- Customization.lyx: add new possible font types uuline, strikeout and uwave

[lyx.git] / lib / doc / es / Math.lyx

#LyX 2.0 created this file. For more info see http://www.lyx.org/
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\pdf_title "Manual detallado de Matemáticas en LyX"
\pdf_author "LyX Team, Uwe Stöhr, Spanish translation: Ignacio Garcia"
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Manual detallado de
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Matemáticas en LyX
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por el Equipo LyX
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status collapsed

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Si tienes comentarios o correcciones de errores envíalos, por favor, a la
 lista de correo de documentación de LyX
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: 
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LatexCommand href
name "lyx-docs@lists.lyx.org"
target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"

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autor: Uwe Stöhr, traducción: Ignacio García
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Versión 2.0.x
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LatexCommand tableofcontents

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Para exportar este documento a PDF, PS o DVI deberían estar instalados los
 paquetes LaTeX 
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braket, cancel, eurosym
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, 
\series bold
mhchem
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 y 
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was
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.
 Si
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no están instalados también puedes exportar el documento pero las secciones
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mhchem
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La última versión PDF de este documento está disponible en:
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\series bold
http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
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\begin_layout Section
Introducción
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\begin_layout Standard
Este documento explica las características matemáticas de LyX y además es
 una colección de comandos LaTeX para caracteres y estructuras matemáticas.
 Las explicaciones están diseñadas para el uso de comandos.
 Por consiguiente es preciso que hayas leído la sección 
\emph on
Ecuaciones matemáticas
\emph default
 de la 
\emph on
Guía del usuario
\emph default
.
\end_layout

\begin_layout Standard
La mayoría de caracteres y muchas estructuras explicadas en este manual
 también son accesibles mediante el menú 
\family sans
Insertar\SpecialChar \menuseparator
Ecuación
\family default
 o la barra de herramientas
\family sans
 Ecuaciones
\family default
.
 Pero todo aquel que tenga que escribir muchas fórmulas observará que es
 mucho más rápido usar comandos que la barra de herramientas.
 Por tanto este manual está enfocado al uso de comandos, aunque también
 se mencionan los botones correspondientes de las barras de herramientas
 cuando están disponibles.
\end_layout

\begin_layout Standard
Si no se especifica lo contrario los comandos sólo están disponibles dentro
 de las fórmulas.
 Para poder usar todos los comandos explicados en este documento, debe usarse
 la opción 
\family sans
Usar el paquete de ecuaciones AMS
\family default
 en la configuración del documento (menú 
\family sans
Documento\SpecialChar \menuseparator
Configuración\SpecialChar \menuseparator
Opciones de ecuación
\family default
)
\begin_inset Foot
status collapsed

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La opción 
\family sans
Usar el paquete de ecuaciones AMS automáticamente
\family default
 sólo usa ecuaciones 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
AmS 
\end_layout

\end_inset


\begin_inset space ~
\end_inset

 si las estructuras matemáticas son soportadas por LyX.
\end_layout

\end_inset

.
\end_layout

\begin_layout Standard
Este documento no recoge todos los comandos de ecuaciones 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
AmS 
\end_layout

\end_inset


\begin_inset Foot
status collapsed

\begin_layout Plain Layout
En el archivo 
\family sans

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LatexCommand href
name "amsguide.ps"
target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"

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\family default
, que forma parte de todas las distribuciones estándar de LaTeX, hay una
 lista con todos los comandos de ecuaciones 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
AmS 
\end_layout

\end_inset

.
\end_layout

\end_inset

 por razones de claridad.
\end_layout

\begin_layout Section
Instrucciones generales
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\begin_layout Standard
Para crear una ecuación en línea
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! en línea
\end_layout

\end_inset

 insertada en una línea de texto, teclea una de las combinaciones 
\family sans
Ctrl+M, Alt+C M, Alt+M M
\family default
 o pulsa el botón 
\begin_inset Graphics
        filename ../../images/math-mode.png
        scale 85

\end_inset

 de la barra de herramientas.
\begin_inset Newline newline
\end_inset

Para crear una ecuación en estilo presentación
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! presentada
\end_layout

\end_inset

, que se verá más grande y en su propio párrafo, teclea
\family sans
 
\family default
una de estas combinaciones: 
\family sans
Ctrl+Mayúsculas+M, Alt+M D.
\end_layout

\begin_layout Standard
Para cambiar una ecuación presentada a ecuación en línea, pon el cursor
 dentro de la ecuación y teclea
\family sans
 Ctrl+M, Alt+C M, Alt+M M 
\family default
o usa el menú 
\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Cambiar tipo de ecuación
\family default
.
 De igual forma se puede cambiar una ecuación en línea a estilo presentación.
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\begin_layout Standard
Para mostrar partes de una ecuación en línea en el tamaño de una ecuación
 presentada, escribe el comando 
\series bold

\backslash
displaystyle
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! D ! 
\backslash
displaystyle
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 en la ecuación y pulsa espacio.
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 de la ecuación.
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En los cuadros sólo se permiten ecuaciones en línea.
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\begin_layout Standard
Las barras 
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Ecuaciones
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 y 
\family sans
Paneles de ecuaciones 
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se pueden visualizar mediante el menú 
\family sans
Ver\SpecialChar \menuseparator
Barras de herramientas
\family default
.
 Si ahí pulsas en 
\begin_inset Quotes fld
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Ecuaciones
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 y/o en 
\begin_inset Quotes fld
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Paneles de ecuaciones
\begin_inset Quotes frd
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, una y/u otra se mostrarán de forma permanente en la parte inferior; este
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 Si en este estado pulsas de nuevo sobre 
\begin_inset Quotes fld
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Ecuaciones
\begin_inset Quotes frd
\end_inset

 y/o 
\begin_inset Quotes fld
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Paneles de ecuaciones
\begin_inset Quotes frd
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 en el menú, las barras sólo se visualizarán cuando el cursor esté dentro
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\begin_inset Quotes fld
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(auto)
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.
 
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\begin_layout Standard
El modo TeX
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T@TeX ! modo
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 se inicia pulsando el botón 
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 de la barra de herramientas o con el menú 
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Insertar\SpecialChar \menuseparator
Código Te
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status collapsed

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{}
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X
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, (atajo 
\family sans
Ctrl+L
\family default
).
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En LyX hay tres 
\begin_inset Quotes fld
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nombres propios
\begin_inset Quotes frd
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 que se ven en la salida con letras sobre o bajo la alineación normal: TeX,
 LaTeX y LyX.
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Para evitar que estas palabras sean reconocidas como tales nombres propios,
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\begin_layout Standard
Para cambiar el preámbulo LaTeX
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LaTeX, preámbulo
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, usa el menú 
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Documento\SpecialChar \menuseparator
Configuración\SpecialChar \menuseparator
Preámbulo LaT
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{}
\end_layout

\end_inset

eX
\family default
.
\end_layout

\begin_layout Standard
Para editar posteriormente matrices, diferenciaciones de casos y ecuaciones
 multilínea, se pueden usar los menús 
\family sans
Editar\SpecialChar \menuseparator
Ecuación
\family default
 y 
\family sans
Editar\SpecialChar \menuseparator
Filas y columnas
\family default
 o la barra de herramientas de 
\family sans
Cuadro
\family default
.
 Cuando las líneas y columnas se intercambian mediante el menú, la columna
 o línea en la que está se cambia con la columna de la derecha o con la
 línea de abajo, respectivamente.
 Si el cursor está en la última columna o fila, el cambio se hace con la
 columna de la izquierda o la línea de arriba.
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\begin_layout Standard
Para escribir texto en fórmulas se usa 
\emph on
texto de ecuaciones
\emph default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Texto ! en ecuaciones
\end_layout

\end_inset

.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Para ecuaciones multilínea se usa el comando 
\series bold

\backslash
intertext
\series default
, véase
\begin_inset space ~
\end_inset


\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Texto-en-multilínea"

\end_inset

.
\end_layout

\end_inset

 Este modo se inicia con el atajo 
\family sans
Alt+M
\begin_inset space ~
\end_inset

M
\family default
 o
\family sans
 Ctrl+M
\family default
 o insertando el comando 
\series bold

\backslash
text
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! T ! 
\backslash
text
\end_layout

\end_inset

.
 El texto se ve en negro en LyX y por tanto puede distinguirse de otras
 partes de la ecuación que se ven en azul.
 En la salida, el texto en una ecuación se imprime en letra redonda, a diferenci
a de otras partes de la fórmula.
\end_layout

\begin_layout Subsection*
Esquema de comandos
\end_layout

\begin_layout Standard
La mayoría de los comandos LaTeX para estructuras matemáticas tienen el
 siguiente esquema:
\end_layout

\begin_layout Standard

\series bold

\backslash
nombre_del_comando[argumento opcional]{argumento requerido}
\end_layout

\begin_layout Standard
Un comando empieza siempre por una barra inversa, 
\begin_inset Quotes fld
\end_inset


\series bold

\backslash

\series default

\begin_inset Quotes frd
\end_inset

.
 Para omitir argumentos opcionales, quita también los corchetes asociados.
 En este documento, las llaves que encierran los argumentos requeridos se
 denominan llaves TeX
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
T@TeX ! llaves
\end_layout

\end_inset

.
 Si en una ecuación añades una llave de apertura al nombre de un comando,
 LyX crea automáticamente una llave TeX.
 En todos los demás casos las llaves TeX se crean en las ecuaciones con
 el comando 
\series bold

\backslash
{
\series default
.
 Las llaves TeX se ven en rojo en LyX, a diferencia de las llaves normales,
 que se muestran en azul.
 En modo TeX no hace falta comando para poner llaves TeX.
 Las llaves TeX no aparecen en la salida.
\end_layout

\begin_layout Standard
En el caso de comandos sin argumentos, como los comandos para símbolos que
 se introducen en modo TeX, 
\emph on
siempre
\emph default
 debe teclearse un espacio tras el comando para finalizarlo.
 Este espacio no aparece en la salida.
 Si ese espacio debiera mostrarse en la salida, el espacio debe ir seguido
 de un espacio protegido en texto normal.
\end_layout

\begin_layout Standard
Un espacio protegido se inserta con 
\family sans
Ctrl+Espacio
\family default
.
\end_layout

\begin_layout Subsection*
Explicación de la sintaxis
\end_layout

\begin_layout Itemize
El símbolo 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Este carácter, espacio visible, se puede componer con el comando 
\series bold

\backslash
textvisiblespace
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! T ! 
\backslash
textvisiblespace
\end_layout

\end_inset

 insertado en código TeX.
\end_layout

\end_inset

 indica que hay que teclear un espacio.
\end_layout

\begin_layout Itemize
Una flecha como 
\begin_inset Formula $\rightarrow$
\end_inset

 indica el uso de la correspondiente tecla de flecha.
 
\end_layout

\begin_layout Subsection*
Unidades disponibles
\end_layout

\begin_layout Standard
\align center
\begin_inset Float table
placement H
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Caption

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "tab:Unidades-disponibles"

\end_inset

Unidades disponibles
\end_layout

\end_inset


\end_layout

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\align center
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Nombre / Descripción
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mm
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cm
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Centímetro
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in
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Pulgada (1
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in = 2,54
\begin_inset space \thinspace{}
\end_inset

cm)
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pt
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Punto (72.27
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pt = 1
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in)
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pc
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\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Pica (1
\begin_inset space \thinspace{}
\end_inset

pc = 12
\begin_inset space \thinspace{}
\end_inset

pt)
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
sp
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Punto escalado (65536
\begin_inset space \thinspace{}
\end_inset

sp = 1
\begin_inset space \thinspace{}
\end_inset

pt)
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
bp
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Punto grande (72
\begin_inset space \thinspace{}
\end_inset

bp = 1
\begin_inset space \thinspace{}
\end_inset

in)
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
dd
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Didot (1
\begin_inset space \thinspace{}
\end_inset

dd 
\begin_inset Formula $\approx$
\end_inset

 0.376
\begin_inset space \thinspace{}
\end_inset

mm)
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
cc
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Cicero (1
\begin_inset space \thinspace{}
\end_inset

cc = 12
\begin_inset space \thinspace{}
\end_inset

dd)
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
ex
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Altura de la letra 
\begin_inset Quotes fld
\end_inset


\emph on
x
\emph default

\begin_inset Quotes frd
\end_inset

 en la tipografía actual
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
em
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Anchura de la letra 
\begin_inset Quotes fld
\end_inset


\emph on
M
\emph default

\begin_inset Quotes frd
\end_inset

 en la tipografía actual
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
mu
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Unidad matemática (1
\begin_inset space \thinspace{}
\end_inset

mu = 
\begin_inset Formula $\nicefrac{1}{18}$
\end_inset


\begin_inset space \thinspace{}
\end_inset

em)
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
\align center
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Funciones básicas
\end_layout

\begin_layout Subsection
Exponentes
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Exponentes
\end_layout

\end_inset

 e índices
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Indices@Índices
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Superíndices|see
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset

Exponentes
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Subíndices|see
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset

Índices
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Los subíndices se componen con un guión bajo 
\begin_inset Quotes fld
\end_inset

_
\begin_inset Quotes frd
\end_inset

 o con el botón de la barra de herramientas de ecuaciones 
\begin_inset Graphics
        filename ../../images/math-subscript.png
        scale 85

\end_inset

, los superíndices con un circunflejo 
\begin_inset Quotes fld
\end_inset

^
\begin_inset Quotes frd
\end_inset

 o con el botón de la barra de herramientas de ecuaciones 
\begin_inset Graphics
        filename ../../images/math-superscript.png
        scale 85

\end_inset

.
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status open

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 sólo se usa como espaciador.
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
B_V
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $B_{V}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
B^V
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

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


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
B^
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}B^{A}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Como en algunos idiomas la tecla circunflejo funciona como acento, en ese
 caso acentuará las vocales y no servirá para entrar en modo exponente.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Dependiendo de la configuración del teclado esto puede suceder también con
 otros caracteres además de las vocales.
\end_layout

\end_inset

 Para conseguir exponentes en estos casos debes pulsar 
\family sans
Espacio
\family default
 tras el circunflejo, como en el último ejemplo, o dos circunflejos seguidos.
 
\end_layout

\begin_layout Subsection
Fracciones
\begin_inset CommandInset label
LatexCommand label
name "sub:Fracciones"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Fracciones
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Las fracciones se generan con el comando 
\series bold

\backslash
frac
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! F ! 
\backslash
frac
\end_layout

\end_inset

 o con el botón 
\begin_inset Graphics
        filename ../../images/math/frac.png
        scale 50

\end_inset

 de la barra de herramientas.
 El tamaño de tipografía se ajusta automáticamente, dependiendo de si la
 fracción está en línea o en estilo presentación.
 Con el botón 
\begin_inset Graphics
        filename ../../images/math/frac-square.png
        scale 85

\end_inset

de la barra de herramientas matemáticas puedes seleccionar distintos tipos
 de fracciones.
\end_layout

\begin_layout Standard
Con el comando 
\series bold

\backslash
dfrac
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! D ! 
\backslash
dfrac
\end_layout

\end_inset

 se puede crear en cualquier caso una fracción que tenga el tamaño del estilo
 presentación.
 Con 
\series bold

\backslash
tfrac
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! T ! 
\backslash
tfrac
\end_layout

\end_inset

 la fracción tiene siempre el tamaño del estilo en línea.
 Un ejemplo:
\end_layout

\begin_layout Standard
Una línea con la fracción 
\begin_inset Formula $\frac{1}{2}$
\end_inset

 creada con el comando 
\series bold

\backslash
frac
\series default
.
 
\end_layout

\begin_layout Standard
Una línea con la fracción 
\begin_inset Formula $\dfrac{1}{2}$
\end_inset

 creada con el comando 
\series bold

\backslash
dfrac
\series default
.
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
frac
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\downarrow$
\end_inset

B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
dfrac
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\downarrow$
\end_inset

B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
dfrac
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

e^
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\backslash
frac
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

1
\begin_inset Formula $\downarrow$
\end_inset

2
\begin_inset Formula $\downarrow$
\end_inset

3
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
Para fracciones anidadas se puede usar el comando 
\series bold

\backslash
cfrac
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! C ! 
\backslash
cfrac
\end_layout

\end_inset

.
 Un ejemplo:
\begin_inset VSpace -3mm
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{align*}
\textrm{creada con \textbf{\textbackslash frac}} &  & \textrm{creada con \textbf{\textbackslash cfrac}}\\
\frac{A}{B+\frac{C+\frac{E}{F}}{D}} &  & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
\end{align*}

\end_inset


\end_layout

\begin_layout Standard
El comando para el ejemplo de arriba es:
\end_layout

\begin_layout Standard

\series bold

\backslash
cfrac
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\downarrow$
\end_inset

B+
\backslash
cfrac
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

C+
\backslash
cfrac
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

E
\begin_inset Formula $\downarrow$
\end_inset

F
\begin_inset Formula $\downarrow$
\end_inset

D
\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard

\series bold

\backslash
cfrac
\series default
 compone la fracción siempre en el tamaño del estilo presentación, también
 cuando es parte de otra fracción.
\end_layout

\begin_layout Standard
Es posible especificar la alineación del numerador.
 El comando 
\series bold

\backslash
cfracleft
\series default
 se usa para alinearlo a la izquierda, el comando 
\series bold

\backslash
cfracright
\series default
 para alinearlo a la derecha, 
\series bold

\backslash
cfrac
\series default
 centra el numerador.
\end_layout

\begin_layout Standard
Estas fracciones muestran las distintas alineaciones:
\end_layout

\begin_layout Standard
\begin_inset Formula $\cfrac[l]{A}{B+C}$
\end_inset

 ; 
\begin_inset Formula $\cfrac{A}{B+C}$
\end_inset

 ; 
\begin_inset Formula $\cfrac[r]{A}{B+C}$
\end_inset


\end_layout

\begin_layout Standard
\noindent
\begin_inset Note Greyedout
status open

\begin_layout Plain Layout

\series bold
Nota
\series default
: 
\series bold

\backslash
cfracleft
\series default
 y
\series bold
 
\backslash
cfracright
\series default
 no son comandos LaTeX reales sino sustituciones del comando 
\series bold

\backslash
cfrac[posición del numerador]{numerador}{denominador}
\series default
 .
 Por tanto no puedes usarlos código TeX.
\end_layout

\end_inset


\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
Muchas veces es adecuado combinar 
\series bold

\backslash
cfrac
\series default
 y 
\series bold

\backslash
frac
\series default
:
\begin_inset Formula 
\[
\cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
\]

\end_inset


\end_layout

\begin_layout Standard
Para componer fracciones en línea con raya de fracción inclinada puedes
 usar el comando 
\series bold

\backslash
nicefrac
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! N ! 
\backslash
nicefrac
\end_layout

\end_inset

: 
\begin_inset Formula $\nicefrac{5}{31}$
\end_inset

 Hay además el comando 
\series bold

\backslash
unitfracthree
\series default
 que permite escribir una fracción en combinación con un número: 
\begin_inset Formula $\unitfrac[2]{1}{3}$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Note Greyedout
status open

\begin_layout Plain Layout

\series bold
Nota
\series default
: 
\series bold

\backslash
unitfracthree
\series default
 no es un comando LaTeX auténtico, sino un equivalente al comando
\begin_inset Newline newline
\end_inset


\series bold

\backslash
unitfrac[número]{numerador}{denominador}
\series default
 .
 Por tanto no puedes usarlo en código TeX.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
En la 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Fracciones-personalizadas"

\end_inset

 se explica cómo componer fracciones personalizadas en las que la raya de
 fracción se puede cambiar.
 
\end_layout

\begin_layout Subsection
Raíces
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Raíces
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Las raíces cuadradas se componen con 
\series bold

\backslash
sqrt
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! S ! 
\backslash
sqrt
\end_layout

\end_inset

 o con el botón 
\begin_inset Graphics
        filename ../../images/math/sqrt.png
        scale 85

\end_inset

 de la barra de ecuaciones; todas las demás raíces con el comando 
\series bold

\backslash
root
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! R ! 
\backslash
root
\end_layout

\end_inset

 o con el botón 
\begin_inset Graphics
        filename ../../images/math/root.png
        scale 85

\end_inset

.
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
sqrt
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A-B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
root
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

3
\begin_inset Formula $\downarrow$
\end_inset

A-B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Una raíz cuadrada se compone también con 
\series bold

\backslash
root
\series default
 dejando vacío el campo del índice.
\end_layout

\begin_layout Standard
Con ciertos índices la distancia a la raíz es demasiado pequeña, como en
 la raíz: 
\begin_inset Formula $\sqrt[\beta]{B}$
\end_inset


\begin_inset Newline newline
\end_inset

La 
\begin_inset Formula $\beta$
\end_inset

 toca la raíz.
 Para evitar esto se usan los comandos 
\series bold

\backslash
leftroot
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! L ! 
\backslash
leftroot
\end_layout

\end_inset

 y 
\series bold

\backslash
uproot
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! U ! 
\backslash
uproot
\end_layout

\end_inset

 con el esquema siguiente:
\end_layout

\begin_layout Standard

\series bold

\backslash
leftroot{distancia}
\series default
 y 
\series bold

\backslash
uproot{distancia}
\end_layout

\begin_layout Standard
Distancia es el número de Puntos Grandes (
\begin_inset Quotes fld
\end_inset

Big Points
\begin_inset Quotes frd
\end_inset

, unidad bp; 
\begin_inset Formula $\mathrm{72\, bp=1\, pulgada}$
\end_inset

) que debería moverse el índice a la izquierda o arriba, respectivamente.
 Los comandos se escriben en el índice.
 Así, el comando:
\begin_inset Newline newline
\end_inset


\series bold

\backslash
root
\backslash
leftroot{-1
\begin_inset Formula $\to$
\end_inset


\backslash
uproot{2
\begin_inset Formula $\to$
\end_inset


\backslash
beta
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\begin_inset Formula $\to$
\end_inset

B
\begin_inset Newline newline
\end_inset


\series default
genera una fórmula correctamente tipografiada: 
\begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
\end_inset


\end_layout

\begin_layout Subsection
Coeficientes de un binomio
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Binomios
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Los coeficientes de un binomio se insertan con el comando 
\series bold

\backslash
binom
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! B ! 
\backslash
binom
\end_layout

\end_inset

 o con el submenú del botón 
\begin_inset Graphics
        filename ../../images/math/frac-square.png
        scale 85

\end_inset

de la barra de herramientas de ecuaciones.
 Como en las fracciones, además de 
\series bold

\backslash
binom
\series default
 hay los comandos 
\series bold

\backslash
dbinom
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! D ! 
\backslash
dbinom
\end_layout

\end_inset

 y 
\series bold

\backslash
tbinom
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! T ! 
\backslash
tbinom
\end_layout

\end_inset

.
 Para otros delimitadores de coeficientes de un binomio hay los comandos
 
\series bold

\backslash
brace
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! B ! 
\backslash
brace
\end_layout

\end_inset

 y 
\series bold

\backslash
brack
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! B ! 
\backslash
brack
\end_layout

\end_inset

.
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="6" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
binom
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\downarrow$
\end_inset

B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
dbinom
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\downarrow$
\end_inset

B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
tbinom
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\downarrow$
\end_inset

B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
brack
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\downarrow$
\end_inset

B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
brace
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\downarrow$
\end_inset

B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Subsection
Diferenciaciones de casos
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Casos
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
cases
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\to$
\end_inset

B>0
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! C ! 
\backslash
cases
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\begin{cases}
A & B>0\end{cases}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
cases
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\family sans
Ctrl+Entrar
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\begin{cases}
A & \textrm{para }x>0\\
B & \textrm{para }x=0
\end{cases}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Después de insertar 
\series bold

\backslash
cases
\series default
 o usar el botón 
\begin_inset Graphics
        filename ../../images/math/cases.png
        scale 85

\end_inset

 de la barra de ecuaciones puedes añadir líneas nuevas con el atajo 
\family sans
Ctrl+Entrar
\family default
 o con el botón
\family sans
 
\family default

\begin_inset Graphics
        filename ../../images/tabular-feature_append-row.png
        scale 85

\end_inset

 de la barra de cuadros.
\end_layout

\begin_layout Standard
El comando 
\series bold

\backslash
cases
\series default
 también está disponible en el menú 
\family sans
Insertar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Entorno casos
\family default
.
\end_layout

\begin_layout Subsection
Negaciones
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Negaciones
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Con el comando 
\series bold

\backslash
not
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! N ! 
\backslash
not
\end_layout

\end_inset

 todo carácter se puede mostrar cancelado.
 Los caracteres son casi tachados con una barra inclinada.
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
not=
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\not=$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
not 
\backslash
le
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\not\le$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
not 
\backslash
parallel
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\not\parallel$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
El último ejemplo muestra que no todas las negaciones tienen buen aspecto.
 Por tanto para algunas negaciones hay comandos especiales (véase 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Símbolos-matemáticos"

\end_inset

 y 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Relaciones"

\end_inset

).
\end_layout

\begin_layout Subsection
Espacios reservados 
\begin_inset CommandInset label
LatexCommand label
name "sub:Espacios-reservados"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Espacios reservados
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Química ! isótopos
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Isótopos|see
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset

Química
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
En la presentación de, p.
\begin_inset space \thinspace{}
\end_inset

e., isótopos,
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Más sobre símbolos químicos en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Símbolos-y-ecuaciones-químicas"

\end_inset


\end_layout

\end_inset

 surge el problema siguiente:
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Índices generados con sub- y superíndices:
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $_{9}^{19}\textrm{F}\raisebox{-3mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Índices correctos:
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $_{\phantom{1}9}^{19}\textrm{F}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Por omisión, el índice más corto se coloca sobre o bajo el primer carácter
 del índice más largo.
 Para evitarlo está el comando 
\series bold

\backslash
phantom
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! P ! 
\backslash
phantom
\end_layout

\end_inset

 o el botón 
\begin_inset space ~
\end_inset


\begin_inset Graphics
        filename ../../images/math/phantom.png
        scale 85

\end_inset

 del submenú de espaciado de ecuaciones
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Botón 
\begin_inset Graphics
        filename ../../images/math/space.png
        scale 85

\end_inset

 de la barra de ecuaciones
\end_layout

\end_inset

, que genera uno o más espacios reservados.
 Al insertar 
\series bold

\backslash
phantom
\series default
 aparece un pequeño marco azul con dos flechas rojas superpuestas
\begin_inset Formula $\phantom{}$
\end_inset

.
 Las flechas indican que se reservará un espacio equivalente a la anchura
 y altura totales del contenido del marco.
 Los espacios reservados son correspondientes al tamaño de los caracteres.
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
^19
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

_
\backslash
phantom
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

1
\begin_inset Formula $\rightarrow$
\end_inset

9
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

F
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\textrm{F}\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
^235
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

_
\backslash
phantom
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

23
\begin_inset Formula $\rightarrow$
\end_inset

9
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

F
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\textrm{F}\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Lambda^
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\backslash
phantom
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

ii
\begin_inset Formula $\rightarrow$
\end_inset

t
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

_MMt
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Además hay los comandos 
\series bold

\backslash
vphantom
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! V ! 
\backslash
vphantom
\end_layout

\end_inset

 (botón 
\begin_inset space ~
\end_inset


\begin_inset Graphics
        filename ../../images/math/vphantom.png
        scale 85

\end_inset

) y 
\series bold

\backslash
hphantom
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! H ! 
\backslash
hphantom
\end_layout

\end_inset

 (botón 
\begin_inset space ~
\end_inset


\begin_inset Graphics
        filename ../../images/math/hphantom.png
        scale 85

\end_inset

).
 
