eLyXer Math Showcase

A non-Unicode version of this page with midspaces.
A Unicode version with mathematical spaces (generated with --unicode).
An ISO-8859-15 version (generated with --iso885915).
An HTML version (generated with --html).
A MathJax remote version with MathJax (generated with --mathjax remote).
A MathJax local version with MathJax (generated with --mathjax and a local URL).
A Google Charts version with Google Charts (generated with --googlecharts).

All of them are generated from the same .lyx source file; they should help you decide which rendering options suit you best.

Also available online is the eLyXer translation of the latest LyX’s detailed Math manual, which contains a lot more examples of LyX maths.

2 Typography

Math formulae use a lot of different symbols and fonts.

2.1 Greek Symbols

Greek symbols are very important in equations: $\phi$ , $\pi$ , $\Xi$ . eLyXer offers a complete set in both upper case: $\Gamma\ldots\Omega$ and lower case: $\alpha\ldots\omega$ . Also the AMS italicized upper case: $\varGamma\ldots\varOmega$ .

2.2 Math Symbols

eLyXer supports the whole set of math symbols in John D. Cook's list: $\exists\partial\nabla\geq$ . It can also render a few more: $\propto\times$ . You also get all symbols from Markus Kuhn's list: $\bigodot\amalg$ .

2.3 Other Symbols

There are other symbols like arrows: $\leftarrow\rightarrow$ , or geometrical shapes: $\circ$ , $\square$ . eLyXer offers limited support for them. You might also want to use financial symbols in formulae: $\yen\euro\$$ .

2.4 Spacing

Equations look good when items are properly separated. The main separation is the Medium Mathematical Space: $x=3$ . Note: if you are viewing the non-Unicode version math.html of this page then you are in fact seeing midspaces, which are very similar but not exactly the same: $\frac{4}{18}\mathrm{em}$ for medium mathematical spaces versus $\frac{1}{2}\mathrm{en}$ , where $1\mathrm{em}=2\mathrm{en}$ . Try out the Unicode version math-unicode.html — and viceversa. You can check out what version this page is in the page title.

The command \raisebox is useful to, surprisingly, raise a little box,

$\raisebox{2mm}{raised}over\raisebox{-2mm}{lowered}\textrm{and back}.$

Like \mbox, it puts its content in a text box. It can also be used just for spacing:
$\raisebox{5mm}{}B^{V}$ .

There are other spacing commands: \hspace: $a\hspace{4mm}b$ , protected space: $a\ b$ , and (at “block level”) \vspace: $a\vspace{1cm}b$ .

There should be 1 cm of vertical space above this paragraph.

2.5 Fonts

By default, letters denote variables and are taken from the \mathnormal font, which is italic, $\alpha x+\alpha y=\alpha(x+y)$ , with the exception of upright capital Greek letters, $G\ne\Gamma$ .

Function names should be upright: $\sin(2\pi),\log(x),\tan\delta$ .

Mathematical fonts used in equations include $\mathrm{Roman}$ (\mathrm), $\mathsf{Sans\: Serif}$ (\mathsf), $\mathtt{Typewriter}$ (\mathtt), $\mathbf{Bold}$ (\mathbf), $\mathscr{SCRIPT}$ (\mathscr), $\mathcal{CALLIGRAPHIC}$ (\mathcal), $\mathbb{BLACKBOARD\: BOLD}$ (\mathbb), and $\mathfrak{Fraktur}$ (\mathfrak). For the latter, some single characters are translated to their Unicode equivalents: $\mathscr{F}$ , $\mathbb{F}$ , $\mathfrak{F}$ .

Regular text in a formula can be achieved via text font commands like \textrm: $5\:\textrm{to}\:10$ , via boxes like \mbox (prevents line breaks): $6\mbox{ is more than }5$ , or the AMSmath \text macro (scales like math symbols) $\text{base}_{\text{sub}}^{\text{super}}$ . The content of an mbox is processed in LaTeX text mode. This allows text font commands, e.g. a switch to sans-serif-bold-italic, or the phonetic alphabet: $\mbox{\textbf{\textsf{\textbf{\textit{sfbfit}}}}, \textipa{tipa}}$ .

Units should be written upright, either with \mathrm or with macros from the units package, e.g. as simple unit, $\unit{km}$ , with magnitude, $\unit[57]{km}$ , with fractional unit, $\unitfrac[200]{km}{h}$ , or with a fraction before the units, $\unit[\nicefrac{3}{2}]{km}$ , $\unit[\frac{7}{16}]{s}$ .

3 Numeration

Equations can be numbered, like (↓)

(1) $\begin{equation} y=x\label{eq:first}\end{equation}$

And also like (↓).

(2) $\begin{equation} x=3\label{eq:second}\end{equation}$

Some equations can be numbered even if they don’t have a label.

(3) $\begin{equation} x=2y\end{equation}$

Notice that equation (↓) comes after (↓).

4 Simple Structures

Let’s now see a few of the simpler structures that eLyXer can output.

