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Index
Mathematica Cookbook Dedication SPECIAL OFFER: Upgrade this ebook with O’Reilly Preface
Introduction MathematicaCookbook.com Structure of This Book Acknowledgments Conventions Used in This Book Using Code Examples Safari® Enabled How to Contact Us
1. Numerics
1.0 Introduction
Numerical Types Exact and Approximate Results Numerical Expressions Numerical Approximations
1.1 Controlling Precision and Accuracy
Problem Solution Discussion See Also
1.2 Mixing Different Numerical Types
Problem Solution
Mixing exact values and symbols Mixing exact values and approximate values Mixing values of different precision and accuracy
Discussion See Also
1.3 Representing Numbers in Other Bases
Problem Solution Discussion See Also
1.4 Extracting the Digits of a Number
Problem Solution Discussion
1.5 Working with Intervals
Problem Solution Discussion See Also
1.6 Converting Between Numerical Types
Problem Solution Discussion See Also
1.7 Displaying Numbers in Alternate Forms
Problem Solution Discussion See Also
2. Functional Programming
2.0 Introduction
Functional Programming The Elements of Functional Programming DownValues and UpValues Function Attributes
Orderless Flat Listable HoldFirst HoldRest HoldAll
See Also
2.1 Mapping Functions with More Than One Argument
Problem Solution Discussion See Also
2.2 Holding Arbitrary Arguments
Problem Solution Discussion See Also
2.3 Creating Functions That Automatically Map Over Lists
Problem Solution Discussion
2.4 Mapping Multiple Functions in a Single Pass
Problem Solution Discussion See Also
2.5 Keeping Track of the Index of Each Item As You Map
Problem Solution Discussion
2.6 Mapping a Function over a Moving Sublist
Problem Solution Discussion See Also
2.7 Using Prefix and Postfix Notation to Produce More Readable Code
Problem Solution Discussion See Also
2.8 Defining Indexed Functions
Problem Solution Discussion
2.9 Understanding the Use of Fold As an Alternative to Recursion
Problem Solution Discussion See Also
2.10 Incremental Construction of Lists
Problem Solution Discussion See Also
2.11 Computing Through Repeated Function Application
Problem Solution Discussion See Also
2.12 Building a Function Through Iteration
Problem Solution Discussion
2.13 Exploiting Function Composition and Inverse Functions
Problem Solution Discussion See Also
2.14 Implementing Closures
Problem Solution Discussion See Also
2.15 Currying in Mathematica
Problem Solution Discussion See Also
2.16 Creating Functions with Default Values
Problem Solution Discussion
2.17 Creating Functions That Accept Options
Problem Solution Discussion
3. Data Structures
3.0 Introduction
List Functions Set Functions Vector Functions Matrix and Tensor Functions
3.1 Ensuring the Most Efficient Representation of Numerical Lists
Problem Solution Discussion See Also
3.2 Sorting Lists
Problem Solution Discussion See Also
3.3 Determining Order Without Sorting
Problem Solution Discussion See Also
3.4 Extracting the Diagonals of a Matrix
Problem Solution Discussion
3.5 Constructing Matrices of Specific Structure
Problem Solution Discussion See Also
3.6 Constructing Permutation and Shift Matrices
Problem Solution Discussion
3.7 Manipulating Rows and Columns of Matrices
Problem Solution Discussion
3.8 Using Sparse Arrays to Conserve Memory
Problem Solution Discussion See Also
3.9 Manipulating Deeply Nested Lists Using Functions with Level Specifications
Problem Solution Discussion See Also
3.10 Implementing Bit Vectors and Using Format to Customize Their Presentation
Problem Solution Discussion See Also
3.11 Implementing Trees and Traversals Using Lists
Problem Solution Discussion See Also
3.12 Implementing Ordered Associative Lookup Using a Red-Black Tree
Problem Solution Discussion See Also
3.13 Exploiting Mathematica’s Built-In Associative Lookup
Problem Solution Discussion
3.14 Constructing Graphs Using the Combinatorica’ Package
Problem Solution Discussion See Also
3.15 Using Graph Algorithms to Extract Information from Graphs
Problem Solution Discussion See Also
4. Patterns and Rule-Based Programming
4.0 Introduction
