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******************************* * * * PROGRAM DOCUMENTATION * * = Non-Commercial Use Only = * * * ******************************* ***************************************** * * * ============== * * = XY-Solve = * * ============== * * * ***************************************** XY-Solve challenges the user to complete the solution of a puzzle consisting of mathematic functions. Each piece of the puzzle represents a graphic solution to a standard formula. Puzzle complexity may vary from simple displays of individual POINTS or LINES, to extremely complex combinations of Quadratics, Trigonometrics, Parametrics, and Composite functions. XY-Solve contains powerful program features designed to guide the user to a better understanding of mathematic concepts. XYSolve's advanced features include: DISKETTE and KEYBOARD prepared solution sets (puzzles). Current session STATUS may be saved and reactivated at will. Cross-hair CURSOR system for identifying function boundaries. Plot ENHANCEMENT techniques. "ZOOM" capability to search for hidden function displays. "HELP" in determining appropriate values for variables. "REPORT" tracks the users performance. TOLERANCE RANGE feature augments "Exact Value" solutions. SOUND and COLOR DOMAIN control. GRAPHIC and NON-GRAPHIC PRINTER support. Minimum System Configuration: IBM-PC or true compatible with 128K RAM and one disk drive. PC-DOS 2.0 or truly compatible MS-DOS 2.0 or greater. IBM-CGA, Hercules Graphics Card or true compatible. Contact Insight Advantage for Hercules monochrome versions. XYSolve Mathematic Functions in Graphic Form. ------------------------------------- Changes and modifications to this program and manual will be made periodically. Consider them as additions to the information supplied herein. Direct your requests for copies of this product to Insight Advantage. Copyright (C) 1988 by Dean M. Thompson. All rights reserved. This product, the software, manual, and any other information included in this package is copyrighted. Copying, duplicating, or otherwise reproducing any part of this product (except where explicitly mentioned in writing) is prohibited by law without the express written consent of Insight Advantage. Voluntary or willful violations of the Copyright Law of the United States can result in civil damages in addition to actual occurring damages. IBM, MS-DOS, Hercules, WordStar, Epson, SideKick are respectively trademarks of: International Business Machines Corp., Microsoft Corp., Hercules Computer Technology, MicroPro International, Epson America Corp., Borland International, Inc. Insight Advantage 4509 Yellowleaf Dr. Fort Worth, TX 76133 XYSolve Table of Contents ========================= 1. Basic Menu Structure 1 2. Sample Session 2 2.1 Backing Up Your Diskettes 2 2.2 Caring For Your Diskettes 2 2.3 The XYSolve Program Disk 2 2.4 Before We Start 3 2.5 First Steps 3 2.6 Conventions 3 2.7 Important Keys 4 2.8 Grand Tour 4 2.9 START Menu Option 6 2.10 Puzzle File Directory 6 2.11 Two Dimensional Point Math Module 6 2.12 Main Plot Display 7 2.13 Numeric Value Entry 8 2.14 First Waiting Position 8 2.15 PLOT OPTIONS Menu 8 2.16 CURSOR Plot Option 8 2.17 ZOOM Plot Option 8 2.18 ENHANCE Plot Option 9 2.19 PRINTER Plot Option 9 2.20 HELP Plot Option 9 2.21 EXITING Plot Options 9 2.22 Second Waiting Position 10 2.23 REPORT Menu Option 10 2.24 Keyboard Puzzle Files 10 2.25 SAVE Menu Option 11 2.26 HELP Menu Option 11 3. Functional Modules 12 3.1 2D Point 12 3.2 Line 12 3.3 Circle 13 3.4 Parabola 13 3.5 Ellipse 13 3.6 Sine 14 3.7 Cosine 14 3.8 Tangent 14 3.9 Parametric #1 15 3.10 Parametric #2 15 3.11 Composite #1 16 3.12 Composite #2 16 4. Advanced Procedures 17 4.1 Preparing Puzzle Files 17 4.2 TOLERANCE Value Recommendations 17 4.3 Puzzle Filenames 19 4.4 Parametric/Composite Procedures 20 5. Using The Printer 21 Appendices 1. Glossary I-1 2. ERROR Messages II-1 3. Demonstration Values III-1 4. Puzzle File Syntax IV-1 5. Practice Puzzle Files V-1 6. Index VI-1 Associated Documents 1. XY-Educational System ORDER FORM. 2. XY-Educational System TROUBLE REPORT. Page 1 XYSolve BASIC MENU STRUCTURE ============================ INTRODUCTION | |______________ SYSTEM CUSTOMIZATION | |_ Sound | |_ Color | |_ MAIN MENU | | | |_START _________________ PUZZLE SOURCE | | | | |_REPORT |_DISKETTE | | | | |_SAVE {Current Status} |_KEYBOARD | | | |_HELP {System} | | | |_END ________|_______________________________ | | | | _GENERAL MENU QUAD-GEOM MENU TRIG MENU SPECIAL MENU | | | |_HELP {Menu Structure} | | |___ 2D Points Line | | |_ _ Circle Parabola Ellipse | | |_ _ Sine Cosine Tangent | | |_ _ Parametric #1 Parametric #2 Composite #1 Composite #2 | | | |________ PLOT OPTIONS MENU | |_CURSOR | |_ZOOM | |_ENHANCEMENT | |_PRINTER {EPSON 0-6} | |_HELP {Variable value} Page 2 XYSolve Sample Session ====================== Backing Up Your Diskettes: Diskettes can be damaged or lost. We recommend that before you use XYSolve, you make a copy of the Master Diskette. Use the copy whenever you run the program, leaving the Master Diskette in a safe place so it can be used to restore your copy should it become necessary. Specific information on making backup copies of disks can be found in your DOS (Disk Operating System) manuals. Caring For Your Diskettes: Handle diskettes carefully. Treat them as you would any valuable object; for, with your files on them, that's exactly what they are. Diskettes should be stored in an upright position in their protective sleeves. They should not be subjected to direct sunlight, magnetic fields (Vacuum cleaners, televisions, microwave ovens etc.), dust, or extreme temperatures. When you handle a diskette, try not to touch the magnetic media. Don't bend them or write on them with anything heavier than a felt tip pen. The XYSolve Program Disk: All of the programs and files used by the XYSolve system reside on a single disk. The XYSolve program itself consumes approximately a third of the available disk space. The remainder of the disk contains the installation program and the practice Puzzle files. Sufficient disk space remains for several of your own Puzzle files. Should more space be needed, we recommend deleting the installation and practice files as well as any user developed Puzzle files that are not immediately needed. Page 3 Before We Start: XYSolve does a lot of exciting things with disk files. To help it do its job efficiently, you should reserve as much file capability