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) |
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| Line 54: | Line 54: | ||
| integrand = <math>p \, {\rm d}V</math> | | integrand = <math>p \, {\rm d}V</math> | ||
}} | }} | ||
| − | < | + | <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> | ||
| − | }}</ | + | }}</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> | ||
}} | }} | ||
| − | < | + | <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> | ||
| − | }}</ | + | }}</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> | ||
}} | }} | ||
| − | < | + | <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> | ||
| − | }}</ | + | }}</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> | ||
}} | }} | ||
| − | < | + | <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> | ||
| − | }}</ | + | }}</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> | ||
}} | }} | ||
| − | < | + | <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> | ||
| − | }}</ | + | }}</syntaxhighlight> |
==See also== | ==See also== | ||
Latest revision as of 13:00, 7 July 2020
| 40px | This is a documentation subpage for Template:Intorient. It contains usage information, categories and other content that is not part of the original template page. |
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
orientationoint = x45px oiint = x45px oiiint = x45px varoint = x45px varoiint = x45px varoiiint = x45px Counterclockwise
orientationointctr = 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
- The work done in a thermodynamic cycle on an indicator diagram: <math>W = </math> x44px<math>{\scriptstyle \Gamma}</math> <math>p \, {\rm d}V</math>
{{intorient
| preintegral = <math>W = </math>
| symbol = varoint
| intsubscpt = <math>{\scriptstyle \Gamma}</math>
| integrand = <math>p \, {\rm d}V</math>
}}
- In complex analysis for contour integrals: x44px<math>{\scriptstyle \Gamma}</math> <math>\frac{{\rm d}z}{(z+a)^3 \, z^{1/2}}</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.