Blanks Alternatives Repeats PatternSequence Except Conditions and Pattern Tests Rules See Also
4.1 Collecting Items That Match (or Don’t Match) a Pattern
Problem Solution Discussion See Also
4.2 Excluding Items That Match (or Don’t Match) a Pattern
Problem Solution Discussion
4.3 Counting Items That Match a Pattern
Problem Solution Discussion See Also
4.4 Replacing Parts of an Expression
Problem Solution Discussion See Also
4.5 Finding the Longest (or Shortest) Match for a Pattern
Problem Solution Discussion See Also
4.6 Implementing Algorithms in Terms of Rules
Problem Solution Discussion See Also
4.7 Debugging Infinite Loops When Using ReplaceRepeated
Problem Solution Discussion See Also
4.8 Preventing Evaluation Until Replace Is Complete
Problem Solution Discussion See Also
4.9 Manipulating Patterns with Patterns
Problem Solution Discussion See Also
4.10 Optimizing Rules
Problem Solution Discussion
4.11 Using Patterns As a Query Language
Problem Solution Discussion See Also
4.12 Semantic Pattern Matching
Problem Solution Discussion
4.13 Unification Pattern Matching
Problem Solution Discussion See Also
5. String and Text Processing
5.0 Introduction
Characters and Character Encodings String and Regular Expressions
String expressions
See Also
5.1 Comparing Strings
Problem Solution Discussion
5.2 Removing and Replacing Characters from Strings
Problem Solution
Using patterns Using positions
Discussion
Stripping comments Changing delimiters
Removing XML markup
Replacing with expression evaluation
See Also
5.3 Extracting Characters and Substrings
Problem Solution
Using patterns Using positions
Discussion See Also
5.4 Duplicating a String
Problem Solution Discussion See Also
5.5 Matching and Searching Text
Problem Solution Discussion See Also
5.6 Tokenizing Text
Problem Solution Discussion
5.7 Working with Natural Language Dictionaries
Problem Solution Discussion
Crossword puzzles Anagrams Palindromes Spell-checker
See Also
5.8 Importing XML
Problem Solution Discussion See Also
5.9 Transforming XML Using Patterns and Rules
Problem Solution Discussion
XML-to-XML transformations
See Also
5.10 Transforming XML Using Recursive Functions (à la XSLT)
Problem Solution Discussion See Also
5.11 Writing Parsers and Grammars in Mathematica
Problem Solution Discussion See Also
6. Two-Dimensional Graphics and Plots
6.0 Introduction 6.1 Plotting Functions in Cartesian Coordinates
Problem Solution Discussion See Also
6.2 Plotting in Polar Coordinates
Problem Solution Discussion
6.3 Creating Plots Parametrically
Problem Solution Discussion See Also
6.4 Plotting Data
Problem Solution Discussion See Also
6.5 Mixing Two or More Graphs into a Single Graph
Problem Solution Discussion
6.6 Displaying Multiple Graphs in a Grid
Problem Solution Discussion
6.7 Creating Plots with Legends
Problem Solution Discussion See Also
6.8 Displaying 2D Geometric Shapes
Problem Solution Discussion See Also
6.9 Annotating Graphics with Text
Problem Solution Discussion
6.10 Creating Custom Arrows
Problem Solution Discussion
7. Three-Dimensional Graphics and Plots
7.0 Introduction
The Symbolic Nature of Graphics See Also
7.1 Plotting Functions of Two Variables in Cartesian Coordinates
Problem Solution Discussion See Also
7.2 Plotting Functions in Spherical Coordinates
Problem Solution Discussion See Also
7.3 Plotting Surfaces in Cylindrical Coordinates
Problem Solution Discussion See Also
7.4 Plotting 3D Surfaces Parametrically
Problem Solution Discussion
7.5 Creating 3D Contour Plots
Problem Solution Discussion See Also
7.6 Combining 2D Contours with 3D Plots
Problem Solution Discussion
7.7 Constraining Plots to Specified Regions
Problem Solution Discussion
7.8 Plotting Data in 3D
Problem Solution Discussion See Also
7.9 Plotting 3D Regions Where a Predicate Is Satisfied
Problem Solution Discussion
7.10 Displaying 3D Geometrical Shapes
Problem Solution Discussion
7.11 Constructing Wireframe Models from Mesh
Problem Solution Discussion See Also
7.12 Controlling Viewing Geometry
Problem Solution Discussion
7.13 Controlling Lighting and Surface Properties
Problem Solution Discussion See Also
7.14 Transforming 3D Graphics
Problem Solution Discussion
