figure elyxer.png eLyXer Math Showcase

Alex Fernández (elyxer@gmail.com)

Table of Contents

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

There are several versions of this page:
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: φ, π, Ξ. eLyXer offers a complete set in both upper case: AΩ and lower case: αω. Also the AMS italicized upper case: ΓΩ.

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: 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 1 em = 2 en. 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.
raisedoverloweredand back.
It can also be used just for spacing.
BV.
There are other spacing commands: \hspace: " ", \vspace: " ", protected space: a b.

2.5 Fonts

Many fonts are used in equations.
Regular text is shown italicized. Variable: length, α, Speed.
Some font styles can be used in equations. Roman: 1 mathrm. Sans serif: 2 mathsf. Typewriter: 3 mathtt. Bold: 4 mathbf.
Regular text. Normal text: 5 textfm. Literal text: 6 mbox text. Phonetic alphabet: 7abcde.
Units can be shown with or without a magnitude. Withouth: km. With: 57 km. With fractional units: 200 kmh. With a fraction before the units: 32 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.

3 Numeration

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↑.

4 Simple Structures

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

4.1 Fractions

A simple fraction:
(1)/(2).
Inlined: (2)/(3).
A big recursive fraction:
(1)/((1 + ((1)/(1 + ((1)/(1 + 2x))))))
A nice fraction: 56. A non-diminishing fraction containing alignments:
(1)/(1 + ((1)/(1 + x) × (1)/(1 + x))).
A similar concept is a binomial coefficient: (A + 1B). It can be prettily presented:
A B + 1 .
A symbol can be stacked over another using \stackrel: xR → y. Anything can be stacked: dx > 3limx, headheels.

4.2 Limits

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 = 1x, 
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 = 1x. Also in integrals: i = 1x.

4.3 Roots

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:
(78((8)/(4)x) + i = 1x)/(s + 5(((78x + 45y) × (Ω))/(sin(x + 1)) + 38 km)).

5 Complex Structures

In this section we will explore arrays and related constructs.

5.1 Arrays

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.

5.2 Brackets

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

5.3 Cases

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 

5.4 Braces

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

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: 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).

7 The End

That’s all folks!