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<title>eLyxer Math Showcase (MathJax local edition)</title>
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<h1 class="title">
<img class="embedded" src="elyxer.png" alt="figure elyxer.png" style="max-width: 160px; max-height: 160px;"/>
eLyXer Math Showcase
</h1>
<h2 class="author">
Alex Fernández (elyxer@gmail.com)
</h2>
<div class="fulltoc">
<div class="tocheader">
Table of Contents
</div>
<div class="tocindent">
<div class="toc">
<a class="Link" href="#toc-Section-1">Section 1: Introduction</a>
</div>
<div class="tocindent">
<div class="toc">
<a class="Link" href="#toc-Subsection-1.1">Subsection 1.1: Versions</a>
</div>
</div>
<div class="toc">
<a class="Link" href="#toc-Section-2">Section 2: Typography</a>
</div>
<div class="tocindent">
<div class="toc">
<a class="Link" href="#toc-Subsection-2.1">Subsection 2.1: Greek Symbols</a>
</div>
<div class="toc">
<a class="Link" href="#toc-Subsection-2.2">Subsection 2.2: Math Symbols</a>
</div>
<div class="toc">
<a class="Link" href="#toc-Subsection-2.3">Subsection 2.3: Other Symbols</a>
</div>
<div class="toc">
<a class="Link" href="#toc-Subsection-2.4">Subsection 2.4: Spacing</a>
</div>
<div class="toc">
<a class="Link" href="#toc-Subsection-2.5">Subsection 2.5: Fonts</a>
</div>
</div>
<div class="toc">
<a class="Link" href="#toc-Section-3">Section 3: Numeration</a>
</div>
<div class="toc">
<a class="Link" href="#toc-Section-4">Section 4: Simple Structures</a>
</div>
<div class="tocindent">
<div class="toc">
<a class="Link" href="#toc-Subsection-4.1">Subsection 4.1: Fractions</a>
</div>
<div class="toc">
<a class="Link" href="#toc-Subsection-4.2">Subsection 4.2: Limits</a>
</div>
<div class="toc">
<a class="Link" href="#toc-Subsection-4.3">Subsection 4.3: Roots</a>
</div>
</div>
<div class="toc">
<a class="Link" href="#toc-Section-5">Section 5: Complex Structures</a>
</div>
<div class="tocindent">
<div class="toc">
<a class="Link" href="#toc-Subsection-5.1">Subsection 5.1: Arrays</a>
</div>
<div class="toc">
<a class="Link" href="#toc-Subsection-5.2">Subsection 5.2: Brackets</a>
</div>
<div class="toc">
<a class="Link" href="#toc-Subsection-5.3">Subsection 5.3: Cases</a>
</div>
<div class="toc">
<a class="Link" href="#toc-Subsection-5.4">Subsection 5.4: Braces</a>
</div>
</div>
<div class="toc">
<a class="Link" href="#toc-Section-6">Section 6: Macros</a>
</div>
</div>
</div>
<h1 class="Section">
<a class="toc" name="toc-Section-1">1</a> Introduction
</h1>
<div class="Unindented">
This document is intended as a showcase of the mathematical abilities of eLyXer; for more information be sure to visit the <a class="URL" href="index.html">main page</a>.
</div>
<h2 class="Subsection">
<a class="toc" name="toc-Subsection-1.1">1.1</a> Versions
</h2>
<div class="Unindented">
There are several versions of this page:
</div>
<ul>
<li>
A <a class="URL" href="math.html">non-Unicode version</a> of this page with midspaces.
</li>
<li>
A <a class="URL" href="math-unicode.html">Unicode version</a> with mathematical spaces (generated with <tt>--unicode</tt>).
</li>
<li>
An <a class="URL" href="math-iso885915.html">ISO-8859-15 version</a> (generated with <tt>--iso885915</tt>).
</li>
<li>
An <a class="URL" href="math-html.html">HTML version</a> (generated with <tt>--html</tt>).
</li>
<li>
A <a class="URL" href="math-mathjax.html">MathJax remote version</a> with <a class="URL" href="http://www.mathjax.org/">MathJax</a> (generated with <tt>--mathjax remote</tt>).