as possible in your computer system. You do this by adding the statement "FILES=20" to what is known as a CONFIG.SYS file on your boot or system disk the first time you use XYSolve. If you have experience in preparing files, but are a little rusty, you can find refresher information in your DOS (Disk Operating System) manuals. If, however, you're not sure what we are talking about, an easier way has been provided to get the job done. A special program called "INSTALL" has been included on your XYSolve master diskette. All you have to do to make or alter a CONFIG.SYS file is to enter the name INSTALL just as you would any other program you wish to run. After INSTALL finishes, you should REBOOT or RESET your computer to enable your operating system to use the instructions you have just prepared. First Steps: Starting the program is simple, merely insert the XYSolve master diskette into your disk drive and enter XYSolve at the DOS A> prompt. In addition to XYSolve itself, your master diskette contains several auxiliary files and programs such as INSTALL. The auxiliary files are practice Puzzles. The Puzzle files contain the sequences of instructions that comprise the individual pieces of each puzzle. (more on this later) These auxiliary files are there to help you become familiar with all the interesting capabilities of your new program. Conventions: Before we can go any further, we need to establish some conventions to help us as we progress. The first concerns keys. When a keypress is called for, the indicated key will be written within brackets like this: <KEY TO PRESS>. In addition, menu selections and commands will be placed within single quotes like this: 'MENU SELECTION'. Page 4 Important Keys: ARROW (CURSOR CONTROL) KEY.. Indicates MENU selections. Positions the PLOT CURSOR. ENTER Key.. Selects MENU levels. Executes FUNCTION selected. Indicates ACCEPTANCE of plot values. ESCape Key.. EXITS from menu levels, plot options, and math function modules. REJECTS unwanted plot parameter values. NUMERIC Keys.. ENTER plot parameter values. Just remember, SELECT with an <ARROW>; ENTER with <ENTER>; DEFINE your plot value with a <NUMERIC>; and EXIT with <ESCape>...Its that simple! Grand Tour: After XYSolve starts executing, the fun begins. Assuming everything goes well, XYSolve will present you with a "SYSTEM INTRODUCTION" screen. This screen is just a reminder of some of the more important points in running the program, such as how to move around within the menus, etc. The comments on setting your particular system's SOUND, and COLOR parameters are of primary importance. This is your opportunity to configure your program for a particular environment. Page 5 Selecting the different parameters to change is done with the <ARROW> keys and <ENTER>. Before XYSolve will let you proceed to the system setup module, however, it first checks to insure that your <ARROW> keys are active. If you notice a "Please press your Number Lock key" request at the bottom of your screen, that is what's happening. Now let's take a little closer look at the SETUP procedures. We do this by pressing <Y> for "Yes". The Setup window will open with the selection bar highlighting the 'SOUND' option. Press <UP> and <DOWN> a couple of times and notice how the FUNCTION and COMMENT windows follow. When you stop at the 'SOUND' selection again, press <ENTER>. Pressing <ENTER> will toggle the sound capability of your system on and off. Let's set it 'ON' during this session. Finally, press <DOWN> to select the 'COLOR' option. The COLOR option toggles between the single 'NORMAL' screen color, and a repeating sequence of 'ALTERNATE' colors. Just press <ENTER> repeatedly until the desired color is active. When you have completed setting the environment, you can get back to the main stream by pressing <ESCape>. XYSolve will then prepare a special file on your master diskette containing your new settings, and will automatically use them as defaults during future sessions. By now you have used almost all of the important keys you will need to know as you continue within XYSolve. Should it become necessary, you can also review these key assignments by accessing any of the menu 'HELP' screens. Ready To Go On? The next screen you will encounter as we proceed is the 'MAIN MENU'. This screen is the gateway to the rest of the program. From here you can select Puzzles to be solved with the START selection, obtain a status REPORT on your progress, SAVE your current status for later re-activation, obtain HELP and END a session. This screen also provides access to other menus with selections of their own. As you can see, the 'MAIN MENU' screen is primarily made up of five windows: The 'PLOT OPTIONS' window on the left. The 'VALUES' window on the right. The 'FUNCTION' and 'COMMENT' windows on the bottom. The PLOT DISPLAY window in the center. Page 6 You will become more familiar with this screen format as we proceed. As we have just arrived, the selection bar is highlighting the 'MAIN MENU' option. By pressing <UP> or <DOWN>; however, you may select other options. By pressing <LEFT> or <RIGHT>, you can move into the FUNCTION window. Go ahead and practice a bit. Notice how the selection bar wraps around the end of it's range just as it did in the SETUP window. When you are ready to proceed, select the 'MAIN MENU' option once again. START. The first step in using XYSolve is to activate a puzzle by selecting 'START'. Press <DOWN>, and you enter the PUZZLE PREPARATION MENU where you may select either the DISKETTE or the KEYBOARD as the source for your puzzle. For now, we will load and activate one of the practice puzzles provided on the XYSolve master diskette. Puzzle File Directory. Press <ENTER> or <RIGHT> and <ENTER> to obtain a directory of all the Puzzle Files on your diskette. let's go with an easy one first, one covering the TWO DIMENSIONAL POINT. Two Dimensional Point Math Module. At the filename prompt, type "TWO-D" followed by <SPACE>. After reading and analyzing the data from the file, XYSolve will plot the point on the display, and we will be ready to proceed with our solution attempt. From the MAIN MENU, press <RIGHT> once then <ENTER>. These steps will place us within the 'GENERAL MENU' level. In addition to the change in the menu name listing, an entirely new set of FUNCTION selections has been provided. All of the lower level menu screens look exactly like this with the exception of displaying their own set of appropriate