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======================================================================= ULTIMATE CALCULATOR (UCALC) 3.2 Copyright (C) 1992-1996 by Daniel Corbier All Rights Reserved. ======================================================================= CONTENTS -------- 1. Introduction 2. UCALC Features 3. Getting Started 3.1 Installation 3.2 Single Calculations at the DOS Prompt 3.3 Interactive Calculations 3.4 Popping UCALC up with a Hot Key 3.4.1 Memory 3.4.2 Swap file 3.4.3 Hot Key 3.4.4 Extra Memory 3.4.5 Text Buffer 3.4.6 Resizing and Moving the Window 4. UCALC Prompt 5. Table of Symbols 6. Order of Precedence 7. Flexible Syntax 8. GRAPHING 8.1 How to Plot 8.1.1 Cartesian 8.1.2 Parametric 8.1.3 Polar 8.1.4 3D Surface 8.1.5 Plotting data from another file 8.1.6 Line Segment 8.1.7 Rectangle 8.1.8 Filling an Area 8.2 Graph Menu 8.2.1 [F2] Reset 8.2.2 [F3] Fill 8.2.3 [F4] Color 8.2.4 [F5] Grid/Axis 8.2.5 [F6] Dot/Connect 8.2.6 [F7] Trace 8.2.7 [F8] Mono 8.2.8 [F9] Zoom In 8.2.9 [F10] Zoom Out 8.3 Special Graphing Commands 8.3.1 AUTOCLR (automatic coloring) 8.3.2 AXIS (sets axis line color) 8.3.3 CONNECT (toggle for dot/connect) 8.3.4 GCOLOR (background color in graphic mode) 8.3.5 GRID (sets grid color & pattern) 8.3.6 MODE (selects graphic card) 8.3.7 MONO (turns colors off) 8.3.8 PLOTF (sends the graph coordinates to a file) 8.3.9 PPLOT (edits previously plotted equations) 8.3.10 PREC (sets graph precision) 8.3.11 WINDOW (sets screen coordinate system) 8.3.12 ZOOM (changes zoom factor) 8.4 Moving the Crosshair 8.5 Adding Text to the Screen 8.6 Printing a Graphic Screen 9. Summation 10. Numerical Integration 11. Solving Equations 12. Numerical Notations 13. Implicit Multiplication 14. Assigning Variables 15. Assigning Functions 16. Miscellaneous Commands 16.1 LOAD 16.2 WRITE 16.3 SHELL 16.4 COLOR 16.5 REDIRECT 17. UCALC.DEF 18. Technical Notes 19. Registration 20. Shareware Author & User Case Study 21. My Address 22. Distribution 23. Acknowledgments 1. Introduction ============ UCALC is a graphing scientific calculator which can be used for simple arithmetic, or intricate scientific calculations. It supports many built-in functions, operators, numerical notations, and modes. It also supports user-defined functions and variables. It can evaluate expressions, solve equations, plot equations, perform numerical integrations, do summations, and more. UCALC can optionally be loaded as a TSR taking less than 6K of main memory. Expressions such as the following are accepted: 63 - 5 + 4.75 (5.9-abs(2.8/5-3))^2 + sin( 3-(pi+3/4)*myfunction(a,b) ) solve 3*x^2+2*x-5 = 27 #b101010 and (#b10101 or #h1CC) * 2^5 plot sin(x)*x^2/10 plot3d sin(x)*z 2. UCALC Features ============== - MATH EXPRESSION EVALUATOR for simple or intricate operations - Arithmetic, bitwise, and relational operators - Decimal, hexadecimal, binary and octal notations - Trig, hyperbolic, and many other common scientific functions - Supports user defined variables & functions with multiple arguments - Radian, degree, and gradient modes for trig functions - High precision: 18 significant digits. +/-3.4E-4932 to +/-1.2E+4932 - Equation solver, summation & sumtable, numerical integration - POP UP WITH A HOT KEY - Window can be resized or moved - Hot key combination can be chosen - Less than 6K main memory using EMS or file - Main memory, EMS, or file, can be chosen for swapping - PASTE command - TSR can be unloaded from memory - FAST EQUATION PLOTTER - Interactive menu with ZOOM, TRACE, COLOR, FILL, GRID, etc... - Support for up to 16 supper-imposed multi-color user graphs - Cartesian (rectangular), polar, and parametric user graphs - 3D surface plotting with hidden line removal - Data from another file can be plotted - Adjustable precision & screen coordinate system - Text can be typed anywhere on the graph screen - VGA, EGA, MCGA, CGA, and Hercules modes (auto detection or select) - Coordinates can be saved to a file - Mouse support - Online help with F1 - Line editor with expression recall - Expressions can be entered at the DOS command line - Support for DOS redirection - Adjustable FIX & DIG notation - LOAD, WRITE, PRINT, SHELL, COLOR, and more 3. Getting Started =============== 3.1 Installation ------------ There is no elaborate procedure for installing UCALC. Simply type UCALC to run the program. To customize UCALC, simply create or modify the UCALC.DEF and UCALC.TSR text files (explained further down). UCALC.EXE, UCALC.DEF, and UCALC.TSR can be placed in a directory defined in the PATH statement of the AUTOEXEC.BAT file (such as the DOS or UTILS directory), for easier access. 3.2 Single Calculations at the DOS Prompt ------------------------------------- There are several ways of running the Ultimate Calculator. The first way is to enter an expression at the DOS command line as follows: UCALC 5+4*8/2 [enter] At the DOS command line, UCALC will accept the following options: /? Help /TSR Loads UCALC as a memory resident program /NODEF Ignores UCALC.DEF UCALC also supports redirection from the DOS command line. If an expression is present at the command line, it is evaluated, and control returns to DOS. If redirection is performed, control also returns to DOS when finished. Otherwise, it goes to the 'ucalc> ' prompt, where you may enter many expressions and quit with [Esc]. If a symbol in the expression is in conflict with DOS, then enclose the expression in quotes. Examples: --------- UCALC 3+6-2 UCALC "5^4 | 5*8" UCALC /NODEF 3+7 UCALC < abc.cal > output.uc 3.3 Interactive Calculations ------------------------ UCALC also provides a line editor for performing multiple calculations. This environment allows you to assign values to variables, and define functions as you go along. To run UCALC in that mode, simply type "UCALC" at the DOS command line without any expression as follows: UCALC [enter] When you are in this mode, you can press [F1] any time for help, and [Esc] to quit the program. See EXAMPLES.DOC to get more ideas on how to use UCALC. For a graphing demo, enter PLOTDEMO from the DOS prompt. 