MATHEMATICA TUTORIAL

# Input Syntax

## Entering Characters

 • Enter it directly (e.g. ) • Enter it by full name (e.g. ) • Enter it by alias (e.g. EscaEsc) (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[expr, form].

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 to . The base itself is given in decimal. For bases larger than , additional digits are chosen from the letters - or -. 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 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 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[h[e]]. However, is interpreted as .

## Two-Dimensional Input Forms

xyPower[x,y]
Divide[x,y]
Sqrt[x]
Power[x,1/n]
 a11 a12 ... a21 a22 ...
{{a11,a12,...},{a21,a22,...}}
xyD[y,x]
x,...yD[y,x,...]
 y x Integrate[y,{x,xmin,xmax}] x Integrate[y w/z,{x,xmin,xmax}] y Sum[y,{x,xmin,xmax}] y Product[y,{x,xmin,xmax}]

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 .

 xy 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[x, y], and is not converted to Power[x, y].

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 .

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