</li>
<li>
A <a class="URL" href="math-mathjax-local.html">MathJax local version</a> with <a class="URL" href="http://www.mathjax.org/">MathJax</a> (generated with <tt>--mathjax</tt> and a local URL).
</li>
<li>
A <a class="URL" href="math-googlecharts.html">Google Charts version</a> with <a class="URL" href="http://code.google.com/apis/chart/index.html">Google Charts</a> (generated with <tt>--googlecharts</tt>).
</li>
</ul>
<div class="Unindented">
All of them are generated from the same <tt>.lyx</tt> source file; they should help you decide which rendering options suit you best.
</div>
<div class="Indented">
Also available online is the eLyXer translation of the latest <a class="URL" href="http://elyxer.nongnu.org/lyx/Math.html">LyX’s detailed Math manual</a>, which contains a lot more examples of LyX maths.
</div>
<h1 class="Section">
<a class="toc" name="toc-Section-2">2</a> Typography
</h1>
<div class="Unindented">
Math formulae use a lot of different symbols and fonts.
</div>
<h2 class="Subsection">
<a class="toc" name="toc-Subsection-2.1">2.1</a> Greek Symbols
</h2>
<div class="Unindented">
Greek symbols are very important in equations: <span class="MathJax_Preview"><script type="math/tex">
\phi
</script>
</span>, <span class="MathJax_Preview"><script type="math/tex">
\pi
</script>
</span>, <span class="MathJax_Preview"><script type="math/tex">
\Xi
</script>
</span>. eLyXer offers a complete set in both upper case: <span class="MathJax_Preview"><script type="math/tex">
\Gamma\ldots\Omega
</script>
</span> and lower case: <span class="MathJax_Preview"><script type="math/tex">
\alpha\ldots\omega
</script>
</span>. Also the AMS italicized upper case: <span class="MathJax_Preview"><script type="math/tex">
\varGamma\ldots\varOmega
</script>
</span>.
</div>
<h2 class="Subsection">
<a class="toc" name="toc-Subsection-2.2">2.2</a> Math Symbols
</h2>
<div class="Unindented">
eLyXer supports the whole set of math symbols in <a class="URL" href="http://www.johndcook.com/math_symbols.html">John D. Cook's list</a>: <span class="MathJax_Preview"><script type="math/tex">
\exists\partial\nabla\geq
</script>
</span>. It can also render a few more: <span class="MathJax_Preview"><script type="math/tex">
\propto\times
</script>
</span>. You also get all symbols from <a class="URL" href="http://www.cl.cam.ac.uk/~mgk25/ucs/examples/TeX.txt">Markus Kuhn's list</a>: <span class="MathJax_Preview"><script type="math/tex">
\bigodot\amalg
</script>
</span>.
</div>
<h2 class="Subsection">
<a class="toc" name="toc-Subsection-2.3">2.3</a> Other Symbols
</h2>
<div class="Unindented">
There are other symbols like arrows: <span class="MathJax_Preview"><script type="math/tex">
\leftarrow\rightarrow
</script>
</span>, or geometrical shapes: <span class="MathJax_Preview"><script type="math/tex">
\circ
</script>
</span>, <span class="MathJax_Preview"><script type="math/tex">
\square
</script>
</span>. eLyXer offers limited support for them. You might also want to use financial symbols in formulae: <span class="MathJax_Preview"><script type="math/tex">
\yen\euro\$
</script>
</span>.
</div>
<h2 class="Subsection">
<a class="toc" name="toc-Subsection-2.4">2.4</a> Spacing
</h2>
<div class="Unindented">
Equations look good when items are properly separated. The main separation is the Medium Mathematical Space: <span class="MathJax_Preview"><script type="math/tex">
x=3
</script>
</span>. <span class="greyedout">
Note: if you are viewing the non-Unicode version <a class="FlexURL" href="math.html">math.html</a> of this page then you are in fact seeing midspaces, which are very similar but not exactly the same: <span class="MathJax_Preview"><script type="math/tex">
\frac{4}{18}\mathrm{em}
</script>
</span> for medium mathematical spaces versus <span class="MathJax_Preview"><script type="math/tex">
\frac{1}{2}\mathrm{en}
</script>
</span>, where <span class="MathJax_Preview"><script type="math/tex">
1\mathrm{em}=2\mathrm{en}
</script>
</span>. Try out the Unicode version <a class="FlexURL" href="math-unicode.html">math-unicode.html</a> — and viceversa. You can check out what version this page is in the page title.
