# 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`).
- 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.

# 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,
Like `\mbox`, it puts its content in a text box. It can also be used just for spacing:
.
There are other spacing commands: `\hspace`:
, protected space:
, and (at “block level”)`\vspace`:
.
There should be 1 cm of vertical space above this paragraph.

## 2.5Fonts

By default, letters denote variables and are taken from the `\mathnormal` font, which is italic,
, with the exception of upright capital Greek letters,
.
Function names should be upright:
.
Mathematical fonts used in equations include
(`\mathrm`),
(`\mathsf`),
(`\mathtt`),
(`\mathbf`),
(`\mathscr`),
(`\mathcal`),
(`\mathbb`), and
(`\mathfrak`). For the latter, some single characters are translated to their Unicode equivalents:
,
,
.
Regular text in a formula can be achieved via text font commands like `\textrm`:
, via boxes like \mbox (prevents line breaks):
, or the AMSmath `\text` macro (scales like math symbols)
. 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:
.
Units should be written upright, either with `\mathrm` or with macros from the `units` package, e.g. as simple unit,
, with magnitude,
, with fractional unit,
, or with a fraction before the units,
,
.

# 3Numeration

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

should appear as
in italics, and «lim» in plain style. In display mode, a limit must appear below the main symbol:
Limits are also used in sums and integrals:
where the sum’s limits should appear below (
) and above (
) the
. The placement of the integral limits depends on the document class: LaTeX standard classes place them right to the
. Limits are shown to the right in inline formulae:
and
The placing of limits can be configured with the `\limits` and `\nolimits` macros:

## 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. In display mode, the array is shown on its own line:
Apart from that the appearance should be the same.

## 5.2Brackets

Arrays are separated by variable-size brackets:
which might also differ on right and left
or use the empty opening
or closing:
. There are also fixed-size big brackets, e.g.
.

## 5.3Cases

Used to switch between several values.
Cases may have more than two rows:

## 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:
.