# 1 Introduction

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

## 1.1 Versions

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: , , . eLyXer offers a complete set in both upper case: and lower case: . Also the AMS italicized upper case: .

## 2.2 Math 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: .

## 2.3 Other 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: .

## 2.4 Spacing

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.

## 2.5 Fonts

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, , .

# 3 Numeration

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 ().

# 4 Simple Structures

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

## 4.1 Fractions

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:

## 4.2 Limits

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:

## 4.3 Roots

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:

# 5 Complex Structures

In this section we will explore arrays and related constructs.

## 5.1 Arrays

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.

## 5.2 Brackets

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. .

## 5.3 Cases

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

## 5.4 Braces

Values can be underbraced or overbraced.
.

# 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: . 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: .