</span>
</div>
<div class="Indented">
The command <tt>\raisebox</tt> is useful to, surprisingly, raise a little box, <span class="MathJax_Preview">
<script type="math/tex;mode=display">
\raisebox{2mm}{raised}over\raisebox{-2mm}{lowered}\textrm{and back}.
</script>
</span>
Like <tt>\mbox</tt>, it puts its content in a text box. It can also be used just for spacing:<br/>
<span class="MathJax_Preview"><script type="math/tex">
\raisebox{5mm}{}B^{V}
</script>
</span>.
</div>
<div class="Indented">
There are other spacing commands: <tt>\hspace</tt>: <span class="MathJax_Preview"><script type="math/tex">
a\hspace{4mm}b
</script>
</span>, protected space: <span class="MathJax_Preview"><script type="math/tex">
a\ b
</script>
</span>, and (at “block level”)<tt> \vspace</tt>: <span class="MathJax_Preview"><script type="math/tex">
a\vspace{1cm}b
</script>
</span>.
</div>
<div class="Indented">
There should be 1 cm of vertical space above this paragraph.
</div>
<h2 class="Subsection">
<a class="toc" name="toc-Subsection-2.5">2.5</a> Fonts
</h2>
<div class="Unindented">
By default, letters denote variables and are taken from the <tt>\mathnormal</tt> font, which is italic, <span class="MathJax_Preview"><script type="math/tex">
\alpha x+\alpha y=\alpha(x+y)
</script>
</span>, with the exception of upright capital Greek letters, <span class="MathJax_Preview"><script type="math/tex">
G\ne\Gamma
</script>
</span>.
</div>
<div class="Indented">
Function names should be upright: <span class="MathJax_Preview"><script type="math/tex">
\sin(2\pi),\log(x),\tan\delta
</script>
</span>.
</div>
<div class="Indented">
Mathematical fonts used in equations include <span class="MathJax_Preview"><script type="math/tex">
\mathrm{Roman}
</script>
</span> (<tt>\mathrm</tt>), <span class="MathJax_Preview"><script type="math/tex">
\mathsf{Sans\: Serif}
</script>
</span> (<tt>\mathsf</tt>), <span class="MathJax_Preview"><script type="math/tex">
\mathtt{Typewriter}
</script>
</span> (<tt>\mathtt</tt>), <span class="MathJax_Preview"><script type="math/tex">
\mathbf{Bold}
</script>
</span> (<tt>\mathbf</tt>), <span class="MathJax_Preview"><script type="math/tex">
\mathscr{SCRIPT}
</script>
</span> (<tt>\mathscr</tt>), <span class="MathJax_Preview"><script type="math/tex">
\mathcal{CALLIGRAPHIC}
</script>
</span> (<tt>\mathcal</tt>), <span class="MathJax_Preview"><script type="math/tex">
\mathbb{BLACKBOARD\: BOLD}
</script>
</span> (<tt><span class="versalitas">\</span>mathbb</tt>), and <span class="MathJax_Preview"><script type="math/tex">
\mathfrak{Fraktur}
</script>
</span> (<tt>\mathfrak</tt>). For the latter, some single characters are translated to their Unicode equivalents: <span class="MathJax_Preview"><script type="math/tex">
\mathscr{F}
</script>
</span>, <span class="MathJax_Preview"><script type="math/tex">
\mathbb{F}
</script>
</span>, <span class="MathJax_Preview"><script type="math/tex">
\mathfrak{F}
</script>
</span>.
