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-------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- -- ┌────────────────┐ │╒═══════════════╧╕ ││ Help File ├───────────────────────────────────── ││ └────────────────────────────────────── ││ ││ AstroEquationSolver 3 Spreadsheet/Calculator ││ ││ Help File Version 3.12 03-01-1994 <ASP> ││ L 10 │ (c) Copyright 1981, 1994 PC SuperComputer Capital, Inc. All rights reserved. Read and understand WARRANTY INFORMATION . Type J twice to read. Instructions on using help file are at end of file. Type K to read. L 20 ╒══════════╕ │ CONTENTS └────────────────────────────────────────────────────────── 0.00 Table of Contents * To quickly jump to Sections, position the Section line number * on the │JUMP│ line (line 12) and type J or type Lxxx (enter) * where xxx is line number. For example, to jump to line 139, * type L139 (ent). Type S or R to skip back/forth to Sections. L 30 SECTION TITLE PAGE│LINE 0.00 ... Table of Contents ................................... 1 25 1.01 ... Equations Display, What is it? ...................... 3 96 1.02 ... How to Use the Calculator. .......................... 4 183 1.03 ... How to find Things With Auto-search Function ........ 6 231 1.04 ... Summary of Letter Commands Used in Equations ........ 6 249 Display 1.05 ... F1-F10 Keys, Commands assigned. .................... 18 812 L 40 1.06 ... Command Sequences Used to Perform Special .......... 19 840 Operations 1.07 ... Editing Keys: Functions During Text Entry .......... 19 861 2.01 ... Entering Equations Into the Program ................ 21 960 2.03 ... Writing Equations: Definition of Terms ............. 22 1010 2.10 ... Rules for Writing Algebraic Expressions, ........... 25 1109 ------------------------------------------ 0.00 -- Table of Contents --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 2 -- Formulas and Equations 2.15 ... Rules for Evaluation of Parentheses ................ 27 1209 2.20 ... Rules for Evaluation of Intrinsic Functions ........ 27 1231 2.25 ... Rules for Evaluation of Mathematical Operations .... 28 1254 L 50 2.30 ... Glossary of Intrinsic MATH FUNCTIONS and ........... 29 1293 Function Operators 2.40 ... Numbers: Format-free, Examples of Formats .......... 34 1526 2.42 ... Controlling the Number of Decimal Digits ........... 34 1562 2.45 ... Maximum Number of Equations, Variables and ......... 35 1600 Constants 2.50 ... Errors During Equation Evaluation and Elsewhere .... 36 1632 3.01 ... Directory Screen: Commands During Display .......... 36 1652 3.05 ... Commands Used While Plot Screen is Displayed ....... 39 1750 4.01 ... Commands Unique to this Program ASOL3.EXE. ......... 41 1845 L 60 4.03 ... Solving (If possible) Linear Simultaneous .......... 42 1929 Equations. 4.05 ... Solving (If possible) Nonlinear Simultaneous ....... 45 2033 Equations. 4.10 ... Shooting a Marble into a Moving Ferris Wheel ....... 47 2151 Car: Solution of Simultaneous Nonlinear equations 4.20 ... Resource Allocation in an Instrument Company: ...... 54 2462 Solving Simultaneous Linear equations 4.30 ... How to Generate (Look-up) Tables. .................. 58 2663 L 70 5.01 ... Summary of Common WARNINGS During Calculations. .... 60 2750 5.05 ... Summary of ERRORS During Evaluation of Equations ... 63 2861 6.01 ... Setting Foreground/background Colors of Main ....... 65 2947 Equations Screen and Program 6.05 ... Clock Screen: Commands During Display .............. 65 2979 6.10 ... Apostrophe Commands: What They Do and How to Use ... 67 3042 Them 7.01 ... Information After Program Name on DOS Command ...... 70 3183 Line. How the Program Uses It and What It Does. 8.01 ... Product License and Warranty. ...................... 71 3244 L 80 8.03 ... User Support. ...................................... 72 3310 8.04 ... Ombudsman/Arbitration Policy. ...................... 73 3331 8.05 ... Product Information and How to Order Complete ...... 73 3353 Package. 8.06 ... Software Included in Astro 3 Registration .......... 75 3443 8.07 ... Order/Registration Form ............................ 77 3528 8.08 ... Instructions for Manually Installing Package. ...... 79 3593 8.09 ... Interested in Becoming the Author of Your Own ...... 80 3635 Interactive Application File? 9.01 ... Help File: Summary of File Viewing Commands ........ 80 3657 L 90 ------------------------------------------ 0.00 -- Table of Contents --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 3 -- ╒═══════════════╕ │ EQUATIONS ??? └────────────────────────────────────────────────────── 1.01 Equations Display, What is it? ──────────────────────────────────────────────────────────────────────── The equations display is the spreadsheet portion of AstroEquationSolver 3. It contains the equations, variable L 100 names, variable values and a comment. Most operations are performed while in the equations display through the use of characters, letters, combinations of characters with letters and the "F" keys. The blinking cursor prompt ">" is always positioned between a variable name like TIME and its current value which might be 2.3. For example: TIME => 2.3. Numbers and math operations are passed to the variable on which the blinking cursor resides. Other characters and combinations serve as commands to activate certain functions such as integration or derivitization. Certain commands require that L 110 two characters be typed consecutively. Commands such as "!C" or "@C" mean that the "!" or "@" is typed first and the "C" next. Representations such as "(esc)", "(enter)" and "(space)" represent single keystrokes. To change the display colors to high-intensity white on blue type Q when the highlight bar is lighted on the EQU below. 'EQU 'COL HWHITE BLUE L 120 'HELP An illustration of the equations display for the equation of a straight line: Y=M*X+B with the blinking cursor on variable X is shown below. A comment which describes the equation is listed first. The equation and the value of its dependent variable Y (=4) is listed next. The current time and date are listed in the middle of the screen. The three independent variables B, M and X are listed in alphabetical order. Finally, a summary of keys and functions is displayed L 130 at the bottom of the screen. The last line scrolls through additional commands and is not shown. ----------------------------------------------------------------------- --- Comment --> Equation of a straight line. Y=M*X+B Y = 4 ----------------------------- 1.01 -- Equations Display, What is it? --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 4 -- 12:23:04 03-07-1981 L 140 B = 4 M = -2 X => 0 F1 hlp, F2 appl hlp, F3 exit, F4 shl, F5 com, F6 equ, F7 dir, F8 get, F9 ----------------------------------------------------------------------- Definitions of terms used to define an equation. L 150 ■ EQUATION. A formula, expression or recipe directing the program on how to execute mathematical operations such as Y=M*X+B which is the mathematical representation of a straight line (Y. vs. X) with slope M and y-intercept B. Equations are written in a symbolic language which is identical to how they would be expressed if written in the popular computer language BASIC. In this equation Y is assigned the value of M multiplied by X and then added to the value of B. ■ DEPENDENT VARIABLE. Unique name associated with every L 160 equation and its value is usually the object of a calculation such as Y in Y=M*X+B. ■ INDEPENDENT VARIABLE(S). Name(s) always to the right of the equal sign such as M, X and B in Y=M*X+B. Independent variables are always used to calculate the values of the dependent variables. ■ STORAGE VARIABLE(S). Names that are generated by simple assignment statements entered in the equations display such L 170 as (space) PI=3.1415926 (enter). They are similar to independent variables and can be used in all equations, expressions and calculations. The storage variables and their values are saved and recalled separately from the equations using the "!]" and "![" commands. Their values are usually hidden unless requested with the "Z" or "Y" commands which toggle through their names or by typing the variable name followed by equal sign: (space) VARNAME= (enter). ╒════════════════╕ L 180 │ CALCULATOR ??? └────────────────────────────────────────────────────── 1.02 How to Use the Calculator. ──────────────────────────────────────────────────────────────────────── --------------------------------- 1.02 -- How to Use the Calculator. --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 5 -- The "blinking cursor" or "=>" is located between a variable name and its value. It begins the ASOL3 command line just like a DOS prompt. Information is passed to the program by typing appropriate characters. Just about any calculation can be performed and stored by assigning its value to a variable name, one that already exists or a new one. L 190 Variables that do not appear on the equations display screen are called "storage variables". For example, if the cursor is on variable B, then one can perform a calculation and save it as a storage variable named Q1: ----------------------------------------------------------------------- --- Comment --> Equation of a straight line. Y=M*X+B Y = 4 L 200 12:25:04 03-07-1981 B => q1=23.45+56.78+12.98-34.56-12.78 (enter) X = 0 F1 hlp, F2 appl hlp, F3 exit, F4 shl, F5 com, F6 equ, F7 dir, F8 get, F9 ----------------------------------------------------------------------- L 210 When "(enter) is typed, the program will evaluate the expression, assign its value to Q1 and display the result on the time/date line. Note, because most letters represent commands, it is wise to start such calculations with a space. Expressions can reference any previously defined variable: dependent, independent or storage. For example (space) x=2*B-y+3*m (enter) or q1=q1+67 (enter). The current values of storage variables can be displayed with the storage toggle commands "Y" and "Z" or by typing their name followed by the equal sign and enter. For example, (space) Q1=(enter). L 220 Storage variables can be used in the equations, if previously defined. Multiple assignment can be made with the 'VAR apostrophe command. For example: 'var y=3 b=4 x=-5 (enter) The storage variables are saved independent of the equations with the command "!]". See below for more discussion on storage variables. ╒═════════════╕ │ AUTO-SEARCH └───────────────────────────────────────────────────────── L 230 --------------- 1.03 -- How to find Things With Auto-search Function --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 6 -- 1.03 How to find Things With Auto-search Function ──────────────────────────────────────────────────────────────────────── This entire file can be automatically searched for words, phrases and other characters using the auto-search command "A". Type "A" and then enter the characters. Search is in uppercase and is case-insensitive. To continue the search, type "A" repeatedly as required until wrap around occurs. To perform another search, it may be necessary to first type "(space)" then "A". For example, to find "Help File:", type "A", then L 240 (end esc) help file: (enter). However, this will only get you back to this line because the search starts at the top of the screen! Type "A" again to continue and find another "hit". Type "A" a few times to get back to here. ╒══════════╕ │ COMMANDS └──────────────────────────────────────────────────────────── 1.04 Summary of Letter Commands Used in Equations Display ──────────────────────────────────────────────────────────────────────── L 250 The following discussion may assume that the "default" equations or amortization equations are currently being displayed. To load these equations from the main equation display, type (F6) or "!/" and type (end esc) "" (enter) in response to the "-- ? Equations ->" prompt. **** Commands, keystrokes, functions and explanations follow **** -> Activate variable: A !A @A L 260 Use "A" to activate an equation and its dependent variable. Used to mark equations which participate in other commands like the "G" and "D" commands used for integration and differentiation, respectively. Only active equations are integrated and differentiated. Also used to specify equations set equal to each other in the intersection command "U" or plotted with the plot command "P". Initially, all equations are active. Inactive equations do not have an "=" following variable name. Use !A to activate all dependent or independent L 270 variables at once. The location of the cursor determines which set. Use @A to activate all variables at once. One can also use the apostrophe command 'ACT VARNAME (enter) to perform activation. See below. Use the commands I, !I or @I to inactivate variables and equation(s). ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 7 -- -> Background/foreground colors: !N @N "!N" toggles next foreground color. Use "@N" to toggle next background color. Colors are normal-intensity black, blue, L 280 green, cyan, red, magenta, brown and white and the high-intensity shades. For monochrome monitor, default values are recommended. Color settings are saved with equations. If fore/back colors are equal then displayed info becomes invisible. Use "!(esc)" to reset monochrome colors: Fore, white (green); Back, black. "!(esc)" sets monochr colors: Fore, white (green) #7; Back, black #0. "@ (esc)" sets monochr colors: Fore, black #0; Back, white (green) #7. One can also use the apostrophe command 'COL color1, color2 (enter) to perform this function. 'COL (enter) resets monochrome colors. L 290 See below for more details. -> Bottom line command scrolling: J !J @J K !K @K "J" toggles to previous command menu display at bottom of screen. "!J" turns on auto-scrolling about every 10 seconds. "@J" turns off auto-scrolling. "K" toggles to next command menu display at bottom of screen. "!K" turns on auto-scrolling about every 10 seconds. "@K" turns off auto-scrolling. L 300 -> Calculate dependent variables: C (enter) (esc) "C" calculates the values of all dependent variables using the current values of the independent and storage variables. "(enter)" calculates dependent variables if used after a valid number or allowed expression is entered. "(esc)" recalculates equations and redraws the display. Also, use the apostrophe command 'CALC (enter) to recalculate without entering a variable. L 310 -> Chaining calculated values to other equations (overlaying equations) Use "@[" to get a file of equation(s), comment and variable status only. Common variables are assigned existing values and new variables are initialized to 0.0. Allows overlay or chain operations to other equation(s) with identical variable names. -> Chaining to other ASTRO3 programs: 'CHAIN The 'CHAIN apostrophe command is used to switch to another L 320 ASTRO3 program and pass it the current equations, dependent and independent variables (as file A.EQU) and storage variables (as ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 8 -- file A.EQU). CALC or C is used to designate AstroFormulaCalculator 3. SOLVE or S is used to designate AstroEquationSolver 3. FIT or F is used to designate AstroDataFitter 3. At the blinking cursor, type 'CHAIN C (enter) to chain to AstroFormCalc, type 'CHAIN S (enter) to chain to AstroEquationSolver and 'CHAIN F (enter) to chain to AstroDataFitter. In AUTOEXEC.BAT, be sure to set a PATH to where the ASTRO 3 programs can be found and set the environment L 330 variable ASTRO3 to that same path. -> Changing displayed precision of dependent variables: !\ @\ Use "!\" for the single-precision display (default) of dependent variables of equations with var name displayed before current value: ABC = 1.234567. Use "@\" for the double-precision display of dependent variables of equations without variable name displayed before current value: = 1.234567890123456. To see the full precision of an independent L 340 variable, type "\". and then type (enter) to return to the blinking cursor ">". Also, use the apostrophe commands 'PRE SINGLE (enter) or 'PRE DOUBLE (enter). -> Changing number of displayed decimal digits in main equation display The number of decimal digits displayed in the main equation display can be globally changed with the 'DEC apostrophe command. For example, to set 2 decimal digits, type 'DEC 2 (enter). To set none, type 'DEC 0 (enter). L 350 To reset, type 'DEC (enter). The decimal operator attached to a variable name will override the global default. For example, a variable named MONEY.2 will always display 2 decimal digits no matter what the global default. Global defaults also apply to the displayed values of the storage variables and numbers displayed on the plot. -> Clock display: !C Use "!C" to display full-screen clock/calendar in which the L 360 alarm is set. Type $ to exit back to the equation display. See below for a summary of the clock commands. Also, use the apostrophe command 'CLO (enter) to jump to the clock. -> Copy an equation Move the cursor to the desired equation, type "@/" and type "(esc) or "(ctrl Q)" to exit to the equation display without ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 9 -- any changes. Remember that the immediate calculation buffer (command "|") now contains this equation. Type (F6) or "!/" to L 370 edit the displayed equations. Move the cursor to the location where the equation is to be inserted and type "(alt 9)" to insert. Remember to add spaces where needed to separate equations and remove or change the other equations/dependent variables. Also, the name of the dependent variable of each equation must be unique. Also, see command "!F", "@F", "!M", "@M", "!L" and "@L" for other ways to copy equations. -> Cursor movement: B F L M N arrow keys (tab) (shift tab) (backspace) L 380 "B" and (shift tab) move the cursor ">" backwards to preceding variable. Also use (backspace) for the same purpose. "F" moves the cursor ">" to the first dependent variable "L" moves the cursor ">" to the last independent variable. "M" moves the cursor ">" to the middle or first independent variable. "N" and (tab) move the cursor ">" to the next variable. Also use (enter) and (ctrl enter) for the same purpose. Arrow keys - Use edit keys: (Home) (up arrow) (PgUp) (left arrow) (right arrow) (End) (down arrow) (PgDn) to move blinking L 390 cursor. Note: Keys (up arrow) and (down arrow) move cursor vertically through variables Keys: (left arrow) and (right arrow) move cursor through independent variables only. The (tab)/(shift tab) and backspace keys moves the cursor to the next/previous variable. -> Cut and Paste (copying equations): !F @F !M @M !L @L These commands save equations in the immediate calc text buffer. This buffer is accessed by the | command and its L 400 contents are further saved in the immediate calc text stack. The contents of this buffer can be "pasted" into equations and other text fields while in the edit mode using the (alt 9) function. "!F" adds the immediate calc text buffer to the text stack, clears the immediate calc buffer and inserts all INACTIVE equations into it. Inactive equations have variable names that are not followed by an "=" sign. The immediate calc buffer can be inserted while in the edit mode using the (alt 9) function. L 410 Use A and I commands to activate/inactivate equations before using these commands. "@F" adds the immediate calc text buffer to the text stack, ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 10 -- clears the immediate calc buffer and inserts all ACTIVE equations into it. Active equations have variable names that are followed by an "=" sign. "!M" appends all INACTIVE equations to the immediate calc text buffer without appending to the text stack. L 420 "@M" appends all ACTIVE equations to the immediate calc text buffer without appending to the text stack. "!L" clears the immediate calc buffer of all text. The buffer is displayed with the | command. "@L" clears the immediate calc text stack. This stack is used to save the immediate calc buffer. L 430 -> Directories of *.EQU, *.STO and *.HLP: (F7) or * !