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  • Book Overview & Buying Sage Beginner's Guide
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Sage Beginner's Guide

Sage Beginner's Guide

By : Craig Finch
3.9 (11)
Buy this Book
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Sage Beginner's Guide

Sage Beginner's Guide

3.9 (11)
By: Craig Finch
Buy this Book

Overview of this book

This is a beginner's guide with clear step-by-step instructions, explanations, and advice. Each concept is illustrated with a complete example that you can use as a starting point for your own work. If you are an engineer, scientist, mathematician, or student, this book is for you. To get the most from Sage by using the Python programming language, we'll give you the basics of the language to get you started. For this, it will be helpful if you have some experience with basic programming concepts.
Table of Contents (17 chapters)
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Sage Beginner's Guide
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Sage Beginner's Guide
Credits
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Credits
About the Author
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About the Author
About the Reviewers
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About the Reviewers
www.PacktPub.com
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www.PacktPub.com
Preface
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Preface
Lock Free Chapter
1
What Can You Do with Sage?
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What Can You Do with Sage?
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Getting started
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Using Sage as a powerful calculator
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More advanced graphics
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A practical example: analysing experimental data
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Time for action – fitting the standard curve
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Time for action – plotting experimental data
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Time for action – fitting a growth model
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Summary
2
Installing Sage
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Installing Sage
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Before you begin
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Installing a binary version of Sage on Windows
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Installing a binary version of Sage on OS X
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Installing a binary version of Sage on GNU/Linux
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Building Sage from source
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Summary
3
Getting Started with Sage
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Getting Started with Sage
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How to get help with Sage
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Starting Sage from the command line
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Using the interactive shell
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Time for action – doing calculations on the command line
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Using the notebook interface
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Time for action – doing calculations with the notebook interface
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Displaying results of calculations
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Operators and variables
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Time for action – using strings
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Callable symbolic expressions
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Time for action – defining callable symbolic expressions
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Functions
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Time for action – calling functions
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Time for action – defining and using your own functions
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Time for action – defining a function with keyword arguments
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Objects
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Time for action – working with objects
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Summary
4
Introducing Python and Sage
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Introducing Python and Sage
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Python 2 and Python 3
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Writing code for Sage
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Sequence types: lists, tuples, and strings
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Time for action – creating lists
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Time for action – accessing items in a list
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Time for action – returning multiple values from a function
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Time for action – working with strings
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For loops
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Time for action – iterating over lists
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Time for action – computing a solution to the diffusion equation
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Time for action – using a list comprehension
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While loops and text file I/O
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Time for action – saving data in a text file
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Time for action – reading data from a text file
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If statements and conditional expressions
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Storing data in a dictionary
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Time for action – defining and accessing dictionaries
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Lambda forms
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Time for action – using lambda to create an anonymous function
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Summary
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Vectors, Matrices, and Linear Algebra
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Vectors, Matrices, and Linear Algebra
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Vectors and vector spaces
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Time for action – working with vectors
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Time for action – manipulating elements of vectors
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Matrices and matrix spaces
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Time for action – solving a system of linear equations
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Time for action – accessing elements and parts of a matrix
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Time for action – manipulating matrices
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Time for action – matrix algebra
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Time for action – trying other matrix methods
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Time for action – computing eigenvalues and eigenvectors
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Time for action – computing the QR factorization
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Time for action – computing the singular value decomposition
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An introduction to NumPy
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Time for action – creating NumPy arrays
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Time for action – working with NumPy arrays
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Time for action – creating matrices in NumPy
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Summary
6
Plotting with Sage
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Plotting with Sage
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Confusion alert: Sage plots and matplotlib
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Plotting in two dimensions
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Time for action – plotting symbolic expressions
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Time for action – plotting a function with a pole
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Time for action – plotting a parametric function
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Time for action – making a polar plot
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Time for action – plotting a vector field
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Time for action – making a scatter plot
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Time for action – plotting a list
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Time for action – plotting with graphics primitives
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Using matplotlib
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Time for action – plotting functions with matplotlib
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Time for action – getting the matplotlib figure object
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Time for action – improving polar plots
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Time for action – making a bar chart
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Time for action – making a pie chart
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Time for action – plotting a histogram
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Plotting in three dimensions
