List Manipulation
Lists are central constructs in the Wolfram Language, 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 the Wolfram Language operate directly on lists, making lists a powerful vehicle for interoperability.
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 ▪ Subdivide ▪ SparseArray ▪ NumericArray ▪ Tuples ▪ NestList ▪ ...
Elements of Lists »
list[[…]] — parts or sequences of parts (;;), resettable with =
First ▪ Last ▪ Take ▪ Drop ▪ TakeList ▪ Extract ▪ Append ▪ ReplacePart ▪ ...
Select — select according to a function
Cases — give cases matching a pattern
Length ▪ Position ▪ MemberQ ▪ DeleteDuplicates ▪ ...
Nothing — an element automatically removed from lists
Splice — sequence of elements to automatically be spliced into a list
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: f/@{a,b,c}⟶{f[a],f[b],f[c]}
Apply (@@) — apply to a list: f@@{x,y,z}⟶f[x,y,z]
MapApply (@@@) — apply to a list: f@@@{x,y,z}⟶{f@@x,f@@y,f@@z}
MapIndexed ▪ Scan ▪ Thread ▪ MapThread ▪ Outer ▪ FoldList ▪ ...
Threaded — thread listable functions at the deepest levels of array arguments
Elementwise — make a function behave as if it were listable
Predicates on Lists
ContainsAll ▪ ContainsNone ▪ ContainsAny ▪ ContainsOnly ▪ ContainsExactly
AllMatch ▪ AnyMatch ▪ NoneMatch
Math & Counting Operations »
{…}+{…}, etc. — automatically operate in parallel on list elements
Total ▪ Differences ▪ Count ▪ CountDistinct ▪ Counts ▪ BinCounts ▪ SequenceCount ▪ ...
Displaying & Visualizing Lists »
Column ▪ Row ▪ Grid ▪ ListPlot ▪ ArrayPlot ▪ ...
Importing & Exporting Lists »
Import ▪ Export ▪ "Table" ▪ "Text" ▪ "CSV" ▪ ...
Creating Associations from Lists »
Counts ▪ GroupBy ▪ PositionIndex ▪ ...
Fast Introduction for Programmers: Lists