\series bold

\backslash
hphantom
\series default
 genera espacio en el marco sólo para la altura máxima de los caracteres,
 no para su anchura.
 
\series bold

\backslash
vphantom
\series default
 genera espacio sólo para la anchura del contenido del marco.
 Por esto los marcos de estos comandos sólo tienen una flecha roja.
\end_layout

\begin_layout Standard
Por ejemplo, 
\series bold

\backslash
vphantom
\series default

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series bold
a
\backslash
int
\series default
 genera espacio de la altura del signo de la integral,
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
El comando 
\series bold

\backslash
int
\series default
 genera un signo de integral, véase 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Operadores-grandes"

\end_inset


\end_layout

\end_inset

 porque este es el carácter más largo.
 En la 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Delimitadores-multilínea"

\end_inset

 hay un ejemplo de aplicación.
\end_layout

\begin_layout Standard
Los espacios reservados también se pueden usar para un texto cuando se insertan
 mediante el menú 
\family sans
Insertar\SpecialChar \menuseparator
Formato\SpecialChar \menuseparator
Fantasma
\family default
:
\end_layout

\begin_layout Standard
Esto es una frase.
\begin_inset Newline newline
\end_inset


\begin_inset Phantom Phantom
status open

\begin_layout Plain Layout
Esto
\end_layout

\end_inset

 es una frase.
\end_layout

\begin_layout Subsection
Líneas
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Lineas@Líneas
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! sub- o superrayada
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
overline
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A+B
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! O ! 
\backslash
overline
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
underline
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A+B
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! U ! 
\backslash
underline
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
overline
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\backslash
underline
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A+B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
En el último ejemplo es indiferente poner primero 
\series bold

\backslash
overline
\series default
 o 
\series bold

\backslash
underline
\series default
.
\end_layout

\begin_layout Standard
Para poner doble subrayado, p.
\begin_inset space \thinspace{}
\end_inset

e.
 en resultados, se usa 
\series bold

\backslash
underline
\series default
 dos veces.
\end_layout

\begin_layout Standard
Es posible colocar hasta 6 líneas sobre o bajo los caracteres.
\begin_inset VSpace bigskip
\end_inset

Se pueden crear líneas personalizadas con el comando 
\series bold

\backslash
rule
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! R ! 
\backslash
rule
\end_layout

\end_inset

 con el esquema siguiente:
\end_layout

\begin_layout Standard

\series bold

\backslash
rule[hueco vertical]{longitud}{grosor}
\end_layout

\begin_layout Standard
El hueco vertical opcional desplaza la línea hacia arriba (o hacia abajo
 si el valor es negativo).
 Las unidades disponibles para los valores están listadas en
\begin_inset space ~
\end_inset


\begin_inset CommandInset ref
LatexCommand ref
reference "tab:Unidades-disponibles"

\end_inset

.
 A continuación hay dos ejemplos de líneas creadas con los comandos
\series bold

\begin_inset Newline newline
\end_inset


\backslash
rule[-2ex]{3cm}{2pt}
\series default
 y 
\series bold

\backslash
rule{2cm}{1pt}
\series default
:
\end_layout

\begin_layout Standard
Esto es una frase 
\begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
\end_inset

 con dos líneas.
\end_layout

\begin_layout Standard

\series bold

\backslash
rule
\series default
 también se puede usar para texto insertando una línea mediante el menú
 
\family sans
Insertar\SpecialChar \menuseparator
Formato\SpecialChar \menuseparator
Línea horizontal
\family default
:
\end_layout

\begin_layout Standard
Esto es una frase 
\begin_inset CommandInset line
LatexCommand rule
offset "0.5ex"
width "3cm"
height "1pt"

\end_inset

 con una línea insertada.
\end_layout

\begin_layout Subsection
Puntos
\begin_inset CommandInset label
LatexCommand label
name "sub:Puntos"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Puntos
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Hay distintos tipos de puntos disponibles.
\begin_inset Foot
status open

\begin_layout Plain Layout
En la barra de herramientas de ecuaciones, en el panel del botón 
\begin_inset Graphics
        filename ../../images/math/ldots.png
        scale 85

\end_inset

.
\end_layout

\end_inset

 Para continuación en enumeraciones se usan puntos bajos, (
\series bold

\backslash
ldots
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! L ! 
\backslash
ldots
\end_layout

\end_inset

), mientras que para operaciones se usan puntos centrados a la misma altura
 que los operadores, (
\series bold

\backslash
cdots
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! C ! 
\backslash
cdots
\end_layout

\end_inset

).
 Si se usa el comando 
\series bold

\backslash
dots
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! D ! 
\backslash
dots
\end_layout

\end_inset

, LaTeX decide el tipo a usar en función del carácter siguiente.
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="9" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
A_1
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

,
\backslash
dots
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

,A_n
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A_{1},\dots,A_{n}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
A_1
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

+
\backslash
dots
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

+A_n
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A_{1}+\dots+A_{n}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
A_1
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

,
\backslash
ldots
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

,A_n
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A_{1},\ldots,A_{n}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
A_1
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

+
\backslash
cdots
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

+A_n
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A_{1}+\cdots+A_{n}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
vdots
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\vdots$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ddots
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\ddots$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
iddots
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\iddots$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Matriz
\begin_inset space \thinspace{}
\end_inset

3×3 con los distintos puntos
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\begin{array}{ccc}
A_{11} & \cdots & A_{1m}\\
\vdots & \ddots & \vdots\\
A_{n1} & \cdots & A_{nm}
\end{array}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Los puntos suspensivos disponibles en el menú 
\family sans
Insertar\SpecialChar \menuseparator
Carácter especial
\family default
 son 
\series bold

\backslash
ldots
\series default
.
\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
Para usar 
\series bold

\backslash
iddots
\series default
, hay que marcar una de las opciones 
\family sans
Usar paquete mathdots (automáticamente)
\family default
 en las 
\family sans
Opciones de ecuación
\family default
 de la configuración del documento.
\begin_inset Newline newline
\end_inset

La opción 
\family sans
Usar paquete mathdots
\family default
 mejorará el aspecto de todos los puntos en los documentos si su estilo
 o tamaño de tipografía no son los predeterminados.
\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset

Hay puntos específicos para matrices que se extienden por varias columnas.
 Se generan con el comando 
\series bold

\backslash
hdotsfor
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! H ! 
\backslash
hdotsfor
\end_layout

\end_inset

, que tiene el siguiente esquema:
\end_layout

\begin_layout Standard

\series bold

\backslash
hdotsfor[distancia]{número de columnas}
\end_layout

\begin_layout Standard
Número de columnas especifica cuántas columnas deben abarcarse.
 Distancia es un factor para la separación entre los puntos.
\end_layout

\begin_layout Standard
En la siguiente matriz se ha insertado el comando 
\series bold

\backslash
hdotsfor[2]{4}
\series default
 en el primer recuadro de la segunda línea para obtener puntos separados
 una distancia equivalente a dos veces la del comando 
\series bold

\backslash
dots
\series default
.
\begin_inset Formula 
\[
\left(\begin{array}{cccc}
A & B & C & D\\
\hdotsfor[2]{4}\\
q & w & e & r
\end{array}\right)
\]

\end_inset


\end_layout

\begin_layout Standard
Ten en cuenta que los campos abarcados de la matriz deben estar vacíos,
 de lo contrario se producen errores de LaTeX.
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
Además, con el comando 
\series bold

\backslash
dotfill
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! D ! 
\backslash
dotfill
\end_layout

\end_inset

 puedes completar con puntos una línea.
 El efecto de este tipo de comandos es como el de 
\series bold

\backslash
hfill
\series default
, véase 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Espacio-variable"

\end_inset

.
\end_layout

\begin_layout Standard
Por ejemplo el comando 
\series bold
A
\backslash
dotfill
\series default

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series bold
B
\series default
 genera
\end_layout

\begin_layout Standard
\begin_inset Formula $A\dotfill B$
\end_inset


\end_layout

\begin_layout Standard
Un comando análogo a 
\series bold

\backslash
dotfill
\series default
 para rellenar con una línea es 
\series bold

\backslash
hrulefill
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! H ! 
\backslash
hrulefill
\end_layout

\end_inset

:
\end_layout

\begin_layout Standard
\begin_inset Formula $A\hrulefill B$
\end_inset


\end_layout

\begin_layout Standard
Para usar estos comandos en el texto, deben insertarse en modo TeX.
\end_layout

\begin_layout Section
Matrices
\begin_inset CommandInset label
LatexCommand label
name "sec:Matrices"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Matrices
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Se pueden insertar con el botón 
\begin_inset Graphics
        filename ../../images/dialog-show_mathmatrix.png
        scale 85

\end_inset

 de la barra de ecuaciones o con el menú 
\family sans
Insertar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Matriz
\family default
.
 Aparece una ventana en la que se pide el número de filas y columnas, la
 alineación y la decoración.
 La alineación vertical sólo es relevante para matrices en línea:
\end_layout

\begin_layout Standard
Esta primera matriz tiene alineación superior 
\begin_inset Formula $\begin{array}[t]{cccc}
A & D & G & J\\
B & E & H & K\\
D & F & I & L
\end{array}$
\end_inset

 , la segunda alineación central 
\begin_inset Formula $\begin{array}{cccc}
A & D & G & J\\
B & E & H & K\\
D & F & I & L
\end{array}$
\end_inset

 , y la tercera alineación inferior 
\begin_inset Formula $\begin{array}[b]{cccc}
A & D & G & J\\
B & E & H & K\\
D & F & I & L
\end{array}$
\end_inset

.
\end_layout

\begin_layout Standard
La alineación horizontal especifica cómo deben alinearse las entradas de
 la columna.
 Se determina mediante una letra para cada columna.
 
\emph on
l
\emph default
 indica alineación a la izquierda, 
\emph on
c
\emph default
 alineación centrada y 
\emph on
r
\emph default
 alineación a la derecha.
 Por ejemplo, para componer una matriz
\begin_inset space ~
\end_inset

4×4 con la primera columna alineada a la izquierda, la segunda y la tercera
 centradas y la última a la derecha, se anota 
\series bold
lccr
\series default
 en la alineación horizontal.
 Normalmente todas las columnas de una matriz están centradas, por tanto
 el valor por omisión es 
\series bold
c
\series default
 para todas ellas.
\end_layout

\begin_layout Standard
Alineación horizontal:
\end_layout

\begin_layout Standard

\series bold
lll
\series default
 : 
\begin_inset Formula $\begin{array}{lll}
10000 & D & G\\
B & 10000 & H\\
C & F & 10000
\end{array}$
\end_inset

 , 
\series bold
ccc 
\series default
: 
\begin_inset Formula $\begin{array}{ccc}
10000 & D & G\\
B & 10000 & H\\
C & F & 10000
\end{array}$
\end_inset

 
\series bold
,
\series default
 
\series bold
rrr 
\series default
: 
\begin_inset Formula $\begin{array}{rrr}
10000 & D & G\\
B & 10000 & H\\
C & F & 10000
\end{array}$
\end_inset


\end_layout

\begin_layout Standard
Para añadir o borrar filas y columnas posteriormente, se pueden usar los
 botones 
\begin_inset Graphics
        filename ../../images/tabular-feature_append-row.png
        scale 85

\end_inset

, 
\begin_inset Graphics
        filename ../../images/tabular-feature_delete-row.png
        scale 85

\end_inset

, etc.
 de la barra de ecuaciones o el menú 
\family sans
Editar\SpecialChar \menuseparator
Filas y columnas
\family default
.
 También se pueden añadir filas nuevas con 
\family sans
Ctrl+Entrar
\family default
.
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
La 
\family sans
Decoración
\family default
 añade paréntesis en el estilo seleccionado alrededor de la matriz.
 Alternativamente, se pueden generar paréntesis con los comandos 
\series bold

\backslash
left
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! L ! 
\backslash
left
\end_layout

\end_inset

 y 
\series bold

\backslash
right
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! R ! 
\backslash
right
\end_layout

\end_inset

 (atajo 
\family sans
Alt+M
\begin_inset space ~
\end_inset

Paréntesis
\family default
), véase 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Tamaño-automático-de"

\end_inset

, o usando los comandos siguientes:
\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bmatrix
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

2
\series bold
×
\series default
2
\begin_inset space \thinspace{}
\end_inset

matriz
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
0 & \textrm{-}\mathrm{i}\\
\mathrm{i} & 0
\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Bmatrix
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

2×2
\begin_inset space \thinspace{}
\end_inset

matriz
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
0 & \textrm{-}\mathrm{i}\\
\mathrm{i} & 0
\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
pmatrix
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

2
\series bold
×
\series default
2
\begin_inset space \thinspace{}
\end_inset

matriz
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
0 & \textrm{-}\mathrm{i}\\
\mathrm{i} & 0
\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
vmatrix
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

2
\series bold
×
\series default
2
\begin_inset space \thinspace{}
\end_inset

matriz
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
0 & \textrm{-}\mathrm{i}\\
\mathrm{i} & 0
\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Vmatrix
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

2
\series bold
×
\series default
2
\begin_inset space \thinspace{}
\end_inset

matriz
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
0 & \textrm{-}\mathrm{i}\\
\mathrm{i} & 0
\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
matrix
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

2
\series bold
×
\series default
2
\begin_inset space \thinspace{}
\end_inset

matriz
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
0 & \textrm{-}\mathrm{i}\\
\mathrm{i} & 0
\end{array}\end{matrix}\raisebox{-5.3mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
Cuando se inserta p.
\begin_inset space \thinspace{}
\end_inset

e.
\begin_inset space ~
\end_inset


\series bold

\backslash
vmatrix
\series default
, aparece un recuadro azul entre dos líneas verticales donde se inserta
 la matriz.
\begin_inset Newline newline
\end_inset

Hay que tener en cuenta que las matrices decoradas ignoran el alineamiento
 vertical.
\end_layout

\begin_layout Standard
\begin_inset Note Greyedout
status open

\begin_layout Plain Layout

\series bold
Nota:
\series default
 LaTeX limita el número de columnas de matrices con decoraciones a 10.
 Si necesitas más de 10
\begin_inset space ~
\end_inset

columnas, debes añadir la siguiente línea en el preámbulo del documento:
\end_layout

\begin_layout Plain Layout

\series bold

\backslash
setcounter{MaxMatrixCols}{número}
\end_layout

\begin_layout Plain Layout
donde 
\emph on
número
\emph default
 es el número de columnas entre 11 y 99.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
Como todas las ecuaciones multilínea son matrices, la longitud 
\series bold

\backslash
arraycolsep
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! A ! 
\backslash
arraycolsep
\end_layout

\end_inset

, que se describe en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Separación-de-columnas"

\end_inset

, también se puede usar para cambiar la separación de las columnas en una
 matriz.
 Para cambiar la separación de las filas, se usa el comando 
\series bold

\backslash
arraystretch
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! A ! 
\backslash
arraystretch
\end_layout

\end_inset

 de la siguiente manera:
\end_layout

\begin_layout Standard

\series bold

\backslash
renewcommand{
\backslash
arraystretch}{factor de separación}
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! R ! 
\backslash
renewcommand
\end_layout

\end_inset


\end_layout

\begin_layout Standard
El comando 
\series bold

\backslash
renewcommand
\series default
 asigna el factor de separación al comando predefinido 
\series bold

\backslash
arraystretch
\series default
.
 Por ejemplo, para doblar la separación de las filas, pones factor 2.
 Además, éste se usa para todas las matrices siguientes.
 Para volver a la separación original, asigna factor 1 a 
\series bold

\backslash
arraystretch
\series default
.
\end_layout

\begin_layout Standard
Para poner matrices en línea se usa el comando 
\series bold

\backslash
smallmatrix
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! S ! 
\backslash
smallmatrix
\end_layout

\end_inset

.
 Al insertarlo aparece un recuadro azul con dos líneas de trazos en el que
 se inserta la matriz.
 
\end_layout

\begin_layout Standard
Esto es una matriz 
\begin_inset Formula $\left(\begin{smallmatrix}A & B\\
C & D
\end{smallmatrix}\right)$
\end_inset

 en línea.
\end_layout

\begin_layout Section
Delimitadores
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Delimitadores
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Delimitadores verticales
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Delimitadores ! verticales
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="9" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
(
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $($
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
{
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\{$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
[
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $[$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
langle
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\langle$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
lceil
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\lceil$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
lfloor
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\lfloor$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
/
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $/$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
|
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $|$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="9" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $)$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
}
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
]
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $]$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
rangle
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\rangle$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
rceil
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\rceil$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
rfloor
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\rfloor$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash

\backslash

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\backslash$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
|
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\|$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Note Greyedout
status open

\begin_layout Plain Layout

\series bold
Nota
\series default
: En modo TeX hay que usar el comando 
\series bold

\backslash
textbackslash
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! T ! 
\backslash
textbackslash
\end_layout

\end_inset

 para la barra invertida, porque si no el comando 
\series bold

\backslash

\backslash

\series default
 genera un salto de línea.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
El tamaño de los caracteres listados arriba se puede ajustar con los comandos
 descritos en las dos subsecciones siguientes.
 Cuando se emplean esos comandos se pueden usar directamente los caracteres
 < y > en vez de los comandos 
\series bold

\backslash
langle
\series default
 y 
\series bold

\backslash
rangle
\series default
.
 
\end_layout

\begin_layout Subsubsection
Tamaño manual de los delimitadores
\begin_inset CommandInset label
LatexCommand label
name "sub:Tamaño-manual-de"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Delimitadores ! tamaño manual
\end_layout

\end_inset


\end_layout

\begin_layout Standard
El tamaño de los delimitadores se puede determinar manualmente con los comandos
 LaTeX 
\series bold

\backslash
big
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! B ! 
\backslash
big
\end_layout

\end_inset

, 
\series bold

\backslash
Big
\series default
, 
\series bold

\backslash
bigg
\series default
, y 
\series bold

\backslash
Bigg
\series default
.
 
\series bold

\backslash
big
\series default
 indica el tamaño menor y 
\series bold

\backslash
Bigg
\series default
 el mayor.
\end_layout

\begin_layout Standard
Estos comandos se usan para resaltar niveles de delimitación:
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
todos los delimitadores de igual tamaño:
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $((A+B)(A-B))^{C}{\normalcolor \raisebox{-4mm}{}}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
así tiene mejor aspecto:
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para la segunda expresión se ha empleado el comando 
\series bold

\backslash
Big((A+B)(A-B)
\backslash
Big)^
\series default

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series bold
C
\series default
.
\end_layout

\begin_layout Standard
He aquí una visión conjunta de todos los tamaños y delimitadores:
\end_layout

\begin_layout Standard
\noindent
\align center

\backslash
Bigg(
\backslash
exp
\backslash
bigg<
\backslash
Big[
\backslash
big{
\backslash
ln(3x)
\backslash
big}^2
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\backslash
sen(x)
\backslash
Big]^
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\backslash
bigg>
\backslash
Bigg)^0,5
\begin_inset Formula 
\[
\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sen(x)\Big]^{A}\bigg>\Bigg)^{0,5}
\]

\end_inset


\end_layout

\begin_layout Standard
Además de los comandos 
\series bold

\backslash
big
\series default
 hay la variante 
\series bold

\backslash
bigm
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! B ! 
\backslash
bigm
\end_layout

\end_inset

, que añade un poco más de espacio entre el delimitador y su contenido,
 y la variante 
\series bold

\backslash
bigl
\series default
-
\series bold

\backslash
bigr
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! B ! 
\backslash
bigl - 
\backslash
bigr
\end_layout

\end_inset

, que no añade espacio adicional.
 La 
\emph on
l
\emph default
 al final del comando 
\series bold

\backslash
bigl 
\series default
es para el delimitador izquierdo, la 
\emph on
r
\emph default
 es para el delimitador derecho.
 Un delimitador izquierdo o derecho puede ser cada uno un delimitador de
 apertura o de cierre.
\end_layout

\begin_layout Standard
En el siguiente cuadro hay una comparación de las variantes:
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Bigm(
\backslash
bigm(
\backslash
ln(3x)
\backslash
bigm)^2
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series default

\backslash
Bigm)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Big(
\backslash
big(
\backslash
ln(3x)
\backslash
big)^2
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series default

\backslash
Big)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Bigl(
\backslash
bigl(
\backslash
ln(3x)
\backslash
bigr)^2
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series default

\backslash
Bigr)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.2mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bigl)
\backslash
ln(3x)
\backslash
bigr(
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Subsubsection
Tamaño automático de los delimitadores
\begin_inset CommandInset label
LatexCommand label
name "sub:Tamaño-automático-de"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Delimitadores ! tamaño automático
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Se pueden insertar delimitadores de tamaño variable con los comandos 
\series bold

\backslash
left
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! L ! 
\backslash
left
\end_layout

\end_inset

 y 
\series bold

\backslash
right
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! R ! 
\backslash
right
\end_layout

\end_inset

 o con el botón de la barra de ecuaciones 
\begin_inset Graphics
        filename ../../images/dialog-show_mathdelimiter.png
        scale 85

\end_inset

.
 El delimitador deseado se debe insertar directamente detrás de 
\series bold

\backslash
left
\series default
 y 
\series bold

\backslash
right
\series default
.
 El tamaño se calculará automáticamente después para la salida.
 
\end_layout

\begin_layout Standard
\noindent
\align center
delimitador normal: El comando 
\series bold

\backslash
ln(
\backslash
frac
\series default

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series bold
A
\begin_inset Formula $\downarrow$
\end_inset

C
\series default

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce
\end_layout

\end_inset


\series bold
)
\series default
 genera
\begin_inset Formula 
\[
\ln(\frac{A}{C})
\]

\end_inset


\end_layout

\begin_layout Standard
\noindent
\align center
delimitador multilínea: El comando 
\series bold

\backslash
ln
\backslash
left(
\backslash
frac
\series default

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series bold
A
\begin_inset Formula $\downarrow$
\end_inset

C
\series default

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series bold

\backslash
right)
\series default
 genera
\begin_inset Formula 
\[
\ln\left(\frac{A}{C}\right)
\]

\end_inset


\end_layout

\begin_layout Standard
En lugar de 
\series bold

\backslash
left
\series default
 y 
\series bold

\backslash
right
\series default
 se puede usar el atajo 
\family sans
Alt+M
\begin_inset space ~
\end_inset

Corchete
\family default
.
 Esto tiene la ventaja de que puedes ver inmediatamente en LyX el tamaño
 real del delimitador y además se genera el correspondiente delimitador
 de cierre.
\begin_inset Newline newline
\end_inset

El comando para el último ejemplo sería 
\series bold

\backslash
ln Alt+M
\series default
 
\series bold
(
\backslash
frac
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\downarrow$
\end_inset

C 
\end_layout

\begin_layout Standard
Para omitir uno de los dos delimitadores se inserta un punto.
 Por ejemplo, el comando 
\series bold

\backslash
left.
\backslash
frac
\series default

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series bold
A
\begin_inset Formula $\downarrow$
\end_inset

B
\series default

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series bold

\backslash
right}
\series default
 da lugar a:
\begin_inset Formula 
\[
\left.\frac{A}{B}\right\} 
\]

\end_inset


\end_layout

\begin_layout Standard
LyX convertirá los comandos 
\series bold

\backslash
left
\series default
 y 
\series bold

\backslash
right
\series default
 a su tamaño adecuado cuando el documento sea recargado y el delimitador
 omitido aparecerá como línea de trazos.
 
\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
Como todas las distribuciones habituales de LaTeX incluyen eTeX, una extensión
 de LaTeX, el comando 
\series bold

\backslash
middle
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! M ! 
\backslash
middle
\end_layout

\end_inset

 está también disponible para todos los delimitadores y límites.
 Con este comando la altura del siguiente carácter se adapta a la de los
 delimitadores circundantes, lo que es necesario, p.
\begin_inset space \thinspace{}
\end_inset

e., para vectores cuánticos: 
\begin_inset Formula 
\[
\left\langle \phi\;\middle|\; J=\frac{3}{2}\,,\, M_{J}\right\rangle 
\]

\end_inset


\end_layout

\begin_layout Standard
Para este tipo de vectores hay un paquete LaTeX específico que se describe
 en
\begin_inset space ~
\end_inset


\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Vectores-cuánticos"

\end_inset

.
\end_layout

\begin_layout Subsection
Delimitadores horizontales
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Delimitadores ! horizontales
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
raisebox{2.3mm}{
\end_layout

\end_inset


\backslash
overbrace
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A+B
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

^
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

3
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! O ! 
\backslash
overbrace
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\overbrace{A+B}^{3}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
raisebox{-2.2mm}{
\end_layout

\end_inset


\backslash
underbrace
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A+B
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

_5
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! U ! 
\backslash
underbrace
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\underbrace{A+B}_{5}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
overbrace
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\backslash
underbrace
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A+B_w
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

_7
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

^
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

C
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
En el último ejemplo no importa en qué orden se introducen los comandos
 
\series bold

\backslash
overbrace
\series default
 y 
\series bold

\backslash
underbrace
\series default
.
\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
Si un delimitador debe estar superpuesto a otro, hay que usar ecuaciones
 multilínea, como se describe en
\begin_inset space ~
\end_inset


\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Ecuaciones-multilínea"

\end_inset

:
\begin_inset Formula 
\begin{eqnarray*}
A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
 &  & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
\end{eqnarray*}

\end_inset

En la primera fila se insertan la ecuación y la primera llave.
 Aquí es importante insertar el comando de espacio
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Los comandos para espacios se explican en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Espacio-predefinido"

\end_inset


\end_layout

\end_inset

 
\series bold

\backslash
:
\series default
 antes de la primera
\series bold
 
\series default

\begin_inset Formula $d$
\end_inset

, porque la llave que termina detrás de 
\begin_inset Formula $q$
\end_inset

 impide que el siguiente 
\begin_inset Quotes fld
\end_inset

+
\begin_inset Quotes frd
\end_inset

 esté rodeado de espacio.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Debido a que la llave no es considerada como carácter, véase 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Operadores-binarios"

\end_inset


\end_layout

\end_inset

 En la segunda fila se inserta la segunda llave: como debe comenzar antes
 de 
\begin_inset Formula $b$
\end_inset

 se inserta antes el comando 
\series bold

\backslash
hphantom{gggg+
\backslash
:}
\series default
.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Más sobre 
\series bold

\backslash
hphantom
\series default
 en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Espacios-reservados"

\end_inset


\end_layout

\end_inset

 Ese espacio es necesario porque el signo 
\begin_inset Quotes fld
\end_inset

+
\begin_inset Quotes frd
\end_inset

 va seguido de un espacio en la ecuación.
 La llave se coloca bajo el comando 
\series bold

\backslash
hphantom{bbqq+dddd}
\series default
.
 
