Welcome ******* Welcome to LAPLACE V0.7 (Evaluation version). This manual describes the installation and usage of the LAPLACE program. The last update was on 17.9.1996. LAPLACE is MAILWARE!! Send me an e-mail or a postcard, if you like it!! Please look at Copyright for more information. Introduction ************ 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. Copyright ========= (C)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 MAILWARE. This means that you should send me a short e-mail or a postcard, if you can't use the Internet. This way I will know, whether there is a demand for my program and it does NOT mean anything like registrating to LAPLACE or like wise. If there should be a SHAREWARE version, you'll have to pay it (if you want ;-) You are not allowed to take money for distributing LAPLACE, except for Urban Mueller and his AMINET CD-collection. You may distribute LAPLACE only as the original archive (Laplace.lha), which can be found in the AMINET in misc/math/Laplace.lha. You are not allowed to distribute modified versions of LAPLACE. You may use modified version for your own, but I take absolutelly NO responsilibity for anything in this case (I even hard for ME to understand, what's happening inside of LAPLACE, so it's quite likely that you won't understand it at all ;-) 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!!! I used the following tools to create LAPLACE: * MUI V3.3 by Stefan Stuntz (see also Docs/Readme.mui). * DICE V2.07 by Matthew Dillon. * ENFORCER V37 by Michael Sinz. * GOLDED V3.1.4 by Dietmar Eilert. * REVUP V1.3 by Boris Folgmann. * FLEXCAT V1.3 by Jochen Wiedmann. * MAKEGUIDE V1.54 by Reinhard Spisser and Sebastiano Vigna. * MUCHMORE V4.1 by Fiedtjof Siebert and Christian Stiens. Registration ============ Since LAPLACE is currently FREEWARE, there's no need to register. But you may send comments, bug report, flames etc. of course. 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. * Writer - Creates totally stupid texts, based on any ASCII input. Even greatest literature will be shamelessly blown up!! * TreeGrow - Create fractal tree images. * GED_Syntax - LaTeX and Texinfo Syntax parser for GoldED4. Can be found at * GED_Syntax - LaTeX and Texinfo Syntax parser for GoldED4. 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. * GED_Syntax - LaTeX and Texinfo Syntax parser for GoldED4. Can be found at text/edit/GED_Syntax.lha. * PGP_GED4 - PGP for GoldED4. Just a modified ARexx script by Lunz O. Wolfgang. Can be found at text/edit/PGP_GED4.lha. Greets ====== Thanks must go to (in alphabetical order): Lauri Aalto (support), Anders Bakkevold (Amiga Translators' Organisation), Volker Barthelmann (support), Lars Bischoff (support), Michael Bock (support), Dirk Burkamp (support), Christoph Dahlen (support), Matthew Dillon (DICE), Walter Dörwald (icons), Dietmar Eilert (GOLDED), Mattias p. Eriksson (icons), Boris Folgmann (REVUP), Grazgur (support), Michael 'Mick' Hohmann (icons), Martin Huttenloher (icons), Mario Kemper (support), Lars Malmborg (support) Konstantinos Margaritis (support), Andreas Mayer (support) Frederik Orinius (support), Sotirios Pappas (support) Christoph Rickers (support), Thomas Schraitle (support), Fiedtjof Siebert (MUCHMORE), Michael Sinz (ENFORCER), Reinhard Spisser (MAKEGUIDE), Christian Stiens (MUCHMORE), Stefan Stuntz (MUI), Tracer, Ken Tyler (support), Sebastiano Vigna (MAKEGUIDE), Jochen Wiedmann (FLEXCAT) And all other folks around this crazy planet, who support the AMIGA!!!! P!\K of /|_ __ . /\ |\__: /|____ /\__:__/\ .   / | \ :/ \ | |/ \/ | \ :   _/ | \_| \ \| _/ |\ \___ ___/ |   \ | | \ \ \ |/ / \ |   \ _________|____\ _/\ ______/\ __|__ / :   \| : \/ \| \/ · \/ . Getting started *************** Requirements ============ * 68020 CPU or better. * OS3.0 (V38) or better. * MUI3.3 (see also Docs/Readme.mui). * 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 debugging...). 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 supplied using this format: 1. KEYWORD 2. KEYWORD=value Syntax 1 is for tooltypes marked as switch. The descripted action is performed, if this keyword is found. To disable it, simple set the keyword in brackets. Tooltypes marked as string use syntax 2. Unknown keyword will be ignored, syntax is caseinsensitive. Supported tooltypes are : AREXXONLY (switch) If specified 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. QUIETEXIT (switch) If specified LAPLACE will not complain about forgotten objects. AUTOLOAD (string) Here you can specify a file to be loaded everytime LAPLACE starts. I needed this mainly for testing... PREFS (string) Specify a path for the preferences file to be used instead of PROGDIR:Laplace.prefs. Usage ***** Working with Laplace ==================== LAPLACE works much like a shell, you enter an expression, press return and LAPLACE gives you the result (after some time;-). See Editing or Menus for more about text editing width LAPLACE. LAPLACE's processing is based on objects. You can define new objects and reference them later. Have a look at Expressions and Definitions. When a new window is opened, LAPLACE will do several things to setup the environment: * load options from Presets/Default.opts. * load F-keys from Presets/Default.fkey. * execute the command include(Init.lh). You may modify all these files, to adjust the environment to your needs. See also Presets or Libraries. 