Mercury is a program for solving equations. With it, you can evaluate mathematical expressions, solve for the roots of an equation, solve a system of equations, maximize or minimize a function, with or without constraints, evaluate derivatives and definite integrals, plot one or more functions, print a report or a graph.
Mercury, originally called Eureka, was marketed by Borland International. Mercury later became a shareware product and was further enhanced by Robert Schlafly of Real Software. Mercury 2.09 works quite well on the HP 200LX. It can produce plots that go way beyond those generated by Solver or Lotus 1-2-3. The package comes with many sample solutions to get you started.
Mercury's graphing function may cause your Palmtop to lock up. The documentation claims that Mercury will work with a CGA screen and I was able to produce a graph of a cardioid function on the first HP 100LX machine that I had. For some unknown reason, the same example locks up my HP 200LX and requires a hard reset (CTRL Left Shift ON).
PolyMath (PM) combines scientific/engineering plotting, a Forth-like programming language, an editor, and a comprehensive documentation system into an interactive calculator-like environment. PM aims to fill the gap between a programmable, scientific calculator and programming in C or Basic. Statements in the PM language may be expressed in algebraic or Reverse Polish notation or a combination of both. Object-oriented data structures are programmed for the data they can hold, as well as for operations that can be applied to these data structures. By merely adding a special character to a word when it is written to the screen, it automatically becomes a menu choice. PolyMath version 4.0 was written in 1989 by Lobster Software. The company has long since gone out of business and the PolyMath name has been taken over by another company.
ProMATHeus is a product designed to solve simple and complicated calculations of all types. It was created by a professional mathematician and actuary who was frustrated by the lack of affordable calculation software back in 1991. ProMATHeus differs from calculator software in that it works like you think rather than the way a calculator keyboard dictates. It differs from spreadsheets in that it does not rely on cell addresses. Rather it uses named variables. Formulas are entered easily, remembered, and interact with each other. Active formulas (i.e., those with variables) are reviewed constantly and partial and/or full solutions are displayed. One-variable, custom functions can be plotted with the Graph feature. Custom functions can be defined easily, they can call other functions thereby simplifying further calculations.
SolveIt! provides the answer to many commonly asked questions dealing with money. The program can be run in either a stand-alone mode or in a memory resident mode. SolveIt! has a "Fill-In-The-Blank" user interface that provides the answers to complex personal financial and business questions. It is much easier to use than some of the programs that simulate H.P. or T.I. financial calculators.
5. MAFIA 2.0
Mafia stands for "Math And Fun International Association." The most recent version was written in 1992 and is designed to run in DOS. It has a very simple menu system with no pop-ups or pull-downs and no mouse support. The menu drives a set of several programs that will let you do numerical integration as well as analytical integration, solve functions, fit curves, perform vector and matrix operations and solve ordinary differential equations. The package includes a programmable calculator. Everything except the plotting functions work on the Palmtop. The plots require an EGA or VGA monitor. All the programs in the set are independent so you don't have to activate the MAFIA menu system to get what you want, you can activate the exact program you need.
The PFSA program was created to do some rather large but simple algebraic computations. PFSA does not have as large a variety of commands as Derive but it is faster and can work with bigger expressions. PFSA runs 10 to 100 times faster than Derive on similar problems. Two versions are provided. The first one uses only rational integer arithmetic (PFSAI.EXE) and another (PFSAF.EXE) which uses decimal arithmetic. The user prepares a text file called "algin" which contains commands that specify the task to be done by PFSA. The commands of PFSA approximate a description of the problem in English. The user runs PFSA, which produces an output file "algout". The program does not do graphs nor does it do symbolic math. However, if you have a particular problem that you solve over and over again, PFSA may be the fastest way to get the numeric answers.
Symbol is the name of the archive file that contains the shareware version of Mathomatic, the algebraic manipulator. The AMTUTOR file in the archive starts out as a tutorial program but it will also let you use the program as a functioning symbolic manipulator program. Mathomatic runs on the HP Palmtop, however the Mathomatic "graph" command requires an EGA or VGA monitor. The number of equation spaces and the equation size are reduced in this shareware version of Mathomatic.
8. Symbolic Math
SymbMath is a computer algebra system that can perform exact numeric, symbolic and graphic computation. It manipulates complicated formulas and returns answers in terms of symbols, formulas, exact numbers, table and graph. SymbMath is also an expert system that is able to learn from user's input. If the user only inputs one formula without writing any code, it will automatically learn many problems related to this formula (e.g. it learns many integrals involving an unknown function f(x) from one derivative f'(x) ).
SymbMath is, in another sense, a programming language in which you can define conditional, case, piecewise, recursion, multi-value functions and procedures, derivatives, integrals and rules.
The program runs on the HP Palmtop and does almost everything that Derive can do.
