Document Amatrix-Doc A m a t r i x ===================== *********************************** * * * A matrix calculation program * * for real and complex elements * * * *********************************** (C) 1993-95 Nicolas Bassen. All right`s reserve Shareware (read registration file!) * PLEASE EXCUSE MY BAD ENGLISH * ------------------------------------------------------------------------- 1. Introduction With Amatrix you are able to calcutate matrices like your pocket-calculator. + - * inversion determinant function transpose, constant multiplikation linear equation all functions for real/complex elements -------------------------------------------------------------------------- 1.1. Copyright Amatrix is Shareware - it isn't free, and all rights are reserved. You are not allowed to sell this program, and you may only copy it for non-commercial purposes. You may take a look at the program for free, but if you like it (or use it), you should register. Please refer to the Register file for further information about registering. -------------------------------------------------------------------------- 1.2. Disclaimer There is no warranty! I made every effort possible to ensure that Amatrix will function as described, but no warranty of any kind, expressed or implied, is made by me. I will not be liable for any direct or indirect damages to either machinal equipment or mental health arising from a failure of the program to operate in the manner desired by the user. In no event will I be liable for any loss of profits or savings. Amatrix must not be used for the construction, development, production or testing of weapons,weapon systems or gene-technology of any kind. -------------------------------------------------------------------------- 2. Author Nicolas Bassen Grafeler Damm 64 D-27356 Rotenburg Germany FidoNet: 2:241/1120.6 (bevorzugt) Internet: k14k@zfn.uni-bremen.de -------------------------------------------------------------------------- 3. INSTALLATION Harddisk Copy the drawer `Amatrix` where you want and start with dobbleklick. Disk Format a disk and copy the drawer `Amatrix` to the disk. Start Amiga with Workbench-Disk and start Amatrix with dobbleklick. 4. System requirements Amatrix should work an any Amiga. A fast processor is nice but not necessary. -------------------------------------------------------------------------- 5. Using 5.1. Status field After the starting routine a window appears and the program check for a Virus. The program need therefore the origin name of the program. Please don`t rename the program. There are 6 buttons for 6 matrix-memory-places. Below these buttons there are the function-buttons. In the bottom of the window there is the "Status field". The Status field shows informations about the program. Important: The first 2 numbers of the Status field shows the last and the last but one marked matrix. That means: You klick on matrix-button 3 You klick on matrix-button 5 Status field shows `35` You klick on `*` and the program calculates matrix3 * matrix5 -------------------------------------------------------------------------- 5.2. Polnish Reverse Notation You want to calculate A+B The Addition is an operation of 2 elements: 1. klick matrix `A` (matrix button of `A` change to marked) 2. klick matrix `B` (matrix button of `B` change to marked) 3. klick `+` The solution will be stored in memory place `7`. Operations of 2 matrices (+,-,*,...) always use the described Polnish Reverse Notation. Operations of 1 matrix (^,^T,DEL,...) always use the last marked matrix. -------------------------------------------------------------------------- 5.3. Menus 5.3.1. Projekt 5.3.1.1. Info Infotext 5.3.1.2. Load You can load matrices which you have saved before. 5.3.1.3. Save You can save matrices to load them later. 5.3.1.4. Quit Quit 5.3.2. Edit 5.3.2.1. edit matrix Edit the matrix elements 5.3.2.2. complex -> real Delete the imaginary part of the marked matrix 5.3.2.3. real -> complex Adds an imaginary part to every matrix element and set it to 0. 5.3.2.4. real part -> 0 Set real part of matrix to 0. 5.3.2.5. imaginary part -> 0 Set imaginary part of matrix to 0. 5.3.2.6. matrix -> identity matrix I If matrix is a sqaure matrix, an identity matrix will be created. 5.3.2.7. delete all The matrices 1-6 will be deleted. 