3.4 Popping UCALC up with a Hot Key ------------------------------- A third way of running UCALC is to first load it as a TSR file. From then on, UCALC can be called instantly at any time with a hot key, without the user having to go to the DOS prompt. To load UCALC as a TSR program, simply type this at the DOS prompt: UCALC /TSR Or, include that line in your AUTOEXEC.BAT file. Once UCALC is memory resident, it can be invoked at any time with a hot key such as "ALT U". Before running UCALC as a TSR for the first time, check the parameters in UCALC.TSR to make sure they match your needs. The presence of a UCALC.TSR file is optional. In the absence of this file, the parameters are set as follows: MEMORY=E/F SWAPFILE=C:\UCALC$.$$$ HOTKEY=ALT U EXTRAMEM=11000 TEXTBUFF=15 The following parameters can be set in UCALC.TSR: 3.4.1 Memory ------ The following line sets how UCALC is loaded into memory as a TSR: MEMORY=<option> where <option> is one of the following: EMS If your computer has EMS memory, then this is the best option. It takes less then 6K of main memory, and pops up quickly when invoked. MAIN If this option is chosen, UCALC will pop up quickly when invoked, but it will also take a lot of bytes from main memory. FILE This option takes up less then 6K of main memory, but instead of swapping to EMS or using up main memory, it swaps to a file. With this option, it generally takes more time for UCALC to pop up when invoked. When using this option, make sure that there is at least 350Kb free on the hard drive. Do not use this option on a floppy drive, as it would be painfully slow, and it would crash if the disk were removed when popping up. If the FILE option is chosen, a file must be defined with "SWAPFILE=". E/F If the "MEMORY=" line is omitted, or if E/F is entered, then UCALC will use EMS if detected or it will swap to a file if there's no EMS. 3.4.2 Swap file --------- If a line with "MEMORY=FILE" is used, then a swap file must be defined as follows: SWAPFILE=<filename> The file name must include the drive letter, and path; for instance "SWAPFILE=C:\UCALC$.$$$". Choose a name that is unique, and unlikely to be used for something else. To protect the user from accidentally erasing this file, it is marked with a hidden attribute. The swapfile parameter is ignored if UCALC loads into EMS or main memory. 3.4.3 Hot Key ------- By default UCALC is popped up by pressing <ALT U>. This can however be changed by placing a line in UCALC.TSR with the following format: HOTKEY=<CTRL and/or ALT and/or SHIFT> <character> The following lines are examples of acceptable hot keys: HOTKEY=ALT 1 HOTKEY=CTRL V HOTKEY=CTRL ALT Z 3.4.4 Extra Memory ------------ When UCALC is loaded from DOS without the TSR option, memory is allocated dynamically. This means that as new variables and functions are being defined, etc... additional main memory is being taken. However, when UCALC is loaded as a TSR, a fixed maximum amount of memory is allocated (which is generally much less than what is available when running it as a non-TSR). This amount can be raised or lowered with the following line: EXTRAMEM=<number> <number> should be greater than 8000. Anything less may cause UCALC to run out of memory even for simple calculations. 3.4.5 Text Buffer ----------- This determines how many lines of text can be recalled. When run from DOS, 100 lines can be recalled. To conserve memory in TSR mode, the number of lines that can be recalled should be reduced. This is done by adding this line. TEXTBUFF=<number> Where <number> is between 2 and 100. 3.4.6 Resizing and Moving the Window ------------------------------ <Ctrl> Up, Down, Left, or Right arrow is used for moving the window. <Alt> Up, Down, Left, or Right changes the window size. NOTE: When resizing the window, do not use the arrows on the numeric keypad, since <Alt> <keypad number> is used for returning ASCII characters. Use the other arrows instead. 4. UCALC Prompt ============ At the 'ucalc> ' prompt, expressions to be evaluated can be entered, functions and variables can be defined, and the following commands and function keys can be used: [F1] Help (same as HELP or ?) [F2] Lists variables (same as LIST) [F3] Displays UCALC.DEF (same as LIST DEF) [F4] DOS shell (same as SHELL) [F5] Lists user functions (same as LISTF) [Esc] Quit (same as QUIT, see also EXIT) AUTOCLR [nn] Sets the number of colors used in graphing. AXIS color Changes the color of the graphic axis lines. CLOSE Closes the file opened with the WRITE command. CLS Clears the screen. COLOR [foregr] [,backg] Changes the text screen colors. CONNECT {ON|OFF} Toggles connected/dotted graphs. DIG nn Changes the total number of digits displayed. EXIT Exits to DOS (or pops down if in TSR mode). EXIT TSR Exits, and de-activates UCALC from memory. FIX nn Changes number of decimal digits displayed. GCOLOR color Changes graph screen background color. GRID color [, pattern] Sets the grid pattern in the graph mode. HELP Gives online help (same as F1 or ?). INTEG fx,a..b [,n] Numerical integration. LIST Lists user defined variables (same as F2). LISTF Lists user defined functions (same as F5). LIST DEF Displays the contents of UCALC.DEF (F3). LOAD"filename" Loads a file. MODE {DEG|RAD|GRA} Changes mode to degree, radian, or gradient. MODE {HGC|CGA|EGA|VGA|MCGA} Sets the graphic mode for plotting. MODE HBO Toggles the hex, binary, octal answer display. MONO Turns graphic mode colors off. MOUSE [ON|OFF] Toggles mouse support for graphs. PASTE Places result on screen after popping down. PLOT [equation] Plots user equations (2D). PLOT3D [equation] Plots a 3d user equation f(x,z). PPLOT Edits previously plotted equations (2D). PREC nn Changes the precision used in graphing. PRINT [ON|OFF] Prints the current session as you work. PROMPT"yourprompt" Changes or removes the 'ucalc> ' prompt. PROMPTA"yourprompt" Changes or removes the 'Answer: ' prompt. QUIT Exits (same as [Esc]). REDIRECT [ON|OFF] Enables or disables redirection. SHELL Shells to DOS (same as F4). SHELL"command" Executes a DOS command. SOLVE fx [=gx] [,a..b] Solves an equation. SUM fx,a..b [,dx] Summation of function fx ranging from a to b. SUMTABLE fx,a..b [,dx] Summation which displays intermediate results. WINDOW(x1,x2,y1,y2) Changes the screen coordinate system. WRITE"filename" Records your session to a file. ZOOM nn Changes the zoom factor. The variable 'last' contains the value of the previous computation. Variable 'x' is the parameter which should be used with SUM, SUMTABLE, and SOLVE. Selections which appear inside brackets [] are optional. At the 'ucalc> ' prompt, the up (or down) arrow keys can be used to recall previous expressions. Several characters may be keyed in before pressing the up arrow in order to recall an expression starting with those characters. 