functions. We are now finally at the point where we can select a function to solve. Use <ARROW> and <ENTER> to select '2D Point'. As we enter the module, the function we are attempting to solve blinks so that it can be identified among other forms that may be present. Let's go over some of the other changes. First, we finally have some values in the 'VALUES' window on the right. In addition, the 'OPTIONS' window has completely changed its contents as has the 'FUNCTION' window which now displays the 'FORMULA' for our '2D Point'. Adjacent to the appropriate formula, a variable is in a position to be updated. Page 7 Since the current plot display is used so much by XYSolve, let's take just a second and go over some of its points. Main Plot Display. First, notice the set of rulers for the "X" and "Y" axis. These rulers define the two dimensions in which we will be plotting while we are in this module. The normal range of this particular set of rulers is +/- 10. You'll also notice that "X=0" and "Y=0" points are defined by vertical and horizontal axis lines. Using the rulers, you can see that the currently displayed point is located at "X=5" and "Y=5" or (5,5) for short. Numeric Value Entry. Our next step is pretty clear. As the comment window states, we can select a new value for the variable "A"; or simply by pressing <ENTER> accept the +0.0 that is currently assigned. After we enter our selections for "A", "X", and "B", XYSolve will plot the solution for us. As you enter the following values, watch the screen carefully. Several things will be happening in quick succession, and I will try to point them out for you. First, go ahead and accept the current +0.0 values for both "A" and "X" by pressing <ENTER> twice. Next, change the value for "B" to -7.5 watching carefully as you enter each part of the value... XYSolve monitors each keypress you make, trying to figure out what you want. When it thinks it knows for sure, it will move to complete the entry for you. XYSolve knows all the rules of the game, as well as the limits for each value. It knows, for example, that SYSTEM LIMITS for variables are set to +/- 99, and that only one decimal place is allowed and then only if the value is less than +10 and greater than -10. Don't be intimidated by this, XYSolve only wants to help us keep our plots under control. As you entered your keypresses, the following sequence was taking place: Your first key, the "-", told XYSolve that you didn't want the currently assigned default value, so it cleared the value and displayed your "-". Your second key, the "7", was no help to XYSolve, so it just displayed it. Your third key, the decimal point ("."), was more helpful. Now XYSolve can figure out what you are doing and set itself up to assist you. It knows to expect another number key (or <ESCape> if you don't like your values) and will not allow other keys to be accepted..except for one, <ENTER>. If during entry of a numeric value, you press <ENTER>, XYSolve will assume you are through and will complete the rest of your value, adding any appropriate decimal point or zeroes. Page 8 Your last key, the "5", was all that XYSolve needed, so it provided the <ENTER>. Since you now have values for all the required variables, XYSolve goes to work. The "B" 'VALUES' display gets updated and the plot moves to a point along the "X=0" axis as expected. First Waiting Position. After completing each plot, XYSolve moves to a waiting position. The 'COMMENT' window then displays key assignments that are currently active. PLOT OPTIONS menu. Press either <UP>, <DOWN>, <LEFT>, or <RIGHT> once. When you are at the waiting point, all arrow keys lead to the 'CURSOR' plot option. Press <ENTER> to select the cursor. 'CURSOR' Plot Option. While in the 'CURSOR' module, you may use <LEFT>, <RIGHT>, <UP>, or <DOWN> to align the cross-hairs with points of interest on your plot. Go ahead and practice a bit. When you are ready to EXIT, press <ESCape>. 'ZOOM' Plot Option. Press <DOWN> once more to get to the 'ZOOM' Option. It is possible within the numeric limits of XYSolve to plot functions partially, or entirely outside the range of the display. In attempting to identify these "hidden" functions, you may toggle the display between the normal +/- 10 range and +/-100. Once identified, functions may be solved in the usual manner. Let's take a quick look at ZOOM. Press <ENTER> once to set the 'ZOOM' option to +/-100. Notice that the plotted point seems to have moved toward the center of the display, just as we would expect it to with our scale change. Press <ENTER> once more to reset the 'ZOOM' option to +/-10. Page 9 'ENHANCEMENT' Plot Option. Press <DOWN> and <ENTER>. The inversion you are seeing is a technique used to more readily identify plot features that might blend into a background. The 'ENHANCE' option is a ON/OFF toggle like the 'ZOOM' option we used a minute ago. Press <ENTER> again to turn it off. 'PRINTER' Plot Option. Press <DOWN> and <ENTER>. The 'PRINTER' selection allows you to save a copy of your work on a printer. Both GRAPHIC and NON-GRAPHIC printers are supported. We won't copy our current plot as it can take several minutes to complete a printout. Press <ESCape> to CANCEL the sequence. 'HELP' Plot Option. Press <DOWN> one last time and <ENTER>. The 'HELP' module identifies variables that are out of tolerance causing a solution to fail. A failure may be due to a single variable or possibly the inter-relationship of several variables. The 'HELP' facility allows you to "lock- in" correct values while attempting to "zero-in" on incorrect ones. In establishing standard limits, XYSolve can augment each correct value with a pre-defined tolerance. When 'HELP' is active, XYSolve compares your input with the "standard" limits. If an input exceeds the limit, the corresponding variable is identified by a reverse color selection bar in the values display. It is important to note however, that the 'HELP' facility merely leads you to one "unique" solution within the entire solution set for the function. Just as there are numerous solutions for any algebraic equation, it is possible, and entirely reasonable, to successfully complete the solution for a function with any one variable, or indeed all variables, exceeding the tolerance limits. EXITING Plot Options. There are a number of ways to EXIT Plot Options. We can press <UP> four times; press <DOWN> once to wrap around the menu range; or just press <ESCape>. Let's use the fast way. Press <ESCape> to jump to the top of the 'PLOT OPTIONS' menu. Press <ESCape> to EXIT from the 'PLOT OPTIONS' menu. Page 10 Second WAITING Point. Whenever we leave the 'PLOT OPTIONS' window, we automatically enter the Second WAITING POINT. From here, we may either EXIT the '2D Points' module by pressing <ESCape>, or continue to solve new plots by pressing <SPACE>. Since we turned the 'HELP' facility ON, let's enter some values and see how it works. Press <SPACE> to continue in the '2D Point' module. Press <ENTER> three times to accept the values we setup previously. Notice that all the variables are indicating excessive values. As we would continue to refine our input values, the out-of-tolerance indicators would extinguish. Press <ESCape> to EXIT the '2D Point' module. Press <ESCape> to EXIT the GENERAL MENU. 