# Punctuation

Extended documentation for mathematical symbols & functions is here.

symbol | meaning
--- | ---
`@` | the at-sign marks a macro 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 for string and expression 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 the `adjoint` (that is, the complex transpose) operator Aᴴ
`*` | the asterisk is used for multiplication, including matrix multiplication and string concatenation
`/` | forward slash divides the argument on its left by the one on its right
`//` | double forward slash performs exact, rational division
`\` | 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 empty `Tuple`
`(a,...)` | parentheses with comma-separated arguments constructs a tuple containing its arguments
`(a=1,...)` | parentheses with comma-separated assignments constructs a `NamedTuple`
`(x;y)` | parentheses can also be used to group one or more semicolon separated expressions
`a[]` | array indexing (calling `getindex` or `setindex!`)
`[,]` | vector literal constructor (calling `vect`)
`[;]` | vertical concatenation (calling `vcat` or `hvcat`)
`[ ]` | with space-separated expressions, horizontal concatenation (calling `hcat` or `hvcat`)
`T{ }` | curly braces following a type list that type's parameters
`{}` | curly braces can also be used to group multiple `where` 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 delimits `String` literals
`""" """` | three double-quote characters delimits string literals that may contain `"` and ignore leading indentation
`' '` | the single-quote character delimits `Char` (that is, character) literals
`` `` | the backtick character delimits external 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 (calling `getproperty` or `setproperty!`)
`f.()` | periods may also prefix parentheses (like `f.(...)`) or infix operators (like `.+`) to perform the function element-wise (calling `broadcast`)
`a:b` | colons (`:`) used as a binary infix operator construct a range from `a` to `b` (inclusive) with fixed step size `1`
`a:s:b` | colons (`:`) used as a ternary infix operator construct a range from `a` to `b` (inclusive) with step size `s`
`:` | when used by themselves, `Colon`s represent all indices within a dimension, frequently combined with indexing
`::` | double-colons represent a type annotation or `typeassert`, 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 is assignment
`==` | double equals sign is value equality comparison
`===` | triple equals sign is programmatically identical equality comparison
`=>` | right arrow using an equals sign defines a `Pair` typically used to populate dictionaries
`->` | right arrow using a hyphen defines an anonymous function on a single line
`|>` | pipe operator passes output from the left argument to input of the right argument, usually a function
`∘` | function composition operator (typed with \circ{tab}) combines two functions as though they are a single larger function
`_` | underscores may be assigned values which will not be saved, often used to ignore multiple return values or create repetitive comprehensions

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This document was generated with Documenter.jl version 1.16.0 on Thursday 20 November 2025. Using Julia version 1.12.2.