Laplace - A symbolic algebra program Copyright (C) 1995 by A Vision of Paradise Welcome ******* Welcome to Laplace V0.4 (Evaluation version). This manual describes the installation and usage of the Laplace program. About ===== Laplace is (or at least should be) an universal tool for mathematical calculations. It lacks such a GUI with hundreds of windows like those other progs I've found on AMIGA. Instead it works like a shell, you enter a command and get the result displayed, which is much more flexible. I started programming Laplace, because I was looking for a program for handling matrices, what I needed for my studies. First all programs I found were only able to handle floatpoints, but especially in matrix calculations this leads quite fast to large errors. So I made a simple prog that handled fractions instead of floatpoints. After that I needed something to handle parameters in matrices, and so I started totally rewrote Laplace. This is the result. Currently I know only one program on AMIGA that is able to do things like this: MAPLE V. Well, it is millions of lightyear better that Laplace, but feature has it's price: DM1500!!!!! You cannot compare Laplace and MAPLE, neither in power nor price... Copyright ========= ©1996 by A Vision of Paradise This is only an evaluation version of Laplace. I plan to make it SHAREWARE, when it reaches a reasonable state. For know Laplace is FREEWARE. You may distribute Laplace only as the original archive. You may uuencode or??? it, but you must not change the contents. You are not allowed to sell it or take more than $4, DM5.- etc for copying it. Use it on your own risk. If you plan to build a nuclear plant, I take absolutely NO responsibility for uncontrolled chain reaction caused by false calculations!!! Laplace uses MUI V3.3 by Stefan Stuntz (see also Readme.mui/Readme.mui). Laplace was compiled with DICE V2.01 by Matthew Dillon. Laplace was debugged with Enforcer V37 by Michael Sinz. Texts were edited with GoldED V3.1.3 by Dietmar Eilert. Registration ============ Since Laplace is currently FREEWARE, there's no need to register. But you may send comments, bug report, flames etc. of course. Address Address ======= This master piece of programming arts was done by P!\K of /|_ __ . /\ |\__: /|____ /\__:__/\ .   / | \ :/ \ | |/ \/ | \ :   _/ | \_| \ \| _/ |\ \___ ___/ |   \ | | \ \ \ |/ / \ |   \ _________|____\ _/\ ______/\ __|__ / :   \| : \/ \| \/ · \/ .  s-mail: Benjamin Stegemann Rohrbacher Str. 66 69115 Heidelberg Germany e-mail: bstegema@ix.urz.uni-heidelberg.de bstegema@urz-mail.urz.uni-heidelberg.de WWW: http://www.rzuser.uni-heidelberg.de/~bstegema Actual versions of Laplace can be found in the Aminet directory misc/math. If you are interested in other programs I've done so far, look at these: * ShuffleRun - Funny arcarde game for two or more players, including tournament mode. * TankHunter - Two-player tank blasting... * Writer - Creates totally stupid texts, based on any ASCII input. Even greatest literature will be shamelessly blown up!! * TreeGrow - Create fractal tree images. These progs are not available on aminet, sorry, but it's quite old stuff.. Oh, almost forgot it, they are published on Fish disks, wait a moment, I will see which ones.. Jo, back again, it's 814 (TreeGrow), 815 (ShuffleRun) and 818 (TankHunter). Writer is (or was) available on BBS. If you are really interested, send me a mail. Greets ====== Thanks must go to: * Stefan Stuntz for is fantastic MUI. * Matthew Dillon for DICE. * Dietmar Eilert for GoldED. * Martin Huttenloher for MagicWB. * Mattias p. Eriksson for additional icons from is MagicRabbit collection. * Kai Iske for MagicCX. * Stefan Sommerfeld and Michael Knoke for MCP. * Michael Sinz for Enforcer. And all other folks around this crazy planet, who support the AMIGA!!!! P!\K of /|_ __ . /\ |\__: /|____ /\__:__/\ .   / | \ :/ \ | |/ \/ | \ :   _/ | \_| \ \| _/ |\ \___ ___/ |   \ | | \ \ \ |/ / \ |   \ _________|____\ _/\ ______/\ __|__ / :   \| : \/ \| \/ · \/ . Requirements ============ OS3.0 (V38) or better. MUI3.3 may be found in aminet: dev/gui/muiXXusr.lha (see also Readme.mui/Readme.mui). avop.library supplied in this archive. and a FAAAAAST AMIGA... Installation ============ Since Laplace is still under development, I didn't write an installer script ;-) But, don't be afraid, installing is really easy!! Just drag the whole Laplace directory to any place you like, no libs, fonts, catalogs to install. Even an assign isn't needed anymore. You may add the assign Laplace: to the Laplace directory, then this assign will be uses as PROGDIR:, but this is currently not very useful at all (except for me, as I need this to find all files when debuging...). Tooltypes ========= You may enter some tooltypes to the icon of laplace. To do this, select the icon on the workbench and choose Icons/Information from the workbench menu. Then modify the list of tooltypes using the (quite bad) edit functions. Tooltypes are supplies using this format : KEYWORD=value Unknown keyword will be ignored, syntax is caseinsensitive. Supported tooltypes are : AREXXONLY (boolean) Set to YES or NO. If set to yes, Laplace won't open a window on startup, but starts iconified; only an application icon will be shown on the workbench. The first window is opened when doubleclicking on the application icon or uniconifying Laplace on another way. This is useful, if you want don't want to use Laplace directly, but only through it's ARexx port. ..not much eh.. Working with Laplace ==================== Laplace works much like a shell, you enter an Expressions press return and Laplace gives you the result (after some time;-). See Editing or Menus for more details. Laplace's processing is based on objects. You can Definitions new objects and reference them later. When a new window is opened, Laplace will do several things to setup the environment: 1) load options from Presets. 2) load F-keys from Presets. 3) execute the command Functions.guide/include(Init.lh). See also Libraries_Init. You may modify all these files, to adjust the environment to your needs. To load and save sessions, see Project. Editing expressions =================== Well, I think the basic edit functions are now available. Clipboard is supported, but currently only whole lines can be cutted, copied and pasted. Insert line inserts a line before the current line; to insert a line at the end, just press  in the last line. Double clicking on a line, works just line pressing return. Here are the keys that you can use for editing : backspace del left right up down guess what.. shift left shift right advance one word alt left goto beginning of line alt right goto end of line alt up goto first line alt down goto last line ctrl up move one item up in history ctrl down move one item down in history ctrl-shift up move to first item in history ctrl-shift down move to last item in history esc undo changes in current line. This work only, as long as you don't leave the line. return evaluate the current line and advance to the next line. shift return evaluate the current line and insert a new line after it. alt return split the current line at the cursor position and insert a new line after it. shift backspace erase current line from cursor position to the beginning of the line. shift del erase current line from cursor position to the end of the line. alt backspace clear the current line. alt del clear the result of the current line. ctrl tab pop up a list of all available objectes of the current context. Select an entry and it will be inserted at the current cursor position. alt tab pop up a list of all available functions Fn shift Fn insert the string linked to a F-key Menus ===== Project About MUI about Readme.mui/MUI, what else About ;-) New window Open a new, blank window Clear Clears the current window Load.. Open a Project file Save Save a Project file. Use the current path or select a new Save as.. Save a Project file. Select a new path MUI Prefs Open MUI preferences window Quit NOOOOOOOO :-O Edit Cut Copy Paste Insert line Remove line see Editing Windows Debug Opens the debug window with a list of all debug strings. Options Options are specific for a project, they are usually saved in the project file. Always use float x - Use always floatpoints even if fractions could be used. Simplify x - Enable simplification. If Disabled calculation is a bit faster, but the result look quite ugly. Precision... x - Laplace tries to convert floatpoints into fractions whenever possible. But the floatpoint routines are not too exact, so there might be an small difference to the correct value (e.g. 1.2000000000000001 when it should be 1.2). If the difference is smaller than the specified precision, Laplace assumes the value as a fraction and converts it (in