5. Table of Symbols ================ Symbol Equivalent Description Example ------ ---------- ----------- ------- ( ) Prioritizes an expression 5*(1+1) = 10 ! Factorial 5! = 120 ^ ** Raised to the power of 4 ^ 5 = 1024 * Multiply by 3 * 6 = 18 / Divide by 9 / 2 = 4.5 % MOD Modulo 7 % 4 = 3 + Add 1 + 1 = 2 - Subtract 9 - 5 = 4 > Greater than 9 > 2 = 1 < Less than 7 < 4 = 0 = == Equal test 5 = 4 = 0 >= => Greater or equal 3 >= 3 = 1 <= =< Less or equal $3E <= 9 = 0 <> Not Equal #b10101 <> 20 = 1 NOT Bitwise 'not' not(15) = -16 AND & Bitwise 'and' #b101 and #h1E = 4 OR | Bitwise 'or' 13 or 6 = 15 XOR Bitwise 'exclusive or' 9 xor 3 = 10 EQV Bitwise 'equivalence' 6 eqv 9 = -16 IMP Bitwise 'implication' 1 imp 5 = -1 SIN Sine sin(pi) = 0 COS Cosine cos(pi) = -1 TAN Tangent tan(pi) = 0 ASIN Arcsine asin(1) = 1.570 ACOS Arccosine acos(-1) = 3.141 ATAN ATN Arctangent atan(0) = 0 SINH Hyperbolic sine sinh(3) = 10.01 COSH Hyperbolic cosine cosh(2) = 3.762 TANH Hyperbolic tangent tanh(1) = 0.761 COTH Hyperbolic cotangent coth(1) = 1.318 SECH Hyperbolic secant sech(0) = 1 CSCH Hyperbolic cosecant csch(1) = 0.850 ASINH Hyperbolic arcsine asinh(2) = 1.443 ACOSH Hyperbolic arccosine acosh(9) = 2.887 ATANH Hyperbolic arctangent atanh(.5) = 1.098 ACOTH Hyperbolic arccotangent acoth(7) = 0.143 ASECH Hyperbolic arcsecant asech(.3) = 1.873 ACSCH Hyperbolic arccosecant acsch(2) = 0.481 ABS Absolute value abs(-8) = 8 EXP e to the power of exp(3) = 20.08 RND Random number rnd(1) = .9686 INT Truncate to an integer int(6.8) = 6 CEIL Round upward ceil(6.8) = 7 EXP2 2 to the xth power exp2(3) = 8 EXP10 10 to the xth power exp10(3) = 1000 FACT Factorial fact(5) = 120 LOG2 Log base 2 log2(8) = 3 LOG10 Log base 10 log10(100) = 2 LOG LN Natural log log(16) = 2.77 SGN SIGN Sign of expression sgn(-9) = -1 SQR SQRT Square root sqr(64) = 8 6. Order of Precedence =================== Here is the precedence list from highest to lowest priority: Anything inside parenthesis is performed first ( ) Factorial ! Exponentiation ^ Multiplication, division *, / Modulo MOD Addition, subtraction +, - Relational operators <, >, >=, <=, =, <> AND OR, XOR (exclusive or) EQV (equivalence) IMP (implication) When consecutive operators have the same priority, UCALC evaluates from left to right. This means that an expression such as "a-b-c" is evaluated as "(a-b)-c". 7. Flexible Syntax =============== UCALC is designed to work in a simple and familiar way, and it accommodates itself to several styles, so that users may start being productive the very first time the program is executed. Refer to '5. Table of Symbols' for the alternative notations of several operators and functions. The entries below which are grouped together are equivalent: ucalc> LOAD"myfile" ; The interchangeability of the quote and ucalc> LOAD myfile ; parenthesis, or lack of either is also possible ucalc> LOAD(myfile) ; for MODE, FIX, DIG, AUTOCLR, and PREC. ucalc> SOLVE(x^2=100) ; The outer parenthesis can also be omitted in ucalc> SOLVE x^2=100 ; WINDOW, INTEG, SUM, and SUMTABLE. ucalc> SUMTABLE(x, 1..10) ; Any entry which uses '..' can ucalc> SUMTABLE(x, 1 to 10) ; also use ' TO ' instead. ucalc> SUMTABLE x, 1 to 10 ucalc> PLOT y=x^2 ; 'y=' can be omitted for these types ucalc> PLOT x^2 ; of graphic equations. ucalc> PLOT x=t, y=t^2, -5..5 ; 'x=' and 'y=' can be omitted ucalc> PLOT t, t^2, -5..5 ucalc> PLOT t, t^2, -5 to 5 8. GRAPHING ======== To see a demonstration of some of UCALC's graphing capabilities, enter the following at the DOS prompt: PLOTDEMO Make sure that the PLOTDEMO.BAT, PLOTDEMO, and GRAPH.DAT files are in the current directory. 8.1 How to Plot ----------- Syntax: PLOT equation or PLOT This plots 2D user equations. If an equation is entered on the same line as the PLOT command, then it will be plotted. If PLOT is entered alone at the 'ucalc> ' command line, then the user will be asked to enter several equations. Press [return] twice when finished entering equations. Up to 16 user equations can be displayed simultaneously. NOTE: Unlike expressions which are evaluated at the 'ucalc> ' prompt, equations that are going to be plotted aren't checked for certain errors. Division by 0, square root of negative numbers, etc... do not stop the graph from being plotted. Examples: --------- ucalc> PLOT sin(x) ucalc> PLOT r=t/5 ucalc> PLOT 2x+7 ucalc> PLOT ; PLOT by itself prompts for multiple equations Equation 1: x^2 ; Plots a parabola Equation 2: fill(1,3) ; Fills an area bounded by the equation above Equation 3: line(2,3,-1,5); Line segment from (2,3) to (-1,5) Equation 4: r=t^2/pi ; Polar equation Equation 5: cos(t), sin(t); Parametric equation Equation 6: After hitting [enter] on the blank line, it will plot the 5 entries above. Any combination of 2D equations can be entered. The plotting of an equation can be aborted at any time, by hitting any key. The following entries can be plotted: 8.1.1 Cartesian --------- Syntax: y = f(x) [,start..finish] (or simply f(x)) This plots a curve in the rectangular coordinate system (Cartesian). As a shortcut, the 'y=' can be omitted. For instance, 'y=x^2' can simply be entered as 'x^2'. The variable parameter is 'x'. Equations can optionally be plotted within an interval defined by start & finish. Examples: --------- PLOT y=tan(x) PLOT sin(x)-3 PLOT 3cos(x), -pi to 2pi PLOT 3x^2-5x+1, 0..2 ; ('0..2' can also be written as '0 to 2') 8.1.2 Parametric ---------- Syntax: x = f(t), y = g(t) [,a..b] (or simply f(t), g(t) [,a..b]) Certain types of curves in the x-y plane cannot be expressed in the form 'y=f(x)'. Parametric equations are more flexible, and can even be used as a superset of equations in the 'y=f(x)' form. 'y=f(x)' can be expressed as 'x=t, y=f(t)'. Equations in the form 'x=f(y)' can also be entered as a parametric equation, in the form 'x=f(t), y=t'. If the optional interval is omitted, UCALC uses 0..2pi. Examples: --------- ucalc> PLOT x= cos(t), y= t-2 ucalc> PLOT cos(t), t-2 ; This is the same as above ucalc> PLOT cos(t)-1, sin(t)+t-5, 0..3pi ucalc> PLOT 2 cos(t), t, -5..5 NOTE: Remember that the variable parameter for parametric equations is 't' and not 'x'. 