# eLyXer Math Showcase

## Alex Fernández (elyxer@gmail.com)

Table of Contents

# 1Introduction

This document is intended as a showcase of the mathematical abilities of eLyXer; for more information be sure to visit the main page.

## 1.1Versions

There are several versions of this page:

- 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`).
- A jsMath version that uses jsMath (generated with `--jsmath`).
- A MathJax version with MathJax (generated with `--mathjax`).

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

# 2Typography

Math formulae use a lot of different symbols and fonts.

## 2.1Greek Symbols

Greek symbols are very important in equations:
,
,
. eLyXer offers a complete set in both upper case:
and lower case:
. Also the AMS italicized upper case:
.

## 2.2Math Symbols

eLyXer supports the whole set of math symbols in John D. Cook's list:
. It can also render a few more:
. You also get all symbols from Markus Kuhn's list:
.

## 2.3Other Symbols

There are other symbols like arrows:
, or geometrical shapes:
,
. eLyXer offers limited support for them. You might also want to use financial symbols in formulae:
.

## 2.4Spacing

Equations look good when items are properly separated. The main separation is the Medium Mathematical Space:
. 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:
for medium mathematical spaces versus
, where
. 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.
It can also be used just for spacing.
.
There are other spacing commands: `\hspace`:
, `\vspace`:
, protected space:
.

## 2.5Fonts

Many fonts are used in equations.
Regular text is shown italicized. Variable:
,
,
.
Some font styles can be used in equations. Roman:
. Sans serif:
. Typewriter:
. Bold:
.
Regular text. Normal text:
. Literal text:
. Phonetic alphabet:
.
Units can be shown with or without a magnitude. Withouth:
. With:
. With fractional units:
. With a fraction before the units:
,
.
Some special fonts are supported:
,
,
,
. For those, some single characters are translated to their Unicode equivalents:
,
,
.

# 3Numeration

Equations can be numbered, like ↓.
And also like ↓.
Some equations can be numbered even if they don’t have a label.
Notice that ↓ comes after ↓.

# 4Simple Structures

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

## 4.1Fractions

A simple fraction:
Inlined:
A big recursive fraction:
A nice fraction:
. A non-diminishing fraction containing alignments:
A similar concept is a binomial coefficient:
It can be prettily presented:
A symbol can be stacked over another using `\stackrel`:
. Anything can be stacked:
,
.

## 4.2Limits

A limit must appear below the main symbol:
which should appear as
in italics, and «lim» in plain style. Note that in HTML the limit does not actually appear below the «lim» but to the right. Inlined:
.
Limits are also used in sums:
where the sum’s limits should appear below (
) and above (
) the
. Again, in HTML the limits are shown to the right. Inlined:
Also in integrals:

## 4.3Roots

A square root:
A more complex root in a fraction:
eLyXer can also do higher-order roots:
. A devilish case mixing everything we have seen so far:

# 5Complex Structures

In this section we will explore arrays and related constructs.

## 5.1Arrays

An inline array
: is always shown in the same line.
An independent array is shown on its own line:
Apart from that the appearance should be the same.

## 5.2Brackets

Arrays are separated by brackets:
. There are also big brackets:
.

## 5.3Cases

Used to switch between several values.

## 5.4Braces

Values can be underbraced or overbraced.
.

# 6Macros

Now it’s time for user-defined commands (sometimes called “macros”).
Definitions can be added as macros. Then they can be used in formulae:
. They can accept default parameters. Again, useful in formulae:
.
Other definitions from the preamble can be used:
.
Definitions on the fly are also possible:
, and used with different values:
.

# 7The End

That’s all folks!