Carlb: Math Help part 7 moved to Help:Math Help part 7

2009-04-09T00:30:45Z

Math Help part 7 moved to Help:Math Help part 7

← Older revision	Revision as of 17:30, 8 April 2009
(No difference)

TimVK4YEH: changed headng

2008-03-08T01:32:25Z

changed headng

← Older revision		Revision as of 18:32, 7 March 2008
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	== Please note~~: Math is~~ not ~~completely enabled yet : some script error? ==~~		'''Please note that non standard characters will probably not render properly'''

	The complete helpfile is over 50kB in size. Some browsers may have difficulty in rendering the page, because many have a notional upper limit of 32kB per page. Please choose from one of the following options to access the help file:		The complete helpfile is over 50kB in size. Some browsers may have difficulty in rendering the page, because many have a notional upper limit of 32kB per page. Please choose from one of the following options to access the help file:
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	__TOC__		__TOC__



	== Spacing ==		== Spacing ==

TimVK4YEH: /* Example */

2008-03-08T01:31:25Z

Example

← Older revision		Revision as of 18:31, 7 March 2008
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	\left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR</math></nowiki>		\left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR</math></nowiki>

	~~===Example===~~
	~~<math>\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}</math>~~

	~~<nowiki><math>\phi_n(\kappa) =~~
	~~0.033C_n^2\kappa^{-11/3},\quad~~
	~~\frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}</math></nowiki>~~

	===Continuation and cases===		===Continuation and cases===

TimVK4YEH: /* Color */

2008-03-08T01:31:00Z

Color

← Older revision		Revision as of 18:31, 7 March 2008
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	:''<nowiki><!-- The \,\! is to keep the formula rendered as PNG instead of HTML. Please don't remove it.--></nowiki>''		:''<nowiki><!-- The \,\! is to keep the formula rendered as PNG instead of HTML. Please don't remove it.--></nowiki>''

	~~== Color ==~~

	~~Equations can use color:~~

	*<code>{\color{Blue}x^2}+{\color{Brown}2x}-{\color{OliveGreen}1}</code>
	*:<math>{\color{Blue}x^2}+{\color{Brown}2x}-{\color{OliveGreen}1}</math>

	*<code>x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}</code>
	*:<math>x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}</math>

	~~See here for [http://oregonstate.edu/%7Epeterseb/tex/samples/docs/color-package-demo.pdf all named colours] supported by LaTeX.~~

	~~Note that color should not be used as the ''only'' way to identify something because color blind people may not be able to distinguish between the two colors.~~

	== Examples ==		== Examples ==

TimVK4YEH: added info as per list

2008-03-07T07:40:17Z

added info as per list

New page

== Please note: Math is not completely enabled yet : some script error? ==

The complete helpfile is over 50kB in size. Some browsers may have difficulty in rendering the page, because many have a notional upper limit of 32kB per page. Please choose from one of the following options to access the help file:

* [[Complete math help file]] - over 50kB in size

* [[Math Help part 1]] - contains information on Syntax, Rendering and Pros and Cons of TeX and HTML for math functions

* [[Math Help part 2]] - contains information on Functions, Symbols and Special characters

* [[Math Help part 3]] - contains information on Subscripts, Superscripts and Integrals

* [[Math Help part 4]] - contains information on Fractions, Matrices and Multilines

* [[Math Help part 5]] - contains information on Alphabets and Typefaces

* [[Math Help part 6]] - contains information on Parenthesising big exprssions, Brackets and Bars

This wiki uses a subset of TeX markup, including some extensions from LaTeX and AMS-LaTeX, for mathematical formulae. It generates either PNG images or simple HTML markup, depending on user preferences and the complexity of the expression. In the future, as more browsers are smarter, it will be able to generate enhanced HTML or even MathML in many cases.

More precisely, MediaWiki filters the markup through Texvc, which in turn passes the commands to TeX for the actual rendering. Thus, only a limited part of the full TeX language is supported; see below for details.

