#LyX 1.6.7 created this file. For more info see http://www.lyx.org/
\lyxformat 345
\begin_document
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%   eLyXer -- convert LyX source files to HTML output.
%
%   Copyright (C) 2009-2010 Alex Fernández
%
%   This program is free software: you can redistribute it and/or modify
%   it under the terms of the GNU General Public License as published by
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% DO NOT ALTER THIS PREAMBLE!!!
%
% This preamble is designed to ensure that the User's Guide prints
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% parts of the User's Guide may not print out as expected.  If you
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% the documentation team
% email: lyx-docs@lists.lyx.org

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\pdf_title "eLyXer Math Showcase"
\pdf_author "Alex Fernández"
\pdf_subject "The amazing all-time-wonder eLyXer Math Showcase"
\pdf_keywords "LyX"
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\begin_body

\begin_layout Title
\begin_inset Graphics
	filename elyxer.svg
	lyxscale 50

\end_inset

eLyXer Math Showcase
\end_layout

\begin_layout Author
Alex Fernández (elyxer@gmail.com)
\end_layout

\begin_layout Standard
\begin_inset CommandInset toc
LatexCommand tableofcontents

\end_inset


\end_layout

\begin_layout Section
Introduction
\end_layout

\begin_layout Standard
This document is intended as a showcase of the mathematical abilities of
 eLyXer; for more information be sure to visit the 
\begin_inset CommandInset href
LatexCommand href
name "main page"
target "index.html"

\end_inset

.
\end_layout

\begin_layout Subsection
Versions
\end_layout

\begin_layout Standard
There are several versions of this page:
\end_layout

\begin_layout Itemize
A 
\begin_inset CommandInset href
LatexCommand href
name "non-Unicode version"
target "math.html"

\end_inset

 of this page with midspaces.
\end_layout

\begin_layout Itemize
A 
\begin_inset CommandInset href
LatexCommand href
name "Unicode version"
target "math-unicode.html"

\end_inset

 with mathematical spaces (generated with 
\family typewriter
--unicode
\family default
).
\end_layout

\begin_layout Itemize
An 
\begin_inset CommandInset href
LatexCommand href
name "ISO-8859-15 version"
target "math-iso885915.html"

\end_inset

 (generated with 
\family typewriter
--iso885915
\family default
).
\end_layout

\begin_layout Itemize
A 
\begin_inset CommandInset href
LatexCommand href
name "jsMath version"
target "math-jsmath.html"

\end_inset

 that uses 
\begin_inset CommandInset href
LatexCommand href
name "jsMath"
target "http://www.math.union.edu/~dpvc/jsMath/welcome.html"

\end_inset

 (generated with 
\family typewriter
--jsmath
\family default
).
\end_layout

\begin_layout Itemize
A 
\begin_inset CommandInset href
LatexCommand href
name "MathJax version"
target "math-mathjax.html"

\end_inset

 with 
\begin_inset CommandInset href
LatexCommand href
name "MathJax"
target "http://www.mathjax.org/"

\end_inset

 (generated with 
\family typewriter
--mathjax
\family default
).
\end_layout

\begin_layout Standard
All of them are generated from the same 
\family typewriter
.lyx
\family default
 source file; they should help you decide which rendering options suit you
 best.
\end_layout

\begin_layout Section
Typography
\end_layout

\begin_layout Standard
Math formulae use a lot of different symbols and fonts.
\end_layout

\begin_layout Subsection
Greek Symbols
\end_layout

\begin_layout Standard
Greek symbols are very important in equations: 
\begin_inset Formula $\phi$
\end_inset

, 
\begin_inset Formula $\pi$
\end_inset

, 
\begin_inset Formula $\Xi$
\end_inset

.
 eLyXer offers a complete set in both upper case: 
\begin_inset Formula $A\Omega$
\end_inset

 and lower case: 
\begin_inset Formula $\alpha\omega$
\end_inset

.
 Also the AMS italicized upper case: 
\begin_inset Formula $\varGamma\varOmega$
\end_inset

.
\end_layout

\begin_layout Subsection
Math Symbols
\end_layout

\begin_layout Standard
eLyXer supports the whole set of math symbols in 
\begin_inset CommandInset href
LatexCommand href
name "John D. Cook's list"
target "http://www.johndcook.com/math_symbols.html"

\end_inset

: 
\begin_inset Formula $\exists\partial\nabla\geq$
\end_inset

.
 It can also render a few more: 
\begin_inset Formula $\propto\times$
\end_inset

