Lists

A list holds values in order, written with curly braces. Lists are the Wolfram Language's workhorse: vectors, matrices, tables, and data are all lists.

Creating lists

{10, 20, 30}
Range[5]
Range[2, 10, 2]
Range[0, 1, 0.25]
Table[i^2, {i, 5}]
Table[i + j, {i, 2}, {j, 3}]

{10, 20, 30}
{1, 2, 3, 4, 5}
{2, 4, 6, 8, 10}
{0., 0.25, 0.5, 0.75, 1.}
{1, 4, 9, 16, 25}
{{2, 3, 4}, {3, 4, 5}}

• Range[start, end, step] — 0. and 1. are approximate numbers because the step was.
• Table[expr, {i, n}] evaluates expr for i from 1 to n. {i, a, b} and {i, a, b, step} also work, and several iterators make nested lists.

Getting parts

list = {10, 20, 30, 40, 50};
list[[1]]
list[[-1]]
list[[2 ;; 4]]
{First[list], Last[list], Length[list]}
Rest[list]

10
50
{20, 30, 40}
{10, 50, 5}
{20, 30, 40, 50}

• Positions start at 1; negative positions count from the end.
• ;; is a span: 2 ;; 4 means positions 2 to 4.

Changing lists

Append[list, 60]
list
list[[2]] = 99;
list
AppendTo[list, 60];
list

{10, 20, 30, 40, 50, 60}
{10, 20, 30, 40, 50}
{10, 99, 30, 40, 50}
{10, 99, 30, 40, 50, 60}

Append returns a new list and leaves list alone. list[[i]] = v and AppendTo change the variable itself.

Arithmetic on whole lists

Most math functions are listable — they work element by element:

{1, 2, 3} + 10
{1, 2, 3} * {4, 5, 6}
{1, 2, 3}^2
Sqrt[{1, 4, 9}]

{11, 12, 13}
{4, 10, 18}
{1, 4, 9}
{1, 2, 3}

No loop needed — and it's much faster than a loop.

Nested lists

m = {{1, 2}, {3, 4}};
m[[2]]
m[[2, 1]]
m[[All, 2]]

{3, 4}
3
{2, 4}

All selects every row, so m[[All, 2]] is the second column.

Practice

Make a list of the cubes of 1 to 6, then show its last three elements.

cubes = Table[n^3, {n, 6}];
cubes[[-3 ;;]]

{64, 125, 216}