7.15 Exploring Polyhedra
Problem Solution Discussion See Also
7.16 Importing 3D Graphics from CAD and Other 3D Software
Problem Solution Discussion
8. Image Processing
8.0 Introduction
Image Representation Image Processing in Mathematica 7 See Also
8.1 Extracting Image Information
Problem Solution Discussion See Also
8.2 Converting Images from RGB Color Space to HSV Color Space
Problem Solution Discussion See Also
8.3 Enhancing Images Using Histogram Equalization
Problem Solution Discussion See Also
8.4 Correcting Images Using Histogram Specification
Problem Solution Discussion See Also
8.5 Sharpening Images Using Laplacian Transforms
Problem Solution Discussion See Also
8.6 Sharpening and Smoothing with Fourier Transforms
Problem Solution Discussion
8.7 Detecting Edges in Images
Problem Solution Discussion
8.8 Image Recognition Using Eigenvectors (Eigenimages)
Problem Solution Discussion See Also
9. Audio and Music Processing
9.0 Introduction 9.1 Creating Musical Notes
Problem Solution Discussion
9.2 Creating a Scale or a Melody
Problem Solution
9.3 Adding Rhythm to a Melody
Problem Solution
9.4 Controlling the Volume
Problem Solution
9.5 Creating Chords
Problem Solution
9.6 Playing a Chord Progression
Problem Solution
9.7 Writing Music with Traditional Chord Notation
Problem Solution Discussion
9.8 Creating Percussion Grooves
Problem Solution
9.9 Creating More Complex Percussion Grooves
Problem Solution Discussion
9.10 Exporting MIDI files
Problem Solution
9.11 Playing Functions As Sound
Problem Solution Discussion
9.12 Adding Tremolo
Problem Solution
9.13 Adding Vibrato
Problem Solution
9.14 Applying an Envelope to a Signal
Problem Solution Discussion
9.15 Exploring Alternate Tunings
Problem Solution Discussion
9.16 Importing Digital Sound Files
Problem Solution Discussion
9.17 Analyzing Digital Sound Files
Problem Solution
9.18 Slicing a Sample
Problem Solution Discussion
A Spectrograph
10. Algebra
10.0 Introduction
See Also
10.1 Solving Algebraic Equations
Problem Solution Discussion
10.2 Finding a Polynomial from a Given Root
Problem Solution Discussion
10.3 Transforming Expressions to Other Forms
Problem Solution Discussion See Also
10.4 Generating Polynomials
Problem Solution Discussion
10.5 Decomposing Polynomials into Their Constituent Parts
Problem Solution Discussion See Also
10.6 Dividing Polynomials by Other Polynomials
Problem Solution Discussion
11. Calculus: Continuous and Discrete
11.0 Introduction
See Also
11.1 Computing Limits
Problem Solution Discussion
11.2 Working with Piecewise Functions
Problem Solution Discussion
11.3 Using Power Series Representations
Problem Solution Discussion
11.4 Differentiating Functions
Problem Solution Discussion
11.5 Integration
Problem Solution Discussion
11.6 Solving Differential Equations
Problem Solution Discussion
11.7 Solving Minima and Maxima Problems
Problem Solution Discussion
11.8 Solving Vector Calculus Problems
Problem Solution Discussion See Also
11.9 Solving Problems Involving Sums and Products
Problem Solution Discussion See Also
11.10 Solving Difference Equations
Problem Solution Discussion See Also
11.11 Generating Functions and Sequence Recognition
Problem Solution Discussion See Also
12. Statistics and Data Analysis
12.0 Introduction 12.1 Computing Common Statistical Metrics of Numerical and Symbolic Data
Problem Solution Discussion See Also
12.2 Generating Pseudorandom Numbers with a Given Distribution
Problem Solution Discussion See Also
12.3 Working with Probability Distributions
Problem Solution Discussion See Also
12.4 Demonstrating the Central Limit Theorem
Problem Solution Discussion See Also
12.5 Computing Covariance and Correlation of Vectors and Matrices
Problem Solution Discussion
12.6 Measuring the Shape of Data
Problem Solution Discussion
12.7 Finding and Adjusting for Outliers
Problem Solution Discussion
12.8 Fitting Data Using a Linear Model
Problem Solution Discussion See Also
12.9 Fitting Data Using a Nonlinear Model
Problem Solution Discussion See Also
12.10 Creating Interpolation Functions from Data
Problem Solution Discussion
12.11 Testing for Statistically Significant Difference Between Groups Using ANOVA