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 ;-) About MUI about MUI, what else New window Open a new, blank window Clear Clears the current window Load.. Open a project file Quickload Fast access to some project files. Use Project/Preferences to modifiy the list. Save Save a project file. Use the current path or select a new Save as.. Save a project file. Select a new path Delete.. Delete project files. They will be lost forever! Preferences.. Opens the preferences window, see below for more information, 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 Edit... Here you specifiy the default values for dynamic options (see Options for a full description) and the strings that are connected to the F-keys. The defined strings will be inserted into the current line, if you you hit an F-key. There 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. The options and F-keys are saved in each project file, but they can explicitly be loaded and saved to preset files. Load... Load options or F-keys from a preset file. You can also select a project file. In this case the options/F-keys will be extracted from the project. Save... Save options or F-keys to a preset file. ARexx A list of ARexx macros. Use Project/Preferences to modify it. Help Index Loads this file, displaying the main page. Functions Loads the file Docs/../Functions, displaying a menu of all functions. Rexx Loads the file Docs/../ARexx, which describes the usage of the ARexx port. 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 the 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. Preferences ----------- bla bla bla... Projects ======== LAPLACE saves project files as plain ASCII files, you may edit them with any standart text\-editor. 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 preset files 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: * object (Types) or * reference (Definitions) or * function (Functions/Functions) or * expression list (see below) or * expression binary_operator expression * unary_operator expression Binary operators are: +, -, *, /, ^ you should know these... × vector product. This is not an usual x, but can be reached by alt-x! || boolean or && boolean and ==, !=, >, <, <=, >= comparison The only unary operator is: ! boolean negation 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 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 debug(). E.g. sin({debug("Hello world!"), pi/2})  Types and objects ================= LAPLACE supports currently six types of objects : Number, Boolean, Vector, Matrix, Equation and Sets. Usually LAPLACE determines the type of an object when it is created. If you declare a constant object, you have to specify the type it should have. To do so, you use the const() function with identifiers of the format name:type. This will create a new object with the specified name and type. Allowed types are n, number number object (default, if you don't give a type) v, vec, vector vector object of any dimension v[d], vec[d], vector[d] vector object of dimension d m, mat, matrix matrix object of any size m[r,c], mat[r,c], matrix[r,c] matrix object with r rows and c columns For example: const(a:vec[3]) [1,2,3;4,5,6;7,8,9] * a Number ------ 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! LAPLACE supports complex numbers. To enter a complex number, simply write something like a + b*i. But they are not fully implemented, e.g. errordistribution is lost when you have complex value in your expression and not all functions work now with complex arguments. 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 work). 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 ;-) A fantastic new feature of LAPLACE is the direct support of Gaussian errordistribution. Now it is possible to enter values with their standart error, do what ever calculations you have to do, and then get the result with the correct error value! This is very useful, if you are calculating with result of some measurements, like I did during my physical practial. For example, you want to measure the earth accelaration by measuring the falling time of a ball. You measured the falling height to 1.119 meters with a precision of one millimeter and the time to 0.50 seconds with a precision of 1/50 second. Now simply enter: t=0.50±0.02 h=1.119±0.001 g=2*s/h^2 and that's all!! (Next time you should do it more precisely..) The ± can be entered by alt-y (on the german keyboard) or alt-z (on others). But you should be aware, that in some cases you might get wrong result, because 10±1 * 10±1 is not the same as 10±1 ^ 2. So, if the same value is used at different places in a formula, it is evaluated as if they had indepented error ranges! The best way to avoid this is declaring all values with