Difference between revisions of "Template:Intorient"

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|varoiiintctr=[[File:VaroiiintctrclockwiseLaTeX.svg|x44px|alt=\varoiiintctrclockwise|link=]]  
 
|varoiiintctr=[[File:VaroiiintctrclockwiseLaTeX.svg|x44px|alt=\varoiiintctrclockwise|link=]]  
 
|[[File:OintclockwiseLaTeX.svg|x44px|alt=\ointclockwise|link=]]
 
|[[File:OintclockwiseLaTeX.svg|x44px|alt=\ointclockwise|link=]]
}}<span style="position:relative; right:8px; top:18px; margin-right:-8px;">{{{intsubscpt|}}}</span> {{{integrand|}}}</span>
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}}<span style="position:relative; right:8px; top:18px; margin-right:-8px;">{{{intsubscpt|}}}</span> {{{integrand|}}}</span><noinclude>
<noinclude>{{documentation}}</noinclude>
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{{documentation}}</noinclude>

Latest revision as of 03:48, 24 December 2019

\ointclockwise

Template documentation[view] [edit] [history] [purge]

This template is used to include the oriented integrals around closed surfaces (or hypersurfaces in higher dimensions), usually in a mathematical formula. They are additional symbols to the non-oriented integrals \oiint and \oiiint which are not yet rendered on Wikipedia.

Arguments

  • preintegral the text or formula immediately before the integral
  • symbol the integral symbol,
Select one of... Arrow up, integrals over a closed Arrow down, integrals over a closed
1-surface 2-surface 3-surface 1-surface 2-surface 3-surface
Clockwise
orientation
oint = \oiint oiint = \oiint oiiint = \oiint varoint = \oiint varoiint = \oiint varoiiint = x45px
Counterclockwise
orientation
ointctr = File:OintctrclockwiseLaTeX.svg oiintctr = File:OiintctrclockwiseLaTeX.svg oiiintctr = File:OiiintctrclockwiseLaTeX.svg varointctr = \oiint varoiintctr = \oiint varoiiintctr = x45px
The default is \oiint
  • intsubscpt the subscript below the integral
  • integrand the text or formula immediately after the formula

All parameters are optional.

Examples

{{intorient
| preintegral = <math>W = </math>
| symbol = varoint
| intsubscpt = <math>{\scriptstyle \Gamma}</math>
| integrand = <math>p \, {\rm d}V</math>
}}
{{intorient|
| preintegral = 
| symbol = varoint
| intsubscpt = <math>{\scriptstyle \Gamma}</math>
| integrand = <math>\frac{{\rm d}z}{(z+a)^3 \, z^{1/2}}</math>
}}
  • Line integrals of vector fields: \ointclockwise<math>{\scriptstyle \partial S}</math> <math>\mathbf{F} \cdot {\rm d}\mathbf{r} = -</math> \ointctrclockwise<math>{\scriptstyle \partial S}</math> <math>\mathbf{F} \cdot {\rm d}\mathbf{r}</math>
{{intorient|<!-- You have to nest things this way to insure everything stays in one line. -->
| preintegral = {{intorient|
| preintegral =
| symbol = oint
| intsubscpt = <math>{\scriptstyle \partial S}</math>
| integrand = <math>\mathbf{F} \cdot {\rm d}\mathbf{r} = -</math>
}}
|symbol=ointctr
| intsubscpt = <math>{\scriptstyle \partial S}</math>
| integrand = <math>\mathbf{F} \cdot {\rm d}\mathbf{r}</math>
}}
  • Other examples: \oiintclockwise<math>{\scriptstyle \Sigma}</math> <math>(E + H \wedge T) \, {\rm d}^2 \Sigma</math>
{{Intorient|
| preintegral = 
| symbol = oiiintctr
| intsubscpt = <math>{\scriptstyle \Sigma}</math>
| integrand = <math>(E + H \wedge T) \, {\rm d}^2 \Sigma</math>
}}
x44px<math>{\scriptstyle \Omega}</math> <math>(E + H \wedge T) \, {\rm d}^4 \Omega</math>
{{Intorient|
| preintegral = 
| symbol = varoiiintctr
| intsubscpt = <math>{\scriptstyle \Omega}</math>
| integrand = <math>(E + H \wedge T) \, {\rm d}^4 \Omega</math>
}}

See also

Non-oriented boundary integrals over a 2-surface and 3-surface can be implemented respectively by:

These symbols are currently not supported in MediaWiki's Math mode and this feature request is tracked in phab:T182127.