\end_layout

\begin_layout Standard
Resulta más complicado cuando una llave debe solapar a otra como en el siguiente
 ejemplo:
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
setlength{
\backslash
jot}{-6pt}
\end_layout

\end_inset


\begin_inset Formula 
\begin{eqnarray*}
 &  & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
\end{eqnarray*}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
setlength{
\backslash
jot}{3pt}
\end_layout

\end_inset

La primera fila de la ecuación es igual que la segunda fila del ejemplo
 anterior, con la diferencia de que la llave está encima.
 La segunda fila contiene la ecuación junto con la segunda llave.
 Para evitar que haya demasiado espacio entre la llave superior en la primera
 fila y la ecuación hay que reducirlo.
 Esto no es fácil de hacer debido a un fallo de LyX.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
\begin_inset CommandInset href
LatexCommand href
name "LyX-bug #1505"
target "http://www.lyx.org/trac/ticket/1505"

\end_inset


\end_layout

\end_inset

 Una solución es cambiar la separación global de filas en la ecuación, 
\series bold

\backslash
jot
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! J ! 
\backslash
jot
\end_layout

\end_inset

, en -6
\begin_inset space \thinspace{}
\end_inset

pt insertando antes de la ecuación el comando 
\series bold

\backslash
setlength{
\backslash
jot}{-6pt}
\series default
 en modo TeX.
 Después de la ecuación se vuelve al valor normal 3
\begin_inset space \thinspace{}
\end_inset

pt de 
\series bold

\backslash
jot
\series default
 usando el mismo comando.
 Más información sobre separación de filas en ecuaciones en
\begin_inset space ~
\end_inset


\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Separación-de-líneas"

\end_inset

.
\end_layout

\begin_layout Section
Flechas
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Flechas
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Las flechas se pueden insertar con el botón 
\begin_inset Graphics
        filename ../../images/math/leftarrow.png
        scale 85

\end_inset

 de la barra de ecuaciones o mediante los comandos listados en las subsecciones
 siguientes.
\end_layout

\begin_layout Subsection
Flechas horizontales
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Flechas ! horizontales
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
gets
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\gets$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Leftarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Leftarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
longleftarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\longleftarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Longleftarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Longleftarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
leftharpoonup
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\leftharpoonup$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
leftharpoondown
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\leftharpoondown$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
hookleftarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\hookleftarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
to
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\to$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Rightarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Rightarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
longrightarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\longrightarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Longrightarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Longrightarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
rightharpoonup
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\rightharpoonup$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
rightharpoondown
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\rightharpoondown$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
hookrightarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\hookrightarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Standard
\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="6" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
leftrightarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\leftrightarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Leftrightarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Leftrightarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
longleftrightarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\longleftrightarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Longleftrightarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Longleftrightarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
rightleftharpoons
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\rightleftharpoons$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hspace{}
\length 25pt
\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
mapsto
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\mapsto$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
longmapsto
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\longmapsto$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
leadsto
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\leadsto$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
dasharrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\dasharrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
Las flechas que se utilizan como acentos, p.
\begin_inset space \thinspace{}
\end_inset

e.
 en vectores, se describen en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Acentos"

\end_inset

.
 
\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
Además hay las flechas etiquetadas
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Flechas ! etiquetadas
\end_layout

\end_inset

 
\series bold

\backslash
xleftarrow
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! X ! 
\backslash
xleftarrow
\end_layout

\end_inset

 y 
\series bold

\backslash
xrightarrow
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! X ! 
\backslash
xrightarrow
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
vspace{4mm}
\end_layout

\end_inset


\end_layout

\end_inset

.
 Cuando se inserta uno de estos comandos en una ecuación aparece una flecha
 con dos marcos azules donde se puede insertar la etiqueta.
 La longitud de la flecha se adapta a la anchura de la etiqueta.
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
F(a)
\backslash
xleftarrow
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

x=a
\begin_inset Formula $\downarrow$
\end_inset

x>0
\begin_inset Formula $\to$
\end_inset

F(x)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
F(x)
\backslash
xrightarrow
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

x=a
\begin_inset Formula $\downarrow$
\end_inset

x>0
\begin_inset Formula $\to$
\end_inset

F(a)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Subsection
Flechas verticales y diagonales
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Flechas ! diagonales
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Flechas ! verticales
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="7" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
uparrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\uparrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Uparrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Uparrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
updownarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\updownarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Updownarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Updownarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Downarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Downarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
downarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\downarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
nearrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\nearrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
searrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\searrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
swarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\swarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
nwarrow
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\nwarrow$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
Las flechas verticales también se pueden usar como delimitadores junto con
 los comandos descritos en
\begin_inset space ~
\end_inset


\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Tamaño-manual-de"

\end_inset

 y 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Tamaño-automático-de"

\end_inset

.
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Acentos
\begin_inset CommandInset label
LatexCommand label
name "sec:Acentos"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Acentos
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Los acentos se pueden insertar con el botón 
\begin_inset Graphics
        filename ../../images/math/hat.png
        scale 85

\end_inset

 o mediante los comandos listados en las siguientes subsecciones.
\end_layout

\begin_layout Subsection
Acentos para un carácter
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
texorpdfstring{
\end_layout

\end_inset


\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Para acentos en texto, véase 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Acentos-en-texto"

\end_inset


\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}{}
\end_layout

\end_inset


\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
texorpdfstring
\series default
 se usa para evitar que la nota al pie aparezca en los marcadores PDF.
\end_layout

\begin_layout Plain Layout
Más sobre 
\series bold

\backslash
texorpdfstring
\series default
 en la sección 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Ecuaciones-en-encabezados"

\end_inset

.
\end_layout

\end_inset


\begin_inset CommandInset label
LatexCommand label
name "sub:Acentos-para-un"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Acentos ! para un carácter
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
dot
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\dot{A}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ddot
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
dddot
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ddddot
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
vec
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Vectores
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\vec{A}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bar
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\bar{A}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
mathring
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="7" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
tilde
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
hat
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\hat{A}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
check
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\check{A}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
acute
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\acute{A}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
grave
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\grave{A}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
breve
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\breve{A}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
En ecuaciones se pueden insertar acentos como 
\begin_inset Quotes fld
\end_inset

é
\begin_inset Quotes frd
\end_inset

 directamente.
 LyX los transformará al comando de acento correspondiente.
 Para poner diéresis
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Dieresis@Diéresis
\end_layout

\end_inset

 es mejor insertar comillas antes de la vocal.
 Estos dos caracteres son considerados por LaTeX como 
\emph on
un solo
\emph default
 carácter si la parte de la ecuación con la diéresis se marca en idioma
 alemán.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
O algún otro idioma que use acentos, p.
\begin_inset space \thinspace{}
\end_inset

e.
 catalán.
 Aunque esto no funciona en español por algún conflicto con el estilo 
\series bold
spanish
\series default
 de 
\series bold
babel
\series default
, no es necesario: se puede escribir 
\begin_inset Formula $ï$
\end_inset

 en una ecuación igual que se hace en texto normal, ï.
 (
\emph on
N.
\begin_inset space \thinspace{}
\end_inset

del t.
\emph default
)
\end_layout

\end_inset

 A diferencia de 
\series bold

\backslash
ddot
\series default
, con este método se generan diéresis 
\begin_inset Quotes fld
\end_inset

reales
\begin_inset Quotes frd
\end_inset

, como se demuestra en el siguiente ejemplo:
\begin_inset VSpace -2mm
\end_inset


\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador.
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
ï
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $ï$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ddot
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

i
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Otra ventaja frente a 
\series bold

\backslash
ddot
\series default
 es que la diéresis puede convertirse directamente a texto matemático, porque
 los anteriores comandos para acentos 
\emph on
no están permitidos en texto matemático
\emph default
.
 Para convertir un carácter acentuado a texto matemático, se debe convertir
 sólo el carácter bajo el acento.
 Esto también se aplica para otras conversiones, p.
\begin_inset space \thinspace{}
\end_inset

e.
\begin_inset space ~
\end_inset

cursiva o negrita.
\end_layout

\begin_layout Standard
En texto matemático, la diéresis y otros acentos pueden insertarse directamente.
\end_layout

\begin_layout Subsection
Acentos para operadores
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Acentos ! en operadores
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Con los comandos 
\series bold

\backslash
overset
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! O ! 
\backslash
overset
\end_layout

\end_inset

 y 
\series bold

\backslash
underset
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! U ! 
\backslash
underset
\end_layout

\end_inset

 se pueden colocar caracteres sobre o bajo un operador, respectivamente.
 Con el comando 
\series bold

\backslash
sideset
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! S ! 
\backslash
sideset
\end_layout

\end_inset

 se pueden poner caracteres delante y detrás de un operador.
 El esquema del comando es:
\end_layout

\begin_layout Standard

\series bold

\backslash
sideset{carácter
\series default
 
\series bold
anterior}{carácter posterior}
\end_layout

\begin_layout Standard

\series bold

\backslash
sideset
\series default
 siempre debe estar delante del operador que debe acentuarse.
 Se puede acentuar con varios caracteres e incluso con otros operadores
 y símbolos.
 Para colocar con
\series bold
 
\backslash
sideset
\series default
 caracteres sólo detrás del operador, por ejemplo, no se escribe nada en
 el primer par de llaves, pero sin quitarlas.
 
\end_layout

\begin_layout Standard
Por ejemplo, el comando 
\series bold

\backslash
sideset{
\begin_inset Formula $\to$
\end_inset


\backslash
{
\series default
'
\series bold

\begin_inset Formula $\to$
\end_inset


\backslash
sum_k=1
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series default
^
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

n
\series default
 genera:
\begin_inset Formula 
\[
\sideset{}{'}\sum_{k=1}^{n}
\]

\end_inset


\end_layout

\begin_layout Standard
El comando 
\series bold

\backslash
overset
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\backslash
maltese
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series default

\begin_inset Formula $\uparrow$
\end_inset


\series bold
a
\series default
 genera:
\begin_inset Formula 
\[
\overset{a}{\maltese}
\]

\end_inset


\end_layout

\begin_layout Standard
Como se ve en el último ejemplo, con 
\series bold

\backslash
overset
\series default
 y 
\series bold

\backslash
underset
\series default
 también se pueden acentuar símbolos y caracteres; con 
\series bold

\backslash
sideset
\series default
 esto no es posible.
\end_layout

\begin_layout Subsection
Acentos para varios caracteres
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Acentos ! en varios caracteres
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
overleftarrow
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
underleftarrow
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
overleftrightarrow
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
underleftrightarrow
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
overrightarrow
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
underrightarrow
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
widetilde
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
widehat
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
Con estos comandos se pueden acentuar tantos caracteres como quieras.
 Pero los acentos 
\series bold

\backslash
widetilde
\series default
 y 
\series bold

\backslash
widehat
\series default
 sólo pueden abarcar tres caracteres en la salida, como se muestra en este
 ejemplo:
\begin_inset Formula 
\[
\widetilde{A+B=C-D}
\]

\end_inset


\end_layout

\begin_layout Standard
Con los comandos 
\series bold

\backslash
overset
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! O ! 
\backslash
overset
\end_layout

\end_inset

 y 
\series bold

\backslash
underset
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! U ! 
\backslash
underset
\end_layout

\end_inset

, descritos en la subsección anterior, también se pueden acentuar varios
 caracteres.
 El comando 
\series bold

\backslash
underset
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\begin_inset Formula $\downarrow$
\end_inset

***
\series default
 da:
\begin_inset Formula 
\[
\underset{***}{A=B}
\]

\end_inset


\end_layout

\begin_layout Section
Espacios
\begin_inset CommandInset label
LatexCommand label
name "sec:Espacio"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Espacio ! horizontal
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Espacio predefinido
\begin_inset CommandInset label
LatexCommand label
name "sub:Espacio-predefinido"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Espacio ! horizontal ! predefinido
\end_layout

\end_inset


\end_layout

\begin_layout Standard
A veces es necesario insertar espacio horizontal en una ecuación.
 Esto se hace insertando un espacio protegido (atajo 
\family sans
Ctrl+Espacio
\family default
).
 Aparece un 
\begin_inset Quotes fld
\end_inset


\color black

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\color inherit

\begin_inset Quotes frd
\end_inset

, y pulsando 
\family sans
Espacio
\family default
 sucesivas veces se pueden seleccionar hasta ocho diferentes tamaños de
 espacio.
 También se pueden insertar espacios mediante el botón 
\begin_inset Graphics
        filename ../../images/math/space.png
        scale 85

\end_inset

 de la barra de ecuaciones o con comandos especiales.
 Independientemente del comando insertado, se puede seleccionar un nuevo
 tamaño pulsando acto seguido 
\family sans
Espacio.
 
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset VSpace -5mm
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="7">
<features tabularvalignment="middle">
<column alignment="center" valignment="middle" width="6.8cm">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
,
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
:
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
;
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
quad
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
qquad
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
!
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Número de pulsaciones de 
\family sans
Espacio
\family default
 tras insertar el espacio protegido
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
2
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
3
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
4
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
5
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A\, B$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A\: B$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A\; B$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A\quad B$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A\qquad B$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A\! B$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
El último tamaño parece no generar espacio.
 A diferencia de los otros se muestra en rojo en LyX, porque es un espacio
 negativo.
 Hay otros dos espacios negativos:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="3">
<features tabularvalignment="middle">
<column alignment="center" valignment="middle" width="6.8cm">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
negmedspace
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
negthickspace
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Número de pulsaciones de 
\family sans
Espacio
\family default
 tras insertar el espacio protegido
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
6
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
7
\end_layout

\end_inset
</cell>
</row>
<row>
<cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A\negmedspace B$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A\negthickspace B$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Los espacios negativos pueden llegar a solapar unos caracteres con otros.
 Así, se pueden usar para forzar ligaduras, lo que es apropiado, por ejemplo,
 para operadores suma: 
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
sum
\backslash
sum
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

f_kl
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
sum
\backslash
negmedspace
\backslash
sum
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

f_kl
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Relaciones como por ejemplo el signo igual siempre están rodeadas por espacios.
 Para suprimirlos, el signo igual se coloca entre llaves TeX.
 El siguiente ejemplo lo ilustra:
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
ecuación normal
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A=B$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\begin_inset Formula $\raisebox{5mm}{}$
\end_inset

ecuación sin espacio
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A{=}B$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
El comando para la segunda ecuación es: 
\series bold
A
\backslash
{=
\begin_inset Formula $\rightarrow$
\end_inset

B
\series default
 
\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
Para las unidades físicas hacen falta espacios, porque entre el valor y
 su unidad se pone un espacio más pequeño que el normal.
 Para unidades en el texto se inserta con el menú 
\family sans
Insertar\SpecialChar \menuseparator
Formato\SpecialChar \menuseparator
Espacio
\begin_inset space ~
\end_inset

delgado
\family default
 (atajo 
\family sans
Ctrl+Mayúscula+Espacio
\family default
).
\end_layout

\begin_layout Standard
Un ejemplo para visualizar la diferencia:
\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="left" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
24 kW
\begin_inset Formula $\cdot$
\end_inset

h
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
espacio entre valor y unidad 
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
24
\begin_inset space \thinspace{}
\end_inset

kW
\begin_inset Formula $\cdot$
\end_inset

h
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
espacio delgado entre valor y unidad
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Subsection
Espacio variable
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
texorpdfstring{
\end_layout

\end_inset


\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Para espacio vertical en ecuaciones véase 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Separación-de-líneas"

\end_inset


\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}{}
\end_layout

\end_inset


\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\backslash
texorpdfstring se usa para evitar que la nota al pie aparezca en los marcadores
 PDF.
\end_layout

\begin_layout Plain Layout
Más sobre 
\backslash
texorpdfstring en la sección 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Ecuaciones-en-encabezados"

\end_inset

.
\end_layout

\end_inset


\begin_inset CommandInset label
LatexCommand label
name "sub:Espacio-variable"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Espacio ! horizontal ! variable
\end_layout

\end_inset


\end_layout

\begin_layout Standard
En LyX se puede insertar espacio con una longitud definida con el comando
 
\series bold

\backslash
hspace
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! H ! 
\backslash
hspace
\end_layout

\end_inset

.
 Aparece un 
\begin_inset Quotes fld
\end_inset


\color black

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\color inherit

\begin_inset Quotes frd
\end_inset

 largo.
 La longitud se puede ajustar haciendo clic izquierdo sobre el 
\begin_inset Quotes fld
\end_inset


\color black

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\color inherit

\begin_inset Quotes frd
\end_inset

.
 La longitud también puede ser negativa.
 Para insertar en una ecuación tanto espacio como esté disponible se usa
 el comando 
\series bold

\backslash
hfill
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! H ! 
\backslash
hfill
\end_layout

\end_inset

.
\begin_inset VSpace -1mm
\end_inset


\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando (
\backslash
hspace longitud)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
A=B
\backslash
hspace
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\begin_inset Formula $\to$
\end_inset

A
\backslash
not=C (3
\begin_inset space \thinspace{}
\end_inset

cm)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A=B\hspace{3cm}A\not=C$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
A
\backslash
hspace
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\begin_inset Formula $\to$
\end_inset

A
\backslash
not=A (-1
\begin_inset space \thinspace{}
\end_inset

mm)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A\hspace{-1mm}A\not=A$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
A=A
\backslash
hfill
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

B=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A=A\hfill B=B$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
En el último ejemplo el espacio disponible viene dado por la entrada más
 larga de columna en el cuadro.
 En una ecuación en línea el espacio depende de la longitud de la línea
 en la que se inserta 
\series bold

\backslash
hfill
\series default
.
 Así, cuando la línea ocupa toda la anchura no se creará espacio.
 
\series bold

\backslash
hfill
\series default
 sólo tiene efecto en ecuaciones presentadas cuando se usa el estilo 
\series bold
Sangrado
\series default
.
 (Los estilos de ecuaciones se explican en
\begin_inset space ~
\end_inset


\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Estilos-de-ecuación"

\end_inset

).
\end_layout

\begin_layout Standard
Además de 
\series bold

\backslash
hfill
\series default
 hay los comandos 
\series bold

\backslash
dotfill
\series default
 y 
\series bold

\backslash
hrulefill
\series default
 que llenan el espacio con un patrón, véase un ejemplo en
\begin_inset space ~
\end_inset


\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Puntos"

\end_inset

.
\end_layout

\begin_layout Standard
Para texto se puede insertar espacio variable con el menú 
\family sans
Insertar\SpecialChar \menuseparator
Formato\SpecialChar \menuseparator
Espacio
\begin_inset space ~
\end_inset

horizontal
\family default
:
\end_layout

\begin_layout Standard
En esta línea hay un espacio
\begin_inset space \hspace{}
\length 2cm
\end_inset

de 2
\begin_inset space \thinspace{}
\end_inset

cm.
\end_layout

\begin_layout Standard
En esta línea hay un
\begin_inset space \hfill{}
\end_inset

espacio máximo.
\end_layout

\begin_layout Subsection
Espacio adicional en ecuaciones en línea
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Espacio ! adicional en línea
\end_layout

\end_inset


\end_layout

\begin_layout Standard
El espacio que rodea a una ecuación en línea se puede ajustar con la longitud
 
\series bold

\backslash
mathsurround
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! M ! 
\backslash
mathsurround
\end_layout

\end_inset

.
 El valor de una longitud se establece con el comando 
\series bold

\backslash
setlength
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! S ! 
\backslash
setlength
\end_layout

\end_inset

 según el siguiente esquema:
\end_layout

\begin_layout Standard

\series bold

\backslash
setlength{nombre de la longitud}{valor}
\end_layout

\begin_layout Standard
Para poner a 
\series bold

\backslash
mathsurround
\series default
 un valor de 5
\begin_inset space \thinspace{}
\end_inset

mm, se inserta el comando
\end_layout

\begin_layout Standard

\series bold

\backslash
setlength{
\backslash
mathsurround}{5mm}
\end_layout

\begin_layout Standard
en modo TeX.
 Se establecerá un espacio de 5
\begin_inset space \thinspace{}
\end_inset

mm alrededor de todas las ecuaciones en línea:
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
setlength{
\backslash
mathsurround}{5mm}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
En esta línea hay una ecuación 
\begin_inset Formula $A=B$
\end_inset

 rodeada por espacios de 5
\begin_inset space \thinspace{}
\end_inset

mm.
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
setlength{
\backslash
mathsurround}{0mm}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para volver al espacio predeterminado, 
\series bold

\backslash
mathsurround
\series default
 se restablece al valor 0
\begin_inset space \thinspace{}
\end_inset

pt.
\end_layout

\begin_layout Section
Marcos y bordes
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Marcos
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Los marcos para texto se describen en el capítulo 
\emph on
Marcos
\emph default
 del manual 
\emph on
Objetos insertados
\emph default
.
\end_layout

\begin_layout Subsection
Marcos con bordes
\begin_inset CommandInset label
LatexCommand label
name "sub:Marcos-con-bordes"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Marcos ! con bordes
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Es posible enmarcar ecuaciones o partes de ellas con los comandos 
\series bold

\backslash
fbox
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! F ! 
\backslash
fbox
\end_layout

\end_inset

 y 
\series bold

\backslash
boxed
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! B ! 
\backslash
boxed
\end_layout

\end_inset

.
\end_layout

\begin_layout Standard
Cuando uno de estos comandos se inserta en una ecuación, aparece un recuadro
 azul en un marco donde se introducen partes de una ecuación.
 Para 
\series bold

\backslash
fbox
\series default
 hay que generar una ecuación adicional con 
\family sans
Ctrl+M
\family default
 dentro del recuadro, porque si no el contenido del mismo sería considerado
 texto matemático.
 Si se usa 
\series bold

\backslash
boxed
\series default
 la nueva ecuación se genera automáticamente dentro del marco.
\end_layout

\begin_layout Standard
El comando 
\series bold

\backslash
fbox
\series default
 no es adecuado para enmarcar ecuaciones en modo presentación, porque la
 ecuación tendría siempre el tamaño del texto.
 Por otra parte, 
\series bold

\backslash
fboxed
\series default
 no es adecuada para enmarcar ecuaciones en línea porque la ecuación tendría
 siempre el tamaño de una ecuación presentada.
\end_layout

\begin_layout Standard
El comando 
\series bold

\backslash
framebox
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! F ! 
\backslash
framebox
\end_layout

\end_inset

 es una extensión de 
\series bold

\backslash
fbox
\series default
, que permite especificar además la anchura del marco y la alineación.
 
\series bold

\backslash
framebox
\series default
 se usa con el siguiente esquema: 
\end_layout

\begin_layout Standard

\series bold

\backslash
framebox[anchura del marco][posición]{contenido del cuadro}
\end_layout

\begin_layout Standard
La posición puede ser 
\emph on
l
\emph default
 o 
\emph on
r
\emph default
, 
\emph on
l
\emph default
 alinea la ecuación a la izquierda del marcro, 
\emph on
r
\emph default
 la alinea a la derecha.
 Si no se da posición la ecuación será centrada.
\begin_inset Newline newline
\end_inset

Si no se pone anchura tampoco puede darse posición.
 En este caso la anchura del borde se ajusta al contenido del cuadro, como
 con 
\series bold

\backslash
fbox
\series default
.
 
