Sage Beginner''''s Guide ppt

www.it-ebooks.info Sage Beginner's Guide Unlock the full potenal of Sage for simplifying and automang mathemacal compung Craig Finch BIRMINGHAM - MUMBAI www.it-ebooks.info Sage Beginner's Guide Copyright © 2011 Packt Publishing All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmied in any form or by any means, without the prior wrien permission of the publisher, except in the case of brief quotaons embedded in crical arcles or reviews. Every eort has been made in the preparaon of this book to ensure the accuracy of the informaon presented. However, the informaon contained in this book is sold without warranty, either express or implied. Neither the author, nor Packt Publishing, and its dealers and distributors will be held liable for any damages caused or alleged to be caused directly or indirectly by this book. Packt Publishing has endeavored to provide trademark informaon about all of the companies and products menoned in this book by the appropriate use of capitals. However, Packt Publishing cannot guarantee the accuracy of this informaon. First published: May 2011 Producon Reference: 1250411 Published by Packt Publishing Ltd. 32 Lincoln Road Olton Birmingham, B27 6PA, UK. ISBN 978-1-849514-46-0 www.packtpub.com Cover Image by Ed Maclean (edmaclean@gmail.com) www.it-ebooks.info Credits Author Craig Finch Reviewers Dr. David Kirkby Minh Nguyen Acquision Editor Usha Iyer Development Editor Hyacintha D'Souza Technical Editor Ajay Shanker Indexers Tejal Daruwale Rekha Nair Project Coordinator Joel Goveya Proofreaders Aaron Nash Mario Cecere Graphics Nilesh Mohite Producon Coordinator Adline Swetha Jesuthas Cover Work Adline Swetha Jesuthas www.it-ebooks.info About the Author Craig Finch is a Ph. D. Candidate in the Modeling and Simulaon program at the University of Central Florida (UCF). He earned a Bachelor of Science degree from the University of Illinois at Urbana-Champaign and a Master of Science degree from UCF, both in electrical engineering. Craig worked as a design engineer for TriQuint Semiconductor, and currently works as a research assistant in the Hybrid Systems Lab at the UCF NanoScience Technology Center. Craig's professional goal is to develop tools for computaonal science and engineering and use them to solve dicult problems. In parcular, he is interested in developing tools to help biologists study living systems. Craig is commied to using, developing, and promong open-source soware. He provides documentaon and "how-to" examples on his blog at http://www.shocksolution.com. I would like to thank my advisers, Dr. J. Hickman and Dr. Tom Clarke, for giving me the opportunity to pursue my doctorate. I would also like to thank my parents for buying the Apple IIGS computer that started it all. www.it-ebooks.info About the Reviewers Dr. David Kirkby is a chartered engineer living in Essex, England. David has a B.Sc. in Electrical and Electronic Engineering, an M.Sc. in Microwaves and OptoElectronics, and a Ph.D. in Medical Physics. Despite David's Ph.D. being in Medical Physics, it was primarily an engineering project, measuring the opcal properes of human ssue, with a mixture of Monte Carlo modeling, radio frequency design, and laser opcs. David was awarded his Ph.D. in 1999 from University College London. Although not a mathemacian, Dr. Kirkby has made extensive use of mathemacal soware. Most of his experience has been with MathemacaTM from Wolfram Research, although he has used both MATLAB TM and Simulink TM too. David is the author of a number of open-source projects, including soware for modeling transmission lines using nite dierence ( http://atlc.sourceforge.net/), design of Yagi-Uda antennas (http://www.g8wrb.org/yagi/) which can use a genec algorithm for opmizaon, as well as soware for data collecon and analysis from electronic test equipment. David once wrote a web-based interface to MathemacaTM (http://witm. sourceforge.net/ ) which allows MathemacaTM to be used from a personal computer, PDA or smartphone. Soon aer the Sage project was started by Professor William Stein, Dr. Kirkby joined the development of Sage. He primarily worked on the successful port of Sage to the Solaris and OpenSolaris operang systems and encourages other developers to write portable code, conforming to POSIX standard, avoiding GNUisms. Professionally, David's skill sets include computer modeling, radio frequency design, analogue circuit design, electromagnec compability and opcs—both free space and integrated. David has also been a Solaris system administrator for the University of Washington where the Sage project is based. When not working on wring soware, David enjoys playing chess, gardening, and spending me with his wife Lin and dog Smudge. Readers wishing to contact Dr. Kirkby can do so via his website http://www.drkirkby. co.uk/ where details of his consulng services may be found. www.it-ebooks.info Minh Nguyen has been a contributor to the Sage project since December 2007. Over the years, he has worked on various aspects of Sage ranging from the standard documentaon and modules such as cryptography, number theory, and graph theory to the Sage build system. He regularly maintains the Sage website and works on book projects that aim to provide in-depth documentaon on using Sage to study cryptography and mathemacs. More of his ranngs can be found at http://mvngu.wordpress.com. www.it-ebooks.info www.PacktPub.com Support les, eBooks, discount offers and more You might want to visit www.PacktPub.com for support les and downloads related to your book. Did you know that Packt oers eBook versions of every book published, with PDF and ePub les available? You can upgrade to the eBook version at www.PacktPub.com and as a print book customer, you are entled to a discount on the eBook copy. Get in touch with us at service@packtpub.com for more details. At www.PacktPub.com, you can also read a collecon of free technical arcles, sign up for a range of free newsleers and receive exclusive discounts and oers on Packt books and eBooks. http://PacktLib.PacktPub.com Do you need instant soluons to your IT quesons? 