Input Syntax

Entering Characters

• Enter it directly (e.g.

)

• Enter it by full name (e.g.

)

• Enter it by alias (e.g. Esc a Esc) (notebook front end only)

• Enter it by choosing from a palette (notebook front end only)

• Enter it by character code (e.g.

)

Typical ways to enter characters.

All printable ASCII characters can be entered directly. Those that are not alphanumeric are assigned explicit names in Mathematica, allowing them to be entered even on keyboards where they do not explicitly appear.

	\[RawSpace]
!	\[RawExclamation]
"	\[RawDoubleQuote]
#	\[RawNumberSign]
$	\[RawDollar]
%	\[RawPercent]
&	\[RawAmpersand]
'	\[RawQuote]
(	\[RawLeftParenthesis]
)	\[RawRightParenthesis]
*	\[RawStar]
+	\[RawPlus]
,	\[RawComma]
-	\[RawDash]
.	\[RawDot]
/	\[RawSlash]
:	\[RawColon]

;	\[RawSemicolon]
<	\[RawLess]
=	\[RawEqual]
>	\[RawGreater]
?	\[RawQuestion]
@	\[RawAt]
[	\[RawLeftBracket]
\	\[RawBackslash]
]	\[RawRightBracket]
^	\[RawWedge]
_	\[RawUnderscore]
`	\[RawBackquote]
{	\[RawLeftBrace]
\|	\[RawVerticalBar]
}	\[RawRightBrace]
~	\[RawTilde]

Full names for non-alphanumeric printable ASCII characters.

All characters which are entered into the Mathematica kernel are interpreted according to the setting for the CharacterEncoding option for the stream from which they came.

\[Name]	a character with the specified full name
\nnn	a character with octal code nnn
\.nn	a character with hexadecimal code nn
\:nnnn	a character with hexadecimal code nnnn

Ways to enter characters.

Codes for characters can be generated using ToCharacterCode. The Unicode standard is followed, with various extensions.

8-bit characters have codes less than 256; 16-bit characters have codes between 256 and 65535. Approximately 900 characters are assigned explicit names in Mathematica. Other characters must be entered using their character codes.

\\	single backslash (decimal code 92)
\	single space (decimal code 32)
\"	double quote (decimal code 34)
\b	backspace or Ctrl+H (decimal code 8)
\t	tab or Ctrl+I (decimal code 9)
\n	newline or Ctrl+J (decimal code 10; full name )
\f	form feed or Ctrl+L (decimal code 12)
\r	carriage return or Ctrl+M (decimal code 13)
\000	null byte (code 0)

Some special 8-bit characters.

Types of Input Syntax

The standard input syntax used by Mathematica is the one used by default in InputForm and StandardForm. You can modify the syntax by making definitions for MakeExpression

Options can be set to specify what form of input should be accepted by a particular cell in a notebook or from a particular stream.

The input syntax in TraditionalForm, for example, is different from that in InputForm and StandardForm.

In general, what input syntax does is to determine how a particular string or collection of boxes should be interpreted as an expression. When boxes are set up, say with the notebook front end, there can be hidden InterpretationBox or TagBox objects which modify the interpretation of the boxes.

Character Strings

	a character string
	a literal in a character string
	a literal in a character string
(at end of line)	ignore the following newline
	a substring representing two-dimensional boxes

Entering character strings.

Character strings can contain any sequence of 8- or 16-bit characters. Characters entered by name or character code are stored the same as if they were entered directly.

In a notebook front end, text pasted into a string by default automatically has appropriate \ characters inserted so that the string stored in Mathematica reproduces the text that was pasted.

Within

any box structures represented using backslash sequences can be used.

StringExpression objects can be used to represent strings that contain symbolic constructs, such as pattern elements.

Symbol Names and Contexts

name	symbol name
`name	symbol name in current context
context`name	symbol name in specified context
context`	context name
context1`context2`	compound context name
`context`	context relative to the current context

Symbol names and contexts.

Symbol names and contexts can contain any characters that are treated by Mathematica as letters or letter-like forms. They can contain digits but cannot start with them. Contexts must end in a backquote

Numbers

digits	integer
digits.digits	approximate number
base^^digits	integer in specified base
base^^digits.digits	approximate number in specified base
mantissa*^n	scientific notation (mantissa×)
base^^mantissa*^n	scientific notation in specified base (mantissa×)
number`	machine-precision approximate number
number`s	arbitrary-precision number with precision
number``s	arbitrary-precision number with accuracy

Input forms for numbers.

Numbers can be entered with the notation

in any base from

. The base itself is given in decimal. For bases larger than

, additional digits are chosen from the letters

. Upper- and lower-case letters are equivalent for these purposes. Floating-point numbers can be specified by including

in the digits sequence.

In scientific notation, mantissa can contain

marks. The exponent

must always be an integer, specified in decimal.

