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------------------------ ALGEBRA AIDER and APS-II ------------------------ Version 1.1 Author: Michael Q. Rieck rieck@javanet.com www.javanet.com/~rieck Overview: APS-II is an algebraic manipulation system for Apple //e, //c or IIGS. It performs several operations commonly found on such systems, such as assigning algebraic expressions as the values of variables, reducing algebraic expressions, solving equations, finding roots of polynomials and graphing functions. ALGEBRA AIDER is a collection of BASIC programs that utilize APS-II to provide tutorials in high school algebra. These include programs con- cerning factorization, evaluation, equations, conic sections, exponential (and logarithmic) functions, and trigonometric functions. Contents: README - this file AlgAid - disk image of front side of the diskette ALGEBRA AIDER v1.1 (DOS 3.3) AlgAid2 - disk image of back side of the diskette ALGEBRA AIDER v1.1 (DOS 3.3) APSII - disk image of the diskette APS-II System v1.1 (ISAAC) ApplePC v2.52b - David Ellsworth's Apple II emulator (freeware) apple2e - Apple //e ROM for the emulator apple2c - Apple //c ROM for the emulator (David Ellsworth was last seen at davidells@aol.com. His emulator with documentation can be found via archie looking for the files containing "ApplePC". The two files used here were archived in ApplePC_2.52.zip and ApplePCroms. ) Sources: An archive containing the source code for APS-II and for the virtual machine ISAAC on which it is built is available from the author. However, this code is not well ndocumented and was never intended for public consumption. Some is Pascal, some is 6502, but most is assembly code in the language of the virtual machine ISAAC. ISAAC includes an operating system, and some of the code is concerned with building this. There are two Pascal disk images, I1 and I2. These are used to build the ISAAC machine and a primitive operating system for it. I3, I4, I5 and I6 are ISAAC disks images and are used to build a better ISAAC system. A1, A2, A21, A22, A3, A4, A5 and A6 are ISAAC disks images used to build the APS-II System. Using the Apple II emulator: Only a basic understanding of the emulator is needed to run ALGERBA AIDER and APS-II. For a complete account of this emulator, you will need to download the whole thing. Also, it should be noted that while some other emulators may work as well, some will not. I believe that this is due to ISAAC's altered version of the RWTS routine from DOS 3.3, but I'm honestly not sure. Note that emulation must be for a //e, //c or IIGS (with at least 128K). The process of running either ALGEBRA AIDER or APS-II begins by starting the ApplePC emulator. Choose option D to load a disk image. Type 1 to choose Disk 1. (We will not be using Disk 2 at all.) Enter either ALGAID or APSII, but go with ALGAID on your first time out. Press escape twice to start the emulation and to boot the disk. Follow the instructions given in the program(s). Running ALGEBRA AIDER: There is a frequent need to swap disks here. There should of course be the possibility of using two drives instead, but this was never implemented. After the ALGEBRA AIDER DOS 3.3 disk is booted into low memory, and when this system requires the computational power of APS-II, it will prompt the user to insert the APS-II disk into Drive 1. It will then boot this system into high memory. Afterward, it will request that the ALGEBRA AIDER disk be reinserted into Drive 1. Unfortunately, ALGEBRA AIDER requires the high memory for other purposes as well, and will then overwrite the APS-II system. So if it needs APS-II again, it will again prompt the user to boot APS-II. (What do you want from 128K?!) All this disk swapping is indeed unpleasant. To effect it on the emulator, proceed as follows: press F10 (to pause emulation), select D (to access drives), select 1 (to choose Drive 1), press backspace and enter the name of the desired disk image, and finally, press escape twice to return to emulation. When running any of the ALGEBRA AIDER drill program, I recommend opting for text mode, as opposed to high-resolution graphics, because of the sluggishness of system and the jittery nature of the display in high-resolution graphics. Also, be aware of the following quirk of this particular emulator: the cap lock key behaves exactly opposite to its normal be- havior. Lower case letters are infrequently needed in ALGEBRA AIDER, and you should put the cap lock on only on these rare occasions (e.g. when entering "Exp[X+Y]"). ALGEBRA AIDER provides on-line documentaion both for itself and for the APS-II System. Here, when prompted to flip over the ALGEBRA AIDER disk, load the disk image ALGAID2. Running APS-II: APS-II is used both to support ALGEBRA AIDER and as a stand-alone system. After booting APS-II (be patient), you will be prompted to enter an algebraic expression or give a com- mand. APS-II can perform a number of mathematical manipulations of the sort found in other symbolic manipulation systems, like Mathematica, Maple, etcetera. After each, you will be returned to the above prompt. This system takes some practice to learn. For details, consult the on-line documentation provided from within ALGEBRA AIDER, as well as the on- line HELP, available on APS-II. Here is an example of something (recursive) you can do with APS-II: Step 1. "Assign" the the expression 1/X - 1/Y to the variable X, and assign the expression 1/X + 1/Y to the variable Y. Step 2. "Evaluate" the variable Y to obtain 1/X + 1/Y. Then evaluate this to get 1 1 --------- + --------- . Then evaluate twice more get a complicated 1/X - 1/Y 1/X + 1/Y fractional expression with nested fractions to a depth of four. (Use the command VIEW to see the whole thing.) Step 3. Ask APS-II to "simplify" this expression. After a while, it returns with the answer: 2 3 -4X Y --------------------- 2 2 4 4 2X Y - X - Y Other features of APS-II include finding roots of polynomials, solving special types of equations, and plotting curves. Known Problems: (1) The "equations" drill in ALGEBRA AIDER is not functioning properly on the ApplePC emulator. Messages intended for the APS-II system are displayed on the screen instead. This is not the case on a physical Apple II computer. (2) The ALGEBRA AIDER routine to process trigonometric functions is also not behaving properly on the emulator. (3) APS-II is unable to solve equations such as XY^2 - X^2Y + X - Y + 1 = 0 for the variable Y on the emulator, although again, it is capable of doing so on a physical machine. (Despite these discrepancies between the emulator and physical machines, I never- theless wish to commend this emulator. Another emulator I tried was unable to deal with ISAAC disks all together, and I was very much surprised and pleased to find one that would. Perhaps later releases of ApplePC can be obtained that el- iminate the above inconsistencies.) Note: ALGEBRA AIDER and APS-II are both freeware, and so may be copied and transmitted freely without violating any copyrights.