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Simply use your login credenals for immediate access. www.it-ebooks.info www.it-ebooks.info Table of Contents Preface 1 Chapter 1: What Can You Do with Sage? 9 Geng started 9 Using Sage as a powerful calculator 12 Symbolic mathemacs 14 Linear algebra 17 Solving an ordinary dierenal equaon 18 More advanced graphics 19 Visualising a three-dimensional surface 20 Typeseng mathemacal expressions 21 A praccal example: analysing experimental data 22 Time for acon – ng the standard curve 22 Time for acon – plong experimental data 24 Time for acon – ng a growth model 25 Summary 26 Chapter 2: Installing Sage 29 Before you begin 29 Installing a binary version of Sage on Windows 30 Downloading VMware Player 30 Installing VMWare Player 30 Downloading and extracng Sage 30 Launching the virtual machine 31 Start Sage 32 Installing a binary version of Sage on OS X 33 Downloading Sage 34 Installing Sage 34 Starng Sage 34 www.it-ebooks.info [...]...Table of Contents Installing a binary version of Sage on GNU/Linux Downloading and decompressing Sage Running Sage from your user account Installing for multiple users Building Sage from source Prerequisites Downloading and decompressing source tarball Building Sage Installation Summary Chapter 3: Getting Started with Sage How to get help with Sage Starting Sage from the command line Using the interactive... http://wiki.sagemath.org/SupportedPlatforms www.it-ebooks.info Preface The mission statement of the Sage project is: Creating a viable, free, open source alternative to Magma, Maple, Mathematica, and Matlab If you are familiar with any of these commercial mathematical software systems, then you already have a good idea what Sage does Sage offers several advantages over its commercial competitors Sage is... the bug list for Sage is public, and it can be accessed at http://trac.sagemath.org/ Users are encouraged to participate in the development of Sage by reporting and fixing bugs, and contributing new capabilities With bugs and source code open for public review, you can have a high degree of confidence that Sage will produce correct results This book is written for people who are new to Sage, and perhaps... experimental data and fitting models Chapter 2, Installing Sage covers how to install a binary version of Sage on Windows and install a binary version of Sage on OS X; install a binary version of Sage on GNU/Linux; compile Sage from source [2] www.it-ebooks.info Preface Chapter 3, Getting Started with Sage covers using the interactive shell; using the notebook interface; learning more about operators and... You Do with Sage? Sage is a powerful tool—but you don't have to take my word for it This chapter will showcase a few of the things that Sage can do to enhance your work At this point, don't expect to understand every aspect of the examples presented in this chapter Everything will be explained in more detail in the later chapters Look at the things Sage can do, and start to think about how Sage might... showcase some of the basics of Sage so that you can follow along using a public notebook server These examples can also be run from an interactive session if you have installed Sage www.it-ebooks.info What Can You Do with Sage? Go to http://www.sagenb.org/ and sign up for a free account You can also browse worksheets created and shared by others If you have already installed Sage, launch the notebook interface... help function to learn more about it." A block of code is set as follows: print('This is a string') print(1.0) print(sqrt) Any command-line input or output is written as follows: sage: R = 250e3 sage: C = 4e-6 sage: tau = R * C sage: tau New terms and important words are shown in bold Words that you see on the screen, in menus or dialog boxes for example, appear in the text like this: "clicking the Next... a small subset of Sage' s capabilities What this book covers Chapter 1, What can You do with Sage? covers how Sage can be used for: making simple numerical calculations; performing symbolic calculations, solving systems of equations and ordinary differential equations; making plots in two and three dimensions; and analyzing experimental data and fitting models Chapter 2, Installing Sage covers how to... Mathematical software systems like Sage have highly optimized functions that implement common numerical operations like integration, solving ordinary differential equations, and solving systems of equations Sage is a collection of nearly 100 mathematical software packages, which are listed at http://www.sagemath.org/links-components.html When possible, existing tools are integrated into Sage, rather than duplicating... can graph it with the following code: f(x) = e^x * cos(x) plot(f, (x, -2, 8)) [ 15 ] www.it-ebooks.info What Can You Do with Sage? Sage will produce the following plot: Sage can also compute definite integrals symbolically: To compute a definite integral, we simply have to tell Sage the limits of integration: f(x) = sqrt(1 - x^2) f_integral = integrate(f, (x, 0, 1)) show(f_integral) The result is: This . extracng Sage 30 Launching the virtual machine 31 Start Sage 32 Installing a binary version of Sage on OS X 33 Downloading Sage 34 Installing Sage 34 Starng Sage. version of Sage on GNU/Linux 35 Downloading and decompressing Sage 35 Running Sage from your user account 36 Installing for mulple users 37 Building Sage from