#LyX 1.6.7 created this file. For more info see http://www.lyx.org/
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%   Copyright (C) 2009-2010 Alex Fernández
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% test macro with a lot of spaces (bug #31243)
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\graphics default
\paperfontsize 12
\spacing single
\use_hyperref true
\pdf_title "Math Test"
\pdf_author "Alex Fernández"
\pdf_subject "Taken from Guía de Usuario de Lyx, Ignacio García"
\pdf_keywords "LyX"
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\author "" 
\author "" 
\end_header

\begin_body

\begin_layout Title
Math Test
\end_layout

\begin_layout Section
Limits
\end_layout

\begin_layout Standard
A limit: 
\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.
 Inlined: 
\begin_inset Formula $\lim_{x\rightarrow\infty}\lyxlock f(x)$
\end_inset

.
\end_layout

\begin_layout Standard
And why not, a sum: 
\begin_inset Formula \[
\sum_{i=1}^{\infty}a_{i},\]

\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

 but to the right.
 Inlined: 
\begin_inset Formula $\sum_{i=1}^{\infty}a_{i}.$
\end_inset

 Integral: 
\begin_inset Formula $\intop_{x=a}^{\infty}x\,\text{d}x.$
\end_inset

 Display mode:
\begin_inset Formula \[
\intop_{x=a}^{\infty}x\,\text{d}x.\]

\end_inset


\end_layout

\begin_layout Standard
We can also integrate without limits: 
\begin_inset Formula $\int A\,\text{d}x$
\end_inset

.
\end_layout

\begin_layout Standard
A sum inside another element (red color):
\end_layout

\begin_layout Standard
\begin_inset Formula \[
\textcolor{red}{\sum_{i=1}^{\infty}a_{i}}.\]

\end_inset


\end_layout

\begin_layout Standard
The placing of limits can be cofigured with the 
\family typewriter

\backslash
limits
\family default
 and 
\family typewriter

\backslash
nolimits
\family default
 macros: 
\begin_inset Formula \[
\lim\nolimits _{x\rightarrow\infty}\lyxlock f(x),\;\sum\nolimits _{i=1}^{\infty}x,\;\int\limits _{0}^{\infty}f(x)\,\mathrm{d}x\]

\end_inset


\end_layout

\begin_layout Subsection
Super- and Subscript
\end_layout

\begin_layout Standard
When any element has both super- and subscript, they should appear like
 inlined limits, one above the other: 
\begin_inset Formula $a_{4}^{3}$
\end_inset

.
 Also before an element: 
\begin_inset Formula $_{2}^{3}\text{He}$
\end_inset

.
 In display mode:
\end_layout

\begin_layout Standard
\begin_inset Formula \[
\sum_{i,j}a_{j}^{i}+\sum_{i,j}a_{i}^{j}=\sum_{i}a_{i}^{i},\]

\end_inset


\begin_inset Formula \[
_{1}^{2}\text{H}+{}_{1}^{2}\text{H}\rightarrow{}_{2}^{3}\text{He}+{}_{0}^{1}\text{n}.\]

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

\end_inset

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

\end_inset

.
\end_layout

\begin_layout Standard
Some equations can also 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
Other equations that contain * should not numbered, but perhaps aligned:
\end_layout

\begin_layout Standard
\begin_inset Formula \begin{align*}
left &  & right\end{align*}

\end_inset


\end_layout

\begin_layout Standard
Some environments allow for multiple labels: 
\begin_inset Formula \begin{eqnarray}
a & = & b\times c\label{eq:third}\\
c\times d\times e & = & i.\label{eq:fourth}\end{eqnarray}

\end_inset


\end_layout

\begin_layout Standard
Now a random environment:
\begin_inset Formula $\begin{gathered}x\end{gathered}
y$
\end_inset

.
\end_layout

\begin_layout Section
Brackets
\end_layout

\begin_layout Standard
An array: 
\begin_inset Formula \[
\left[\begin{array}{lc}
12 & 2\\
3 & 4\times y^{x}\end{array}\right]\]

\end_inset

And an inline array 
\begin_inset Formula $\left[\begin{array}[t]{cc}
a & b\\
c & dio\end{array}\right]$
\end_inset