this case to 6/5). This is not applied to value near zero, so 1e-30 won't be converted to 0. Exp. display.. x - Select number of digits to be displayed before switching to exponential display. Display precision.. x - Select number of digits to be displayed beyond decimal point. F-Keys.. Define strings linked to the F-keys. The specified text will be inserted into the current line, if you you hit an F-key. The are some special code that can be inserted into the string. They are introduced with a %. If a % should be inserted, you have to enter %%. Possible codes are : %l move the cursor one step to the left. %(l n) move the cursor n steps to the left. %r move the cursor one step to the right. %(r n) move the cursor n steps to the right. %(run command) execute the given shell command. Load F-Keys.. Save F-Keys.. Opens a requester to Presets a set of F-keys. You may load F-keys from other project files. Load options.. Save options.. Opens a requester to Presets the state of the upper options marked with a x. You may load options from other project files. Help Index Loads this file, displaying the main page. Functions Loads this file, displaying Functions.guide/this page. Search... Opens a window, where you can specify a keyword to search for. If the keyword is found the file will be opened on the correct page. Note that text window runs asyncron, which means that you can leave the window opened while working. You don't even have to close the window to continue the search. Just bring the 'Searching...' window to front, select 'Continue' and the next page containing the keyword will be loaded into the textwindow. Projects ======== Laplace saves project files as plain ASCII files, you may edit them with any standart texteditor. Projects are usually placed in the Projects directory. All options (see Menus) and the F-key definitions are save in the project file, the same format as in Presets is used. Presets ======= Options are saved as plain ASCII files, and are usually stored in the Presets directory. The can be edited by any standart texteditor. The line format is quite simple: a line starts with an # followed by a keyword, a = and the value for this option. You must not insert any spaces, except otherwise stated below. E.g. #USEFLOAT=TRUE #ERRBND=12 Options ------- Options (marked with a x in Menus) are saved in files ending with .opts. The keywords are : #USEFLOAT set to TRUE or FALSE #SIMPLIFY set to TRUE or FALSE #ERRBND an integer value between 1 and 32 #EXPDSP an integer value between 1 and 12 #PREC an integer value between 0 and 15 F-keys ------ The F-key definitions are saved in files ending with .fkey. The keyword is followed by the string for the key, the whole rest of the line is used, including all spaces. #F1 ... #F10 normal F-keys 1..10 #F11 ... #F20 shifted F-keys 1..10 Expressions =========== Expressions are entered in a usual manner, e.g. 1+2/3*(4-2)  Guess what's the result... More formally, an correct expression is : * Types or * Definitions or * Functions.guide/functions or * ExpressionList or * expression operator expression Valid operators are : +, -, *, / or ^ You may enter several expression at once, seperated by commas, e.g. 1+2,2/4,12+10  The results will be displayed seperated by lines. Expression List --------------- An expression list is an list of expression seperated by commas embedded in {} brackets or supplied to the Functions.guide/do() command. All expressions will be evaluated, but only the last result will be used. The result of the list will be this last result. This makes only sense with functions like Functions.guide/debug(). E.g. sin({debug("Hello world!"), pi/2})  Types and objects ================= Laplace supports currently five types of objects : Real, Vector, Matrix, Equation and Sets. Real : These are just numbers as well all know them (or do we know them all?!). Numbers can be entered in exponential style, which is {+/-/}ddddd[.ddddd][e{+/-/}dddd]. Ufff, but it's quite easy;-) to enter e.g. 6.626 * 10^(-34) write 6.626e-34. The (whole) number after e is just the exponent. Don't use brackets, if the exponent is negative! As long as you enter only whole numbers, Laplace tries to use fractions, so enter 1/2 instead of 0.5 (in this simple case Laplace converts 0.5 to 1/2 itself, but this may not always word). This way you can enter things like 1/7 exactly, and you won't get result which