'REPORT' Menu Option. As we have activated a puzzle, we are now able to obtain a report on our progress. Press <DOWN> twice and <ENTER>. The REPORT module provides several pieces of information that describe our performance as well as define the complexity of each puzzle. Take a moment and review the report criteria on the screen. While your at it, can you explain our miserable score? Press <SPACE>. Press <DOWN>, <LEFT>, and <ENTER> to select the KEYBOARD puzzle file preparation module. Keyboard Puzzle Files. The Keyboard Puzzle File Preparation module is extremely handy when preparing and activating short Puzzle Files. Let's prepare a quick Puzzle containing just a Circle. Press <3> for a Tolerance value assignment of "0.3". Press <3> again to select the 'Circle' module. Enter a value of "1.0" for the "A" variable. Enter a value of "3.0" for the "B" variable. Enter a value of "5.0" for the "R" variable. Press <ENTER> at the function prompt to activate the Puzzle. A more in-depth explanation of Puzzle File Preparation may be found in the Advanced Procedures section. Page 11 'SAVE' Menu Option. Press <DOWN> three times and <ENTER>. The 'SAVE' module will copy our current status onto the disk where it will remain until we wish to reactivate it. We are now free to continue to solve for the copy which is still in the computer. It is important to note however, that there can be only ONE CURRENT STATUS file on the diskette at a time. Thus the contents of any existing status file will be overwritten with each new 'SAVE'. As you may have already noticed, XYSolve will give you the chance to reconsider your 'SAVE' request if it detects the presence of a previous status file. Should you decide to abort the attempt by pressing <ESCape>, XYSolve will reactivate your present puzzle as if nothing happened. Just for fun, let's load the puzzle from the "CURRENT.PZL" file. Use your <ARROW> keys etc. to gain access to 'START', and select the 'DISK FILE' option. Finally, enter "CURRENT" at the filename prompt to load and activate the Puzzle. 'HELP' Menu Option. Press <UP> twice and <ENTER> to select the 'MENU HELP' module. As you have learned, XYSolve's menu system is multi- leveled. You move from one level to another by way of the <ARROW>, <ENTER>, and <ESCape> keys. All the menu 'HELP' screens have similar diagrams to assist you in determining how to get from place to place. Press <SPACE> to return to the 'MAIN MENU'. This just about completes the "Grand Tour". There's still lots to see and do within XYSolve, but for now, you have a good idea of how to: Move around within the menus and modules. Work the various displays. EXIT back out. One last thing, to 'END' using XYSolve, you merely have to press <UP> and <ENTER>. That's quite a bit for one session, Let's take a break! Page 12 XYSolve Functional Modules ========================== XYSolve functional modules are designed to provide a rich educational environment. Each function has been provided with as much interactive flexibility as is suitable for its form. The following individual explanations cover some of the more important aspects of each module such as the type of input expected and possible error messages. In addition, several of the advanced modules are covered in more detail in other parts of this manual. ================================================================ Functional Module: 2D Point. Formula: Y=AX+B Description: Plots a point on a two dimensional plane. Discussion: The Two Dimensional Point module accepts one positional and two parameter values which are used to define a position on a two dimensional plane. ** Warning! ** Messages: None. ================================================================ Functional Module: Line. Formula: AX+BY+C=0 Description: Plots a Line with desired rotation on a two dimensional plane. Discussion: The Line module accepts one positional and three parameter values which define the horizontal and vertical location of points along a line segment. The horizontal limits of the line are defined by the magnitude of the positional value. ** Warning! ** Messages: A warning message will be displayed if an attempt is made to set the "B" variable to zero. This would lead to division by zero. Page 13 ================================================================ Functional Module: Circle. Formula: (X-A)^2 + (Y-B)^2 = R^2 Description: Plots a Circle on a two dimensional plane. Discussion: The circle module accepts three parameter values which define the position of the center of a circle on the plane, and it's radius. ** Warning! ** Messages: A warning message will be displayed if an attempt is made to set the "R" variable to a negative value. This would represent a negative radius length which cannot exist. ================================================================ Functional Module: Parabola. Formula: Y=AX^2 + DX+F Description: Plots a Parabola on a two dimensional plane. Discussion: The parabola module accepts three parameter values which define the position of the parabola on the plane. ** Warning! ** Messages: None. ================================================================ Functional Module: Ellipse. Formula: (X^2/A^2)+(Y^2/B^2)=1 Description: Plot a Vertical or Horizontal Ellipse. Discussion: The Ellipse module accepts two parameter values which define the form of an ellipse at the origin. ** Warning! ** Messages: A warning message will be displayed if an attempt is made to set the "A" variable to a value less than or equal to zero. A warning message will be displayed if an attempt is made to set the "B" variable to a value less than zero. Both of these errors represent an invalid length