\end_layout

\begin_layout Standard
Cuando se inserta el comando 
\series bold

\backslash
framebox
\series default
 aparece un recuadro con tres marcos azules.
 Los dos primeros marcos están encerrados entre corchetes e indican los
 dos argumentos opcionales.
 El tercer marco es para partes de la ecuación, como para 
\series bold

\backslash
fbox
\series default
.
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
fbox
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\family sans
Ctrl+M
\family default
 
\backslash
int
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
boxed
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\backslash
int
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
A+
\backslash
fbox
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
framebox
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

20mm
\begin_inset Formula $\to$
\end_inset


\begin_inset Formula $\to$
\end_inset


\family sans
Ctrl+M
\family default
 
\backslash
frac
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\downarrow$
\end_inset

B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{6mm}{}$
\end_inset


\begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
\end_inset


\begin_inset Formula $\raisebox{-4mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
El grosor del borde también se puede ajustar.
 Para ello hay que insertar los siguientes comandos en modo TeX antes de
 la fórmula:
\end_layout

\begin_layout Standard

\series bold

\backslash
fboxrule
\series default
 
\series bold

\begin_inset Quotes fld
\end_inset

grosor
\begin_inset Quotes frd
\end_inset


\series default
 
\series bold

\backslash
fboxsep
\series default
 
\series bold

\begin_inset Quotes fld
\end_inset

distancia
\begin_inset Quotes frd
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Quotes fld
\end_inset

distancia
\begin_inset Quotes frd
\end_inset

 especifica la distancia mínima entre el borde y el primer carácter en el
 cuadro.
 Un ejemplo de esto es la siguiente ecuación enmarcada:
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
fboxrule 2mm 
\backslash
fboxsep 3mm
\end_layout

\end_inset


\begin_inset Formula 
\[
\boxed{A+B=C}
\]

\end_inset


\end_layout

\begin_layout Standard
Delante de esta ecuación se han insertado los comandos
\end_layout

\begin_layout Standard

\series bold

\backslash
fboxrule
\series default
 
\series bold
2mm
\series default
 
\series bold

\backslash
fboxsep
\series default
 
\series bold
3mm
\end_layout

\begin_layout Standard
en modo TeX.
 Los valores dados se usan para todos los marcos siguientes.
\end_layout

\begin_layout Standard
Para volver al tamaño estándar del marco se inserta el comando
\end_layout

\begin_layout Standard

\series bold

\backslash
fboxrule
\series default
 
\series bold
0.4pt
\series default
 
\series bold

\backslash
fboxsep
\series default
 
\series bold
3pt
\series default

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
fboxrule 0.4pt 
\backslash
fboxsep 3pt
\end_layout

\end_inset


\end_layout

\begin_layout Standard
en modo TeX antes de la ecuación siguiente.
\end_layout

\begin_layout Subsection
Marcos sin bordes
\begin_inset CommandInset label
LatexCommand label
name "sub:Marcos-sin-bordes"

\end_inset


\begin_inset Index idx
status open

\begin_layout Plain Layout
Marcos ! sin borde
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para marcos sin borde hay los comandos: 
\series bold

\backslash
mbox
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! M ! 
\backslash
mbox
\end_layout

\end_inset

, 
\series bold

\backslash
makebox
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! M ! 
\backslash
makebox
\end_layout

\end_inset

 y 
\series bold

\backslash
raisebox
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! R ! 
\backslash
raisebox
\end_layout

\end_inset

.
\end_layout

\begin_layout Standard
Con 
\series bold

\backslash
raisebox
\series default
 se puede poner un marco subíndice o superíndice, pero a diferencia de los
 normales, los caracteres en el marco mantienen su tamaño de tipografía.
 
\series bold

\backslash
raisebox
\series default
 se usa con el siguiente esquema: 
\end_layout

\begin_layout Standard

\series bold

\backslash
raisebox{altura}{contenido del marco}
\end_layout

\begin_layout Standard
Cuando el marco tenga que contener una ecuación, hace falta una ecuación
 extra, como con 
\series bold

\backslash
fbox
\series default
.
 
\begin_inset Note Greyedout
status open

\begin_layout Plain Layout

\series bold
Nota
\series default
: Para
\series bold

\backslash
raisebox
\series default
 se ha creado esta ecuación extra tecleando 
\family sans
Ctrl+M
\family default
 dos veces en vez de una porque LyX aún no soporta 
\series bold

\backslash
raisebox
\series default
 directamente.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
H
\backslash
raisebox{2mm
\begin_inset Formula $\to$
\end_inset


\backslash
{al
\begin_inset Formula $\to$
\end_inset

 lo
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $H\raisebox{2mm}{al}lo$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
H
\backslash
raisebox{-2mm
\begin_inset Formula $\to$
\end_inset


\backslash
{al
\begin_inset Formula $\to$
\end_inset

lo
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $H\raisebox{-2mm}{al}lo$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
A=
\backslash
raisebox{-2mm
\begin_inset Formula $\to$
\end_inset


\backslash
{
\family sans
Ctrl+M Ctrl+M
\family default
 
\backslash
sqrt
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

B 
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
El comando 
\series bold

\backslash
mbox
\series default
 es equivalente a 
\series bold

\backslash
fbox
\series default
 y 
\series bold

\backslash
makebox
\series default
 es equivalente a 
\series bold

\backslash
framebox
\series default
, con la diferencia de que no hay marco.
\end_layout

\begin_layout Subsection
Marcos coloreados
\begin_inset CommandInset label
LatexCommand label
name "sub:Marcos-coloreados"

\end_inset


\begin_inset Index idx
status open

\begin_layout Plain Layout
Marcos ! coloreados
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para poder usar todos los comandos explicados en esta sección hay que cargar
 en el preámbulo LaTeX el paquete LaTeX 
\series bold
color
\series default

\begin_inset Foot
status collapsed

\begin_layout Plain Layout
El paquete LaTeX 
\series bold
color
\series default
 forma parte de toda distribución LaTeX estándar.
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Paquetes ! color
\end_layout

\end_inset

, con la línea
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Cuando hay texto coloreado con un color predefinido en alguna parte del
 documento, LyX carga automáticamente el paquete LaTeX 
\series bold
color
\series default
.
 Por tanto es posible que el paquete sea cargado dos veces, pero esto no
 origina problemas.
\end_layout

\end_inset


\begin_inset Note Note
status collapsed

\begin_layout Plain Layout
Para evitar que el paquete sea cargado dos veces se ha insertado una macro
 en el preámbulo LaTeX.
\end_layout

\end_inset


\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage{color}
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
Para colorear marcos se usa el comando 
\series bold

\backslash
colorbox
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! C ! 
\backslash
colorbox
\end_layout

\end_inset

 con el siguiente esquema:
\end_layout

\begin_layout Standard

\series bold

\backslash
colorbox{color}{contenido del marco}
\end_layout

\begin_layout Standard
El contenido del marco puede ser otro marco, y también un 
\backslash

\series bold
colorbox
\series default
 puede ser parte de otro marco (véanse los ejemplos 2º y 3º).
 Si el marco debe contener una ecuación debe crearse una ecuación extra,
 como con 
\series bold

\backslash
raisebox
\series default
.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Esto también se aplica para el comando 
\series bold

\backslash
fcolorbox
\series default
.
\end_layout

\end_inset

 
\end_layout

\begin_layout Standard
Se puede elegir uno de los siguientes colores predefinidos:
\end_layout

\begin_layout Standard

\series bold
black
\series default
, 
\series bold
blue
\series default
, 
\series bold
cyan
\series default
, 
\series bold
green
\series default
, 
\series bold
magenta
\series default
, 
\series bold
red
\series default
, 
\series bold
white
\series default
, 
\series bold
yellow
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
colorbox{yellow
\begin_inset Formula $\to$
\end_inset


\backslash
{A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
colorbox{green
\begin_inset Formula $\to$
\end_inset


\backslash
{
\backslash
fbox
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
fbox
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\backslash
colorbox{green
\begin_inset Formula $\to$
\end_inset


\backslash
{
\family sans
Ctrl+M Ctrl+M
\family default
 
\backslash
int
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

C=D
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard

\series bold

\backslash
colorbox
\series default
 sólo colorea el marco pero no los caracteres.
 Para colorear todos los caracteres se selecciona toda la ecuación y se
 elige un color en el diálogo 
\family sans
Estilo
\begin_inset space ~
\end_inset

del
\begin_inset space ~
\end_inset

texto
\family default
.
 El diálogo puede abrirse con el botón 
\begin_inset Graphics
        filename ../../images/dialog-show_character.png
        scale 85

\end_inset

 de la barra de herramientas o con el menú 
\family sans
Editar\SpecialChar \menuseparator
Estilo
\begin_inset space ~
\end_inset

del
\begin_inset space ~
\end_inset

texto\SpecialChar \menuseparator
Personalizado
\family default
.
 El número de la ecuación tendrá en ese caso el mismo color que la ecuación.
 Si el número de la ecuación debe tener otro color que el de los caracteres
 de la ecuación, el color debe cambiarse dentro de la ecuación.
\end_layout

\begin_layout Standard
Un ejemplo:
\color red

\begin_inset Formula 
\begin{equation}
{\color{red}\int A=B}\label{eq:rojo}
\end{equation}

\end_inset


\color green

\begin_inset Formula 
\begin{equation}
{\color{green}{\color{red}\int A=B}}\label{eq:rojoverde}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
La ecuación 
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:rojo"

\end_inset

 está toda coloreada en rojo.
\begin_inset Newline newline
\end_inset

La ecuación 
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:rojoverde"

\end_inset

 se ha coloreado en primer lugar toda en verde para colorear el número de
 la ecuación.
 Posteriormente se han coloreado en rojo los caracteres.
\family sans

\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
Para colorear diferente el borde y el marcose usa el comando 
\series bold

\backslash
fcolorbox
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! F ! 
\backslash
fcolorbox
\end_layout

\end_inset

 con el siguiente esquema:
\end_layout

\begin_layout Standard

\series bold

\backslash
fcolorbox{color del borde}{color}{contenido del marco}
\end_layout

\begin_layout Standard
Así pues 
\series bold

\backslash
fcolorbox
\series default
 es una extensión del comando 
\series bold

\backslash
colorbox
\series default
.
 La anchura del borde se establece, como para 
\series bold

\backslash
framebox
\series default
, con 
\series bold

\backslash
fboxrule
\series default
 y 
\series bold

\backslash
fboxsep
\series default
.
 Un ejemplo:
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
fboxrule 1mm 
\backslash
fboxsep 1mm
\end_layout

\end_inset


\begin_inset Formula 
\[
\fcolorbox{cyan}{magenta}{A=B}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
fboxrule 0.4pt 
\backslash
fboxsep 3pt
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Esta ecuación se ha compuesto con el comando
\begin_inset Newline newline
\end_inset


\series bold

\backslash
fcolorbox{cyan
\begin_inset Formula $\to$
\end_inset


\backslash
{magenta
\begin_inset Formula $\to$
\end_inset


\backslash
{A=B
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
Para usar colores distintos de los predefinidos deben ser definidos previamente.
\end_layout

\begin_layout Standard
Por ejemplo, se puede definir el color 
\begin_inset Quotes fld
\end_inset


\series bold
verdeoscuro
\series default

\begin_inset Quotes frd
\end_inset

 con la línea de preámbulo LaTeX:
\end_layout

\begin_layout Standard

\series bold

\backslash
definecolor{verdeoscuro}{cmyk}{0.5, 0, 1, 0.5}
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! D ! 
\backslash
definecolor
\end_layout

\end_inset


\end_layout

\begin_layout Standard

\series bold
cmyk
\series default
 es el espacio de color referido a los colores 
\series bold
cyan
\series default
, 
\series bold
magenta
\series default
, 
\series bold
yellow
\series default
 y 
\series bold
black
\series default
.
 Los cuatro números separados por coma son el factor de cuota para los colores
 correspondientes del espacio de color.
 Los factores pueden estar en el rango 0-1.
 En vez de 
\series bold
cmyk
\series default
 se puede usar el espacio de color 
\series bold
rgb
\series default
, que se refiere a 
\series bold
red
\series default
, 
\series bold
green
\series default
 y 
\series bold
blue
\series default
, así pues en este caso hay tres factores de cuota para los correspondientes
 colores.
 Además hay el espacio de color 
\series bold
gray
\series default
 con un factor de cuota para el valor gris.
\end_layout

\begin_layout Standard
Como ejemplo he aquí un marco con el nuevo color definido 
\series bold
verdeoscuro
\series default
 y los caracteres en color amarillo:
\color black

\begin_inset Formula 
\begin{equation}
\colorbox{verdeoscuro}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[3]{B}}{\ln\left(\frac{1}{3}\right)}}}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
Los colores personalizados también se pueden usar para texto con la ayuda
 del comando 
\series bold

\backslash
textcolor
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Texto ! coloreado
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textcolor{verdeoscuro}{
\end_layout

\end_inset

Esta frase en 
\begin_inset Quotes fld
\end_inset

verdeoscuro
\begin_inset Quotes frd
\end_inset

.
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\begin_layout Standard

\series bold

\backslash
textcolor
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! T ! 
\backslash
textcolor
\end_layout

\end_inset

 se usa con el esquema 
\series bold

\backslash
textcolor{color}{caracteres a colorear}
\series default
.
\end_layout

\begin_layout Subsection
Marcos de párrafo
\begin_inset CommandInset label
LatexCommand label
name "sub:Marcos-de-párrafo"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Marcos ! para párrafos
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Un marco que puede contener varias líneas y párrafos, denominado marco de
 párrafo (parbox), se puede generar con el menú 
\family sans
Insertar\SpecialChar \menuseparator
Marco
\family default
 o con el botón 
\begin_inset Graphics
        filename ../../images/box-insert.png
        scale 85

\end_inset

 de la barra de herramientas.
\end_layout

\begin_layout Standard
El siguiente ejemplo muestra un marco de párrafo en línea:
\begin_inset VSpace medskip
\end_inset

Esta línea contiene 
\begin_inset Box Boxed
position "c"
hor_pos "c"
has_inner_box 1
inner_pos "c"
use_parbox 1
use_makebox 0
width "5cm"
special "none"
height "1in"
height_special "totalheight"
status collapsed

\begin_layout Plain Layout
Esto es un marco de párrafo.
 Tiene exactamente 5
\begin_inset space \thinspace{}
\end_inset

cm de largo y además puede contener ecuaciones: 
\begin_inset Formula $\int A\,\mathrm{d}s=C$
\end_inset


\end_layout

\end_inset


\begin_inset space ~
\end_inset

 un marco de párrafo.
\begin_inset VSpace medskip
\end_inset

Ese marco se compone haciendo clic derecho sobre el rectángulo gris insertado.
 Surge un diálogo con las propiedades del marco.
 En este caso: 
\emph on
Decoración
\emph default
: Marco rectangular, 
\emph on
marco interior
\emph default
: Párrafo, 
\emph on
Ancho
\emph default
: 5
\begin_inset space \thinspace{}
\end_inset

cm, 
\emph on
Alineación Vertical
\emph default
 
\emph on
marco
\emph default
: Medio.
\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset

En LaTeX, un marco de párrafo se inserta con el comando 
\series bold

\backslash
parbox
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! P ! 
\backslash
parbox
\end_layout

\end_inset

 con el esquema siguiente:
\end_layout

\begin_layout Standard

\series bold

\backslash
parbox[posición]{anchura}{contenido}
\end_layout

\begin_layout Standard
Son posibles las posiciones 
\emph on
b
\emph default
 y 
\emph on
t
\emph default
, 
\emph on
b
\emph default
 por 
\begin_inset Quotes fld
\end_inset

bottom
\begin_inset Quotes frd
\end_inset

 (abajo), que alinea la última línea del marco con el texto de alrededor.
 Con 
\emph on
t
\emph default
, por 
\begin_inset Quotes fld
\end_inset

top
\begin_inset Quotes frd
\end_inset

 (arriba), la alineación se hace con la primera línea.
 Si no se da posición, el marco se centrará verticalmente, véase la sección
 
\emph on
Marcos
\emph default
 del manual 
\emph on
Objetos insertados
\emph default
 para ejemplos.
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

Para enmarcar ecuaciones completas, incluso el número de la ecuación, deben
 ponerse en un marco de párrafo.
 Para ello se inserta el comando
\begin_inset Newline newline
\end_inset


\series bold

\backslash
fbox{
\backslash
parbox{
\backslash
linewidth-2
\backslash
fboxsep-2
\backslash
fboxrule}{
\begin_inset Newline newline
\end_inset


\series default
en modo TeX delante de la ecuación.
 Aquí 
\series bold

\backslash
linewidth
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! L ! 
\backslash
linewidth
\end_layout

\end_inset

 es la anchura de línea establecida para el documento.
 Como el marco está por fuera del marco de párrafo, hay que restar de dicha
 anchura dos veces la separación del marco y el grosor.
 Como LyX no lo hace automáticamente debido a un fallo,
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
\begin_inset CommandInset href
LatexCommand href
name "LyX-bug #4483"
target "http://www.lyx.org/trac/ticket/4483"

\end_inset


\end_layout

\end_inset

 hay que usar modo TeX.
 Para poder multiplicar y restar en los argumentos hay que cargar en el
 preámbulo LaTeX el paquete LaTeX 
\series bold
calc
\series default
,
\begin_inset Foot
status collapsed

\begin_layout Plain Layout

\series bold
calc
\series default
 es parte de toda instalación LaTeX estándar.
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Paquetes ! calc
\end_layout

\end_inset

 con la línea
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage{calc}
\end_layout

\begin_layout Standard
Detrás de la ecuación se cierran ambos marcos con 
\series bold
}}
\series default
 en modo TeX.
 Aquí hay un ejemplo:
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
fboxsep 5mm 
\backslash
fboxrule 5mm
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
fbox{
\backslash
parbox{
\backslash
linewidth-2
\backslash
fboxsep-2
\backslash
fboxrule}{
\end_layout

\end_inset


\begin_inset Formula 
\begin{equation}
\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
fboxrule 0.4pt 
\backslash
fboxsep 3pt
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
Como se ha usado el marco de párrafo como argumento de 
\series bold

\backslash
fbox
\series default
, en este caso no hay diferencia entre 
\series bold

\backslash
fbox
\series default
 y 
\series bold

\backslash
boxed
\series default
.
 
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
Los marcos de párrafo son muy útiles para comentar ecuaciones directamente.
 Para hacerlo, se usa 
\series bold

\backslash
parbox
\series default
 en combinación con el comando 
\series bold

\backslash
tag
\series default
.
 (Véase más sobre 
\series bold

\backslash
tag
\series default
 en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Numeración-personalizada"

\end_inset

).
\end_layout

\begin_layout Standard
Un ejemplo de ecuación comentada con 
\series bold

\backslash
parbox
\series default
:
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
[5x-7b=3b
\backslash
tag*{
\backslash
parbox{5cm}{
\end_layout

\end_inset

Esto es una descripción.
 Está claramente separada de la ecuación y es multilínea.
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}}
\backslash
]
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Tales ecuaciones deben insertarse completamente en modo TeX porque LyX aún
 no soporta el comando 
\series bold

\backslash
parbox
\series default
 en ecuaciones.
 La ecuación se compone con la siguiente secuencia de comandos:
\end_layout

\begin_layout Standard
El comando 
\series bold

\backslash
[5x-7b=3b
\backslash
tag*
\backslash
{
\backslash
parbox{5cm}{
\series default
 se inserta en modo TeX.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Si se usa el estilo de ecuación 
\series bold
Sangrado
\series default
, 
\series bold

\backslash
tag*
\backslash

\series default
 se puede reemplazar por 
\series bold

\backslash
hfill
\series default
.
 (Véanse los estilos de ecuación en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Estilos-de-ecuación"

\end_inset

).
\end_layout

\end_inset

 Después sigue la descripción en texto normal, y por último 
\series bold
}}
\backslash
]
\series default
 en modo TeX.
 Aquí los comandos 
\series bold

\backslash
[
\series default
 y 
\series bold

\backslash
]
\series default
 crean una ecuación presentada.
\end_layout

\begin_layout Standard
Las ventajas de 
\series bold

\backslash
parbox
\series default
 pueden verse en este ejemplo que se ha 
\begin_inset Quotes fld
\end_inset

comentado
\begin_inset Quotes frd
\end_inset

 usando el modo texto matemático:
\begin_inset Formula 
\[
5x-7b=3b\textrm{ Esto es una descripción. No está separada de la ecuación...}
\]

\end_inset


\end_layout

\begin_layout Section
Operadores
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Operadores
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Operadores grandes
\begin_inset CommandInset label
LatexCommand label
name "sub:Operadores-grandes"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Operadores ! grandes
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Sumatorios
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Integrales
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para poder usar todos los comandos de integrales listados aquí, debe estar
 marcada la opción 
\family sans
Usar paquete esint automáticamente
\family default
 en el apartado 
\family sans
Opciones de ecuación
\family default
 de la configuración del documento.
 
\end_layout

\begin_layout Standard
\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="11" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
int
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! I ! 
\backslash
int
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\int$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
oint
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\oint$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ointctrclockwise
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\ointctrclockwise$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ointclockwise
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\ointclockwise$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
sqint
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\sqint$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
fint
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
 
\begin_inset Formula $\fint$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
landupint
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
 
\begin_inset Formula $\landupint$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
landdownint
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
 
\begin_inset Formula $\landdownint$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bigcap
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bigcap$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bigcup
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bigcup$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="11" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
sum
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! S ! 
\backslash
sum
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\sum$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
prod
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! P ! 
\backslash
prod
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\prod$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
coprod
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\coprod$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bigodot
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bigodot$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bigotimes
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bigotimes$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bigoplus
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bigoplus$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bigwedge
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bigwedge$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bigvee
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bigvee$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bigsqcup
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bigsqcup$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
biguplus
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\biguplus$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Standard
Todos los operadores grandes se pueden insertar con el botón 
\begin_inset Graphics
        filename ../../images/math/intop.png
        scale 85

\end_inset

 de la barra de ecuaciones.
\end_layout

\begin_layout Standard
Estos operadores son llamados grandes porque son mayores que los operadores
 binarios de aspecto semejante.
 Todos los operadores grandes pueden tener límites, como se describe en
 la subsección siguiente.
\end_layout

\begin_layout Standard
Para todos los operadores de integral hay una segunda versión disponible,
 terminando en 
\series bold
op
\series default
: 
\series bold

\backslash
intop
\series default
, 
\series bold

\backslash
ointop
\series default
 etc.
 Estos operadores difieren de 
\series bold

\backslash
int
\series default
, etc., en el estilo en que se presentan los límites, véase
\series bold
 
\series default

\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Límites-de-operadores"

\end_inset

.
\end_layout

\begin_layout Subsubsection*
Sugerencias para las integrales
\end_layout

\begin_layout Standard
La letra 
\emph on
d
\emph default
 en una integral es un operador, por consiguiente debe escribirse en redonda.
 Esto se hace resaltando la 
\emph on
d
\emph default
 y usando el atajo de teclado 
\family sans
Alt+C
\begin_inset space ~
\end_inset

R
\family default
.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
véase estilos de letras en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Estilos-de-tipografías"

\end_inset

 
\end_layout

\end_inset

 Delante de la 
\emph on
d
\emph default
 se inserta un espacio delgado, como es habitual en los operadores.
 Un ejemplo:
\end_layout

\begin_layout Standard
incorrecto: 
\begin_inset Formula $\int A(x)dx$
\end_inset


\begin_inset Newline newline
\end_inset


\begin_inset Phantom HPhantom
status open

\begin_layout Plain Layout
in
\end_layout

\end_inset

correcto: 
\begin_inset Formula $\int A(x)\,\mathrm{d}x$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Newpage pagebreak
\end_inset


\end_layout

\begin_layout Standard
Para integrales múltiples hay los siguientes comandos:
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
iint
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
oiint
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
sqiint
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
iiint
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
iiiint
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
dotsint
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Subsection
Límites de operadores
\begin_inset CommandInset label
LatexCommand label
name "sub:Límites-de-operadores"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Operadores ! límites de
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Los límites se crean mediante superíndices y subíndices:
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
prod^
\backslash
infty
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\begin_inset Formula $\to$
\end_inset

_0
\begin_inset Formula $\to$
\end_inset

A(x)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
En ecuaciones en línea los límites se colocan al lado derecho del operador.
 En ecuaciones presentadas se colocan encima y debajo, excepto en las integrales.
\end_layout

\begin_layout Standard
Para forzar que los límites se coloquen junto al operador, se pone el cursor
 directamente detrás del operador y se elige 
\series bold
Alineado
\series default
 en el menú 
\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Cambiar tipo de límites
\family default
 (atajo 
\family sans
Alt+M
\begin_inset space ~
\end_inset

L
\family default
).
 Un ejemplo:
\end_layout

\begin_layout Standard
El tipo de límites por omisión es:
\begin_inset Formula 
\[
\sum_{x=0}^{\infty}\frac{1}{x^{2}}
\]

\end_inset


\end_layout

\begin_layout Standard
Así se ven si se cambia el tipo de límites a 
\series bold
Alineado
\series default
:
\begin_inset Formula 
\[
\sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
\]

\end_inset


\end_layout

\begin_layout Standard
En integrales, excepto las que terminan en 
\series bold
op
\series default
 como 
\series bold

\backslash
intop
\series default
, 
\series bold

\backslash
ointop
\series default
, etc., los límites se colocan por omisión junto al operador.
 Pero en integrales múltiples los límites se ponen con frecuencia bajo el
 operador.
 Por tanto, en el siguiente ejemplo se ha elegido el tipo 
\series bold
Presentado
\series default
 para poner el límite debajo:
\begin_inset Formula 
\begin{equation}
\iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:IntVol}
\end{equation}

\end_inset


\begin_inset VSpace medskip
\end_inset

Para especificar condiciones en los límites se usan los comandos 
\series bold

\backslash
subarray
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! S ! 
\backslash
subarray
\end_layout

\end_inset

 y 
\series bold

\backslash
substack
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! S ! 
\backslash
substack
\end_layout

\end_inset

.
 Por ejemplo, para componer la expresión
\begin_inset Formula 
\begin{equation}
\sum_{\begin{subarray}{c}
0<k<1000\\
\\
k\,\in\,\mathbb{N}
\end{subarray}}^{n}k^{-2}\label{eq:substack}
\end{equation}

\end_inset

se ha hecho lo siguiente: primero se escribe el comando 
\series bold

\backslash
sum^n
\series default

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series bold
_
\series default
.
 Ahora el cursor está en un marco azul bajo el operador sumatorio y ahí
 se inserta el comando 
\series bold

\backslash
subarray
\series default

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

.
 Ahora el marco azul está en un marco púrpura donde pueden escribirse líneas
 distintas.
 Cada línea nueva se crea con un salto de línea (
\family sans
Ctrl+Entrar
\family default
).
 Si ahora se teclea en ella
\begin_inset Newline newline
\end_inset


\series bold
0<k<1000 Ctrl+Entrar
\begin_inset Newline newline
\end_inset


\series default
aparece debajo un nuevo marco para la línea nueva.
\end_layout

\begin_layout Standard
La alineación de las líneas puede cambiarse a la izquierda con la 
\family sans
barra de herramientas de cuadros
\family default
 o con el menú 
\family sans
Editar\SpecialChar \menuseparator
Filas y columnas
\family default
.
 Para obtener alineación derecha se inserta 
\series bold

\backslash
hfill
\series default

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

 al principio de la línea.
\end_layout

\begin_layout Standard
El comando 
\series bold

\backslash
substack
\series default
 es equivalente a 
\series bold

\backslash
subarray
\series default
 con la diferencia de que las líneas están siempre centradas.
\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
Puede ocurrir que haya demasiado espacio entre el operador y los caracteres
 siguientes, como en la ecuación 
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:substack"

\end_inset

, porque éstos se colocan junto a los límites.
\end_layout

\begin_layout Standard
Para evitarlo se puede usar la siguiente macro en el preámbulo:
\end_layout