are almost exact zero, when it should be exact ;-) Vector : A vector is a tupel of reals. To create a vector (2,4,1) enter vector(2,4,1) or as a short form [2,4,1]. A vector may of course contain references to other (real) objects. You can add and multiply (scalar) two vectors, or multiply a real or matrix with a vector (in this order, not vector * real!). Matrix : A matrix is something like a 2-dimensional vector.. (if you don't know what's this, you probably won't need them ;-) A matrix is created by e.g. matrix([1,a,3],[5,7,b],[c,3,4]) or as a short form [[1,a,3],[5,7,b],[c,3,4]] where [..] is a column of the matrix. All columns must be of the same height of course. You can add and multiply two matrices, or multiply a real and a matrix (in this order, not matrix * real!). Equation : To create a equation use the Functions.guide/eq command. You can of cource calculate with equations. The operations will be applied on both side of the equation. You can add or multiply two equations. If you add or multiply a real, vector or matrix to an equation, the equation has to be on the left side, e.g. a=eq(2*x+4,0)  a=a-4  a=a/2  You can also apply functions line sin(), exp()... on equations, e.g. a=eq(ln(x),12*e)  a=exp(a)  Set : To create a set use the Functions.guide/set command. A set is a set (?!?) of objects of the same type. Currently there are some statistic functions that can be applied to sets. If you calculate with sets, all operations (exept those affecting the set directly) are applied to all elements of the set, e.g. s=set(1,2,3)  s+2  This will return the set {3,4,5} Definitions =========== If you want to use an result later or just define a variable, write name = expression. This creates an objects that can be referenced by it's name in later(!) lines. If you reference to an object, Laplace searches from the actual line back, so you may define an object several times, but only the latest version is used. E.g. [1] a=1/2  [2] 2*a  gets 'a' from [1] [3] a=a+1  'a' on the right side references to the definition in [1] and creates a new object called 'a' to be referenced below [4] a  gets 'a' from [3] If you move back to [2], you still get the same result, because the new a is defined below and cannot be reference from [2]. There are some special conventions for object names. Valid characters are A..Z Ö Ä Ü a..z ö ä ü 0..9 § $ '. You may not use a number as the first character. There are two special characters which may be used : ~ (tilde) and _ (underscore). _ as the first character will create a line above the name, which is often used in mathematics. Inside the name _ will create an index, character after _ will be used as the index at the bottom of the name. ~ work similar, but creates an index at the top. You can use both indexes. E.g. _a, a_1, a~1 or everything at once _a~2_1. Starting with version 0.3 Laplace support the usage of greek symbols. If the name or an index matches the name of a greek letter, then this letter is used to display the variable. Number may follow the letter name. E.g. alpha1_beta. A name in lower case represents a small greek letter; if the first character of the name is uppercase, then you get an big greek letter. All supported names are : alpha, beta, gamma, delta, epsilon, zeta, eta, theta, jota, kappa, lambda, my, ny, xi, omikron, pi, rho, sigma, tau, ypsilon, phi, chi, psi, omega, Alpha, Beta, Gamma, Delta, Epsilon, Zeta, Eta, Theta, Jota, Kappa, Lambda, My, Ny, Xi, Omikron, Pi, Rho, Sigma, Tau, Ypsilon, Phi, Chi, Psi, Omega There are three difference kinds of definitions : variables, parameters and constants. When you reference a variable, it's contents will be inserted. Variable are defined using name = expression. E.g. a=3  a+1  -> 4 A reference to a parameter will not be evaluated, it will remain in the result. Use name := expression to create a parameter. If you want to get the final result use the Functions.guide/eval() function. E.g. a:=3  2*(a+2)  -> 2*a+4 eval(2*(a+2))  -> 10 Constants have no value, so they won't be evaluate, even with the Functions.guide/eval() function. They are defined using the Functions.guide/const() function. E.g. const(a)  2*(a+2)  -> 2*a+4 eval(2*(a+2))  -> 2*a+4 You can also define functions. Just enter a argument list embedded in bracket after the object name, e.g. f(x):=x^3  The arguments will be handled like constants in the function expression. If