* @* "(F7)" or "*" gives directory of *.equ in directory of specified path. "!*" gives directory of *.sto in directory of specified path. "@*"gives directory of *.hlp in directory of specified path. Enter path for desired directory in response to prompt. For example: (end esc) \project1\analysis (enter). A filename can be included in path but it must have a period. For example (end esc) \calc\*.dat (enter) or \calc\beta???. If no extension, then the default extension is used. Use cursor L 440 keys to locate file and (enter) to select. Program will always load file as EQU, STO or HLP even if extension differs from default. Use (esc) or (ctrl Q) to exit. Use "(space)" to get information about the current highlighted file. -> Designate coordinate variable O - Designate an independent variable as the coordinate for the X-axis of a plot. One or more equations can be plotted vs. a single coordinate. A ":" designates a coordinate and will L 450 appear in place of the "=". Use A or I to change status to active or inactive as required. -> Display all 16 digits of variables value \ - Display the full 16 digit precision and position the cursor for editing the number. Type (enter) to return to the blinking cursor. For example, to subtract 1000 from the current number, type "\", and type (end) -1000 (enter). After typing "\", the cursor is always positioned at beginning of number. Type (end) L 460 ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 11 -- to move the cursor to the end of the number and (esc) to clear the number. Always type (enter) to perform a calculation or exit. -> Display entire comment: (comma key) Type the comma from the equations display in order to see the entire text of the comment. If the comment ends in "...", then it was terminated because of a lack available screen space. If the "||" pairs are used within a lengthy comment L 470 then only the part enclosed by the || is displayed. If a double single quote '' is used, then only the part before the '' is displayed. In these cases, use the comma command to display the full text. Type any key to return to the main equation display. -> Display/remove storage variables: Y !Y @Y Z !Z @Z "Y" displays the name and value of storage variable, if any. Repeat "Y" to toggle to previous storage variables and so on. L 480 "!Y" displays the current storage variable without toggling. "!Z" has the same functions as "!Z". "@Y" removes all storage variables. Program will prompt "? equations" to check for any references to the erased storage vars. If present, they now become independent vars. "Z" displays the name and value of storage variable, if any. Repeat "Z" to toggle to next storage variable and so on. Up to 256 storage variables can be entered with user-defined names. For example: =PI=3.1415926 (enter) (spc) DATA1=: (ent) Always start first with "(space)" or "=" because most commands begin with letters. "!Z" like "!Y" L 490 displays the current storage variable. Use "@Z" to remove the current storage variable. If a storage variable is removed, the immediate calc buffer (command "|" ) is assigned: VARNAME = value. To restore storage var or assign value to storage var which has become independent var, type "|" (enter). Storage variables are not displayed like other variables. To display the value of any storage variable, type (space) VARNAME= (enter). The storage-index counters are positioned on this variable. Type "!Z" to check and type "@Z" to remove, if necessary. Type "|" to recall this calc, if it needs to be L 500 recovered. -> DOS shell: !E @E "!E" executes DOS command and then returns control to program. Type the DOS command in response to the prompt. "@E" shells by ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 12 -- exiting to DOS. The program is still memory resident. Enter DOS commands and other operations. Must type EXIT (enter) to return to program. L 510 -> Edit an individual equation: @/ "@/" edits a single equation and updates the immediate calc buffer with that equation. Move cursor to dependent var of desired equation and type "@/". To inspect and return to equation display without changes, type "(esc)" or "(ctrl Q)". To update, type changes followed by "(enter)". To remove equation, type the null string "" (enter). Can also be used to copy and/or move equation. See "Entering Equations", below. "@/" always causes immediate calc ( | ) to be updated. L 520 -> Entering comment: (F5) / Use "(F5) or "/" to enter or modify a comment only. Comment can contain up to 1840 characters (23 lines). Use "||" pairs to designate segment of comment to be displayed. If the text is "first part || second part || third part" then the displayed comment will be "second part". Use the double single-quote "''" to indicate the end for the displayed comment. If the text is "first part''second part" then only "first part" is L 530 displayed. A double single-quote "''" or four "|" at beginning of text: "'' rest of text" or "|||| rest of text", suppresses comment. To view entire comment, type (comma key). Type any key to exit. The amount of the displayed comment depends on number of equations/variables. Quotes are not required for strings but may be needed to prevent string compression or loss of desired spaces. Complete equations and comment are save with screen dump. See command "V" for more details. -> Entering equations: (F6) !/ L 540 Type "(F6) or "!/" to enter 1 or more equations. Equations are entered in BASIC symbolism. Leave at least one space between each equation. Read rules discussed below. Total equations can contain up to 1840 characters (23 lines). Current maximum of 63 equations with up to 66 independent and dependent variables. -> Entering number without calculating main equations: (ctrl enter) L 550 To enter a number into a variable of the main equations without calculating the dependent variables type the number and ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 13 -- terminate it with (ctrl enter) instead of (enter). -> Escaping from the "? Enter Equation(s)" prompt. If the equations contain only constants, then typing (esc) will result in program termination. For example, starting with ASOL3 45.19+56.78+89.34 (enter) and then typing (esc) will get to the "? Enter Equation(s)" prompt. L 560 Typing (esc) now will terminate the program. In some situations, the (ctrl Q) or (esc) sequences may not return to the equations display. This event will usually occur when a previously-entered valid equation does not exist. For example, if the program is started with an improper equation entered on the DOS command line, then one must either correct the equation or type (end esc) then "" (enter) to load the default equations. To exit from the program while in the edit mode, one must use the apostrophe command: 'exit (enter). L 570 -> Exit program: E Use "E" to exit from the program. If equations or storage need to be saved, the program will inform you. Save them immediately because the use of "E" clears the reminders. If necessary type "E" a second time to exit. Type Y (enter) to exit/terminate. or N (enter), "(enter)", "(ctrl Q)" to return to equation display. L 580 -> Generate "Definition of variables" template as comment: ! (comma) "! (comma)" will generate a comment which is a template of variable names each followed by the define character "≡". The comment must be empty for this to happen. If the comment contains text, set it to a null comment by typing (F5) then (end esc) "" (enter) or type the apostrophe command 'com "" (enter). If the equation is y=m*x+b then the comment will look something like: Definition of variables. Y ≡ L 590 B ≡ M ≡ X ≡ Type (F5) to edit the comment and type in the meanings of the variables. -> Get/save file of equations: (F8) [ (F9) ] ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 14 -- "(F8)" or "[" gets a file of equations and the values of variables. Enter the path/filename followed by "(enter)" in L 600 response to prompt. "(F9)" or "]" saves a file of the equations and the values of variables. These two commands save equations, dep and ind vars but not storage vars. Filenames can be specified with paths. For example: \data\results.001, \project\z21\analysis.equ, d:\appl\line.equ. Default extension for equation files is ".EQU". Use "." at end of filename if does not have extension. For get operation, if .HLP is the extension, then program will re-initialize and attempt to read file as application file. The extension .HLP cannot be used with a filename for the save (F9) operation. L 610 -> Get/save file of storage variables: ![ !] Use "![" to get a file of storage variables and values only. Note: Use "!*" to generate a directory on the screen from which the name of an existing file can be located and selected. Use "!]" to save a file of storage variables and values only. Default extension for storage files is ".STO". Use "." at end of filename if does not have extension. If .HLP is the extension, then program will re-initialize and attempt to read L 620 file as application file. -> Help files: Using on-line help file, user-manual help file and application help file. To use the on-line help file, type (F1) or the letter "H". To use the on-line user-manual, type "!H" or type (F2) and enter its name. To use the application help file type "(F2)" or "@H". Type the name followed by "(enter)". After reading the application help file, to get the program to prompt for a new L 630 name, first type "@C" to display version number or type "(F1)" to access the on-line help file. Type "(esc)" or "E" to exit and then type "(F2)". Set DOS environment variable ASTRO3 to the path where ASOL3HLP.HLP can be found prior to running this program. Summary: (F1) or H Read on-line condensed help file ASOL3HLP.HLP. L 640 !H Read on-line user-manual help file ASOL3MAN.HLP. (F2) or @H Read application help file *.HLP. Enter filename in response to prompt. If found, program will not ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 15 -- prompt unless (F1), H, !H or @C is typed. -> Inactivate variable: I !I @I "I" inactivates an equation or variable. The "=" will disappear. Used to indicate dummy eqns for D, G and U. L 650 Inactive equations are not plotted. "!I" inactivates all dependent or independent variables at once. The location of the cursor determines which set. "@I" inactivates all variables at once. Also use the apostrophe command 'INA varname (enter) for the same purpose. See below for more details. Use the commands "A", "!A" or "@A" to activate an equation or variable. -> Inspect a too-long-to-display equation L 660 Move the cursor to the desired equation, type "@/" and type "(esc) (enter)" or "(ctrl Q)" to exit to the equation display without any changes. Remember that the immediate calc buffer (command "|") now contains this equation and it can be dumped with the "(alt 9)" command in the edit mode. -> Modify an equation: @/ Move the cursor to the desired equation, type "@/" and make changes. Type "(enter)". Remember that the immediate calc L 670 buffer (command "|") now contains the original equation. -> Multiple calculations: apostrophe command 'IMM The apostrophe command 'IMM allows multiple calculations to be performed from the main equation display. These calculations can reference any defined variable and if a calculation results in the creation of a new variable it is assigned as a storage variable. The main display equations are not evaluated during/after these calculations. For example the immediate L 680 calc: 'IMM y=sqr(2*x)+b z=2*y (enter) would assign variables Y and Z the results of these calculations. The immediate calc buffer is updated following this calculation. The ":" implies the value of the variable the cursor resides on. For example the immediate calc: 'imm sqr(2*:+45) (enter) would use the value of the variable the cursor is on and would assign the result to this variable. -> Plot equation: P L 690 ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 16 -- "P" plots the active equation(s) vs. coordinate. See below for a complete discussion of the additional commands that can be used while the plot screen is displayed. The cursor should reside on the independent variable to be the coordinate of the x-axis, if some var is not already designated. A coordinate variable has a ":" following its name. -> Printer initialization: !P @P Use "!P" to initialize printer for NLQ (double strike) L 700 printing. Use "@P" to reset printer and cancel NLQ printer. -> Program name and version number: @C Use "@C" to recalculate with the program name and version #. -> Recalling last immediate calculation: | "|" displays the last immediate calculation and position the cursor after an imbedded apostrophe ('). Use edit keys to L 710 change a calculation and use (enter) to execute. Use (alt 9) to insert the current immediate calc before the cursor when in the edit mode. Use (alt 4) and (alt 5) to toggle to previous calculations saved on the immediate calc text stack. The "|" command allows a single calculation to be entered and the main display equations are evaluated after this calculation. On the other hand, the immediate calc apostrophe command 'IMM allows multiple calculations to be entered and the main display equations are not evaluated during/after these calculations. L 720 -> Reference to current value of variable in calculations Use ":" to designate the current value of variable on which the cursor resides while entering an immediate calculation. For example, if the cursor is on variable A which currently equals 10, then typing 2*:+6 (enter) will result in A being set to 26. -> Remove an equation: @/ Move the cursor to the desired equation, type "@/" and type L 730 (end esc) "" (enter). Remember that the immediate calc buffer (command "|") now contains the original equation. Should you wish to add it back, type "(F6) or "!/" to edit equations, locate cursor and type "(alt 9)" to insert it before the cursor. ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 17 -- -> Repetitive calculations without variables To perform repetitive calculations without variables such as adding and subtracting numbers, get to the "-- ? Equations(s)" L 740 prompt by typing (F6) or "!/". Type (end esc) to clear the field. Enter the calculations such as 23.45+46.78-32.00 (enter). The text of the calculations is now stored on the immediate calc text stack. Use the (alt 4) and (alt 5) keys to toggle back and forth to previous calculations. The (alt 6) key is used to insert the entire immediate calc text stack into the present calculation and the (alt 7) key is used to replace the current calculation with the entire contents of the immediate calc text stack. To exit the Program, type (end esc) "" (enter) to return to equation display and then type "E". L 750 -> Saving equation in immediate calc text buffer: !| "!|" replaces immediate calc buffer with the equation on which cursor resides and updates the immediate calc text stack with the previous contents. -> Saving comment in immediate calc text stack: @| "@|" replaces immediate calc buffer with comment and updates L 760 immediate calc text stack with the previous contents of the buffer. One can use "@|" to transfer equations/values from the comment to the equations and or variables. Once the comment is on the immediate calc text buffer it can be recalled in the edit mode by using (alt 4) and (alt 5) keystrokes. The text can be edited to select what is desired. -> Screen dump to text file: V "V" dumps the equations display (or the plot) to a text file. L 770 Used to save calculations or plots for inclusion in reports, etc. Program name and date/time are appended. The complete equations, comment and values/status of the variables are appended at the end in the 'EQU format. These files can be used to build a user-generated application file. Enter filename in response to prompt. Note: Filenames ending in numeric extensions from "000" to "999" are automatically incremented each time the command is used. Thus, SCRN.001 --> SCRN.002 --> SCRN.003 and so on. Filenames can be specified with paths. For example: \data\calc.001, L 780 \project\p23\screen.056, d:\appl\calc10.new If a file already exists, the program will prompt to "APPEND" or to "REPLACE". ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 18 -- -> Set all variables to same value: ? !? @? "?" sets values of all variables to a constant. Active/inactive status of variables not affected. Use "!?" to set all dependent or independent variables only. The location of the cursor determines which set. Use "@?" to set all variables to a constant and to change status of all variables L 790 to active. Constant may be explicitly specified or be the current value of any variable or the result of a simple calculation such as 2*A. -> Turn sound on/off: !B @B "!B" turns beeping sound "on" at various locations in program. "@B" Turns beeping "off" at most places including warnings. The default is sound "off". L 800 -> Universal quit: (ctrl Q) "(ctrl Q)" will cause control to return to the equation display but only if valid equations exist in the program. "The universal quit". Use the (ctrl Q) anywhere to get back to a familiar part of the program which is usually the main equation display. ╒═══════════════╕ │ F1 - F10 KEYS └─────────────────────────────────────────────────────── L 810 1.05 F1-F10 Keys, Commands assigned. ──────────────────────────────────────────────────────────────────────── Key Command Purpose F1 help Access on-line help file ASOL3HLP.HLP F2 appl help Access application on-line help file. L 820 F3 exit Exit from program F4 shell Shell to DOS, type exit (enter) to return. F5 comment "? comment" prompt F6 equation "? equation" prompt. ---------------------------- 1.05 -- F1-F10 Keys, Commands assigned. --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 19 -- F7 directory "Directory of *.EQU" prompt. L 830 F8 get file Get a file of equations (*.equ) F9 save file Save the current equations (*.equ) F10 prod info List product information. ╒════════════════════╕ │ SPECIAL OPERATIONS └────────────────────────────────────────────────── 1.06 Command Sequences Used to Perform Special Operations L 840 ──────────────────────────────────────────────────────────────────────── -> Saving and inserting one or more equations into existing equations. 1) Type @L to clear immediate text stack. 2) Move cursor to each equation. Type !| 3) Type !/ to edit equations. L 850 4) Mover cursor to place for insert, type (alt 6). Remember: all dependent vars must have different and unique names to first 8 characters. Edit as necessary. 