.
 You also get all symbols from 
\begin_inset CommandInset href
LatexCommand href
name "Markus Kuhn's list"
target "http://www.cl.cam.ac.uk/~mgk25/ucs/examples/TeX.txt"

\end_inset

: 
\begin_inset Formula $\bigodot\amalg$
\end_inset

.
\end_layout

\begin_layout Subsection
Other Symbols
\end_layout

\begin_layout Standard
There are other symbols like arrows: 
\begin_inset Formula $\leftarrow\rightarrow$
\end_inset

, or geometrical shapes: 
\begin_inset Formula $\circ$
\end_inset

, 
\begin_inset Formula $\square$
\end_inset

.
 eLyXer offers limited support for them.
 You might also want to use financial symbols in formulae: 
\begin_inset Formula $\yen\euro\$$
\end_inset

.
\end_layout

\begin_layout Subsection
Spacing
\end_layout

\begin_layout Standard
Equations look good when items are properly separated.
 The main separation is the Medium Mathematical Space: 
\begin_inset Formula $x=3$
\end_inset

.
 
\begin_inset Note Greyedout
status open

\begin_layout Plain Layout
Note: if you are viewing the non-Unicode version 
\begin_inset Flex URL
status collapsed

\begin_layout Plain Layout

math.html
\end_layout

\end_inset

 of this page then you are in fact seeing midspaces, which are very similar
 but not exactly the same: 
\begin_inset Formula $\frac{4}{18}\mathrm{em}$
\end_inset

 for medium mathematical spaces versus 
\begin_inset Formula $\frac{1}{2}\mathrm{en}$
\end_inset

, where 
\begin_inset Formula $1\mathrm{em}=2\mathrm{en}$
\end_inset

.
 Try out the Unicode version 
\begin_inset Flex URL
status collapsed

\begin_layout Plain Layout

math-unicode.html
\end_layout

\end_inset

 -- and viceversa.
 You can check out what version this page is in the page title.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
The command 
\family typewriter

\backslash
raisebox
\family default
 is useful to, surprisingly, raise a little box.
\end_layout

\begin_layout Standard
\begin_inset Formula $\raisebox{2mm}{raised}over\raisebox{-2mm}{lowered}\textrm{and back}.$
\end_inset


\end_layout

\begin_layout Standard
It can also be used just for spacing.
\end_layout

\begin_layout Standard
\begin_inset Formula $\raisebox{5mm}{}B^{V}$
\end_inset

.
\end_layout

\begin_layout Standard
There are other spacing commands: 
\family typewriter

\backslash
hspace
\family default
: 
\begin_inset Formula $"\hspace{4mm}"$
\end_inset

, 
\family typewriter

\backslash
vspace
\family default
: 
\begin_inset Formula $"\vspace{1cm}"$
\end_inset

, protected space: 
\begin_inset Formula $a\ b$
\end_inset

.
\end_layout

\begin_layout Subsection
Fonts
\end_layout

\begin_layout Standard
Many fonts are used in equations.
\end_layout

\begin_layout Standard
Regular text is shown italicized.
 Variable: 
\begin_inset Formula $length$
\end_inset

, 
\begin_inset Formula $\alpha$
\end_inset

, 
\begin_inset Formula $Speed$
\end_inset

.
\end_layout

\begin_layout Standard
Some font styles can be used in equations.
 Roman: 
\begin_inset Formula $1\mathrm{mathrm}$
\end_inset

.
 Sans serif: 
\begin_inset Formula $2\mathsf{mathsf}$
\end_inset

.
 Typewriter: 
\begin_inset Formula $3\mathtt{mathtt}$
\end_inset

.
 Bold: 
\begin_inset Formula $4\mathbf{mathbf}$
\end_inset

.
\end_layout

\begin_layout Standard
Regular text.
 Normal text: 
\begin_inset Formula $5\textrm{textfm}$
\end_inset

.
 Literal text: 
\begin_inset Formula $6\mbox{mbox text}$
\end_inset

.
 Phonetic alphabet: 
\begin_inset Formula $7\text{\textipa{abcde}}$
\end_inset

.
\end_layout

\begin_layout Standard
Units can be shown with or without a magnitude.
 Withouth: 
\begin_inset Formula $\unit{km}$
\end_inset

.
 With: 
\begin_inset Formula $\unit[57]{km}$
\end_inset

.
 With fractional units: 
\begin_inset Formula $\unitfrac[200]{km}{h}$
\end_inset

.
 With a fraction before the units: 
\begin_inset Formula $\unit[\nicefrac{3}{2}]{km}$
\end_inset