errors as parameters, construct you (possibly big) formula and simplify it, so that every parameter occures only a single time, e.g.: x := 10±1 y := 12±2 a = 3*x^2*y^3 b = 5*x^3*y^2 result = a/b eval(result) If you on the other hand have something like this: x := 10±1 result = x/(x+1) you'll get a wrong error value and there is no way to avoid it, sorry. Boolean ------- A boolean object can only contain the two values TRUE and FALSE. Possible operation for boolean objects are: && (and), || (or) and ! (not). a=TRUE b=FALSE c=TRUE a && (b || !c) Vector ------ A vector is a tupel of numbers. To create a vector (2,4,1) enter [2,4,1]. Any expression can be (of course) a component of a vector. You can add and multiply (scalar) two vectors, or multiply a number or matrix with a vector (in this order, not vector * number!). You get the vector product of two 3-dimensional vector by typing vector × vector. The × is not an ordinary x, but can be entered by alt-x (on the german keyboard and probably all others, too). 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 with the columnvectors (1,2,3), (4,5,6) and (7,8,9) can be created with [1,2,3;4,5,6;7,8,9]. If you have rowvector in mind, use [1,4,7;2,5,8;3,6,9]~ instead (append a 'tilde'). You can add and multiply two matrices, or multiply a number and a matrix (in this order, not matrix * number!). Equation -------- To create a equation use the 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 number, 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 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]. If LAPLACE encounters a object name, that was not defined earlier, an constant will be automatically created: f(x) = x^2  f(a)  => a^2 This is the same as f(x) = x^2  const(a)  f(a)  => a^2 This work only for number constants. If you require e.g. a constant vector object, you have to use const() to declare it. Generally you should always declare constants with const(), otherwise you are in danger that the reference has already been defined (e.g. in a library file) and you get an type error, look at this: a=[1,2] .... [thousand of lines...] .... f(x)=x^2 f(a) error--> Not defined to vectors. Conventions ----------- 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 Usage. 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 Definition types ---------------- There are three difference kinds of definitions : variables, parameters and constants. Variables ......... When you reference a variable, it's contents will be inserted. Variable are defined using name = expression. E.g. a=3  a+1  => 4 Parameters .......... 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 eval() function. E.g. a:=3  2*(a+2)  => 2*a+4 eval(2*(a+2))  => 10 Constants ......... Constants have no value, so they won't be evaluate, even with the eval() function. They are defined using the const() function. E.g. const(a)  2*(a+2)  => 2*a+4 eval(2*(a+2))  => 2*a+4 Functions ......... 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 numbers, you have to specify the type in the parameter list, the format is line in 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 It is also possible to omit the arguments; if you do so, LAPLACE will insert the arguments as they were defined, e.g. f(x,y) = x^2 + y^2  f'(x,y) = diff(f(x,y),x)  f'(x,y) = diff(f,x)  Note that the last two lines are the same, because f will be expanded to f(x,y). 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 include() command to gain access to a library. Some basic files are included: Init.lh This file will always processed, when a new window is opened. InitARexx.lh This file will be processed during the initialization of the ARexx-port. math.lh Some useful mathmatical definition. physic.lh Some useful physical definition. If you want a library to be available on startup add a line include(libname.lh) to the file Include/Init.lh, which is always processed on startup. Options ======= There are some options to influence to calculation or presentation of expression. They are marked with a $ (dollar sign) following a keyword, a = and the new value. As always, LAPLACE searches backwards until it finds an option, this way setting an option will not influence the lines above. If not explicit assignment has been done, the default value is used. To modify these defaults, use the menu item Options/Edit.... These are the keyword: $usefloat Possible value: TRUE, FALSE. If set to TRUE, LAPLACE will always use floatpoints and never converts them to fractions. $useerror Possible value: TRUE, FALSE. If set to FALSE, LAPLACE will not use and display error ranges. $simplify Possible value: TRUE, FALSE. Enable/Disable simplification pass. Without simplification, the calculation will be faster, but the result might look quite ugly. $dispprec Possible value: 1..15. Select maximum number of decimal digits to be displayed. $dispexp Possible value: 1..12. Select number of digits to be displayed before switching to exponential display. $convprec Possible value: 1..32. 