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CAS Maxima Workbook Roland Salz January 7, 2021 Vers. 0.3.6 This work is published under the terms of the Creative Commons (CC) BY-NC-ND 4.0 license. You are free to: Share — copy and redistribute the material in any medium or format Under the following terms: Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. NonCommercial — You may not use the material for commercial purposes. NoDerivatives — If you remix, transform, or build upon the material, you may not distribute the modified material. No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits. As an exception to the above stated terms, the Maxima team is free to incorporate any material from this work into the official Maxima manual, and to remix, transform, or build upon this material within the official Maxima manual, to be published under its own license terms. No attribution is required in this case. Copyright © Roland Salz 2018-2021 No warranty whatsoever is given for the correctness or completeness of the information provided. Maple, Mathematica, Windows, and YouTube are registered trademarks. This project is work in progress. Comments and suggestions for improvement are welcome. Roland Salz Braunsberger Str. 26 D-44809 Bochum [email protected] i In some cases the objective is clear, and the results are surprising. Richard J. Fateman ii Preface Maxima was developed from 1968-1982 at MIT (Massachusetts Institute of Tech- nology) as the first comprehensive computer algebra system (CAS). Allowing not only for numerical, but also symbolical computation it was used by the leading US universities, by US Government institutions like the DOE, by the US Navy, or NASA. Having been enhanced and improved ever since, now Maxima is free (GPL) soft- ware and counts about 150.000 users worldwide. It is employed in education and research by mathematicians, physicists, engineers, and economists, coping with the major commercial CAS’ of today. Since 2000 the software is maintained by an energetic group of volunteers called the Maxima team. The author wishes to thank its kind and helpful members, in particular Dr. Robert Dodier, who is in charge of the project, Gunter Königsmann, in charge of the frontend wxMaxima, as well as Prof. Richard J. Fateman and Dr. Stavros Macrakis, who participated in the original MIT project and have been contributing to Maxima ever since, for almost half a century now. The intention of the Maxima Workbook is to provide a new documentation of the CAS Maxima. It is aimed at both users and developers. As a users’ manual it contains a description of the Maxima language, here abbreviated MaximaL. User functions written by the author are added wherever he felt that Maxima’s stan- dard functionality is lacking them. As a developers’ manual it describes a possible software development environment. Maxima is written in Common Lisp, so the in- terrelation between MaximaL and Lisp is highlighted. We are convinced that there is no clear distinction between a Maxima user and a developer. Any sophisticated user tends to become a developer, too, and he can do so either on his own or by joining the Maxima team. iii Contents Preface iii I Historical Evolution, Documentation 1 1 Historical evolution 2 1.1 Overview . 2 1.2 MAC, MACLisp and MACSyMa: The project at MIT . 2 1.2.1 Initialization and basic design concepts . 2 1.2.2 Major contributors . 3 1.2.3 The users’ community . 4 1.3 Users’ conferences and first competition . 4 1.3.1 The beginning of Mathematica . 4 1.3.2 Announcement of Maple . 4 1.4 Commercial licensing of Macsyma . 5 1.4.1 End of the development at MIT . 5 1.4.2 Symbolics, Inc. and Macsyma, Inc. 5 1.5 Academic and US government licensing . 6 1.5.1 Berkeley Macsyma and DOE Macsyma . 