specification. Page 14 ================================================================ Functional Module: Sine. Formula: Y=A*Sin(BX+C) Description: Plot the Sine periodic function. Discussion: The Sine module accepts three parameter values which define the form of the function on a two dimensional plane. ** Warning! ** Messages: None. ================================================================ Functional Module: Cosine. Formula: Y=A*Cos(BX+C) Description: Plot the Cosine periodic function. Discussion: The Cosine module accepts three parameter values which define the form of the function on a two dimensional plane. ** Warning! ** Messages: None. ================================================================ Functional Module: Tangent Formula: Y=A*Tan(BX+C) Description: Plot the Tangent periodic function. Discussion: The Tangent module accepts three parameter values which define the form of the function on a two dimensional plane. ** Warning! ** Messages: None. Page 15 ================================================================ Functional Module: Parametric #1. Formula: Y=A*Sin(B*PI*T) (+) X=C*Cos(D*PI*T) Description: Plot a Parametric of Sine and Cosine functions. Discussion: The first Parametric module accepts four parameter values which define the forms of three functions. The first two forms are partials with the third being a combined display. Parameter value sets are provided to allow individual manipulation of each partial. ** Warning! ** Messages: None. ================================================================ Functional Module: Parametric #2. Formula: Y=A*Sin((T+PI)/B) (+) X=C*Sin(DT) Description: Plot a Parametric of Sine functions. Discussion: The second Parametric module accepts four parameter values which define the forms of three functions. The first two forms are partials with the third being a combined display. Parameter value sets are provided to allow individual manipulation of each partial. ** Warning! ** Messages: A warning message will be displayed if an attempt is made to set the "B" variable to zero. This would lead to division by zero which is undefined. Page 16 ================================================================ Functional Module: Composite #1. Formula: Y=AX/B (+) Y=-C*Cos(DX) Description: Plot the Composite of a line and a Cosine function. Discussion: The first Composite module accepts four parameter values which define the forms of three functions. The first two forms are partials with the third being a combined display. Parameter value sets are provided to allow individual manipulation of each partial. ** Warning! ** Messages: A warning message will be displayed if an attempt is made to set the "B" variable to zero. This would lead to division by zero which is undefined. ================================================================ Functional Module: Composite #2. Formula: Y=A*Cos(BX) (+) Y=C*Sin(DX) Description: Plot the Composite of Cosine and Sine functions. Discussion: The second Composite module accepts four parameter values which define the forms of three functions. The first two forms are partials with the third being a combined display. Parameter value sets are provided to allow individual manipulation of each partial. ** Warning! ** Messages: None. Page 17 XYSolve Advanced Procedures =========================== XYSolve implements advanced procedures such as Puzzle File Preparation, and Parametric and Composite routines. Preparing Puzzle Files: The format required by the Puzzle File system is straightforward in that there is only three types of information "required" to complete a file; a TOLERANCE value, Function NAME, and NUMERIC VALUES for any associated variables. In addition, an optional non-displayed COMMENT may be added to each line in the file to explain it's usage. In establishing "standard" limits for variables, XYSolve can augment the normal "exact value" solution criteria by adding the pre-defined tolerance value. A single tolerance is active for each solution set, and is saved with the puzzle on diskette. As you become more familiar with a solution set, you may choose to tighten-up the tolerance value, or even eliminate it altogether. TOLERANCE VALUE Recommendations: "0.0"-"0.3" Advanced level users or simple functions. "0.4"-"0.6" Intermediate level users and functions. "0.7"-"0.9" Novice level users or advanced functions. The syntax requirements for the Tolerance value and all other numerics within a puzzle is the same. Each value must occupy it's own line, contain a prefix of "#", and be followed by at least one space! NUMERIC Examples: #0.1 comment recommended. #2.3 #45 #-0.6 #-7.8 #-90 Page 18 Sequences of FUNCTIONS with their associated variables follow the tolerance value in the Puzzle file. There is no theoretical limit to the number of functions (pieces) that can make up an individual puzzle; however, there is a practical limit to the complexity of a display. Too many pieces, poorly placed, can make a puzzle overly difficult to solve. A full listing of available functions and associated variables can be found in the "Functional Modules" section of this manual. Puzzle function sequences may be developed by documenting your keypresses as you go through the steps to manually accomplish your desired goal. Once the steps have been listed, you merely prepare a TEXT file containing your values. Don't be overly concerned with this procedure. I'm sure you will find it significantly easier than writing a letter with a common word processor. If an error is found when you try out the puzzle, merely re-edit your TEXT file and try again.. The required syntax for puzzle functions is even simpler then that required for numerics. Each VALID function name must occupy it's own line, and like the numeric, be followed by at least one space! FUNCTION Examples: LINE comment recommended. Parabola circle SiNe (Upper/Lower case okay.) COMMENTS are highly recommended! An optional comment can be added to each line in your file. As your work becomes more sophisticated (lengthy), remembering exactly where you are in a sequence at any particular moment may become more and more challenging. The liberal use of comments can do much to alleviate this problem. Please note however, that comments, if used, may extend only to the end of the current line. Page 19 PUZZLE Filenames: XYSolve is designed to assist you in managing large numbers of Puzzle files. It does this through a unique file extension technique. All Puzzle files