5) Type (enter) to load equations and return to main equation display. ╒══════════════╕ │ EDITING KEYS └──────────────────────────────────────────────────────── L 860 1.07 Editing Keys: Functions During Text Entry ──────────────────────────────────────────────────────────────────────── Editing keys can be used whenever the underscore cursor "_" is flashing on the screen. At these instances, any character above the cursor will also blink. A summary of the editing keys follows. (esc) - Clear the entire text, line or number. If cursor on first position of field, specifies the escape sequence (ctrl Q) L 870 discussed below. Note, if the program is started with an improper equation, either correct the equation or type (end esc) then "" (enter) to load the default equations. ------------------ 1.07 -- Editing Keys: Functions During Text Entry --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 20 -- (backspace) - Delete character directly in front of cursor. (tab) - Move cursor 5 characters to right. (shift tab) - Move cursor 5 characters to left. L 880 (home) - Move cursor to beginning of text. (ctrl) (home) - Delete all before cursor to beginning of text. (ctrl) (PrtSc) - Redraw all lines of the current text. (arrow up) - Move cursor one line up, if possible. (arrow left) - Move cursor one character to left. L 890 (ctrl) (arrow left) - Move cursor 5 characters to left. (arrow right) - Move cursor one character to right. (ctrl) (arrow right) - Move cursor 5 characters to right. (end) - Move cursor to end of text. (ctrl) (end) - Delete all from cursor to end of text. L 900 (arrow down) - Move cursor one line down, if possible (ins) - Insert text before cursor. Toggle on and off. (del) - Delete character at cursor. In insert mode (large cursor), the cursor character is deleted and the entire remaining text is shifted left. In the replace mode (small cursor), the cursor character is deleted but only text on the current line is shifted left. L 910 (enter) - Used to terminate a string of information which is to be entered into the program. (ctrl enter) - Same function as enter but prevents the program from calculating the main equations when appropriate. (ctrl Q) - Quit entry, erase information and return back into the program. Used to return to program if the wrong command was typed. "The universal quit". L 920 ------------------ 1.07 -- Editing Keys: Functions During Text Entry --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 21 -- (alt 1) - Fill current line to end with spaces (if necessary) and move cursor to the next line. Used to provide the "carriage return" function in the text edit mode. (alt 2) - Split line at cursor. To insert a blank line, position cursor on start of line and type (alt 2). Line is inserted before cursor. (alt -) Join function. Cursor must be on space (blank). The opposite of the split function (alt 2). Removes the cursor L 930 blank and all following blanks up to first non-blank character across the entire text. (alt 3) - Add all remaining lines and fill with spaces. This is essentially full-screen edit because information can be enter anywhere in the allowed field. (alt 4) - Toggle to previous calculation or text stored in the immediate calculation text stack and replace current text. Note: If a mistake occurs, type (ctrl Q) to exit. The imm L 940 calc text stack is updated with information from the immediate calculation, command |. (alt 5) - Toggle in opposite direction to that of (alt 4). (alt 6) - Insert the entire text of the immediate calculation text stack before the cursor. (alt 7) - Replace current text with entire contents of immediate calculation text stack. L 950 (alt 8) - Clear all text from immediate calculation text stack. (alt 9) - Insert the text of the last immediate calculation before the cursor. The immediate calculation is command |. ╒════════════════╕ │ EQUATION ENTRY └────────────────────────────────────────────────────── 2.01 Entering Equations Into the Program L 960 ──────────────────────────────────────────────────────────────────────── An equation or a series of equations is entered into the program in response to the prompt "-- ? Equation(s) -->". While the screen is displaying the equations, type (F6) or "!/". Use the edit keys, as discussed above, to enter the ------------------------ 2.01 -- Entering Equations Into the Program --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 22 -- equations. In particular note that the "(end esc)" key clears the screen. Following a successful evaluation of the equations, the program will prompt "-- ? Comment -->". At this time a comment can be added to describes the equations, L 970 their use, meaning of of variables, etc. Double quote marks are required to preserve string spacing. To clear away an old comment type (end esc) "" (enter). The "" signifies an empty or null character string. To enter three equations, one might type (F6) then: (end esc) y1=a+b+c y2=a-b-c y3=a-b+c (enter) Next, to enter a comment, one might type: L 980 (end esc) "Three equations with three unknowns." (enter) Note: The string does not have to be enclosed in quotes, however if quotes are used, make sure that there are 2 -- one at each end! If one enters equations without any independent variables, then the program will perform the calculations and prompt "? Equation(s)". For example, one can enter a series of equations: L 990 (end esc) y1=1+2+3 y2=1-2-3 y3=1-2+3 (enter) The values of y1, y2 and y3 are remember and can be referenced in the next calculation. For example: (end esc) y1=y1-10 y2=y2-20 y3=y3-30 (enter) Also, more than one calculation can be performed if expressions are enclosed in parentheses. For example: L 1000 (end esc) (1-45) (23+45+67) (sqr(4/98)) (enter) Use the (ctrl Q) keys to abruptly and immediately terminate anything! ╒═══════════════════╕ │ WRITING EQUATIONS └─────────────────────────────────────────────────── 2.03 Writing Equations: Definition of Terms L 1010 ──────────────────────────────────────────────────────────────────────── --------------------- 2.03 -- Writing Equations: Definition of Terms --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 23 -- Before any further discussion of equations and their evaluation, the user should become familiar with the following terms: ■ EQUATION: A symbolic recipe for calculating a number associated with a dependent variable. An equation consists of a dependent variable followed by an equal sign and ending with a series of mathematical operations involving constants, L 1020 independent variables, functions and dependent variables. An INCONSISTENT EQUATION is one in which the final value of the dependent variable depends on its initial value in some way. Counters, such as COUNT=COUNT+1, and summers, such as TOTAL=TOTAL+X, are good examples. ■ DEPENDENT VARIABLE: A name, beginning with a letter, which identifies a variable whose value is calculated. The dependent variable usually appears to the left of the equal sign but it may also appear to the right in certain cases. Each equation L 1030 must have a unique name for its dependent variable. ■ INDEPENDENT VARIABLE: A name, beginning with a letter, which identifies a variable whose value is assigned. The value of an independent variable usually does not change as the result of a calculation. An independent variable always appears to the right of the equal sign. ■ STORAGE VARIABLE: A variable which is used similarly to an independent variable and is created as the result of an L 1040 assignment statement. For example, an assignment statement might be PI=3.1415926 and an equation using PI might be AREA=PI*RADIUS^2. The values of the storage variables are saved independently of the dependent and independent variables. ■ CONSTANT: A number whose value is explicitly defined and does not ever change. Numbers may be in the integer format (no decimal point), decimal format or floating (exponential) format. Some examples are: L 1050 INTEGER: -50, 100, 0 DECIMAL: -49.95, 99.67, 0.0 FLOATING or EXPONENTIAL: -1E-3, 1.674E+6, 0.0E0, 3.2D-3 Note: E-3 or D-3 means 10^-3 ■ FUNCTION: A special mathematical recipe that has an argument --------------------- 2.03 -- Writing Equations: Definition of Terms --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 24 -- enclosed in parentheses. A special number is calculated from the value of the argument. See help file for more details. L 1060 For example: E=M*C^2 AVERAGE=(ITEM1+ITEM2)/ABS(N) Y=3*COS(X)^2-1 Dependent variables: E, AVERAGE, Y Constants: 2, 3, 1 Independent variables: M, C, ITEM1, ITEM2, N, X Functions: ABS(...), COS(...) Math operations: * (multiplication), ^ (power), + (addition), / (division) L 1070 - (subtraction) Note: Parentheses specify the order of the calculation. All equations begin with a dependent variable, whose value is calculated by the equation. The dependent variable is followed by an equal sign "=". Following the "=" sign are a collection of constants, independent variables, dependent variables and functions. Pairs of parentheses are used to group terms and to specify the the order of a given calculation, especially when L 1080 the desired order opposes the default priorities discussed below. More than one equation can be entered in response to the "? Equation(s)" prompt. If you enter more than one equation, you should be careful with the use of spaces! The equations, including spaces, cannot exceed 1840 characters (23 lines). An example of a group of equations is: H=1+C*R1*R2/(R1+R2) L 1090 A=20*LOG(X^(2*Y)) E=P*(A-D)/2 REL_MIN=SQR(1+DMIN^2) EMAX[Q]=-LOG10(SQR(1-Q^2)) Dependent variables: H, A, E, REL_MIN, EMAX[Q] Constants: 1, 20, 2 Independent variables: C, R1, R2, X, Y, A, D, DMIN, Q Functions: LOG(...), SQR(...), LOG10(...) L 1100 Math operations: + (addition), * (multiplication), / (division), ^ (power) - (subtraction), - (negation) --------------------- 2.03 -- Writing Equations: Definition of Terms --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 25 -- ╒════════════════╕ │ EQUATION RULES └────────────────────────────────────────────────────── 2.10 Rules for Writing Algebraic Expressions, Formulas and Equations L 1110 ──────────────────────────────────────────────────────────────────────── Algebraic expressions, formulas and equations are virtually identical mathematically and will all be collectively called "equations" in this Manual. The rules for writing equations are fairly universal. Equations are entered using the conventions found in the BASIC computer language. In particular, the user should note that an implied multiplication is not allowed. Thus AB would be interpreted as a variable name and A*B, as multiplication. Also, operations of equal L 1120 priority always execute from left to right. The rules are: ■ All variable names must begin with either an English capital letter. (Lower case letters will be converted to upper case) or a Greek letter such as α, ß, Γ, π, Σ, σ, µ, τ, Φ, Θ, Ω, or δ. To enter these Greek letters use the keypad numbers. Hold down the (alt) key and type the following ASCII codes on the keypad and then release the (alt) key. α 224, ß 225, Γ 226, π 227, Σ 228, σ 229, µ 230, τ 231, Φ 232, Θ 233, Ω 234, δ 235. Variable names such as AMAX, EMIN, TIME_OF_DAY, F[T] are ok but L 1130 123ABC is invalid. The remaining characters can be any ASCII characters with values greater than ASCII 32 which is the "(space)". For example, "R║" and "R┴" may be used to define variables where the ║ (ASCII 186) conveys "parallel" and the ┴ (ASCII 193) conveys "perpendicular". If an embedded space is desired, use ASCII 255 which is the "alternate" blank. Note, the "normal" space (ASCII 32) is a separator. ■ Variable names can be any length of characters but only the first 8 are significant. Thus variable names such as MINIMUM_, L 1140 MINIMUM_HEIGHT, MINIMUM_VALUE and MINIMUM_LENGTH are all equivalent. ■ Variable names must be different from the names of the intrinsic functions described above. Thus Y=SINZ+LOGQ would be ok but Y=SINH*LOG is invalid because SINH and LOG are the names of intrinsic functions. The names of the intrinsic functions are reserved words. Don't use them for the names of variables! ■ Equations must begin with the name of a single dependent L 1150 ---------- 2.10 -- Rules for Writing Algebraic Expressions, Formulas --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 26 -- variable. If a group of equations is entered, each equation must have a dependent variable with a unique, different and allowed name. For example, Y1=A+B Y2=A-B not Y=A+B Y=A-B. ■ The dependent variable must be followed by an equal sign and the remainder of the equation. Intervening spaces are ok. For example: Y=M*X+B not Y-B=M*X. Operations are not allowed to the left of the equal sign. See other rules below. ■ Spaces and commas are allowed within the equation(s). Most L 1160 are ignored and removed by the program. Use them in numbers for ease of entry: 1,000,000 or 1 000 000 or 1000000. Y = 2,000 * ( X + 3 0 * Z ) is equivalent to Y=2000*(X+30*Z). If exponential notation is used in a number then the "E" or "D" must immediately follow the last digit of the number. Thus, 1.45E-2, 1 . 4 5E - 2 and 1.45E -2 are equivalent but 1.45 E-2 signifies two equations: The first contains the number 1.45 and the second, the variable E minus 2. Separate all equations by at least one space. L 1170 ■ There must be at least one constant, independent variable or dependent variable to the right of the equal sign. For Example: Y=3, Z=X, W=SIN(0.7), A=A+1. A single equation with only constants to the right of the equal sign, such as Y=SQR(4)+ABS(-3), is calculated and then the program prompts for a new equation. ■ Parentheses must always be matched. They must always occur in pairs. For example: Y=(3*X)-2 and Y=3*(X-2) not Y=LOG(SQR(1-X^2). L 1180 ■ An empty pair of parentheses is not allowed. Y=SIN() and Y=3+()-4 are not allowed. ■ Independent variables with the same names, that are used in different equations, always share the same memory locations. Their values are always in common to all equations. To make an independent variable unique, it should be given a unique name. ■ If a group of equations is entered, the first equation is the L 1190 "nearest to start" of the string and the last equation is the "nearest to end". Calculations proceed from the first equation to the last. For example, a group of equations might be: N=N+1 YTOTAL=YTOTAL+X ---------- 2.10 -- Rules for Writing Algebraic Expressions, Formulas --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 27 -- YAVE=YTOTAL/N Each time that a calculation is made, the following happens. The current value of N, a counter, will be increased by 1. To L 1200 the current value of YTOTAL is added the value of X. The average value, YAVE, is calculated as YTOTAL divided by N. "N" and "YTOTAL" are termed inconsistent equations because they do not represent math equalities. ╒═════════════╕ │ PARENTHESES └───────────────────────────────────────────────────────── 2.15 Rules for Evaluation of Parentheses ──────────────────────────────────────────────────────────────────────── L 1210 ■ Nested parentheses, that is, parentheses within parentheses, are evaluated from innermost to outermost matched pairs. For example, if Y=ABS(5+LOG10(3*X+2)-6) then 3*X+2 would be performed first, then 5+LOG10(..)+6, then ABS(...). If Y=(((X+1)/2)*3)+4, then X+1 would be performed first, then /2, then *3, then +4. ■ Matched parentheses are always evaluated from left to right. For example: if Y=(3+X)+(4-X)/(X^2-1) then 3+X would be L 1220 performed first followed by 4-X and X^2-1. Finally, the results of the last two parentheses would be divided and that result added to the first parentheses. ■ The maximum number of pairs of parentheses in any equation is 128 and parentheses may be nested in any depth up to 128. ╒════════════════════╕ │ BUILT-IN FUNCTIONS └────────────────────────────────────────────────── L 1230 2.20 Rules for Evaluation of Intrinsic Functions ──────────────────────────────────────────────────────────────────────── ■ The names of the intrinsic functions are reserved words and these names cannot be used as the names of variables. For example, Y=SIN(X) is ok but Y=SIN+X is not allowed. ■ Operations within a function are always performed prior to the evaluation of that function. For example if Y=SIN(2*PI*X) then the order of evaluation would be 2*PI*X and then SIN(...). L 1240 ■ Nested functions are always evaluated from innermost to ---------------- 2.20 -- Rules for Evaluation of Intrinsic Functions --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 28 -- outermost function. For example if Y=LOG(ABS(SIN(X))) then the order of evaluation would be SIN(...) then ABS(...) then LOG(...). ■ Functions are evaluated from left to right. For example, if Y=SIN(X)+COS(X)+LOG(X) then the order of evaluation would be SIN(...) then COS(...) then LOG(...). L 1250 ╒═════════════════╕ │ MATH OPERATIONS └───────────────────────────────────────────────────── 2.25 Rules for Evaluation of Mathematical Operations ──────────────────────────────────────────────────────────────────────── ■ Highest priority: power (exponentiation) Y=X^2 leading negation Y=-X multiplication, division Y=3*X, Y=X/4 lowest priority: addition, subtraction Y=X+10, Y=X-7 L 1260 ■ Operations of the same priority are evaluated from left to right. For example: Y=2^2^3 (=64, not 256!) Y=8+4/4-2*5 (=-1, not 5!) Y=-4^2 (=-16, not 16!) Y=2+4*2^2/4 (=6, not 36!) ■ Parentheses can be used to change the order of mathematical L 1270 operations. For example: Y=2^(2^3) (=256, not 64!) Y=((8+4)/4-2)*5 (=5, not -1!) Y=(-4)^2 (=16, not -16!) Y=((2+4)*2)^2/4 (=36, not 6!) ■ Redundant or superfluous operations will be simplified and/or eliminated from the equations. These operations usually include multiple combinations of the "+" and "-" with L 1280 themselves or other operators. For example: Y=-+A or Y=+-A --> Y=-A Y=--A or Y=++A --> Y=A Y=A^-+2 or Y=A^+-2 --> Y=A^-2 Y=10/+A --> Y=10/A Y=A*+50 --> Y=A*50 Y=-+-+-+A --> Y=-A ------------ 2.25 -- Rules for Evaluation of Mathematical Operations --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 29 -- ╒════════════════╕ L 1290 │ MATH FUNCTIONS └────────────────────────────────────────────────────── 2.30 Glossary of Intrinsic MATH FUNCTIONS and Function Operators ──────────────────────────────────────────────────────────────────────── The program contains intrinsic mathematical functions which perform well-know calculations based on the value of their arguments. All functions have names which start with a letter and contain from 3 to 5 characters. The name is followed by an L 1300 argument which may be a simple constant, a variable or an expression. The argument is always enclosed in a matched set of parentheses. For example: Y=SIND(45) has a constant, 45, as the argument. Y=ALOG(X) has a variable, X, as the argument. Y=ABS(4*X-6) has an expression, 4*X-6, as the argument. Y=SQR(ABS(X)) has another function, ABS(...), as the argument. Functions are "built in" recipes for performing well-known mathematical operations which are described below. The argument of a function may be a number or an expression which L 1310 is always enclosed in parentheses. Function operators are 2 letter suffixes attached to numbers. Thus SIND(45) and 45SD are equivalent. Function operators can be attached to any number except the constants in equations entered in response to the prompt "-- ? Equation(s) -->". There are one-to-one correspondences between functions and operators. The allowed functions and function operators and their uses are: Op Function Purpose L 1320 AB ABS(X) The absolute value of X. If X > or = 0 then ABS(X)=X, but if X<0 then ABS(X)=-X. op: -5AB 10AB -20AB func: Y=ABS(-5), Y=5. Y=ABS(10), Y=10 OC ACOS(X) The inverse cosine of X. The result is in radians. ABS(X) must always be < or = to 1.0. op: 1OS 0OC .5OC func: Y=ACOS(1), Y=0. Y=ACOS(0), Y=1.570796 L 1330 DC ACOSD(X) The inverse cosine of X. The result is in degrees. ABS(X) must always be < or = to 1.0. op: 1DC 0DC -.61DC func: Y=ACOSD(1), Y=0. Y=ACOSD(0), Y=90 ---------- 2.30 -- Glossary of Intrinsic MATH FUNCTIONS and Function --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 30 -- HC ACOSH(X) The inverse hyperbolic cosine of X. X must always be > or = to 1.0. op: 1.54308HC 1HC 2HC func: Y=ACOSH(1.54308), Y=1. Y=ACOSH(1), Y=0 L 1340 IS ASIN(X) The inverse sine of X. The result is in radians. ABS(X) must always be < or = to 1.0. op: 1IS 0IS .707IS func: Y=ASIN(1), Y=1.570796. Y=ACOS(0), Y=0 DS ASIND(X) The inverse sine of X. The result is in degrees. ABS(X) must always be < or = to 1.0. op: 1DS 0DS .707DS func: Y=ASIND(1), Y=90. Y=ASIND(0), Y=0 L 1350 HS ASINH(X) The inverse hyperbolic sine of X. op: 1.17520HS 0HS 1.5HS func: Y=ASINH(1.17520), Y=1. Y=ASINH(0), Y=0 AT ATAN(X) The inverse tangent of X. The result is in radians. op: 1AT 0AT 2AT func: Y=ATAN(1), Y=.7853982. Y=ATAN(0), Y=0. DT ATAND(X) The inverse tangent of X. The result is in degrees. op: 1DT 0DT 2DT L 1360 func: Y=ATAND(1), Y=45. Y=ATAND(0), Y=0 HT ATANH(X) The inverse hyperbolic tangent of X. X must always be > -1.0 and < 1.0 op: 0.76159HT 0HT -.435HT func: Y=ATANH(0.76159), Y=1. Y=ATANH(0), Y=0 CI CINT(X) Convert X to an integer by rounding. The absolute value of X must always be less than 1E16 for this to be a meaningful calculation. L 1370 op: -5.75CI 12.65CI 4.567CI func: Y=CINT(-5.75), Y=-6. Y=CINT(12.65), Y=13. CO COS(X) The cosine of X. X is in radians. op: 0CO 1.7CO -.567CO func: Y=COS(0), Y=1. Y=COS(1.570796), Y=0. CD COSD(X) The cosine of X. X is in degrees. op: 0CD 90CD 45CD func: Y=COSD(0), Y=1. Y=COSD(90), Y=0 L 1380 ---------- 2.30 -- Glossary of Intrinsic MATH FUNCTIONS and Function --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 31 -- CH COSH(X) The hyperbolic cosine of X. op: 1CH 0CH 0.567CH func: Y=COSH(1), Y=1.54308. Y=COSH(0), Y=1 DE DECM(X) The signed decimal fraction of the number X with no rounding. op: -123.456DE 456.789DE 789.123DE func: Y=DECM(-123.456), Y=-.456 Y=DECM(456.789), Y=.789 L 1390 Can be used to calculate the MOD(X) to base Z which may be decimal. Use Y=Z*DECM(X/Z). Y=16*DECM(19/16), Y=3 Y=.5*DECM(1.3/.5), Y=.3 EX EXP(X) The natural or Naperian antilog, base "e". op: 1EX 0EX .51534EX func: Y=EXP(1), Y=2.71828. Y=EXP(0), Y=1. FA FACT(X) Factorial of X. X may be a signed integer or decimal. FACT(6) = 6 * 5 * 4 * 3 * 2 *1 L 1400 X=0, FACT(0)=1 X>0, FACT(X)= X*(X-1)*(X-2)....