Template:Atop/doc

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The {{atop}} mathematical formatting template typesets (in either HTML+CSS or LaTeX) an expression above another expression, surrounded by optional fences (parentheses, double parentheses, [square] brackets, double [square] brackets, [angle] brackets, double [angle] brackets, [curly] braces or double [curly] braces). It is equivalent to the { {{{1|}}} \atop {{{2|}}} } LaTeX command, not considering the [optional] fences.

Usage

{{atop|expression above|expression below|format}}

or

{{atop|expression above|expression below|fences|format}}

where [optional third argument, default: no fences] fences is among

• ( ): parentheses, or
• (( )): double parentheses, or
• [ ]: [square] brackets, or
• [[ ]]: double [square] brackets, or
• < >: [angle] brackets, or
• << >>: double [angle] brackets, or
• { }: [curly] braces, or
• {{ }}: double [curly] braces;

and where [optional last argument] format is among

• htm: HTML+CSS text style (default), or
• HTM: HTML+CSS display style, or
• tex: LaTeX text style, or
• TEX: LaTeX display style.

Examples

The code

: {{repeat|12|yadda}}{{nl}}{{repeat|12|yadda}}{{nl}}before {{math|{{atop|''n''|''k''}}, {{atop|''n''|''k''|( )}}, {{atop|''n''|''k''|(( ))}}, {{atop|''n''|''k''|[ ]}}, {{atop|''n''|''k''|[[ ]]}}, <!--
-->{{atop|''n''|''k''|< >}}, {{atop|''n''|''k''|<< >>}}, {{atop|''n''|''k''|{ }|htm}}, {{atop|''n''|''k''|{{ }}|htm}},
|tex = {{atop|n|k|tex}}, {{atop|n|k|( )|tex}}, {{atop|n|k|(( ))|tex}}, {{atop|n|k|[ ]|tex}}, {{atop|n|k|[[ ]]|tex}}, {{atop|n|k|< >|tex}}, {{atop|n|k|<< >>|tex}}, {{atop|n|k|{ }|tex}}, {{atop|n|k|{{ }}|tex}},|&}} <!--
-->and after{{nl}}{{repeat|12|yadda}}{{nl}}{{repeat|12|yadda}}

yields the text style HTML+CSS

yaddayaddayaddayaddayaddayaddayaddayaddayaddayaddayaddayadda
yaddayaddayaddayaddayaddayaddayaddayaddayaddayaddayaddayadda
before

nk  , (  nk  ) , ((  nk  )) , [  nk  ] , [[  nk  ]] ,   〈  nk  〉  ,   〈 〈  nk  〉 〉  , {  nk  }, {{  nk  }},

and after
yaddayaddayaddayaddayaddayaddayaddayaddayaddayaddayaddayadda
yaddayaddayaddayaddayaddayaddayaddayaddayaddayaddayaddayadda

The code

: {{repeat|12|yadda}}{{nl}}{{repeat|12|yadda}}{{nl}}before {{math|{{atop|''n''|''k''}}, {{atop|''n''|''k''|( )}}, {{atop|''n''|''k''|(( ))}}, {{atop|''n''|''k''|[ ]}}, {{atop|''n''|''k''|[[ ]]}}, <!--
-->{{atop|''n''|''k''|< >}}, {{atop|''n''|''k''|<< >>}}, {{atop|''n''|''k''|{ }|htm}}, {{atop|''n''|''k''|{{ }}|htm}},
|tex = {{atop|n|k|tex}}, {{atop|n|k|( )|tex}}, {{atop|n|k|(( ))|tex}}, {{atop|n|k|[ ]|tex}}, {{atop|n|k|[[ ]]|tex}}, {{atop|n|k|< >|tex}}, {{atop|n|k|<< >>|tex}}, {{atop|n|k|{ }|tex}}, {{atop|n|k|{{ }}|tex}},|$}} <!--
-->and after{{nl}}{{repeat|12|yadda}}{{nl}}{{repeat|12|yadda}}

yields the text style LaTeX

yaddayaddayaddayaddayaddayaddayaddayaddayaddayaddayaddayadda
yaddayaddayaddayaddayaddayaddayaddayaddayaddayaddayaddayadda
before $\textstyle {{n \atop k},\left({n \atop k}\right)\!,\left(\!\left({n \atop k}\right)\!\right)\!,\left[{n \atop k}\right]\!,\left[\left[{n \atop k}\right]\right]\!,\left\langle {n \atop k}\right\rangle \!,\left\langle \!\left\langle {n \atop k}\right\rangle \!\right\rangle \!,\left\{{n \atop k}\right\}\!,\left\{\!\left\{{n \atop k}\right\}\!\right\}\!,}$ and after
yaddayaddayaddayaddayaddayaddayaddayaddayaddayaddayaddayadda
yaddayaddayaddayaddayaddayaddayaddayaddayaddayaddayaddayadda

