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Sage Beginner's Guide. Unlock the full potential of Sage for simplifying and automating mathematical computing with this book and

Craig Finch

E-book

SageBeginners Guide
- Table of Contents
- Sage Beginner's Guide
- Credits
- About the Author
- About the Reviewers
- www.PacktPub.com
  - Support files, eBooks, discount offers and more
    - Why Subscribe?
    - Free Access for Packt account holders
- Preface
  - What this book covers
  - What you need for this book
  - Who this book is for
  - Conventions
  - Time for action heading
    - What just happened?
    - Pop quiz heading
    - Have a go hero heading
  - Reader feedback
  - Customer support
    - Downloading the example code
    - Errata
    - Piracy
    - Questions
- 1. What Can You Do with Sage?
  - Getting started
  - Using Sage as a powerful calculator
    - Symbolic mathematics
    - Have a go hero
    - Linear algebra
    - Solving an ordinary differential equation
  - More advanced graphics
    - Visualising a three-dimensional surface
    - Typesetting mathematical expressions
  - A practical example: analysing experimental data
  - Time for action fitting the standard curve
    - What just happened?
  - Time for action plotting experimental data
    - What just happened?
  - Time for action fitting a growth model
    - What just happened?
  - Summary
- 2. Installing Sage
  - Before you begin
  - Installing a binary version of Sage on Windows
    - Downloading VMware Player
    - Installing VMWare Player
    - Downloading and extracting Sage
    - Launching the virtual machine
    - Start Sage
  - Installing a binary version of Sage on OS X
    - Downloading Sage
    - Installing Sage
    - Starting Sage
  - 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
- 3. Getting Started with Sage
  - How to get help with Sage
  - Starting Sage from the command line
  - Using the interactive shell
  - Time for action doing calculations on the command line
    - What just happened?
    - Getting help
    - Command history
    - Tab completion
    - Interactively tracing execution
  - Using the notebook interface
    - Starting the notebook interface
  - Time for action doing calculations with the notebook interface
    - What just happened?
    - Getting help in the notebook interface
    - Working with cells
    - Working with code
    - Closing the notebook interface
    - Have a go hero using the notebook interface
  - Displaying results of calculations
  - Operators and variables
    - Arithmetic operators
    - Pop quiz working with operators
    - Numerical types
      - Integers and rational numbers
      - Real numbers
      - Complex numbers
      - Symbolic expressions
      - Defining variables on rings
      - Combining types in expressions
    - Pop quiz understanding types
    - Strings
  - Time for action using strings
    - What just happened?
  - Callable symbolic expressions
  - Time for action defining callable symbolic expressions
    - What just happened?
    - Automatically typesetting expressions
  - Functions
  - Time for action calling functions
    - What just happened?
    - Have a go hero make some more plots
    - Built-in functions
      - Numerical approximations
      - The reset and restore functions
    - Defining your own functions
  - Time for action defining and using your own functions
    - What just happened?
    - Functions with keyword arguments
  - Time for action defining a function with keyword arguments
    - What just happened?
  - Objects
  - Time for action working with objects
    - What just happened?
    - Getting help with objects
  - Summary
- 4. Introducing Python and Sage
  - Python 2 and Python 3
  - Writing code for Sage
    - Long lines of code
    - Running scripts
  - Sequence types: lists, tuples, and strings
  - Time for action creating lists
    - What just happened?
    - Getting and setting items in lists
  - Time for action accessing items in a list
    - What just happened?
    - Pop quiz lists and indexing
    - List functions and methods
    - Tuples: read-only lists
  - Time for action returning multiple values from a function
    - What just happened?
    - Strings
  - Time for action working with strings
    - What just happened?
    - Other sequence types
  - For loops
  - Time for action iterating over lists
    - What just happened?
  - Time for action computing a solution to the diffusion equation
    - What just happened?
    - Pop quiz lists and for loops
    - Have a go hero adding another for loop
    - List comprehensions
  - Time for action using a list comprehension
    - What just happened?
  - While loops and text file I/O
  - Time for action saving data in a text file
    - What just happened?
  - Time for action reading data from a text file
    - What just happened?
    - While loops
    - Parsing strings and extracting data
    - Alternative approach to reading from a text file
    - Have a go hero define a function for reading the text file
    - Have a go hero replace a for loop with a while loop
  - If statements and conditional expressions
  - Storing data in a dictionary
  - Time for action defining and accessing dictionaries
    - What just happened?
  - Lambda forms
  - Time for action using lambda to create an anonymous function
    - What just happened?
  - Summary
- 5. Vectors, Matrices, and Linear Algebra
  - Vectors and vector spaces
  - Time for action working with vectors
    - What just happened?
    - Creating a vector space
