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Text File | 1996-06-06 | 17.0 KB | 351 lines

Help text for the Algebra Editor Copyright (c) 1994,1996 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 and that both that copyright notice and this permission notice appear in supporting documentation. All programs contained herein are provided to you "as is". The implied warranties of merchantability and fitness for a particular purpose are expressly disclaimed. ╔═════════════╗ ║ QUICK START ║ ╚═════════════╝ To load the sample data file: 1. Click "Load" in the upper right corner (or press 'l'). 2. Type "alged" and press Enter. Play with the sample data file and if you have any trouble, print the short tutorial in the alged.doc file. (Press Esc to return, or press any key for more help...) ---------------------------------------------------------------------------- My name is John Henckel (internet: henckel@vnet.ibm.com). I am a computer hobbyist; I like to write computer programs to amuse myself, and this is one of them. I also recommend my 2D collision simulator "Impact" found in http://www.coast.net/SimTel/msdos/simulatn.html. Thanks to my family for letting me work on this. Thanks to my manager at IBM in Rochester, Minnesota for permitting me to offer this program for free to the public. Alged is a program for solving algebra problems. There are other programs that can do symbolic formula manipulations, such as MathCad and Mathematica. The advantages of Alged are that it is * Free! The source code is also free! * Light weight (it runs on a PC/XT with 256K of memory) * Easy to use, ideal for education * Fast and flexible 2D and 3D graphics * Can be customized and translated (Flemish and French included). Of course, there are limitations. Alged is by no means a "commercial grade" product (though I've seen worse!) Alged does not handle matrices, series, integrals, derivatives, or transcendental transformations. Imaginary numbers are supported only with the five basic operators (add, subt, mult, div, exp). Alged is a tool for symbolic math, so I have purposely avoided the "number crunching" algorithms. ---------------------------------------------------------------------------- Input Instructions: The Alged screen has a menu at the top and a work area at the bottom. At the lower left is the time of day and the percentage of heap memory used. (When the heap reaches 100% Alged will exit.) You manipulate the formulas in the work area by clicking on parts of them and then clicking on the menu. You click the left mouse button in the work area to select the current expression or the PICK. The pick is highlighted. You click the right mouse button in the work area to select the KEY expression. The key is copied to the bottom of the screen. Notice that it is legal to click on the key, so the pick may be a subset of the key. To scroll the work area, you can click on the border. If your computer does not have a mouse, (or you just don't like to use it) you can use the [pageup], [pagedown] and [end] keys to select the pick. These keys descend the binary tree stored in memory. You can copy the pick to the key by pressing '.'. You can type the key by pressing 'k'. You can copy the key to the work area by pressing [Insert]. You can delete the key by pressing [Enter]. To scroll the work area, you can use the arrow keys. Some of the operations on the menu only use the pick, and some use both the pick and the key. Unless otherwise specified, the menu descriptions below apply to the pick only. (New for version 3.4) The polynomial operations (such as PolyFact and PolyDiv) do not require you to specify the key. If no key is specified, they will use the variable 'x' or the first variable found in the expression. If the pick is an equation, the polynomial operations will automatically select one side or the other. ---------------------------------------------------------------------------- Menu Description: Simplify [space] simplify expression. It sorts it, combines common terms, calculates numbers, and rewrites it in canonical form. Note: Another similar function is SimpStep which is assigned to the 'x'. The SimpStep function shows the intermediate steps of the simplification. Distribute [d] distribute multiplication over add and subtract, and distribute exponents over multiplication and division. Note: Another similar function is DistChild which is assigned to the 'D' (press shift and 'd'). The DistChild function is different in two ways. 1. DistChild does a top-down distribution. For example, (x*(a + b))^2 ---> (x^2)*(a + b)^2 using DistChild (x*(a + b))^2 ---> (x*a + x*b)^2 using Distribute 2. DistChild does not distribute the top level factors in an expression or equation. You can use DistChild to simplify the result of a factorization, like FactPoly or FactQuad. Calculate [c] calculate all numbers. e.g. 3*2 => 6. PrimeFact [v] find the prime factorization of integers. (This is limited by the ?d user option). Integer [i] convert real numbers to integers if possible. e.g. 1.5 => 3/2 This algorithm has two strategies. First, it looks for repeating patterns in the fractional part of the number. At least two repeating digits must be significant. If that fails, it searches for an integer, d, such that d*x is an integer. The user parameters ?e and ?d are used here. Associate [a] rotates the elements of an associative group. Comm-Deno [m] This is a TOGGLE