, 
\begin_inset Formula $\unit[\frac{7}{16}]{s}$
\end_inset

.
\end_layout

\begin_layout Standard
Some special fonts are supported: 
\begin_inset Formula $\mathscr{mathscr}$
\end_inset

, 
\begin_inset Formula $\mathcal{MATHCAL}$
\end_inset

, 
\begin_inset Formula $\mathbb{MATHBB}$
\end_inset

, 
\begin_inset Formula $\mathfrak{mathfrak}$
\end_inset

.
 For those, some single characters are translated to their Unicode equivalents:
 
\begin_inset Formula $\mathscr{F}$
\end_inset

, 
\begin_inset Formula $\mathbb{F}$
\end_inset

, 
\begin_inset Formula $\mathfrak{F}$
\end_inset

.
\end_layout

\begin_layout Section
Numeration
\end_layout

\begin_layout Standard
Equations can be numbered, like 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:first"

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Formula \begin{equation}
y=x\label{eq:first}\end{equation}

\end_inset


\end_layout

\begin_layout Standard
And also like 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:second"

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Formula \begin{equation}
x=3\label{eq:second}\end{equation}

\end_inset


\end_layout

\begin_layout Standard
Some equations can be numbered even if they don't have a label.
\end_layout

\begin_layout Standard
\begin_inset Formula \begin{equation}
x=2y\end{equation}

\end_inset


\end_layout

\begin_layout Standard
Notice that 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:second"

\end_inset

 comes after 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:first"

\end_inset

.
\end_layout

\begin_layout Section
Simple Structures
\end_layout

\begin_layout Standard
Let's now see a few of the simpler structures that eLyXer can output.
\end_layout

\begin_layout Subsection
Fractions
\end_layout

\begin_layout Standard
A simple fraction: 
\begin_inset Formula \[
\frac{1}{2}.\]

\end_inset

Inlined: 
\begin_inset Formula $\frac{2}{3}.$
\end_inset


\end_layout

\begin_layout Standard
A big recursive fraction: 
\begin_inset Formula \[
\frac{1}{\left(1+\left(\frac{1}{1+\left(\frac{1}{1+2x}\lyxlock\right)}\lyxlock\right)\right)}\lyxlock\]

\end_inset


\end_layout

\begin_layout Standard
A nice fraction: 
\begin_inset Formula $\nicefrac{5}{6}$
\end_inset

.
 A non-diminishing fraction containing alignments:
\begin_inset Formula \[
\cfrac{1}{1+\left(\cfrac[l]{1}{1+x}\times\cfrac[r]{1}{1+x}\right)}.\]

\end_inset


\end_layout

\begin_layout Standard
A similar concept is a binomial coefficient: 
\begin_inset Formula $\binom{A+1}{B}.$
\end_inset

 It can be prettily presented: 
\begin_inset Formula \[
\dbinom{A}{B+1}.\]

\end_inset


\end_layout

\begin_layout Standard
A symbol can be stacked over another using 
\family typewriter

\backslash
stackrel
\family default
: 
\begin_inset Formula $x\stackrel{R}{\rightarrow}y$
\end_inset

.
 Anything can be stacked: 
\begin_inset Formula $d\stackrel{x>3}{\lim}x$
\end_inset

, 
\begin_inset Formula $\stackrel{head}{heels}$
\end_inset

.
\end_layout

\begin_layout Subsection
Limits
\end_layout

\begin_layout Standard
A limit must appear below the main symbol: 
\begin_inset Formula \[
\lim_{x\rightarrow\infty}\lyxlock f(x),\]

\end_inset

which should appear as 
\begin_inset Formula $x\rightarrow\infty$
\end_inset

 in italics, and 
\begin_inset Quotes fld
\end_inset

lim
\begin_inset Quotes frd
\end_inset

 in plain style.
 Note that in HTML the limit does not actually appear below the 
\begin_inset Quotes fld
\end_inset

lim
\begin_inset Quotes frd
\end_inset

 but to the right.
 Inlined: 
\begin_inset Formula $\lim_{x\rightarrow\infty}\lyxlock f(x)$
\end_inset

.
\end_layout

\begin_layout Standard
Limits are also used in sums: 
\begin_inset Formula \[
\sum_{i=1}^{\infty}x,\]

\end_inset

where the sum's limits should appear below (
\begin_inset Formula $i=1$
\end_inset

) and above (
\begin_inset Formula $\infty$
\end_inset

) the 
\begin_inset Formula $\sum$
\end_inset

.
 Again, in HTML the limits are shown to the right.
 Inlined: 
\begin_inset Formula $\sum_{i=1}^{\infty}x.$
\end_inset