*1 X<0, FACT(X)= X*(X+1)*(X+2)....*-1 op: 4FA=24, -4FA=24, 3FA=6, -3FA=-6, 0FA=1, 1FA=1 -3.3FA=-9.867, -4.3FA=+42.4281 func: Y=FACT(4), Y=24. Y=FACT(-3), Y=-6. FI FIX(X) Truncate X to an integer. No rounding. The value of X must always be less than 1E16 for this to be a meaningful calculation. L 1410 op: -5.75FI 12.65FI 4.567FI func: Y=FIX(2.3), Y=2. Y=FIX(-56.70), Y=-56. LN LOG(X) The natural or Naperian log of X. X must be greater than 0.0 op: 2.71828LN 1LN 6.784LN func: Y=LOG(2.71828), Y=1. Y=LOG(1), Y=0. LG LOG10(X) The log, base 10, of X. X must be > 0.0. op: 10LG 1LG 1002LG L 1420 func: Y=LOG10(10), Y=1. Y=LOG10(1), Y=0. NZ NZE(X) The "not zero" function. If X=0 then X=10^-30, a very small number. Useful in division to prevent divide by zero errors. op: 0NZ 1NZ .000001NZ ---------- 2.30 -- Glossary of Intrinsic MATH FUNCTIONS and Function --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 32 -- func: Y=NZE(0), Y=1D-30 Y=NZE(1D-15), Y=1D-15 RA RAND(X) Generates a random number from 0 to 1. The argument X controls the seeding: L 1430 X<0 reseeds the random number generator. X=0 repeats the last number generate. X>0 generates the next number in the sequence. op: -1RA, new sequence. 1RA, generates the next random number. func: Y=RAND(-1), new sequence. Y=RAND(1), generates the next random number. RN RND(X) Round the number X to two decimal places. Useful in financial calculations in order to round decimal L 1440 fractions to cents. op: 123.456RN -123.543RN 735.196RN func: Y=RND(123.456), Y=123.46 Y=RND(-123.543), Y=-123.54 To round to other numbers of decimal digits, use the function CINT. For example, to round X to 3 decimal places use CINT(1000*X)/1000. SF SFACT(X) "Skip" factorial of X. X may be a signed integer or decimal. Similar to FACT(X) except decrement is by L 1450 2.0. If X is an even integer than SFACT(X) is the product of the even integers and if X is an odd integer than SFACT(X) is the product of the odd integers. SFACT(6) = 6 * 4 * 2, SFACT(7) = 7 * 5 * 3 * 1 X=0, SFACT(0)=1 X>0, SFACT(X)= X*(X-2)*(X-4)....*(1 or 2) X<0, FACT(X)= X*(X+2)*(X+4)....*(-1 or -2) op: 6SF=48, -5SF=-15, 3SF=3, -3SF=3, 0SF=1, 1SF=1 -3.3SF=+4.29, -5.3SF=-22.737 L 1460 func: Y=SFACT(8), Y=384. Y=SFACT(-7), Y=105. SG SIGN(X) Returns the sign of the argument X. op: -123SG 0SG 256SG func: Y=SIGN(-123), Y=-1. Y=SIGN(0), Y=0. Y=SIGN(256), Y=1. SI SIN(X) The sine of X. X is in radians. op: 0SI 1.085SI .657SI func: Y=SIN(0), Y=0. Y=SIN(1.570796), Y=1. L 1470 SC SINC(X) The sinc function ( SIN(X)/X ) of X. ---------- 2.30 -- Glossary of Intrinsic MATH FUNCTIONS and Function --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 33 -- op: 0SI 3.0SC -9.9SC func: Y=SINC(0), Y=1. Y=SINC(4.9), Y=-0.200501 SD SIND(X) The sine of X. X is in degrees. op: 0SD 90SD 45SD func: Y=SIND(0), Y=0. Y=SIND(90), Y=1 SH SINH(X) The hyperbolic sine of X. L 1480 op: 1SH 0SH .56123SH func: Y=SINH(1), Y=1.17520. Y=SINH(0), Y=0 SQ SQR(X) The square root of the argument X. X must be > or = to 0.0 op: 144SQ 100SQ 256SQ func: Y=SQR(144), Y=12. Y=SQR(100), Y=10. SN SUMN(X) Summation of integers with sign. 0+1+2+3+...+X. If X<0 then SUMN(X)<0. If X is decimal than L 1490 SUMN(X) is intermediate between nearest integers. op: 5SN -6SN 5.5SN func: Y=SUMN(5), Y=15. Y=SUMN(6), Y=21. Y=SUMN(5.5), Y=17.875. TA TAN(X) The tangent of X. X is in radians. op: .815TA 0TA .312TA func: Y=TAN(3.15193/4), Y=1. Y=TAN(0), Y=0. TD TAND(X) The tangent of X. X is in degrees. L 1500 op: 45TD 0TD 60TD func: Y=TAND(45), Y=1. Y=TAND(0), Y=0 TH TANH(X) The hyperbolic tangent of X. op: 1TH 0TH .3765TH func: Y=TANH(1), Y=0.76159. Y=TANH(0), Y=0 UI UIF(X) The unit impulse (delta) function of X. If X = 0 then UIF(X)=1 or if X < 0 or X > 0 then UIF(X)=0. op: 0UI 6UI -56UI L 1510 func: Y=UIF(3), Y=0. Y=USF(X-6), X=6, Y=1, X=5, Y=0. UR URF(X) The unit ramp function of X. If X > 0 then URF(X)=X or if X < 0 or X = 0 then URF(X)=0. op: 0UR 6UR -56UR func: Y=URF(3), Y=3. Y=URF(X-6), X=6, Y=0, X=5, Y=0. US USF(X) The unit step function of X. If X > 0 or X = 0 then ---------- 2.30 -- Glossary of Intrinsic MATH FUNCTIONS and Function --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 34 -- USF(X)=1 or if X < 0 then USF(X)=0. op: 3US -6US -56US L 1520 func: Y=USF(3), Y=1. Y=USF(X-6), X=7, Y=1, X=5, Y=0. ╒════════════════╕ │ NUMBER FORMATS └────────────────────────────────────────────────────── 2.40 Numbers: Format-free, Examples of Formats ──────────────────────────────────────────────────────────────────────── Numbers can be entered in many convenient forms which usually depend on their magnitudes. L 1530 ■ DECIMALS: 0.567, -.903 ■ FRACTIONS: 1/4, -45/64, 16/4 ■ INTEGERS: -1, 2, -123 ■ FLOATING POINT: 1.2E3, 1.2e3, -123e-2, 1.2D4, 34d1 (Note: E means 10^ thus 1E2 equal 1*10^2 or 100 and usage of L 1540 "E" and "D" are equivalent. Thus 1E2 and 1D2 are identical. Maximum FP value of 1E+25. FP numbers with exponents greater than +25 will be ignored.) Numbers can also be entered as the result of a mathematical expression: (34+45)/2, (10+34+56+78)*45, 2*COSD(30)-.467 and so. Commas and spaces within numbers are ignored. Thus 1,002 and 1 002 and 1002 are all equivalent. Also 18.89 and 1,8.8,9 and 1 L 1550 8 . 8 9 and 1,,,8 .,,,,8 9 and so on are also equivalent. Numbers can also include references to previously defined variables. For example: PAYMT$-100, PRINCPL$+100. Numbers can also have function operators attached: 45SD, 3*60CD-1/3 and so on. ╒════════════════╕ │ DECIMAL DIGITS └────────────────────────────────────────────────────── L 1560 2.42 Controlling the Number of Decimal Digits ──────────────────────────────────────────────────────────────────────── ------------------- 2.42 -- Controlling the Number of Decimal Digits --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 35 -- The number of significant decimal digits shown in the main equation display can be controlled in two ways: globally with the 'DEC apostrophe command and locally for any variable by appending the decimal operator to dependent and independent variable name. The 'DEC apostrophe command sets the default number of decimal digits. For example, 'DEC 2 (enter) would L 1570 specify 2 decimal digits. Global defaults also apply to the displayed values of the storage variables and numbers displayed on the plot. A variable such as "A" will display up to 7 decimal digits in single precision and up to 16 in double precision. Appending a period followed by an integer from 0 to 16 to the end of the variable name will result in from 0 to 16 decimal digits being displayed. However, the internal representation of the number always has full 16 digit resolution. for example, if A L 1580 =7.123456789012345 then a variable A.1 would display 7.1, A.2, 7.12, ...., A.14, 7.1234567890123 (if double precision display) and so on. A.0 or A. would round out the decimal and display 7. The decimal operator overrides the global default. The variable names are now A.1, A.2, .... and they must be referenced that way. For example, a.3=2*x-67. The decimal operator is most useful for dependent variables since it can be used to display more digits when a lower value L 1590 has been globally set with the 'DEC apostrophe command. As with the foreground and background colors, the global value of the decimal digits is saved with the equations and remains in effect when new equations are read into the program. ╒════════════════╕ │ PROGRAM LIMITS └────────────────────────────────────────────────────── 2.45 Maximum Number of Equations, Variables and Constants L 1600 ──────────────────────────────────────────────────────────────────────── ■ The maximum number of equations that may be entered is 63. For 61 to 63 equations, there is a maximum of 3 independent vars and the comment is not displayed. For 58 to 60 equations, 6 ind vars. For 1 to 3 equations, 63 independent vars, etc. The equations and ind vars must add up to 64 to 66 or less. The equation(s) can contain a maximum of 1840 characters (23 lines). The maximum number of operations such as additions, multiplications, etc. is approximately 1000. "% USE" is the L 1610 ------- 2.45 -- Maximum Number of Equations, Variables and Constants --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 36 -- percentage of codespace in use and is displayed after the program name/version. About 12 operations equal 1 %. If % USE exceeds 99% then immediate calculations may not have sufficient codespace. ■ The maximum number of dependent and independent variables is 66. The maximum number of storage variables is 256. Note: With storage variables, 63 equations with 259 independent variables can be entered if the storage variables are first defined. Only 3 independent variables can be displayed. Three L 1620 or less equations can contain up to 319 variables: 63 independent variables and 256 storage vars. ■ The minimum number of constants is 256 and the maximum number is (322-[total number of variables]). For example, if there are 2 dependent and 2 independent variables, then there can be a maximum of (322-[2+2])=318 constants. ╒═══════════════════╕ │ ERROR EXPLANATION └─────────────────────────────────────────────────── L 1630 2.50 Errors During Equation Evaluation and Elsewhere ──────────────────────────────────────────────────────────────────────── The program will evaluate the equations by the rules and regulations discussed above. If an error is detected, then the program will display the location of the error in the equation and a brief error comment describing its nature. Type any key to continue the program. The user should correct these errors and evaluate the equations again. An equation-error summary L 1640 can be found within this help file. Other errors, particularly overflows, may cause the program to display the EXEC ERROR message and return to the "? Equation(s)" prompt. Type (enter) to return to the main equation display. Record the error # and line number and report it! See below. ╒══════════════════╕ │ DIRECTORY SCREEN └─────────────────────────────────────────────────── L 1650 3.01 Directory Screen: Commands During Display ──────────────────────────────────────────────────────────────────────── The asterisk commands: * or (F7), !* and @* are used to generate a directory of 1) equation files with the default ------------------ 3.01 -- Directory Screen: Commands During Display --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 37 -- extension of .EQU, 2) storage files with the default extension of .STO or 3) application help files with the default extension of .HLP, respectively. A path for the location of the directory can be specified. If the desired directory is the L 1660 current one, simply type (enter) at the prompt or (end esc) "" (enter) to clear any existing path. The extensions of the files need not be the default ones (.equ, .sto or .hlp). However, the selected file will always be loaded as EQU, STO or HLP depending on what asterisk command was used. The directory does not use the DOS SHELL and COMMAND.COM is not required in any directory. PATH descriptions can be the same as for the DOS DIR command. Note: If a filename is used then it must end in a period or the default extension is used and and if there is no extension then the default extension will always be used. L 1670 Wildcards "*" and "?" can be used. Some paths might be: \CALC \CALC\ANALYSIS \CALC\data??? FORMULA??. *.DAT and so on. To search for all files beginning with the letter "a", only, enter a path like \CALC\A* and so on. A summary of the commands used to locate and select a file follow: Note: If less than 8 filenames, some commands have no function. If more than 192 files, then only the last 192 are listed. -> move to first file name of current row L 1680 (home) - Move highlighted cursor to column 1, the first file of a row -> move to first file of first row (ctrl) (home) - Move cursor to column 1, row 1, the first file. -> move to last file of current row (end) - Move cursor to column 8 of the current row, if L 1690 possible. -> move to last file of last row (ctrl) (end) - Move cursor to column 8, last row, if possible. -> move to top file of current column (PgUp) - Move cursor to top row of current column. L 1700 -> move to bottom file of current column ------------------ 3.01 -- Directory Screen: Commands During Display --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 38 -- (PgDn) - Move cursor to bottom row of current column. -> move cursor to next file (cursor) (right) or (tab) - Move cursor to next file. -> move cursor to previous file L 1710 (cursor) (left) or (backspace) - move cursor backwards. -> move up by one row (cursor) (up) - move cursor up one file in a column. -> move down by one row (cursor) (Dn) - move down one file in a column. L 1720 -> return info on highlighted file (space) - returns date and other file info for .EQU files only. Displays date (saved with equations) and approx. 68 characters of comment and equations (if comment is less than 68 characters). -> new path prompt \ - Prompt for new path description. Use (end esc) "" (enter) L 1730 to clear the old name. -> exit directory screen to main equation screen (esc) or (ctrl Q) - exit from directory to main equation display -> choose a file (enter) - Select file and load as EQU, STO or HLP. L 1740 -> search names by first letter letters and other characters - jump to next filename starting with that character, if possible. ------------------ 3.01 -- Directory Screen: Commands During Display --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 39 -- ╒═══════════════╕ │ PLOT COMMANDS └─────────────────────────────────────────────────────── 3.05 Commands Used While Plot Screen is Displayed L 1750 ──────────────────────────────────────────────────────────────────────── Only "active equations" are plotted versus an x-axis which is one of the independent variables which is designated as a coordinate variable. Active equations have dependent vars followed by a visible "=". If more than one equation, one must activate/inactivate equations, as desired, with commands "A" and "I". If more than one independent var, one must designate x-axis coordinate with command "O" or place the cursor on the desired independent var before typing "P". A coordinate var L 1760 has a ":" following its name. To plot, in the equations display type "P". Enter coordinate range (like from 10 to 20) for x-axis in form: 10 to 20 (enter) or 10;20 (enter). While in the plot screen, the following letter commands are active. -> display cursor: C C - Use cursor. X and Y values of cursor are displayed. L 1770 While ">" is displayed, the following keys are used to move it around: (Home) - Move cursor to top left corner (Up Arrow) - Move cursor one small division up (PgUp) - Move cursor to top right corner (Left Arrow) - Move cursor one small division to left L 1780 (Right Arrow) - Move cursor one small division to right (End) - Move cursor to lower left corner (origin) (Down arrow) - Move cursor one small division down (PgDn) - Move cursor to lower right corner. 