.
\end_layout

\begin_layout Standard
Arrays are separated by variable-size brackets: 
\begin_inset Formula $\left(\begin{array}{cc}
a & b\\
c & d\end{array}\right)$
\end_inset

 
\begin_inset Formula $\left[\begin{array}{cc}
a & b\\
c & d\end{array}\right]$
\end_inset

 
\begin_inset Formula $\left\{ \begin{array}{cc}
a & b\\
c & d\end{array}\right\} $
\end_inset

 
\begin_inset Formula $\left\langle \begin{array}{cc}
a & b\\
c & d\end{array}\right\rangle $
\end_inset

 
\begin_inset Formula $\left|\begin{array}{cc}
a & b\\
c & d\end{array}\right|$
\end_inset

which might also differ on right and left 
\begin_inset Formula $\left(\begin{array}{cc}
a & b\\
c & d\end{array}\right)$
\end_inset

 or use the empty opening 
\begin_inset Formula $\left\{ \begin{array}{cc}
a & b\\
c & d\end{array}\right.$
\end_inset

 or closing: 
\begin_inset Formula $\left.\begin{array}{cc}
a & b\\
c & d\end{array}\right|$
\end_inset

.
 There are also fixed-size big 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

 
\begin_inset Formula $\bigl\langle f\bigr\rangle$
\end_inset

.
\end_layout

\begin_layout Standard
Aligned brackets can be present: 
\begin_inset Formula $\left(toText\right)$
\end_inset

.
 One of them may be omitted: 
\begin_inset Formula $\left.toText\right)$
\end_inset

.
\end_layout

\begin_layout Standard
Aligned brackets can be applied to complex items:
\begin_inset Formula \[
s\times\left(1+\left(\begin{array}{cc}
a_{11} & a_{21}\\
a_{12} & a_{22}\end{array}\right)\times\left(\begin{array}{cc}
1 & -1\\
-1 & -1\end{array}\right)+\left\Vert \begin{array}{ccc}
1 & -1 & 0\\
-1 & 1 & 0\\
0 & 0 & r\end{array}\right\Vert \right).\]

\end_inset


\end_layout

\begin_layout Standard
Math brackets should not be mistaken for TeX brackets: 
\begin_inset Formula $\frac{\mathcal{F}\left\{ s(x)\right\} }{2}$
\end_inset

.
\end_layout

\begin_layout Section
Fraction
\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

.
\end_layout

\begin_layout Standard
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 $\stackrel{head}{heels}$
\end_inset

.
\end_layout

\begin_layout Section
Roots
\end_layout

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

 A root in a fraction: 
\begin_inset Formula $\sqrt{\frac{(78x+45y)\times\sqrt{Height}}{\sin(x+1)}+5}.$
\end_inset


\end_layout

\begin_layout Standard
A more complex square 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
Higher order roots: 
\begin_inset Formula $\sqrt[3]{x+y}$
\end_inset

, 
\begin_inset Formula $\sqrt[x+1]{Weight}$
\end_inset

.
 In a fraction:
\begin_inset Formula \[
\frac{\sqrt[\nicefrac{7}{8}]{\frac{8}{4}x}}{\sqrt[s+5]{\frac{(78x+45y)\times\sqrt{Height}}{\sin(x+1)}+5}}\lyxlock.\]

\end_inset


\end_layout

\begin_layout Section
Decorations
\end_layout

\begin_layout Subsection
Cases
\end_layout

\begin_layout Standard
Used to switch 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 Standard
Cases may have more than two rows:
\end_layout

\begin_layout Standard
\begin_inset Formula \[
f(x)=\begin{cases}
0 & x<0,\\
\infty & x=0,\\
0 & x>0\end{cases}\]

\end_inset


\end_layout

\begin_layout Subsection
Braces
\end_layout

\begin_layout Standard
Values can be underbraced or overbraced.
\begin_inset Formula \[
\underbrace{a-b}=\overbrace{c+d+e}+f.\]