are assigned extensions of ".PZL". If you are preparing your Puzzle files with a general purpose text editor, you will have to explicitly assign this extension. If however, you are using the system editor XY-Edit, it will assign the extension for you automatically. ** WARNING! ** Puzzle files that are mis-labeled will not be able to be selected for use by XYSolve. You may obtain further examples of function and numeric variable usage by printing out the practice Puzzle files that have been provided on your XYSolve master diskette. In addition, the required syntax is diagrammed in the Appendices. Page 20 Parametric/Composite Procedures. The 'PARAMETRIC' and 'COMPOSITE' functional areas are advanced modules designed to display the effects of parameter changes on "systems" of related equations. Each group solves two individual equations simultaneously. In the 'PARAMETRIC' modules, the equations are related through a common parameter such as "T". Changes due to this shared parameter will be reflected in the contribution each formula makes to the form of the combined display. In the 'COMPOSITE' module, the individual equations are related by their solutions for "Y" at identical values of "X". For example, if your solution at a particular "X" results in a value of "5" for "Y" when using equation #1, and "-5" using equation #2, the resulting combination plot could have a value of "0". The plot for equation #1 would place a point at location (X,5), and equation #2 at (X,-5). The combined display would have its point placed at (X,0). A second major difference between Composites and Parametrics is that the Parametrics are solved using perpendicular axis, i.e. "Y=f(T)" for one equation and "X=g(T)" for the other. Composite equations however, are usually solved along a common axis, say "(gof)(X)=g(f(X))". Composite equations are not restricted to any arbitrary type. The equation for a line might be combined with one for a curve, or two curves might be combined, etc. XYSolve provides examples of each of these standard types. Interesting examples of both Parametrics and Composites are provided in the Appendices. Page 21 Using the PRINTER: XYSolve has built-in support for both GRAPHIC and NON- GRAPHIC printers. All you have to do to print out a plot is: 1. Insure that your desired plot is on the screen. 2. Enter the PLOT OPTIONS MENU and proceed to the PRINTER selection. 3. <ENTER> the PRINTER module. 4. Select an EPSON compatible printing mode. Your printer's manual will help in selecting the best mode for your particular system.. 5. Follow the directions and insure your printer is ON LINE and ready with paper etc., then press <SPACE>. That's all there is to it! The XYSolve Appendices ====================== Collected here for your use are: 1. A Glossary of terms used in this manual. 2. A full listing of Error Messages, their causes and recommended corrections. 3. A comprehensive set of Demonstration Values for each function module. 4. A listing of Puzzle File Syntax with examples. 5. A directory of Practice Puzzle files. 6. A topic Index. Page I-1 The XYSolve Glossary ==================== A ASCII: A system which allows the representation of text without the addition of "special" word processing codes. XYSolve can use Puzzle files prepared with a word processor operating in ASCII Text mode. Asymptotes: A straight line (X=0 or Y=0 axis) which may be approached but never touched by a curve. Axis: The horizontal X and vertical Y base lines on your display. B Backup: Duplication of data or a program to allow recovery following loss or damage to the original. Boot/Reset: To start an operating system on a computer. Once the operating system is running, you can execute programs like XYSolve. C Command: An instruction given to the computer. Comment window: The area at the bottom of a common XYSolve display where helpful notes and error messages are displayed. Composite curve: The combining of two related functions into a third function display. In XYSolve, the original functions are called partials of the composite. Cursor: A movable set of horizontal and vertical axis lines which can be used to indicate points of interest on a plot. D Default: The response that XYSolve will assume unless a change is specified by the user. DOS: Your Disk Operating System is a collection of procedures which enables your computer to execute programs like XYSolve. Page I-2 E ERROR message: A message displayed on the screen which informs the user of an anomalous condition. Consult the ERROR message listing in the Appendices for message specific information. F File: A collection of related information stored on your disk. A file can contain either programs or data. Puzzle files, and the INSTALL program are examples of disk files used by XYSolve. Foci: A point whose position can define the form of an ellipse, hyperbola, or parabola. It appears as the source or destination of rays. Function: A correspondence that assigns to each element x of X a unique element y of Y. NOTE: The term "Function" is used to describe a particular module within the XYSolve system, regardless of whether it meets this rigid definition or not. That is to say, the circle is a functional module in XYSolve. Functional module: See Function. Function window: The area at the bottom of a common XYSolve display that lists menu selections, active keys, or input requirements. H HELP screen: A source of information about functions or tasks available to the user at a given point in the program. Hercules: A high resolution graphics monochrome display standard. Contact Insight Advantage for Hercules versions of these programs. Install: An auxiliary program designed to adapt your computers operating environment to the needs of XYSolve. L Lissajous: A fundamental pattern named after the 19th-century French scientist. Useful in displaying relationships between periodic functions. A simple example is the comparison of the frequency ratio of a wave on the X-axis to one on the Y-axis. Page I-3 M Magnetic media: The fragile coating on a diskette which actually holds your data. The openings on a diskette allow access to the media for your computer. NEVER TOUCH MAGNETIC MEDIA! Master Diskette: The original XYSolve program diskette which was provided by the manufacturer. This diskette should never be used to actually run XYSolve. Use a backup copy. Menu: A list of functions or tasks available to the user at a given point in the program. The user selects the function desired from