to create a common denominator or to distribute division over add and subtract. CharMode [8] toggle ascii 7-bit or 8-bit. This is useful if you use print-screen. Poly-Coef [p] collect the coefficients of a polynomial. The pick must be a polynomial (not an equation) and the key must be the expression use as the base of the polynomial. e.g. pick is a*x + b*x + c, key is x ==> result is c + (a + b)*x Center [home] horizontally center the formulas (this is default). Poly-Div [\] polynomial division. The pick must be a division (not an equation) and the numerator must be a polynomial with degree greater than or equal to the denominator. The key must be the base variable. e.g. pick is (x^2 - y^2)/(x - y) and key is x. ==> result is x + y. FactQuad [q] factor a 2nd degree polynomial using the quadratic equation. The pick must be a 2nd degree polynomial (not an equation) The key must be the base variable. e.g. pick is (x^2 - y^2) and key is x. ==> result is (x + y)(x - y). FactCubic [3] factor a 3rd degree polynomial using the cubic equation. The pick must be a 3rd degree polynomial (not an equation) The key must be the base variable. e.g. pick is (x^3 - y^3) and key is x. ==> result (after integer and several calculate and simplify) is (x - y)*(x + (0.5 - 0.86i)*y)*(x + (0.5 + 0.86i)*y). Note: This function isn't working very well. Sometimes it gives the wrong answer, and sometimes it uses up all memory. The problem appears to be with non-singular roots. Only use it as a last resort. FactPoly [f] factor a polynomial using rational roots. The coefficients of the polynomial should not contains any non-integer numbers. The pick must be a polynomial. The key must be the base variable. e.g. pick is (x^4 - y^4) and key is x. ==> result is (x - y)(x + y)(x - iy)(x + iy). Note: If the polynomial has non-integer coefficients, sometimes FactPoly will still work if you "fix" it using Calculate & Integer. To force integer coefficients, put the terms of the polynomial over a common denominator. e.g. with x^2 - 0.5*x - 3 press Integer, Simplify, CommDeno, to get (x^2*2 - x - 3*2)/2. Now select the numerator (press End) and then FactPoly. Substitute [u] performs substitution using the key over the pick. The key must be an equation. e.g. pick is a*x + b, key is x = y - 1 ==> result is a*(y - 1) + b. Notes: the LHS of key can be an expression, but you may need to change the association on the pick in order for the substitute to work. You can use this with EqualKey: to replace the pick with the key, press =u. ^N Expand [n] expand integer exponents. e.g. x^3 ==> x*x*x ExpJoin [j] join exponents of common base. This is the opposite of distribute for exponents. EqualKey [=] Change the key to an equation using the pick. Neither pick nor key can be an equation prior to this operation. e.g. pick is x + y, key is z ==> result key is x + y = z Note: you can use = and u to replace the pick with the key. Add-key [+] add the key to the pick. If pick is an equation then key is added to both sides. If key is an equation then the corresponding sides are added to the pick. If neither is an equation then the key is both added and subtracted. e.g. pick is x, key is y ==> result is x + y - y. Sub-key [-] subtract the key from the pick. See notes on add-key. Mult-key [*] multiply the pick by the key. See notes on add-key. Div-key [/] divide the pick by the key. See notes on add-key. Exp-key [e] raise the pick to the key power. See notes on add-key. DeleteTop [del] delete the expression at the top of the screen. EnterKey [k] prompt to type in a new key. You must type the key and press F6 Enter when you are done. (The F6 key should produce a ^Z, but if it doesn't work, then you can press ctrl-z.) You can use either infix or postfix, depending on the ?f user option. Infix example z = (x^2 + y^2)^.5. Postfix example z x 2 ^ y 2 ^ + .5 ^ =. You cannot use parentheses and the tokens must be separated with blanks. Note: You can use EnterKey to type anything that could appear in a data file. This includes visible comments (") and user options like ?m 41. (Exception: you cannot change bgi drivers with ?g, but you can change the mode or palette. The ?f option does not take effect until end-of-file.) Use the InsertKey command to add the new key to the expression list. InsertKey [Ins] copies the key to the expression list. EraseAll [Alt-e] delete all expressions from the work area (except the key). DebugMode [Alt-d] dump the pick node tree for debugging purposes. Load [l] load more expressions from a file. Note: the previous expression list is not erased. Save [s] save the expression list to a file. The key is not saved. Write [w] write the expression list in postfix notation. This function is not very useful unless you like postfix. I just left it in because it was in alged version 2.1. EquRight ']' move the right operand from the left side of an equation to the right side. e.g. pick is x + y = 3, result is x = 3 - y. EquLeft '[' move the left operand from the left side of an equation to the right side. e.g. pick is x + y = 3, result is y = x + 3. Graph [g] switch to graphics mode and plot the function. Press F1 for help text about graphics control keys. To use graphics you need a CGA, EGA, VGA, or Hercules video adapter, and you need you have the corresponding bgi file (like EGAVGA.BGI) in the current directory. Alged can auto-detect these four modes. If you have another bgi file you