The code (broken in 2 to avoid the 10000 character limit for template arguments)

{{indent}}{{math|{{atop|''n''|''k''|HTM}}, {{atop|''n''|''k''|( )|HTM}}, {{atop|''n''|''k''|(( ))|HTM}}, {{atop|''n''|''k''|[ ]|HTM}}, {{atop|''n''|''k''|[[ ]]|HTM}},
|tex = {{atop|n|k|TEX}}, {{atop|n|k|( )|TEX}}, {{atop|n|k|(( ))|TEX}}, {{atop|n|k|[ ]|TEX}}, {{atop|n|k|[[ ]]|TEX}},|&&}} <!--
-->{{math|{{atop|''n''|''k''|< >|HTM}}, {{atop|''n''|''k''|<< >>|HTM}}, {{atop|''n''|''k''|{ }|HTM}}, {{atop|''n''|''k''|{{ }}|HTM}}, ...
|tex = {{atop|n|k|< >|TEX}}, {{atop|n|k|<< >>|TEX}}, {{atop|n|k|{ }|TEX}}, {{atop|n|k|{{ }}|TEX}}, \ldots|&&}}

yields the display style HTML+CSS

     

n k , ( n k ), (( n k )), [ n k ], [[ n k ]],

〈 n k 〉  ,   〈 〈 n k 〉 〉  , { n k }, {{ n k }}, ...

The code

{{indent}}{{math|{{atop|''n''|''k''|HTM}}, {{atop|''n''|''k''|( )|HTM}}, {{atop|''n''|''k''|(( ))|HTM}}, {{atop|''n''|''k''|[ ]|HTM}}, {{atop|''n''|''k''|[[ ]]|HTM}}, <!--
-->{{atop|''n''|''k''|< >|HTM}}, {{atop|''n''|''k''|<< >>|HTM}}, {{atop|''n''|''k''|{ }|HTM}}, {{atop|''n''|''k''|{{ }}|HTM}}, ...
|tex = {{atop|n|k|TEX}}, {{atop|n|k|( )|TEX}}, {{atop|n|k|(( ))|TEX}}, {{atop|n|k|[ ]|TEX}}, {{atop|n|k|[[ ]]|TEX}}, {{atop|n|k|< >|TEX}}, {{atop|n|k|<< >>|TEX}}, {{atop|n|k|{ }|TEX}}, {{atop|n|k|{{ }}|TEX}}, \ldots|$$}}

yields the display style LaTeX

     ${\begin{array}{l}\displaystyle {{n \atop k},\left({n \atop k}\right)\!,\left(\!\left({n \atop k}\right)\!\right)\!,\left[{n \atop k}\right]\!,\left[\left[{n \atop k}\right]\right]\!,\left\langle {n \atop k}\right\rangle \!,\left\langle \!\left\langle {n \atop k}\right\rangle \!\right\rangle \!,\left\{{n \atop k}\right\}\!,\left\{\!\left\{{n \atop k}\right\}\!\right\}\!,\ldots }\end{array}}$

Examples of mathematical notations

The code (see permutation)

: The permutation {{math|''{{Gr|sigma}}'' {{=}} {{atop|''a''{{sp|7}}''b''{{sp|7}}''c''|''b''{{sp|7}}''c''{{sp|7}}''a''|( )}}|tex = \sigma = {{atop|a \ b \ c|b \ c \ a|( )|tex}}|&}} is one of 6...

yields the text style HTML+CSS

The permutation

σ = (  a  b  cb  c  a  )

is one of 6...

The code

: The permutation {{math|''{{Gr|sigma}}'' {{=}} {{atop|''a''{{sp|7}}''b''{{sp|7}}''c''|''b''{{sp|7}}''c''{{sp|7}}''a''|( )}}|tex = \sigma = {{atop|a \ b \ c|b \ c \ a|( )|tex}}|$}} is one of 6...

yields the text style LaTeX

The permutation $\textstyle {\sigma =\left({a\ b\ c \atop b\ c\ a}\right)\!}$ is one of 6...

See also

• (  nk  )

   (binomial coefficient,

  n

  choose

  k

  , number of

  k

  -combinations of

  n

  elements without repetition)  (use template {{binomial}} or {{binom}} or {{C(n,k)}})

• ((  nk  ))

   (multiset coefficient,

  n

  multichoose

  k

  , number of

  k

  -combinations of

  n

  elements with repetition)

• [  nk  ]

   (unsigned Stirling numbers of the first kind)

• {  nk  }

   (Stirling numbers of the second kind)

• 〈  nk  〉

   (Eulerian numbers, number of permutations of the numbers 1 to

  n

  in which exactly

  m

  elements are greater than the previous element)