Symbolic Math comes in one of three versions: Shareware, Student, and Advanced. Its three versions are available from the author, Dr. Weiguang Huang.
Statistics and Business Math
HP Calc has the List Stat function to do simple statistics. However if you want more of this good stuff you'll need a full-fledged statistics program. In this genre of software the most widely known package is the Statistical Program for the Social Sciences (SPSS). The only version of SPSS that is guaranteed to be Y2K compliant (ver 9.0) requires Win95.
The shareware SIMSTAT program appears to be the best alternative to SPSS. Release 3.5e of the program works on the Palmtop but it needs help from the add-on, CGAHLP program to make the program readable on the Palmtop's black and white display. The procedures that SIMSTAT can perform include the following: summary statistics (mean, variance, standard deviation, etc.), crosstabulation, frequencies analysis, breakdown analysis, multiple responses analysis, time series analysis including one-way analysis of variance, paired and independent sample t-tests, Pearson correlation matrix, covariance and cross product deviation, regression analysis, multiple regression analysis including:, GLM Anova/Ancova (up to 5 factors and covariates) including: single-case experimental design analysis, reliability analysis, sensitivity analysis, nonparametric analysis including: nonparametric association matrix including bootstrap analysis, high-resolution graphics, SIMSTAT is the work of Normand Peladeau.
Another statistics package that is worthy of note is Easistat. Easistat is an inexpensive statistics program that runs on IBM PC's and performs the following statistical procedures: Mean, mode, median, standard deviation, variance, standard error of mean, skewness, kurtosis, chi-squared test, Fisher's exact test, Wilcoxon's rank sum and signed rank sum, Kolmogorov-Smirnov, Kendall's rank correlation, paired and unpaired t tests, one way analysis of variance, Kruskal-Wallis analysis of variance by ranks, linear regression with Pearson's correlation coefficient, multiple linear regression, principal component analysis and general minimization. There is a spreadsheet- type data editor to enter or modify data, and data is kept in simple ASCII files to allow easy conversion to and from other formats. With 640k of RAM a total of about seventy thousand data points can be accommodated in practically any number of rows or columns. The program is controlled by commands and an important feature is that it can be run either interactively from the keyboard or in batch mode from command files.
11. Operations Research
There is one set of problems that none of the above programs can handle: namely, the problems from a typical Operations Research or Quantitative Analysis course. Such problems could be programmed in Derive or one of the other computer algebra systems. However there is a book and a disk that will teach you how to use the mathematical techniques and let you solve textbook problems with relative ease.
Qsb+: Quantitative Systems for Business Plus: Version 2.1 is a book/disk package that contains the most useful quantitative methods in management science and operations research, namely, Linear Programming, Transportation and Transshipment Problems, Network Modeling, Critical Path Method, Program Evaluation and Review Technique, Inventory Theory, Queuing Theory, Decision and Probability Theory, Markov Process and Time Series Forecasting.
Besides the emulation of the TI 81 scientific, graphing calculator mentioned in the New Products column of this issue of The HP Palmtop Paper, we found a dozen or so calculator programs that work on the HP Palmtop. We've uploaded all of these programs to the SUPER site to make them readily available for downloading and trying.
We still favor the built-in HP Calc program for solving most math problems. There is no other calculator program that has anything like HP Solve. None of the calculator programs will let you key in an equation from a book and automatically generate a function-key-driven, interchangeable, solution for the variables in the equation. HP Solve outperforms even Derive in this regard.
Rather than describe all the calculators on the SUPER site, let me mention just a few that caught my attention.
12. The Kennedy Collection
John Kennedy is a math instructor and an inveterate programmer. Any of the several math programs by this author are worth the download. You may not need some of the programs but the extensive documentation in his packages is worth looking at. For example, the HP 41C calculator emulator (RPNDEMO.ZIP) contains several documents that will tell you more about Reverse Polish Notation (RPN) than you ever wanted to know. If you have an old HP 41C program, you can key it into the RPNDEMO program and watch it run on your Palmtop.
The author's matrix calculator is just what is needed for someone covering this topic in a math course. It combines ease of use and good documentation.
ChemCalc Ver 4.00 is a System Manager compliant, molecular weight calculator for chemists and chemistry students. The program also serves as a converter to the formula in the Hill System order. Enter a molecular formula in the 'Input Formula' box and Press [Enter]. Its molecular weight will be displayed in the 'Molecular Weight' box and converted to Hill System order in the 'Hill' box. If you use an abbreviation in your input, it will be expanded into full notation and shown in the 'Transformation' box. The result (molecular weight) is also held in the clipboard. You can use this result in HP Calc or other System Manager compliant applications. To avoid the hassle of entering chemical formulae, the program contains a specialized "spell checker" in which you can set up the correct entry for up to 22 different formulas. With that feature, you can enter 'nahco3' and the program will convert it to 'NaHCO3' automatically.