want to use, then specify it with the ?g user option. ------------------------------------------------------------------------------ Comments On Other Things 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. When you run alged from the command line you can specify one or more filenames for it to load. Alged always tries to load the file ALGED.1ST first. I suggest that you put the user option flags in this file, but you can put formulas there as well. See alged.1st for a list of all the user options. Alged uses the current video mode, so before starting alged you can set it, for example, by typing MODE co80,43 (you may need ANSI.SYS for this command.) The display algorithm used by alged is not perfect, for instance the following expression 1 2 ──── y 2 + ──── x b the horizontal bars should be lined up. You can make them line up by setting user option ?y to 0, but this causes other things to be ugly. When you click on an expression with the mouse, it is mostly obvious. The exception is exponentials. To click on an exponential, point just above the top right corner of the base. e.g. in 2 (x + y) point just above the ')' and click. You will notice at the top left of the menu are Simplify and Distribute. These operations are very useful for reducing a large complicated expression. After a PolyDiv, for instance, I usually hit Distribute and Simplify alternately until nothing changes. This program does not support unary minus operator, thus to say -x, you must say -1*x. It does not support roots, so to say sqrt(x) you must say x^0.5. All numeric values are stored as IEEE 8-byte floats (double). This allows the exponent to be -307 to +307 and the base has 16 significant digits. Alged only displays 15 digits, because the last one is sometimes garbage. This leads to a situation where sometimes numbers that look like integers really are not. For instance, you might see 1*x and when you Simplify it doesn't change to x. To fix this, press Integer, and the garbage digits are thrown out. A word of caution: if your problem uses very small numbers, like 1.23e-10, then you should not use Integer or else significant digits are removed. The following special symbols are recognized... pi = 3.14159265358979292 e = 2.71828182845904509 Alged allows any function with up to 5 arguments. However, only the following functions are recognized in calculations and graphs. With one argument: sin, cos, tan, acos, asin, atan, cosh, sinh, tanh, ln (base e), log (base 10), abs, rand, sign. With two arguments: min, max, r, mod, atan2. The trigonometric functions are in radians. The function r(x,y) uses the hypot function in C which is equal to (x^2 + y^2)^0.5 which is the hypotenuse. The atan2(y,x) is the angle (in radians, -pi to pi) of the line connecting (x,y) to the origin. Variable names can be up to 24 characters. However, function names can only be 7 characters. This is because function parm pointers use part of the name memory. The special variable "i" is recognized to be the square root of negative one. Thus, i*i is simplified to -1. Also i^7.3 becomes -1*i^1.3. Imaginary numbers are supported in exponentials, (1+2i)^3 is evaluated to 2.24^3*(cos(1.11*3) + i*sin(1.11*3)) which is -11-2i. I used the convention in which -pi<theta<=pi. Imaginary numbers are not computed in functions like sin(3*i). Both Simplify and Calculate will compute numerical results. However, the difference is that Simplify will not attempt an operation on whole numbers that may produce a non-whole number. For example, 4^0.5 is not reduced by Simplify, but it is by Calculate. Some of the Poly operations will not work unless the expression is first completely distributed and simplified. You should practice using Associate and PolyCoef. These operations are useful for many things. Associate will rearrange add/sub or mul/div or =, whichever is currently selected. The FactrPoly operation can be very slow. On a 486DX-33 to factor a 4th degree polynomial may take 15 seconds. In general, I must admit that I made no effort at all to make Alged efficient. It was already hard enough. Customizing: The Alged menu and other program text is stored in the ALGED.MNU file. You can customize this file using a text editor. You can change the size and layout of the menu, the hotkeys, or any of the text. You can translate this file into another language (e.g. Italian). If you do, send it to me so that I can distribute it! When Alged starts, it loads ALGEDxyz.MNU from the current directory, where xyz is the language option specified with ?l. If ?l is not specified in ALGED.1ST or any of the data files, then the ALGED.MNU is loaded. Final Notes: One final note on reliability. This program was thrown together as a hobby and it is not reliable. You should check your answers by reversing the operation if possible. You should save your work often. When I developed this program, several times it hung the system. I had to turn off the power of the PC. So be careful, especially on very large operations like FactrPoly. "This is what the Lord says: 'Let not the wise man boast of his wisdom or the strong man boast of his strength or the rich man boast of his riches, but let him who boasts boast about this: that he understands and know me, that I am the Lord, who exercises kindness, justice and righteousness on earth, for in these I delight,' declares the Lord." Jeremiah 9.23-24 End of help text. Press any key to return.