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List Manipulation
Lists are central constructs in Mathematica, used to represent collections, arrays, sets, and sequences of all kinds. Lists can have any structure and size, and can routinely involve even millions of elements. Well over a thousand built-in functions throughout Mathematica operate directly on lists, making lists a powerful vehicle for interoperability.
Featured Examples |
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Analyze Words in a Block of Text
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Arbitrarily Nested Tables
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Arrange Controls Using Typesetting Constructs
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Automatically Parallelize Computations
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Boolean Operations and Graphs
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Build a Manipulate with Indexed Controls
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Combine Charts to Create New Presentations
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Construct a Globe Showing All Weather Stations
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Create a Tabbed Interface
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Differences between Prime Numbers
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Display Numeric Approximations
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Emulate a Touch-Tone Dialer
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Export a Spreadsheet
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Find Leap Years
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Flatten Nested Arrays
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Frame Prime Integers
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Generate an Array from a Function on Indices
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Generate and Display Elements in a Lattice
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Get and Plot Data from a Database
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Implement the Bubble Sort Algorithm with Patterns and Rules
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Implement the Heap Sort Algorithm with Patterns and Rules
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Lexical Analysis
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Rapidly Search the Human Genome
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Selection Sort Algorithm
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Show Gray Codes of a Given Length
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Successively Replace Entries in an Array
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Use Wolfram|Alpha to Get Information on a Stock
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View Lists as Matrices
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Visualize a Wavelet Scalogram
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Visualize GDP for the G8 Countries
Reference
Constructing Lists »
{a,b,...} (List) — specify a list explicitly
Table — make a table of values of an expression
Array — make an array of any dimension from a function
Range ▪ SparseArray ▪ Tuples ▪ NestList ▪ Sow ▪ Reap ▪ ...
Elements of Lists »
list[[...]] (Part) — parts or sequences of parts (
), resettable with 
First ▪ Last ▪ Take ▪ Drop ▪ Extract ▪ Append ▪ ReplacePart ▪ ...
Select — select according to a function
Cases — give cases matching a pattern
Length ▪ Position ▪ MemberQ ▪ DeleteDuplicates ▪ ...
Rearranging & Restructuring Lists »
Flatten — flatten out nested lists
Join ▪ Partition ▪ Transpose ▪ Reverse ▪ Sort ▪ Split ▪ Gather ▪ Riffle ▪ ...
Applying Functions to Lists »
Map (/@) — map a function over a list: 
Apply (@@, @@@) — apply a function to a list: 
MapIndexed ▪ Scan ▪ Thread ▪ MapThread ▪ Outer ▪ FoldList ▪ ...
Math & Counting Operations »
{..}+{..}, etc. — automatically operate in parallel on list elements
Total ▪ Differences ▪ Tally ▪ Count ▪ BinCounts ▪ ...
Displaying & Visualizing Lists »
Column ▪ Row ▪ Grid ▪ ListPlot ▪ ArrayPlot ▪ ...