\begin_layout Standard

\series bold

\backslash
def
\backslash
clap#1{
\backslash
hbox to 0pt{
\backslash
hss #1
\backslash
hss}}
\begin_inset Newline newline
\end_inset


\backslash
def
\backslash
mathclap {
\backslash
mathpalette 
\backslash
mathclapinternal}
\begin_inset Newline newline
\end_inset


\backslash
def
\backslash
mathclapinternal #1#2{
\backslash
clap{$
\backslash
mathsurround =0pt #1{#2}$}}
\end_layout

\begin_layout Standard
En ella se define el comando 
\series bold

\backslash
mathclap
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! M ! 
\backslash
mathclap
\end_layout

\end_inset

 que establece la anchura del límite en 0
\begin_inset space \thinspace{}
\end_inset

pt.
 El esquema del comando es:
\end_layout

\begin_layout Standard

\series bold

\backslash
mathclap{límite}
\end_layout

\begin_layout Standard
donde el límite puede consistir en varias condiciones.
\end_layout

\begin_layout Standard
Aplicado en la ecuación 
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:substack"

\end_inset

 se usa el comando
\end_layout

\begin_layout Standard

\series bold

\backslash
sum_
\backslash
mathclap{
\backslash
substack
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

0<k<1000 Ctrl+Entrar
\end_layout

\begin_layout Standard
para componer el límite inferior.
 Ahora el sumando está junto al sumatorio:
\begin_inset Formula 
\[
\sum_{\mathclap{\substack{0<k<1000\\
\\
k\,\in\,\mathbb{N}
}
}}^{n}k^{-2}
\]

\end_inset


\begin_inset VSpace bigskip
\end_inset

Cómo utilizar un límite para varios operadores se describe en la 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Operadores-de-usuario"

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Subsection
Operadores binarios
\begin_inset CommandInset label
LatexCommand label
name "sub:Operadores-binarios"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Operadores ! binarios
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Los operadores binarios se rodean por espacios si llevan un carácter delante
 o detrás.
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="13" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Operador
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
+
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $+$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
-
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $-$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
pm
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\pm$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
mp
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\mp$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
cdot
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\cdot$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
times
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\times$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
div
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\div$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
raisebox{-1.2mm}{
\end_layout

\end_inset

*
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $*$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
star
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\star$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
circ
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\circ$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
diamond
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\diamond$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bullet
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bullet$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="13" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Operador
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
nabla
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\nabla$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bigtriangledown
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bigtriangledown$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bigtriangleup
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bigtriangleup$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Box
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Box$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
cap 
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\cap$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
cup
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\cup$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
dagger
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\dagger$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ddagger
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\ddagger$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
wr
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\wr$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bigcirc
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bigcirc$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
wedge
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\wedge$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
vee
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\vee$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="13" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Operador
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
oplus
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\oplus$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ominus
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\ominus$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
otimes
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\otimes$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
oslash
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\oslash$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
odot
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\odot$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
amalg
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\amalg$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
uplus
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\uplus$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
setminus
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\setminus$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
sqcap
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\sqcap$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
sqcup
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\sqcup$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
triangleleft
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\triangleleft$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
triangleright
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\triangleright$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Standard
Todos los operadores binarios se pueden insertar también con el botón 
\begin_inset Graphics
        filename ../../images/math/pm.png
        scale 85

\end_inset

 de la barra de ecuaciones.
\end_layout

\begin_layout Standard
Para imprimir el operador Laplace se pueden usar 
\series bold

\backslash
Delta
\series default
 o 
\series bold

\backslash
nabla
\series default
^
\series bold
2
\series default
 (
\begin_inset Formula $\nabla^{2}$
\end_inset

) en vez de 
\series bold

\backslash
bigtriangleup
\series default
.
\end_layout

\begin_layout Standard
El carácter 
\family sans
Separador de menú
\family default
 del menú 
\family sans
Insertar\SpecialChar \menuseparator
Carácter especial
\family default
 es el operador 
\series bold

\backslash
triangleright
\series default
.
\end_layout

\begin_layout Subsection
Operadores definidos por el usuario
\begin_inset CommandInset label
LatexCommand label
name "sub:Operadores-de-usuario"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Operadores ! personalizados
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Con ayuda del comando 
\series bold

\backslash
DeclareMathOperator
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! D ! 
\backslash
dbinom@
\backslash
DeclareMathOperator
\end_layout

\end_inset

 se pueden definir operadores personalizados en el preámbulo LaTeX.
 Su esquema es:
\end_layout

\begin_layout Standard

\series bold

\backslash
DeclareMathOperator{comando nuevo}{presentación}
\end_layout

\begin_layout Standard
Presentación puede ser un carácter o símbolo que define el aspecto del operador
 en la salida.
 Para definir un operador grande hay que añadirle un * detrás.
 Todos los operadores grandes personalizados pueden tener límites como se
 describe en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Límites-de-operadores"

\end_inset

.
\end_layout

\begin_layout Standard
Por ejemplo, la línea en el preámbulo LaTeX
\end_layout

\begin_layout Standard

\series bold

\backslash
DeclareMathOperator*{
\backslash
Lozenge}{
\backslash
blacklozenge}
\end_layout

\begin_layout Standard
define el comando 
\series bold

\backslash
Lozenge
\series default
, que inserta un operador grande que es el símbolo blacklozenge de la 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Símbolos-misceláneos"

\end_inset

.
\begin_inset Formula 
\[
\Lozenge_{n=1}^{\infty}
\]

\end_inset

El comando para esta expresión es: 
\series bold

\backslash
Lozenge^
\backslash
infty
\begin_inset Formula $\rightarrow$
\end_inset

_n=1
\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
Si los operadores personalizados no se van a usar varias veces en el documento,
 se pueden también definir con los comandos 
\series bold

\backslash
mathop
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! M ! 
\backslash
mathop
\end_layout

\end_inset

 y 
\series bold

\backslash
mathbin
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! M ! 
\backslash
mathbin
\end_layout

\end_inset

, con el siguiente esquema:
\end_layout

\begin_layout Standard

\series bold

\backslash
mathop{presentación}
\series default
 y 
\series bold

\backslash
mathbin{presentación}
\end_layout

\begin_layout Standard

\series bold

\backslash
mathop
\series default
 define operadores grandes, 
\series bold

\backslash
mathbin
\series default
 operadores binarios.
\end_layout

\begin_layout Standard

\series bold

\backslash
mathop
\series default
 se puede usar, p.e., para poner un límite a varios operadores:
\begin_inset Formula 
\[
\mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
\]

\end_inset


\end_layout

\begin_layout Standard
El comando para la expresión anterior es:
\begin_inset Newline newline
\end_inset


\series bold

\backslash
mathop{
\backslash
sum
\backslash
negmedspace
\backslash
sum
\series default

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series bold

\begin_inset Formula $\to$
\end_inset

^N
\series default

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series bold
_i,j=1
\end_layout

\begin_layout Section
Tipografías
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Tipografías
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Estilos de tipografías
\begin_inset CommandInset label
LatexCommand label
name "sub:Estilos-de-tipografías"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Tipografías ! estilos de
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Las letras latinas en las ecuaciones se pueden poner en uno de los siguientes
 estilos:
\end_layout

\begin_layout Standard
\begin_inset VSpace -2mm
\end_inset


\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="7" columns="3">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
atajo
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
mathbb
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series default
ABC
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\mathbb{ABC}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family sans
Alt+C C
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
mathbf
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series default
AbC
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\mathbf{AbC}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family sans
Ctrl+B
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
boldsymbol
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series default
AbC
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\boldsymbol{AbC}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family sans
Ctrl+Alt+B , Alt+C B
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
mathcal
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series default
ABC
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\mathcal{ABC}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family sans
Ctrl+E , Alt+C E
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
mathfrak
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series default
AbC
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\mathfrak{AbC}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
-
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
mathscr
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series default
AbC
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\mathscr{AbC}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
-
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="3">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
atajo
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
mathit
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series default
AbC
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\mathit{AbC}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
-
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
mathrm
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series default
AbC
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\mathrm{AbC}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family sans
Alt+C R
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
mathsf
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series default
AbC
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\mathsf{AbC}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family sans
Alt+C S
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
mathtt
\series bold

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series default
AbC
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\mathtt{AbC}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family sans
Ctrl+Mayúsculas+P
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Note Greyedout
status open

\begin_layout Plain Layout

\series bold
Nota
\series default
: Los estilos 
\series bold

\backslash
mathbb
\series default
 y 
\series bold

\backslash
mathcal
\series default
 sólo se aplican a letras mayúsculas.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
El estilo predeterminado es 
\series bold

\backslash
mathnormal
\series default
.
\end_layout

\begin_layout Standard
Los comandos de estilo funcionan también en estructuras matemáticas:
\begin_inset Formula 
\[
\mathfrak{A=\frac{b}{C}}
\]

\end_inset


\end_layout

\begin_layout Standard
Los caracteres en texto matemático no aparecen en un estilo tipográfico
 de ecuaciones sino en el estilo tipográfico de texto 
\series bold

\backslash
textrm
\series default
.
 Este estilo no se puede poner correctamente con el diálogo de estilo de
 texto por un fallo de LyX.
\begin_inset Foot
status open

\begin_layout Plain Layout
\begin_inset CommandInset href
LatexCommand href
name "LyX-bug #4629"
target "http://www.lyx.org/trac/ticket/4629"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
En vez de comandos se puede usar el menú 
\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Estilo del texto
\family default
 o el botón 
\begin_inset Graphics
        filename ../../images/math/font.png
        scale 85

\end_inset

.
\end_layout

\begin_layout Subsection
Ecuaciones en negrita
\begin_inset CommandInset label
LatexCommand label
name "sub:Ecuaciones-en-negrita"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! en negrita
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para poner en negrita una ecuación completa no se puede usar el comando
 
\series bold

\backslash
mathbf
\series default
, porque no funciona con minúsculas griegas.
 Además, siempre imprime en redonda las letras latinas, como en la ecuación:
\begin_inset Formula 
\[
\mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{ecuación con \textbackslash mathbf}
\]

\end_inset


\end_layout

\begin_layout Standard
Para presentar la ecuación correctamente se usa el comando 
\series bold
boldsymbol
\series default
:
\begin_inset Formula 
\[
\boldsymbol{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{ecuación con \textbackslash boldsymbol}
\]

\end_inset


\end_layout

\begin_layout Standard
También es posible poner la fórmula en un 
\series bold
entorno boldmath
\series default
, que se inserta con el comando 
\series bold

\backslash
boldmath
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! B ! 
\backslash
boldmath
\end_layout

\end_inset

 en modo TeX.
 Para finalizar el entorno se usa el comando 
\series bold

\backslash
unboldmath
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! U ! 
\backslash
unboldmath
\end_layout

\end_inset

 en modo TeX.
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
boldmath
\end_layout

\end_inset


\begin_inset Formula 
\[
\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{ecuación en un entorno boldmath}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
unboldmath
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Ecuaciones coloreadas
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! coloreada
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Las ecuaciones se pueden colorear como texto normal: selecciona una ecuación
 o una parte de una ecuación y usa el diálogo 
\family sans
Estilo del texto
\family default
.
 Aquí hay una ecuación en magenta:
\begin_inset Formula 
\[
{\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
\]

\end_inset

También puedes definir tus propios colores como se describe en
\begin_inset space ~
\end_inset


\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Marcos-coloreados"

\end_inset

.
 Pueden usarse con el comando en código TeX 
\series bold

\backslash
textcolor
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! T ! 
\backslash
textcolor
\end_layout

\end_inset

 según el esquema
\end_layout

\begin_layout Standard

\series bold

\backslash
textcolor{color}{caracteres o ecuación}
\end_layout

\begin_layout Standard
El ejemplo siguiente se ha coloreado completamente en verde oscuro y parcialment
e en rojo:
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textcolor{verdeoscuro}{
\end_layout

\end_inset


\begin_inset Formula 
\[
\int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
\]

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Debido a un error en LyX los colores personalizados se pueden aplicar sólo
 a ecuaciones completas.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
\begin_inset CommandInset href
LatexCommand href
name "LyX-bug #5269"
target "http://www.lyx.org/trac/ticket/5269"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Tamaños de tipografías
\begin_inset CommandInset label
LatexCommand label
name "sub:Tamaños-de-tipografías"

\end_inset


\begin_inset Index idx
status open

\begin_layout Plain Layout
Tipografías ! tamaño
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para los caracteres en ecuaciones hay, como para caracteres en texto, los
 siguientes comandos de tamaño:
\end_layout

\begin_layout Standard

\series bold

\backslash
Huge
\series default
, 
\series bold

\backslash
huge
\series default
, 
\series bold

\backslash
LARGE
\series default
, 
\series bold

\backslash
Large
\series default
, 
\series bold

\backslash
large
\series default
, 
\series bold

\backslash
normalsize
\series default
, 
\series bold

\backslash
small
\series default
,
\begin_inset Newline newline
\end_inset


\series bold

\backslash
footnotesize
\series default
, 
\series bold

\backslash
scriptsize
\series default
, y 
\series bold

\backslash
tiny
\end_layout

\begin_layout Standard
El tamaño dado por los comandos depende del tamaño base de la tipografía
 en el documento, dado por el comando 
\series bold

\backslash
normalsize
\series default
.
 Los demás comandos producen tamaños menores o mayores que 
\series bold

\backslash
normalsize
\series default
.
 No obstante, puede que el tamaño de tipografía no exceda de cierto valor.
 Si, por ejemplo, la tipografía del documento es de 12
\begin_inset space \thinspace{}
\end_inset

pt, el comando 
\series bold

\backslash
Huge
\series default
 da el mismo tamaño que 
\series bold

\backslash
huge
\series default
.
\end_layout

\begin_layout Standard
Un comando de tamaño se inserta en modo TeX antes de la ecuación, y se aplica
 a todas las ecuaciones y texto siguientes.
 Para volver al tamaño anterior hay que insertar el comando 
\series bold

\backslash
normalsize
\series default
 en modo TeX detrás de la ecuación.
\end_layout

\begin_layout Standard
Dentro de una ecuación, el tamaño se puede cambiar usando los siguientes
 comandos de tamaño:
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
displaystyle
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! D ! 
\backslash
displaystyle
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
textstyle
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
scriptstyle
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
scriptscriptstyle
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Después de introducir estos comandos, aparece un marco azul en el que se
 insertan las partes de la fórmula.
\end_layout

\begin_layout Standard
Hay un método más para cambiar el tamaño de tipografía, aunque solo funciona
 para símbolos o letras en texto matemático.
 Para usarlo se inserta en texto matemático uno de los comandos de tamaño
 de texto anteriores.
 Todos los caracteres siguientes, hasta el final del texto matemático o
 hasta otro comando de tamaño, tendrán el tamaño seleccionado.
 Dos ejemplos:
\begin_inset VSpace -2mm
\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
huge
\end_layout

\end_inset


\begin_inset Formula 
\[
A=\frac{B}{c}\cdot\maltese
\]

\end_inset


\begin_inset Formula 
\[
\maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
normalsize
\end_layout

\end_inset


\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
Antes de las ecuaciones se ha insertado el comando 
\series bold

\backslash
huge
\series default
.
 Para la segunda ecuación el comando es:
\begin_inset Newline newline
\end_inset


\series bold

\backslash
maltese
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A Alt+M M 
\backslash
Large
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\backslash
maltese
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\backslash
textit
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\to$
\end_inset


\begin_inset Formula $\to$
\end_inset


\begin_inset Newline newline
\end_inset


\begin_inset space \hspace*{}
\length 1cm
\end_inset

Alt+M M 
\backslash
tiny
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\backslash
maltese
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\backslash
textit
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\end_layout

\begin_layout Standard
Si un símbolo no se puede mostrar en distintos tamaños se usará siempre
 el tamaño por omisión.
\end_layout

\begin_layout Section
Letras griegas
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Letras griegas
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Las letras griegas se pueden insertar además mediante el botón 
\begin_inset Graphics
        filename ../../images/math/alpha.png
        scale 85

\end_inset

 de la barra de ecuaciones.
 Las normas internacionales de tipografía proponen que las letras griegas
 en ecuaciones deben escribirse en cursiva/inclinada.
 No obstante, en algunos idiomas, como francés o ruso, a veces se escriben
 en redonda.
 Para las normas en español, véase
\begin_inset space ~
\end_inset


\begin_inset CommandInset citation
LatexCommand cite
key "Bezos"

\end_inset

.
\end_layout

\begin_layout Subsection
Minúsculas
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status collapsed

\begin_layout Plain Layout
Letras griegas ! minúsculas
\end_layout

\end_inset


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\begin_layout Standard
\begin_inset space \hfill{}
\end_inset


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beta
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gamma
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delta
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epsilon
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varepsilon
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zeta
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eta
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theta
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vartheta
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\begin_inset space \hfill{}
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iota
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kappa
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varkappa
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lambda
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mu
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
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nu
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xi
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o
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pi
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varpi
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rho
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\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="11" columns="2">
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Comando
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varrho
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sigma
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varsigma
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tau
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upsilon
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phi
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varphi
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chi
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psi
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omega
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\begin_layout Standard
\begin_inset VSpace medskip
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\begin_layout Standard
Cómo escribir letras griegas especiales en redonda se explica en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Griegas-en-redonda"

\end_inset

.
\end_layout

\begin_layout Subsection
Mayúsculas
\begin_inset Index idx
status collapsed

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Letras griegas ! mayúsculas
\end_layout

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Upsilon
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\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Upsilon$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Phi
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Phi$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Psi
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Psi$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Omega
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Omega$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
Las mayúsculas griegas se imprimen en redonda debido a un fallo de diseño
 cuando se desarrolló TeX.
 Para obtener mayúsculas en cursiva, inicia cada comando con 
\series bold
var
\series default
.
 Por ejemplo, el comando 
\series bold

\backslash
varGamma
\series default
 genera 
\begin_inset Formula $\varGamma$
\end_inset

.
 Otra forma es cargar el paquete 
\series bold
fixmath
\series default

\begin_inset Foot
status collapsed

\begin_layout Plain Layout

\series bold
fixmath
\series default
 forma parte del paquete LaTeX 
\series bold
was
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Paquetes ! was
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
vspace{4mm}
\end_layout

\end_inset


\end_layout

\end_inset

.
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Paquetes ! fixmath
\end_layout

\end_inset

 con la línea siguiente en el preámbulo LaTeX
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage{fixmath}
\end_layout

\begin_layout Standard
Entonces, todas las mayúsculas griegas en el documento se imprimirán automáticam
ente en cursiva.
\end_layout

\begin_layout Subsection
Letras en negrita
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Letras griegas ! en negrita
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Las letras griegas no admiten diferentes estilos de letra como las latinas.
 Sólo se pueden poner en negrita con el comando 
\series bold

\backslash
boldsymbol
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! B ! 
\backslash
boldsymbol
\end_layout

\end_inset

.
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Símbolo
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Upsilon
\backslash
boldsymbol
\backslash
Upsilon
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
theta
\backslash
boldsymbol
\backslash
theta
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\theta\boldsymbol{\theta}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
Símbolos
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
texorpdfstring{
\end_layout

\end_inset


\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Se puede encontrar una lista con todos los símbolos de la mayoría de paquetes
 LaTeX en 
\begin_inset CommandInset citation
LatexCommand cite
key "Symbols"

\end_inset

.
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}{}
\end_layout

\end_inset


\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\backslash
texorpdfstring se usa para evitar que la nota al pie aparezca en los marcadores
 PDF.
\end_layout

\begin_layout Plain Layout
Más sobre 
\backslash
texorpdfstring en la sección 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Ecuaciones-en-encabezados"

\end_inset

.
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Símbolos
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Muchos de los símbolos listados en esta sección se pueden insertar además
 mediante los botones 
\begin_inset Graphics
        filename ../../images/math/nabla.png
        scale 85

\end_inset

 y 
\begin_inset Graphics
        filename ../../images/math/digamma.png
        scale 85

\end_inset

 de la barra de ecuaciones.
\end_layout

\begin_layout Subsection
Símbolos matemáticos
\begin_inset CommandInset label
LatexCommand label
name "sub:Símbolos-matemáticos"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Símbolos ! matemáticos
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="10" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Símbolo
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
neg
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\neg$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Im
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Im$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Re
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Re$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
aleph
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\aleph$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
partial
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\partial$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
infty
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\infty$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
wp
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\wp$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
imath
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\imath$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
jmath
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\jmath$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="10" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Símbolo
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
forall
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\forall$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
exists
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\exists$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
nexists
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\nexists$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
emptyset
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\emptyset$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
varnothing
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\varnothing$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
dag
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\dag$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ddag
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\ddag$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
complement
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
raisebox{-0.8mm}{
\end_layout

\end_inset


\begin_inset Formula $\complement$
\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Bbbk
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Bbbk$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="10" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Símbolo
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
prime
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\prime$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
backprime
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\backprime$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
mho
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\mho$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
triangle
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\triangle$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
angle
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\angle$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
measuredangle
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\measuredangle$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
sphericalangle
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\sphericalangle$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
top
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\top$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bot
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bot$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Subsection
Símbolos misceláneos
\begin_inset CommandInset label
LatexCommand label
name "sub:Símbolos-misceláneos"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Símbolos ! misceláneos
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="10" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Símbolo
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
flat
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\flat$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
natural
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\natural$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
sharp
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\sharp$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
surd
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\surd$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
checkmark
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\checkmark$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
yen
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\yen$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
pounds
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\pounds$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
$
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\$$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
§
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $§$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="10" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Símbolo
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
hbar
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\hbar$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
hslash
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\hslash$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
clubsuit
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\clubsuit$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
spadesuit
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\spadesuit$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bigstar
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bigstar$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
blacklozenge
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\blacklozenge$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
blacktriangle
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\blacktriangle$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
blacktiangledown
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\blacktriangledown$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bullet
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bullet$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="10" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Símbolo
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
diamondsuit
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\diamondsuit$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Diamond
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Diamond$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
heartsuit
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\heartsuit$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
P
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\P$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
copyright
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\copyright$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
circledR
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\circledR$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
maltese
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\maltese$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
diagup
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\diagup$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
diagdown
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\diagdown$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
Hay más símbolos en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Caracteres-especiales-misceláneos"

\end_inset

.
\end_layout

\begin_layout Standard
Algunos símbolos pueden presentarse en distintos tamaños, véase 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Tamaños-de-tipografías"

\end_inset


\end_layout

\begin_layout Subsection
El símbolo del euro, €
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Símbolos ! euro
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout

\backslash
@
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
officialeuro
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para usar el símbolo del euro en ecuaciones debe estar instalado el paquete
 LaTeX 
\series bold
eurosym
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Paquetes ! eurosym
\end_layout

\end_inset

, y cargado en el preámbulo LaTeX con la línea
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage[gennarrow]{eurosym}
\end_layout

\begin_layout Standard
Actualmente también se puede insertar con el comando 
\series bold

\backslash
euro
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! E ! 
\backslash
euro
\end_layout

\end_inset

.
\end_layout

\begin_layout Standard
El símbolo del euro puede insertarse directamente con la tecla € en texto
 matemático sin tener 
\series bold
eurosym
\series default
 instalado.
 Si 
\series bold
eurosym
\series default
 está instalado, se puede insertar 
\series bold

\backslash
euro
\series default
 en modo TeX.
 El símbolo oficial de la moneda se puede insertar con el comando 
\series bold

\backslash
officialeuro
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! O ! 
\backslash
officialeuro
\end_layout

\end_inset

, que sólo está disponible en modo TeX.
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ifeurosym
\end_layout

\end_inset


\begin_inset Note Note
status collapsed

\begin_layout Plain Layout
El cuadro siguiente sólo se mostrará si está instalado el paquete LaTeX
 
\series bold
eurosym
\series default
.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Un vistazo a los diferentes símbolos del euro.
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="3">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Símbolo
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
ecuación
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
euro
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\euro$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
texto matemático
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
€
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\mbox{€}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
modo TeX
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
officialeuro
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
officialeuro
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
else
\end_layout

\end_inset


\begin_inset Note Note
status collapsed

\begin_layout Plain Layout
Se mostrará lo siguiente si no está instalado el paquete LaTeX 
\series bold
eurosym
\series default
:
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para ver la salida completa de esta subsección debe estar instalado el paquete
 LaTeX 
\series bold
eurosym
\series default
.
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
fi
\end_layout

\end_inset


\end_layout

\begin_layout Section
Relaciones
\begin_inset CommandInset label
LatexCommand label
name "sec:Relaciones"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Relaciones
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comparaciones|see
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset

Relaciones
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Todas las relaciones se pueden insertar también con el botón 
\begin_inset Graphics
        filename ../../images/math/leq.png
        scale 85

\end_inset

 de la barra de ecuaciones.
\end_layout

\begin_layout Standard
\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="17" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Relación
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
<
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $<$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
le
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\le$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ll
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\ll$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
prec
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\prec$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
preceq
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\preceq$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
subset
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\subset$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
subseteq
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\subseteq$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
sqsubseteq
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\sqsubseteq$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
in
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\in$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
vdash
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\vdash$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
smile
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\smile$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
lhd
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\lhd$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
unlhd
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\unlhd$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
gtrless
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\gtrless$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
mid
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\mid$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
nmid
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\nmid$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="17" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Relación
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
=
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $=$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
not=
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\not=$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
equiv
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\equiv$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
sim
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\sim$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
simeq
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\simeq$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
approx
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\approx$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
cong
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\cong$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bowtie
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\bowtie$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
notin
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\notin$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
perp
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\perp$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
propto
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\propto$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
asymp
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\asymp$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
doteq
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\doteq$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
circeq
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\circeq$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
models
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\models$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
widehat=
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\widehat{=}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="17" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Relación
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
>
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $>$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ge
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\ge$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
gg
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\gg$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
succ
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\succ$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
succeq
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\succeq$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
supset
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\supset$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
supseteq
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\supseteq$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
sqsupseteq
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\sqsupseteq$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ni
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\ni$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
dashv
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\dashv$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
frown
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\frown$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
rhd
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\rhd$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
unrhd
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\unrhd$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
lessgtr
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\lessgtr$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
parallel
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\parallel$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
nparallel
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\nparallel$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
Los caracteres 
\series bold

\backslash
lhd
\series default
 y 
\series bold

\backslash
rhd
\series default
 son mayores que los operadores de aspecto similar 
\series bold

\backslash
triangleleft
\series default
 y 
\series bold

\backslash
triangleright
\series default
, respectivamente.
\end_layout

\begin_layout Standard
Las relaciones, a diferencia de los símbolos, siempre se rodean de espacios.
\end_layout

\begin_layout Standard
Se pueden componer relaciones con etiquetas con el comando 
\series bold

\backslash
stackrel
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! S ! 
\backslash
stackrel
\end_layout

\end_inset

:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
A(r)
\backslash
stackrel
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

r
\backslash
to
\backslash
infty
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\begin_inset Formula $\downarrow$
\end_inset


\backslash
approx
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Section
Funciones
\end_layout

\begin_layout Subsection
Funciones predefinidas
\begin_inset CommandInset label
LatexCommand label
name "sub:Funciones-predefinidas"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Funciones ! predefinidas
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Funciones ! en español
\end_layout

\end_inset


\end_layout

\begin_layout Standard
En general las variables se escriben en 
\emph on
cursiva
\emph default
 en expresiones matemáticas, pero no los nombres de las funciones, porque
 
\begin_inset Formula $sen$
\end_inset

 podría confundirse con 
\begin_inset Formula $s\cdot e\cdot n$
\end_inset

.
 Por eso hay funciones predefinidas, que además se separan un poco del factor
 precedente.
 Se insertan como comandos con una barra inversa delante de su nombre.
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="4">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Asen(x)+B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $Asen(x)+B$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
A
\backslash
sen(x)+B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A\sen(x)+B$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Las funciones siguientes están predefinidas:
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Se han añadido los comandos equivalentes proporcionados por el estilo 
\series bold
spanish
\series default
 de 
\series bold
babel
\series default
.
 (Estos no están disponibles en el panel de funciones).
 Además, en su caso, las funciones serán acentuadas automáticamente en la
 salida, p.
\begin_inset space \thinspace{}
\end_inset

e.
 