\end_inset


\end_layout

\begin_layout Standard
Underbraces and overbraces can contain text.
\begin_inset Formula \[
\overbrace{a-b}^{over}=\underbrace{c+\overbrace{d+e}^{over}+f}_{under}+g.\]

\end_inset

They can also be inlined: 
\begin_inset Formula $\overbrace{a+b}^{over}$
\end_inset

.
\end_layout

\begin_layout Section
Spacing
\end_layout

\begin_layout Standard
The command 
\family typewriter

\backslash
raisebox
\family default
 is useful to, surprisingly, raise a little box, 
\begin_inset Formula \[
\raisebox{2mm}{raised}over\raisebox{-2mm}{lowered}\textrm{ and back}.\]

\end_inset

Like 
\family typewriter

\backslash
mbox
\family default
, it puts its content in a text box.
 It can also be used just for spacing:
\begin_inset Newline newline
\end_inset

 
\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 $a\hspace{4mm}b$
\end_inset

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

, and at 
\begin_inset Quotes eld
\end_inset

block level
\begin_inset Quotes erd
\end_inset


\family typewriter
 
\backslash
vspace
\family default
: 
\begin_inset Formula $a\vspace{1cm}b$
\end_inset

.
\end_layout

\begin_layout Standard
There should be 1
\begin_inset space ~
\end_inset

cm of vertical space above this paragraph.
\end_layout

\begin_layout Section
Fonts
\end_layout

\begin_layout Standard
This section tests font support.
\end_layout

\begin_layout Subsection
Variables and Functions
\end_layout

\begin_layout Standard
By default, letters denote variables and are taken from the 
\family typewriter

\backslash
mathnormal
\family default
 font, which is italic: 
\begin_inset Formula $\alpha x+\alpha y=\alpha(x+y)$
\end_inset

, with the exception of upright capital Greek letters, 
\begin_inset Formula $G\ne\Gamma$
\end_inset

.
 Letters run together represent different variables: 
\begin_inset Formula $abcd=a\times b\times c\times d$
\end_inset

.
 
\end_layout

\begin_layout Standard
There has been some trouble over some commands like Greek letters; some
 of them should be italicized, as in: 
\begin_inset Formula $\mu$
\end_inset

 or 
\begin_inset Formula $\AA$
\end_inset

.
 Others should not, as in 
\begin_inset Formula $\Omega$
\end_inset

.
 Upright Greek letters are also available: 
\begin_inset Formula $\upmu\neq\mu$
\end_inset

.
 An example from the LyX math guide: 
\begin_inset Formula \[
\uppi^{+}\to\upmu^{+}+\upnu_{\upmu}.\]

\end_inset


\end_layout

\begin_layout Standard
Functions names should be upright: 
\begin_inset Formula $\sin(2\pi),\log(x),\tan\delta$
\end_inset

.
\end_layout

\begin_layout Subsection
Mathematical Fonts
\end_layout

\begin_layout Standard
Mathematical fonts used in equations include 
\begin_inset Formula $\mathrm{Roman}$
\end_inset

 (
\family typewriter

\backslash
mathrm
\family default
), 
\begin_inset Formula $\mathsf{Sans\: Serif}$
\end_inset

 (
\family typewriter

\backslash
mathsf
\family default
), 
\begin_inset Formula $\mathtt{Typewriter}$
\end_inset

 (
\family typewriter

\backslash
mathtt
\family default
), 
\begin_inset Formula $\mathbf{Bold}$
\end_inset

 (
\family typewriter

\backslash
mathbf
\family default
), 
\begin_inset Formula $\mathscr{SCRIPT}$
\end_inset

 (
\family typewriter

\backslash
mathscr
\family default
), 
\begin_inset Formula $\mathcal{CALLIGRAPHIC}$
\end_inset

 (
\family typewriter

\backslash
mathcal
\family default
), 
\begin_inset Formula $\mathbb{BLACKBOARD\: BOLD}$
\end_inset

 (
\family typewriter
\noun on

\backslash

\noun default
mathbb
\family default
), and 
\begin_inset Formula $\mathfrak{Fraktur}$
\end_inset

 (
\family typewriter

\backslash
mathfrak
\family default
).
 For the latter, 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 Standard
Regular text in a formula can be achieved via text font commands like 
\family typewriter