the menu. Monochrome: A single color display made up of bright text or graphics against a dark background. Portions of a graphics display can be inverted by XYSolve using the ENHANCE Plot Option. O Origin: An arbitrary point separating the real number system into positive and negative values with a one-to-one correspondence. Overlay: A procedure which visually places one display over another. The contents of the individual displays are combined. P Parameter values: Values which either totally define a positional value directly (A=X or A=Y) or which adjust its final computed value (A*X or A*Y.) Parametric value: A value which is common between two or more expressions. Altering the parametric value would result in changing all related expressions. Positional values: A combination of X and Y values which represent a position on the two dimensional plane. For example, the set (X,Y) equal to (5,-3), would define a position five units to the right and three units down from the origin. Page I-4 Printer: A device for producing a permanent copy of an XYSolve graphic display. The quality of the printout is dependent upon the graphics capabilities of the printer. Prompt: A symbol that appears on the screen indicating the need for a typed response from the user. R Read: Moving stored data or a program from a disk file into the computer for processing. Retrieve: Recovering a graphic display from a special part of memory where it was "saved" by XYSolve. S Save: Placing a graphic display into a special part of memory where it will remain unchanged until "retrieved" by XYSolve. Scale factor: A level of adjustment applied to data or a display to insure conformity to system limits. System limits: A set of maximum and minimum values that define the capabilities of a system. XYSolve has system numeric limits of +/-99 with one decimal place accuracy. W Waiting point: A position or step within XYSolve where the program will pause waiting for a response from the user. Word Processor: A program which manipulates text and possibly graphics in the preparation of documents. XYSolve can use Puzzle files prepared with a word processor operating in ASCII Text mode. Write: Moving stored data or a program from the computer into a disk file after processing. Page II-1 XYSolve ERROR MESSAGES ====================== This appendix is an alphabetic compilation of all the error messages used within XYSolve. Included with each message is an expanded explanation of what caused the error, as well as any possible remedies. Fatal error: Hercules compatible graphics required to run XYSolve. XYSolve has not found a compatible graphics capability within your system. Contact Insight Advantage for IBM-CGA versions of these programs. Fatal error: Color Graphics system required to run XYSolve. XYSolve has not found a IBM-CGA compatible graphics capability within your system. Contact Insight Advantage for Hercules versions of these programs. File EMPTY! . . . Select another File. The Puzzle file that was selected that did not contain any data. Select another file. File NOT Found... A Puzzle file was not found when execution was attempted. This error resets automatically. Re-enter a valid filename. Invalid SETUP file DATA..defaults active. The file "SETSOLVE.DTA" is contaminated. Re-copy from the Master Diskette. Incorrect_SEQUENCE! . . . Select another file. A Tolerance value was not found at the beginning of the Puzzle file. Edit the Puzzle file, or select another file. Incorrect SETUP file VERSION..defaults active. The file "SETSOLVE.DTA" is from another version of XYSolve. A Hercules/CGA/EGA version mix has occurred. Re-copy from the Master Diskette. NUMERIC quantity contaminated. Keyboard input value failed numeric test. Select another key. Required DATA FILE NOT FOUND..program terminating. The file "MENUSOLV.DTA" was not found. Re-copy from the Master Diskette. Page II-2 Save ABORTED . . . A manual ESCape from saving the "Current Status" was detected. Select "START" There must be a Puzzle activated before attempting to solve for it's pieces. SETUP CONVERSION failed...color default is active. The Color value in the Setup file failed a validity test. Re-copy "SETSOLV.DTA" from the Master Diskette. SETUP file NOT FOUND..defaults active. The file "SETSOLV.DTA" was not found. Re-copy from the Master Diskette. SORRY! file was found EMPTY.. A selected Puzzle file had no values in it. Edit your Puzzle file. SORRY! . . . No <Functions> of that type are present. An attempt to solve for a function that was not part of the currently active puzzle was detected. Analyze the display and select another function. SORRY! . . . Nothing to report, select "START" first. An attempt to obtain a puzzle solution report without having solved for a puzzle was detected. Activate a puzzle. SORRY! . . . There are no <Function> present. An attempt to solve for a function that was not part of the currently active puzzle was detected. Analyze the display and select another function. SORRY!... Printer NOT READY. XYSolve has determined that your printer is not ready to plot. Possible causes include being out of paper, not being properly selected ON-LINE, or an equipment failure. Check your printer. Unexpected END OF DATA..program terminating. The file "MENUSOLV.DTA" is contaminated. Re-copy from the Master Diskette. Page II-3 WARNING! . . . Invalid FUNCTION. A function not supported by this version of XYSolve was detected in your Puzzle File. Edit the Puzzle File or select another file. WARNING!..."?" must not be =< "0". WARNING!..."?" must not be < "0". WARNING!..."