4.1 Fractions

A simple fraction:

$\frac{1}{2}.$

Inlined: $\frac{2}{3}.$

A big recursive fraction:

$\frac{1}{\left(1+\left(\frac{1}{1+\left(\frac{1}{1+2x}\lyxlock\right)}\lyxlock\right)\right)}\lyxlock$

A nice fraction: $\nicefrac{5}{6}$ . A non-diminishing fraction containing alignments:

$\cfrac{1}{1+\left(\cfrac[l]{1}{1+x}\times\cfrac[r]{1}{1+x}\right)}.$

A similar concept is a binomial coefficient: $\binom{A+1}{B}.$ It can be prettily presented:

$\dbinom{A}{B+1}.$

A symbol can be stacked over another using \stackrel: $x\stackrel{R}{\rightarrow}y$ . Anything can be stacked:

$d\stackrel{x>3}{\lim}x,\quad\stackrel{\mathrm{head}}{\mathrm{heels}}.$

4.2 Limits

$\lim_{x\rightarrow\infty}f(x)$ should appear as $x\rightarrow\infty$ in italics, and «lim» in plain style. In display mode, a limit must appear below the main symbol:

$\lim_{x\rightarrow\infty}\lyxlock f(x).$

Limits are also used in sums and integrals:

$\sum_{i=1}^{\infty}x,\;\int_{0}^{\infty}f(x)\,\mathrm{d}x$

where the sum’s limits should appear below ( $i=1$ ) and above ( $\infty$ ) the $\sum$ . The placement of the integral limits depends on the document class: LaTeX standard classes place them right to the $\int$ . Limits are shown to the right in inline formulae: $\sum_{i=1}^{\infty}x$ and $\intop_{i=1}^{\infty}x.$

The placing of limits can be configured with the \limits and \nolimits macros:

$\lim\nolimits _{x\rightarrow\infty}\lyxlock f(x),\;\sum\nolimits _{i=1}^{\infty}x,\;\int\limits _{0}^{\infty}f(x)\,\mathrm{d}x$

4.3 Roots

A square root: $\sqrt{3}.$ A more complex root in a fraction:

$\frac{1}{\left(1+\sqrt{2}\left(\frac{1}{1+\sqrt{2}}\lyxlock\right)+\sqrt{\frac{1}{2}}\right)}\lyxlock.$

eLyXer can also do higher-order roots: $\sqrt[3]{x+y}$ . A devilish case mixing everything we have seen so far:

$\frac{\sqrt[\nicefrac{7}{8}]{\frac{8}{4}x}+\sum_{i=1}^{\infty}x}{\sqrt[s+5]{\frac{(78x+45y)\times\sqrt{\Omega}}{\sin(x+1)}+\unit[38]{km}}}\lyxlock.$

5 Complex Structures

In this section we will explore arrays and related constructs.

5.1 Arrays

An inline array $\left[\begin{array}{cc} a & b\\ c & d\end{array}\right]$ is always shown in the same line. In display mode, the array is shown on its own line:

$\left[\begin{array}{lc} 12 & 2\\ 3 & 4\times y^{x}\end{array}\right]$

Apart from that the appearance should be the same.

5.2 Brackets

Arrays are separated by variable-size brackets: $\left(\begin{array}{cc} a & b\\ c & d\end{array}\right)$ $\left[\begin{array}{cc} a & b\\ c & d\end{array}\right]$ $\left\{ \begin{array}{cc} a & b\\ c & d\end{array}\right\}$ $\left\langle \begin{array}{cc} a & b\\ c & d\end{array}\right\rangle$ $\left|\begin{array}{cc} a & b\\ c & d\end{array}\right|$ which might also differ on right and left $\left(\begin{array}{cc} a & b\\ c & d\end{array}\right)$ or use the empty opening $\left\{ \begin{array}{cc} a & b\\ c & d\end{array}\right.$ or closing: $\left.\begin{array}{cc} a & b\\ c & d\end{array}\right|$ . There are also fixed-size big brackets, e.g. $\bigl\langle f\bigr\rangle$ .

5.3 Cases

Used to switch between several values.

$y=\begin{cases} x & i=0,\\ x+1 & i<3\end{cases}$

Cases may have more than two rows:

$f(x)=\begin{cases} 0 & x<0,\\ \infty & x=0\\ 0 & x>0\end{cases}$

5.4 Braces

Values can be underbraced or overbraced.

$\underbrace{a-b}=\overbrace{b+c+d+e}$ .

6 Macros

Now it’s time for user-defined commands (sometimes called “macros”).

Definitions can be added as macros. Then they can be used in formulae: $\stupidroot 12$ . They can accept default parameters. Again, useful in formulae: $\defaultroot$ .

Other definitions from the preamble can be used: $\preambleroot{3}{4}$ .

Definitions on the fly are also possible: $\newcommand{\ontheflyroot}[2]{\sqrt[#1]{#2}}\ontheflyroot{7}{8}$ , and used with different values: $\ontheflyroot{a}{b}$ .