1 to 9 - Change the increment of cursor movement when the L 1790 arrows are used and move the cursor to the right by that amount. At entry, default is 1. ; - designate first and last values for range to be plotted. --------------- 3.05 -- Commands Used While Plot Screen is Displayed --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 40 -- After ; is typed the second time, the program will prompt with the chosen range. Modify if needed and type (enter) to plot. (ctrl Q) or most other keys - Exit back to plot. -> dump plot screen as text file: V L 1800 V - Dumps the plot to a text file. Used to save calculations or plots for inclusion in reports, etc. Includes program name, date/time, equations, comment. Enter filename in response to prompt. Note: Filenames ending in numeric extensions from "000" to "999" are automatically incremented each time the command is used. Thus, PLOT.001 --> PLOT.002 --> PLOT.003 and so on. If file exists, program will ask to "APPEND" or to "REPLACE". L 1810 -> exit back to equations display: E (esc) Use "E" or "(esc) to exit back to equations display. -> plot range for x-axis: Use semicolon. ; - Set new range for X-axis. Enter a new range in the form num1 to num2 or num1;num2. For example -45 to 123 or -45;123. If a single number is entered then only the first or last limit L 1820 is replaced. For example, -30 (enter) or -30 to (enter) or -30; (enter) will only cause -45 to be replaced in -45;123 and to 106 (enter) or ;106 (enter) will cause only 123 to be replaced. -> shift plot left L - Shift plot to left along X-axis by 1 major scale division -> shift plot right L 1830 R - Shift plot to right along X-axis by 1 major scale division -> zoom in N - Move nearer to plot. Show less of X-axis. -> zoom out F - Move far away from plot. Show more of the X-axis. L 1840 --------------- 3.05 -- Commands Used While Plot Screen is Displayed --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 41 -- ╒════════════════════╕ │ ASTROSOLV COMMANDS └────────────────────────────────────────────────── 4.01 Commands Unique to this Program ASOL3.EXE. ──────────────────────────────────────────────────────────────────────── -> Reset active dependent variables to previous values: R Command R is used to restore the active dependent variables to L 1850 their values at the time just before the commands S, U or W were typed. Use to reset the initial values if a calculation did not converge and is attempted with a new set of guesses. -> Solve active linear simultaneous equations for values of active independent variables: S Command S is used to solve for the values of the active independent variables using the values of the active dependent variables. Solution by linear method. Number of active L 1860 dependent and independent variables must be equal and 30 or less of each type. -> Create a table of values indexed to an independent variable: T Command T is used to create a table of values of one or more active dependent variables indexed to a single independent variable which is designated as a coordinate (":" following name). Calculations are always based on the current values of L 1870 the independent variables. Enter the range of the table to be listed in the form number1 to number2 or number1;number2. For example, 1 to 6 or 1;6. When more than one coordinate, the program will list that coordinate on which cursor resides when "T" is typed. After entering the table range, next enter the table increment which must be a positive number. Values are calculated by substituting the lower table limit into the coordinate variable, calculating all active independent variables, increasing the coordinant by the increment, repeating the calculation, and so on up to the upper table L 1880 limit. The table columns start with the variable names and are followed by the calculated values. The coordinate variable and dependent variables (up to 15) are headers of the columns. -> List the table to system printer LPT1: !T ----------------- 4.01 -- Commands Unique to this Program ASOL3.EXE. --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 42 -- Command !T lists the table to the printer (LPT1:). While printing, type any key to speed up. Use "!P" to set the printer to nlq mode, if necessary. L 1890 -> List the results of the fit to a file: @T Command @T lists the table to a file for subsequent use such as generation of a lookup table, inclusion in a report and so on. Enter range, increment and filename in response to prompts. For example: 1 to 60, 1, TAB1.TXT (enter). Program will automatically increment number extensions. RESULTS.001 ==> RESULTS.002 ==> RESULTS.003 and so on. -> Solve active nonlinear simultaneous equations for values of L 1900 active independent variables: U Command U is used to "unite" all active dependent variables and to solve for the values of all active independent variables such that the values of all active dependent variables are all equal to the same number. The active equations are set equal. Solution by nonlinear method. Number of active dependent and independent variables may be unequal and 30 or less of each type. Set independent variables to accurate initial guesses. Type "U". Enter tolerance. Typically 0.1 (default) for L 1910 accurate guesses and 1.0 or more for inaccurate guesses. -> Solve active nonlinear simultaneous equations for values of active independent variables: W Command W is a straight nonlinear solution and is used to solve for the values of one or more active independent variables using the values of the active dependent variables. Solution by nonlinear method. Number of active dependent and independent variables may be unequal and 30 or less of each L 1920 type. First, set ind vars to accurate initial guesses. Next set active dep vars to desired solution. Type "W". Enter tolerance. Typically 0.1 (default) for accurate guesses and 1.0 or more for inaccurate guesses. ╒════════════════════════╕ │ LINEAR SIMUL EQUATIONS └────────────────────────────────────────────── 4.03 Solving (If possible) Linear Simultaneous Equations. ──────────────────────────────────────────────────────────────────────── L 1930 To solve simultaneous linear equations use subcommand "S". The ------- 4.03 -- Solving (If possible) Linear Simultaneous Equations. --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 43 -- use of this subcommand will be illustrated by an interactive example intended to illustrate the general procedures only. The four coefficients A, B, C and D of a third-order polynomial that passes through four (x,y) points will be determined. The third-order polynomials are not linear equations with respect to the variable X but they are linear with respect to the coefficients A, B, C and D. In order to use the subcommand "S", one must first enter an equation into the program with at L 1940 least 1 independent variable. Note: You will frequently start to see apostrophe commands like 'EQU, 'VAR and 'COM appearing in the helpfile. The 'EQU field provides info for the equations display which is loaded when the highlight bar lights up on the 'EQU line and the "Type Q...." message appears at the bottom of the screen. To learn more about these commands, read the discussion of apostrophe commands in this helpfile. L 1950 ║ To automatically load these equations, type Q when the ║ ║ highlight bar appears on the screen. Scroll down, if ║ ║ necessary, to light it. ║ 'EQU Y1=A+B*X1+C*X1^2+D*X1^3 Y2=A+B*X2+C*X2^2+D*X2^3 Y3=A+B*X3+C*X3^2+D*X3^3 Y4=A+B*X4+C*X4^2+D*X4^3 'INA X1 X2 X3 X4 'COM "Type (F1) to return to the helpfile" L 1960 If the equations are loaded, then skip to step (4). 1) When the Program is displaying the equations screen, type (F6) or "!/" in order to get the "Equations" prompt. In response to the prompt "? Equation(s)", type: (end esc) Y1=A+B*X1+C*X1^2+D*X1^3 Y2=A+B*X2+C*X2^2+D*X2^3 Y3=A+B*X3+C*X3^2+D*X3^3 Y4=A+B*X4+C*X4^2+D*X4^3 (enter) 2) In response to the prompt for a comment Type (end esc) "" L 1970 (enter). Remember to type (F1) to return to this file. 3) If necessary, inactivate variables X1, X2, X3 and X4. Move the cursor to each variable and type "I". The equal sign will disappear. Note there are 4 equations and there must be 4 and only 4 unknowns: A, B, C and D. If more than 4 equations were to be entered, inactivate any equation which is supplemental to the other equations and not actually involved in the problem. ------- 4.03 -- Solving (If possible) Linear Simultaneous Equations. --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 44 -- To inactivate an equation move the cursor to that variable and typing I. The equal sign will disappear. The S operations are L 1980 not performed on inactive equations but these equations can still be used as intermediate equations in the calculation of the active equations. 4) Set X1, X2, X3 and X4 to desired values and load in the desired solutions for Y1, Y2, Y3 and Y4. ║ To automatically load these values, type Q when the ║ ║ highlight bar appears on the screen. Scroll down, if ║ ║ necessary, to light it. ║ L 1990 'EQU 'VAR X1=1 X2=2 X3=3 X4=4 'VAR Y1=-2 Y2=-23 Y3=-86 Y4=-215 'COM The four (x,y) data points are (1,-2), (2,-23), (3,-86), (4,-215). If necessary, set X1=1, X2=2, X3=3 and X4=4. Next, set Y1=-2, Y2=-23, Y3=-86, Y4=-215. Always set the dependent variables last. Type S to solve as a linear system. The result should be A=1, B=-2, C=3 and D=-4. Type (F1) to return to the helpfile L 2000 To plot the equations, load the following comment and follow the directions. ║ To automatically load this comment, type Q when the ║ ║ highlight bar appears on the screen. Scroll down, if ║ ║ necessary, to light it. ║ 'EQU 'COM To plot the polynomial, move the cursor to X1 and type P. In response to the prompt for the X1 range, type (esc) 1 to 4 (enter). The Program L 2010 will plot all 4 equations. Equation 'a' will pass through all four (x,y) points. Note Equations 'b', 'c' and 'd' are constants with respect to variable X1 and they intersect the 'a' plot at (2,-23), (3,-86) and (4,-215), respectively. Type E to exit the plot. Type (F1) to return to the helpfile Summary of steps to solve linear simultaneous equations: 1) Enter the equation(s) and message. If there are more independent variables than equations, use "I" to inactivate L 2020 excess. There may be more independent variables than equations but the number of active independent variables must always equal the number of active equations for a linear solution. ------- 4.03 -- Solving (If possible) Linear Simultaneous Equations. --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 45 -- 2) Set the active dependent variables to the desired values and type "S" to attempt a linear solution for the active independent variables. If a linear solution is not found, the Program will prompt with a warning message. ╒═══════════════════════════╕ L 2030 │ NONLINEAR SIMUL EQUATIONS └─────────────────────────────────────────── 4.05 Solving (If possible) Nonlinear Simultaneous Equations. ──────────────────────────────────────────────────────────────────────── To solve nonlinear simultaneous equations either the subcommand "W" or "U" can be used. The "W" method is the general nonlinear optimization procedure in which 1 or more active independent variables is solved subject to the constraints of the values of the active dependent equation. The "U" method is L 2040 a special case of the more general "W" method. In the "U" method, the equations are "united" or set equal to each other and the problem is solved for the best values of the active independent variables. The use of the "W" and "U" nonlinear methods will be illustrated with an examples which is intended to illustrate the general procedures only. First, three nonlinear equations Y1, Y2 and Y3 will be solved for three independent variables A, B and C. Second, the values of variables A, B and C will be L 2050 determined such that Y1=Y2=Y3. In order to use the commands, one must enter at least one equation into the Program with at least one independent variable. Any equation will do. Note: ║ To automatically load these equations, type Q when the ║ ║ highlight bar appears on the screen. Scroll down, if ║ ║ necessary, to light it. ║ 'EQU Y1=A^2+B+C Y2=A-SQR(ABS(B))+C L 2060 Y3=A+B-C^3 'VAR #ALL=0 'COM "Type (F1) to return to the helpfile" If the equations are loaded, then skip to step (4). 1) When the Program is displaying the equations screen, type (F6) or "!/" in order to get the "Equations" prompt. In response to the prompt "? Equation(s)", type: (end esc) Y1=A^2+B+C Y2=A-SQR(ABS(B))+C Y3=A+B-C^3 (enter) L 2070 -- 4.05 -- Solving (If possible) Nonlinear Simultaneous Equations... --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 46 -- 2) In response to the prompt for a comment Type (end esc) "" (enter). Remember to type (F1) to return to this file. 3) Note: there are 3 equations and there are 3 unknowns: A, B, C. In general, the number of unknowns does not have to equal the number of equations. If necessary, inactivate any independent variables as well as any equations which are supplemental to the other equations and not actually involved in the problem. To inactivate an equation move the cursor to L 2080 that variable and typing I. The equal sign will disappear. The W operations are not performed on inactive equations but these equations can still be used as intermediate equations in the calculation of the active equations. 4) Set the variables A, B and C to reasonable initial "guesses". Enter A=1.5, B=3.5 and C=3.5. Set the dependent variables Y1, Y2 and Y3 to the desired solution. Enter Y1=8, Y2=2 and Y3=-22. L 2090 ║ To automatically load this comment, type Q when the ║ ║ highlight bar appears on the screen. Scroll down, if ║ ║ necessary, to light it. ║ 'EQU 'VAR A=1.5 B=3.5 C=3.5 Y1=8 Y2=2 Y3=-22 'COM If necessary, set the variables A, B and C to reasonable initial 'guesses'. Enter A=1.5, B=3.5 and C=3.5. Set the dependent variables Y1, Y2 and Y3 to the desired solution. Enter Y1=8, Y2=2 and Y3=-22. To attempt a nonlinear solution, type W. In response to the prompt for L 2100 a tolerance, type (end esc) .1 (enter). After about 100 iterations, the program will calculate A as 1 and B as 4 and C as 3. Type any key to stop iterations after # 100 or so. Note the magnitudes of the ERROR and SIG FIGS. As the solution 'improves', the ERROR will tend toward a minimum and SIG FIGS will grow toward 16. Type (F1) to return to the helpfile The W method is the general method of solving for the values of independent variables. A variation of this method is the U or "unite" method. To solve for Y1=Y2=Y3 follow the same L 2110 procedure as described above. ║ To automatically load this comment, type Q when the ║ ║ highlight bar appears on the screen. Scroll down, if ║ ║ necessary, to light it. ║ 'EQU -- 4.05 -- Solving (If possible) Nonlinear Simultaneous Equations... --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 47 -- 'VAR A=1 B=1 C=1 'COM If necessary, set A, B and C to reasonable initial guesses. Enter A=1, B=1 and C=1. Now type U to unite the active equations. Enter a L 2120 tolerance of 0.1. After about 100 iterations or so, Y1=Y2=Y3=.824, A=.849, B=-2.27E-2 and C=.126. Type (F1) to return to the helpfile Summary of steps to solve nonlinear simultaneous equations: 1) Enter the equation(s) and message. Use "I" to inactivate equations and/or independent variables that are not involved with the solution. The number of active independent variables does not have to equal the number of active equations! L 2130 2) Set the active independent variables to reasonable initial "guesses" 3) Set the active dependent variables to the desired values and type "W" or just designate the active equations and type "U". "W" attempts to optimize the active independent variables for the specified values of the active equations at the moment "W" is typed. "U" attempts the solution where all active equations are set equal to each other. Enter a tolerance (0.1 is default). L 2140 4) After ERROR or SIG FIGS is reached, type any key to stop. Nonlinear equations may not have 0 or many solutions! You should have a good idea of what values you are expecting to calculate, beforehand, if you attempt to solve nonlinear equations! ╒═══════════════════════════╕ │ NONLINEAR SIMUL EQUATIONS └─────────────────────────────────────────── L 2150 4.10 Shooting a Marble into a Moving Ferris Wheel Car: Solution of Simultaneous Nonlinear equations ──────────────────────────────────────────────────────────────────────── In this example, a user will calculate the required angle of elevation of his marble shooter in order for him to shoot his marble into a moving ferris-wheel car. A set of simultaneous nonlinear equations must be solved in order to make predictions. L 2160 The marble shooter is located at the origin of a X-Y coordinate system. The ferris wheel is located a distance DWHEEL from the -- 4.10 -- Shooting a Marble into a Moving Ferris Wheel Car: Solu... --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 48 -- shooter and has a radius RWHEEL about its center which is a height of HWHEEL above the ground. The wheel turns at a speed of REVS revolutions per second. A diagram of the problem is shown below. ..................................................................... FERRIS WHEEL L 2170 path of marble | |-/--| | * * * * * * RWHEEL |/ | | * * / | | * * /| | | * *___/_ | | | * _car_ | | HWHEEL | /* | | | / / | | | / / | | L 2180 |/ / <-ALPHA (angle of elevation) | | |_/_______________________________________________|____|_____________ x=0 x=DWHEEL ...................................................................... If all distances are in units of feet, all times are in seconds, there is no wind to divert the marble and air resistance is neglected, then the equations of motion for the marble and ferris wheel can be shown to be: L 2190 XWHEEL = -RWHEEL*SIN(6.28*REVS*T)+DWHEEL YWHEEL = RWHEEL*COS(6.28*REVS*T)+HWHEEL XMARBLE = (LSHOOTER+VMARBLE*T)*COSD(ALPHA) YMARBLE = (LSHOOTER+VMARBLE*T)*SIND(ALPHA)-16.08*T^2 DELTAX = XWHEEL-XMARBLE L 2200 DELTAY = YWHEEL-YMARBLE where: XWHEEL = horizontal position of ferris-wheel car at time T RWHEEL = radius of wheel -- 4.10 -- Shooting a Marble into a Moving Ferris Wheel Car: Solu... --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 49 -- T = time in seconds reference to the ferris-wheel car being located at the extreme top of the wheel at T=0 L 2210 DWHEEL = distance from the bottom of the marble shooter to directly below the center of the wheel. The bottom of the shooter is the origin. YWHEEL = vertical position of the ferris wheel car at time T HWHEEL = height of the center of the wheel above ground XMARBLE = horizontal position of marble during its flight L 2220 from the marble shooter. Its initial speed is VMARBLE and angle of elevation is ALPHA. LSHOOTER = length of the barrel of the marble shooter VMARBLE = exit speed of marble in feet/second from marble shooter ALPHA = angle of elevation of marble shooter in degrees above the ground L 2230 YMARBLE = vertical position of marble during its flight from the marble shooter. Its initial speed is VMARBLE and angle of elevation is ALPHA. DELTAX = difference in horizontal positions of ferris wheel car and marble DELTAY = difference in vertical position of ferris wheel car and marble L 2240 In this example, the barrel of the marble shooter is 4 feet long and initially has its elevation angle at 45 degrees. It is located 400 feet from directly below the center of the wheel. The ferris wheel rotates at 1 revolution in 20 seconds (.05 revs/sec) and its radius is 40 feet. The center of the wheel is 45 feet above the ground. With the built-in propulsion mechanism, the user can shoot the marble such that its exit speed can reach a maximum speed of 150 feet/sec. L 2250 If the user shoots the marble out of the shooter at T=0, what must its angle of elevation be in order for the marble to land in the car? At what time T will it land in the car? -- 4.10 -- Shooting a Marble into a Moving Ferris Wheel Car: Solu... --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 50 -- The user needs to determine ALPHA and T. The six equations which govern the motions form a system of nonlinear equations. The values of ALPHA and T can be determine by numerical methods if reasonable initial "guesses" for ALPHA and T are supplied. In order to solve the problem, the previously mentioned L 2260 equations need to be loaded into the equation display. ║ To automatically load these equations, type Q when the ║ ║ highlight bar appears on the screen. Scroll down, if ║ ║ necessary, to light it. ║ 'EQU XWHEEL = -RWHEEL*SIN(6.28*REVS*T)+DWHEEL YWHEEL = RWHEEL*COS(6.28*REVS*T)+HWHEEL XMARBLE = (LSHOOTER+VMARBLE*T)*COSD(ALPHA) YMARBLE = (LSHOOTER+VMARBLE*T)*SIND(ALPHA)-16.08*T^2 L 2270 DELTAX = XWHEEL-XMARBLE DELTAY = YWHEEL-YMARBLE 'INA XWHEEL YWHEEL XMARBLE YMARBLE DWHEEL HWHEEL LSHOOTER REVS RWHEEL VMARBLE 'COM Shoot marble into ferris wheel car. T is time in seconds. Alpha is angle of elevation of shooter. Type (F1) to return to the helpfile The screen should appear similar to what is shown below. L 2280 ...................................................................... --- Comment --> Shoot marble into ferris wheel car. T is time in