    - Creating and manipulating vectors
  - Time for action manipulating elements of vectors
    - What just happened?
    - Vector operators and methods
  - Matrices and matrix spaces
  - Time for action solving a system of linear equations
    - What just happened?
    - Creating matrices and matrix spaces
    - Accessing and manipulating matrices
  - Time for action accessing elements and parts of a matrix
    - What just happened?
    - Manipulating matrices
  - Time for action manipulating matrices
    - What just happened?
    - Pop quiz manipulating matrices
    - Matrix algebra
  - Time for action matrix algebra
    - What just happened?
    - Other matrix methods
  - Time for action trying other matrix methods
    - What just happened?
    - Eigenvalues and eigenvectors
  - Time for action computing eigenvalues and eigenvectors
    - What just happened?
    - Have a go hero verifying the eigenvalues and eigenvectors
    - Decomposing matrices
  - Time for action computing the QR factorization
    - What just happened?
  - Time for action computing the singular value decomposition
    - What just happened?
  - An introduction to NumPy
  - Time for action creating NumPy arrays
    - What just happened?
    - Creating NumPy arrays
    - NumPy types
    - Indexing and selection with NumPy arrays
  - Time for action working with NumPy arrays
    - What just happened?
    - Have a go hero replacing lists with NumPy arrays
    - NumPy matrices
  - Time for action creating matrices in NumPy
    - What just happened?
    - Learning more about NumPy
  - Summary
- 6. Plotting with Sage
  - Confusion alert: Sage plots and matplotlib
  - Plotting in two dimensions
    - Plotting symbolic expressions with Sage
  - Time for action plotting symbolic expressions
    - What just happened?
  - Time for action plotting a function with a pole
    - What just happened?
  - Time for action plotting a parametric function
    - What just happened?
  - Time for action making a polar plot
    - What just happened?
  - Time for action plotting a vector field
    - What just happened?
    - Plotting data in Sage
  - Time for action making a scatter plot
    - What just happened?
  - Time for action plotting a list
    - What just happened?
    - Using graphics primitives
  - Time for action plotting with graphics primitives
    - What just happened?
  - Using matplotlib
  - Time for action plotting functions with matplotlib
    - What just happened?
    - Using matplotlib to "tweak" a Sage plot
  - Time for action getting the matplotlib figure object
    - What just happened?
  - Time for action improving polar plots
    - What just happened?
    - Plotting data with matplotlib
  - Time for action making a bar chart
    - What just happened?
  - Time for action making a pie chart
    - What just happened?
  - Time for action plotting a histogram
    - What just happened?
  - Plotting in three dimensions
  - Time for action make an interactive 3D plot
    - What just happened?
    - Higher quality output
    - Parametric 3D plotting
  - Time for action parametric plots in 3D
    - What just happened?
    - Contour plots
  - Time for action making some contour plots
    - What just happened?
  - Summary
- 7. Making Symbolic Mathematics Easy
  - Using the notebook interface
  - Defining symbolic expressions
  - Time for action defining callable symbolic expressions
    - What just happened?
    - Relational expressions
  - Time for action defining relational expressions
    - What just happened?
  - Time for action relational expressions with assumptions
    - What just happened?
  - Manipulating expressions
  - Time for action manipulating expressions
    - What just happened?
    - Manipulating rational functions
  - Time for action working with rational functions
    - What just happened?
    - Substitutions
  - Time for action substituting symbols in expressions
    - What just happened?
    - Expanding and factoring polynomials
  - Time for action expanding and factoring polynomials
    - What just happened?
    - Manipulating trigonometric expressions
  - Time for action manipulating trigonometric expressions
    - What just happened?
    - Logarithms, rational functions, and radicals
  - Time for action simplifying expressions
    - What just happened?
  - Solving equations and finding roots
  - Time for action solving equations
    - What just happened?
    - Finding roots
  - Time for action finding roots
    - What just happened?
  - Differential and integral calculus
  - Time for action calculating limits
    - What just happened?
    - Derivatives
  - Time for action calculating derivatives
    - What just happened?
    - Integrals
  - Time for action calculating integrals
    - What just happened?
  - Series and summations
  - Time for action computing sums of series
    - What just happened?
    - Taylor series
  - Time for action finding Taylor series
    - What just happened?
    - Have a go hero Taylor series
  - Laplace transforms
  - Time for action computing Laplace transforms
    - What just happened?
  - Solving ordinary differential equations
  - Time for action solving an ordinary differential equation
    - What just happened?
  - Summary
- 8. Solving Problems Numerically
  - Sage and NumPy
  - Solving equations and finding roots numerically
  - Time for action finding roots of a polynomial
    - What just happened?
  - Finding minima and maxima of functions
  - Time for action minimizing a function of one variable
    - What just happened?