__TOC__

== Spacing ==
Note that TeX handles most spacing automatically, but you may sometimes want manual control.
<table border="2" cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 0; background: #f9f9f9; border: 1px #aaa solid; border-collapse: collapse;">

<tr>
<th>Feature</th>
<th>Syntax</th>
<th>How it looks rendered</th>
</tr>

<tr>
<td>double quad space</td>
<td>a \qquad b</td>
<td><math>a \qquad b</math></td>
</tr>

<tr>
<td>quad space</td>
<td>a \quad b</td>
<td><math>a \quad b</math></td>
</tr>

<tr>
<td>text space</td>
<td>a\ b</td>
<td><math>a\ b</math></td>
</tr>

<tr>
<td>text space without PNG conversion</td>
<td>a \mbox{ } b</td>
<td><math>a \mbox{ } b</math></td>
</tr>

<tr>
<td>large space</td>
<td>a\;b</td>
<td><math>a\;b</math></td>
</tr>

<tr>
<td>medium space</td>
<td>a\>b</td>
<td>[not supported]</td>
</tr>

<tr>
<td>small space</td>
<td>a\,b</td>
<td><math>a\,b</math></td>
</tr>

<tr>
<td>no space</td>
<td>ab</td>
<td><math>ab\,</math></td>
</tr>

<tr>
<td>small negative space</td>
<td>a\!b</td>
<td><math>a\!b</math></td>
</tr>

</table>

== Align with normal text flow ==
Due to the default css

<pre>img.tex { vertical-align: middle; }</pre>

an inline expression like <math>\int_{-N}^{N} e^x\, dx = 2 \sinh N</math> should look good.

If you need to align it otherwise, use <code><nowiki><font style="vertical-align:-100%;"><math>...</math></font></nowiki></code> and play with the <code>vertical-align</code> argument until you get it right; however, how it looks may depend on the browser and the browser settings.

Also note that if you rely on this workaround, if/when the rendering on the server gets fixed in future releases, as a result of this extra manual offset your formulae will suddenly be aligned incorrectly. So use it sparingly, if at all.

== Forced PNG rendering ==

To force the formula to render as PNG, add <code>\,</code> (small space) at the end of the formula (where it is not rendered). This will force PNG if the user is in "HTML if simple" mode, but not for "HTML if possible" mode (math rendering settings in preferences.

You can also use <code>\,\!</code> (small space and negative space, which cancel out) anywhere inside the math tags. This ''does'' force PNG even in "HTML if possible" mode, unlike <code>\,</code>.

This could be useful to keep the rendering of formulae in a proof consistent, for example, or to fix formulae that render incorrectly in HTML (at one time, a^{2+2} rendered with an extra underscore), or to demonstrate how something is rendered when it would normally show up as HTML (as in the examples above).

For instance:

<table border="2" cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 0; background: #f9f9f9; border: 1px #aaa solid; border-collapse: collapse;">

<tr>
<th>Syntax</th>
<th>How it looks rendered</th>
</tr>

<tr>
<td>a^{c+2}</td>
<td><math>a^{c+2}</math></td>
</tr>

<tr>
<td>a^{c+2} \,</td>
<td><math>a^{c+2} \,</math></td>
</tr>

<tr>
<td>a^{\,\!c+2}</td>
<td><math>a^{\,\!c+2}</math> </td>
</tr>

<tr>
<td>a^{b^{c+2}}</td>
<td><math>a^{b^{c+2}}</math> (WRONG with option "HTML if possible or else PNG"!)</td>
</tr>

<tr>
<td>a^{b^{c+2}} \,</td>
<td><math>a^{b^{c+2}} \,</math> (WRONG with option "HTML if possible or else PNG"!)</td>
</tr>

<tr>
<td>a^{b^{c+2}}\approx 5</td>
<td><math>a^{b^{c+2}}\approx 5</math> (due to "<math>\approx</math>" correctly displayed, no code "\,\!" needed)</td>
</tr>

<tr>
<td>a^{b^{\,\!c+2}}</td>
<td><math>a^{b^{\,\!c+2}}</math></td>
</tr>

<tr>
<td>\int_{-N}^{N} e^x\, dx</td>
<td><math>\int_{-N}^{N} e^x\, dx</math></td>
</tr>

</table>

This has been tested with most of the formulae on this page, and seems to work perfectly.