5.3.1. Option 5.3.1.1. display -all matrices will be displayed -only the marked matrix will be displayed 5.3.1.2. mode The values of the elements shown in the display will always be formated: +000.000 8 numbers wide (+10e+3 = +10 * (10*10*10)) +000 4 numbers wide 0.009 is displayed as 0 10000 is displayed as *** +0 2 numbers wide 0.1 is displayed as 0 100 is displayed as *** 5.4. Buttons 5.4.1. Def. Define marked matrix. Matrix Input Window apears on screen. 5.4.2. Name Define matrix-name 5.4.3. <-> Change marked matrices 5.4.4. a*Matrix a * A (a real constant) (a+bi) * A (A is a complex matrix and a,b are real constants) 5.4.5. ^T transpose marked matrix 5.4.6. ^-1 inverse marked matrix (must be a square matrix) 5.4.7. Det calculate the determinant of the marked matrix (must be a square matrix) 5.4.8. Ax=B solve A * x = B B last marked matrix A last but one marked matrix possibilities: -exactly one solution -no solution -infinitely many solutions 5.4.9. +,- Marked matrix is +/- of the last but one marked matrix Both matrices must the same typ 5.4.10. * Multiply marked matrix with the last but one marked matrix. Remark: A*B <> B*A (not ever, but mostly) 5.4.11. ^ A^a (a is a real integer constant and a>1) 5.4.12. DEL Delete marked matrix on doubleklick 5.4.13. View Shows all or only the marked matrix 5.4.14. Stat Status of matrix memory places 5.4.15. 1-6 6 matrix memory places 5.4.16. (7) Matrix memory place of the solution-matrix 5.4.17. (8) free matrix memory `-->' 5.4.18. --> copy 7 to 8 `(8)' 5.4.19. TXT->RAM Copy text of window to RamDisk: 5.5. INPUT Here you have to input the matrix elements. There are 2 Modes: In the Define mode you specify the matrix. In the Input mode you enter the elements. `Start` change from Define to Input mode. `Reset` change from Input to Define mode. 5.5.1. What? `OK` You transfer the matrix to main program `Cursortaten` When no field is activ (klick on title bar) you move the entries with the cursor-key. here you are able to see the not rounded values of the elements! -------------------------------------------------------------------------- 6. And now to something... ...comletely different! Hello translator! The english version use very bad english. I hope you understand that it is a math program and not a pic-viewer. As long as this part is in the version of Amatrix in Aminet, every translator is welcome to translate this doc or better the german version and the following catalog files to good english. Please sent the translation to me and you will get a free key-file for your job per E-Mail. Translations to other languages are just so welcome and rewarded by a free key-file. You have to translate the two catalog files and the english or better the german version of the documentation. 6.1. catalog1 Let TV1="What`s to do?" Let TV2="Wait - Virus checking... !?!" Let TV3="Wasn`t able to check for Virus!" Let TV4="The Program may be hold a Virus!" Let TV5="Please read the manual !!!!!" Let TV6="I think there is no Virus!" Let TV7="First you have to define the matrices!!" Let TV8="The file is not of valid type:" Let TV9="Matrix" Let TV10=" isn`t define (loaded)!" Let TV11="Only with matrices in 1-6!" Let TV12="Only with defined matrices!" Let TV13="Only with complex matrices!" Let TV14="Imaginary part delete." Let TV15="Matrices in 1-6 delete!" Let TV16="Both matrices have to be defined first!" Let TV17="Equal typ of matrix required!" Let TV18=" ...wait, calculating " Let TV19="Matrix has to defined first!!" Let TV20="This function multiply the matrix in" Let TV21="with a numerical constant!" Let TV22="Please enter the constant below" Let TV23="in the statusfield!" Let TV24="Enter the real part below" Let TV25="This Version is registrated to your name." Let TV26="The file `Mathematrix.key` is only" Let TV27="for you and contains your personal data" Let TV28="Don`t copy it!" Let TV29="You are allowed to copy the program" Let TV30="without `Mathematrix.key`!" Let TV31="This is a Demo-Version! The registrated-Version" Let TV32="is availabe by the Author. Read the manual!" Let TV33=" ***" Let TV34="This version only calculate 2x2 matrices!" Let TV35="The Reg-Version calculate `any` matrix." Let TV36=" ***" Let TV37="Imaginary part set to 0" Let TV38="-The matrix in " Let TV39=" has maximum Rank: " Let TV40="-All row (column) are linear indepent." Let TV41="-the correspondent system has" Let TV42=" exactly one solution." Let TV43=" => A*x=B