\backslash
textrm
\family default
: 
\begin_inset Formula $5\:\textrm{to}\:10$
\end_inset

, via boxes like 
\backslash
mbox (prevents line breaks): 
\begin_inset Formula $6\mbox{ is more than }5$
\end_inset

, or the AMSmath 
\family typewriter

\backslash
text
\family default
 macro (scales like math symbols) 
\begin_inset Formula $\text{base}_{\text{sub}}^{\text{super}}$
\end_inset

.
 The content of an mbox is processed in LaTeX text mode.
 This allows text font commands, e.g.
 a switch to 
\family sans
\series bold
\shape italic
sans-serif-bold-italic
\family default
\series default
\shape default
, or the phonetic alphabet: 
\begin_inset Formula $\mbox{\textbf{\textsf{\textbf{\textit{sfbfit}}}}, \textipa{tipa}}$
\end_inset

.
\end_layout

\begin_layout Subsection
Units
\end_layout

\begin_layout Standard
Units should be written upright, either with 
\family typewriter

\backslash
mathrm
\family default
 or with macros from the 
\family typewriter
units
\family default
 package, e.g.
 as simple unit, 
\begin_inset Formula $\unit{km}$
\end_inset

, with magnitude, 
\begin_inset Formula $\unit[57]{km}$
\end_inset

, with fractional unit, 
\begin_inset Formula $\unitfrac[200]{km}{h}$
\end_inset

, or 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 Subsection
Sizes
\end_layout

\begin_layout Standard
Sizes can be specified in formulas: 
\begin_inset Formula ${\displaystyle \text{display}},{\textstyle \text{text}},{\scriptstyle \text{script}},{\scriptscriptstyle \text{scriptscript}}$
\end_inset

.
\end_layout

\begin_layout Section
Colors and Boxes
\end_layout

\begin_layout Standard
A colored box: 
\begin_inset Formula $\colorbox{red}{aaa}$
\end_inset

.
\end_layout

\begin_layout Standard
A framed box: 
\begin_inset Formula $\framebox[2cm][c]{box}$
\end_inset

.
 It can be aligned left: 
\begin_inset Formula $\framebox[2cm][l]{box}$
\end_inset

 or right: 
\begin_inset Formula $\framebox[2cm][r]{box}$
\end_inset

.
\end_layout

\begin_layout Section
Macros
\end_layout

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

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

.
\end_layout

\begin_layout Standard
Macro definitions can accept default parameters
\begin_inset FormulaMacro
\renewcommand{\defaultroot}[2][4][5]{\sqrt[#1]{#2}}
{#1\sqrt{#2}}
\end_inset

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

.
 Default parameters can then be overriden: 
\begin_inset Formula $\defaultroot[][y]+\defaultroot[x]$
\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 Standard
Macros may contain a literal parameter
\begin_inset FormulaMacro
\renewcommand{\colort}[1]{\colorbox{#1}{t}}
{\colorbox{#1}{t}}
\end_inset

.
 It should parse correctly: 
\begin_inset Formula $\colort{red}$
\end_inset

.
\end_layout

\begin_layout Standard
A macro with four parameters from the LyX detailed math guide
\begin_inset FormulaMacro
\renewcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
\end_inset

.
 Now in use: 
\begin_inset Formula $1+\qG x{(1-x)}5-B$
\end_inset

.
\end_layout

\begin_layout Section
Pathological Cases
\end_layout

\begin_layout Standard
Empty equations have been known to fail: 
\begin_inset Formula $ $
\end_inset

.
\end_layout

\begin_layout Standard
An equation with an mbox containing a comment: 
\begin_inset Formula $\mbox{text %comment
more}$
\end_inset

, and a comment inside textrm: 
\begin_inset Formula $\textrm{text %comment
more}$
\end_inset

.
 Finally, a comment at the end of a text function: 
\begin_inset Formula $\mbox{only text%comment
}$
\end_inset

.
\end_layout

\begin_layout Section
Bye-bye
\end_layout

\begin_layout Standard
That's all folks!
\end_layout

\end_body
\end_document
