At

The element at the given position; a negative index counts from the end.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguagePart!↗

At(collection, index)the element at index; a negative index counts from the end.

At(collection, [i1, i2, …])the elements at several positions at once.

At(collection, Range(start, end))a contiguous slice selected by a Range.

At(collection, Span(i, j, step))a contiguous (or stepped) slice selected by a Span, negative step included.

At(matrix, rows, columns)the submatrix at the given rows and columns; rows (or columns) as All takes every row (or column).

At(expr, index)a part of ANY expression, not just a collection's — the second term of a sum, say.

Typed signatures

Type	Package	Applies
(value: any, index: (boolean | character | indexed_collection<any> | number | string)+) -> unknown	combinatoricsreplaces compute-engine	always
(value: any, index: (boolean | character | indexed_collection<any> | number | string)+) -> unknown	compute-engine	always

Domain: Collections

Details

• Negative indices count from the end: $At(c, -1)$ is the last element. See Last.
• Chaining reaches into nested collections, like indexing a matrix row then column.
• An out-of-range index evaluates to $NaN$ rather than raising an error.
• Index 0 is the collection's own head, matching Wolfram's Part[c, 0] — compute-engine gave $NaN$ before.
• Positional element access, 1-based; negative indices count from the end.
• Two index lists at the row and column positions extract a submatrix; a $Span$ takes a contiguous (optionally stepped or reversed) slice.
• Works on the operands of any expression, not just a collection's — Wolfram's Part reaches into any head.

Examples

11 more kept as data, checked against the oracles

Basic #

live ↗

In$\bigl\lbrack1, 2, 3, 4\bigr\rbrack[2]$Out$2$

live ↗

In$\bigl\lbrack1, 2, 3, 4\bigr\rbrack[-1]$Out$4$

live ↗

In$\bigl\lbrack a, b, c, d\bigr\rbrack[-2]$Out$c$

live ↗

In$\bigl\lbrack a, b, c, d\bigr\rbrack[3]$Out$c$

live ↗

In$\bigl\lbrack a, b, c, d, k, f\bigr\rbrack[3]$Out$c$

live ↗

In$\bigl\lbrack a, b, c, d, k, f\bigr\rbrack[-2]$Out$k$

live ↗

In$\bigl\lbrack a, b, c, d, k, f\bigr\rbrack[\mathrm{Span}(2, 4)]$Out$\bigl\lbrack b, c, d\bigr\rbrack$

Scope #

A list of indices selects several elements at once

live ↗

In$\bigl\lbrack a, b, c, d\bigr\rbrack[\bigl\lbrack1, 3\bigr\rbrack]$Out$\bigl\lbrack a, c\bigr\rbrack$

A Range also works as an index list, extracting a contiguous slice

live ↗

In$\bigl\lbrack a, b, c, d, e\bigr\rbrack[2..4]$Out$\bigl\lbrack b, c, d\bigr\rbrack$

Index 0 is the collection's own head, matching Wolfram's Part[c, 0]

live ↗

In$\bigl\lbrack1, 2, 3\bigr\rbrack[0]$Out$\mathrm{List}$

Several indices reach into successive levels: row 2, column 3

live ↗

In$\bigl\lbrack\bigl\lbrack1, 2, 3\bigr\rbrack, \bigl\lbrack4, 5, 6\bigr\rbrack\bigr\rbrack[2, 3]$Out$6$

Negative indices work at every level

live ↗

In$\bigl\lbrack\bigl\lbrack1, 2\bigr\rbrack, \bigl\lbrack3, 4\bigr\rbrack\bigr\rbrack[-1, -1]$Out$4$

Negative indices inside an index list

live ↗

In$\bigl\lbrack a, b, c, d, f\bigr\rbrack[\bigl\lbrack-1, -2\bigr\rbrack]$Out$\bigl\lbrack f, d\bigr\rbrack$

A stepped Range takes every other element

live ↗

In$\bigl\lbrack a, b, c, d, f\bigr\rbrack[1..3..5]$Out$\bigl\lbrack a, c, f\bigr\rbrack$

Negative bounds count from the end: the last three elements

live ↗

In$\bigl\lbrack a, b, c, d, f\bigr\rbrack[(-3)..(-1)]$Out$\bigl\lbrack c, d, f\bigr\rbrack$

A lazy Range is indexed directly

live ↗

In$(5..10)[2]$Out$6$

$All$ at the first level takes a whole column

live ↗

In$\bigl\lbrack\bigl\lbrack1, 2, 3\bigr\rbrack, \bigl\lbrack4, 5, 6\bigr\rbrack\bigr\rbrack[\mathrm{All}, 2]$Out$\bigl\lbrack2, 5\bigr\rbrack$

Index lists at two levels extract a submatrix (rows 1 and 3, columns 2 and 3)

live ↗

In$\bigl\lbrack\bigl\lbrack1, 2, 3\bigr\rbrack, \bigl\lbrack4, 5, 6\bigr\rbrack, \bigl\lbrack7, 8, 9\bigr\rbrack\bigr\rbrack[\bigl\lbrack1, 3\bigr\rbrack, \bigl\lbrack2, 3\bigr\rbrack]$Out$\bigl\lbrack\bigl\lbrack2, 3\bigr\rbrack, \bigl\lbrack8, 9\bigr\rbrack\bigr\rbrack$

A Span ($2;;4$ in Wolfram) takes a contiguous slice

live ↗

In$\bigl\lbrack a, b, c, d, f\bigr\rbrack[\mathrm{Span}(2, 4)]$Out$\bigl\lbrack b, c, d\bigr\rbrack$

