages for the packages(s) you have purchased. From these links you can immediately download and install the package(s). I do not receive any credit card information nor do I believe that Kagi retains any credit card information as they hand it off to a credit card processing firm. The installation is basically very simple. You simply unzip the downloaded file into your personal Mathematica/Applications folder and rebuild the Help index. There are more detailed installation instructions on the package pages and also included in the package zip files. The many purchasers so far seem to have had no trouble with installation.

If you have any questions about the packages please email me at I appreciate the support of those who have purchased my packages and all those who have encouraged me.

Packages for Sale
The following links give fuller descriptions of the packages and provide download links.

Presentations/DrawGraphics General purpose Mathematica packages for producing custom graphics, presentations and to use Mathematica to study, teach or communicate. DrawGraphics is pre Version 6. Presentations is the Version 6, 7 and 8 package.
Cardano3 A DrawGraphics add-on for graphical representation of complex functions. Pre-Version 6 only. Complex function graphics is now incorporated in Presentations.
ExtendUnits Version 6.0+ ready. General purpose Mathematica package for working with units in physical problems.
Tensorial Version 6.0 ready. General purpose tensor calculus package.

Creating Style Sheets in Version 6.0
Creating style sheets in Mathematica Version 6.0 is considerable different than in earlier versions. The following zip file contains notebooks and style sheets that can be used as an example for creating a style sheet. Put them in one of your working folders, not in any system folder. The notebooks are:

StyleSheetNotes2.nb: This takes you step by step through the creation of a new style sheet doing most of the common things. You should be able to create the style sheet with this notebook alone. The other notebooks can be used as a check if you have difficulty.
TempStyle2Practice.nb: A working notebook that uses the new style created.
TempStyle2.nb: The new style sheet that is created. 16 KB, Notes and examples on making style sheets in Version 6.0.

A Style Sheet that I Like.
Other than the Default style sheet for Mathematica there are no others that I especially like. The following is a style sheet with useful features when using Mathematica for standard textbook study and other uses.
Its features are:
• There is an extra title section called Chaptertitle.
• There is an extra level of grouping called Subexercise
• The Section, Subsection, Subsubsection and Subexercise groupings have open/close icons.
• The Text, Input and Output font sizes are nearly equal and, in general, there is a smaller range of font sizes. Textbooks and research papers use nearly equal font sizes for equations and text while many of the Mathematica style sheets use a much smaller Text font and a much too large Title font.
• The various shortcut keys for the cell types remain the same as in the standard DefaultStyle.
You can always edit the style sheet if you would like a different color scheme or font sizes. However, I hope you will find the style convenient and tasteful.
ParkStyle.nb 67 KB, Mathematica style sheet for general use.

The following is the Version 6.0 style sheet. Instead of Subexercise it incorporates the two addition grouping levels provided by Mathematica. Notice that the new cascading style sheets are much more space efficient.
ParkStyle6.nb 5 KB, Mathematica style sheet for general use in Version 6.0.

Spacetime Geometry

The following Mathematica notebook is a tutorial on the geometric aspects of special relativity. It has many animations illustrating various concepts such as events, world lines, proper time, the Lorentz transformation, Bondi triangles, measuring time, distance and velocity, derivation of the spacetime interval and other topics. It requires the Presentations package above.

Stationary and Moving Pi Mesons

Download 75KB Mathematica Notebook, 22 Jan 2007.

The notebook draws in part upon the following two papers:
Spacetime and Euclidean Geometry by Dieter Brill and Ted Jacobson.
From Einstein's 1905 Postulates to the Geometry of Flat Space-Time by N. David Mermin.


Solves most conic section problems in the plane. There is complete Help documentation and extra Examples. The extra Examples require the DrawGraphics package above for the plots, but the main Help examples don't.

Download 63KB Mathematica Package, 1 Oct 2002.
ConicSectionsReadMe.txt 2KB Instructions for installation, 1 Oct 2002.

Rotations and Euler Angles

This application consists of two packages and four notebooks that serve as a tutorial for understanding and visualizing 2D rotations, 3D rotations and Euler angles. It uses the DrawGraphics package below.

One of the packages contains routines for visualizing rotations. For example, there is a routine for a side by side animation of two different rotation sequences of a book. The other package contains general routines useful with rotations. One of the routines will, given a rotation matrix, calculate both sets of Euler angles for any rotation matrix and for any choice of rotation sequence. (There are actually 12 possible axes rotation sequences and thus 24 possible sets of Euler angles.)

xyz and zyx axis book rotations

The notebooks are:
1. 2D Rotations, Alias and Alibi Interpretations.
2. 3D Rotation Matrices.
3. Euler Angles.
4. Unfinished Experiments.