seconds. Alpha is angle of elevation of shooter. XWHEEL=-RWHEEL*SIN(6.28*REVS*T)+DWHEEL XWHEEL 0 YWHEEL=RWHEEL*COS(6.28*REVS*T)+HWHEEL YWHEEL 0 XMARBLE=(LSHOOTER+VMARBLE*T)*COSD(ALPHA) XMARBLE 0 L 2290 YMARBLE=(LSHOOTER+VMARBLE*T)*SIND(ALPHA)-16.08*T^2 YMARBLE 0 DELTAX=XWHEEL-XMARBLE DELTAX = 0 DELTAY=YWHEEL-YMARBLE DELTAY = 0 11:24:06 *** Accuracy ? Warning # 8 *** 12-18-1980 ALPHA = 0 DWHEEL 0 HWHEEL 0 L 2300 LSHOOTER 0 REVS 0 RWHEEL 0 T = 0 VMARBLE > 0 ...................................................................... -- 4.10 -- Shooting a Marble into a Moving Ferris Wheel Car: Solu... --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 51 -- Active equations and independent variables are designated. There are six equations; however, only the last two, DELTAX and DELTAY, determine when the marble lands in the car (at DELTAX=0 and DELTAY=0). The first four equations should be inactivated because they calculate intermediate results. Note: Inactive L 2310 equations do not display the "=" following the name of the dependent variable. The program will attempt to solve for the values of the active independent variables only. In this case they are ALPHA and T. Only ALPHA and T should have their names followed by "=". The screen should appear as shown above. At this time, the Program is set up to solve for the values of ALPHA and T using equations DELTAX and DELTAY. The marble will reach the car when DELTAX=0 and DELTAY=0. The Program will use numerical methods to determine the values of ALPHA and T that L 2320 satisfy these equations starting with "reasonable" initial values supplied by the user. The fit. The Program will optimize the values of the active independent variables, whose names are followed by the '='( ALPHA and T), in order to attempt to minimize the squared error between the calculated values of the active dependent variables DELTAX and DELTAY and the desired values of 0.0 and 0.0, respectively. The desired values are always the values of the active dependent variables at the instant the optimization L 2330 starts. Note: The values of the dependent variables of the Equations will be calculated if a number is entered or if C is typed. Don't type C at this time or enter a value for an independent variable or the values of DELTAX and DELTAY will no longer be set to 0.0. ║ To automatically load these equations, type Q when the ║ ║ highlight bar appears on the screen. Scroll down, if ║ ║ necessary, to light it. ║ 'EQU L 2340 'VAR ALPHA=45 DWHEEL=400 HWHEEL=45 LSHOOTER=4 REVS=.05 RWHEEL=40 T=0 VMARBLE=150 DELTAX=0 DELTAY=0 'COM Begin the fit. Type 'W' to solve the active Equations by nonlinear methods. The program will prompt: Relative tolerance = 0. The -- 4.10 -- Shooting a Marble into a Moving Ferris Wheel Car: Solu... --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 52 -- initial guesses are believed accurate so a tolerance of 0.1 (10%) is used. Set the tolerance to 0.1 by typing (end esc) 0.1 (enter). The Program will update the parameters after each iteration and display an error value and an estimate of the number of significant figures. L 2350 Watch as the error decreases and the SIG FIGS increase. Simultaneously, the values of DELTAX and DELTAY will approach 0.0 and ALPHA and T will approach the desired solution. After Iteration # 76, type any key to stop the fit and type (F1) to return to the help file. Remember, the error indicates the accuracy of the current values and the SIG FIGS indicates the stability. It is usually better to wait for a minimum error and large SIG FIGS. However, an error which is considerably less than 1E-16 is acceptable provided that SIG FIGS is large. a very low error L 2360 is reached, stop the fit. A good rule is to monitor the error and allow 20 to 30 Iterations past the point when the error and significant figures have both become fairly constant at acceptable values (in this case SIG FIGS is 4). While the fit is in progress, type any key to terminate it. Following the optimization for ALPHA and T, the converged (minimum error) solution should appear similar to that shown below. ...................................................................... --- Comment --> Shoot marble into ferris wheel car. T is time in L 2370 seconds. Alpha is angle of elevation of shooter. XWHEEL=-RWHEEL*SIN(6.28*REVS*T)+DWHEEL XWHEEL 369.5772 YWHEEL=RWHEEL*COS(6.28*REVS*T)+HWHEEL YWHEEL 70.97021 XMARBLE=(LSHOOTER+VMARBLE*T)*COSD(ALPHA) XMARBLE 369.5772 YMARBLE=(LSHOOTER+VMARBLE*T)*SIND(ALPHA)-16.08*T^2 YMARBLE 70.97 L 2380 DELTAX=XWHEEL-XMARBLE DELTAX = -1.46E-05 DELTAY=YWHEEL-YMARBLE DELTAY => 1.40E-05 Iteration # 76 ERROR = 2.030347824645198D-05 SIG FIGS = 4 ALPHA = 27.54638 DWHEEL 400 HWHEEL 45 LSHOOTER 4 REVS .05 RWHEEL 40 L 2390 T = 2.752203 VMARBLE 150 ...................................................................... -- 4.10 -- Shooting a Marble into a Moving Ferris Wheel Car: Solu... --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 53 -- The elevation angle is ALPHA=27.55 degrees. The marble will land in the car 2.75 seconds after launch and the car will be 369.6 feet from the marble shooter and 71 feet above the ground. It may be informative to plot the y-coordinates of the marble and the ferris wheel car in order to determine if the marble L 2400 actually landed in the car or merely struck it and bounced away. For the marble to land in the car it must fall from above into the car. ║ To automatically load these equations, type Q when the ║ ║ highlight bar appears on the screen. Scroll down, if ║ ║ necessary, to light it. ║ 'EQU 'INA #DEP 'ACT YWHEEL YMARBLE L 2410 'COO T 'COM Plot setup. The program will plot all ACTIVE equations versus one independent variable which is designated as a COORDINATE. In this case, Equations YWHEEL and YMARBLE are to be plotted vs. T from T = 2 to T = 3. If necessary, designate the active equations and the coordinate. Active variables has a '=' following their names A coordinate has its name followed by a ':'. Type P to plot. Enter the range for T as 2 to 3 by typing (end esc) 2 to 3 (enter). Type E to exit the plot and type (F1) to return to the help file. L 2420 The results of the plot should be similar to what is shown below. ....................................................................... 77.3-bb | * bd d d |dd b b d d | b b d d | b b d L 2430 74.3- b b d | b b d | b b d marble falls | b d into car at | b bd <-this time. 71.3- bd | db b | d b | d b | d L 2440 68.2- d | d | | | 65.2- ||--------------|--------------|--------------|--------------|---- 2 2.22 2.43 2.65 2.87 YWHEEL[b] YMARBLE[d] vs. T ....................................................................... L 2450 -- 4.10 -- Shooting a Marble into a Moving Ferris Wheel Car: Solu... --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 54 -- The active equations are plotted with the symbols "b" and "d" which represent YWHEEL and YMARBLE, respectively. It can be seen from the plot that the "d" points rise above the "b" at about 2.15 seconds where the marble's height is about 76.7 feet. Thus, the marble is on its way down when it reaches the car and it will land in it! ╒════════════════════════╕ │ SIMUL LINEAR EQUATIONS └───────────────────────────────────────────── L 2460 4.20 Resource Allocation in an Instrument Company: Solving Simultaneous Linear equations ──────────────────────────────────────────────────────────────────────── This example will show how the resource planners in a small instrument company can estimate what their current space allocations must be in order for their company to grow to a predicted size over a ten year period. The company planners will use a mathematical model generated by a consulting firm. L 2470 This model has been constructed from known growth patterns of similarly sized companies. One must solve simultaneous linear equations in order to make predictions. The instrument company allocates space for 6 major functions which are: 1) demonstration laboratories, 2) research and engineering labs, 3) office space, 4) storage, 5) warehouse and 6) parking lots. The current allocations of space are predicted to change over a 10 year period by a consulting firm who has studied the developments of similarly sized companies. L 2480 They have supplied the company planners with a Space Allocation Table which is tabulated below. SPACE ALLOCATION TABLE ----- 4.20 -- Resource Allocation in an Instrument Company: Solving --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 55 -- Allocations at end of 10 year period C means current; F, future D - Demonstration labs, R - Research and engineering labs, L 2490 O - Office space, S - Storage, W - Warehouse, P - Parking CD CR CO CS CW CP FD .90 .05 .07 .05 0 .05 FR .04 .90 .05 .05 0 .05 L 2500 FO .05 .03 .75 .05 .20 .05 FS .01 .01 .03 .51 .05 0 FW 0 .01 .05 .30 .60 .05 FP 0 0 .05 .04 .15 .80 --- --- --- --- --- --- 1 1 1 1 1 1 L 2510 Each column represents the future distribution of the given space. For example, the first column represents the demonstration lab space. If the current allocation is 1 unit, then 90 % will remain as demonstration labs after 10 years; 4 % will be converted to research labs; 5 %, to office space; 1 %, to storage; 0 %, to warehouse space and 0 % to parking. A similar breakdown holds for the future space allocations represented by columns 2 through 6. Note that all columns must add up to 1 (or 100 %). L 2520 The company planners want to organize the current space in accordance with the space-conversion factors so that their resources can grow to their expectations 10 years from now. Such early planning is hoped to eventually minimize expensive conversions and remodeling as the revenue and size of the instrument company grow. The information in the Table can be arranged into 6 equations which are formulated by summing the conversion factors along each row. These six equations are: L 2530 ----- 4.20 -- Resource Allocation in an Instrument Company: Solving --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 56 -- FD = .9*CD+.05*CR+.07*CO+.05*CS+.05*CP FR = .04*CD+.9*CR+.05*CO+.05*CS+.05*CP FO = .05*CD+.03*CR+.75*CO+.05*CS+.20*CW+.05*CP FS = .01*CD+.01*CR+.03*CO+.51*CS+.05*CW FW = .01*CR+.05*CO+.3*CS+.6*CW+.05*CP FP = .05*CO+.04*CS+.15*CW+.80*CP Ten years from now, the company planners want the future percentages of space to be allocated: L 2540 FD = 10 % FR = 10 % FO = 20 % FS = 5 % FW = 40 % FP = 15 % What should the current space allocations be in order for the future space allocations to reach the predicted levels? L 2550 In order to solve the problem, the previously mentioned equations need to be loaded into the equation display. ║ To automatically load these equations, type Q when the ║ ║ highlight bar appears on the screen. Scroll down, if ║ ║ necessary, to light it. ║ 'EQU FD=.9*CD+.05*CR+.07*CO+.05*CS+.05*CP FR=.04*CD+.9*CR+.05*CO+.05*CS+.05*CP L 2560 FO=.05*CD+.03*CR+.75*CO+.05*CS+.20*CW+.05*CP FS=.01*CD+.01*CR+.03*CO+.51*CS+.05*CW FW=.01*CR+.05*CO+.3*CS+.6*CW+.05*CP FP=.05*CO+.04*CS+.15*CW+.80*CP 'VAR FD=10 FR=10 FO=20 FS=5 FW=40 FP=15 'COM Space allocations --- D demo labs,R research,O office, S storage,W warehouse,P parking--- C current,F future. Type (F1) to return to the helpfile L 2570 The 6 equations described above form a group of simultaneous linear equations. The equations can be solved for the current values (CD, CR, CO, CS, CW and CP) given the future values (FD, FR, FO, FS, FW and FP). After the equations, comment and values for the dependent variables are entered into AstroEquationSolver 3, the equation display should look similar ----- 4.20 -- Resource Allocation in an Instrument Company: Solving --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 57 -- to what is shown below. ...................................................................... --- Comment --> Space allocations --- D demo labs,R research,O office, L 2580 S storage,W warehouse,P parking--- C current,F future FD=.9*CD+.05*CR+.07*CO+.05*CS+.05*CP FD = 10 FR=.04*CD+.9*CR+.05*CO+.05*CS+.05*CP FR = 10 FO=.05*CD+.03*CR+.75*CO+.05*CS+.20*CW+.05*CP FO = 20 FS=.01*CD+.01*CR+.03*CO+.51*CS+.05*CW FS = 5 L 2590 FW=.01*CR+.05*CO+.3*CS+.6*CW+.05*CP FW = 40 FP=.05*CO+.04*CS+.15*CW+.80*CP FP => 15 13:52:54 *** Accuracy ? Warning # 8 *** 12-20-1980 CD = 0 CO = 0 CP = 0 CR = 0 CS = 0 CW = 0 L 2600 ...................................................................... To solve this problem, one supplies values for the dependent variables FD ....FP and the Program calculates the values of the independent variables CD..CW. This type of calculation is "inverted" with respect to most calculations. These equations are linear with respect to the unknowns CD..CW. However, they can also be solved by nonlinear methods, discussed above, which are more general. For the time being, the equations will be solved as linear equations. In the event they were not linear L 2610 equations, the Program will inform the user with a warning comment and the nonlinear method should then be tried. The future percentages are set to their desired values as as shown above. Notice that the values of CD..CW are all zero and the warning comment #8 informs the user that there may be, and is not in this case, any relationship between the displayed values of FD...FP and the values of CD..CW. ║ To automatically load this comment, type Q when the ║ L 2620 ║ highlight bar appears on the screen. Scroll down, if ║ ║ necessary, to light it. ║ ----- 4.20 -- Resource Allocation in an Instrument Company: Solving --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 58 -- 'EQU 'COM Type 'S' to solve for CD..CW using linear methods, Some conditions must be satisfied, one of which is that the number of active independent and independent variables must be equal. In this example, the numbers are both 6. The Program will solve the simultaneous equations and display the current allocation percentages required in order to achieve the future ones at the end of the 10 year period. Notice that the L 2630 calculated values of both the current and future allocations always sum to 100. Type (F1) to return to help file. The screen should now look similar to what is shown below. ...................................................................... --- Comment --> Space allocations --- D demo labs,R research,O office, S storage,W warehouse,P parking--- C current,F future FD=.9*CD+.05*CR+.07*CO+.05*CS+.05*CP FD = 10 L 2640 FR=.04*CD+.9*CR+.05*CO+.05*CS+.05*CP FR = 10 FO=.05*CD+.03*CR+.75*CO+.05*CS+.20*CW+.05*CP FO = 20 FS=.01*CD+.01*CR+.03*CO+.51*CS+.05*CW FS = 5 FW=.01*CR+.05*CO+.3*CS+.6*CW+.05*CP FW = 40 FP=.05*CO+.04*CS+.15*CW+.80*CP FP => 15 L 2650 13:58:43 12-20-1980 CD = 9.458092 CO = 7.996075 CP = 6.118691 CR = 9.757506 CS = 2.683652 CW = 63.98599 ........................................................................ ╒═══════════════════╕ L 2660 │ GENERATING TABLES └─────────────────────────────────────────────────── 4.30 How to Generate (Look-up) Tables. ──────────────────────────────────────────────────────────────────────── This example will show how to create tables using the table command T. Tables are column listings of active dependent variables (Names are followed by equal signs.) as functions of -------------------------- 4.30 -- How to Generate (Look-up) Tables. --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 59 -- an index variable (Name is followed by colon.). One specifies which dependent variables are to be included in the table by L 2670 using the active and inactive commands (A and I, respectively). The independent variable that serves as the index of the table is specified with the coordinate command or colon (:). The table is calculated at fixed increments from the minimum to maximum limits, all of which are specified by the user. The table can be listed on the system printer (command !T) or saved as a file (command @T). The following example illustrates the table command T. A calculation and comparison is made of the depreciation charges L 2680 using the straight-line (SLM), double-declining-balance (DDB) and the sum-of-the-years digits (SYD) methods for an item costing $8,000 new at 1, 3 and 6 years over a 10 year depreciation. The equations and values of the variables can be loaded directly into the program. ║ To automatically load these equations, type Q when the ║ ║ highlight bar appears on the screen. Scroll down, if ║ L 2690 ║ necessary, to light it. ║ 'EQU DEPR_SLM=ORIGCOST/NYEARS DEPR_DDB=ORIGCOST*((1-(2/NYEARS))^(N-1)-(1-(2/NYEARS))^(N)) DEPR_SYD=(1+NYEARS-N)*2/(NYEARS+NYEARS^2)*ORIGCOST 'VAR N=1 NYEARS=10 ORIGCOST=8000 'COO N 'COM Calculate and compare the depreciation charges using the straight-line, double-declining-balance and the sum-of-the-years digits methods for an L 2700 item costing $8,000 new at 1, 3 and 6 years over a 10 year depreciation. Type (F1) to return to the helpfile. These 3 equations calculate depreciation charges as a function of N, the time in years. One desires the yearly charges in a table as a function of N. ║ To automatically load this comment, type Q when the ║ ║ highlight bar appears on the screen. Scroll down, if ║ ║ necessary, to light it. ║ L 2710 'EQU 'COM To generate a table, move the cursor to variable N and type the table command T. For the range of the table, type (end esc) 1 to 10 (enter). -------------------------- 4.30 -- How to Generate (Look-up) Tables. --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 60 -- For the increment of the table, type (end esc) 1 (enter). Notice that the table starts with the index variable N followed by the calculated values of the depreciations. Type (F1) to return to the helpfile. The table should look similar to what is shown below. L 2720 N DEPR_SLM DEPR_DDB DEPR_SYD 1 800 1600 1454.55 2 800 1280 1309.09 3 800 1024 1163.64 4 800 819.2 1018.18 5 800 655.36 872.73 6 800 524.29 727.27 7 800 419.43 581.82 8 800 335.54 436.36 9 800 268.44 290.91 L 2730 10 800 214.75 145.45 The table can be calculated to a file if the @T command is used. Type "@" first and then "T". The decimal digits of the table can be controlled with the apostrophe command 'DEC. To specify 1 decimal digit, one would type 'DEC 1 (enter) from the equation display. There may be more than one coordinate. In that case, the index is chosen as the coordinate on which the cursor resides when L 2740 the command T is typed. If more than 5 variables, the screen display will be truncated but the printer "!T" and file "@T" listings will be full. Up to 15 dependent variables may be specified. Typing any key during the scroll will cause the table to jump nearer its end and will speed up the display. ╒══════════╕ │ WARNINGS └──────────────────────────────────────────────────────────── 5.01 Summary of Common WARNINGS During Calculations. L 2750 ──────────────────────────────────────────────────────────────────────── The warning numbers followed by an explanation follow: 1 - Attempt to raise negative number to non-integer power. Operation was ignored. Y=X^W is ok if X=-1.3 and W=2 but is not allowed if W=2.1. - Also, attempt to raise number to power such that the result is greater than 1E30 (overflow) or less than 1E-30 (underflow). The number was set to 1E30 for overflow and 1E-30 for underflow. L 2760 ------------ 5.01 -- Summary of Common WARNINGS During Calculations. --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 61 -- 2 - Overflow from multiplication. The result of the multiplication of two numbers exceeded 1E30 in magnitude. The result of the multiplication was set to a magnitude of 1E30. 