# 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.
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: φ, π, Ξ. eLyXer offers a complete set in both upper case: AΩ and lower case: α ω. Also the AMS italicized upper case: Γ Ω.

## 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: 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: (4)/(18)em for medium mathematical spaces versus (1)/(2)en, where 1em= 2en. 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.
raised over lowered and back.
It can also be used just for spacing.
BV.
There are other spacing commands: `\hspace`: " ", `\vspace`: " ", protected space: a b.

## 2.5Fonts

Many fonts are used in equations.
Regular text is shown italicized. Variable: length, α, Speed.
Some font styles can be used in equations. Roman: 1mathrm. Sans serif: 2mathsf. Typewriter: 3`mathtt`. Bold: 4mathbf.
Regular text. Normal text: 5textfm. Literal text: 6mbox text. Phonetic alphabet: 7 abcde.
Units can be shown with or without a magnitude. Withouth: km. With: 57km. With fractional units: 200km⁄h. With a fraction before the units: 3⁄2 km, (7)/(16)s.
Some special fonts are supported: mathscr, MATHCAL, MATHBB, mathfrak. For those, some single characters are translated to their Unicode equivalents: ℱ, 𝔽, 𝔉.

# 3Numeration

Equations can be numbered, like 1↓.
(1) y=x
And also like 2↓.
(2) x= 3
Some equations can be numbered even if they don’t have a label.
(3) x= 2y
Notice that 2↑ comes after 1↑.

# 4Simple Structures

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

## 4.1Fractions

A simple fraction:
(1)/(2).
Inlined: (2)/(3).
A big recursive fraction:
(1)/((1 +((1)/(1 +((1)/(1 + 2x))))))
A nice fraction: 5⁄6. A non-diminishing fraction containing alignments:
(1)/(1 +((1)/(1 +x)×(1)/(1 +x))).
A similar concept is a binomial coefficient: (A+ 1 B). It can be prettily presented:
⎛ A ⎞ ⎜ ⎟ ⎝ B+ 1 ⎠ .
A symbol can be stacked over another using `\stackrel`: x R→y. Anything can be stacked: d x> 3 lim x, head heels.

## 4.2Limits

A limit must appear below the main symbol:
limx→ ∞f(x),
which should appear as x→ ∞ 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: limx→ ∞f(x).
Limits are also used in sums:
∞⎲⎳i= 1 x,
where the sum’s limits should appear below (i= 1) and above (∞) the ∑. Again, in HTML the limits are shown to the right. Inlined: ∑∞i= 1 x. Also in integrals: ∫∞i= 1 x.

## 4.3Roots

A square root: √(3). A more complex root in a fraction:
(1)/((1 +√(2)((1)/(1 +√(2)))+√((1)/(2)))).
eLyXer can also do higher-order roots: 3√(x+y). A devilish case mixing everything we have seen so far:
(7⁄8√((8)/(4)x)+∞⎲⎳i= 1 x)/(s+ 5√(((78x+ 45y) ×√(Ω))/(sin(x+ 1))+ 38km)).

# 5Complex Structures

In this section we will explore arrays and related constructs.

## 5.1Arrays

An inline array ⎡ a b ⎤ ⎢ ⎥ ⎣ c dio ⎦ : is always shown in the same line.
An independent array is shown on its own line:
⎡ 12 2 ⎤ ⎢ ⎥ ⎣ 3 4 ×yx ⎦
Apart from that the appearance should be the same.

## 5.2Brackets

Arrays are separated by brackets: (a) [b] {c} ⟨d⟩ |e|. There are also big brackets: ⟨f⟩.

## 5.3Cases

Used to switch between several values.
y= ⎧ x i= 0, ⎨ ⎩ x+ 1 i< 3
Cases may have more than two rows:
f(x) = ⎧ 0 x< 0, ⎪ ⎨ ∞ x= 0 ⎪ ⎩ 0 x> 0

## 5.4Braces

Values can be underbraced or overbraced.
a−b=b+c+d+e.

# 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: 1√(2). They can accept default parameters. Again, useful in formulae: 4√(5).
Other definitions from the preamble can be used: 3√(4).
Definitions on the fly are also possible: 7√(8), and used with different values: a√(b).

# 7The End

That’s all folks!