Download 134KB Mathematica Package, 20 Jul 2003.
RotationsReadMe.txt 2KB Instructions for installation, 20 Jul 2003.

Two High School Tutorials

The following two tutorials are for high school students, or earlier. They introduce some of the functional programming constructs. StepByStepEquations shows how to solve equations "by hand" using pure functions and Map, and mixes in a little Greek mythology. KarlFriedrich is centered around Gauss's childhood feat of summing the numbers 1 to 100. It also introduces Nest, Fold, Apply, triangular numbers and proof by induction.

StepByStepEquations.nb 21KB Mathematica Notebook.
KarlFriedrich.nb 44KB Mathematica Notebook, 27 Jul 1999.

Elastic Collision Animation

The following notebook was done in response to a MathGroup question. It shows how to make an animation of an elastic collision of two balls along a line.

ElasticCollision.nb 10KB Mathematica Notebook.

Expression Manipulation

There has been a major update to this package in April 2001. The package is useful in the controlled manipulation of expressions. Pieces of held expressions can be selectively evaluated with the routines EvaluateAt and EvaluateAtPattern. Extended positions are introduced and allow the manipulation of selected level parts of a subexpression. There are two aids to finding the positions of subexpressions in patterns. One is a Position palette which allows subexpressions to be highlighted and the position returned. A routine, ColorPositions, allows positions, including extended positions to be colored and labeled. There are other routines commonly useful in manipulating expressions. The EvaluationTutorial not only shows how to use the routines in the package but is an introduction to manipulating expressions with Mathematica. It contains examples from simple step by step fraction problems to integration by substitution. Ted Ersek is the coauthor of this package. The package works only in Version 4 or later. The package should be placed in the AddOns/ExtraPackages/Algebra directory.

EvaluationTutorial.nb 229KB Mathematica Notebook, 21 Apr 2001.
ExpressionManipulation.m 35KB Mathematica Package, 26 Oct 2006.

Extending the Through Command

The Through command is not used as often as it might be. The following package contains the commands, PushThrough and PushOnto, which facilitate the application of Through to most expressions. The notebook explains why they are useful and gives many examples of their use. The package should be placed in the AddOns/ExtraPackages/Algebra directory.

PushThroughTutorial.nb 39KB Mathematica Notebook. 5 Mar 2002
PushThrough.m 10KB Mathematica Package. 26 Oct 2006


The CombinatoricaGraphics package is for the new version of Combinatorica, Mathematica Version 4.2 or better. The new version of Combinatorica has much better graphics than the old version so there is less need for an extra package. Nevertheless I have produced one that works with the DrawGraphics package above, which will also need to be installed. Its main advantages are:
1) It uses ProportionalArrows and ArrowCurves to allow arrowheads anywhere along a directed edge.
2) It uses the DrawGraphics CirclePoint for vertices.
3) Labels have backgrounds so they stand out better.
4) Instead of a range of options, there is complete freedom in the rendering routines for edges, vertices and labels.
5) Highlighted graphs with multiedges and multi self-loops are more correctly rendered.
6) It has complete Help documentation for each command with examples.

Download 74KB zip file. 14 Mar 2004
CombGraphicsReadMe.txt 2KB Installation Instructions. 14 Mar 2004

The CombinatoricaPlots package below provides extended plotting capability for the OLD Combinatorica package. It allows the graphs to be both directed and labeled. Edges can be labeled as well as vertices. Directed edges can have the arrowheads at any position along the edge. Self-loops may also be shown. It allows plotting directives to be given for both the vertices, edges and labels and the position of labels can be controlled both globally and individually. It corrects a defect in ShowLabeledGraph which cuts off some of the labels if a larger type size has been specified. It allows overall plotting options to be specified. In addition to PlotGraph, there is a DrawGraph routine which works in the DrawingPaper paradigm. The tutorial illustrates the use of each of the features. The CombinatoricaPlots.m package should be placed in the AddOns/ExtraPackages/DiscreteMath directory.

CombPlotsTutorial.nb 39KB Mathematica Notebook. 6 Feb 2000
CombinatoricaPlots.m 15KB Mathematica Package. 6 Feb 2000

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