8.1.3 Polar ----- Syntax: r = f(t) [,a..b] 'r=' is what makes UCALC recognize that it's a polar equation, so 'r=' is not optional. If the optional a..b interval is not entered, then the default 0..2pi will be used. The variable parameter for polar equations is 't'. Examples: --------- ucalc> PLOT r=t/pi, 0..10pi ucalc> PLOT r=sin(t) ucalc> PLOT r=t*sin(t) 8.1.4 3D Surface ---------- Syntax: y = f(x,z) [,start..finish] (or simply f(x,z)) This plots a surface in 3D space. As a shortcut, the 'y=' can be omitted. For instance, 'y=sin(x)*z' can simply be entered as 'sin(x)*z'. The variable parameters are 'x' and 'z'. Equations can optionally be plotted within an interval defined by start & finish. Graphs are plotted in the following xyz view point. y | | / z | / ------- x Examples: --------- PLOT3D y=sin(x)*z PLOT3D sin(sqrt(x^2+z^2))*5 PLOT3D sin(x), -5 to 5 8.1.5 Plotting data from another file ------------------------------- Syntax: "mygraph.dat" Graphs from a text file can be plotted by entering the name of the file inside quotes. The file must consist of a list of x and y coordinates which are separated by spaces, or a comma. The file may look something like this: -10 .5440211108893698 -9 -.4121184852417566 -8 -.9893582466233818 -7 -.6569865987187891 etc... Examples: --------- ucalc> PLOT"mygraph.dat" ucalc> PLOT Equation 1: "mygraph.dat" 8.1.6 Line Segment ------------ Syntax: LINE(x1,y1,x2,y2) This produces a line segment with endpoints (x1,y1) and (x2,y2). Example: -------- ucalc> PLOT line(3,2,5,7) 8.1.7 Rectangle --------- Syntax: RECT(x1,y1,x2,y2) This produces a rectangle which has opposing corners (x1,y1) and (x2,y2). Example: -------- ucalc> PLOT rect(0,0,5,6) 8.1.8 Filling an Area --------------- Syntax: FILL(x,y) This fills a bounded area on the screen in which (x,y) is located. In monochrome mode, it fills the area around (x,y) enclosed within any other curve, or the edge of the screen. If the graphs are in multiple colors, then the FILL statement only uses the color of the preceding graph as a boundary. See the example in '8.1 Plotting'. 8.2 Graph menu ---------- When graphing is completed, a menu with function keys appears at the top. Due to limited space, the descriptions on screen are very brief. Here is a more detailed explanation of each option. 8.2.1 [F2] Reset ---------- This clears the screen, sets graphs to their original sizes, and then replots them. 8.2.2 [F3] Fill --------- Move the cursor inside an enclosed area of the screen, and press F3. This will fill the enclosed area. This works best in the MONO mode (press F8 for MONO). 8.2.3 [F4] Color ---------- 1. When the cursor is in the free-floating mode (default) the background color changes. 2. If a graph is being traced, F4 will change the color of that graph. 8.2.4 [F5] Grid/Axis -------------- This sets or removes the grid and axis lines for 2D graphs. Press it several times to cycle through the options. 8.2.5 [F6] Dot/Connect ---------------- This toggle plots equations as connected curves, or with disconnected dots. When the precision is set high enough, dots are close together and may seem connected. 8.2.6 [F7] Trace ---------- This allows users to trace through polar, parametric, and y=f(x) equations. Use the right and left arrow keys (or mouse) to trace through a graph. Pressing F7 again will put the cursor back in the free-floating mode. Use the up or down arrow keys to choose the previous or next equation. For a "y=f(x)" type of equation, tracing starts on the x coordinate of the current cursor location. For polar & parametric equations, tracing starts at the origin, and additional coordinates are displayed. 8.2.7 [F8] Mono --------- Due to lack of space, this option is not displayed on the menu. This sets all the graphs to the same color, allowing the F3 FILL option to work more effectively. Pressing it a second time sets it back to color again. 8.2.8 [F9] Zoom In ------------ In order to zoom in on an area, place the cursor in the center of the area of interest, and press F9 or the left mouse button. The zoom factor can be changed with the ZOOM command. 8.2.9 [F10] Zoom Out -------------- This zooms out. The right mouse button can also be used. 8.3 Special Graphing Commands ------------------------- The following commands can be entered at the 'ucalc> ' prompt, or placed in the UCALC.DEF file: 8.3.1 AUTOCLR (automatic coloring) ---------------------------- Syntax: AUTOCLR [nn] This command causes each consecutive graph to be displayed in a different color. The optional 'nn' parameter indicates how many different colors can be used. The default is 15. If some graphs turn out to be invisible, then a smaller number should be chosen for 'nn'. The CGA and MCGA modes in UCALC do not support color. Examples: --------- ucalc> AUTOCLR ; Allows 15 different colors (default) ucalc> AUTOCLR 3 ; Tells UCALC to use only 3 different colors 8.3.2 AXIS (sets axis line color) --------------------------- Syntax: AXIS color This sets the axis line color. Color 0 turns the axis lines off. It can be toggled interactively in the graphic screen with F5. Examples: --------- ucalc> AXIS 0 ; Turns the axis lines off. ucalc> AXIS 1 ; Axis lines set to blue 8.3.3 CONNECT (toggle for dot/connect) -------------------------------- Syntax: CONNECT {ON | OFF} When CONNECT is OFF, graphs will be drawn as a series of dots, as opposed to a continuously connected curve. A dot graph is better for plotting certain discontinuous graphs, such as "y=INT(x)". When in the graphic screen, F6 will interactively toggle the connect option. Example: -------- ucalc> CONNECT OFF 8.3.4 GCOLOR (background color in graphic mode) ----------------------------------------- Syntax: GCOLOR color This sets the background color on the graphic screen. In the VGA mode, a number between 0 and 63 is accepted. The graphic color can also be changed interactively by pressing F4 in the graphic screen. Example: -------- ucalc> GCOLOR 10 8.3.5 GRID (sets grid color & pattern) -------------------------------- Syntax: GRID color [,pattern] This command sets the color and pattern of the grid that will be used in the graphic screen. In order for the grid not to appear, set GRID to 0. The optional "pattern" parameter sets a pattern for the line. The default is #b1000100010001000 . . . . . . . . . . As illustrated with the dots above, this represents a pattern with each 1 corresponding to a pixel (the pixel dots are of course much closer together in the graphic screen). A pattern of -1 makes it a continuous line. The