Template:Ceiling

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

The {{ceiling}} or {{ceil}} mathematical formatting template and/or mathematical function template gives an HTML+CSS or a LaTeX formatted ceiling function of an expression and/or the numerical result of the ceiling of an expression (in which case it must evaluate to a real number).

Usage

{{ceil|expression}}

or

{{ceil|expression|format}}

where the last argument (format) is from

• htm: HTML+CSS [single line] (default);
• HTM: HTML+CSS [multiline];
• tex: LaTeX [single line];
• TEX: LaTeX [multiline];

or

• #: numerical result.

As an alternative to using LaTeX rendered PNG images (tex or TEX options), the htm or HTM options will produce an HTML+CSS formatted expression. (Do not use this option inside <math>...</math> tags.)

NOTE: To get rendered LaTeX, you must use the {{math}} template, since you cannot evaluate templates, parser functions or magic words inside <math>...</math> tags.

Examples

The code {{math|{{ceil}}|&}} yields the text style HTML+CSS 

⌈·⌉

The code {{math|{{ceil|HTM}}|&}} yields the text style HTML+CSS 

·

The code {{math|{{ceil|tex}}|$}} yields the text style LaTeX$\textstyle {\lceil {\cdot }\rceil }$

The code {{math|{{ceil|TEX}}|$}} yields the text style LaTeX$\textstyle {\left\lceil {\cdot }\right\rceil }$

The code {{math|{{ceil|''x''}}|&}} yields the text style HTML+CSS 

⌈ x⌉

The code {{math|{{ceil|''x''|HTM}}|&}} yields the text style HTML+CSS 

x

The code {{math|{{ceil|''x''|tex}}|$}} yields the text style LaTeX$\textstyle {\lceil {x}\rceil }$

The code {{math|{{ceil|''x''|TEX}}|$}} yields the text style LaTeX$\textstyle {\left\lceil {x}\right\rceil }$

The code {{math|{{ceil|''x''}}|&&}} yields the display style HTML+CSS

     

⌈ x⌉

The code {{math|{{ceil|''x''|HTM}}|&&}} yields the display style HTML+CSS

     

x

The code {{math|{{ceil|''x''|tex}}|$$}} yields the display style LaTeX

     ${\begin{array}{l}\displaystyle {\lceil {x}\rceil }\end{array}}$

The code {{math|{{ceil|''x''|TEX}}|$$}} yields the display style LaTeX

     ${\begin{array}{l}\displaystyle {\left\lceil {x}\right\rceil }\end{array}}$

The code {{math|{{ceil|5.3}} {{=}} {{ceil|5.3|#}}|&}} yields the text style HTML+CSS 

⌈ 5.3⌉ = 6

The code {{math|{{ceil|5.3|HTM}} {{=}} {{ceil|5.3|#}}|&}} yields the text style HTML+CSS 

5.3 = 6

The code {{math|{{ceil|5.3|tex}} {{=}} {{ceil|5.3|#}}|$}} yields the text style LaTeX$\textstyle {\lceil {5.3}\rceil =6}$

The code {{math|{{ceil|5.3|TEX}} {{=}} {{ceil|5.3|#}}|$}} yields the text style LaTeX$\textstyle {\left\lceil {5.3}\right\rceil =6}$

The code {{math|{{ceil|5.3}} {{=}} {{ceil|5.3|#}}|&&}} yields the display style HTML+CSS

     

⌈ 5.3⌉ = 6

The code {{math|{{ceil|5.3|HTM}} {{=}} {{ceil|5.3|#}}|&&}} yields the display style HTML+CSS

     

5.3 = 6

The code {{math|{{ceil|5.3|tex}} {{=}} {{ceil|5.3|#}}|$$}} yields the display style LaTeX

     ${\begin{array}{l}\displaystyle {\lceil {5.3}\rceil =6}\end{array}}$

The code {{math|{{ceil|5.3|TEX}} {{=}} {{ceil|5.3|#}}|$$}} yields the display style LaTeX

     ${\begin{array}{l}\displaystyle {\left\lceil {5.3}\right\rceil =6}\end{array}}$

Quotients

The code

{{indent}}{{math|{{ceil|{{frac|''x'' + ''m''|''n''}}|HTM}} {{=}} {{ceil|{{frac|{{ceil|''x''}} + ''m''|''n''}}|HTM}}.
| title = \left\lceil \frac {x + m}{n} \right\rceil = \left\lceil \frac {\lceil x \rceil + m}{n} \right\rceil .  
|&&}}

yields the display style HTML+CSS

     

x + m n = ⌈ x⌉ + m n .

The code

{{indent}}{{math|{{ceil|{{frac|''x'' + ''m''|''n''}}|HTM}} {{=}} {{ceil|{{frac|{{ceil|''x''|HTM}} + ''m''|''n''}}|HTM}}.
| title = \left\lceil \frac {x + m}{n} \right\rceil = \left\lceil \frac {\lceil x \rceil + m}{n} \right\rceil .  
|&&}}

yields the display style HTML+CSS

     

x + m n = x + m n .

The code

{{indent}}{{math|{{ceil|{{frac|''x'' + ''m''|''n''|tex}}|TEX}} {{=}} {{ceil|{{frac|{{ceil|''x''|tex}} + ''m''|''n''|tex}}|TEX}}.|$$}}

yields the display style LaTeX

     ${\begin{array}{l}\displaystyle {\left\lceil {\frac {x+m}{n}}\right\rceil =\left\lceil {\frac {\lceil {x}\rceil +m}{n}}\right\rceil .}\end{array}}$

The code

{{indent}}{{math|\displaystyle \left\lceil \frac {x + m}{n} \right\rceil {{=}} \left\lceil \frac {\lceil x \rceil + m}{n} \right\rceil .|$$}}

yields the display style LaTeX

     ${\begin{array}{l}\displaystyle {\displaystyle \left\lceil {\frac {x+m}{n}}\right\rceil =\left\lceil {\frac {\lceil x\rceil +m}{n}}\right\rceil .}\end{array}}$

See also

• {{floor}}
• {{ceil}} ({{ceiling}})