Problem Solution Discussion See Also
12.12 Hypothesis Testing with Categorical Data
Problem Solution Discussion See Also
12.13 Grouping Data into Clusters
Problem Solution Discussion See Also
12.14 Creating Common Statistical Plots
Problem Solution Discussion See Also
12.15 Quasi-Random Number Generation
Problem Solution Discussion See Also
12.16 Creating Stochastic Simulations
Problem Solution Discussion See Also
13. Science and Engineering
13.0 Introduction 13.1 Working with Element Data
Problem Solution Discussion
13.2 Working with Chemical Data
Problem Solution Discussion
13.3 Working with Particle Data
Problem Solution Discussion
13.4 Working with Genetic Data and Protein Data
Problem Solution Discussion
13.5 Modeling Predator-Prey Dynamics
Problem Solution Discussion See Also
13.6 Solving Basic Rigid Bodies Problems
Problem Solution Discussion
13.7 Solving Problems in Kinematics
Problem Solution Discussion See Also
13.8 Computing Normal Modes for Coupled Mass Problems
Problem Solution Discussion See Also
13.9 Modeling a Vibrating String
Problem Solution Discussion See Also
13.10 Modeling Electrical Circuits
Problem Solution Discussion
13.11 Modeling Truss Structures Using the Finite Element Method
Problem Solution Discussion See Also
14. Financial Engineering
14.0 Introduction
See Also
14.1 Leveraging Mathematica’s Bundled Financial Data
Problem Solution Discussion
14.2 Importing Financial Data from Websites
Problem Solution Discussion See Also
14.3 Present Value of Future Cash Flows
Problem Solution Discussion See Also
14.4 Interest Rate Sensitivity of Bonds
Problem Solution Discussion
14.5 Constructing and Manipulating Yield Curves
Problem Solution Discussion See Also
14.6 Black-Scholes for European Option Pricing
Problem Solution Discussion See Also
14.7 Computing the Implied Volatility of Financial Derivatives
Problem Solution Discussion
14.8 Speeding Up NDSolve When Solving Black-Scholes and Other PDEs
Problem Solution Discussion See Also
14.9 Developing an Explicit Finite Difference Method for the Black-Scholes Formula
Problem Solution Discussion See Also
14.10 Compiling an Implementation of Explicit Trinomial for Fast Pricing of American Options
Problem Solution Discussion See Also
14.11 Modeling the Value-at-Risk of a Portfolio Using Monte Carlo and Other Methods
Problem Solution Discussion See Also
14.12 Visualizing Trees for Interest-Rate Sensitive Instruments
Problem Solution Discussion See Also
15. Interactivity
15.0 Introduction 15.1 Manipulating a Variable
Problem Solution Discussion
15.2 Manipulating a Symbolic Expression
Problem Solution Discussion
15.3 Manipulating a Plot
Problem Solution Discussion
15.4 Creating Expressions for Which Value Dynamically Updates
Problem Solution Discussion See Also
15.5 Intercepting the Values of a Control Attached to a Dynamic Expression
Problem Solution Discussion See Also
15.6 Controlling Updates of Dynamic Values
Problem Solution Discussion See Also
15.7 Using DynamicModule As a Scoping Construct in Interactive Notebooks
Problem Solution Discussion
15.8 Using Scratch Variables with DynamicModule to Balance Speed Versus Space
Problem Solution Discussion See Also
15.9 Making a Manipulate Self-Contained
Problem Solution Discussion
15.10 Remembering the Values Found Using Manipulate
Problem Solution Discussion
15.11 Improving Performance of Manipulate by Segregating Fast and Slow Operations
Problem Solution Discussion
15.12 Localizing a Function in a Manipulate
Problem Solution Discussion
15.13 Sharing DynamicModule Variables across Cell or Window Boundaries
Problem Solution Discussion See Also
15.14 Creating Your Own Custom Controls
Problem Solution Discussion
15.15 Animating an Expression
Problem Solution Discussion See Also
15.16 Creating Custom Interfaces
Problem Solution Discussion See Also
15.17 Managing a Large Number of Controls in Limited Screen Real Estate
Problem Solution Discussion See Also
16. Parallel Mathematica
16.0 Introduction 16.1 Configuring Local Kernels
Problem Solution Discussion See Also
16.2 Configuring Remote Services Kernels
Problem Solution Discussion See Also
16.3 Sending a Command to Multiple Kernels for Parallel Evaluation