grid can be toggled on or off interactively with F5. Example: -------- ucalc> GRID 4 ; Sets a grid with color 4 ucalc> GRID 1, #b1010101010101010 ; Sets a dotted grid with every ; other pixel turned on ucalc> GRID 5, -1 ; -1 makes it a continuous line 8.3.6 MODE (selects graphic card) --------------------------- Syntax: MODE {CGA | EGA | HGC | VGA | MCGA} This changes the graphic mode that is used for plotting. When UCALC loads up, it automatically determines the highest resolution supported by your computer. To change it to another screen mode, put a MODE statement in UCALC.DEF (or type it at the 'ucalc> ' prompt), with the proper selection. Example: -------- ucalc> MODE EGA ; Sets the monitor to EGA mode 8.3.7 MONO (turns colors off) ----------------------- Syntax: MONO This turns all colors off in the graphic mode. Those who do not have a color monitor may want to include this command in UCALC.DEF. This command may also be useful for a better printout, or when filling the area between graphs. 8.3.8 PLOTF (sends the graph coordinates to a file) --------------------------------------------- Syntax: PLOTF"filename" This sends all the coordinates of the next 2D graph to the specified file. Follow this command with the PLOT or PPLOT command. 8.3.9 PPLOT (edits previously plotted equations) ------------------------------------------ Syntax: PPLOT In order to modify a few things in a set of equations that have been plotted before, use the PPLOT command at the 'ucalc> ' prompt to avoid retyping everything. Sometimes you may want to simply change a setting such as the zoom factor or graph precision, and plot the previous set of equations without modification. In this case, type "PLOT" and press [enter] twice. Examples: --------- ucalc> PPLOT ; This lets you modify previously graphed equations. ucalc> PLOT Equation 1: ; Press [enter] without typing an equation to replot the previous set, if no modifications are desired. 8.3.10 Graphing precision (PREC) ------------------------- Syntax: PREC nn This changes the precision used in graphing. 'nn' represents the number of pixels per unit (x-axis). The higher 'nn' is, the higher the precision will be. More precision naturally means slower plotting. The default precision is 10, and should be fine for many graphs. If stray lines appear in an unbounded graph, or if the graph appears jagged, or if the curve doesn't quite reach the starting or ending points (such as in polar graphs) then raising the precision will often solve the problem. Example: -------- ucalc> PREC 100 8.3.11 WINDOW (sets screen coordinate system) -------------------------------------- Syntax: WINDOW(x1,x2,y1,y2) This modifies the graphic screen coordinate system. x1 and x2 represent the screen end locations of the X axis, and the Y axis goes from y1 to y2. The X and Y axes cross at (0,0). The default setting is WINDOW(-10,10,-7.5,7.5), which means that the origin (0,0) is at the center of the screen, with point (-10,-7.5) at the bottom left of the screen and (10,7.5) at the top right of the screen. Examples: --------- ucalc> WINDOW(0,10,0,7.5) This sets the origin at the bottom left of the screen. ucalc> WINDOW(-1,1,-1,1) The origin is at the center, and x goes from -1 to 1, and so does y. ucalc> WINDOW(-10,10,-7,7) This creates a better proportional window in the EGA mode. 8.3.12 ZOOM (changes zoom factor) -------------------------- Syntax: ZOOM factor This sets the zoom factor. The default is 5. When a graph is on the screen, place the cursor on an area that you want to magnify. Press F9 to zoom in, or F10 to zoom out. Examples: --------- ucalc> ZOOM 10 ; When you later press the Zoom In key, the image ; will be magnified 10 times. 8.4 Moving the Crosshair -------------------- For mouseless systems, after the graphs have been plotted, a crosshair (graphic cursor) is placed at the upper left hand corner of the screen. It can be moved with the arrow keys in order to pinpoint coordinates on the screen. The Home, End, PgUp, and PgDn keys can also be used, for diagonal movement. To move the crosshair slowly, press the key and release it quickly. To move it faster, hold the key down as it accelerates. A mouse can be used to move the mouse pointer. 8.5 Adding Text to the Screen ------------------------- To add text on the graphic screen, simply start typing wherever the crosshair cursor (or mouse pointer) is located. 8.6 Printing a Graphic Screen ------------------------- For DOS users, in order to be able to send graphs to the printer, run GRAPHICS.COM (which comes with DOS) before loading UCALC. Then, when a graph is on the screen, press the 'Print Screen' key to send it out to the printer. For better results on printers which do not support color, issue the MONO command at the 'ucalc> ' prompt before plotting. See the DOS manual for more details on GRAPHICS.COM. This version of UCALC has no built-in mechanism for printing. NOTE: Windows 95 users may press ALT ENTER to downsize the graph, and cut the desired portion of the screen, and past it into a word processor. 9. Summation ========= Syntax: SUM fx, a..b [,dx] b ____ \ f(x) is written as 'SUM f(x), a..b', where f(x) is your /___ function, and a..b is the range. x= a The summation cannot be part of another expression. The optional dx parameter can be used in order to indicate an increment other than the default 1. Examples: --------- ucalc> sum x^2+2*x+14, 5..1000 Answer: 334848394 ucalc> sum x^3-2, 1..15, .1 Answer: 127971.6 SUMTABLE is the same as SUM, except that intermediate values are displayed as the sum is being added. ucalc> sumtable x^2/fact(x), 1..3 Count Value Cumulative 1 1 1 2 2 3 3 1.5 4.5 Answer: 4.5 A long list can be aborted with the [Esc] key. 10. Numerical Integration ===================== Syntax: INTEG fx,a..b [,n] This approximates the value for the definite integral of fx, using Simpson's rule. This rule requires that n be an even number. UCALC takes care of that by automatically transforming n to the next highest even number (n = n + n mod 2). If no value for n is given, then 100 is used as the default number of subdivisions. This command works properly only when fx is a continuous function. INTEG cannot be part of another expression. Examples: --------- ucalc> integ x*sin(x), 0..pi Answer: 3.14159267059288459 ucalc> integ 1-x^2, 0..1, 8 Answer: .666666666666666667 11. Solving Equations ================= Syntax: