Tutorial for Algebra Editor John Henckel, henckel@vnet.ibm.com Copyright (c) 1994 John Henckel Permission to use, copy, modify, distribute and sell this software and its documentation for any purpose is hereby granted without fee, provided that the above copyright notice appear in all copies. Getting Started --------------- Download the alged zip using ftp or almcopy (or anything else) using the BINARY (/b) option. Unzip it using pkunzip. This will extract into the current directory into... alged.exe <--- the program alged.hlp <--- online help alged.1st <--- user options file alged.doc <--- tutorial (this file) alged.dat <--- sample data file alged.c <--- source code mouse.h <--- source code Before you run the alged program, you might want to change your video mode. The alged program does NOT change your video mode, it runs in whatever the current mode is. You can sent this using the DOS command MODE co80,43 or whatever (type HELP MODE). When you start alged you may specify one or more datafile names. The datafile is just a text file you create with a text editor. Start alged with the sample data file... ALGED ALGED.DAT Now you should see a screen with a menu on the top and some formulas in the middle. The first thing to learn is how to see the help text. Press F1. The first part is a brief intro and how to use the mouse. Then you see a description of each menu item. Notice that each menu item has a hotkey. In this tutorial, I will assume you have a mouse. If you don't, you can use the [end] [pagedown] and [pageup] keys to select parts of a formula. Now let's try some of the sample formulas. The first formula is... x*(5 + 2*x) - 2 ----------------- - 2*x + 1 = 13 3 + x (It looks prettier than this if you use 8-bit ascii.) To solve this problem, you need to find a common denominator for the left hand side. You can either click on the "Comm-Deno" menu item or press the hotkey 'm'. The result is... x*(5 + 2*x) - 2 - 2*x*(3 + x) + 1*(3 + x) ------------------------------------------- = 13 3 + x To complete the problem do the following 1. press 'd' for Distribute 2. press space for Simplify 3. click the RIGHT mouse button on the '+' in the denominator 4. press '*' to Mult-Key 5. click the RIGHT mouse button on the '13' 6. press '/' to Div-Key 7. click the RIGHT mouse button on the '3' (any will do) 8. press '-' to Subtr-Key By now it is getting pretty messy. Press space (two times) to Simplify, and you should see... 1 --- - 3 = x 13 There is two ways to simplify this. We can find a common denominator, or we can calculate. 9. press 'c' to Calculate 10. press 'a' to reverse the equality (Associate) 11. press 'i' to convert to integer expression. You should get the answer -38/13. Press down-arrow to select the next formula. 3 / 2 \ |x - ---| \ 3 / 1. press 'n' expand integer exponents 2. press 'd' Distribute 3. press space to Simplify Press down-arrow to select the next formula. / 2 \ 3 2 \x - 2/*(x + 1) = x + x - 2*x - 2 To solve this one, let's factor the RHS. 1. click the LEFT button on the last '-' in the formula. You should see the right-hand-side of the equation highlighted. 2. click the RIGHT button on any 'x'. 3. press 'f' to Factor Polynomial. 4. press space to Simplify Press down-arrow to select the next formula. 2 (2*x) x *a a ------------ a -------------- (x + 1) a You can see in this problem many exponents all with the same base. (Note: the top numerator is a^x^2 * a^(2*x), and not a^(x^2 * a^(2*x)), because there are no parentheses.) To solve it we need to combine all the exponents. 1. press 'j' for Exp Join 2. press space to Simplify Now let's move forward to simultaneous equations. Press down-arrow until the following two formulas are at the top of the screen. 3 y = x y = 4*x - 3 There are several ways to solve this pair of equations. We could substitute one equation into the other, or we could subtract one equation from the other. Let's try subtraction. The first equation is already highlighted; it is the pick. 1. click the RIGHT mouse button on the '=' in the second equation. Now it is copied to the bottom of the screen; it is the key. 2. press '-' to Subtr Key 3. press space to Simplify 4. click the LEFT mouse button on RHS of the first equation (you need to click on the '+'). 5. click the RIGHT mouse button on an 'x' 6. press 'f' to factor polynomial 7. click the LEFT button on the quadratic factor (the last '-' sign) 8. press 'q' to factor quadratic Hopefully you now have this.... / 0.5 \ / 0.5 \ | 13 + 1 | | -1*13 + 1 | 0 = (x - 1)*|x + -----------|*|x + --------------| \ 2 / \ 2 / To separate these factors into separate equations, you can do... 1. copy (x - 1) to the key 2. pick 0 3. press '=' for Equal Key 4. press Ins to add new formula 5. repeat 1..4 for the other factors. Press down-arrow until the last three equations are at the top of the screen. 5*x + y + z = a x + 2*y + z = b x + y + 3*z = c (end of list) To solve these you can use substitution... 1. copy (5*x + y) in first equation to the key 2. press '-' to Subtr Key 3. press space to Simplify Now substitute the first into the second... 4. copy (z = a - 5*x - y) to the key 5. pick the second equation 6. press 'u' to substitute 7. press space to Simplify 8. copy (a - 4*x) to the key 9. press '-' to Subtr Key 10. press space to Simplify The solution is left up to the student :-) You need to substitute the first and second equations into the last one. Then you can solve for x and substitute backwards. If you enjoy Alged or have any suggestions, please send me an email. I do not want you to send me any money, but I like to get mail. Did you know that the freeware concept is biblical? Ecclesiastes 11.1 says "Cast your bread upon the waters, for after many days you will find it again." John Henckel henckel@vnet.ibm.com