You might want to include a comment in the HTML so people don't "correct" the formula by removing it:

:''<nowiki></nowiki>''

== Color ==

Equations can use color:

*<code>{\color{Blue}x^2}+{\color{Brown}2x}-{\color{OliveGreen}1}</code>
*:<math>{\color{Blue}x^2}+{\color{Brown}2x}-{\color{OliveGreen}1}</math>

*<code>x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}</code>
*:<math>x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}</math>

See here for [http://oregonstate.edu/%7Epeterseb/tex/samples/docs/color-package-demo.pdf all named colours] supported by LaTeX.

Note that color should not be used as the ''only'' way to identify something because color blind people may not be able to distinguish between the two colors.

== Examples ==

<center>
===Quadratic Polynomial===
<math>ax^2 + bx + c = 0</math>

<nowiki><math>ax^2 + bx + c = 0</math></nowiki>

===Quadratic Polynomial (Force PNG Rendering)===
<math>ax^2 + bx + c = 0\,\!</math>

<nowiki><math>ax^2 + bx + c = 0\,\!</math></nowiki>

===Quadratic Formula===
<math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>

<nowiki><math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math></nowiki>

===Tall Parentheses and Fractions ===
<math>2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)</math>

<nowiki><math>2 = \left(
\frac{\left(3-x\right) \times 2}{3-x}
\right)</math></nowiki>

<math>S_{new} = S_{old} + \frac{ \left( 5-T \right) ^2} {2}</math>

<nowiki><math>S_{new} = S_{old} +
\frac{ \left( 5-T \right) ^2} {2}</math></nowiki>

===Integrals===
<math>\int_a^x \int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy</math>

<nowiki><math>\int_a^x \int_a^s f(y)\,dy\,ds
= \int_a^x f(y)(x-y)\,dy</math></nowiki>

===Summation===
<math>\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}{3^m\left(m\,3^n+n\,3^m\right)}</math>

<nowiki><math>\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}
{3^m\left(m\,3^n+n\,3^m\right)}</math></nowiki>

=== Differential Equation ===
<math>u'' + p(x)u' + q(x)u=f(x),\quad x>a</math>

<nowiki><math>u'' + p(x)u' + q(x)u=f(x),\quad x>a</math></nowiki>

===Complex numbers===
<math>|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)</math>

<nowiki><math>|\bar{z}| = |z|,
|(\bar{z})^n| = |z|^n,
\arg(z^n) = n \arg(z)</math></nowiki>

===Limits===
<math>\lim_{z\rightarrow z_0} f(z)=f(z_0)</math>

<nowiki><math>\lim_{z\rightarrow z_0} f(z)=f(z_0)</math></nowiki>

===Integral Equation===
<math>\phi_n(\kappa)
= \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R} \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR</math>

<nowiki><math>\phi_n(\kappa) =
\frac{1}{4\pi^2\kappa^2} \int_0^\infty
\frac{\sin(\kappa R)}{\kappa R}
\frac{\partial}{\partial R}
\left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR</math></nowiki>

===Example===
<math>\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}</math>

<nowiki><math>\phi_n(\kappa) =
0.033C_n^2\kappa^{-11/3},\quad
\frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}</math></nowiki>

===Continuation and cases===
<math>f(x) = \begin{cases}1 & -1 \le x < 0 \\
\frac{1}{2} & x = 0 \\ 1 - x^2 & 0 < x \le 1\end{cases}</math>

<nowiki><math>
f(x) =
\begin{cases}
1 & -1 \le x < 0 \\
\frac{1}{2} & x = 0 \\
1 - x^2 & 0 < x\le 1
\end{cases}
</math></nowiki>

===Prefixed subscript===
<math>{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdot\cdot\cdot(a_p)_n}{(c_1)_n\cdot\cdot\cdot(c_q)_n}\frac{z^n}{n!}</math>

<nowiki> <math>{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z)
= \sum_{n=0}^\infty
\frac{(a_1)_n\cdot\cdot\cdot(a_p)_n}{(c_1)_n\cdot\cdot\cdot(c_q)_n}
\frac{z^n}{n!}</math></nowiki>

</center>

Help:Math Help part 7 - Revision history

Carlb: Math Help part 7 moved to Help:Math Help part 7

TimVK4YEH: changed headng

TimVK4YEH: /* Example */

TimVK4YEH: /* Color */

TimVK4YEH: added info as per list