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# Template:Kronecker

The {{Kronecker}} (or {{Kron}}) mathematical formatting template gives an HTML+CSS or a LaTeX formatted Kronecker symbol.

## Usage

{{Kron|nonzero integer|modulo}}

or

{{Kron|nonzero integer|modulo|format}}

where format is taken from

• htm: text style HTML+CSS Kronecker symbol (default);
• HTM: display style HTML+CSS Kronecker symbol;
• tex: text style LaTeX Kronecker symbol;
• TEX: display style LaTeX Kronecker symbol;

## Examples

The code (see Kronecker symbol)

The '''Kronecker symbol''' {{math|{{Kron|''a''{{sp|1}}|''n''{{sp|1}}}}|tex = {{Kron|a|n|tex}}|&}} is defined as{{nl|1.35}}

: {{math|{{Kron|{{sp|1}}''a''{{sp|1}}|{{sp|1}}''n''{{sp|1}}|HTM}} {{sp}}{{rel|def}}{{sp}} {{Kron|{{sp|1}}''a''{{sp|1}}|{{sp|1}}''u''{{sp|1}}|HTM}} <!--
-->{{sp|1}}{{prod|''i''{{=}}1|''{{Gr|omega}}''{{sp|1}}(''n'')|HTM}} {{Kron|''a''|{{sp|2}}''p{{sub|i}}''{{sp|1}}|HTM}}{{^|{{^|{{^|''e''{{sub|''i''}}|100%}}|100%}}}},
|tex = {{Kron|a|n|TEX}} := {{Kron|a|u|TEX}} \prod_{i=1}^{\omega(n)} {{Kron|a|p_i|TEX}}^{e_i},|&&}}


yields the HTM+CSS

The Kronecker symbol
 (a  | n )
is defined as
 a n
:=
 a u
 ω (n) ∏ i  = 1

 a pi
ei,

The code

The '''Kronecker symbol''' {{math|{{Kron|''a''{{sp|1}}|''n''{{sp|1}}}}|tex = {{Kron|a|n|tex}}|$}} is defined as{{nl|1.35}} : {{math|{{Kron|{{sp|1}}''a''{{sp|1}}|{{sp|1}}''n''{{sp|1}}|HTM}} {{sp}}{{rel|def}}{{sp}} {{Kron|{{sp|1}}''a''{{sp|1}}|{{sp|1}}''u''{{sp|1}}|HTM}} <!-- -->{{sp|1}}{{prod|''i''{{=}}1|''{{Gr|omega}}''{{sp|1}}(''n'')|HTM}} {{Kron|''a''|{{sp|2}}''p{{sub|i}}''{{sp|1}}|HTM}}{{^|{{^|{{^|''e''{{sub|''i''}}|100%}}|100%}}}}, |tex = {{Kron|a|n|TEX}} := {{Kron|a|u|TEX}} \prod_{i=1}^{\omega(n)} {{Kron|a|p_i|TEX}}^{e_i},|$\$}}


yields the LaTeX

The Kronecker symbol ${\displaystyle \textstyle {(a\mid n)}}$ is defined as
${\displaystyle {\begin{array}{l}\displaystyle {\left({\frac {a}{n}}\right):=\left({\frac {a}{u}}\right)\prod _{i=1}^{\omega (n)}\left({\frac {a}{p_{i}}}\right)^{e_{i}},}\end{array}}}$