eLyXer Math Showcase
Alex Fernández (elyxer@gmail.com)
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
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.
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: 7 abcde.
Units can be shown with or without a magnitude. Withouth: km. With: 57 km. With fractional units: 200 km⁄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.
3 Numeration
Equations can be numbered, like
1↓.
Some equations can be numbered even if they don’t have a label.
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:
5⁄6. 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.
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 = 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⟩.
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!