</div>
<div class="Indented">
Regular text in a formula can be achieved via text font commands like <tt>\textrm</tt>: <span class="MathJax_Preview"><script type="math/tex">
5\:\textrm{to}\:10
</script>
</span>, via boxes like \mbox (prevents line breaks): <span class="MathJax_Preview"><script type="math/tex">
6\mbox{ is more than }5
</script>
</span>, or the AMSmath <tt>\text</tt> macro (scales like math symbols) <span class="MathJax_Preview"><script type="math/tex">
\text{base}_{\text{sub}}^{\text{super}}
</script>
</span>. The content of an mbox is processed in LaTeX text mode. This allows text font commands, e.g. a switch to <span class="sans"><b><i>sans-serif-bold-italic</i></b></span>, or the phonetic alphabet: <span class="MathJax_Preview"><script type="math/tex">
\mbox{\textbf{\textsf{\textbf{\textit{sfbfit}}}}, \textipa{tipa}}
</script>
</span>.
</div>
<div class="Indented">
Units should be written upright, either with <tt>\mathrm</tt> or with macros from the <tt>units</tt> package, e.g. as simple unit, <span class="MathJax_Preview"><script type="math/tex">
\unit{km}
</script>
</span>, with magnitude, <span class="MathJax_Preview"><script type="math/tex">
\unit[57]{km}
</script>
</span>, with fractional unit, <span class="MathJax_Preview"><script type="math/tex">
\unitfrac[200]{km}{h}
</script>
</span>, or with a fraction before the units, <span class="MathJax_Preview"><script type="math/tex">
\unit[\nicefrac{3}{2}]{km}
</script>
</span>, <span class="MathJax_Preview"><script type="math/tex">
\unit[\frac{7}{16}]{s}
</script>
</span>.
</div>
<h1 class="Section">
<a class="toc" name="toc-Section-3">3</a> Numeration
</h1>
<div class="Unindented">
Equations can be numbered, like (<a class="Reference" href="#eq:first">↓</a>) <span class="MathJax_Preview">
<script type="math/tex;mode=display">
\begin{equation}
y=x\label{eq:first}\end{equation}
</script>
</span>
And also like <a class="Reference" href="#eq:second">(↓)</a>. <span class="MathJax_Preview">
<script type="math/tex;mode=display">
\begin{equation}
x=3\label{eq:second}\end{equation}
</script>
</span>
Some equations can be numbered even if they don’t have a label.
</div>
<div class="Indented">
<span class="MathJax_Preview">
<script type="math/tex;mode=display">
\begin{equation}
x=2y\end{equation}
</script>
</span>
Notice that equation (<a class="Reference" href="#eq:second">↓</a>) comes after (<a class="Reference" href="#eq:first">↓</a>).
</div>
<h1 class="Section">
<a class="toc" name="toc-Section-4">4</a> Simple Structures
</h1>
<div class="Unindented">
Let’s now see a few of the simpler structures that eLyXer can output.
</div>
<h2 class="Subsection">
<a class="toc" name="toc-Subsection-4.1">4.1</a> Fractions
</h2>
<div class="Unindented">
A simple fraction: <span class="MathJax_Preview">
<script type="math/tex;mode=display">
\frac{1}{2}.
</script>
</span>
Inlined: <span class="MathJax_Preview"><script type="math/tex">
\frac{2}{3}.
</script>
</span>
</div>
<div class="Indented">
A big recursive fraction: <span class="MathJax_Preview">
<script type="math/tex;mode=display">
\frac{1}{\left(1+\left(\frac{1}{1+\left(\frac{1}{1+2x}\lyxlock\right)}\lyxlock\right)\right)}\lyxlock
</script>
</span>
</div>
<div class="Indented">
A nice fraction: <span class="MathJax_Preview"><script type="math/tex">
\nicefrac{5}{6}
</script>
</span>. A non-diminishing fraction containing alignments:<span class="MathJax_Preview">
<script type="math/tex;mode=display">
\cfrac{1}{1+\left(\cfrac[l]{1}{1+x}\times\cfrac[r]{1}{1+x}\right)}.
</script>
</span>
</div>
<div class="Indented">
A similar concept is a binomial coefficient: <span class="MathJax_Preview"><script type="math/tex">
\binom{A+1}{B}.
</script>
</span> It can be prettily presented: <span class="MathJax_Preview">
<script type="math/tex;mode=display">
\dbinom{A}{B+1}.
