Template:~(

The following documentation is located at Template:~(/doc. [<Edit> Template:~(/doc]
[⧼Purge⧽ Template:~(]

The {{~(|expression to delimit|)~}} mathematical formatting template delimits expressions with normal or larger size curly brackets (braces) for either HTML+CSS or $L a T e X$ .

Note: neither a {{[|...|]}} (square bracket) template nor a {{{|...|}}} (brace) template works with MediaWiki!

Usage

{{~(|expression to delimit|)~}}

or

{{~(|expression to delimit|)~|type}}

or

{{~(|expression to delimit|)~|format}}

or

{{~(|expression to delimit|)~|type|format}}

where the mandatory [dummy] second argument must be )~ for visual balancing of left and right delimiters, viz.

{{~(|expression to delimit|)~}}

and the [optional] third argument (type) is from

default: normal { ... }, corresponds to \{ ... \} in $L a T e X$ ;
big: corresponds to \big\{ ... \big\} in $L a T e X$ ;
Big: corresponds to \Big\{ ... \Big\} in $L a T e X$ ;
bigg: corresponds to \bigg\{ ... \bigg\} in $L a T e X$ ;
Bigg: corresponds to \Bigg\{ ... \Bigg\} in $L a T e X$ ;
auto: corresponds to \left\{ ... \right\} in $L a T e X$ ;

and the [optional] format (either fourth argument, or third argument if type is omitted) is from

htm: HTML+CSS (default);
tex: $L a T e X$ .

Examples

The code

A065918: Logarithm of {{math|2 + {{sqrt|3}}|tex = 2 + \sqrt{3}|&}}.

{{SoD's t or c| 1.3169578969248... }}

This number figures in the search for [[Mersenne primes]] thus: the [[Mersenne numbers|Mersenne number]] {{math|''M'' {{=}} 2{{^|''n''}} {{op|-}} 1|tex = M = 2^n - 1|&}} is [[prime]] if and only if {{math|''M''|tex = M|&}} divides{{nl|2}} 

{{indent}}{{math|
{{begin|align}}
cosh{{sp|1}}(2{{^|''n''{{sp|1}}{{op|-}}2}} log{{sp|1}}(2 + {{sqrt|3}}{{sp|1}})) 
  {{&=}} {{frac|''e''{{^|{{op|+}}{{~(|2{{^|''n''{{sp|1}}{{op|-}}2|87%}} log{{sp|1}}(2 + {{sqrt|3}}{{sp|1}})|)~}}}} + 
    ''e''{{^|{{op|-}}{{~(|2{{^|''n''{{sp|1}}{{op|-}}2|87%}} log{{sp|1}}(2 + {{sqrt|3}}{{sp|1}})|)~}}}}|2|HTM}} {{\\}} 
  {{&=}} {{frac|(2 + {{sqrt|3}}{{sp|1}}){{^|{{op|+}}{{~(|2{{^|''n''{{sp|1}}{{op|-}}2{{sp|1}}|87%}}|)~}}}} + 
    (2 + {{sqrt|3}}{{sp|1}}){{^|{{op|-}}{{~(|2{{^|''n''{{sp|1}}{{op|-}}2{{sp|1}}|87%}}|)~}}}}|2|HTM}}{{sp|1}},
{{end|align}} 
|tex =
\begin{align}
\cosh(2^{n-2} \log(2 + \sqrt{3})) 
  &= \frac{ e^{ + \{ 2^{n-2} \log(2 + \sqrt{3}) \} } + e^{ - \{ 2^{n-2} \log(2 + \sqrt{3}) \} } }{2} \\ 
  &= \frac{ (2 + \sqrt{3})^{ + \{ 2^{n-2} \} } + (2 + \sqrt{3})^{ - \{ 2^{n-2} \} } }{2},
\end{align}
|&&}}{{clear}}

where {{math|cosh{{sp|1}}(''x'')|tex = \cosh(x)|&}} is the [[hyperbolic cosine]] function. {{User|David W. Wilson|David Wilson}} has proposed calling the number {{math|log{{sp|1}}(2 + {{sqrt|3}}{{sp|1}})
|tex = \log(2 + \sqrt{3})|&}} the [[Helms constant]].{{nl}}

The number {{math|2 + {{sqrt|3}} {{=}} tan {{tfrac|5{{sp|1}}{{Gr|pi}}|12}} {{=}} cot {{tfrac|{{Gr|pi}}|12}}|tex = 2 + \sqrt{3} = \tan \frac{5 \pi}{12} = \cot \frac{\pi}{12}|&}} is sometimes called the [[Kasner constant]] (see A019973 for decimal expansion).

yields

A065918: Logarithm of

2 +

2√ 3

.

1.3169578969248...

This number figures in the search for Mersenne primes thus: the Mersenne number

M = 2 n − 1

is prime if and only if

M

divides

cosh (2 n − 2 log (2 +

2√ 3

))

=

e + { 2 n − 2 log (2 +

2√ 3

) } + e − { 2 n − 2 log (2 +

2√ 3

) }

2

=

(2 +

2√ 3

) + { 2 n − 2 } + (2 +

2√ 3

) − { 2 n − 2 }

2

,

where

cosh (x)

is the hyperbolic cosine function. David Wilson has proposed calling the number

log (2 +

2√ 3

)

the Helms constant.
The number

2 +

2√ 3

= tan

5 π

12

= cot

π

12

is sometimes called the Kasner constant (see A019973 for decimal expansion).

