Template:Floor/doc

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

Usage

{{floor|expression}}

or

{{floor|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];
• #: 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 inside the <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 the <math>...</math> tags.

Examples

The code : before {{math|{{floor}}|&}} after yields the text style HTML+CSS

before 

⌊ ·⌋

after

The code : before {{math|{{floor|HTM}}|&}} after yields the text style HTML+CSS

before 

·

after

The code : before {{math|{{floor|tex}}|$}} after yields the text style LaTeX

before$\textstyle {\lfloor {\cdot }\rfloor }$ after

The code : before {{math|{{floor|TEX}}|$}} after yields the text style LaTeX

before$\textstyle {\left\lfloor {\cdot }\right\rfloor }$ after

The code : before {{math|{{floor|''x''}}|&}} after yields the text style HTML+CSS

before 

⌊  x⌋

after

The code : before {{math|{{floor|''x''|HTM}}|&}} after yields the text style HTML+CSS

before 

x

after

The code : before {{math|{{floor|''x''|tex}}|$}} after yields the text style LaTeX

before$\textstyle {\lfloor {x}\rfloor }$ after

The code : before {{math|{{floor|''x''|TEX}}|$}} after yields the text style LaTeX

before$\textstyle {\left\lfloor {x}\right\rfloor }$ after

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

     

⌊  x⌋

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

     

x

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

     ${\begin{array}{l}\displaystyle {\lfloor {x}\rfloor }\end{array}}$

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

     ${\begin{array}{l}\displaystyle {\left\lfloor {x}\right\rfloor }\end{array}}$

The code : before {{math|{{floor|5.3}} {{=}} {{floor|5.3|#}}|&}} after yields the text style HTML+CSS

before 

⌊  5.3⌋ = 5

after

The code : before {{math|{{floor|5.3|HTM}} {{=}} {{floor|5.3|#}}|&}} after yields the text style HTML+CSS

before 

5.3 = 5

after

The code : before {{math|{{floor|5.3|tex}} {{=}} {{floor|5.3|#}}|$}} after yields the text style LaTeX

before$\textstyle {\lfloor {5.3}\rfloor =5}$ after

The code : before {{math|{{floor|5.3|TEX}} {{=}} {{floor|5.3|#}}|$}} after yields the text style LaTeX

before$\textstyle {\left\lfloor {5.3}\right\rfloor =5}$ after

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

     

⌊  5.3⌋ = 5

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

     

5.3 = 5

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

     ${\begin{array}{l}\displaystyle {\lfloor {5.3}\rfloor =5}\end{array}}$

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

     ${\begin{array}{l}\displaystyle {\left\lfloor {5.3}\right\rfloor =5}\end{array}}$

Willans’s formula

Starting from Wilson’s theorem, C. P. Willans derived the following formula for the

n

th prime

The code

{{indent}}{{math|
''p''{{sub|''n''|HTM}} {{=}} 1 + <!--

-->{{sum|''m''{{=}}1|2{{^|''n''|80%}}|HTM}}<!--
  -->{{floor|<!--
    -->{{root|''n''|<big>''n''</big>}} <!--

    -->{{(|<!--
      -->{{sum|''x''{{=}}1|''m''|HTM}}<!--
        -->{{floor|cos{{^|2}} {{Gr|pi}} {{frac|(''x'' {{op|-}} 1)! + 1|''x''|HTM}}|HTM}}{{nbsp}}<!--
    -->|)}}{{^|{{^|{{^|{{op|-}}1{{op|/}}''n''}}|100%}}|100%}} 
     |HTM}}.
| tex = p_n = 1 + \sum_{m=1}^{2^n} {{floor| \sqrt[n]{n} \left( \sum_{x=1}^{m} {{floor| \cos^2 \pi \frac{(x-1)! + 1}{x} |TEX}} \right)^{-1/n } |TEX}} .
|&&}}

yields the display style HTML+CSS

     

pn = 1 +   2 n ∑   m  = 1    n√  n     m ∑   x  = 1    cos 2 π (x − 1)! + 1 x      − 1 / n .

and, with the $$ argument to {{math}}, yields the display style LaTeX

     ${\begin{array}{l}\displaystyle {p_{n}=1+\sum _{m=1}^{2^{n}}\left\lfloor {{\sqrt[{n}]{n}}\left(\sum _{x=1}^{m}\left\lfloor {\cos ^{2}\pi {\frac {(x-1)!+1}{x}}}\right\rfloor \right)^{-1/n}}\right\rfloor .}\end{array}}$

See also

• {{floor}}
• {{ceil}} ({{ceiling}})

• {{abs}}
• {{norm}}