The precision or accuracy

can be any real number; it does not need to be an integer.

In the form

the precision

is given in decimal, but it gives the effective number of digits of precision in the specified base, not in base 10.

An approximate number

is taken to be machine precision if the number of digits given in it is Ceiling[$MachinePrecision]+1 or less. If more digits are given, then

is taken to be an arbitrary-precision number. The accuracy of

is taken to be the number of digits that appear to the right of the decimal point, while its precision is taken to be Log[10, Abs[x]]+Accuracy[x].

A number entered in the form 0``s is taken to have precision 0 and accuracy

Bracketed Objects

Bracketed objects use explicit left and right delimiters to indicate their extent. They can appear anywhere within Mathematica input, and can be nested in any way.

The delimiters in bracketed objects are matchfix operators. But since these delimiters explicitly enclose all operands, no precedence need be assigned to such operators.

(any text)	comment
(expr)	parenthesization: grouping of input

Bracketed objects without comma-separated elements.

Comments can be nested, and can continue for any number of lines. They can contain any 8- or 16-bit characters.

Parentheses must enclose a single complete expression; neither

nor

are allowed.

{e₁,e₂,...}	List[e₁,e₂,...]
e₁,e₂,...	AngleBracket[e₁,e₂,...]
expr	Floor[expr]
expr	Ceiling[expr]
e₁,e₂,...	BracketingBar[e₁,e₂,...]
e₁,e₂,...	DoubleBracketingBar[e₁,e₂,...]
$input$	input or grouping of boxes

Bracketed objects that allow comma-separated elements.

The notation ... is used to stand for any sequence of expressions.

can include any number of elements, with successive elements separated by commas.

is List

, a list with zero elements.

can be entered as

The character

can be used interchangeably with ordinary commas; the only difference is that

will not be displayed.

When the delimiters are special characters, it is a convention that they are named

and

is used to enter boxes using one-dimensional strings. Note that within the outermost

in a piece of input the syntax used is slightly different from outside, as described in "Input of Boxes".

h[e₁,e₂,...]	standard expression
e[[i₁,i₂,...]]	Part[e,i₁,i₂,...]
ei₁,i₂,...	Part[e,i₁,i₂,...]

Bracketed objects with heads.

Bracketed objects with heads explicitly delimit all their operands except the head. A precedence must be assigned to define the extent of the head.

The precedence of

is high enough that

is interpreted as Not

. However,

is interpreted as

Two-Dimensional Input Forms

x^y

Power[x,y]

Divide[x,y]

Sqrt[x]

Power[x,1/n]

a₁₁	a₁₂	...
a₂₁	a₂₂	...

{{a₁₁,a₁₂,...},{a₂₁,a₂₂,...}}

_xy

D[y,x]

_x,...y

D[y,x,...]

y x	Integrate[y,{x,x_min,x_max}]
x	Integrate[y w/z,{x,x_min,x_max}]
y	Sum[y,{x,x_min,x_max}]
y	Product[y,{x,x_min,x_max}]

Two-dimensional input forms with built-in evaluation rules.

Any array of expressions represented by a GridBox is interpreted as a list of lists. Even if the GridBox has only one row, the interpretation is still

In the form

the limits

and

can be omitted, as can

and

x_y	Subscript[x,y]
x₊	SubPlus[x]
x_-	SubMinus[x]
x_*	SubStar[x]
x⁺	SuperPlus[x]
x^-	SuperMinus[x]
x^*	SuperStar[x]
x^†	SuperDagger[x]

	Overscript[x,y]
	Underscript[x,y]
	OverBar[x]
	OverVector[x]
	OverTilde[x]
	OverHat[x]
	OverDot[x]
	UnderBar[x]

Two-dimensional input forms without built-in evaluation rules.

There is no issue of precedence for forms such as

and

in which operands are effectively spanned by the operator. For forms such as

and

a left precedence does need to be specified, so such forms are included in the main table of precedences above.

Input of Boxes

• Use a palette

• Use control keys

Ways to input boxes.

Control Keys

Ctrl+2 or Ctrl+@	square root
Ctrl+5 or Ctrl+%	switch to alternate position (e.g. subscript to superscript)
Ctrl+6 or Ctrl+^	superscript
Ctrl+7 or Ctrl+&	overscript
Ctrl+9 or Ctrl+(	begin a new cell within an existing cell
Ctrl+0 or Ctrl+)	end a new cell within an existing cell
Ctrl+- or Ctrl+_	subscript
Ctrl+4 or Ctrl+$	underscript
Ctrl+Enter	create a new row in a table
Ctrl+,	create a new column in a table
Ctrl+.	expand current selection
Ctrl+/	fraction
Ctrl+Space	return from current position or state
Ctrl+, Ctrl+, Ctrl+, Ctrl+	move an object by minimal increments on the screen

Standard control keys.