SOLVE fx [=gx] [,a..b] This solves an equation for the value of 'x'. The statements in brackets are optional. If the expression on the right of the = sign is 0, then you can simply do: 'SOLVE expression'. For instance, 'SOLVE 3*x+2=0 can be written as SOLVE 3*x+2. If the equation happens to have several solutions, you can indicate the interval (a..b) of the particular solutions you are interested in. The algorithm used in this program for solving equations is the Bisection Method, which is a special case of the Intermediate Value Theorem. A solution can be found for continuous functions in the interval a < x < b, where f(a) < 0 < f(b). If a..b is not defined, then the default interval is from -1E6 to 1E6. If a real solution does exist, but cannot be found with the default interval, then try narrowing the interval as much as possible. Examples: --------- ucalc> solve exp(x+x^2)-sqr(x+5) = 127 Answer: -2.75962472778054749 Answer: 1.76151609179570087 ucalc> solve sin(x)=cos(x), 0..pi Answer: .78539816339744831 ucalc> solve x^3+2*x+5 = 10+7 Answer: 2 ucalc> solve 2*x^2-3 Answer: -1.22474487139158905 Answer: 1.22474487139158905 12. Numerical Notations =================== The default numerical type is DECIMAL. Binary, octal, and hexadecimal number types are also supported. The latter types must be preceded by the # (number sign) symbol, and one of the letters "h", "b", or "o", for hexadecimal, binary, or octal in that respective order. The $ sign for hexadecimal notation can be used as a shortcut. See examples. In order to see all your answers in hex, binary, and octal, issue the command: mode HBO Exponential notation is also supported. These are numbers followed by the letter E, and an exponent number. For instance: 3.4E+5 translates to 3.4*10^5, and 3.4E-5 translates to 3.4*10^(-5). Examples: --------- #b110101110, #o656, #h1AE, $1AE, 430, 4.3E2 are all the same number. #b10101^2 * 5/$1EF + sin(5.8+2)*cos(#o302)-7E6 is a valid expression. 13. Implicit Multiplication ======================= When writing math expressions, it is common to omit the times symbol (*), when multiplication is implied. For instance, one may write '2x+5', which is the same as '2*x+5'. The following are examples of implied multiplications supported by UCALC. Expression Equivalent ---------- ---------- x y x*y 3pi+10 3*pi+10 5(4+8) 5*(4+8) (5+5)(3+9) (5+5)*(3+9) (3+2)8 (3+2)*8 NOTE: Implicit multiplication has the same priority as regular multiplication. For instance '1/2q' is the equivalent of '1/2*q' not '1/(2q)'. (This is subject to change in a future version). 14. Assigning Variables =================== Variables can be used to store values, which can later become part of an expression. Variables are composed of letters of the alphabet, and may contain numerical digits, as long as a numerical digit is not the first character. A variable can be up to 1024 characters long. Examples: --------- mynumber = 12345 mass = 15 speed = 23+10.5 m1 = 10*pi^2 cb26 = sqrt(37) + mynumber 15. Assigning Functions =================== Once defined, a user function behaves in the same way as a built-in function. Argument names used in defining functions are temporary, and do not affect user variables with the same name. The name of the function itself, however, should be unique. The naming convention of functions is similar to that of variables. User functions can accept many arguments. Examples: --------- cube(x) = x^3 area(r,h) = pi*r*sqr(r^2+h^2) ; area of right circular cone logx(base,num) = ln(num) / ln(base) abc(x,y,z) = 5 + logx(x,y)*z 16. Miscellaneous Commands ====================== 16.1 LOAD command ------------ Syntax: LOAD"filename" This command loads up the contents of a file into the UCALC workspace. The file may contain any UCALC command. A file saved with the WRITE command however, cannot be loaded directly if it contains 'ucalc> ' prompts. Examples: --------- ucalc> load"convert.def" ucalc> load"finance.def" ucalc> load"formula.asc" 16.2 WRITE command ------------- Syntax: WRITE"filename" This command records your UCALC session to the file name that you specify. Everything that is displayed on the screen will go to that file verbatim, until you issue the CLOSE command, or exit. If the file already exists, the WRITE command will append to it without removing what is already in the file. Example: -------- ucalc> write"ucalc.log" 16.3 SHELL command ------------- Syntax: SHELL This allows you to drop to DOS temporarily. To resume your session, type EXIT at the DOS prompt. [F4] does the same thing as the SHELL command. You may also pass a command for DOS to execute. Examples: --------- ucalc> shell"dir" ; This executes the DIR command. ucalc> shell ; This drops you to DOS until you type EXIT. NOTE: The SHELL command cannot be used in TSR mode. 16.4 COLOR (text color) ------------------ Syntax: COLOR [foreground] [,background] The foreground and background colors of the text screen can be set at the 'ucalc> ' prompt (or in UCALC.DEF) with this command. On color monitors, the foreground color can be a number between 0 and 31. Background colors can be between 0 and 7. UCALC also clears the screen when this command is entered. See a DOS or programming manual for color values. Examples: --------- ucalc> COLOR 7,1 ; sets the screen to white over blue ucalc> COLOR 11,0 ; light cyan over black ucalc> COLOR 5 ; changes only the foreground ucalc> COLOR ,3 ; changes only the background 16.5 REDIRECT -------- Syntax: REDIRECT {ON|OFF} Turning redirection off allows text to be displayed on the screen faster. Also, the color statement may work better when redirection is off, depending on your screen configuration. By default, UCALC redirection is ON if UCALC is executed from DOS, and OFF when UCALC is loaded as a TSR. 17. UCALC.DEF ========= Commonly used constants & functions, such as e, and logx(x,y) and any others that are used regularly, and start-up settings, such as COLOR, and PROMPT, etc... can be defined in UCALC.DEF. This file can be created or modified with any ASCII text editor. The semicolon (;) can be used as a remark. Anything following it will be ignored. Every time UCALC is run, it looks for UCALC.DEF in the current directory first. If it's not found there, it searches the directory which UCALC.EXE was loaded from. If the file is found, its functions and variables are loaded. The /NODEF option at the command line is equivalent to not having a UCALC.DEF file. Here is an example of what UCALC.DEF may look like: color 11,1 grid 3,#b10101 mode HBO window(-10,10,-7,7) load"convert.def" prompt"" ; Removes the default 'ucalc> ' prompt prompta"A:" ; Replaces the default 'Answer: ' prompt with 'A:' e = 2.718281828459045 ; Natural log constant gravity = 9.8 ; Acceleration due to gravity na = 6.0221367E+23 ; Avogadro's number 1/mol logx(base,num) = log(num) / log(base) A total maximum of 300 variables, and 200 user functions can be defined (and usually much less in TSR mode). 