14. Electronic Circuits CAD
ELCAD is a program that may appeal to electronic tinkerers, and perhaps a few electronic engineers. The program draws the circuit used and then queries the user for knowns. It then computes unknowns: resistors, capacitors, inductors, transistor circuits, unijunctions, AC, DC, heatsinks, phase angles, transformers, 555 timers and more. It displays the formulas used on simpler circuits.
This program would have helped me through several home-study electronic courses twenty years ago. The only drawback to using the program on the HP Palmtop is the display. The program uses CGA graphics but the text and drawings are so faint that you may suffer eye strain from trying to view it.
CALCPLUS is an RPN style calculator but it uses a stack of 20 registers and there are 20 stacks of registers. A stack of registers is called a "memory." You can work with just the bottom registers in each memory or perform mathematical operations on all the registers in a memory. The memories can be rearranged and printed in formatted columns complete with headers and totals or averages. The calculator, in many ways acts like a small 20 by 20 spreadsheet but, in other ways, it acts like twenty different calculators that can operate independently. CALC PLUS version 2.0 is the work of David Alexander and is offered as freeware but a $5 donation is requested. If you could register, you might get a version that would do graphing and statistical operations.
Loki is an RPN calculator by Craig Finseth written in 1994. It was designed for use on the HP 95LX but it will run on the HP 200LX and even on a desktop computer. Like other RPN calculators, it has a fourfold stack and ten memory registers. It has some of the look and feel of the built-in HP Calc. It can do both binary math as well as standard arithmetic. The program was originally designed to run on Unix computers and might appeal to people who like the command structure of the EMACs editor. To roll the stack down, you press the 'r' key. To swap the X and Y registers, you press 's'. You can access many of the operations by pressing the F9 key to flip through the different function key definitions. Pressing the F10 key will present a menu with many other operations.
HP created a series of calculators that included the HP 12C business calculator, the HP 11C scientific and the HP 16C computer math calculator. The Xact set of programs contains "exact" emulations of these three calculators. They present a picture of the calculator on the screen and you can try to figure out which key on the keyboard will work with a given calculator key. The HP 11C, 12C and 16C all had a blue and yellow "shift" key. That feature is visible when you run these programs on a computer with a color screen. On the Palmtop, it's somewhat difficult to figure out how to get the [f] and [g] shift keys to work. The upside of the Xact series of programs is that all the calculators are programmable, just like the real ones. If you have a set of routines from an HP 12C business calculator, you can key the routines into the Xact program and save it to disk. The Xact series of calculators does have one quirk when run on the HP 200LX. Other than having to toggle the ON / and ON * keys to get the most viewable display, when you want to use the +, -, * or / keys, you must press the MENU key first. It's a nuisance feature for which there is probably no chance of an upgrade.
This is a scientific calculator by J. Andrzej Wrotniak. When operating, it will accept an arithmetic expression, compute its value, and store the result in a variable. For example, typing in 2.5*12+log 1000 = t will evaluate the expression, display the result (33) and store it in the variable t. The variable t can then be used in further calculations such as integration, differentiation, summation or root finding. EXCalc also has a plotting capability and simple statistical routines. Version 1.55 also will let you perform operations on vectors and matrices (linear algebra). The program has more than 100 different functions that it can handle, e.g., stat. distributions, Euler, user-defined, conditional), function graphs, statistics (mean, s.d., histograms, poly regression), column operations on stat data, linear algebra. The registered version ($30) unleashes more of the functions and extends the basic capabilities of this algebraic calculator. The author maintains a Web site and still encourages registration of his software: www.freeflight.com/wrotniak/
The Calculus Calculator by David Meredith has been renamed to XPLORE, The Mathematical Tool Chest (XPL.EXE). It is more than a calculator. It's more like Solver in the HP Palmtop. You can enter formulas of up to 256 characters. The program can handle complex number arithmetic, differentiation and integration. You can also create a function that is equal to the derivative of an expression, e.g. g(t) = D(sin(2*x),x=t). Integration is done numerically using an adaptive Simpson's algorithm. There is also a Fast Integration function that will speed up the number crunching at the expense of some accuracy. The plotting capabilities of CCalc go beyond those in HP Calc. For example, you can show more than one graph on the screen and even shade in an area of integration. However getting a graph to appear may be an agonizingly slow process. Be sure to have fresh batteries or use an AC adapter. Xplore (CCalc) is shareware. The College Division of Prentice Hall has published the current version of the program with a 200 page manual. The ISBN number is 0-13-117441-X. The cost is around $30.00
The TAPE100 program, also known as REAL Numbers, from BU Systems Company, provides multiple scrolling calculator tapes that can be edited, printed, and saved. REAL Numbers combines the ease of use of a desktop calculator with many powerful features found in spreadsheet programs. The REAL Numbers report writer produces reports suitable for a wide range of uses, from checkbooks to financial statements. The program can handle 15 calculator tapes in separate windows, an unlimited number of memory variables. It has over thirty built-in functions and operators for mathematics and business. You can change the values on the tapes and recalculate the bottom line. The tapes are independent of each other. There does not appear to be any way to use the results of one tape in another. Although the program has some clever features, I would prefer using a spreadsheet such as Lotus 1-2-3 for this kind of task. The program would be beneficial for users of the HP 1000CX that does not have a spreadsheet built-in.