3 - Overflow from division. The result of the division of two numbers exceeded 1E30 in magnitude. The result of the division was set to a magnitude of 1E30. 8 - The displayed values of the equation(s) may not be L 2770 accurate. In other words, the values of the dependent variables may not be related to the values of the independent variables by the recipes of the equations. The most common warning message. Will be produce if a dependent variable is set to any number. Always produced after "?" command and at the entry into a calculation. Type "C" to recalculate if uncertain about the values of the dependent variables. 15 - Attempt to take the arccosine, ACOS(...) or ACOSD(...), of a number whose absolute value is greater than 1.0. Operation L 2780 was ignored. 16 - Attempt to take the arcsine, ASIN(...) or ASIND(...), of a number whose absolute value is greater than 1.0. Operation was ignored. 18-19 - Same as for 15 and 16 but for ACOSD(...) and ASIND(...). 24 - Attempt to take the arccosine hyperbolic, ACOSH(...), of a L 2790 number whose value is less than 1.0. Operation was ignored. 26 - Attempt to take the arctangent hyperbolic, ATANH(...), of a number whose absolute value is greater than 1.0. Operation was ignored. 28 - Attempt to take a natural antilog of a number such that the result exceeded 1E30 (overflow) or was less than 1E-30 (underflow). The program set the magnitude of the result to 1E30 for overflow and 1E-30 for underflow. L 2800 31 - Attempt to take the square root, SQR(...), of a negative number. Operation was ignored. 32 - Attempt to take natural log, LOG(...), of zero or a negative number. Operation was ignored. ------------ 5.01 -- Summary of Common WARNINGS During Calculations. --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 62 -- 33 - Attempt to take log base 10, LOG10(...), of zero or a negative number. Operation was ignored. L 2810 43 - Overflow from factorial. The result exceeded FP magnitude limit. The result of the operation was set to the sign of the number at overflow times 1D+30. Currently, X must be 33 or less in FACT(X) for no overflow. ╒═══════════════╕ │ ASOL3 WARNINGS└─────────────────────────────────────────────────────── :WKP.5.03 Summary of WARNINGS From AstroEquationSolver 3 L 2820 ──────────────────────────────────────────────────────────────────────── Warnings for command "S": 201 - Solution of this set of equations is not possible. Equations are not linearly independent. 202 - Calculated solutions differ from desired solutions. They are two major reasons for this warning: Nonlinear equations and/or insufficient precision of the numbers. Equations may L 2830 not be linear with respect to one or more of the independent variables. The values of the coefficients of the equations may vary so widely in magnitudes that there is insufficient number precision, to 16 digits, to solve the equations. 203 - Number of active dependent variables does not equal number of independent variables. Fixup: The program will decrease the larger number to that of the smaller by making dependent variables or independent variables inactive. L 2840 205 - Severe error encountered in solving linear equations. The magnitudes of the coefficients may be too large! Warnings for commands "W" and "U": 213 - Error in defining the number of active equations and/or the number of active independent variables. There must be at least 1 active equation and 1 active independent variable. The maximum number of active equations is 30. The maximum number of active independent variables is 30. The program will always L 2850 use default conditions to insure that these limits are satisfied. ------------ 5.01 -- Summary of Common WARNINGS During Calculations. --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 63 -- 214 - The active dependent variables may have been set to values which are not consistent with the prior active/inactive states when the command "S", "U" or "W" was used. ╒════════╕ │ ERRORS └────────────────────────────────────────────────────────────── L 2860 5.05 Summary of ERRORS During Evaluation of Equations ──────────────────────────────────────────────────────────────────────── The equation evaluation error numbers with an explanation follow. 1 - ILLEGAL OPERATION. All mathematical operations such as ^, *, /, + and - must have two operands. Y=A*+C is not allowed. Only leading negation is allowed: Y=-A. Y=+A is not proper. L 2870 2 - OPERATION ON WRONG SIDE OF EQUATION. Only the dependent variable can appear to the left of the equal sign. Y+3=X+4 is not allowed. 3 - VARIABLE MUST BEGIN WITH A LETTER. 123ABC, %DEF, etc. are not allowed as variable names. 4 - UNMATCHED PARENTHESIS. All parentheses must be used in pairs. Total must be even. L 2880 5 - EMPTY OR ILLEGAL PARENTHESES. All parentheses must enclose something. No SIN(), Y=(), etc. 6 - MISSING ARGUMENT, ALGEBRA OPERATION. All mathematical operations such as ^, *, /, + and - must have two operands. Y=A*+C is not allowed. Only leading negation is allowed: Y=-A. Y=+A is not proper. 7 - ILLEGAL USE OF FUNCTION. L 2890 A function name cannot be used as a variable name. Y=A+SIN*X is not allowed. Y=A+SIN(X) is proper. The name of something that is not an intrinsic function cannot be used as a function. Y=COTH(X) is not allowed. Y=1/TANH(X) is proper. 8 - TOO MANY EQUAL SIGNS. Only one equal sign per equation is allowed. ----------- 5.05 -- Summary of ERRORS During Evaluation of Equations --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 64 -- 9 - EQUATION INCOMPLETE. An equation must contain a dependent variable, equal sign and L 2900 something after the equal sign. Y= is not valid. 10 - ILLEGAL CHARACTER. Only ASCII characters, decimal 33 (!) and higher can be used as characters in equations. This range includes the numbers, upper and lower case letters, and other symbols such as the Greek letters. Remember, lower case letters are always converted to upper case. Variable names such as ABC, 123, are not allowed. L 2910 11 - DUPLICATE NAME FOR DEPENDENT VARIABLE. Each equation of a group must have a different, and unique to 8 characters, name for the dependent variable. 12 - OUT OF ROOM! DECREASE CONSTANTS. Too many constants and variables, decrease one or the other. 13 - OUT OF ROOM! DECREASE VARIABLES. Too many variables and constants, decrease one or the other. L 2920 14 - OUT OF ROOM! WORKSPACE. Too many operations such as nested parentheses "((()))". Try to rewrite the equation(s) in a more compact way. 15 - OUT OF ROOM! CODESPACE. Too many operations. Try to rewrite equation(s) in a more compact way. Make common expressions separate equations. 16 - UNDEFINED VARIABLE. An attempt has been made to reference a variable which has L 2930 not been defined. Will only occur when immediate calculations are made. 17 - OUT OF ROOM! STORAGE VARIABLES. Attempt to define more than 256 storage variables. Save storage variables with "!]". Use "Z", "!Z" and "@Z" to locate and remove unwanted variables. 18 - ILLEGAL USE OF STORAGE VARIABLE! Attempt to define a storage variable as a dependent variable L 2940 of one of the equations entered in response to the prompt "? Equation(s)". Not allowed! ----------- 5.05 -- Summary of ERRORS During Evaluation of Equations --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 65 -- ╒════════════════╕ │ DISPLAY COLORS └────────────────────────────────────────────────────── 6.01 Setting Foreground/background Colors of Main Equations Screen and Program ──────────────────────────────────────────────────────────────────────── L 2950 For a monochrome monitor, only the default colors white on black (command "!(esc)") or the opposite colors black on white (command "@(esc)") should be used. For color monitors, there are 16 shades of foreground colors and 8 shades of background colors. The text of the comment, equations and variables are in the foreground color. The clock display and bottom-screen menu are in reverse video of these colors. Colors by number are: 0=black, 1=blue, 2=green, 3=cyan, 4=red, 5=magenta, 6=brown, 7=white and 8 to 15 are corresponding high-intensity shades. Use command !N to toggle the next foreground color and L 2960 use command @N to toggle the next background color. If the foreground and background colors are equal, then the displayed information becomes invisible. Colors wrap around from #15 to #0. Use commands "!(esc)" to set fore=#7 (white or green) and back=#0 (black) or command "@(esc)" to set fore=#0 and back=#7. Colors (except white on black, the default) are saved with the equations and are reset when equations are read by the commands "(F8)" or "[" and "@[". Start the program with a set of equations previously saved with the desired startup colors. L 2970 For example: ASOL3 CONFIG.EQU (enter). Note: Type "!(esc)" to reset the monochrome colors before exiting or the DOS colors may remain those at the program exit. ╒═══════════════╕ │ CLOCK DISPLAY └─────────────────────────────────────────────────────── 6.05 Clock Screen: Commands During Display ──────────────────────────────────────────────────────────────────────── L 2980 To start the clock, type !C from the equations display. -> restart/redraw clock screen ! - Restart the clock and redraw the display. Use if the display is overwritten. -> check/enter alarm time L 2990 ---------------------- 6.05 -- Clock Screen: Commands During Display --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 66 -- @ - Check the current alarm time, just type (enter) to exit, or set a new one, type y (enter). -> changing 12/24 hour format # - Toggle between 12 and 24 hour time format (12 hr. default). -> exit back to equations display L 3000 $ - Exit back to the equation display. (ctrl Q) - Exit back to the equation display. -> Dos shell % - Shell (exit) to DOS. Type EXIT (enter) to return to clock. -> lock-up keyboard in security mode L 3010 ^ - Security mode. Enter a password up to 8 characters. To unlock, type exact password. Alarm will stay active. If program does not respond, type (enter) first and then the exact password. While in the security mode, the (alt) and (ctrl) keys are forced off. Most "TSR" programs and emulators which are activated by hot keys should be locked out! During security mode, program will remember date/time's of unauthorized use. If password contains "@", then typing incorrect password will immediately activate alarm-- displaying comment, sounding music and flashing screen! Type any key to L 3020 return to clock. Password still must be entered correctly (with "@") to exit. The apostrophe command 'clo can be used to display the clock, to display the clock and lock with a password and to set the alarm time and comment. Apostrophe commands can be entered almost anywhere in the program. Some examples: 'clo (enter) Display the clock, exit to equations. L 3030 'clo =big (enter) display the clock and lock-up with a security password "big". The "=" is used to indicate a password but is not part of the password. 'clo 13:23 meeting in cr 864 (enter). Set the alarm at 1:30 pm and set the comment to "meeting in cr 864". Clock is not ---------------------- 6.05 -- Clock Screen: Commands During Display --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 67 -- displayed. ╒═════════════════════╕ │ APOSTROPHE COMMANDS └───────────────────────────────────────────────── L 3040 6.10 Apostrophe Commands: What They Do and How to Use Them ──────────────────────────────────────────────────────────────────────── The apostrophe commands can be entered at most locations in the program as well as in the 'EQU fields of application help files. The apostrophe commands begin with an apostrophe and the first three letters of the key words described below. Only the first L 3050 three letters are significant. Thus 'variable, 'var, 'variety, etc. all imply the same apostrophe command: 'var. apostrophe command are case insensitive except for the 'EQU field designator in an application help file. Apostrophe commands perform many of the functions that are also performed by the single-letter commands discussed above. Some examples: Enter an equation: 'equ y=a+b*x+c*x^2 (enter) L 3060 Enter a comment: 'com This is a second-order polynomial. (enter) Assign values to many variables at one time: 'var x=1 a=2 b=3 c=4 (ent) or 'x=1 a=2 b=3 c=4 (enter). Note, if a variable name is the name of an apostrophe command, use the 'var first; otherwise, the program will interpret the variable name as an apostrophe command. For example if a variable were named COL then 'col=1 (enter) would be interpreted as an improper use of L 3070 the apostrophe command 'col; but, 'var col=1 (enter) is OK. Assign all variables the value of sqr(2): 'var #all=sqr(2) (enter). Make X a coordinate variable: 'coo x (enter) Change the colors to high-intensity white on red: 'col hwhite red (ent) Move the cursor to variable X: 'cur x (enter) or '' x (enter) L 3080 A summary of the apostrophe commands follows: ------ 6.10 -- Apostrophe Commands: What They Do and How to Use Them --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 68 -- PURPOSE COMMAND SIGNIF. SYNTAX ABBREV. Activate variables 'activate 'act 'act varname1,varname2... 'act #all Calc dependent vars 'calculate 'cal 'cal L 3090 display clock 'clock 'clo 'clo clock with password 'clo =password set alarm time and 'clo hr:mn:se comment comment Chain to other ASTRO3 'chain 'cha 'cha calc programs with current 'cha solve variables + equations. 'cha fit L 3100 Make coordinates 'coordinate 'coo 'coo varname1,varname2... 'coo #ind Set display colors, 'color 'col 'col forecolor,backcolor Color names below Set Comment 'comment 'com 'com text...... Set decimal digits 'decimal 'dec 'dec 2 L 3110 Move cursor to 'cursor 'cur 'cur varname1 variable varname1 or '' ''varname1 Get an equation file 'eget 'ege 'ege mycalc named "mycalc.equ" Save equation file 'esave 'esa 'esa mycalc Enter equations 'equation 'equ 'equ equation1.... Erase storage vars 'erase 'era 'era #all L 3120 Exit from program 'exit 'exi 'exi Read application help 'help 'hel 'hel \calc\science file "\calc\science" Only 'help will access last opened help file. ------ 6.10 -- Apostrophe Commands: What They Do and How to Use Them --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 69 -- Immediate calculation 'immediate 'imm 'imm y=25-sqr(144) 'imm y=2*4 z=sqr(144) L 3130 Inactivate variables 'inactivate 'ina 'ina varname1,varname2... 'ina #dep Lite mode. 'lite 'lit 'lit Removes (F5), (F6), (F9), Y, Z functions Set precision 'precision 'pre 'pre single or double L 3140 Turn off sound 'quiet 'qui Assign values to 'variable 'var 'var varname1=value1... variables. Create 'var #all=value2 storage variables. or '' ''varname1=value1... ''#all=value2 Get a storage file 'sget 'sge 'sge mystor named "mystor.sto" L 3150 Jump to spreadsheet 'spread 'spr 'spr (equations display) Save a storage file 'ssave 'ssa 'ssa mystor The options #ALL, #DEP and #IND specify ALL variables, only the DEPENDENT variables or only the INDEPENDENT variables and can be used with 'act, 'ina, 'coo and 'var. Foreground (forecolor) and background (backcolor) colors are: L 3160 0. BLACK 5. MAGENTA 10. LGREEN 1. BLUE 6. BROWN 11. LCYAN 2. GREEN 7. WHITE 12. LRED 3. CYAN 8. GRAY 13. LMAGENTA 4. RED 9. LBLUE 14. YELLOW 15. HWHITE Note: Enter the colors not numbers in 'COLOR command. L means light and H means high-intensity. Also, Only colors from 0 to 7 should be used as backgrounds. L 3170 The screen dump command "V" appends the complete equations, comment, and variable values and status to the screen display in the 'EQU field format. These files can be used to build ------ 6.10 -- Apostrophe Commands: What They Do and How to Use Them --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 70 -- user-generated application help files from which equations etc. can be directly loaded into this program as the help file is read. See the ASTRO3 Utility program, A3UTIL.EXE and documentation for more details. ╒══════════════════╕ L 3180 │ DOS COMMAND LINE └──────────────────────────────────────────────────── 7.01 Information After Program Name on DOS Command Line. How the Program Uses It and What It Does. ──────────────────────────────────────────────────────────────────────── Perform certain functions from information entered after program name in DOS command line. ■ Start with a previously stored file of equations like MYCALC.EQU: L 3190 ASOL3 MYCALC.EQU (enter) or ASOL3 "MYCAL.EQU" (enter) Note: Use quotes if file name contains symbols = + - * / ( or ^. Foreground/background colors are those saved with equations. Start with both storage variable file and equation file: ASOL3 MYVAR.STO MYCAL.EQU (enter) Note: Storage file must come before equation file. Default extensions are ".STO" for storage and ".EQU" for equations. If math symbols are in filename(s), enclose both filenames in single set of quotes: ASOL3 "STO++ EQU--" (enter). L 3200 ■ Start with equation(s) like Y=A*X+B: ASOL3 Y=A*X+B (enter) Note: Equation(s) must contain at least one independent variable. Foreground/background colors are the defaults. ■ Start with a directory listing of a directory such as \calc or a: ASOL3 \calc\ (enter) or ASOL3 a:\ (enter) Note: Directory must be enclosed in "\". "\\" signifies the root directory and "\" signifies the current directory. The directory of a drive must end in "\". L 3210 ■ Perform a single-shot calculations like: ASOL3 23+36+67 (enter) or ASOL3 60,123,456,789.02-40,123,456,789.01 (enter) Note: Single-shot calculations calculate one or more results and prompt "Type any key to continue...". Type (esc) to continue the program or any other key to terminate program and return to DOS. Information must not be enclosed in quotes, must not contain independent variables, and must have at least one operation such as = + - * / ( or ^. L 3220 -------- 7.01 -- Information After Program Name on DOS Command Line. --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 71 -- ■ Enclose each separate calculation in parentheses: ASOL3 (23+78-90) (32-SQR(56)) (2*SIND(87)) (enter) ■ Example of a single-shot calc with 4 dependent variables: ASOL3 A=1 B=2 X=3 Y=A*X+B (enter) ■ To start a program by reading an application help file such as A3UTIL.HLP, simply include the filename with the .HLP extension anywhere on the command line. Note, must maintain L 3230 order of .STO and .EQU files as discussed above! For example: ASOL3 MYVAR.STO MYCAL.EQU A3UTIL.HLP (enter) or ASOL3 A21UTIL.HLP MYVAR MYCAL (enter) or ASOL3 MYVAR A21UTIL.HLP MYCAL (enter) or ASOL3 A21UTIL.HLP MYCAL (enter) ASOL3 ? (enter) and ASOL3 ASOL3HLP.HLP (enter) are equivalent. ■ Do not mix equations or calculations and filenames! For example: Y=A*X+B MYCAL.EQU should not be entered! L 3240 ╒═════════╕ │ LICENSE └───────────────────────────────────────────────────────────── 8.01 Product License and Warranty. ──────────────────────────────────────────────────────────────────────── Software License Agreement (Registered Users) If you are a registered user, PCSCC grants you the right to use this Software for a single-user computer or a workstation not L 3250 attached to a network. You may not rent or lease this Software without the expressed written permission of PCSCC. You may not decompile, disassemble, reverse engineer, copy, create a derivative work, or otherwise use this Software except as stated in this agreement. The license authorizes you to create and use an extra copy of the Software