Difference between revisions of "Template:Intorient/doc"

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imported>Vanisaac
m (→‎See also: clean up per WP:CAT#T and WP:AWBREQ add template:Sandbox other)
imported>WOSlinker
m (change source to syntaxhighlight)
 
Line 54: Line 54:
 
| integrand = <math>p \, {\rm d}V</math>
 
| integrand = <math>p \, {\rm d}V</math>
 
}}
 
}}
<source lang="tex">{{intorient
+
<syntaxhighlight lang="tex">{{intorient
 
| preintegral = <math>W = </math>
 
| preintegral = <math>W = </math>
 
| symbol = varoint
 
| symbol = varoint
 
| intsubscpt = <math>{\scriptstyle \Gamma}</math>
 
| intsubscpt = <math>{\scriptstyle \Gamma}</math>
 
| integrand = <math>p \, {\rm d}V</math>
 
| integrand = <math>p \, {\rm d}V</math>
}}</source>
+
}}</syntaxhighlight>
  
 
*In [[complex analysis]] for [[contour integral]]s: {{intorient|
 
*In [[complex analysis]] for [[contour integral]]s: {{intorient|
Line 67: Line 67:
 
| integrand = <math>\frac{{\rm d}z}{(z+a)^3 \, z^{1/2}}</math>
 
| integrand = <math>\frac{{\rm d}z}{(z+a)^3 \, z^{1/2}}</math>
 
}}
 
}}
<source lang="tex">{{intorient|
+
<syntaxhighlight lang="tex">{{intorient|
 
| preintegral =  
 
| preintegral =  
 
| symbol = varoint
 
| symbol = varoint
 
| intsubscpt = <math>{\scriptstyle \Gamma}</math>
 
| intsubscpt = <math>{\scriptstyle \Gamma}</math>
 
| integrand = <math>\frac{{\rm d}z}{(z+a)^3 \, z^{1/2}}</math>
 
| integrand = <math>\frac{{\rm d}z}{(z+a)^3 \, z^{1/2}}</math>
}}</source>
+
}}</syntaxhighlight>
  
 
*Line integrals of vector fields: {{intorient|<!-- You have to nest things this way to insure everything stays in one line. -->
 
*Line integrals of vector fields: {{intorient|<!-- You have to nest things this way to insure everything stays in one line. -->
Line 85: Line 85:
 
| integrand = <math>\mathbf{F} \cdot {\rm d}\mathbf{r}</math>
 
| integrand = <math>\mathbf{F} \cdot {\rm d}\mathbf{r}</math>
 
}}
 
}}
<source lang="tex">{{intorient|<!-- You have to nest things this way to insure everything stays in one line. -->
+
<syntaxhighlight lang="tex">{{intorient|<!-- You have to nest things this way to insure everything stays in one line. -->
 
| preintegral = {{intorient|
 
| preintegral = {{intorient|
 
| preintegral =
 
| preintegral =
Line 95: Line 95:
 
| intsubscpt = <math>{\scriptstyle \partial S}</math>
 
| intsubscpt = <math>{\scriptstyle \partial S}</math>
 
| integrand = <math>\mathbf{F} \cdot {\rm d}\mathbf{r}</math>
 
| integrand = <math>\mathbf{F} \cdot {\rm d}\mathbf{r}</math>
}}</source>
+
}}</syntaxhighlight>
  
 
*Other examples: {{Intorient|
 
*Other examples: {{Intorient|
Line 103: Line 103:
 
| integrand = <math>(E + H \wedge T) \, {\rm d}^2 \Sigma</math>
 
| integrand = <math>(E + H \wedge T) \, {\rm d}^2 \Sigma</math>
 
}}
 
}}
<source lang="tex">{{Intorient|
+
<syntaxhighlight lang="tex">{{Intorient|
 
| preintegral =  
 
| preintegral =  
 
| symbol = oiiintctr
 
| symbol = oiiintctr
 
| intsubscpt = <math>{\scriptstyle \Sigma}</math>
 
| intsubscpt = <math>{\scriptstyle \Sigma}</math>
 
| integrand = <math>(E + H \wedge T) \, {\rm d}^2 \Sigma</math>
 
| integrand = <math>(E + H \wedge T) \, {\rm d}^2 \Sigma</math>
}}</source>
+
}}</syntaxhighlight>
  
 
:{{Intorient|
 
:{{Intorient|
Line 116: Line 116:
 
| integrand = <math>(E + H \wedge T) \, {\rm d}^4 \Omega</math>
 
| integrand = <math>(E + H \wedge T) \, {\rm d}^4 \Omega</math>
 
}}
 
}}
<source lang="tex">{{Intorient|
+
<syntaxhighlight lang="tex">{{Intorient|
 
| preintegral =  
 
| preintegral =  
 
| symbol = varoiiintctr
 
| symbol = varoiiintctr
 
| intsubscpt = <math>{\scriptstyle \Omega}</math>
 
| intsubscpt = <math>{\scriptstyle \Omega}</math>
 
| integrand = <math>(E + H \wedge T) \, {\rm d}^4 \Omega</math>
 
| integrand = <math>(E + H \wedge T) \, {\rm d}^4 \Omega</math>
}}</source>
+
}}</syntaxhighlight>
  
 
==See also==
 
==See also==

Latest revision as of 13:00, 7 July 2020

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 = x45px oiint = x45px oiiint = x45px varoint = x45px varoiint = x45px varoiiint = x45px
Counterclockwise
orientation
ointctr = x45px oiintctr = x45px oiiintctr = x45px varointctr = x45px varoiintctr = x45px varoiiintctr = x45px
The default is x45px
  • 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: x44px<math>{\scriptstyle \partial S}</math> <math>\mathbf{F} \cdot {\rm d}\mathbf{r} = -</math> x44px<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: x44px<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.