you want to use other object type than reals, you have to specify the type in the parameter list, the format is line in Functions.guide/const(). When referencing a function you have to specify the arguments to be inserted into the function's expression, e.g. f(3)  -> 27 const(a)  f(a+1)  -> (a+1)^3 Libraries ========= Laplace offers the ability to process external files. These files are plain ASCII files and may be edited with every texteditor. These files will be processed, just as if each line would be entered, blank lines and lines with leading ; will be ignored. The results won't be displayed, so this is only useful for constant and function definitions. Library files have a trailing .lh and are located in the Include directory. Use the Functions.guide/include() command to gain access to a library. Some basic files are included : * Libraries_Init * Libraries_Math * Libraries_Physic If you want a library to be available on startup add a line source(libname.lh) to the file Include/Init.lh, which is always processed on startup. Init.lh ------- This file will always be processed on startup. Any definitions or commands that should always be done can be placed here. math.lh ------- some useful mathematical definitions pi:=3.141592653589793 ;-) e:=2.718281828459045 :-> err(x):=exp(-x^2) error function physic.lh --------- some useful physical definitions G:=6.67e-11 gravity constant g:=9.81 earth acceleration N_A:=6.0225e23 avogadro number R:=8.31 gas constant k:=eval(R/N_A) well, R/N_A m_p:=1.6725e-27 a proton's mass in kg m_n:=1.6747e-27 a neutron's mass in kg m_e:=0.911e-30 an electron's mass in kg u:=1.66042e-27 nuclear mass unit in kg (1/12 of C12 atom nucleus) h:=6.626e-34 planck constant _h:=eval(h/(2*pi)) h/(2*pi) m_sun:=1.99e30 the sun's mass in kg r_sun:=6.96e8 the sun's radius in m m_earth:=5.98e24 the earth's mass in kg r_earth:=6.37e6 the earth's radius in m d_earth:=1.49e11 the earth orbits's radius in m m_moon:=7.34e22 the moon's mass in kg r_moon:=1.74e6 the moon's radius in m d_moon:=3.84e8 the moon orbits's radius in m To do ***** As I said before, this is only an evaluation version, so there are quiet a lot of things left to do, before I release Laplace as SHAREWARE. If you have any suggestions, you are invited to send me a note!! Here is a list of some major things: * editing is not very comfortable now, improve it (history, block editing..) * use CGFonts for output (is there anyone out there knowing how to work with the bullet.library?) * support complex numbers * function plotting, perhaps internal or external using ARexx (seems that Graph2D needs a better ARexx port..) * export expressions as TeX,... * calculate integrals (do you REALLY believe, I manage this...) * the greek font is rendered by IntelliFont and doesn't look very pretty (does any have a designed one??) * a whole bunch of small improvementes... Known bugs ********** If you find a bug, not documented feature etc. don't hesitate, TELL ME. Here are those nasty things I know, but didn't manage to remove 'em (for now): * my MUI-CustomClass 'eats' all keyboard input, disabling the tab-key and button shortcuts.. Currently there is only a workaround for the tab-key, but things are still quite ugly... * you get sometimes problems with object names ending with an 'e', try m_e+pi (no spaces!!). m_e + pi (with spaces!!) works... * I'm using the mathieeedoub*.library for floatpoint processing. Seems that it's not too precise; 0.4 * 5.0 is 2 ± 1e-16!! When trying to convert floats into fraction, Laplace ignore differences smaller than 1e-15... * Taylor approximation crashes, if you try to evaluate at an a, where the function is not defined, e.g. taylor( (ln(x))(x), 0, 2 ). Index ***** About About Address Address Constants Definitions Copyright Copyright Definitions Definitions Editing Editing Equation Types Expression list ExpressionList Expressions Expressions F-keys Menus Functions Definitions General usage GeneralUsage Greets Greets Grek letters Definitions Init.lh Libraries_Init Installation Installation Known bugs KnownBugs Libraries Libraries math.lh Libraries_Math Matrix Types Menus Menus Objects Types Parameters Definitions physic.lh Libraries_Physic Presets Presets Project Project Real Types Registration Registration Requirements Requirements Set Types To do ToDo Tooltypes Tooltypes Types Types Usage GeneralUsage Variables Definitions Vector Types