?" must not be = "0". An attempt was made to set a variable value to less than or equal to zero. This can cause several problems such as: illogical negative lengths, square roots of negative numbers, division by zero, etc. Select an appropriate value. WARNING! . . . No current status to save. A puzzle must be active before a status can be saved. WARNING! "Save-Status" file exists, Replace? (Y/N) This warning merely informs you that a previously saved "Status" file is about to be overwritten. Page III-1 XYSolve DEMONSTRATION VALUES ============================ FUNCTION VALUES EFFECT ---------------------------------------------------------------- GENERAL MENU LEVEL ********************************* 2D POINT 1, 5, 0 STANDARD 1, 0, 5 X=0 AXIS 0, 5, 0 Y=0 AXIS 1, 10, 0 MAXIMUM + OFFSET 1,-10, 0 MAXIMUM - OFFSET LINES -2, 3, 1, 4 + SLOPE/- OFFSET -2, 3, 1,-4 + SLOPE/+ OFFSET 0, 3, 1, 1 0 SLOPE/- OFFSET QUADRATIC-GEOMETRIC MENU LEVEL ********************************* CIRCLES -5, 0, 4 Y=0 AXIS -5,-5, 4 3rd QUADRANT 0, 0, 1 ORIGIN PARABOLAS 2,-5, 0 PHASE SHIFT -1, 0, 0 POLARITY REVERSAL 0.2, 0, 0 WIDE 7, 0,-30 NEGATIVE OFFSET ELLIPSES 4, 8 MAJOR AXIS VERTICAL 8, 4 MAJOR AXIS HORIZONTAL 5, 5 TRANSITION INTO CIRCLE 3, 2 FOCI=2.2 TRIGONOMETRIC MENU LEVEL *************************************** SINE 3, 1, 0 STANDARD WAVE 9, 1, 0 AMPLITUDE CHANGE 5, 2, 0 PERIOD CHANGE 7, 1, 1 57.3 DEG PHASE SHIFT COSINE 3, 1, 0 STANDARD WAVE 9, 1, 0 AMPLITUDE CHANGE 5, 2, 0 PERIOD CHANGE 7, 1,-1.6 91.7 DEG PHASE SHIFT TANGENT 3, 1, 0 STANDARD WAVE 5, 1, 0 AMPLITUDE CHANGE 5, 5, 0 PERIOD CHANGE 5, 1,-1 -57.3 DEG PHASE SHIFT Page III-2 SPECIAL MENU LEVEL ********************************************* PARAMETRIC #1 8,1.6, 8,1.1 LISSAJOUS 8,2.4, 8,2.4 1:1 RATIO=CIRCLE 8, 2, 8, 4 1:2 FREQUENCY RATIO 4.5, 1, 6, 5 1:5 FREQUENCY RATIO 4.5, 5, 6, 3 5:3 FREQUENCY RATIO PARAMETRIC #2 9, 3, 1, 1 120 DEG PHASE SHIFT -9,1.6, 3, 3 112 DEG PHASE SHIFT 9, 1, 6, 3 LISSAJOUS VARIATION COMPOSITE #1 -3, 2, 3, 1 SLOPE INVERSION 1, 2, 2, 6 RAMPING COSINE 0, 2, 6, 1 ZERO SLOPE COMPOSITE #2 5, 2, 4, 3 COMPLEX WAVEFORM 4, 1, 2, 3 COMPLEX WAVEFORM 5, 2, 4, 1 COMPLEX WAVEFORM Page IV-1 XYSolve PUZZLE Syntax ===================== EXAMPLE FILENAME: C-CIRCLE.PZL PUZZLE FILE SYNTAX: <A><B><SPACE><C> <D><SPACE><E> A = '#' Numeric (TOLERANCE or Variable) prefix. B = Numeric value. C = Optional step comment. D = Function NAME. E = Optional step comment. EXAMPLE Statements: #0.8 Novice level Tolerance assigned. Circle First Concentric circle. #-1.0 Vertical offset of center. EXAMPLE Puzzle: Plots four forms. #0.2 Use Advanced-level tolerances. {Filename-FIRST.PZL} LiNe Plot a line with a negative polarity slope. #1.3 "A" value-Vertical magnitude multiplier. #4.0 "X" value-Horizontal extent of the line. #1.0 "B" value-Slope polarity variable. #0.0 "C" value-No vertical offset defined. Circle Plot a Circle offset from the origin. #-5.0 "X" value-Horizontal offset of the center of the circle. #0.0 "Y" value-Vertical offset of the center. #4.0 "R" value-Radius of the circle. 2D-POINT Plot a first quadrant Point. #1.0 "A" value-Vertical magnitude multiplier. #5.0 "X" value-Horizontal offset. #1.0 "B" value-Vertical offset. PARA#1 Plot a Parametric with the following variable values: #8.0 "A" value-Vartical magnitude of Partial #1. #2.0 "B" value-Frequency of Partial #1 set to two Hertz. #8.0 "C" value-Same vertical magnitude as Partial #1. #4.0 "D" value-Frequency of Partial #2 is double that of Partial #1. SINE Plot a Sine Wave with the following variable values: #9.0 "A" value-Vertical magnitude multiplier. #1.0 "B" value-Frequency of wave is set to one Hertz. #0.0 "C" value-There is no phase shift defined. Page V-1 XYSolve Practice Puzzle Files ============================= Files mentioned in the text: TWO-D.PZL FIRST.PZL CURRENT.PZL Specific function files: POINT.PZL LINE.PZL CIRCLE.PZL ELLIPSE.PZL PARABOLA.PZL SINE.PZL COSINE.PZL TANGENT.PZL PARA1.PZL PARA2.PZL COMP1.PZL COMP2.PZL Combined Function files: FIRST.PZL TWOLINE.PZL Page VI-1 XYSolve Index ============= 2D Point 12 Advanced Procedures 17 Backing Up Your Diskettes 2 Basic Menu Structure 1 Before We Start 2 Caring For Your Diskettes 2 Circle 13 Composite #1 16 Composite #2 16 Composite Procedures 20 Conventions 3 Cosine 14 CURSOR Plot Option 8 Demonstration Values III-1 Ellipse 13 ENHANCE Plot Option 9 ERROR Messages II-1 EXITING Plot Options 9 First Steps 3 First Waiting Position 8 Functional Modules 12 Glossary I-1 Grand Tour 4 HELP Plot Option 9 HELP Menu Option 11 Important Keys 4 Keyboard Puzzle Files 10 Line 12 Puzzle Files, Preparing 17 Puzzle Files, Syntax IV-1 Puzzle Filenames 19 Practice Puzzle Files V-1 Main Plot Display 7 Page VI-2 Numeric Value Entry 7 Parabola 13 Parametric #1 15 Parametric #2 15 Parametric Procedures 20 PLOT OPTIONS Menu 8 PRINTER Plot Option 9 Printer, Using The 21 Program Disk, XYSolve 2 REPORT Menu Option 10 Sample Session 2 SAVE Menu Option 11 Second Waiting Position 10 Sine 14 START Menu Option 6 Tangent 14 Tolerance Value Recommendations 17 Dated: XY-Educational System ORDER FORM ================================ All XY-Educational System products may be obtained directly from Insight Advantage. Please enclose check or money order for the CORRECT AMOUNT with your order. Insight Advantage will pay shipping and handling costs within the United States (foreign customers: Please contact Insight Advantage.) Insight Advantage Ship to: _________________________________ 4509 Yellowleaf Dr. _________________________________ Fort Worth, TX 76133 _________________________________ _________________________________ ( ) Copies of XYSee @ $30.00 each: $ ________ ( ) Copies of XYSolve @ $20.00 each: $ ________ * ( ) Copies of XY-Edit @ $15.00 each: $ ________ Subtotal: $ ________ TX residents add 7.00% sales tax: $ ________ TOTAL: $ ________ XYSee and XYSolve are available in IBM-CGA (color) and Hercules (monochrome) compatible graphics formats. The format I am ordering is: IBM-CGA _____ Hercules _____ * Note: XY-Edit is included with orders for XYSee and XYSolve. Please use this form for additional requirements. We attempt to ship all orders within 48 business hours of our receipt. IBM and Hercules are respectively trademarks of: International Business Machines. Hercules Computer Technology. Dated: XY-Educational System TROUBLE REPORT ==================================== Although significant care has been expended to insure the reliability of this program, we would like to know if you experience any problems. Thank-you for your help! Your name:(Please print) Company/Organization: Telephone:(AC & Ext.) PROGRAM: (Example: XYSee, Install, Access-System) NATURE OF PROBLEM: (Example: Scrambled display, Program halted.) MODULE BEING RUN: (Example: Enhance option of Sine module.) ALL INPUT VALUES USED: (Example: A=3, B=2, C=9.0) LAST FEW KEYPRESSES: (Example: 9.0, <ENTER>.) DISPLAYED ERROR CODES: (Example: Error F0, PC=6D3F, Traceback 93FD.) {If display scrambles and program seems to have stopped, place printer on-line and press <SHIFT> and <Prt Sc> simultaneously for printout of ERROR codes prior to re-booting system.} ENVIRONMENT: (Example: Power fluctuation just before error.) ADDITIONAL COMMENTS: Return to: Insight Advantage 4509 YellowLeaf Dr. Fort Worth, TX 76133 XYSolve Mathematic Functions in Graphic Form Copyright (C) 1988, Dean M. Thompson All Rights Reserved.