\begin_inset Quotes fld
\end_inset

lím
\begin_inset Quotes frd
\end_inset

 o 
\begin_inset Quotes fld
\end_inset

máx
\begin_inset Quotes frd
\end_inset

.
 Más información en 
\begin_inset CommandInset citation
LatexCommand cite
key "spanish"

\end_inset

.
 (
\emph on
N.
\begin_inset space \thinspace{}
\end_inset

del t.
\emph default
)
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace -2mm
\end_inset


\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="9" columns="7">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
español
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
español
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
español
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
sin
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
sen
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
sinh
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
senh
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
arcsin
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
arcsen
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
sup
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
cos
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
cosh
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
arccos
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
inf
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
tan
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
tg
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
tanh
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
tgh
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
arctan
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
arctg
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
lim
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
cot
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
cotg
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
coth
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
arg
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
liminf
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
sec
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
min
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
deg
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
limsup
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
csc
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
cosec
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
max
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
det
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Pr
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ln
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
exp
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
dim
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
hom
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
lg
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
log
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ker
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
gcd
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
También se pueden insertar con el botón 
\begin_inset Graphics
        filename ../../images/math/functions.png
        scale 85

\end_inset

 de la barra de ecuaciones.
\end_layout

\begin_layout Subsection
Funciones definidas por el usuario
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Funciones ! personalizadas
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para usar una función no predefinida, como por ejemplo la función signo,
 sgn(x), hay dos posibilidades:
\end_layout

\begin_layout Itemize
Define la función añadiendo al preámbulo LaTeX la línea
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Más sobre 
\series bold

\backslash
DeclareMathOperator
\series default
 en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Operadores-de-usuario"

\end_inset


\end_layout

\end_inset


\begin_inset Newline newline
\end_inset


\begin_inset VSpace -3mm
\end_inset


\begin_inset Newline newline
\end_inset


\series bold

\backslash
DeclareMathOperator{
\backslash
sgn}{sgn}
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! D ! 
\backslash
dbinom@
\backslash
DeclareMathOperator
\end_layout

\end_inset


\begin_inset Newline newline
\end_inset


\begin_inset VSpace -2mm
\end_inset


\begin_inset Newline newline
\end_inset

Ahora la función recién definida se puede obtener con el comando 
\series bold

\backslash
sgn
\series default
.
\end_layout

\begin_layout Itemize
Escribe la ecuación de la forma habitual, marca el nombre de la ecuación,
 en nuestro ejemplo las letras 
\emph on
sgn
\emph default
, y cámbialo a texto matemático.
 Entre el factor precedente y la función se inserta un espacio.
\end_layout

\begin_layout Standard
El resultado con ambos métodos es el mismo que con una función predefinida:
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
En LyX, las funciones personalizadas se ven en rojo, las predefinidas en
 negro.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
A
\backslash
sgn(x)+B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A\sgn(x)+B$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
A
\backslash
,
\begin_inset Formula $\underbrace{\textrm{sgn}}_{\mathsf{Alt+M\, M}}$
\end_inset

(x)+B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A\,\mbox{sgn}(x)+B$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
El primer método es preferible si la función se va a usar varias veces.
\end_layout

\begin_layout Subsection
Límites
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Limites@Límites
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para límites, además de 
\series bold

\backslash
lim
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! L ! 
\backslash
lim
\end_layout

\end_inset

, 
\series bold

\backslash
liminf
\series default
 y 
\series bold

\backslash
limsup
\series default
 están definidas las siguientes funciones:
\series bold
 
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
varliminf
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\varliminf$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
varlimsup
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\varlimsup$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
varprojlim
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\varprojlim$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
varinjlim
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\varinjlim$
\end_inset


\begin_inset Formula $\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
El límite se crea insertando un subíndice.
 Se imprime a la derecha junto a la función en una fórmula en línea:
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="2" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top" width="0pt">
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset space \hspace{}
\length 1cm
\end_inset

Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
lim_x
\backslash
to
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

x=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\rightarrow A}x=B$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
En una ecuación presentada el límite se imprime debajo, como es habitual:
\begin_inset Formula 
\[
\lim\limits _{x\rightarrow A}=B
\]

\end_inset


\end_layout

\begin_layout Subsection
Función módulo
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Funciones ! módulo
\end_layout

\end_inset


\end_layout

\begin_layout Standard
La función módulo es especial, porque existe en cuatro variantes.
\end_layout

\begin_layout Standard
En una ecuación presentada:
\begin_inset Formula 
\begin{align*}
\underline{\textrm{Comando}} &  & \underline{\textrm{Resultado}}\\
\mathrm{a\backslash mod\textrm{\spce}b} &  & a\mod b\\
\mathrm{a\backslash pmod\textrm{\spce}b} &  & a\pmod b\\
\mathrm{a\backslash bmod\textrm{\spce}b} &  & a\bmod b\\
\mathrm{a\backslash pod\textrm{\spce}b} &  & a\pod b
\end{align*}

\end_inset

En una ecuación en línea se pone menos espacio delante del nombre de la
 función para todas las variantes.
\end_layout

\begin_layout Section
Caracteres especiales
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Caracteres especiales
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Caracteres especiales en texto matemático
\end_layout

\begin_layout Standard
Los siguientes comandos sólo se pueden usar en texto matemático o en modo
 TeX:
\end_layout

\begin_layout Standard
\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="2">
<features tabularvalignment="middle">
<column alignment="block" valignment="top" width="0">
<column alignment="block" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
oe
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\textrm{œ}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
OE
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\textrm{Œ}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ae
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\textrm{æ}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
AE
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\textrm{Æ}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
aa
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\textrm{\aa}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
AA
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout

\backslash
@
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textrm{
\backslash
AA}
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\textrm{Å}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
i
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\textrm{ı}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="2">
<features tabularvalignment="middle">
<column alignment="block" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
o
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\textrm{ø}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
O
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\textrm{Ø}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
l
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\textrm{ł}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
L
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\textrm{Ł}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
!
\begin_inset space \hspace{}
\length 0mm
\end_inset

`
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\textrm{!`}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
?
\begin_inset space \hspace{}
\length 0mm
\end_inset

`
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\textrm{?`}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
j
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\textrm{ȷ}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Standard
Los caracteres 
\begin_inset Formula $\textrm{\textrm{Å}}$
\end_inset

 y 
\begin_inset Formula $\textrm{\textrm{Ø}}$
\end_inset

 también se pueden insertar mediante el botón 
\begin_inset Graphics
        filename ../../images/math/digamma.png
        scale 85

\end_inset

 de la barra de ecuaciones.
\end_layout

\begin_layout Standard
Los comandos 
\series bold
!
\begin_inset space \hspace{}
\length 0mm
\end_inset

`
\series default
 y 
\series bold
?
\begin_inset space \hspace{}
\length 0mm
\end_inset

`
\series default
 son una excepción porque se pueden insertar directamente a texto en LyX.
 
\end_layout

\begin_layout Subsection
Acentos en texto
\begin_inset CommandInset label
LatexCommand label
name "sub:Acentos-en-texto"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Acentos ! en texto
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Con los siguientes comandos se pueden acentuar todas las letras.
 Los comandos deben ponerse en modo TeX.
\end_layout

\begin_layout Standard
\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="2">
<features tabularvalignment="middle">
<column alignment="block" valignment="top" width="0">
<column alignment="block" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash

\begin_inset Quotes grd
\end_inset

e
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
"e
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
`e
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
`e
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
^
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

e
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
^e
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
=e
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
=e
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
u
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

e
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
u e
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
b
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

e
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
b e
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
t
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

ee
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
t ee
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="2">
<features tabularvalignment="middle">
<column alignment="block" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
H
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

e
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
H e
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
'e
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
'e
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
~e
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Tilde
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
~e
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
.e
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
.e
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
v
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

e
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
v e
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
d
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

e
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
d e
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
c
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

e
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
c e
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset space \hfill{}
\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
Con el comando 
\series bold

\backslash
t
\series default
 también se pueden acentuar dos caracteres distintos.
 El comando 
\series bold

\backslash
t
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

sz
\series default
 genera 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
t sz
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Los acentos 
\series bold
`
\series default
 , 
\series bold
'
\series default
 y 
\series bold
^
\series default
 se pueden insertar directamente con el teclado sobre vocales sin usar modo
 TeX.
 Lo mismo se aplica a la tilde
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Esto sólo se aplica a teclados en los que la tilde está definida como acento.
\end_layout

\end_inset

 con 
\emph on
a
\emph default
, 
\emph on
o
\emph default
 y 
\emph on
n.
\end_layout

\begin_layout Standard
Los comandos 
\series bold

\backslash
b
\series default
 , 
\series bold

\backslash
c
\series default
 , 
\series bold

\backslash
d
\series default
 , 
\series bold

\backslash
H
\series default
 , 
\series bold

\backslash
t
\series default
 , 
\series bold

\backslash
u
\series default
 , 
\series bold

\backslash
v
\series default
, y acentos insertados directamente con el teclado también están disponibles
 en texto matemático.
 Para otros acentos hay comandos especiales para usar en ecuaciones, véase
 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Acentos-para-un"

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
Además, con el comando 
\series bold

\backslash
textcircled
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! T ! 
\backslash
textcircled
\end_layout

\end_inset

 se pueden insertar en un círculo todos los números y letras, de forma parecida
 al símbolo copyright.
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
textcircled{w}
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textcircled{w}
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Large 
\backslash
textcircled{
\backslash
normalsize
\backslash
protect
\backslash
raisebox{-1.5pt}{W}}
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}$
\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
Large 
\backslash
textcircled{
\backslash
normalsize
\backslash
protect
\backslash
raisebox{-1.5pt}W}
\end_layout

\end_inset


\begin_inset Formula $\raisebox{-2mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Hay que tener cuidado que el carácter se ajuste al círculo.
 Por eso 
\series bold

\backslash
Large
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
véase 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Tamaños-de-tipografías"

\end_inset


\end_layout

\end_inset


\series default
 especifica el tamaño del círculo.
 Con ayuda de 
\series bold

\backslash
raisebox
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
véase 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Marcos-sin-bordes"

\end_inset


\end_layout

\end_inset


\series default
 se puede centrar el carácter.
\end_layout

\begin_layout Subsection
Números en estilo antiguo
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Numeros@Números ! en estilo antiguo
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Los números en estilo antiguo o elzevirianos se componen con el comando
 
\series bold

\backslash
oldstylenums
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! O ! 
\backslash
oldstylenums
\end_layout

\end_inset

.
 El comando se puede usar en ecuaciones y en modo TeX.
 Su esquema es:
\end_layout

\begin_layout Standard

\series bold

\backslash
oldstylenums{número}
\end_layout

\begin_layout Standard
El comando 
\series bold

\backslash
oldstylenums{0123456789}
\series default
 genera: 
\begin_inset Formula $\oldstylenums{0123456789}$
\end_inset


\end_layout

\begin_layout Subsection
Caracteres especiales misceláneos
\begin_inset CommandInset label
LatexCommand label
name "sub:Caracteres-especiales-misceláneos"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Caracteres especiales ! misceláneos
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Los siguientes caracteres sólo pueden insertarse en ecuaciones mediante
 comandos:
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
^
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\mathcircumflex$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
_
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\_$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
^
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\backslash
circ
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout

\backslash
@°
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $^{\circ}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
El símbolo grado ° puede no obstante insertarse directamente si el preámbulo
 LaTeX contiene la línea:
\begin_inset Foot
status open

\begin_layout Plain Layout
Más sobre este asunto en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Caracteres-de-texto"

\end_inset


\end_layout

\end_inset

 
\end_layout

\begin_layout Standard

\series bold

\backslash
DeclareInputtext{176}{
\backslash
ifmmode^
\backslash
circ
\backslash
else
\backslash
textdegree
\backslash
fi}
\end_layout

\begin_layout Section
Estilos de ecuación
\begin_inset CommandInset label
LatexCommand label
name "sec:Estilos-de-ecuación"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! estilos de
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Hay dos estilos diferentes de alineación:
\end_layout

\begin_deeper
\begin_layout Description
Centrado es el estándar predefinido
\end_layout

\begin_layout Description
Sangrado para este estilo debe insertarse la opción de clase 
\series bold
fleqn
\series default
 en el menú 
\family sans
Documento\SpecialChar \menuseparator
Configuración
\family default
 bajo 
\family sans
Clase de documento
\end_layout

\begin_layout Standard
Cuando se usa 
\series bold
Sangrado
\series default
, éste se puede ajustar con la longitud 
\series bold

\backslash
mathindent
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! M ! 
\backslash
mathindent
\end_layout

\end_inset

.
 Para 15
\begin_inset space \thinspace{}
\end_inset

mm, por ejemplo, se inserta esta línea de comando en el preámbulo LaTeX:
\end_layout

\begin_layout Standard

\series bold

\backslash
setlength{
\backslash
mathindent}{15mm}
\end_layout

\begin_layout Standard
Si no se especifica longitud se usa el valor predeterminado de 30
\begin_inset space \thinspace{}
\end_inset

pt.
\end_layout

\end_deeper
\begin_layout Itemize
Y dos estilos diferentes de numeración:
\end_layout

\begin_deeper
\begin_layout Description
Derecha es el estándar predefinido
\end_layout

\begin_layout Description
Izquierda para este estilo debe insertarse la opción de clase 
\series bold
leqno
\series default
 en el menú 
\family sans
Documento\SpecialChar \menuseparator
Configuración
\family default
 bajo 
\family sans
Clase de documento
\end_layout

\end_deeper
\begin_layout Standard

\series bold
fleqn
\series default
 y 
\series bold
leqno
\series default
 también se pueden usar juntos.
 En ese caso se insertan ambas opciones, separadas por una coma.
\end_layout

\begin_layout Standard
Los estilos escogidos se aplican a todas las ecuaciones presentadas del
 documento.
 Si un documento debe tener ecuaciones centradas y sangradas, se usa el
 estilo 
\series bold
Centrado
\series default
 y las ecuaciones sangradas se ponen en un entorno flalign; véase 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Entorno-flalign"

\end_inset

.
\end_layout

\begin_layout Section
Ecuaciones multilínea
\begin_inset CommandInset label
LatexCommand label
name "sec:Ecuaciones-multilínea"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! multilínea
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
General
\end_layout

\begin_layout Standard
En LyX se generan nuevas líneas en una ecuación con 
\family sans
\series bold
Ctrl+Entrar
\family default
\series default
.
 Esto crea un 
\series bold
entorno eqnarray
\series default
, que se describe en
\begin_inset space ~
\end_inset


\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Entorno-eqnarray"

\end_inset

 o, si se ha marcado la opción 
\family sans
Usar
\begin_inset space ~
\end_inset

el
\begin_inset space ~
\end_inset

paquete
\begin_inset space ~
\end_inset

de
\begin_inset space ~
\end_inset

ecuaciones
\begin_inset space ~
\end_inset

AMS
\family default
 en la configuración del documento
\family sans
, un 
\series bold
entorno
\family default
\series default
 
\series bold
align
\series default
, que se describe en
\begin_inset space ~
\end_inset


\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Entorno-align-estándar"

\end_inset

.
\end_layout

\begin_layout Standard
Hay otros entornos para fórmulas multilínea que se pueden introducir mediante
 el menú 
\family sans
Insertar\SpecialChar \menuseparator
Ecuación
\family default
.
 En las siguientes secciones se describen estos entornos.
\end_layout

\begin_layout Standard
En todos los entornos de ecuación multilínea la combinación 
\family sans
Ctrl+Entrar
\family default
 genera una línea nueva.
 Para añadir o quitar líneas se pueden usar los botones 
\begin_inset Graphics
        filename ../../images/tabular-feature_append-row.png
        scale 85

\end_inset

 o 
\begin_inset Graphics
        filename ../../images/tabular-feature_delete-row.png
        scale 85

\end_inset

de la barra de herramientas, respectivamente, o el menú 
\family sans
Editar\SpecialChar \menuseparator
Filas y columnas
\family default
.
\end_layout

\begin_layout Subsubsection
Separación de líneas
\begin_inset CommandInset label
LatexCommand label
name "sub:Separación-de-líneas"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! multilínea ! separación de filas
\end_layout

\end_inset


\end_layout

\begin_layout Standard
A veces no hay suficiente espacio entre las líneas de una ecuación multilínea:
\begin_inset Formula 
\begin{eqnarray*}
B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\
4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0
\end{eqnarray*}

\end_inset

En LaTeX un espacio adicional para una línea se especifica como argumento
 opcional del comando de nueva línea.
 Esto aún no es posible en LYX,
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
véase 
\begin_inset CommandInset href
LatexCommand href
name "LyX-bug #1505"
target "http://www.lyx.org/trac/ticket/1505"

\end_inset


\end_layout

\end_inset

 por lo que toda la ecuación debe insertarse en modo TeX.
 Para añadir espacio en nuestro ejemplo se inserta el comando 
\series bold

\backslash

\backslash
[3mm]
\series default
 al final de la primera línea.
 Así: 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
begin{eqnarray*}
\end_layout

\begin_layout Plain Layout

B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
 = & 
\backslash
textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
\backslash

\backslash
[3mm]
\end_layout

\begin_layout Plain Layout

4x^{2}
\backslash
left(B^{2}+x_{0}^{2}
\backslash
right)+4x_{0}x
\backslash
left(D-B^{2}
\backslash
right)+B^{2}
\backslash
left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
\backslash
right) & = & 0
\end_layout

\begin_layout Plain Layout


\backslash
end{eqnarray*}
\end_layout

\end_inset


\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
Para obtener separación en todas las líneas hay que cambiar la longitud
 
\series bold

\backslash
jot
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! J ! 
\backslash
jot
\end_layout

\end_inset

.
 La definición es: 
\begin_inset Formula $\mbox{separación de línea}=\mathrm{6\, pt+\backslash jot}$
\end_inset

.
 El valor predeterminado para 
\series bold

\backslash
jot
\series default
 es 3
\begin_inset space \thinspace{}
\end_inset

pt.
 Para establecer una separación adicional de 3
\begin_inset space \thinspace{}
\end_inset

mm como en el ejemplo anterior, se inserta el comando
\end_layout

\begin_layout Standard

\series bold

\backslash
setlength{
\backslash
jot}{3mm+3pt}
\end_layout

\begin_layout Standard
en modo TeX antes de la ecuación.
 Es necesario cargar el paquete 
\series bold
calc
\series default

\begin_inset Foot
status collapsed

\begin_layout Plain Layout

\series bold
calc
\series default
 forma parte de toda instalación LaTeX estándar.
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Paquetes ! calc
\end_layout

\end_inset

 en el preámbulo con la línea
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage{calc}
\end_layout

\begin_layout Standard
Se obtiene:
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
setlength{
\backslash
jot}{3mm+3pt}
\end_layout

\end_inset


\begin_inset Formula 
\begin{eqnarray*}
B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\
4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0
\end{eqnarray*}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
setlength{
\backslash
jot}{3pt}
\end_layout

\end_inset

 Para volver a la distancia predeterminada, 
\series bold

\backslash
jot
\series default
 se establece en 3
\begin_inset space \thinspace{}
\end_inset

pt.
\end_layout

\begin_layout Subsubsection
Separación de columnas
\begin_inset CommandInset label
LatexCommand label
name "sub:Separación-de-columnas"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! multilínea !separación de columnas
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Una ecuación multilínea forma una matriz.
 Una ecuación en un entorno eqnarray, por ejemplo, es una matriz con tres
 columnas.
 Cambiando la separación de columnas en este entorno se puede cambiar el
 espacio junto al signo de relación.
\end_layout

\begin_layout Standard
La separación de columnas se especifica con la longitud
\series bold
 
\backslash
arraycolsep
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! A ! 
\backslash
arraycolsep
\end_layout

\end_inset

 según:
\begin_inset Newline newline
\end_inset

separación de columnas = 2
\begin_inset space \thinspace{}
\end_inset


\series bold

\backslash
arraycolsep
\series default

\begin_inset Newline newline
\end_inset

Así, el comando en modo TeX
\end_layout

\begin_layout Standard

\series bold

\backslash
setlength{
\backslash
arraycolsep}{1cm}
\end_layout

\begin_layout Standard
establece para todas las ecuaciones siguientes una separación de columnas
 de 2
\begin_inset space \thinspace{}
\end_inset

cm.
 Para volver al valor predefinido, 
\series bold

\backslash
arraycolsep
\series default
 se pone en 5
\begin_inset space \thinspace{}
\end_inset

pt.
\end_layout

\begin_layout Standard
Una ecuación con separación de 2
\begin_inset space \thinspace{}
\end_inset

cm entre columnas:
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
setlength{
\backslash
arraycolsep}{1cm}
\end_layout

\end_inset


\begin_inset Formula 
\begin{eqnarray*}
A & = & B\\
C & \ne & A
\end{eqnarray*}

\end_inset

Una ecuación con la separación predefinida para matrices, 10
\begin_inset space \thinspace{}
\end_inset

pt:
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
setlength{
\backslash
arraycolsep}{5pt}
\end_layout

\end_inset


\begin_inset Formula 
\begin{eqnarray*}
A & = & B\\
C & \ne & A
\end{eqnarray*}

\end_inset


\end_layout

\begin_layout Subsubsection
Ecuaciones largas
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! larga
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Se pueden componer ecuaciones largas mediante estos métodos:
\end_layout

\begin_layout Itemize
Si un lado de la ecuación es mucho más corto que la anchura de línea, este
 se elige para el lado izquierdo y el derecho se imprime en dos líneas:
\begin_inset Formula 
\begin{eqnarray}
H & = & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\nonumber \\
 &  & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\label{eq:cortolargo}
\end{eqnarray}

\end_inset

El signo menos al principio de la segunda línea normalmente no aparece como
 operador porque es el primer carácter de la línea.
 No se rodearía de espacio y podría no distinguirse de la raya de fracción.
 Para evitarlo se ha insertado 3
\begin_inset space \thinspace{}
\end_inset

pt de espacio detrás del menos con el comando 
\series bold

\backslash
hspace
\series default
.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
véase más sobre 
\series bold

\backslash
hspace
\series default
 en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Espacio-variable"

\end_inset


\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! H ! 
\backslash
hspace
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Si ambos lados de la ecuación son demasiado largos se usa el comando 
\series bold

\backslash
lefteqn
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! L ! 
\backslash
lefteqn
\end_layout

\end_inset

.
 Se inserta en la primer columna de la primera línea y hace que todas las
 inserciones posteriores sobreescriban las columnas siguientes:
\begin_inset Formula 
\begin{eqnarray}
\lefteqn{4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}}\nonumber \\
 &  & -\hspace{3pt}B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\nonumber \\
 &  & =B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\label{eq:lefteqn}
\end{eqnarray}

\end_inset

Tras la inserción de 
\series bold

\backslash
lefteqn
\series default
 el cursor está en un marco púrpura un poco a la izquierda del azul.
 La ecuación se inserta en éste.
\begin_inset Newline newline
\end_inset

El contenido de las restantes líneas se inserta en la segunda columna o
 en otra.
 A mayor número de columna donde se inserte, mayor sangrado.
\begin_inset VSpace medskip
\end_inset


\begin_inset Newline newline
\end_inset


\begin_inset Note Greyedout
status collapsed

\begin_layout Plain Layout
Ten en cuenta lo siguiente si usas 
\series bold

\backslash
lefteqn
\series default
:
\end_layout

\begin_layout Itemize
La ecuación no usa la anchura total de la página.
 Cuando se añade, p.
\begin_inset space \thinspace{}
\end_inset

e., el término 
\begin_inset Formula $-B^{2}$
\end_inset

 en la primera línea del ejemplo, debería estar fuera del margen.
 Para aprovechar mejor la anchura, se puede insertar espacio negativo al
 principio de la primera línea.
\end_layout

\begin_layout Itemize
Debido a un fallo en LyX el cursor no se puede poner con el ratón en la
 primera línea.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
\begin_inset CommandInset href
LatexCommand href
name "LyX-bug #1429"
target "http://www.lyx.org/trac/ticket/1429"

\end_inset


\end_layout

\end_inset

 Sólo se puede poner el cursor al principio de la línea y moverlo con las
 teclas de flecha.
\end_layout

\end_inset

 
\end_layout

\begin_layout Itemize
Se describen otros métodos para escribir fórmulas largas en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Entorno-multilínea"

\end_inset

 y 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Partes-multilínea"

\end_inset

.
\end_layout

\begin_layout Subsubsection
Delimitadores multilínea
\begin_inset CommandInset label
LatexCommand label
name "sub:Delimitadores-multilínea"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Delimitadores ! para varias líneas
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para poner delimitadores que cubran varias líneas hay un problema:
\begin_inset Formula 
\begin{eqnarray*}
A & = & \sen(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
 &  & \left.\cdots+B-D\right]
\end{eqnarray*}

\end_inset

El delimitador de cierre es más pequeño que el de apertura porque los delimitado
res con tamaño variable no abarcan líneas múltiples.
\end_layout

\begin_layout Standard
Para obtener el tamaño adecuado de delimitador para la segunda línea, la
 primera línea se finaliza con 
\series bold

\backslash
right.
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! R ! 
\backslash
right
\end_layout

\end_inset

 y la segunda con 
\series bold

\backslash
left.
\series default
.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Más sobre 
\series bold

\backslash
left.

