MathTools

Math routines for the TI-89/92+/V200
Linear Algebra, Polynomials, Calculus, Statistics, Special Functions, Vector Analysis, and more

Version: 2.4.2

Author: Bhuvanesh Bhatt (bbhatt1@towson.edu)

Introduction

A Computer Algebra System (CAS) is a kind of mathematical software that enables you to use a computer to manipulate mathematical expressions. A CAS has symbolics, numerics, graphics, programming, and typesetting capabilities, and usually also data import/export. CAS’s are used in many fields such as mathematics, physics, chemistry, engineering, computer science, computational biology, economics, and education. The TI-68k devices (TI-89, TI-92 Plus, and Voyage 200) are great tools, especially for education. They are the most advanced calculators available today. Once you have learned a topic such as vector analysis, you can use the TI-68k CAS to automate some or all of your work, so that you can concentrate on more advanced and/or abstract topics without worrying about calculational errors. The TI-68k are also invaluable when learning a topic, since they allow you to explore the topic in a variety of ways.

One problem with the TI-68k is that a lot of commonly used functions are not built-in. MathTools aims to bridge that gap, mainly in the area of mathematics. Since math is used in all of science, MathTools can be used in those fields as well. Besides education, MathTools can also be used in industry and research. One of my goals in maintaining MathTools and its extensive documentation is to introduce people to the beauty of mathematics. MathTools has helped me gain a deeper understanding of computer algebra, and has also introduced me to many new areas in math, far better than from any amount of reading. MathTools mainly consists of TI-Basic functions, but there are also TI-Basic programs, utilities written in C, and a Flash application.

MathTools is far from complete. Some categories that need more work are factorization, Gröbner bases, GMP, differential equations, and logic. Some of these have performance problems, while others have missing functionality. However, MathTools has good organization and is quite powerful, with well over 340 routines.

Installation

· Without GMP and the C utilities, MathTools takes up approximately 230 KB space (if everything is installed).

· I recommend using TI Connect 1.2. Extract the appropriate group file (.89g or .9xg), right-click on it, and in the context menu click Send To ® Connected TI Device ® Archive. If you get a garbage collection message on the calculator, reply “OK” to it, and when it is done, click “Retry” in TI Connect to send the rest of MathTools.

· To install the MathTools Flash application, which requires AMS 2.04 or higher:

u If you are using TI Connect, connect the cable to the calculator, right click on the Flash app file and from the context menu select Send To ® Connected TI Device ® Archive.

u If you are using the Graph-Link software, connect the cable to your calculator, click on Link ® Send Flash Software ® Applications and Certificates, select the Flash app in the dialog, click on Add, then click on OK. The Graph-Link software will report installation success/failure.

Important notes

These mode settings are recommended: Angle ® Radian, Complex ® Rectangular, Vector ® Rectangular, Exact/Approx ® Auto, Base ® Dec (these are what I use).
You can choose the functions you want to install on your calculator. The dependencies are not given recursively, for example, the Eigenval help entry shows that it needs mZeros and Sort, but Sort also needs ListSwap. All TI-Basic routines have Catalog help.

Functionality

· Linear Algebra

§ Eigenvalues/Eigenvectors, Decompositions, and PseudoInverse

§ Special Matrices

§ Other functions

· Polynomials

§ Coefficients and terms

§ Polynomial division[†]

§ Resultants

§ Factorization

§ Gröbner bases

§ Other functions

· Miscellaneous

§ Arbitrary-precision arithmetic (GMP)

§ Calculus

§ Combinatorics

§ Continued Fractions

§ Data Analysis

§ Differential and Recurrence Equations

§ Equation/Inequality Solving

§ Lists

§ Logic

§ Number theory

§ Optimization

§ Pattern-matching

§ Special Functions

§ Statistics

§ Strings

§ Summation and Series

§ Vector/Tensor Analysis

§ Other functions

§ C Utilities

§ MathTools Flash app

Links to other sections

Computer Algebra links

Screenshots

Copyright notice and disclaimer

MathTools may be freely distributed, provided it is not modified, is distributed as a whole (besides Gosper and MultMod/PowerMod), is not sold/licensed for monetary profit, and this documentation is provided with it. If you wish to distribute a modified version, please contact the author. MathTools is subject to change without notice. MathTools is not intended for use in a mission/life-critical environment, and although I have tested it, there may still be bugs and/or inaccuracies. The author and copyright holder will not be liable for any damages or losses related to the MathTools software or documentation. If something happens to me, all rights for all of my software transfer to Doug Burkett.

Thank you for using MathTools! I hope you like it and it is useful to you.

Contact information

Questions/comments/suggestions/bug-reports are welcomed at bbhatt1@towson.edu
For updates and other packages/resources, visit: http://triton.towson.edu/users/bbhatt1/ti/