Brackets

Standard brackets: () and []

() and [] can both be used to delimit a subexpression. Used for this purpose, they are exactly equivalent, but they must be properly matched.

3 + [2 − (3 + 3 + 8)]/2

−3

In addition, () are used for function application:

sin(π)

0

(n ↦ n^2 + 1)(5)

26

Further, [] are also used to access subscripted values:

❨5, 1, 2, 3❩[3]

2

"Test"[1]

T

IdentityMatrix(5)[2, 2]

1

Finally, [] can be used to denote a closed interval:

[0, 2⋅π]

See [] for more details.

Ceiling and floor: ⌈⌉ and ⌊⌋

⌈⌉ and ⌊⌋ are used to compute ceiling and floor of numbers.

'(⌈π⌉, ⌊π⌋)

4  3

Curly brackets: {}

{} are used to create sets:

{1, 2, 3} ∩ {2, 3, 4}

{2, 3}

Vector brackets: ❨❩

❨❩ are used to create vectors and matrices:

❨5, 3, 0❩

 ⎛5⎞
e⎜3⎟
 ⎝0⎠

❨❨3, 1, 2❩, ❨6, 4, 2❩❩

⎛3  1  2⎞
⎝6  4  2⎠