Sage -- Sage -- 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.