\series default
 y 
\series bold

\backslash
right.

\series default
 en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Tamaño-automático-de"

\end_inset


\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! L ! 
\backslash
left
\end_layout

\end_inset

 Después de 
\series bold

\backslash
left.

\series default
 se inserta el comando 
\series bold

\backslash
vphantom
\series default

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series bold

\backslash
prod
\series default
^
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series bold

\backslash
infty
\series default

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\series bold

\begin_inset Formula $\downarrow$
\end_inset

_R=1}
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! V ! 
\backslash
vphantom
\end_layout

\end_inset

, porque el operador de multiplicación con sus límites es el símbolo mayor
 en la primera línea y ese debería ser el tamaño para el delimitador en
 la segunda línea.
\end_layout

\begin_layout Standard
El resultado es: 
\begin_inset Formula 
\begin{eqnarray*}
A & = & \sen(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
 &  & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
\end{eqnarray*}

\end_inset


\end_layout

\begin_layout Subsection
Entornos align
\end_layout

\begin_layout Standard
Los entornos align se pueden usar para todo tipo de ecuaciones multilínea.
 Son especialmente apropiados para poner ecuaciones adosadas.
\end_layout

\begin_layout Standard
Los entornos align constan de columnas.
 Las columnas impares se alinean a la derecha, las pares a la izquierda.
 En un entorno align se puede numerar cada línea.
\end_layout

\begin_layout Standard
Los entornos align se crean con el menú 
\family sans
Insertar\SpecialChar \menuseparator
Ecuación
\family default
.
 Una ecuación existente se puede convertir a align con el menú 
\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Cambiar tipo de ecuación
\family default
.
\end_layout

\begin_layout Standard
Para añadir o quitar columnas se pueden usar los botones 
\begin_inset Graphics
        filename ../../images/tabular-feature_append-row.png
        scale 85

\end_inset

 o 
\begin_inset Graphics
        filename ../../images/tabular-feature_delete-row.png
        scale 85

\end_inset

 de la barra de ecuaciones o el menú 
\family sans
Editar\SpecialChar \menuseparator
Filas y columnas
\family default
.
\end_layout

\begin_layout Subsubsection
Entorno align estándar
\begin_inset CommandInset label
LatexCommand label
name "sub:Entorno-align-estándar"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! multilínea ! entorno align
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Este entorno align se crea pulsando 
\family sans
Ctrl+Entrar
\family default
 en una ecuación o con el menú 
\family sans
Insertar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Entorno AMS align
\family default
.
\end_layout

\begin_layout Standard
Un ejemplo para dos ecuaciones adosadas, que se componen con un entorno
 align de cuatro columnas:
\begin_inset Formula 
\begin{align*}
A & =\sen(B) & C & =D\\
C & \neq A & B & \neq D
\end{align*}

\end_inset

Como se puede ver, las ecuaciones en este entorno se colocan como si hubiera
 un 
\series bold

\backslash
hfill
\series default

\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Más sobre 
\series bold

\backslash
hfill
\series default
 en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Espacio-variable"

\end_inset


\end_layout

\end_inset

 antes de la primera y detrás de cada columna par.
 Si se pone en estilo 
\series bold
Sangrado
\series default
,
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
véase estilos de ecuación en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Estilos-de-ecuación"

\end_inset


\end_layout

\end_inset

 la ecuación queda sin el 
\series bold

\backslash
hfill
\series default
 ante la primera columna.
\end_layout

\begin_layout Subsubsection
Entorno alignat
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! multilínea ! entorno alignat
\end_layout

\end_inset


\end_layout

\begin_layout Standard
El entorno alignat no tiene separación predefinida de columnas.
 Se puede insertar manualmente con los espacios descritos en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Espacio"

\end_inset

.
\end_layout

\begin_layout Standard
El ejemplo anterior en el entorno alignat, con un espacio de 1
\begin_inset space \thinspace{}
\end_inset

cm al comienzo da la segunda ecuación:
\begin_inset Formula 
\begin{alignat*}{2}
A & =\sen(B)\hspace{1cm} & C & =D\\
C & \neq A & B & \neq D
\end{alignat*}

\end_inset

Como cada columna puede tener un espacio diferente, este entorno es especialment
e apropiado para poner tres o más ecuaciones adosadas.
\end_layout

\begin_layout Subsubsection
Entorno flalign
\begin_inset CommandInset label
LatexCommand label
name "sub:Entorno-flalign"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! multilínea ! entorno flalign
\end_layout

\end_inset


\end_layout

\begin_layout Standard
En este entorno las dos primeras columnas están siempre tan a la izquierda
 como sea posible y las dos últimas a la derecha.
 Ejemplo:
\begin_inset Formula 
\begin{flalign*}
A & =1 & B & =2 & C & =3\\
X & =\mbox{-}1 & Y & =\mbox{-}2 & Z & =4
\end{flalign*}

\end_inset

En un entorno flalign con un número impar de columnas, en la última de las
 cuales se inserta una llave TeX vacía, se pueden poner varias ecuaciones
 alineadas a la izquierda, aunque se use el estilo 
\series bold
Centrado
\series default
.
 Un ejemplo de fórmula sangrada 
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:IntVol"

\end_inset

:
\begin_inset Formula 
\begin{flalign}
\hspace{30pt}\iiint_{V}X\mbox{d}V & =U & {}
\end{flalign}

\end_inset

Las dos primeras columnas contienen la fórmula.
 Para sangrarla como con el estilo 
\series bold
Sangrado
\series default
, se añade un espacio de 30
\begin_inset space \thinspace{}
\end_inset

pt al comienzo de la primera columna.
 
\end_layout

\begin_layout Subsection
Entorno eqnarray
\begin_inset CommandInset label
LatexCommand label
name "sub:Entorno-eqnarray"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! multilínea ! entorno eqnarray
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! multilínea ! entorno eqnarray
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Al introducir este entorno aparecen tres marcos azules.
 El contenido del primero se alinea a la derecha, el del último a la izquierda.
 El contenido del marco central está centrado y algo más pequeño, porque
 está diseñado para insertar sólo caracteres de relación.
\begin_inset Formula 
\begin{eqnarray*}
\frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
AB & AB & AB\\
A & = & A
\end{eqnarray*}

\end_inset


\end_layout

\begin_layout Subsection
Entorno gather
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! multilínea ! entorno gather
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Este entorno consta de una sola columna centrada.
 Se puede numerar cada línea.
\begin_inset Formula 
\begin{gather}
A=1\\
X=\mbox{-}1
\end{gather}

\end_inset


\end_layout

\begin_layout Subsection
Entorno multilínea
\begin_inset CommandInset label
LatexCommand label
name "sub:Entorno-multilínea"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! multilínea ! entorno multilínea
\end_layout

\end_inset


\end_layout

\begin_layout Standard
El entorno multilínea, como gather, consta de una sola columna.
 Pero la primera línea está alineada a la izquierda, la última a la derecha.
 Las demás están centradas.
 Por tanto este entorno es apropiado para ecuaciones largas.
 Como ejemplo, la ecuación
\begin_inset space ~
\end_inset


\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:lefteqn"

\end_inset

 en entorno multilínea:
\begin_inset Formula 
\begin{multline}
4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\
-B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\\
=B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}
\end{multline}

\end_inset

En la salida sólo aparece numerada la última (primera) línea si la numeración
 del documento es a la derecha (izquierda).
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
véanse los estilos de numeración en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Estilos-de-ecuación"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Con los comandos 
\series bold

\backslash
shoveright
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! S ! 
\backslash
shoveright
\end_layout

\end_inset

 y 
\series bold

\backslash
shoveleft
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! S ! 
\backslash
shoveleft
\end_layout

\end_inset

, una línea centrada se puede alinear a la derecha o a la izquierda, respectivam
ente.
 Los comandos se usan como sigue:
\end_layout

\begin_layout Standard

\series bold

\backslash
shoveright{contenido de la línea}
\series default
 y 
\series bold

\backslash
shoveleft{contenido de la línea}
\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
La longitud 
\series bold

\backslash
multlinegap
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! M ! 
\backslash
multlinegap
\end_layout

\end_inset

 especifica la distancia de la primera línea desde el margen izquierdo de
 la página.
 Esta longitud es 0
\begin_inset space \thinspace{}
\end_inset

pt por omisión.
\end_layout

\begin_layout Standard
Como ejemplo la ecuación anterior con el comando
\end_layout

\begin_layout Standard

\series bold

\backslash
setlength{
\backslash
multlinegap}{2cm}
\end_layout

\begin_layout Standard
insertado previamente en modo TeX:
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
setlength{
\backslash
multlinegap}{2cm}
\end_layout

\end_inset


\begin_inset Formula 
\begin{multline}
4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\
\shoveleft{-B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}\\
=B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}
\end{multline}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
setlength{
\backslash
multlinegap}{0pt}
\end_layout

\end_inset

La segunda línea se ha alineado a la izquierda con 
\series bold

\backslash
shoveleft
\series default
.
\end_layout

\begin_layout Subsection
Ecuación con partes multilínea
\begin_inset CommandInset label
LatexCommand label
name "sub:Partes-multilínea"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! multilínea ! solo parte
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para mostrar solo partes de una ecuación en modo multilínea usa uno de los
 siguientes entornos: 
\series bold
aligned
\series default
, 
\series bold
alignedat
\series default
, 
\series bold
gathered
\series default
 o 
\series bold
split
\series default
.
 Se pueden elegir en el menú 
\family sans
Insertar\SpecialChar \menuseparator
Ecuación
\family default
 o usando los comandos aquí descritos.
\end_layout

\begin_layout Standard
Los tres primeros tienen las mismas propiedades que los correspondientes
 entornos multilínea, pero es posible poner al lado más partes de la ecuación.
 Un ejemplo:
\begin_inset Formula 
\[
\left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
\Delta E\Delta t & \ge\frac{\hbar}{2}
\end{aligned}
\right\} \mbox{Relaciones de incertidumbre}
\]

\end_inset

Para componer esta expresión se inserta una ecuación presentada y en ella
 se introduce el comando 
\series bold

\backslash
aligned
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! A ! 
\backslash
aligned
\end_layout

\end_inset

.
 Aparece un marco púrpura alrededor del marco azul en el que ahora se pueden
 añadir filas y columnas.
 Fuera del entorno multilínea se pueden poner otras partes de la ecuación,
 como la llave.
\end_layout

\begin_layout Standard
El entorno aligned también es apropiado para ecuaciones largas cuyas líneas
 se alinean horizontalmente.
 Usar aligned en una ecuación presentada tiene la ventaja de que el número
 de ecuación se centra verticalmente con las líneas.
 Como ejemplo, la ecuación 
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:cortolargo"

\end_inset

 en entorno aligned: 
\begin_inset Formula 
\begin{equation}
\begin{aligned}H=\; & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\\
 & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}
\end{aligned}
\end{equation}

\end_inset

Para usar los entornos 
\series bold
alignedat
\series default
, 
\series bold
gathered
\series default
, o 
\series bold
split
\series default
, se insertan respectivamente los comandos
\series bold
 
\backslash
alignedat
\series default
,
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! A ! 
\backslash
alignedat
\end_layout

\end_inset

 
\series bold

\backslash
gathered
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! G ! 
\backslash
gathered
\end_layout

\end_inset

, o 
\series bold

\backslash
split
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! S ! 
\backslash
split
\end_layout

\end_inset

.
 El entorno split tiene las mismas propiedades que aligned pero sólo puede
 tener dos columnas.
\end_layout

\begin_layout Subsection
Texto en ecuaciones multilínea
\begin_inset CommandInset label
LatexCommand label
name "sub:Texto-en-multilínea"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Texto ! en ecuaciones
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! multilínea ! texto en
\end_layout

\end_inset


\end_layout

\begin_layout Standard
En los entornos align, multilínea y gather, se puede insertar texto que
 se mostrará en una línea separada y que no afecta la alineación de columna.
 Para esto se usa el comando 
\series bold

\backslash
intertext
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! I ! 
\backslash
intertext
\end_layout

\end_inset

 con el siguiente esquema:
\end_layout

\begin_layout Standard

\series bold

\backslash
intertext{texto}
\end_layout

\begin_layout Standard
El texto no debería ocupar más de una línea porque no se puede partir con
 guión.
 Como LyX aún no soporta 
\series bold

\backslash
intertext
\series default
 directamente, el texto se escribe como texto matemático.
 
\series bold

\backslash
intertext
\series default
 debe por tanto estar al comienzo de una línea y en la salida se presenta
 sobre esta línea.
 Un ejemplo en el que se ha insertado texto al inicio de la segunda línea:
\begin_inset Formula 
\begin{align}
I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
\intertext{\text{el integrando es simétrico para \ensuremath{\phi=\pi}, por tanto}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
\end{align}

\end_inset


\end_layout

\begin_layout Section
Numeración de ecuaciones
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! numeración|see
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset

Numeración de ecuaciones
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Numeración de ecuaciones
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
General
\end_layout

\begin_layout Standard
Las ecuaciones numeradas se insertan con el menú 
\family sans
Insertar\SpecialChar \menuseparator
Ecuación
\family default
 
\family sans
\SpecialChar \menuseparator
Numerada
\family default
 (atajo 
\family sans
Ctrl+Alt
\begin_inset space ~
\end_inset

N
\family default
).
 Ecuaciones existentes se pueden numerar con el menú 
\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Numerar la ecuación
\family default
 (atajo
\family sans
 Alt+M
\begin_inset space ~
\end_inset

N
\family default
).
 En LyX se muestra detrás de la ecuación el signo almohadilla entre paréntesis.
 En la salida se muestra el número real.
\end_layout

\begin_layout Standard
Si se activa la numeración en ecuaciones multilínea se numerarán todas las
 líneas.
 No obstante, la numeración se puede controlar en cada línea con el menú
 
\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Numerar la línea
\family default
 (atajo
\family sans
 Alt+M
\begin_inset space ~
\end_inset

Mayúsculas+N
\family default
).
\end_layout

\begin_layout Standard
Todas las ecuaciones, excepto en línea, pueden numerarse con dos estilos
 distintos, véase 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Estilos-de-ecuación"

\end_inset

.
\end_layout

\begin_layout Subsection
Referencias cruzadas
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! referencias cruzadas a
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Todas las ecuaciones con etiqueta se pueden referir.
 La etiqueta se añade con el menú 
\family sans
Insertar\SpecialChar \menuseparator
Etiqueta
\family default
 o con el botón 
\begin_inset Graphics
        filename ../../images/label-insert.png
        scale 85

\end_inset

 de la barra de herramientas.
 El cursor debe estar dentro de una ecuación en modo presentación.
 Surge un diálogo con el prefijo 
\series bold
eq:
\series default
, detrás del cual se escribe el texto de la etiqueta.
 El prefijo significa 
\begin_inset Quotes fld
\end_inset

equation
\begin_inset Quotes frd
\end_inset

 y hace más fácil encontrar etiquetas en documentos extensos porque así
 se distingue p.
\begin_inset space \thinspace{}
\end_inset

e.
\begin_inset space ~
\end_inset

de las etiquetas de sección.
 Para cambiar una etiqueta se usa de nuevo el menú 
\family sans
Insertar\SpecialChar \menuseparator
Etiqueta
\family default
.
\end_layout

\begin_layout Standard
En LyX, el nombre de la etiqueta se muestra entre paréntesis detrás de la
 ecuación.
 Una ecuación con etiqueta se numera siempre.
\end_layout

\begin_layout Standard
Las referencias cruzadas se insertan mediante el menú 
\family sans
Insertar\SpecialChar \menuseparator
Referencia cruzada
\family default
 o con el botón 
\begin_inset Graphics
        filename ../../images/dialog-show-new-inset_ref.png
        scale 85

\end_inset

.
 Una referencia a una ecuación aparece en la salida con su número.
 Si en el diálogo de referencia cruzada se elige el formato 
\series bold
(<referencia>)
\series default
, la referencia se muestra en la salida entre paréntesis.
 
\begin_inset Newline newline
\end_inset

En LyX, pulsando clic derecho sobre una referencia cruzada el cursor salta
 a la ecuación de referencia.
\end_layout

\begin_layout Standard
He aquí ejemplos de referencias cruzadas a ecuaciones de las subsecciones
 siguientes:
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout
Observa los distintos tipos de referencias cruzadas.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Las ecuaciones 
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:tag"

\end_inset

 y 
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:c"

\end_inset

 son equivalentes.
 En (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Lat"

\end_inset

) se usan mayúsculas latinas para la numeración, a diferencia de (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Rom"

\end_inset

).
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
Si el argumento de 
\series bold

\backslash
tag
\begin_inset Foot
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
tag
\series default
 se describe en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Numeración-personalizada"

\end_inset


\end_layout

\end_inset


\series default
 contiene un marco, como se describe en la 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Marcos-de-párrafo"

\end_inset

, no se puede referir la ecuación.
\end_layout

\begin_layout Subsection
Subnumeración
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Numeración de ecuaciones ! subnumeración
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Con ayuda de los comandos 
\series bold

\backslash
begin{subequations}
\series default
 y 
\series bold

\backslash
end{subequations}
\series default
 en modo TeX se pueden subnumerar ecuaciones.
\end_layout

\begin_layout Standard
Ejemplo:
\begin_inset Formula 
\begin{equation}
A=C-B\label{eq:a}
\end{equation}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
addtocounter{equation}{-1}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
begin{subequations}
\end_layout

\end_inset


\begin_inset VSpace -5mm
\end_inset


\begin_inset Formula 
\begin{equation}
B=C-A\label{eq:b}
\end{equation}

\end_inset


\begin_inset Formula 
\begin{equation}
C=A+B\label{eq:c}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
end{subequations}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para este ejemplo se ha hecho lo siguiente:
\end_layout

\begin_layout Enumerate
se inserta la primera ecuación
\end_layout

\begin_layout Enumerate
después de ella se inserta
\series bold

\begin_inset Newline newline
\end_inset


\backslash
addtocounter{equation}{-1} 
\backslash
begin{subequations}
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! A ! 
\backslash
addtocounter
\end_layout

\end_inset


\end_layout

\begin_layout Enumerate
se inserta la segunda ecuación
\end_layout

\begin_layout Enumerate
se inserta la tercera ecuación
\end_layout

\begin_layout Enumerate
se inserta 
\series bold

\backslash
end{subequations}
\series default
 tras la tercera ecuación
\end_layout

\begin_layout Standard
Toda ecuación entre los comandos 
\series bold

\backslash
begin
\series default
 y 
\series bold

\backslash
end
\series default
 se subnumera con a, b, c\SpecialChar \ldots{}
 En ecuaciones multilínea se subnumerará cada línea.
 Todas las ecuaciones subnumeradas son tratadas como 
\emph on
una
\emph default
 ecuación numerada.
 Pero como cada ecuación numerada aumenta el contador 
\series bold
equation
\series default
 en uno, hay que disminuir el comando 
\series bold

\backslash
addtocounter
\series default
.
 De lo contrario, las ecuaciones 
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:a"

\end_inset

, 
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:b"

\end_inset

, 
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:c"

\end_inset

 se numerarían 
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:a"

\end_inset

, 
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:d"

\end_inset

, 
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:f"

\end_inset

.
\end_layout

\begin_layout Standard
Al insertar los comandos en modo TeX se crea un espacio entre las dos primeras
 ecuaciones.
 Para evitarlo se inserta ese espacio vertical de -5
\begin_inset space \thinspace{}
\end_inset

mm detrás del comando 
\series bold

\backslash
begin{subequations}
\series default
.

\series bold
 
\series default
Si se usa el estilo 
\series bold
Sangrado
\series default

\begin_inset Foot
status collapsed

\begin_layout Plain Layout
véase estilos de ecuación en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Estilos-de-ecuación"

\end_inset


\end_layout

\end_inset

, entonces se inserta -7
\begin_inset space \thinspace{}
\end_inset

mm.
\end_layout

\begin_layout Standard
Un ejemplo de ecuación multilínea en la que se ha eliminado la numeración
 de la segunda línea:
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
begin{subequations}
\end_layout

\end_inset


\begin_inset Formula 
\begin{eqnarray}
A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
\end{eqnarray}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
end{subequations}
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Numeración definida por el usuario
\begin_inset CommandInset label
LatexCommand label
name "sub:Numeración-personalizada"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Numeración de ecuaciones ! personalizada
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Con la numeración estándar el número se coloca entre paréntesis.
 Para reemplazar los paréntesis con barras verticales, p.
\begin_inset space \thinspace{}
\end_inset

e., se añade al preámbulo LaTeX la línea: 
\end_layout

\begin_layout Standard

\series bold

\backslash
def
\backslash
tagform@#1{
\backslash
maketag@@@{|#1|}}
\series default

\begin_inset Note Note
status collapsed

\begin_layout Plain Layout
Esta macro ya está declarada en el preámbulo LaTeX para pruebas.
 Para activarlo, quita el % del principio.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para usar otros caracteres, se reemplazan las barras al lado de 
\series bold
#1
\series default
 por ellos.
 Para obtener sólo el número de ecuación se omiten las barras verticales.
\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
Si quieres poner una expresión entre paréntesis en vez del número de ecuación
 consecutivo, se usa el comando 
\series bold

\backslash
tag
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! T ! 
\backslash
tag
\end_layout

\end_inset


\series default
:
\begin_inset Formula 
\begin{equation}
A+B=C\tag{algo}\label{eq:tag}
\end{equation}

\end_inset

En este ejemplo se ha insertado el comando
\series bold
 
\backslash
tag
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

algo
\series default
 en la ecuación.
\end_layout

\begin_layout Standard
Si se usa en su lugar el comando con asterisco 
\series bold

\backslash
tag*
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

algo
\series default
 no se imprimen los paréntesis:
\begin_inset Formula 
\[
A+B=C\tag*{algo}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
Para reiniciar la numeración en nuevas partes o secciones del documento
 se usan los siguientes comandos:
\end_layout

\begin_layout Standard

\series bold

\backslash
@addtoreset{equation}{part}
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

"
\end_layout

\end_inset

@
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

"
\end_layout

\end_inset

 ! 
\backslash

\begin_inset ERT
status collapsed

\begin_layout Plain Layout

"
\end_layout

\end_inset

@
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

"
\end_layout

\end_inset

addtoreset
\end_layout

\end_inset


\begin_inset Newline newline
\end_inset


\series bold

\backslash
@addtoreset{equation}{section}
\end_layout

\begin_layout Standard
Pata poder usar estos comandos en modo TeX, el carácter 
\begin_inset Quotes fld
\end_inset

@
\begin_inset Quotes frd
\end_inset

 debe 
\begin_inset Quotes fld
\end_inset

activarse
\begin_inset Quotes frd
\end_inset

 para LaTeX con el comando 
\series bold

\backslash
makeatletter
\series default
.
 El comando 
\series bold

\backslash
makeatother
\series default
 deshace esto.
 Así pues, la secuencia de comandos en modo TeX es:
\end_layout

\begin_layout Standard

\series bold

\backslash
makeatletter
\begin_inset Newline newline
\end_inset


\backslash
@addtoreset{equation}{section}
\begin_inset Newline newline
\end_inset


\backslash
makeatother
\end_layout

\begin_layout Standard
En el preámbulo LaTeX se pueden omitir 
\series bold

\backslash
makeatletter
\series default
 y 
\series bold

\backslash
makeatother
\series default
 pues son automáticamente insertados por LyX.
\end_layout

\begin_layout Standard
Para el comando 
\series bold

\backslash
@addtoreset
\series default
,
\series bold
 
\series default
hay que cargar en el preámbulo LaTeX el archivo 
\series bold
remreset.sty
\series default

\begin_inset Foot
status collapsed

\begin_layout Plain Layout

\series bold
remreset
\series default
 es parte del paquete LaTeX 
\series bold
carlisle
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Paquetes ! carlisle
\end_layout

\end_inset

, incluido en las instalaciones estándar de LaTeX.
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Paquetes ! remreset
\end_layout

\end_inset

 con la línea
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage{remreset}
\end_layout

\begin_layout Standard
Entonces se puede usar el comando 
\series bold

\backslash
@removefromreset
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

"
\end_layout

\end_inset

@
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

"
\end_layout

\end_inset

 ! 
\backslash

\begin_inset ERT
status collapsed

\begin_layout Plain Layout

"
\end_layout

\end_inset

@
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

"
\end_layout

\end_inset

removefromreset
\end_layout

\end_inset

 con el mismo esquema que 
\series bold

\backslash
@addtoreset
\series default
.
\begin_inset VSpace bigskip
\end_inset


\end_layout

\begin_layout Standard
A veces las ecuaciones deberían numerarse de la siguiente manera:
\end_layout

\begin_layout Standard

\family typewriter
(número de sección.número de ecuación)
\end_layout

\begin_layout Standard
El número de ecuación empezaría con 
\begin_inset Quotes fld
\end_inset

1
\begin_inset Quotes frd
\end_inset

 en cada sección.
\end_layout

\begin_layout Standard
Para este caso hay el comando 
\series bold

\backslash
numberwithin
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! N ! 
\backslash
numberwithin
\end_layout

\end_inset

, que se usa con el esquema:
\end_layout

\begin_layout Standard

\series bold

\backslash
numberwithin{counter}{sectioning}
\end_layout

\begin_layout Standard
\begin_inset Quotes fld
\end_inset

counter
\begin_inset Quotes frd
\end_inset

 indica qué clase de numeración es afectada, 
\begin_inset Quotes fld
\end_inset

sectioning
\begin_inset Quotes frd
\end_inset

 indica qué número va delante del punto.
 