 Also in integrals: 
\begin_inset Formula $\intop_{i=1}^{\infty}x.$
\end_inset


\end_layout

\begin_layout Subsection
Roots
\end_layout

\begin_layout Standard
A square root: 
\begin_inset Formula $\sqrt{3}.$
\end_inset

 A more complex root in a fraction:
\begin_inset Formula \[
\frac{1}{\left(1+\sqrt{2}\left(\frac{1}{1+\sqrt{2}}\lyxlock\right)+\sqrt{\frac{1}{2}}\right)}\lyxlock.\]

\end_inset


\end_layout

\begin_layout Standard
eLyXer can also do higher-order roots: 
\begin_inset Formula $\sqrt[3]{x+y}$
\end_inset

.
 A devilish case mixing everything we have seen so far:
\begin_inset Formula \[
\frac{\sqrt[\nicefrac{7}{8}]{\frac{8}{4}x}+\sum_{i=1}^{\infty}x}{\sqrt[s+5]{\frac{(78x+45y)\times\sqrt{\Omega}}{\sin(x+1)}+\unit[38]{km}}}\lyxlock.\]

\end_inset


\end_layout

\begin_layout Section
Complex Structures
\end_layout

\begin_layout Standard
In this section we will explore arrays and related constructs.
\end_layout

\begin_layout Subsection
Arrays
\end_layout

\begin_layout Standard
An inline array 
\begin_inset Formula $\left[\begin{array}{cc}
a & b\\
c & dio\end{array}\right]$
\end_inset

: is always shown in the same line.
\end_layout

\begin_layout Standard
An independent array is shown on its own line: 
\begin_inset Formula \[
\left[\begin{array}{lc}
12 & 2\\
3 & 4\times y^{x}\end{array}\right]\]

\end_inset

Apart from that the appearance should be the same.
\end_layout

\begin_layout Subsection
Brackets
\end_layout

\begin_layout Standard
Arrays are separated by brackets: 
\begin_inset Formula $\left(a\right)$
\end_inset

 
\begin_inset Formula $\left[b\right]$
\end_inset

 
\begin_inset Formula $\left\{ c\right\} $
\end_inset

 
\begin_inset Formula $\left\langle d\right\rangle $
\end_inset

 
\begin_inset Formula $\left|e\right|$
\end_inset

.
 There are also big brackets: 
\begin_inset Formula $\bigl\langle f\bigr\rangle$
\end_inset

.
\end_layout

\begin_layout Subsection
Cases
\end_layout

\begin_layout Standard
Used to switch between several values.
\end_layout

\begin_layout Standard
\begin_inset Formula $y=\begin{cases}
x & i=0,\\
x+1 & i<3\end{cases}$
\end_inset


\end_layout

\begin_layout Subsection
Braces
\end_layout

\begin_layout Standard
Values can be underbraced or overbraced.
\end_layout

\begin_layout Standard
\begin_inset Formula $\underbrace{a-b}=\overbrace{b+c+d+e}$
\end_inset

.
\end_layout

\begin_layout Section
Macros
\end_layout

\begin_layout Standard
Now it's time for user-defined commands (sometimes called 
\begin_inset Quotes eld
\end_inset

macros
\begin_inset Quotes erd
\end_inset

).
\end_layout

\begin_layout Standard
Definitions can be added as macros
\begin_inset FormulaMacro
\newcommand{\stupidroot}[2]{\sqrt[#1]{#2}}
{\sqrt[#1]{#2}}
\end_inset

.
 Then they can be used in formulae: 
\begin_inset Formula $\stupidroot 12$
\end_inset

.
 They can accept default parameters
\begin_inset FormulaMacro
\newcommand{\defaultroot}[2][4][5]{\sqrt[#1]{#2}}
{#1\sqrt{#2}}
\end_inset

.
 Again, useful in formulae: 
\begin_inset Formula $\defaultroot$
\end_inset

.
\end_layout

\begin_layout Standard
Other definitions from the preamble can be used: 
\begin_inset Formula $\preambleroot{3}{4}$
\end_inset

.
\end_layout

\begin_layout Standard
Definitions on the fly are also possible: 
\begin_inset Formula $\newcommand{\ontheflyroot}[2]{\sqrt[#1]{#2}}\ontheflyroot{7}{8}$
\end_inset

, and used with different values: 
\begin_inset Formula $\ontheflyroot{a}{b}$
\end_inset

.
\end_layout

\begin_layout Section
The End
\end_layout

\begin_layout Standard
That's all folks!
\end_layout

\end_body
\end_document
