9.4.4 Functional Names

Functions such as log and tan can't simply be typed in as log or tan otherwise they will come out looking like the variables l times o times g ( ) or t times a times n ( ). Instead you should use one of the commands listed in Table 9.5. The functions denoted with ^† can have limits by using the subscript command _ or the superscript command ^[Sub- and superscript positioning for operators]. In addition, the modulo commands listed in Table 9.6 are also available.

**Table 9.5:** Function Names (^† indicates command may have limits, ^‡defined by `amsmath`).
`\arccos`	$\arccos$	`\arcsin`	$\arcsin$	`\arctan`	$\arctan$
`\arg`	$\arg$	`\cos`	$\cos$	`\cosh`	$\cosh$
`\cot`	$\cot$	`\coth`	$\coth$	`\csc`	$\csc$
`\deg`	$\deg$	`\det`^†	$\det$	`\dim`	$\dim$
`\exp`	$\exp$	`\gcd`^†	$\gcd$	`\hom`	$\hom$
`\inf`^†	$\inf$	`\injlim`^†‡	$\injlim$	`\ker`	$\ker$
`\lg`	$\lg$	`\lim`^†	$\lim$	`\liminf`^†	$\liminf$
`\limsup`^†	$\limsup$	`\ln`	$\ln$	`\log`	$\log$
`\max`^†	$\max$	`\min`^†	$\min$	`\Pr`^†	$\Pr$
`\projlim`^†‡	$\projlim$	`\sec`	$\sec$	`\sin`	$\sin$
`\sinh`	$\sinh$	`\sup`^†	$\sup$	`\tan`	$\tan$
`\tanh`	$\tanh$	`\varinjlim`^†‡	$\varinjlim$	`\varliminf`^†‡	$\varliminf$
`\varlimsup`^†‡	$\varlimsup$	`\varprojlim`^†‡	$\varprojlim$

**Table 9.6:** Modulo Commands (^‡ defined by `amsmath` package)
Command	Example Input	Example Output
`\bmod`	$m \bmod n$	$m \bmod n$
`\pmod{<maths>}`	$m \pmod{n}$	$m \pmod{n}$
`\mod{<maths>}`^‡	$m \mod{n}$	$m \mod{n}$
`\pod{<maths>}`^‡	$m \pod{n}$	$m \pod{n}$

Example (Trigonometric Functions):

This example uses the cos and sin functions and also the Greek letter theta.

\[ z = r(\cos\theta + i\sin\theta) \]

Example (Limit):

The command \infty is the infinity symbol , and the command \to displays an arrow pointing to the right. Note the use of _ since the limit is a subscript.

\[ \lim_{x\to\infty} f(x) \]

The operators with limits behave differently depending on whether they are in displayed or in-line maths. Notice the difference when the same code appears in-line:

In a line of text $\lim_{x\to\infty} f(x)$

which now displays as:

Example (With Subscript):

This is another example of a functional name using a subscript:

\[ \min_x f(x) \]

Again, notice the difference when it is used in-line:

In a line of text $\min_x f(x)$

9.4.4.1 Defining New Functional Operators

It may be that you want a function that isn't specified in Table 9.5. In this case, the amsmath provides the preamble only command

\DeclareMathOperator{<cmd>}{<operator name>}

or its starred variant

\DeclareMathOperator*{<cmd>}{<operator name>}

[Defining a new log-like function in LaTeX]Both versions define a command called <cmd>, which must start with a backslash, that typesets <operator name> as a function name. The starred version is for function names that can take limits (like \lim and \min described above).

Example (Operator Without Limits):

Suppose I want a function called card, which represents the cardinality of a set $\mathcal{S}$ . First I need to define the new operator command (which I'm going to call \card) in the preamble :

\DeclareMathOperator{\card}{card}

This operator doesn't take any limits, so I have used the unstarred version.

Later in the document, I can use this new operator command:

\[ n = \card(\mathcal{S}) \]

In this example \mathcal is used as sets are typically represented in a calligraphic font.

Example (Operator With Limits):

Suppose I now want a function called mode, which represents the mode of a set of numbers. First, I define the operator command in the preamble:

\DeclareMathOperator*{\mode}{mode}

This operator needs to be able to have a subscript, so I have used the starred version.

Later in the document, I can use this new operator command:

\[ x_m = \mode_{x \in \mathcal{S}}(x) \]

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