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Time for action – make an interactive 3D plot
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Time for action – parametric plots in 3D
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Time for action – making some contour plots
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Summary
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Making Symbolic Mathematics Easy
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Making Symbolic Mathematics Easy
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Using the notebook interface
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Defining symbolic expressions
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Time for action – defining callable symbolic expressions
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Time for action – defining relational expressions
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Time for action – relational expressions with assumptions
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Manipulating expressions
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Time for action – manipulating expressions
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Time for action – working with rational functions
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Time for action – substituting symbols in expressions
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Time for action – expanding and factoring polynomials
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Time for action – manipulating trigonometric expressions
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Time for action – simplifying expressions
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Solving equations and finding roots
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Time for action – solving equations
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Time for action – finding roots
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Differential and integral calculus
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Time for action – calculating limits
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Time for action – calculating derivatives
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Time for action – calculating integrals
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Series and summations
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Time for action – computing sums of series
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Time for action – finding Taylor series
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Laplace transforms
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Time for action – computing Laplace transforms
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Solving ordinary differential equations
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Time for action – solving an ordinary differential equation
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Summary
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Solving Problems Numerically
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Solving Problems Numerically
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Sage and NumPy
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Solving equations and finding roots numerically
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Time for action – finding roots of a polynomial
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Finding minima and maxima of functions
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Time for action – minimizing a function of one variable
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Time for action – minimizing a function of several variables
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Numerical approximation of derivatives
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Time for action – approximating derivatives with differences
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Time for action – computing gradients
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Numerical integration
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Time for action – numerical integration
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Time for action – numerical integration with NumPy
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Discrete Fourier transforms
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Time for action – computing discrete Fourier transforms
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Time for action – plotting window functions
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Solving ordinary differential equations
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Time for action – solving a first-order ODE
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Time for action – solving a higher-order ODE
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Time for action – alternative method of solving a system of ODEs
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Numerical optimization
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Time for action – linear programming
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Time for action – least squares fitting
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Time for action – a constrained optimization problem
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Probability
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Time for action – accessing probability distribution functions
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Summary
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Learning Advanced Python Programming
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Learning Advanced Python Programming
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How to write good software
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Object-oriented programming
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Time for action – defining a class that represents a tank
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Time for action – making the tanks move
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Time for action – creating your first module
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Time for action – creating a vehicle base class
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Time for action – creating a combat simulation package
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Potential pitfalls when working with classes and instances
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Time for action – using class and instance attributes
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Time for action – more about class and instance attributes
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Time for action – creating empty classes and functions
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Handling errors gracefully
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Time for action – raising and handling exceptions
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Time for action – creating custom exception types
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Unit testing
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Time for action – creating unit tests for the Tank class
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Summary
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Where to go from here
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Where to go from here
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Typesetting equations with LaTeX
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Time for action – PDF output from the notebook interface
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Time for action – working with LaTeX markup in the notebook interface
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Time for action – putting it all together
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Speeding up execution
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Time for action – detecting collisions between spheres
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Time for action – detecting collisions: command-line version
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Time for action – faster collision detection
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Time for action – using NumPy
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Time for action – optimizing collision detection with Cython
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Calling Sage from Python
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Time for action – calling Sage from a Python script
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Introducing Python decorators
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Time for action – introducing the Python decorator
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Making interactive graphics
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Time for action – making interactive controls
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Using interactive controls
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Summary
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Index
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Index

Using matplotlib

We can access matplotlib directly to do things that we can't do with Sage plotting functions. matplotlib has such a large number of options and features that it deserves a separate book. We will only touch on a few basic features. If you want to know more, the matplotlib website has excellent documentation:

http://matplotlib.sourceforge.net/contents.html

CONTINUE READING
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Tech Concepts
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Programming languages
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