# 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: φ, π, Ξ. eLyXer offers a complete set in both upper case: Γ…Ω 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.
Like `\mbox`, it puts its content in a text box. It can also be used just for spacing:
BV.
There are other spacing commands: `\hspace`: a b, protected space: a b, and (at “block level”)`\vspace`: a b.
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, α x+α y=α(x+y), with the exception of upright capital Greek letters, G≠ Γ.
Function names should be upright: sin(2π), log(x), tanδ.
Mathematical fonts used in equations include Roman (`\mathrm`), Sans Serif (`\mathsf`), `Typewriter` (`\mathtt`), Bold (`\mathbf`), SCRIPT (`\mathscr`), CALLIGRAPHIC (`\mathcal`), BLACKBOARD BOLD (`\mathbb`), and Fraktur (`\mathfrak`). For the latter, some single characters are translated to their Unicode equivalents: ℱ, 𝔽, 𝔉.
Regular text in a formula can be achieved via text font commands like `\textrm`: 5to10, via boxes like \mbox (prevents line breaks): 6is more than 5, or the AMSmath `\text` macro (scales like math symbols) base supersub. 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: sfbfit, tipa.
Units should be written upright, either with `\mathrm` or with macros from the `units` package, e.g. as simple unit, km, with magnitude, 57km, with fractional unit, 200km⁄h, or with a fraction before the units, 3⁄2 km, (7)/(16)s.

# 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 equation (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

limx→ ∞f(x) should appear as x→ ∞ in italics, and «lim» in plain style. In display mode, a limit must appear below the main symbol:
limx→ ∞f(x).
Limits are also used in sums and integrals:
∞⎲⎳i= 1 x,∞⌠⌡0 f(x) d x
where the sum’s limits should appear below (i= 1) 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: ∑∞i= 1 x and ∫∞i= 1 x.
The placing of limits can be configured with the `\limits` and `\nolimits` macros:
limx→ ∞f(x),⎲⎳∞i= 1 x,∞⌠⌡0 f(x) d 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 d ⎤⎥⎦ is always shown in the same line. In display mode, the 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 variable-size brackets: ⎛⎜⎝ a b c d ⎞⎟⎠ ⎡⎢⎣ a b c d ⎤⎥⎦ ⎧⎨⎩ a b c d ⎫⎬⎭ ⟨ a b c d ⟩ ||| a b c d |||which might also differ on right and left ⎛⎜⎝ a b c d ⎞⎟⎠ or use the empty opening ⎧⎨⎩ a b c d or closing: a b c d |||. There are also fixed-size big brackets, e.g. ⟨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).