Problem Solution Discussion See Also
16.4 Automatically Parallelizing Existing Serial Expressions
Problem Solution Discussion
16.5 Distributing Data Segments in Parallel and Combining the Results
Problem Solution Discussion
16.6 Implementing Data-Parallel Algorithms by Using ParallelMap
Problem Solution Discussion
16.7 Decomposing a Problem into Parallel Data Sets
Problem Solution Discussion
16.8 Choosing an Appropriate Distribution Method
Problem Solution Discussion See Also
16.9 Running Different Algorithms in Parallel and Accepting the First to Complete
Problem Solution Discussion
16.10 Sharing Data Between Parallel Kernels
Problem Solution Discussion
16.11 Preventing Race Conditions When Multiple Kernels Access a Shared Resource
Problem Solution Discussion See Also
16.12 Organizing Parallel Processing Operations Using a Pipeline Approach
Problem Solution Discussion
16.13 Processing a Massive Number of Files Using the Map-Reduce Technique
Problem Solution Discussion See Also
16.14 Diagnosing Parallel Processing Performance
Problem Solution Discussion
16.15 Measuring the Overhead of Parallelization in Your Environment
Problem Solution Discussion
17. Interfacing Mathematica
17.0 Introduction 17.1 Calling External Command Line Programs from Mathematica
Problem Solution Discussion See Also
17.2 Launching Windows Programs from Mathematica
Problem Solution Discussion
17.3 Connecting the Frontend to a Remote Kernel
Problem Solution Discussion
17.4 Using Mathematica with C and C++
Problem Solution Discussion See Also
17.5 Using Mathematica with Java
Problem Solution Discussion See Also
17.6 Using Mathematica to Interact with Microsoft’s .NET Framework
Problem Solution Discussion See Also
17.7 Using the Mathematica Kernel from a .NET Application
Problem Solution Discussion See Also
17.8 Querying a Database
Problem Solution Discussion See Also
17.9 Updating a Database
Problem Solution Discussion See Also
17.10 Introspection of Databases
Problem Solution Discussion See Also
18. Tricks of the Trade
18.0 Introduction 18.1 Cleaning Up During Incremental Development
Problem Solution Discussion See Also
18.2 Modifying Built-in Functions and Constants
Problem Solution Discussion
18.3 Locating Undocumented Functions
Problem Solution Discussion See Also
18.4 Packaging Your Mathematica Solutions into Libraries for Others to Use
Problem Solution Discussion See Also
18.5 Compiling Functions to Improve Performance
Problem Solution Discussion
18.6 Automating and Standardizing the Appearance of Notebooks Using Stylesheets
Problem Solution Discussion
18.7 Transforming Notebooks into Other Forms
Problem Solution Discussion See Also
18.8 Calling into the Mathematica Frontend
Problem Solution Discussion See Also
18.9 Initializing and Cleaning Up Automatically
Problem Solution Discussion See Also
18.10 Customizing Frontend User Interaction
Problem Solution Discussion See Also
19. Debugging and Testing
19.0 Introduction 19.1 Printing as the First Recourse to Debugging
Problem Solution Discussion See Also
19.2 Debugging Functions Called Many Times
Problem Solution Discussion See Also
19.3 Stack Tracing to Debug Recursive Functions
Problem Solution Discussion See Also
19.4 Taming Trace to Extract Useful Debugging Information
Problem Solution Discussion See Also
19.5 Creating a Poor Man’s Mathematica Debugger
Problem Solution Discussion See Also
19.6 Debugging Built-In Functions with Evaluation and Step Monitors
Problem Solution Discussion See Also
19.7 Visual Debugging with Wolfram Workbench
Problem Solution Discussion See Also
19.8 Writing Unit Tests to Help Ensure Correctness of Your Code
Problem Solution Discussion See Also
19.9 Creating MUnit Tests Where Success Is Not Based on Equality Testing
Problem Solution Discussion
19.10 Organizing and Controlling MUnit Tests and Test Suites
Problem Solution Discussion
19.11 Integrating Wolfram Workbench’s MUnit Package into the Frontend
Problem Solution Discussion See Also
A. About the Author Index About the Author Colophon SPECIAL OFFER: Upgrade this ebook with O’Reilly Copyright
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