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 (precision 12 means 10^(-12)), 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. For example: $usefloat=FALSE sin(2) => sin(2) $usefloat=TRUE $dispprec=5 sin(2) => 0.9093 $dispprec=8 sin(2) => 0.90929743 a=12000.3 $dispexp=3 a => 1.20003*10^4 $dispexp=6 a => 12000.3 Online help =========== To get a short description of a function, you can enter ?functionname, e.g. ?const => const(name1[:type],name2[:type],...) : create constant objects To get a full description use ??functionname. You can also use ??intro as an entrypoint to the complete online documentation. 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 * 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??) * use integers of arbitary length * OS independet kernel and different portations * rewrite the parser, offering things like procedures, for, while, if statements, enter complex numbers as e.g. 2i, etc. * 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 ). * Support for complex numbers is not fully implemented. And that's what already done is quite crappy ;-) Try something like i^2 and you see what I mean... * ARexx port is currently not working, and the docs for it are neither converted to Texinfo nor translated to german. * Things like constant operator set and constant operator equation don't work. This is not a real bug, but a conceptual problem of LAPLACE. To change it some internal changes have to be done that are not insignificant! * It is reported, that the amigaguide.datatype V40 has problems with some parts of the AmigaGuide-manual (the german Anleitung cannot be loaded). This doesn't happen with V39. Has anyone the same problem and knows the reason and/or a solution? Competitors *********** There are many other math programs for different operating systems, but I will only look at those available for AMIGA. Well most of them are quite professional projects, with lots of studied coders and mathematicians behind, so I cannot compete with them. But just have a look at them. MAPLEV ====== Well, what to say about it? I didn't see the AMIGA version, but I know the UN*X version, and I think there are not many differences, at least I think the mathematical functionality is the same. MapleV does almost everythink for you, you can think of. Integrals, differential equations, eigenvectors, function plotting etc. If there would not be a small problem, I would have never written LAPLACE: the price. DM1500.- is a lot of money, which I cannot afford. This was probably the main reason to create LAPLACE. Although there is a cheaper student version for AMIGA systems, I will continue my work, 'cause it's too much work to be wasted! If the price is not a problem for you, don't hesitate to erase LAPLACE from your harddisk. PARI ==== PARI is a freeware project of the university of Bordeaux, France. It lack a graphical user interface, but offers some interesting features. The biggest advantage is: it's really fast! PARI's best sides are algebraic calculus, polynomials and power series. On the other side, it is not able to integrate functions other than polynomials. For transcendential functions a taylor expansion will be integrated, which is at least a good approximation, but it just gives up on broken rational functions. It has a simple function plotter and basic online help, plus a 500k dvi-manual. PARI is available on AMINET, in misc/math/gpamiga_1_38_3.lha (binary) and misc/math/pari_1_38_3.lha (source and docs). Other versions are available at megrez.ceremab.u-bordeaux.fr (147.210.16.17) and math.ucla.edu (FTP). You can contact the authors via e-mail at pari@ceremab.u-bordeaux.fr. MuPAD ===== MuPAD is also free project of the university of Paderborn, Germany. The AMIGA version is still an alpha release and lacks a graphical user interface. It requires an FPU (which I don't own), so I wasn't able to test it. There might be an UN*X version that I can test. You can find MuPAD at math-ftp.uni-paderborn.de/pub/MuPAD/ (FTP) and http://math-www.uni-paderborn.de/MuPAD/ (WWW). Biography ********* Not available now... Index ***** MAPLEV Competitors PARI Competitors About About Address Address binary operators Expressions Boolean Bool Bugs KnownBugs Competitors Competitors complex numbers Number Constants Definitions Copyright Copyright Definitions Definitions Editing Editing Equation Equation errordistribution Number Expression list Expressions Expressions Expressions F-keys Menus F-keys Presets Functions Definitions General usage GeneralUsage Getting started Getting started Greets Greets Grek letters Definitions Installation Installation Introduction Introduction Known bugs KnownBugs Laplace, P. S. Marquis de Biography Libraries Libraries Matrix Matrix Menus Menus MuPAD Competitors Name conventions Definitions Number Number Objects Types Online help OnlineHelp operators Expressions Options Options Parameters Definitions Presets Presets Project Project Registration Registration Requirements Requirements Set Set To do ToDo Tooltypes Tooltypes Types Types unary operators Expressions Usage Usage Usage GeneralUsage Variables Definitions Vector Vector