A stepped Span ($1;;-1;;2$) takes every other element up to the end

live ↗

In$\bigl\lbrack a, b, c, d, f\bigr\rbrack[\mathrm{Span}(1, -1, 2)]$Out$\bigl\lbrack a, c, f\bigr\rbrack$

A negative step ($-1;;1;;-1$) walks backwards, reversing the list

live ↗

In$\bigl\lbrack a, b, c, d, f\bigr\rbrack[\mathrm{Span}(-1, 1, -1)]$Out$\bigl\lbrack f, d, c, b, a\bigr\rbrack$

Negative bounds: the last two elements

live ↗

In$\bigl\lbrack a, b, c, d, f\bigr\rbrack[\mathrm{Span}(-2, -1)]$Out$\bigl\lbrack d, f\bigr\rbrack$

Parts of any expression, not just lists: the second term of a sum

live ↗

In$(a+b+c)[2]$Out$b$

Reaches into a named collection, not just a literal list — here the 5th triangular number, 1-indexed

live ↗

In$\mathrm{TriangularNumbers}[5]$Out$15$

Also works on a parameterized collection like $PolygonalNumbers(k)$

live ↗

In$\mathrm{PolygonalNumbers}(5)[3]$Out$12$

live ↗

In$\mathrm{FibonacciNumbers}[1]$Out$0$

At(BellNumbers, 5) is Bell(4) = 15 (1-indexed At, 0-indexed term)

live ↗

In$\mathrm{BellNumbers}[5]$Out$15$

Two indices descend into nested lists

live ↗

In$\bigl\lbrack(x,4), (y,5)\bigr\rbrack[1, 2]$Out$4$

live ↗

In$\bigl\lbrack a, b, c, d, k, f\bigr\rbrack[\bigl\lbrack1, 3, 1, 2, -1, 6\bigr\rbrack]$Out$\bigl\lbrack a, c, a, b, f, f\bigr\rbrack$

live ↗

In$\bigl\lbrack a, b, c, d, k, f\bigr\rbrack[\mathrm{Span}(1, -3)]$Out$\bigl\lbrack a, b, c, d\bigr\rbrack$

live ↗

In$\bigl\lbrack a, b, c, d, n, f, g, h, m, j, k\bigr\rbrack[\mathrm{Span}(3, -3, 2)]$Out$\bigl\lbrack c, n, g, m\bigr\rbrack$

live ↗

In$\bigl\lbrack\bigl\lbrack a, b, c\bigr\rbrack, \bigl\lbrack d, m, f\bigr\rbrack, \bigl\lbrack g, h, k\bigr\rbrack\bigr\rbrack[2, 3]$Out$f$

live ↗

In$\bigl\lbrack\bigl\lbrack a, b, c\bigr\rbrack, \bigl\lbrack d, m, f\bigr\rbrack, \bigl\lbrack g, h, k\bigr\rbrack\bigr\rbrack[2]$Out$\bigl\lbrack d, m, f\bigr\rbrack$

live ↗

In$\bigl\lbrack\bigl\lbrack a, b, c\bigr\rbrack, \bigl\lbrack d, m, f\bigr\rbrack, \bigl\lbrack g, h, k\bigr\rbrack\bigr\rbrack[\bigl\lbrack1, 3\bigr\rbrack]$Out$\bigl\lbrack\bigl\lbrack a, b, c\bigr\rbrack, \bigl\lbrack g, h, k\bigr\rbrack\bigr\rbrack$

live ↗

In$\bigl\lbrack\bigl\lbrack a, b, c\bigr\rbrack, \bigl\lbrack d, m, f\bigr\rbrack, \bigl\lbrack g, h, k\bigr\rbrack\bigr\rbrack[\bigl\lbrack1, 3\bigr\rbrack, \bigl\lbrack2, 3\bigr\rbrack]$Out$\bigl\lbrack\bigl\lbrack b, c\bigr\rbrack, \bigl\lbrack h, k\bigr\rbrack\bigr\rbrack$

One-based indexing

live ↗

In$\bigl\lbrack a, b, c, d, k\bigr\rbrack[3]$Out$c$

A span selects a contiguous range

live ↗

In$\bigl\lbrack a, b, c, d, k\bigr\rbrack[\mathrm{Span}(2, 4)]$Out$\bigl\lbrack b, c, d\bigr\rbrack$

Applications #

Chaining $At$ reaches into nested collections, like indexing a matrix row then column

live ↗

In$\bigl\lbrack\bigl\lbrack1, 2\bigr\rbrack, \bigl\lbrack3, 4\bigr\rbrack\bigr\rbrack[2][1]$Out$3$

A list of positions reorders the elements

live ↗

In$\bigl\lbrack a, b, c, d, k\bigr\rbrack[\bigl\lbrack4, 5, 1, 2, 3\bigr\rbrack]$Out$\bigl\lbrack d, k, a, b, c\bigr\rbrack$

Properties #

Index $0$ gives the head of the expression

live ↗

In$\bigl\lbrack a, b, c\bigr\rbrack[0]$Out$\mathrm{List}$

An empty list of positions selects nothing

live ↗

In$\bigl\lbrack1, 2, 3\bigr\rbrack[\bigl\lbrack\bigr\rbrack]$Out$\bigl\lbrack\bigr\rbrack$

Possible issues #

An out-of-range index evaluates to $NaN$ rather than raising an error

live ↗

In$\bigl\lbrack1, 2, 3\bigr\rbrack[10]$Out$\operatorname{NaN}$

About

Examples	53
Checked against	Wolfram Language 38 agree1 differ
Crosswalk	Wolfram Language

See also: First, Last, IndexOf, Span