6 1.5.2 William Schelter at the University of Texas . 7 1.6 GNU public licensing . 7 1.6.1 Maxima, the open source project since 2001 . 7 1.7 Further reading . 8 2 Documentation 9 2.1 Introduction . 9 2.2 Official documentation . 10 2.2.1 Manuals . 10 2.2.1.1 English current version . 10 2.2.1.2 German version from 2011 . 10 2.3 External documentation . 10 2.3.1 Manuals . 10 2.3.1.1 Paulo Ney de Souza: The Maxima Book, 2004 . 10 2.3.2 Tutorials . 10 2.3.2.1 Michel Talon: Rules and Patterns in Maxima, 2019 . 11 2.3.2.2 Jorge Alberto Calvo: Scientific Programming, 2018 . 11 2.3.2.3 Zachary Hannan: wxMaxima for Calculus I + II, 2015 . 11 2.3.2.4 Wilhelm Haager: Computeralgebra mit Maxima: Grund- lagen der Anwendung und Programmierung, 2014 . 11 iv 2.3.2.5 Wilhelm Haager: Grafiken mit Maxima, 2011 . 11 2.3.2.6 Roland Stewen: Maxima in Beispielen, 2013 . 11 2.3.3 Mathematics . 12 2.3.3.1 G. Jay Kerns: Multivariable Calculus with Maxima, 2009 12 2.3.4 Physics . 12 2.3.4.1 Edwin L. (Ted) Woollett: "Maxima by Example", 2018, and "Computational Physics with Maxima or R" . 12 2.3.4.2 Timberlake and Mixon: Classical Mechanics with Max- ima, 2016 . 12 2.3.5 Engineering . 12 2.3.5.1 Andreas Baumgart: Toolbox Technische Mechanik, 2018 12 2.3.5.2 Wilhelm Haager: Control Engineering with Maxima, 2017 12 2.3.5.3 Tom Fredman: Computer Mathematics for the Engi- neer, 2014 . 13 2.3.5.4 Gilberto Urroz: Maxima: Science and Engineering Ap- plications, 2012 . 13 2.3.6 Economics . 13 2.3.6.1 Hammock and Mixon: Microeconomic Theory and Com- putation, 2013 . 13 2.3.6.2 Leydold and Petry: Introduction to Maxima for Eco- nomics, 2011 . 13 2.4 Articles and Papers . 13 2.4.1 Publications by Richard Fateman . 13 2.5 Comparison with other CAS . 14 2.5.1 Tom Fredman: Computer Mathematics for the Engineer, 2014 . 14 2.6 Internal and program documentation . 14 2.7 Mailing list archives . 14 II Basic Operation 15 3 Basics 16 3.1 Introduction . 16 3.1.1 REPL: The read-evaluate-print loop . 16 3.1.2 Command line oriented vs. graphical user interfaces . 17 3.2 Basic operation . 18 3.2.1 Executing an input line or cell . 18 3.3 Basic notation . 18 3.3.1 Output description and numbering conventions . 18 3.3.2 Syntax description operators . 18 3.3.3 Compound and separation operators . 18 3.3.4 Assignment operators . 19 3.3.4.1 Basic : . 19 3.3.4.2 Indirect :: . 20 3.3.5 Miscellaneous operators . 21 3.3.5.1 Comment . 21 3.3.5.2 Documentation reference . 21 v 3.4 Naming of identifiers . 21 3.4.1 MaximaL naming specifications . 21 3.4.1.1 Case sensitivity . 21 3.4.1.2 ASCII standard . 22 3.4.1.3 Unicode support . 22 3.4.1.3.1 Implementation notes . 23 3.4.2 MaximaL naming conventions . 23 3.4.2.1 System functions and variables . 23 3.4.2.2 System constants . 23 3.4.3 Correpondence of MaximaL and Lisp identifiers . 23 4 Using the Maxima REPL at the interactive prompt 25 4.1 Input and output . 25 4.1.1 Input and output tags . 25 4.1.2 Multiplication operator . 26 4.1.3 Special characters . 26 4.2 Input . 26 4.2.0.1 One-dimensional form . 26 4.2.1 Statement termination operators . 26 4.2.2 System variables for backward references . 27 4.2.3 General option variables . 28 4.3 Output . 28 4.3.0.1 One- and two-dimensional form . 28 4.3.0.2 System variables for backward references . 28 4.3.1 Functions for output . 29 4.3.2 General option variables . 29 4.3.3 Variables generated by Maxima . 29 4.3.4 Pretty print for wxMaxima . 29 5 Graphical representation of functions 31 5.1 Introduction . 31 5.2 Plot . 31 5.2.1 General . 31 5.2.1.1 Options, (user) standard options, and system standard options . 31 5.2.1.2 Options for both 2D and 3D plots . 32 5.2.1.3 Zooming the plot . 34 5.2.2 2D . 34 5.2.2.1 plot2d . 34 5.2.2.1.1 Explicit plot . 34 5.2.2.1.2.
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