Extended documentation for mathematical symbols & functions ishere.
| symbol | meaning |
|---|---|
@ | the at-sign marks amacro invocation; optionally followed by an argument list |
! | an exclamation mark is a prefix operator for logical negation ("not") |
a! | function names that end with an exclamation mark modify one or more of their arguments by convention |
# | the number sign (or hash or pound) character begins single line comments |
#= | when followed by an equals sign, it begins a multi-line comment (these are nestable) |
=# | end a multi-line comment by immediately preceding the number sign with an equals sign |
$ | the dollar sign is used forstring andexpression interpolation |
% | the percent symbol is the remainder operator |
^ | the caret is the exponentiation operator |
& | single ampersand is bitwise and |
&& | double ampersands is short-circuiting boolean and |
| | single pipe character is bitwise or |
|| | double pipe characters is short-circuiting boolean or |
⊻ | the unicode xor character is bitwise exclusive or |
~ | the tilde is an operator for bitwise not |
' | a trailing apostrophe is theadjoint (that is, the complex transpose) operator Aᴴ |
* | the asterisk is used for multiplication, including matrix multiplication andstring concatenation |
/ | forward slash divides the argument on its left by the one on its right |
\ | backslash operator divides the argument on its right by the one on its left, commonly used to solve matrix equations |
() | parentheses with no arguments constructs an emptyTuple |
(a,...) | parentheses with comma-separated arguments constructs a tuple containing its arguments |
(a=1,...) | parentheses with comma-separated assignments constructs aNamedTuple |
(x;y) | parentheses can also be used to group one or more semicolon separated expressions |
a[] | array indexing (callinggetindex orsetindex!) |
[,] | vector literal constructor (callingvect) |
[;] | vertical concatenation (callingvcat orhvcat) |
[ ] | with space-separated expressions,horizontal concatenation (callinghcat orhvcat) |
T{ } | curly braces following a type list that type'sparameters |
{} | curly braces can also be used to group multiplewhere expressions in function declarations |
; | semicolons separate statements, begin a list of keyword arguments in function declarations or calls, or are used to separate array literals for vertical concatenation |
, | commas separate function arguments or tuple or array components |
? | the question mark delimits the ternary conditional operator (used like:conditional ? if_true : if_false) |
" " | the single double-quote character delimitsString literals |
""" """ | three double-quote characters delimits string literals that may contain" and ignore leading indentation |
' ' | the single-quote character delimitsChar (that is, character) literals |
` ` | the backtick character delimitsexternal process (Cmd) literals |
A... | triple periods are a postfix operator that "splat" their arguments' contents into many arguments of a function call or declare a varargs function that "slurps" up many arguments into a single tuple |
a.b | single periods access named fields in objects/modules (callinggetproperty orsetproperty!) |
f.() | periods may also prefix parentheses (likef.(...)) or infix operators (like.+) to perform the function element-wise (callingbroadcast) |
a:b | colons (:) used as a binary infix operator construct a range froma tob (inclusive) with fixed step size1 |
a:s:b | colons (:) used as a ternary infix operator construct a range froma tob (inclusive) with step sizes |
: | when used by themselves,Colons represent all indices within a dimension, frequently combined withindexing |
:: | double-colons represent a type annotation ortypeassert, depending on context, frequently used when declaring function arguments |
:( ) | quoted expression |
:a | Symbol a |
<: | subtype operator |
>: | supertype operator (reverse of subtype operator) |
= | single equals sign isassignment |
== | double equals sign is value equality comparison |
=== | triple equals sign is programmatically identical equality comparison |
=> | right arrow using an equals sign defines aPair typically used to populatedictionaries |
-> | right arrow using a hyphen defines ananonymous function on a single line |
|> | pipe operator passes output from the left argument to input of the right argument, usually afunction |
∘ | function composition operator (typed with \circ{tab}) combines two functions as though they are a single largerfunction |
_ | underscores may be assigned values which will not be saved, often used to ignoremultiple return values or create repetitivecomprehensions |
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This document was generated withDocumenter.jl version 1.8.0 onWednesday 9 July 2025. Using Julia version 1.11.6.