with x = A^-1 * B" Let TV44="-the rows (coloumns) of matrix " Let TV45=" are" Let TV46=" Base of " Let TV47="-dimensional vector-" Let TV48=" space R^" Let TV49="Remark:A^-n = (A^-1)^n A^r * A^s = A^(r+s)" Let TV50=" (A^r)^s = A^(r*s)" Let TV51="The matrix isn`t invertible!" Let TV52="The determinante ist 0" Let TV53="=>" Let TV54="-The matrix in" Let TV55=" isn`t invertible." Let TV56=" has NOT maximum Rank." Let TV57=" Rank <" Let TV58="-the rows (columns) are linear independent." Let TV59="-the corespondent system has NO exactly" Let TV60=" solution." Let TV61="not a square matrix!" Let TV62="the determinant of the matrix in" Let TV63=" is (" Let TV64="Infinitely many solutions!" Let TV65="Identity matrix created!" Let TV66="Real part set to 0." Let TV67="Only real matrices!" Let TV68="Imaginary part created and set to 0." Let TV69="...wait " Let TV70="Show:" Let TV71="Not the same number of rows!" Let TV72="The system has no solution!" Let TV73="Base" Let TV74="is special solution / the space of the" Let TV75="correspondent homogen systems" Let TV76="has the dimension :" Let TV77="-parametric equations)" Let TV78="(7) + t1 * (8a) + t2 * (8b) +... is the" Let TV79="parametric equation and t1,t2...are the parameter." Let TV80="(-oo < t < +oo)" Let TV81="8a,8b,...are base vectors of the solution." Let TV82="In 8 all base vectors stand columnwise" Let TV83="together: [8a 8b ...]" Let TV84="Set all parameter t1,t2,.. =0, so" Let TV85="matrix 7 is a special solution of" Let TV86="A*x=B <=> A*(7)=B." Let TV87="is the exactly solution!" Let TV88="Ready - Solution in 7." Let TV89="Really want to define the matrix?" Let TV90=" For define the matrix press `Return`!" Let TV91="Attention:" Let TV92="The actual matrix will be deleted!" Let TV93="The `n`-key followed by" Let TV94=" `Return` will cancel define! (No definition)" Let TV95="row number [" Let TV96="] <> column number [" Let TV97="This function execpt only positiv" Let TV98="exponets. Please enter below:" Let TV99="(integer ; >1)" Let TV100="Remark: A is a square (n x n) matrix," Let TV101="-> A^0 = I (nxn)-identity-matrix" Let TV102=" A^1 = A" Let TV103=" delete" Let TV104="Enetr the new name for (" Let TV105=") and" Let TV106="press the `Return`-key!" Let TV107="(7 copy to 8)" Let TV109="the determinant of the matrix in" Let TV110=" is (" Let TV111="Ready" Let TV112=" was renamed." Let TV113="Exponent must be greater than 1" Let TV114="Syntax unknown!" Let TV115="Enter the imaginary part of the constant below" Let TV116=" matrix wasn`t defined new!" 6.2. catalog2 Let TV1="(Demo version -> only 2x2 matrices)" Let TV2="Real part" Let TV3="Imaginary part" Let TV4="File contents isn`t valid:" Let TV5="...wait " Let TV6="matrix isn`t defined (loaded)!" Let TV7="Enter the matrix elements" Let TV8="- use cursor-key to change location when" Let TV9=" NO field is activated." Let TV10="The display may be show the ROUNDED values!" Let TV11="This is a DEMO version:" Let TV12="-only calculate 2x2 Matrizen" Let TV13="-the registrated version calculate any matrix" Let TV14="Klick on EXIT-Gadget again to exit without" Let TV15="transfer the matrix." Let TV16="" Let TV17="With `OK` you transfer the matrix to main-program!" Let TV18="" -------------------------------------------------------------------------- 7. Glossar 7.1. *** *** appears, when the value be unfit for the choosen format (See Menu: `mode') 7.2. Virus The program check itself for virus. Please do not rename the program. 7.3. Demo This Demo-version only calculate 2x2-matrices. With the registrated version you`re able to calculate `any` matrix. For the key-file you have to fill out the registration order. See registration file. 7.4. key-file `Demo' -------------------------------------------------------------------------- 8. Literature [1] Merziger,Wirth: Repetitorium der höheren Mathematik ca. 29.80 DM Feldmann Verlag, Am Bergfelde 28, 3257 Springe ISBN 3-923923-33-3 Gutes Nachschlagewerk mit zahlreichen Beispielen: Integral-, Differential-, Vektorrechnung, Matrizen, Determinanten, Folgen, Reihen, Lineare Abbildungen, Determinanten. Dieses Buch eignet sich für interessierte Schüler und Studenten [2] Howard Anton: Elementary Linear Algebra 5e, (English) John Wiley & Sons, Inc. 605 Third Avenue, New York 10158 ISBN 0-471-85223-6 ------------------------------ E N D -------------------------------------