Nonmathematical examples

The code

{{indent}}{{math|
{{~(|
{{begin|align}}       
First: {{&}} 1 
{{end|align}}
|)~|auto}}
|&&}}{{nbsp|2}}<!--

-->{{math|
{{~(|
{{begin|align}}       
First: {{&}} 1 {{\\}}  
Second: {{&}} 1, 2
{{end|align}}
|)~|auto}}
|&&}}{{nbsp|2}}<!--

-->{{math|
{{~(|
{{begin|align}}       
First: {{&}} 1 {{\\}}  
Second: {{&}} 1, 2 {{\\}}  
Third: {{&}} 1, 2, 3 {{\\}}
Fourth: {{&}} 1, 2, 3, 4
{{end|align}}
|)~|auto}}
|&&}}{{nbsp|2}}<!--

-->{{math|
{{~(|
{{begin|align}}       
First: {{&}} 1 {{\\}}  
Second: {{&}} 1, 2 {{\\}}  
Third: {{&}} 1, 2, 3 {{\\}}
Fourth: {{&}} 1, 2, 3, 4 {{\\}}
Fifth: {{&}} 1, 2, 3, 4, 5 {{\\}}
Sixth: {{&}} 1, 2, 3, 4, 5, 6
{{end|align}}
|)~|auto}}
|&&}}

yields the display style HTML+CSS

First:

1

First:	1
Second:	1, 2

First:	1
Second:	1, 2
Third:	1, 2, 3
Fourth:	1, 2, 3, 4

First:	1
Second:	1, 2
Third:	1, 2, 3
Fourth:	1, 2, 3, 4
Fifth:	1, 2, 3, 4, 5
Sixth:	1, 2, 3, 4, 5, 6

The code

{{indent}}{{math|
{{~(|
{{begin|align|tex}}       
\text{First:} {{&|tex}}\text{ 1}
{{end|align|tex}}
|)~|auto|tex}}
{{sp|tex}}<!--

-->{{~(|
{{begin|align|tex}}       
\text{First:} {{&|tex}}\text{ 1} {{\\|tex}}  
\text{Second:} {{&|tex}}\text{ 1, 2} 
{{end|align|tex}}
|)~|auto|tex}}
{{sp|tex}}<!--

-->{{~(|
{{begin|align|tex}}       
\text{First:} {{&|tex}}\text{ 1} {{\\|tex}}  
\text{Second:} {{&|tex}}\text{ 1, 2} {{\\|tex}}  
\text{Third:} {{&|tex}}\text{ 1, 2, 3} {{\\|tex}}
\text{Fourth:} {{&|tex}}\text{ 1, 2, 3, 4}
{{end|align|tex}}
|)~|auto|tex}}
{{sp|tex}}<!--

-->{{~(|
{{begin|align|tex}}       
\text{First:} {{&|tex}}\text{ 1} {{\\|tex}}  
\text{Second:} {{&|tex}}\text{ 1, 2} {{\\|tex}}  
\text{Third:} {{&|tex}}\text{ 1, 2, 3} {{\\|tex}}
\text{Fourth:} {{&|tex}}\text{ 1, 2, 3, 4} {{\\|tex}}
\text{Fifth:} {{&|tex}}\text{ 1, 2, 3, 4, 5} {{\\|tex}}
\text{Sixth:} {{&|tex}}\text{ 1, 2, 3, 4, 5, 6}
{{end|align|tex}}
|)~|auto|tex}}
|$$}}

yields the display style $L a T e X$

${\begin{array}{l}\displaystyle {\left\{{\begin{aligned}{\text{First:}}&{\text{ 1}}\end{aligned}}\right\}{\;\;\!\!}\left\{{\begin{aligned}{\text{First:}}&{\text{ 1}}\\{\text{Second:}}&{\text{ 1, 2}}\end{aligned}}\right\}{\;\;\!\!}\left\{{\begin{aligned}{\text{First:}}&{\text{ 1}}\\{\text{Second:}}&{\text{ 1, 2}}\\{\text{Third:}}&{\text{ 1, 2, 3}}\\{\text{Fourth:}}&{\text{ 1, 2, 3, 4}}\end{aligned}}\right\}{\;\;\!\!}\left\{{\begin{aligned}{\text{First:}}&{\text{ 1}}\\{\text{Second:}}&{\text{ 1, 2}}\\{\text{Third:}}&{\text{ 1, 2, 3}}\\{\text{Fourth:}}&{\text{ 1, 2, 3, 4}}\\{\text{Fifth:}}&{\text{ 1, 2, 3, 4, 5}}\\{\text{Sixth:}}&{\text{ 1, 2, 3, 4, 5, 6}}\end{aligned}}\right\}}\end{array}}$

Template:~(

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Nonmathematical examples

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