The HP Palmtop comes with Lotus 1-2-3 release 2.4 built in. 1-2-3 generates .WK1 files which are importable into most desktop spreadsheet programs. These same programs usually have the ability to save their native files in the .WK1 format. This means that you could start developing a spreadsheet on the Palmtop, continue to work on it in Excel 2000 and, as long as you don't use any functions peculiar to Excel, put the final version back on the Palmtop in 1-2-3.
For those who are using an HP 1000CX, there are a few alternatives to a complete version of Lotus 1-2-3 for use on their machine. We mentioned VisiCalc in the New Products column of this issue. VisiCalc 1.0 is indeed small (just 27K bytes) but there are other spreadsheets that have all the power of VisiCalc and work better on the Palmtop. Here are a few of the ones that we discovered.
21. ALITE and AsEasyAs
AsEasyAs has long been the best DOS, shareware, spreadsheet program. Unfortunately, for Palmtop users, the latest versions of AsEasyAs (ver. 5.70f) requires at least an 80386 processor to work. Earlier versions of AEA may run on the Palmtop but Trius, Inc., the distributors, clearly states that the older versions are not Y2K compliant. On the other hand Trius offers ALITE, a Lite version of AsEasyAs. This program does run on the Palmtop and is Y2K compliant. ALITE can generate graphs similar to those in 1-2-3 and it can be used as a TSR if desired. It can handle up to seventy functions in the areas of math, finance, dates, strings, and statistics. It incorporates a macro language and has 2048 rows and 128 columns. The program is shareware (cost, $30) and is supported at the Web site www.triusinc.com.
22. Thinker and TurboCalc
Two more spreadsheets that work on an HP Palmtop are called Thinker and TurboCalc. Thinker has some of the look and feel of 1-2-3. It just doesn't have as many functions built in nor does it do graphs or database functions. It is also limited in the amount of data it can handle: 1000 cells. TurboCalc version 9.03 will let you have up to 16384 cells containing data. It too does not support database operations. It will let you generate a bar chart or two. Both of these programs were originally written in the 1980's so there's no guarantee that they're Y2K compliant. The programs are available on the Internet but have been apparently abandoned by their authors.
23. Rebel 3.45
Rebel is a totally different kind of spreadsheet program, one that might appeal only to people who work with vectors and matrices. Each cell in the Rebel spreadsheet can accommodate a matrix and referencing the cell can do matrix operations. Rebel 3.54 is available on the CD InfoBase. It is shareware but the author has apparently abandoned it. His email address is no longer valid. The program has not been tested for Y2K compatibility.
Summing Up the Math Programs
If Lewis Carroll who coined the phrase "Through the Looking Glass," were alive today he'd probably do a double take at this article. Charles Dobson (Lewis Carroll) was a logician and a mathematician as well as the author of children's books. I think he'd be amazed at how people have used the ideas of logic to turn a pile of electronic switches into tools that make mathematics almost "child's play." He'd be even more amazed that people could put all the power of mathematics in their pocket.
The list of software mentioned in this article is exhaustive but not all-inclusive. I searched my own archives, the 1999 CD InfoBase and the Internet for math programs. I found dozens of programs that veteran Palmtoppers will recognize. I also found several programs that have not been mentioned before. On the other hand I'm sure that I inadvertently overlooked a few math programs that might have merit. If you know of any more math programs let me know and I'll add them to the list.
Please note that the mentioned have not been checked for Y2K compliancy. Most of programs were written in the 1980's and the authors no longer support them. There's little likelihood that the programs will ever be upgraded. On the other hand, unless the program uses date functions, the Y2K bug may not be a problem.
If you're looking for math software that will work on the HP Palmtop you will soon have a couple of sources close at hand: the SUPER site (www.palmtop.net ) and the upcoming 2000 CD InfoBase from Thaddeus Computing, Inc. There are dozens of programs in this collection: 36 of them are new to the SUPER site.
If you want to perform your own search for more math software on the Internet, here are some sites that seem to have most of the program files in one location:
The Washington University Archives in St. Louis, MO, USA: wuarchive.wustl.edu:edu/edu/math/software/msdos-files.txt
Channel 1 software repository at www.filelibrary.com/Contents/DOS/33/15.html
The SIMTEL collection www.sim tel.net/simtel.net/msdos n