On English-language keyboards both forms will work where alternates are given. On other keyboards the first form should work but the second may not.

Boxes Constructed from Text

When textual input that you give is used to construct boxes, as in StandardForm or TraditionalForm cells in a notebook, the input is handled slightly differently from when it is fed directly to the kernel.

The input is broken into tokens, and then each token is included in the box structure as a separate character string. Thus, for example,

is broken into the tokens

• symbol name (e.g.

)

• number (e.g.

)

• operator (e.g.

)

• spacing (e.g.

)

• character string (e.g.

)

Types of tokens in text used to construct boxes.

A RowBox is constructed to hold each operator and its operands. The nesting of RowBox objects is determined by the precedence of the operators in standard Mathematica syntax.

Note that spacing characters are not automatically discarded. Instead, each sequence of consecutive such characters is made into a separate token.

String-Based Input

$...$	input raw boxes
\!$...$	input and interpret boxes

Inputting raw and interpreted boxes.

Any textual input that you give between

and

is taken to specify boxes to construct. The boxes are only interpreted if you specify with

that this should be done. Otherwise

is left for example as SuperscriptBox

, and is not converted to Power

Within the outermost

, further

specify grouping and lead to the insertion of RowBox objects.

$box₁,box₂,...$	RowBox[box₁,box₂,...]
box₁\^box₂	SuperscriptBox[box₁,box₂]
box₁\_box₂	SubscriptBox[box₁,box₂]
box₁\_box₂\%box₃	SubsuperscriptBox[box₁,box₂,box₃]
box₁\&box₂	OverscriptBox[box₁,box₂]
box₁\+box₂	UnderscriptBox[box₁,box₂]
box₁\+box₂\%box₃	UnderoverscriptBox[box₁,box₂,box₃]
box₁\/box₂	FractionBox[box₁,box₂]
\@box	SqrtBox[box]
form\` box	FormBox[box,form]
\*input	construct box by interpreting input
\	insert a space
\n	insert a newline
\t	indent at the beginning of a line

String-based ways of constructing raw boxes.

In string-based input between

and

spaces, tabs and newlines are discarded.

can be used to insert a single space. Special spacing characters such as \[ThinSpace], \[ThickSpace], or \[NegativeThinSpace] are not discarded.

When you input typesetting forms into a string, the internal representation of the string uses the above forms. The front end displays the typeset form, but uses the

notation when saving the content to a file or when sending the string to the kernel for evaluation.

The Extent of Input Expressions

Mathematica will treat all input that you give on a single line as being part of the same expression.

Mathematica allows a single expression to continue for several lines. In general, it treats the input that you give on successive lines as belonging to the same expression whenever no complete expression would be formed without doing this.

Thus, for example, if one line ends with

, then Mathematica will assume that the expression must continue on the next line. It will do the same if for example parentheses or other matchfix operators remain open at the end of the line.

If at the end of a particular line the input you have given so far corresponds to a complete expression, then Mathematica will normally begin immediately to process that expression.

You can however explicitly tell Mathematica that a particular expression is incomplete by putting a

or a

(\[Continuation]) at the end of the line. Mathematica will then include the next line in the same expression, discarding any spaces or tabs that occur at the beginning of that line.

Special Input

?symbol	get information
??symbol	get more information
?s₁s₂...	get information on several objects
!command	execute an external command (text-based interface only)
!!file	display the contents of an external file (text-based interface only)

Special input lines.

In most implementations of Mathematica, you can give a line of special input anywhere in your input. The only constraint is that the special input must start at the beginning of a line.

Some implementations of Mathematica may not allow you to execute external commands using !command.

Front End Files

Notebook files as well as front end initialization files can contain a subset of standard Mathematica language syntax. This syntax includes:

Any Mathematica expression in FullForm.

Lists in {...} form. The operators , , and . Function slots in form.

Various Mathematica operators such as , , , etc.

Special characters in , , or form.

String representation of boxes involving , , and other backslash operators.

Mathematica comments delimited by and .

MORE ABOUT

Low-Level Notebook Structure

Syntax

\(box₁,box₂,...\)	RowBox[box₁,box₂,...]
box₁\^box₂	SuperscriptBox[box₁,box₂]
box₁\_box₂	SubscriptBox[box₁,box₂]
box₁\_box₂\%box₃	SubsuperscriptBox[box₁,box₂,box₃]
box₁\&box₂	OverscriptBox[box₁,box₂]
box₁\+box₂	UnderscriptBox[box₁,box₂]
box₁\+box₂\%box₃	UnderoverscriptBox[box₁,box₂,box₃]
box₁\/box₂	FractionBox[box₁,box₂]
\@box	SqrtBox[box]
form\` box	FormBox[box,form]
\*input	construct box by interpreting input
\	insert a space
\n	insert a newline
\t	indent at the beginning of a line