</script>
</span>
</div>
<div class="Indented">
A symbol can be stacked over another using <tt>\stackrel</tt>: <span class="MathJax_Preview"><script type="math/tex">
x\stackrel{R}{\rightarrow}y
</script>
</span>. Anything can be stacked: <span class="MathJax_Preview">
<script type="math/tex;mode=display">
d\stackrel{x>3}{\lim}x,\quad\stackrel{\mathrm{head}}{\mathrm{heels}}.
</script>
</span>
</div>
<h2 class="Subsection">
<a class="toc" name="toc-Subsection-4.2">4.2</a> Limits
</h2>
<div class="Unindented">
<span class="MathJax_Preview"><script type="math/tex">
\lim_{x\rightarrow\infty}f(x)
</script>
</span> should appear as <span class="MathJax_Preview"><script type="math/tex">
x\rightarrow\infty
</script>
</span> in italics, and «lim» in plain style. In display mode, a limit must appear below the main symbol: <span class="MathJax_Preview">
<script type="math/tex;mode=display">
\lim_{x\rightarrow\infty}\lyxlock f(x).
</script>
</span>
</div>
<div class="Indented">
Limits are also used in sums and integrals: <span class="MathJax_Preview">
<script type="math/tex;mode=display">
\sum_{i=1}^{\infty}x,\;\int_{0}^{\infty}f(x)\,\mathrm{d}x
</script>
</span>
where the sum’s limits should appear below (<span class="MathJax_Preview"><script type="math/tex">
i=1
</script>
</span>) and above (<span class="MathJax_Preview"><script type="math/tex">
\infty
</script>
</span>) the <span class="MathJax_Preview"><script type="math/tex">
\sum
</script>
</span>. The placement of the integral limits depends on the document class: LaTeX standard classes place them right to the <span class="MathJax_Preview"><script type="math/tex">
\int
</script>
</span>. Limits are shown to the right in inline formulae: <span class="MathJax_Preview"><script type="math/tex">
\sum_{i=1}^{\infty}x
</script>
</span> and <span class="MathJax_Preview"><script type="math/tex">
\intop_{i=1}^{\infty}x.
</script>
</span>
</div>
<div class="Indented">
The placing of limits can be configured with the <tt>\limits</tt> and <tt>\nolimits</tt> macros: <span class="MathJax_Preview">
<script type="math/tex;mode=display">
\lim\nolimits _{x\rightarrow\infty}\lyxlock f(x),\;\sum\nolimits _{i=1}^{\infty}x,\;\int\limits _{0}^{\infty}f(x)\,\mathrm{d}x
</script>
</span>
</div>
<h2 class="Subsection">
<a class="toc" name="toc-Subsection-4.3">4.3</a> Roots
</h2>
<div class="Unindented">
A square root: <span class="MathJax_Preview"><script type="math/tex">
\sqrt{3}.
</script>
</span> A more complex root in a fraction:<span class="MathJax_Preview">
<script type="math/tex;mode=display">
\frac{1}{\left(1+\sqrt{2}\left(\frac{1}{1+\sqrt{2}}\lyxlock\right)+\sqrt{\frac{1}{2}}\right)}\lyxlock.
</script>
</span>
</div>
<div class="Indented">
eLyXer can also do higher-order roots: <span class="MathJax_Preview"><script type="math/tex">
\sqrt[3]{x+y}
</script>
</span>. A devilish case mixing everything we have seen so far:<span class="MathJax_Preview">
<script type="math/tex;mode=display">
\frac{\sqrt[\nicefrac{7}{8}]{\frac{8}{4}x}+\sum_{i=1}^{\infty}x}{\sqrt[s+5]{\frac{(78x+45y)\times\sqrt{\Omega}}{\sin(x+1)}+\unit[38]{km}}}\lyxlock.
</script>
</span>
</div>
<h1 class="Section">
<a class="toc" name="toc-Section-5">5</a> Complex Structures
</h1>
<div class="Unindented">
In this section we will explore arrays and related constructs.
</div>
<h2 class="Subsection">
<a class="toc" name="toc-Subsection-5.1">5.1</a> Arrays
</h2>
<div class="Unindented">
An inline array <span class="MathJax_Preview"><script type="math/tex">
\left[\begin{array}{cc}
a & b\\
c & d\end{array}\right]
</script>
</span> is always shown in the same line. In display mode, the array is shown on its own line: <span class="MathJax_Preview">
<script type="math/tex;mode=display">
\left[\begin{array}{lc}
12 & 2\\
3 & 4\times y^{x}\end{array}\right]
</script>
</span>
Apart from that the appearance should be the same.