18. Technical Notes =============== o UCALC is not case sensitive. Upper case letters are treated just the same as lower case letters. For instance, pi, PI, and Pi are all treated the same. o Rounding: The rounding method in UCALC is called banker's rounding. With this method, numbers ending with the digit 5 are rounded towards the closest even digit. For instance, both 11.5 and 12.5 are rounded to 12, and both 13.5 and 14.5 are rounded to 14, when FIX is set to 0. Only the displayed number is rounded, while the actual calculations are always performed in high precision. o Random Numbers: The RND function produces a random number between 0 and 1. RND(1) returns a new random number each time it is used. RND(0) returns the previously used random number. If x is negative, then RND(x) returns a predictable number. For instance, RND(-5) will produce the same number each time. To get a random number between 0 & x, simply use RND(1)*x. For instance, RND(1)*50 will return a random number between 0 & 50. o Ugly Numbers: Occasionally, numbers are not displayed as one might expect. For instance you might get .499999999999999999 instead of .5, or 8.23423423982432343E-18 instead of 0, which is actually pretty close to the answer. This may happen as a result of lengthy operations, or certain types of functions. One solution is to reduce the number of decimal digits that are displayed with the FIX command. o HBO mode: When this mode is on, it will display the hex, binary, and octal notations, only for values between -32766 and 65535. Numbers beyond that range are displayed only in decimal form. Negative numbers are represented in "two's complement" form. Only the integer part of a number is displayed in hex, bin, and oct. Entering 'MODE HBO' turns the HBO mode on. Typing it again turns it back off. o Relational operators return a 1 for true expressions, and 0 for false ones. For instance, '5 > 3' returns 1, and '5 < 3' returns 0. o Compound Functions: Functions with multiple entries may be defined by using relational operators. For instance: / 2+x^2, x > 0 f(x) = | 3, x = 0 \ x*2+8, x < 0 can be written as: f(x) = (2+x^2)*(x > 0) + (3)*(x = 0) + (x*2+8)*(x < 0) o Equal Sign: The single equal sign, =, can be used both for assigning functions & variables, and as a relational operator. If there is a conflict in the logic of an expression such that it can be taken either way, then use the double equal sign, ==, when a relational operator is intended. An assignment is assumed only when the expression left of the left-most equal sign is a valid function or variable name. To avoid all confusion, use == for relational operations. o Limited Function Space: There is a limit of instructions (such as +, -, *, etc...) which can be used for defining functions. Every time a function is defined or redefined, part of the instruction list is filled, and cannot be reclaimed during a UCALC session. An error message is given when too many functions have been defined. o Each expression can use a maximum of 33 instructions. If an expression is too long, UCALC returns an error message. Expressions can be broken down into several shorter ones. o The graphic screen is optimized for the VGA mode. With lower resolution, the crosshair will give a less accurate reading of its location on the screen. WINDOW(-10,10,-7,7) is a better match for the proportions of the EGA screen mode. o UCALC can be de-activated from memory with the command "EXIT TSR". However, in order for UCALC to be able to remove itself successfully from memory, UCALC should be the last TSR to be loaded, and the unloading should take place when UCALC is popped up at the DOS prompt. o End-of-file: When doing redirection from the DOS command line, make sure that the input file ends with an end-of-file marker (^Z, or ASCII 26). Many text editors take care of this automatically, but a few don't. An input file may alternatively end with a ^C (ASCII 3) or the EXIT command. Be sure to add several blank lines at the end of the input file. An input file with no ^C, ^Z or EXIT, and no blank lines at the end may cause UCALC to freeze. o Redirection mode is forced off when UCALC is loaded as a memory resident program. If the REDIRECT ON command is manually issued when in TSR mode, UCALC may crash when popping down. This will hopefully be changed in a future version. 19. Registration ============ You are granted a 30 day period for evaluating UCALC. Continued usage of this program beyond this trial period requires payment of a registration fee to the author. The fee is only $25 for one person, or less per unit (see UCALCREG.DOC) when purchasing a site license for use on several computers. Continued development of this program depends on users like you who pay for it. Registered users receive a special code that permanently deactivates all registration reminders. Notice that there is no extra shipping charge in this version because of this, even for international users. In order to help me better support this program, please answer the questions in QUEST.DOC, whether you decide to register or not. This will allow me to keep the price down, and add the right features in the next version. Use the form in UCALCREG.DOC to place your registration. Easy Service ------------ For your convenience, you can order UCALC from the Public Software Library with your Visa, Master Card, American Express, or Discover card by calling toll-free at 1-800-242-4PSL (overseas: 713-524-6394) or by FAX to 713-524-6398, and even by Compuserve at 71355,470. PSL NUMBERS ARE FOR ORDERING ONLY. I cannot be reached through PsL. To reach me personally, call 305-233-2604, or send e-mail at Dancorbier@aol.com (or corbier@satelnet.org). The PsL part number for UCALC is 10655. Compuserve users can register by typing GO SWREG, and choosing registration ID: 