    - Functions of more than one variable
  - Time for action minimizing a function of several variables
    - What just happened?
  - Numerical approximation of derivatives
  - Time for action approximating derivatives with differences
    - What just happened?
    - Computing gradients
  - Time for action computing gradients
    - What just happened?
  - Numerical integration
  - Time for action numerical integration
    - What just happened?
    - Numerical integration with NumPy
  - Time for action numerical integration with NumPy
    - What just happened?
  - Discrete Fourier transforms
  - Time for action computing discrete Fourier transforms
    - What just happened?
    - Window functions
  - Time for action plotting window functions
    - What just happened?
    - Have a go hero using window functions
  - Solving ordinary differential equations
  - Time for action solving a first-order ODE
    - What just happened?
    - Solving a system of ODEs
  - Time for action solving a higher-order ODE
    - What just happened?
    - Solving the system using the GNU Scientific Library
  - Time for action alternative method of solving a system of ODEs
    - What just happened?
  - Numerical optimization
  - Time for action linear programming
    - What just happened?
    - Fitting a function to a noisy data set
  - Time for action least squares fitting
    - What just happened?
    - Constrained optimization
  - Time for action a constrained optimization problem
    - What just happened?
  - Probability
  - Time for action accessing probability distribution functions
    - What just happened?
  - Summary
- 9. Learning Advanced Python Programming
  - How to write good software
  - Object-oriented programming
  - Time for action defining a class that represents a tank
    - What just happened?
    - Making our tanks move
  - Time for action making the tanks move
    - What just happened?
    - Have a go hero checking the values passed to __init__
    - Creating a module for our classes
  - Time for action creating your first module
    - What just happened?
    - Expanding our simulation to other kinds of vehicles
  - Time for action creating a vehicle base class
    - What just happened?
    - Creating a package for our simulation
  - Time for action creating a combat simulation package
    - What just happened?
    - Have a go hero adding another derived class
  - Potential pitfalls when working with classes and instances
  - Time for action using class and instance attributes
    - What just happened?
  - Time for action more about class and instance attributes
    - What just happened?
    - Creating empty classes and functions
  - Time for action creating empty classes and functions
    - What just happened?
  - Handling errors gracefully
  - Time for action raising and handling exceptions
    - What just happened?
    - Exception types
    - Have a go hero raising exceptions in the __init__ method of Tank
    - Creating your own exception types
  - Time for action creating custom exception types
    - What just happened?
  - Unit testing
  - Time for action creating unit tests for the Tank class
    - What just happened?
    - Strategies for unit testing
    - Have a go hero creating some unit tests
  - Summary
- 10. Where to go from here
  - Typesetting equations with LaTeX
    - Installing LaTeX
  - Time for action PDF output from the notebook interface
    - What just happened?
    - The view function in the interactive shell
    - LaTeX mark-up in the notebook interface
  - Time for action working with LaTeX markup in the notebook interface
    - What just happened?
  - Time for action putting it all together
    - What just happened?
    - Have a go hero Bessel functions of the second kind
  - Speeding up execution
  - Time for action detecting collisions between spheres
    - What just happened?
  - Time for action detecting collisions: command-line version
    - What just happened?
    - Tips for measuring runtimes
    - Optimizing our algorithm
  - Time for action faster collision detection
    - What just happened?
    - Optimizing with NumPy
  - Time for action using NumPy
    - What just happened?
    - More about NumPy
    - Optimizing with Cython
  - Time for action optimizing collision detection with Cython
    - What just happened?
    - Have a go hero further optimization with Cython
  - Calling Sage from Python
  - Time for action calling Sage from a Python script
    - What just happened?
    - Have a go hero solving an ODE symbolically from Python
  - Introducing Python decorators
  - Time for action introducing the Python decorator
    - What just happened?
    - Pop quiz understanding function decorators
    - Have a go hero improving the decorator
    - Have a go hero the memoize decorator
  - Making interactive graphics
  - Time for action making interactive controls
    - What just happened?
  - Using interactive controls
    - Time for action an interactive example
      - What just happened?
      - Have a go hero Taylor series
  - Summary
- Index

Titel: Sage Beginner's Guide. Unlock the full potential of Sage for simplifying and automating mathematical computing with this book and
Autor: Craig Finch
Originaler Titel: Sage Beginner's Guide. Unlock the full potential of Sage for simplifying and automating mathematical computing with this book and eBook
ISBN: 9781849514477, 9781849514477
Veröffentlichungsdatum: 2011-05-11
Format: E-book
Artikelkennung: e_3c7q
Verleger: Packt Publishing

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