</div>
<h2 class="Subsection">
<a class="toc" name="toc-Subsection-5.2">5.2</a> Brackets
</h2>
<div class="Unindented">
Arrays are separated by variable-size brackets: <span class="MathJax_Preview"><script type="math/tex">
\left(\begin{array}{cc}
a & b\\
c & d\end{array}\right)
</script>
</span> <span class="MathJax_Preview"><script type="math/tex">
\left[\begin{array}{cc}
a & b\\
c & d\end{array}\right]
</script>
</span> <span class="MathJax_Preview"><script type="math/tex">
\left\{ \begin{array}{cc}
a & b\\
c & d\end{array}\right\}
</script>
</span> <span class="MathJax_Preview"><script type="math/tex">
\left\langle \begin{array}{cc}
a & b\\
c & d\end{array}\right\rangle
</script>
</span> <span class="MathJax_Preview"><script type="math/tex">
\left|\begin{array}{cc}
a & b\\
c & d\end{array}\right|
</script>
</span>which might also differ on right and left <span class="MathJax_Preview"><script type="math/tex">
\left(\begin{array}{cc}
a & b\\
c & d\end{array}\right)
</script>
</span> or use the empty opening <span class="MathJax_Preview"><script type="math/tex">
\left\{ \begin{array}{cc}
a & b\\
c & d\end{array}\right.
</script>
</span> or closing: <span class="MathJax_Preview"><script type="math/tex">
\left.\begin{array}{cc}
a & b\\
c & d\end{array}\right|
</script>
</span>. There are also fixed-size big brackets, e.g. <span class="MathJax_Preview"><script type="math/tex">
\bigl\langle f\bigr\rangle
</script>
</span>.
</div>
<h2 class="Subsection">
<a class="toc" name="toc-Subsection-5.3">5.3</a> Cases
</h2>
<div class="Unindented">
Used to switch between several values.
</div>
<div class="Indented">
<span class="MathJax_Preview">
<script type="math/tex;mode=display">
y=\begin{cases}
x & i=0,\\
x+1 & i<3\end{cases}
</script>
</span>
</div>
<div class="Indented">
Cases may have more than two rows:
</div>
<div class="Indented">
<span class="MathJax_Preview">
<script type="math/tex;mode=display">
f(x)=\begin{cases}
0 & x<0,\\
\infty & x=0\\
0 & x>0\end{cases}
</script>
</span>
</div>
<h2 class="Subsection">
<a class="toc" name="toc-Subsection-5.4">5.4</a> Braces
</h2>
<div class="Unindented">
Values can be underbraced or overbraced.
</div>
<div class="Indented">
<span class="MathJax_Preview"><script type="math/tex">
\underbrace{a-b}=\overbrace{b+c+d+e}
</script>
</span>.
</div>
<h1 class="Section">
<a class="toc" name="toc-Section-6">6</a> Macros
</h1>
<div class="Unindented">
Now it’s time for user-defined commands (sometimes called “macros”).
</div>
<div class="Indented">
Definitions can be added as macros. Then they can be used in formulae: <span class="MathJax_Preview"><script type="math/tex">
\stupidroot 12
</script>
</span>. They can accept default parameters. Again, useful in formulae: <span class="MathJax_Preview"><script type="math/tex">
\defaultroot
</script>
</span>.
</div>
<div class="Indented">
Other definitions from the preamble can be used: <span class="MathJax_Preview"><script type="math/tex">
\preambleroot{3}{4}
</script>
</span>.
</div>
<div class="Indented">
Definitions on the fly are also possible: <span class="MathJax_Preview"><script type="math/tex">
\newcommand{\ontheflyroot}[2]{\sqrt[#1]{#2}}\ontheflyroot{7}{8}
</script>
</span>, and used with different values: <span class="MathJax_Preview"><script type="math/tex">
\ontheflyroot{a}{b}
</script>
</span>.
</div>
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