on a home or laptop computer, as long as the extra copy is never loaded at the same time this Software is loaded on the primary computer on which you use this Software. L 3260 If any provision of this agreement is found to be unlawful, void, or unenforceable, then that provision shall be severed from this Agreement and will not affect the validity and enforceability of any of the remaining provisions. This agreement shall be governed by the laws of the State of Delaware. ------------------------------ 8.01 -- Product License and Warranty. --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 72 -- The Software and accompanying materials are provided with Restricted Rights. Use, duplication, or disclosure by the Government is subject to restrictions as set forth in L 3270 subparagraph (c) (1) (ii) of The Rights in Technical Data and Computer Software clause at DFARS 252.227-7013, or subparagraphs (c) (1) and (2) of the Commercial Computer Software--Restricted Rights at 48 CFR 52.227-19, as applicable. Contractor/manufacturer is PC SuperComputer Capital, Incorporated, at the address listed below. Non registered users must comply with the Shareware policy described elsewhere in this software Pacakage. L 3280 Type T to return to the Table of Contents. Warranty Information PC SuperComputer Capital, Inc. (PCSCC) hereby disclaims all warranties relating to this Software, whether express or implied, including without limitation any implied warranties of merchantability or fitness for a particular purpose. PCSCC will not be liable for any special, incidental, consequential, indirect or similar damages due to loss of data, loss of L 3290 profits, lost savings or any other reason, even if PCSCC or an agent of PCSCC has been advised of the possibility of such damages. In no event shall PCSCC's liability for any damages ever exceed the price paid for the license to use Software, regardless of the form of the claim. The person using the Software bears all risk as to the quality and performance of the Software. This Software is licensed AS IS. Any action or proceeding brought by either party against the other arising out of or related to this agreement shall be L 3300 brought in a STATE or FEDERAL COURT of competent jurisdiction located in Fairfield County, Connecticut. The parties hereby consent to in personam jurisdiction of said courts. Type T to return to the Table of Contents. ╒══════════════╕ │ USER SUPPORT └──────────────────────────────────────────────────────── 8.03 User Support. L 3310 ──────────────────────────────────────────────────────────────────────── ---------------------------------------------- 8.03 -- User Support. --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 73 -- This program has undergone over 5 years of "beta testing" around the world. The algorithms have been in use since 1976, are user-firendly and believed highly reliable. However, comprehensive programs of this nature may require clarification or may develop what are called "bugs". User support is provided to all registered users for a minimum of 3 months without charge. Registered users can receive such help via phone, regular mail and E-mail. Registration also enrolls the L 3320 user for notification of "bug" fixes, upgrades, new versions, new products and many more benefits. For the phone number/mail addresses see below or position the jump line here and type J. ∙Registration∙. Support will be provided to non-registered users and users beyond the free support period on a time and materials basis. ╒═════════════╕ │ ARBITRATION └───────────────────────────────────────────────────────── L 3330 8.04 Ombudsman/Arbitration Policy. ──────────────────────────────────────────────────────────────────────── PCSCC, Inc. will follow arbitration guidelines as set forth and published by the Association of Shareware Professionals (ASP). The current ASP policy is stated here: "This program is produced by a member of the Association of Shareware Professionals (ASP). ASP wants to make sure that the shareware principle works for you. If you are unable to L 3340 resolve a shareware-related problem with an ASP member by contacting the member directly, ASP may be able to help. The ASP Ombudsman can help you resolve a dispute or problem with an ASP member, but does not provide technical support for members' products. Please write to the ASP Ombudsman at 545 Grover Road, Muskegon, MI 49442-9427 USA, FAX 616-788-2765 or send a CompuServe message via CompuServe Mail to ASP Ombudsman 70007,3536" ╒═══════════════╕ L 3350 │ PRODUCT INFO └─────────────────────────────────────────────────────── 8.05 Product Information and How to Order Complete Package. ──────────────────────────────────────────────────────────────────────── AstroFormulaCalculator 3 Product Description 11-01-1993 AstroFormulaCalculator 3 is a unique and innovative mathematics ----- 8.05 -- Product Information and How to Order Complete Package. --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 74 -- tool which offers productivity enhancements not found in any other software package either retail or shareware. This L 3360 hands-on program combines the functions of both a spreadsheet and calculator; but it is better. Why? Because it is right between the two: Easier than a spreadsheet and more powerful than a calculator. With its special format-free interface, formula or equation-based iterations are much easier to set up than in a spreadsheet. It is designed to be "smarter" which makes it very user-friendly for Professionals of all levels, especially for the infrequent or "computer-shy" user. Broad applications exist in many disciplines where calculations with formulas, equations or other math recipes are required such as L 3370 in Economics, Genetics, Chemistry, Electrical Engineering, Engineering Mechanics, Fluid Mechanics & Hydraulics, Finance, Physics, Statistics and even Nursing. Features include: ■ DOS or Windows as non-Windows application. Runs on all PC compatibles. DOS 2.1+, Monochrome display, 200K RAM, floppy or disk. ■ DOS command line support for any direct calculation such as addition, multiplication, subtraction and division. L 3380 ■ Format-free entry of up to 63 equations with at least 256 independent variables and 256 constants. Smart and "hassle-free" interpreter. ■ Equations and formulas are written according to the BASIC conventions. Versatile library of built-in functions. ■ Advanced calculator functions including many automated numerical methods such as: L 3390 ∙ Newton-Raphson for solving x in y=f(x) ∙ Advanced simplex for solving x at W=Y=Z in W=f(x), Y=g(x), Z=h(x) ∙ Numerical integration (two methods) ∙ Numerical differentiation ∙ Summation ∙ Finding maxima and minima ∙ Plotting equations ∙ Saving/retrieving data files with full file management L 3400 support ∙ Screen dumps as DOS text files for inclusion in documents ■ Highly-structured documentation, on-line with Table of ----- 8.05 -- Product Information and How to Order Complete Package. --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 75 -- Contents, Glossary and search function. Interactive with program. ∙ On-line helpfile. Comprehensive summary of commands/functions with step-by-step examples on uses of all advanced functions. L 3410 ∙ On-line user manual. A "learn by example" document which illustrates the universal nature of problem-solving with many step-by-step examples from Science, Engineering and Finance. ■ Full support for ACTION21 and ACTION11 data sets. ■ Comments from users: ∙ "... calculate circuit board drilling and routing speeds...easy to use, versatile and powerful with good documentation." L 3420 J. L. New York ∙ "...used the integration capability to determine defect density...do not have any tool (either PC or host based) that does for me what ...(AstroFormCalc 3)...does." J. R. Virginia ∙ "...for Electrical Engineering practice it is better than a spreadsheet and a calculator..." C. B. Florida ∙ "...used to do frequency spectrum work and calculations on circuits, ...of real value and a productivity tool." L 3430 E. S. California ∙ "...one of a handful of scarcely available packages...in the types of numeric problems they solve." W. C. Chile This productivity-enhancing tool has been developed by the team at PC SuperComputer Capital, Inc. Order the complete Astro 3 Package today! ╒════════════════╕ L 3440 │ OTHER PRODUCTS └────────────────────────────────────────────────────── 8.06 Software Included in Astro 3 Registration ──────────────────────────────────────────────────────────────────────── Register for AstroFormulaCalculator 3 and receive, in addition to the most recent version of ACAL3.EXE and ACAL3HLP.HLP, these 3 powerful math analysis programs: AstroEquationSolver 3, AstroDataFitter 3 and AstroShadowBox 3. Each has its own extensive and interactive on-line helpfile written just like L 3450 ------------------ 8.06 -- Software Included in Astro 3 Registration --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 76 -- the one your reading now. A print program is included which prints theses helpfiles to the standard printer or to a DOS text file. All Astro 3 programs are written with the same high-level user-friendly front-end requiring minimal effort to setup and execute relatively elaborate calculations. All data sets and helpfiles are compatible among members of the family. A brief summary of the other members of the Astro 3 shareware family included with the registration package follows: ■ AstroEquationSolver 3 - Solves both linear and nonlinear L 3460 simultaneous equations with up to 30 unknowns. Characterized by extremely easy setup. Uses active/inactive method of AstroEquationSolver 3 to select variables. Strictly high level. No reference to matrices at all!. Includes program ASOL3.EXE and extensive on-line help file ASOL3HLP.HLP that includes many learn-and-use examples. ■ AstroDataFitter 3 - Fit data to any algebraic expression. Nonlinear optimization. Fully-automated polynomial regression with automatic "equation generator". Easy to use, even by a L 3470 novice. Will generate interpolated tables from fitted equations. Up to 30 "active" variables. Up to 500 data points. "Smart" algorithm requires minimal user input to solve problems. DOS text plots of "fit". Point-by-point listing of fitted data. Residual variance, correlation coefficient, coefficient of determination and much more! Includes program AFIT3.EXE and extensive on-line help file AFIT3HLP.HLP that includes many illustrated examples. ■ AstroShadowBox 3 - The pop-up resident member (TSR) of the L 3480 Astro 3 team. Provides math support for other DOS programs. Pop-up via hot key, surround calculation in "shadow box", and type "(enter)" to pass result down through keyboard buffer or pop up, enter calculation and pass result down. Great for adding powerful and interactive math capabilities to DOS text editors such as Brief (tm, Borland), PE2 (tm, IBM) or WordPerfect (tm, WordPerfect). Extensive features also include screen dumps with appends as DOS text files or as parsed columns in 123 (tm, Lotus) .WK1 files. Requires as little as 15K of main memory. Includes program ABOX3.EXE and on-line L 3490 help file ABOX3HLP.HLP If you like Engineering, Science or Finance and you have ideas that you could transform into an interactive helpfile like SCIFIN.HLP (The Astro 3 Science Manual) or PHYCAL.HLP ( The Astro 3 Physics Manual) or FINCAL.HLP (The Astro 3 Finance ------------------ 8.06 -- Software Included in Astro 3 Registration --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 77 -- Manual), then you should write one and market it! If you write it in a commercial spreadsheet format, you will not likely be able to distribute a fully functional package which is the mark of a true Shareware program and the policy of the Association L 3500 of Shareware Professionals! However, the AstroUtility 3 program provides the tools needed to generate an Astro 3 interactive application file with a minimum of effort AND REGISTERED USERS OF THE AstroUtility 3 PROGRAM RECEIVE A LIMITED DISTRIBUTION LICENSE WHICH ALLOWS INCLUSION OF ANY OR ALL OF THE ASTRO 3 PROGRAMS IN YOUR PACKAGE! ■ AstroUtility 3 - Support for authors to construct their own on-line application help files. Develop equation files in your favorite editor and translate them into .EQU format for final L 3510 "test and touch-up". Likewise, develop an application file in your favorite editor, automatically include information from previously developed .EQU files, and then compile a full-feature .HLP with automatic Table of Contents, line numbers and so on. .HLP files support all apostrophe commands and many other useful features such as CalcMerge with lets you dynamically stuff values calculated in the main equation display into the application file. As with the other Astro 3 programs, AstroUtility 3 comes with its own interactive and extensive on-line help file which can be printed, if needed. L 3520 Application files can contain up to 32,000 lines! See below for instructions on ∙Registration∙. ╒══════════════╕ │ REGISTRATION └─────────────────────────────────────────────────────── 8.07 Order/Registration Form ──────────────────────────────────────────────────────────────────────── L 3530 If a printer is available, position the order form (part 1) on the screen and type the "(print screen)" key to make a copy. Then, advance the text and position the order form (part 2) on the screen and type "(print screen)" again to finish. ------------------------------------ 8.07 -- Order/Registration Form --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 78 -- ASTRO 3 Products Order/Registration Form Name:________________________________ Title:________________ Company:_____________________________________________________ L 3540 Address:____________________________ City:___________________ State:___________ Zip:_____________ Country:______________ Date:_____/_____/_____ (Fill out form completely) --------------------------------------------------------------- Product # Price/ea S&H Total --------------------------------------------------------------- L 3550 AstroEquationSolver 3 ___ _$29.95_ _$5.00_ _______ Complete Package includes ACAL3, ASOL3, AFIT3 + ABOX3 AstroUtility 3 + ASTRO3 ___ _$99.95_ _$5.00_ _______ distribution license L 3560 * Canadian Orders, Add $2.00 per copy _______ * International Orders, Add $6.00 per copy _______ * CT Residents add appropriate sales tax _______ TOTAL ENCLOSED __________ Disk Size: [ ] 5-1/4" [ ] 3-1/2" [ ] Check [ ] Visa [ ] MC L 3570 Card# __________________________________ Exp. Date ________ Signature ______________________________ How did you hear about our Products? [ ] BBS [ ] Friend [ ] Other _____________________________________________________ Mail Completed form with Payment to: PCSCC, Inc. Dept. AS3H L 3580 P. O. Box 173 Botsford, CT 06404 USA Support ONLY, 1-203-270-9079 E-mail to CIS, 72263,1657 [Mar 1994] Prices subject to change without notice. Type T to return to the Table of Contents. ------------------------------------ 8.07 -- Order/Registration Form --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 79 -- ╒═════════════════════╕ L 3590 │ MANUAL INSTALLATION └───────────────────────────────────────────────── 8.08 Instructions for Manually Installing Package. ──────────────────────────────────────────────────────────────────────── The following are minimal instructions for manually installing AstroEquationSolver 3. ■ Minimum distribution files: README.1ST, ASOL3.ICO, ASOL3.EXE, and ASOL3HLP.HLP L 3600 ■ These files will probably be bundled in a compressed file such as SCIFIN.ZIP, SCIFIN.LHZ, or something similar. Please unload. ■ Create a DOS directory named ASTRO3 and change to it: cd\ (enter) md\astro3 (enter) cd \astro3 (enter) ■ Copy ASOL3.EXE, ASOL3HLP.HLP and ASOL3.ICO into the directory ASTRO3 ■ Add these statements to AUTOEXEC.BAT in the base directory: L 3610 SET ASTRO3=C:\ASTRO3 append to existing PATH statement ;C:\ASTRO3; ■ Running Under Windows as a Non-Windows Application Follow the installation instructions and install on the hard drive C. Start WINDOWS (tm, MicroSoft). Click on FILE then click on PROPERTIES. Enter the following information for each of the fields. Description: AstroFormCalc 3, Command: ASOL3.EXE, Working Directory: \ASTRO3. Click on CHANGE ICON. Enter Filename: C:\astro3\ASOL3.ico. Click on L 3620 OK to exit and click on OK to exit FILE. The AstroFormCalc 3 icon should appear in the accessory window. Click on it to run ASOL3. ■ To start with user manual: cd\astro3 (enter) ASOL3 ? (enter) To start with equation like y=a*x+b: ASOL3 y=a*x+b (enter) To start with calculation like 45.67+56.23: ASOL3 45.67+56.23 (ent) Type (esc) to enter another calculation or any other key to exit. Access on-line help (file: ASOL3HLP.HLP) from equations display with (F1) key. L 3630 -------------- 8.09 -- Interested in Becoming the Author of Your Own --- -------- ASOL3HLP.HLP ----------- ASOL3 Help File -------------- 80 -- ╒═════════════╕ │ AUTHOR ???? └───────────────────────────────────────────────────────── 8.09 Interested in Becoming the Author of Your Own Interactive Application File? ──────────────────────────────────────────────────────────────────────── Many technologies are based on math/algebra. AstroEquationSolver 3 and its interactive, problem-solving L 3640 application files offer distinct advantages to the Author. The *.EQU templates are easy to develop and PCSCC offers complete support for compiling these into the interactive application files such as the help file ASOL3HLP.HLP which you are currently reading or SCIFIN.HLP (The Astro 3 Science Manual) or PHYCAL.HLP (The Astro 3 Physics Manual) or FINCAL.HLP (The Astro 3 Finance Manual). Application files can be written for any level of user from the very beginner to the Ph.D. and distributed with any or all of the ASTRO 3 family of programs. See the OTHER PRODUCTS section above for more details. To L 3650 automatically jump type "J" if the jump bar is highlighted on those words. ╒═══════════╕ │ HELP FILE └─────────────────────────────────────────────────────────── 9.01 Help File: Summary of File Viewing Commands ──────────────────────────────────────────────────────────────────────── A - Auto-search of entire text for user-supplied string. Search is L 3660 in uppercase and is case insensitive. If string found, type A to continue or to enter new string, type (space) A. B,N - Move back or ahead 18 lines. Also use (backspace) for "B". E, (esc) - Exit from help file to equations display. F,T,K - Jump to the first (beginning), T.O.C or last (end) line. G - Skip to Glossary of terms or summary of functions, if present. J,(ent) - Search line on │JUMP│, Reference is after . Jump to line number or perform autosearch ahead if text reference. L,P - Jump to line/page. Type Lxxx(ent) or Pyy(ent) to jump to line #xxx or page #yy. With + or -, ahead or back 56 lines. L 3670 S,R - Skip ahead (S) or back (R) in help file to major headings W - Skip to Summary of useful calculations or warnings, if present 1 to 9 - Typing 1 to 9 advances the text by 1 to 9 lines. (ctrl Q) - Exit from help file. Same as command "E". Edit keys - Use edit keys: (Home) (up arrow) (PgUp) (left arrow) (right arrow) (End) (down arrow) (PgDn). Entry into the application file is at/near the last position. Type: T to return to Table of Contents or E to exit the file. L 3680 ---------------- 9.01 -- Help File: Summary of File Viewing Commands ---