3591. Support ------- I will try to extend my support to unregistered users during their evaluation period, however, I reserve the right to limit this support. The preferred method of communication is via e-mail whenever possible. See section 21 for other ways of reaching the author. License ------- For this license agreement, a site is considered to be any corporation, institution, government agency, computer lab, or non-personal organization, with more than one computer capable of running the UCALC software. A site may use the unregistered version for evaluation purposes only. If the site decides to continue using UCALC after 30 days, a site license must be purchased. The site license arrangement provides for volume discounts. See the file named UCALCREG.DOC for the low rates that are available. A site license is for use of the software within your site, and is not transferable. This license allows the internal use and copying of the software by as many computers as contracted for. Distribution, repackaging, or reselling of the licensed version to third parties is not allowed under this agreement. The unregistered version however may be freely distributed, as long is it contains all original files, in unmodified form. The LICENSER (Daniel Corbier) warrants that he is the sole owner of the UCALC software and has full power and authority to grant this license herein without consent of any other party. Disclaimer ---------- The Ultimate Calculator (UCALC) is provided on an "as is" basis without warranty of any kind, expressed or implied. The person using the software bears all risk as to the quality and performance of the software. The author will not be held liable for any special, incidental, consequential, direct or indirect damages due to any malfunctions. Aside from the legal stuff, I'm eager to support this program as much as possible. I want to hear your suggestions for the next release. 20. Shareware Author & User Case Study ================================== In the process of developing UCALC, and searching for ways to make it profitable, I did some research to find the right ingredients for getting people to pay for shareware programs they use. So, I conducted a survey asking many shareware users what motivates them to register. I also asked a number of well-known successful shareware authors what they have done to receive many registrations. The results are written in a document which can be found in many online places. Here's the description: Filename: SAUCS1.ARJ (or .ZIP, .LZH, .SDN, ..) Description: SHAREWARE AUTHOR & USER CASE STUDY v1 - Answers questions that shareware authors often ask, such as what motivates users to register, what prevents them from doing so, how much they are willing to pay, how to get one's program "out there", whether or not crippling and nagging works, how long users take to evaluate programs before paying, etc ... Answers are based on survey responses from shareware users and successful authors. Size: 42k (when compressed with ARJ) 21. My Address ========== For information about dealer pricing, volume discounts, site licensing, latest versions, suggestions, or for technical information, you can contact me through one of the following means: US Mail: Daniel Corbier 20410 SW 92 Place Miami, FL 33189 FAX: 305-233-2604 Voice: 305-233-2604 Internet: Dancorbier@aol.com (or corbier@satelnet.org, or corbier@delphi.com) World Wide Web (WWW): http://members.aol.com/Dancorbier/ucalc.html Fidonet: Daniel Corbier at 1:135/110 Compuserve: 75541,1523 The following addresses can also be used from Compuserve: INTERNET: Dancorbier@aol.com (or INTERNET: corbier@satelnet.org) I try my best to answer all e-mail inquiries. Sometimes e-mail can get lost. If several days pass without a response, please try sending e- mail to another listed address. Your messages are important. 22. Distribution ============ You are encouraged to distribute the shareware version of UCALC. The following files must all be present and unmodified when distributed: UCALC.DEF Sample UCALC.DEF file UCALC.TSR Options for TSR mode UCALC.EXE Executable UCALC.DOC Documentation QUEST.DOC Questionnaire HISTORY.DOC Lists the features that were added in each version EXAMPLES.DOC Examples for UCALC UCALCREG.DOC Registration form PLOTDEMO Demo of equations that UCALC can plot PLOTDEMO.BAT Graphing demo batch file GRAPH.DAT Sample coordinate data file for the graphic demo CONVERT.DEF Conversion functions SDN.ID Description for the Shareware Distribution Network (SDN) FILE_ID.DIZ Brief program description for bulletin boards The compressed file name prefix must be UCALC32 or UCAL32 or UCALC (followed by ARJ, ZIP, LZH, or other). Vendors ------- Vendors may distribute UCALC, as long as it is not labeled "free", "cheap", "copyright free", or "public domain". It must be made clear to customers that this program is shareware, and that a payment must be made to the author if they continue using it. All ASP distributors in good standing may distribute the Ultimate Calculator without my written permission (although I would appreciate a copy of your catalog). Vendors who operate with good business ethics should feel free to distribute UCALC without my written permission. 23. Acknowledgments =============== I would like to thank those who have registered UCALC, and everyone who has sent suggestions. I would like to thank Dr. Steven Gunhouse for suggestions on graphic features such as zoom, trace, etc.... I would also like to thank the following people for being beta testers: Aaron Beharrell Jonathan Borwein University of Waterloo David G. Caraballo Princeton University Elan Feingold Cornell University Daryl Gungadoo Andrews University Steven Gunhouse University of Texas James Hague Rich Holland Kansas State University Fred Hapgood John Lim Eng Hooi Willie Hutton University of Colorado Mark W Jacobs Stanford University Michael D. Lawler Ball State University Chris Long Rutgers University Mark E. Mallett Peter Paul Meiler TNO Physics & Electronics Lab, the Netherlands Marty Milette Mitel Corporation Matt Pardo North Carolina Medical Center Alexander Pruss University of British Columbia Glauber Ribeiro O.C. International, Brazil Dave Sklar Temple University John Steele Video Business Systems David Steinman University of Toronto Sue Widemark Shi-Chang Wooh Northwestern University, Illinois <<<< END OF UCALC DOCUMENTATION >>>>