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.

ReferenceReference

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 ▪ ...

Importing & Exporting Lists »

Import ▪ Export ▪ "Table" ▪ "Text" ▪ "CSV" ▪ ...

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