\end_layout

\begin_layout Standard
Así pues, en nuestro caso se ha usado la siguiente línea en código TeX o
 en el preámbulo LaTeX:
\end_layout

\begin_layout Standard

\series bold

\backslash
numberwithin{equation}{section}
\end_layout

\begin_layout Standard
Este es el resultado::
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
numberwithin{equation}{section}
\end_layout

\end_inset


\begin_inset Formula 
\begin{equation}
A+B=C
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
Para numerar cuadros de modo que, p.
\begin_inset space \thinspace{}
\end_inset

ej., 
\begin_inset Quotes fld
\end_inset

sectioning
\begin_inset Quotes frd
\end_inset

 sea el número de la parte se usa
\begin_inset Newline newline
\end_inset


\series bold

\backslash
numberwithin{table}{part}
\end_layout

\begin_layout Standard
Para volver a la numeración estándar o evitar esta clase numeración cuando
 es definida por la clase de documento, se inserta el siguiente comando
 en código TeX o en el preámbulo LaTeX:
\end_layout

\begin_layout Standard

\series bold

\backslash
renewcommand{
\backslash
theequation}{
\backslash
arabic{equation}}
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! A ! 
\backslash
arabic
\end_layout

\end_inset


\series default

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
renewcommand{
\backslash
theequation}{
\backslash
arabic{equation}}
\end_layout

\end_inset


\series bold

\begin_inset Newline newline
\end_inset


\series default
o
\series bold

\begin_inset Newline newline
\end_inset


\backslash
renewcommand{
\backslash
thetable}{
\backslash
arabic{table}}
\end_layout

\begin_layout Standard

\series bold

\backslash
numberwithin
\series default
 usa internamente el comando 
\series bold

\backslash
@addtoreset
\series default
, descrito arriba, que también debe ser restaurado.
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
makeatletter
\end_layout

\begin_layout Plain Layout


\backslash
@removefromreset{equation}{section}
\end_layout

\begin_layout Plain Layout


\backslash
makeatother
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Numeración con números romanos y letras
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Numeración de ecuaciones ! con números romanos
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Numeración de ecuaciones ! con letras
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Las ecuaciones también se pueden numerar con números romanos y letras latinas.
 Por ejemplo, para numerar con romanos en minúscula,
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Como en español no se usan romanos en minúscula, el estilo 
\series bold
spanish
\series default
 del sistema 
\series bold
babel
\series default
 redefine 
\series bold

\backslash
roman
\series default
 para que los dé en versalitas.
 Véase 
\begin_inset CommandInset citation
LatexCommand cite
key "spanish"

\end_inset

 (
\emph on
N.
\begin_inset space \thinspace{}
\end_inset

del t
\emph default
).
\end_layout

\end_inset

 se inserta el comando
\end_layout

\begin_layout Standard

\series bold

\backslash
renewcommand{
\backslash
theequation}{
\backslash
roman{equation}}
\end_layout

\begin_layout Standard
antes de la ecuación en modo TeX.
 
\series bold

\backslash
renewcommand
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! R ! 
\backslash
renewcommand
\end_layout

\end_inset

 redefine el comando predefinido 
\series bold

\backslash
theequation
\series default
 como 
\series bold

\backslash
roman{equation}
\series default
.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
El comando 
\series bold

\backslash
renewcommand
\series default
 tiene el mismo esquema que el comando 
\series bold

\backslash
newcommand
\series default
, descrito en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:El-comando-newcommand"

\end_inset

.
\end_layout

\end_inset

 
\series bold
equation
\series default
 es el contador de ecuaciones.
 Si se usa el comando 
\series bold

\backslash
the
\series default
 como prefijo de un contador, el valor del contador sale en números arábigos.
 Si una ecuación es numerada, LaTeX pone internamente el comando 
\series bold

\backslash
theequation
\series default
 detrás de la ecuación.
 
\series bold

\backslash
roman{equation}
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! R ! 
\backslash
roman
\end_layout

\end_inset

 pone el contador en romanos en minúscula.
\end_layout

\begin_layout Standard
Todas las ecuaciones siguientes a 
\series bold

\backslash
renew
\series default
c
\series bold
ommand
\series default
 se numerarán en romanos.
 Para cambiar a números romanos en mayúscula se inserta de nuevo el comando,
 cambiando 
\series bold

\backslash
roman
\series default
 por 
\series bold

\backslash
Roman
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! R ! 
\backslash
roman@
\backslash
Roman
\end_layout

\end_inset

.
 Para 
\begin_inset Quotes fld
\end_inset

numerar
\begin_inset Quotes frd
\end_inset

 con minúsculas latinas hay el comando 
\series bold

\backslash
alph
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! A ! 
\backslash
alph
\end_layout

\end_inset

, y para mayúsculas el comando 
\series bold

\backslash
Alph
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! A ! 
\backslash
alph@
\backslash
Alph
\end_layout

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Note Greyedout
status open

\begin_layout Plain Layout

\series bold
Nota:
\series default
 Con letras latinas sólo se puede numerar hasta un máximo de 26 ecuaciones.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
renewcommand{
\backslash
theequation}{
\backslash
roman{equation}}
\end_layout

\end_inset


\begin_inset Formula 
\begin{equation}
A=\textrm{romanos en minúscula}
\end{equation}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
renewcommand{
\backslash
theequation}{
\backslash
Roman{equation}}
\end_layout

\end_inset


\begin_inset Formula 
\begin{equation}
B=\textrm{romanos en mayúscula}\label{eq:Rom}
\end{equation}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
renewcommand{
\backslash
theequation}{
\backslash
alph{equation}}
\end_layout

\end_inset


\begin_inset Formula 
\begin{equation}
C=\textrm{latinas en minúscula}
\end{equation}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
renewcommand{
\backslash
theequation}{
\backslash
Alph{equation}}
\end_layout

\end_inset


\begin_inset Formula 
\begin{equation}
D=\textrm{latinas en mayúscula}\label{eq:Lat}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
Para volver a la numeración por omisión se inserta el comando:
\end_layout

\begin_layout Standard

\series bold

\backslash
renewcommand{
\backslash
theequation}{
\backslash
arabic{equation}}
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! A ! 
\backslash
arabic
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
renewcommand{
\backslash
theequation}{
\backslash
arabic{equation}}
\end_layout

\end_inset


\begin_inset Formula 
\begin{equation}
E=\mbox{arábigos}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
Como ves, las ecuaciones se numeran consecutivamente independientemente
 del estilo de numeración.
 Cuando la numeración haya de empezar con 
\begin_inset Quotes fld
\end_inset

1
\begin_inset Quotes frd
\end_inset

 al cambiar el estilo, hay que definir nuevos contadores de ecuación.
 Una descripción sobre esto se encuentra en el archivo 
\begin_inset CommandInset href
LatexCommand href
name "Formula-numbering.lyx"
target "run:Formula-numbering.lyx"

\end_inset

.
\end_layout

\begin_layout Section
Símbolos y ecuaciones químicas
\begin_inset CommandInset label
LatexCommand label
name "sub:Símbolos-y-ecuaciones-químicas"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Química ! símbolos
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Química ! caracteres
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! química|see
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset

Química
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Química ! iones
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Iones|see
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

{
\end_layout

\end_inset

Química
\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}
\end_layout

\end_inset


\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Química ! reacción
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Un ejemplo de texto de química:
\end_layout

\begin_layout Quote
El ion 
\begin_inset Formula $\mathrm{SO_{4}^{2-}}$
\end_inset

 reacciona con dos iones 
\begin_inset Formula $\mathrm{Na^{+}}$
\end_inset

 para dar sulfato de sodio 
\begin_inset Formula $\mathrm{(Na_{2}SO_{4})}$
\end_inset

.
 La ecuación química es:
\begin_inset Formula 
\begin{equation}
\mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:reaccion-quimica}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
Esta ecuación química puede componerse directamente en modo ecuación.
 Para evitar que los símbolos se impriman en cursiva, se selecciona todo
 y con el atajo 
\family sans
Alt+C
\begin_inset space ~
\end_inset

R
\family default
 se cambia en redonda.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
véase estilos de tipografías en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Estilos-de-tipografías"

\end_inset

.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para escribir ecuaciones químicas es más conveniente usar el comando 
\series bold

\backslash
ce
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! C ! 
\backslash
ce
\end_layout

\end_inset

, que está disponible si está instalado el paquete LaTeX 
\series bold
mhchem
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Paquetes ! mhchem
\end_layout

\end_inset

.
 Al insertar 
\series bold

\backslash
ce
\series default
 en modo matemático aparece un nuevo marco azul en el que se pueden escribir
 ecuaciones químicas de una forma intuitiva.
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="9" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ce
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

H2CO3
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ce
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

SO4^2-
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ce
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

(NH4)2S
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ce
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

KCr(SO4)2.12H2O
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ce
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A-B
\backslash
dbond
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

C
\backslash
tbond
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

D
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ce
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

^227
\begin_inset Formula $\downarrow$
\end_inset

_90
\begin_inset Formula $\to$
\end_inset

Th+
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ce
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

CO2
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

+
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

C
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

<=>
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

2CO
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
ce
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

CO2
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

+
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

C
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

->[
\backslash
alpha][
\backslash
beta]
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

2CO}
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Note Greyedout
status open

\begin_layout Plain Layout

\series bold
Nota:
\series default
 Insertar modo matemático en un marco 
\series bold

\backslash
ce
\series default
 provocará errores de LaTeX.
 En estos casos hay que usar código TeX, como en 
\series bold

\backslash
ce{$
\backslash
mu
\backslash
hyphen$Cl}
\series default
: 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ce{$
\backslash
mu
\backslash
hyphen$Cl}
\end_layout

\end_inset

 
\end_layout

\end_inset


\end_layout

\begin_layout Standard
El comando 
\series bold

\backslash
ce
\series default
 para la 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:reaccion-quimica"

\end_inset

 es
\begin_inset Newline newline
\end_inset


\series bold
 
\backslash
ce
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

2Na+
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

+
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

SO4^2-
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

->
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

Na2SO4
\end_layout

\begin_layout Standard
Para componer ecuaciones químicas multilínea primero se crea una ecuación
 multilínea, tal como se describe en la 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Ecuaciones-multilínea"

\end_inset

.
 Después se utiliza el comando 
\series bold

\backslash
ce
\series default
 en cada cuadrito azul de la ecuación.
 La 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:TEOS-reac-1"

\end_inset

 y la 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:TEOS-reac-2"

\end_inset

 son ejemplos de una reacción química en dos fases en la que cada ecuación
 tiene su propio número.
\begin_inset Formula 
\begin{eqnarray}
\ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reac-1}\\
\ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reac-2}
\end{eqnarray}

\end_inset


\end_layout

\begin_layout Standard
Además de 
\series bold

\backslash
ce
\series default
 el paquete 
\series bold
mhchem
\series default
 suministra el comando 
\series bold

\backslash
cf
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! C ! 
\backslash
cf
\end_layout

\end_inset

 que ha de utilizarse en casos especiales.
 Para más información sobre 
\series bold

\backslash
cf
\series default
 y más ejemplos echa un vistazo a la documentación de 
\series bold
mhchem
\series default
, 
\begin_inset CommandInset citation
LatexCommand cite
key "mhchem"

\end_inset

.
\end_layout

\begin_layout Section
Diagramas
\end_layout

\begin_layout Standard
Lyx soporta dos tipos de diagramas conmutativos: 
\series bold
amscd
\series default
 y 
\series bold
xymatrix
\series default
, que se explican a continuación.
\end_layout

\begin_layout Subsection
Diagramas amscd
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Diagramas ! amscd
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Los diagramas de este tipo visualizan relaciones mediante líneas o flechas
 verticales y horizontales:
\begin_inset Formula 
\[
\begin{CD}A@)))B@)))C\\
@AAA@.@VVV\\
F@(((E@(((D
\end{CD}
\]

\end_inset

Para obtener el diagrama se inserta en la ecuación el comando 
\series bold

\backslash
CD
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! C ! 
\backslash
CD
\end_layout

\end_inset


\series default
.
 Surge un marco azul entre dos líneas de trazos en el que se insertan a
 continuación comandos.
 Con 
\family sans
Ctrl+Entrar
\family default
 se inicia una nueva línea.
 En las líneas impares se insertan relaciones horizontales, en las pares
 verticales.
\end_layout

\begin_layout Standard
Para componer las relaciones hay los siguientes comandos:
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fn:sinónimos"

\end_inset

Los comandos con 
\family sans
'
\series bold
>
\series default
'
\family default
 o 
\family sans
'
\series bold
<
\series default
'
\family default
 pueden generar errores con el estilo 
\series bold
spanish
\series default
 de 
\series bold
babel
\series default
.
 Para evitarlo se pueden sustituir por sus sinónimos 
\family sans
'
\series bold
)
\series default
'
\family default
 y 
\family sans
'
\series bold
(
\series default
'
\family default
 respectivamente.
 Véase 
\begin_inset CommandInset citation
LatexCommand cite
key "spanish"

\end_inset

.
 (
\emph on
N.
\begin_inset space \thinspace{}
\end_inset

del t.
\emph default
)
\end_layout

\end_inset


\end_layout

\begin_layout Itemize

\series bold
@<<<
\series default
 genera una flecha hacia la izquierda, 
\series bold
@>>>
\series default
 una hacia la derecha, y 
\series bold
@=
\series default
 un signo igual largo
\end_layout

\begin_layout Itemize

\series bold
@AAA
\series default
 genera una flecha hacia arriba, 
\series bold
@VVV
\series default
 una hacia abajo, y 
\series bold
@|
\series default
 un signo igual vertical
\end_layout

\begin_layout Itemize

\series bold
@.

\series default
 genera una ubicación vacía para relaciones inexistentes
\end_layout

\begin_layout Standard
Todas las flechas pueden etiquetarse como sigue:
\end_layout

\begin_layout Itemize
Si se inserta texto entre el primero y el segundo 
\series bold
<
\series default
 o 
\series bold
>
\series default
, respectivamente, se muestra sobre la flecha.
 Si se inserta entre el segundo y el tercero, bajo la flecha.
\end_layout

\begin_layout Itemize
Para flechas verticales, si se inserta texto entre la primera y la segunda
 
\series bold
A
\series default
 o 
\series bold
V
\series default
, respectivamente, se muestra al lado izquierdo de la flecha.
 Si se inserta entre la segunda y la tercera, al lado derecho.
 Si el texto contiene A o V, estas letras deben ponerse entre llaves TeX.
\end_layout

\begin_layout Standard
Como ejemplo un diagrama con todas las relaciones posibles:
\begin_inset Formula 
\[
\begin{CD}A@)j))B@))k)C@=F\\
@AmAA@.@VV{V}V@|\\
D@((j\,(E@)k))F@=C
\end{CD}
\]

\end_inset

El comando para este diagrama es:
\begin_inset Newline newline
\end_inset


\series bold

\backslash
CD
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A@>j>>B@>>k>C@=F Ctrl+Entrar
\begin_inset Newline newline
\end_inset


\begin_inset Phantom HPhantom
status open

\begin_layout Plain Layout

\series bold

\backslash
CD
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\end_layout

\end_inset

@AmAA@.@VV
\backslash
{V
\series default

\begin_inset Formula $\to$
\end_inset


\series bold
V@| Ctrl+Entrar
\begin_inset Newline newline
\end_inset


\begin_inset Phantom HPhantom
status open

\begin_layout Plain Layout

\series bold

\backslash
CD
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset


\end_layout

\end_inset

D@<<j<E@>k>>F@=C
\end_layout

\begin_layout Subsection
Diagramas xymatrix
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Diagramas ! xymatrix
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para usar matrices xy debe estar instalado el paquete LaTeX 
\series bold
xypic
\series default
.
 Una matriz xy se crea insertando el comando 
\series bold

\backslash
xymatrix
\series default
 en una ecuación.
 Después podrás añadir nuevas columnas y filas como en matrices normales,
 véase
\begin_inset space ~
\end_inset


\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Matrices"

\end_inset

.
\end_layout

\begin_layout Standard
A diferencia de los diagramas amscd, las matrices xy soportan flechas diagonales
 y curvadas, y mucho más.
 Todas las posibilidades para generar diagramas conmutativos y decoraciones
 se explican en el 
\emph on
Manual de XY-pic
\emph default
 que se encuentra en el menú 
\family sans
Ayuda\SpecialChar \menuseparator
Manuales
\begin_inset space ~
\end_inset

específicos
\family default
.
\end_layout

\begin_layout Subsection
Diagramas 
\noun on
Feynman
\noun default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Diagramas ! Feynman
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para usar diagramas 
\noun on
Feynman
\noun default
 debe estar instalado el paquete LaTeX 
\series bold
feyn
\series default
.
 Un diagrama 
\noun on
Feynman
\noun default
 se crea insertando el comando 
\series bold

\backslash
Diagram
\series default
 en una ecuación.
 Después podrás añadir nuevas columnas y filas como en matrices normales,
 véase
\begin_inset space ~
\end_inset


\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Matrices"

\end_inset

.
\end_layout

\begin_layout Standard
En el 
\emph on
Manual de diagramas Feynman
\emph default
, disponible en 
\family sans
Ayuda\SpecialChar \menuseparator
Manuales
\begin_inset space ~
\end_inset

específicos
\family default
, hay ejemplos de diagramas de este tipo.
\end_layout

\begin_layout Section
Comandos definidos por el usuario
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos de usuario
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Note Greyedout
status open

\begin_layout Plain Layout

\series bold
Nota:
\series default
 Los nombres de los comandos definidos por el usuario y macros solo pueden
 contener letras latinas.
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
El comando 
\backslash
newcommand
\begin_inset CommandInset label
LatexCommand label
name "sub:El-comando-newcommand"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos de usuario ! 
\backslash
newcommand
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! N ! 
\backslash
newcommand
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Muchos comandos LaTeX son demasiado largos para usarlos con frecuencia.
 Pero es posible definir nuevos comandos más cortos con el comando 
\series bold

\backslash
newcommand
\series default
.
 
\end_layout

\begin_layout Standard
El esquema del comando 
\series bold

\backslash
newcommand
\series default
 es:
\end_layout

\begin_layout Standard

\series bold

\backslash
newcommand{nombre nuevo de comando}[número de argumentos]
\begin_inset Newline newline
\end_inset


\begin_inset Phantom HPhantom
status open

\begin_layout Plain Layout

\series bold

\backslash
newcommand
\end_layout

\end_inset

[valor opcional]{definición de comando}
\end_layout

\begin_layout Standard
\begin_inset Note Greyedout
status open

\begin_layout Plain Layout

\series bold
Nota:
\series default
 Asegúrate de que el nombre del nuevo comando no está definido ya en el
 documento o en paquetes LaTeX que uses.
 Por ejemplo, si defines el comando 
\series bold

\backslash
le
\series default
 para 
\series bold

\backslash
Leftarrow,
\series default
 se producirán errores porque 
\series bold

\backslash
le
\series default
 ya existe para 
\begin_inset Quotes fld
\end_inset


\begin_inset Formula $\le$
\end_inset


\begin_inset Quotes frd
\end_inset

.

\series bold
 
\end_layout

\end_inset


\end_layout

\begin_layout Standard
El número de argumentos es un entero en el rango 0-9 y especifica cuántos
 argumentos debería tener el nuevo comando.
 Con el valor opcional se puede predefinir un valor para un argumento opcional.
 Cuando se hace esto, el 
\emph on
primer
\emph default
 argumento del nuevo comando es automáticamente opcional.
\end_layout

\begin_layout Standard
Veamos unos ejemplos:
\end_layout

\begin_layout Itemize
Para definir el comando 
\series bold

\backslash
gr
\series default
 para 
\series bold

\backslash
Longrightarrow
\series default
, la línea de preámbulo LaTeX es:
\begin_inset VSpace medskip
\end_inset


\begin_inset Newline newline
\end_inset


\series bold

\backslash
newcommand{
\backslash
gr}{
\backslash
Longrightarrow}
\end_layout

\begin_layout Itemize
Para definir el comando 
\series bold

\backslash
us
\series default
 para 
\series bold

\backslash
underline
\series default
, el argumento (que sería subrayado) debe tenerse en cuenta.
 Para esto la línea de preámbulo es:
\begin_inset VSpace medskip
\end_inset


\begin_inset Newline newline
\end_inset


\series bold

\backslash
newcommand{
\backslash
us}[1]{
\backslash
underline{#1}}
\series default

\begin_inset VSpace medskip
\end_inset


\begin_inset Newline newline
\end_inset

El carácter 
\series bold
#
\series default
 actúa como colocador del argumento, el 
\series bold
1
\series default
 indica que es el colocador para el primer argumento.
\end_layout

\begin_layout Itemize
Para 
\series bold

\backslash
framebox
\series default
 se puede definir, por ejemplo, el comando 
\series bold

\backslash
fb
\series default
:
\begin_inset VSpace medskip
\end_inset


\begin_inset Newline newline
\end_inset


\series bold

\backslash
newcommand{
\backslash
fb}[3]{
\backslash
framebox#1#2{$#3$}}
\series default

\begin_inset VSpace medskip
\end_inset


\begin_inset Newline newline
\end_inset

Los dos signos dólar generan la ecuación extra necesaria para 
\series bold

\backslash
framebox
\series default
, véase 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Marcos-con-bordes"

\end_inset

.
\end_layout

\begin_layout Itemize
Para crear un nuevo comando para 
\series bold

\backslash
fcolorbox
\series default
 donde no es necesario especificar el color para el marco, el argumento
 para el color se define opcional:
\begin_inset VSpace medskip
\end_inset


\begin_inset Newline newline
\end_inset


\series bold

\backslash
newcommand{
\backslash
cb}[3][white]{
\backslash
fcolorbox{#2}{#1}{$#3$}}
\series default

\begin_inset VSpace medskip
\end_inset


\begin_inset Newline newline
\end_inset

Si el color no es especificado al usar 
\series bold

\backslash
cb
\series default
, se elige el color 
\series bold
white
\series default
 predefinido.
\end_layout

\begin_layout Standard
Un ensayo con los nuevos comandos definidos:
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="6" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
A
\backslash
gr
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $A\gr B$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
us{ABcd
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
fb{[2cm]
\begin_inset Formula $\to$
\end_inset


\backslash
{
\begin_inset Formula $\to$
\end_inset


\backslash
{
\backslash
int
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
cb{red
\begin_inset Formula $\to$
\end_inset


\backslash
{
\backslash
int
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
cb[green]
\backslash
{red
\begin_inset Formula $\to$
\end_inset


\backslash
{
\backslash
int
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Subsection
Macros de ecuaciones
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos de usuario ! Macros de ecuaciones
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Macros
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Los comandos definidos por el usuario son especialmente convenientes para
 expresiones complejas.
 Por ejemplo, si estás trabajando en un documento con ecuaciones cuadráticas,
 el mismo tipo de solución se repite varias veces.
 La forma general de una ecuación de segundo grado es:
\begin_inset Formula 
\[
0=\lambda^{2}+p\lambda+q
\]

\end_inset

La forma general de la solución es:
\begin_inset Formula 
\[
\lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
\]

\end_inset


\end_layout

\begin_layout Standard
Para definir un comando para la ecuación de la solución, en donde solo hay
 que especificar los tres parámetros 
\begin_inset Formula $\lambda$
\end_inset

, 
\begin_inset Formula $p$
\end_inset

, y 
\begin_inset Formula $q$
\end_inset

, y el índice de 
\begin_inset Formula $\lambda$
\end_inset

 puede darse opcionalmente, la línea de preámbulo LaTeX es
\begin_inset Newline newline
\end_inset


\series bold

\backslash
newcommand{
\backslash
qG}[4][1,
\backslash
,2]{#2_{#1}=-
\backslash
frac{#3}{2}
\backslash
pm
\begin_inset Newline newline
\end_inset


\begin_inset Phantom HPhantom
status open

\begin_layout Plain Layout

\series bold

\backslash
newcommand
\end_layout

\end_inset


\backslash
sqrt{
\backslash
frac{#3^{2}}{4}-#4}}
\end_layout

\begin_layout Standard
Para generar la solución se inserta el comando
\begin_inset Newline newline
\end_inset


\series bold

\backslash
qG{
\backslash
lambda
\begin_inset Formula $\to$
\end_inset


\backslash
{p
\begin_inset Formula $\to$
\end_inset


\backslash
{q
\series default
 en una ecuación
\series bold
.
\end_layout

\begin_layout Standard
La definición del nuevo comando no es intuitiva porque hay que conocer los
 esquemas de todos los comandos LaTeX usados, por ejemplo, que una fracción
 se inserta en LaTeX como
\series bold
 
\backslash
frac{numerador}{denominador}
\series default
.
 Además, uno puede olvidar fácilmente una llave en la definición y no puede
 ver en LyX lo que el nuevo comando está haciendo.
 Para evitar estos problemas, LyX ofrece la posibilidad de usar macros de
 ecuación en vez del comando
\series bold
 
\backslash
newcommand
\series default
.
\end_layout

\begin_layout Standard
Una macro de ecuación se crea con el menú 
\family sans
Insertar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Macro
\family default
 o con el botón 
\begin_inset Graphics
        filename ../../images/math-macro_newmacroname_newcommand.png
        scale 85

\end_inset

 de la barra de herramientas.
 Aparecen entonces la barra de herramientes de macros de ecuación y un recuadro
 como el siguiente donde se define la macro:
\begin_inset Newline newline
\end_inset


\end_layout

\begin_layout Standard
\begin_inset space \hspace*{\fill}
\end_inset


\begin_inset Graphics
        filename ../clipart/macrobox.png

\end_inset


\begin_inset space \hspace*{\fill}
\end_inset


\begin_inset Newline newline
\end_inset


\begin_inset FormulaMacro
\newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
\end_inset


\backslash
newmacroname es el nombre por omisión y debería cambiarse por alguno sensato.
 En el primer marco azul se inserta la ecuación buscada.
 Con el comando 
\series bold

\backslash
#númerodeargumento
\series default
, , o con el botón 
\begin_inset Graphics
        filename ../../images/math-macro-add-param.png
        scale 85

\end_inset

 de la barra de herramientas de macros se inserta un colocador de argumento,
 p.
\begin_inset space \thinspace{}
\end_inset

e
\begin_inset space \space{}
\end_inset


\series bold

\backslash
#1
\series default
.
 Los colocadores de argumento se muestran en rojo.
 Se pueden poner 9 argumentos como máximo.
 Con el botón 
\begin_inset Graphics
        filename ../../images/math-macro-add-optional-param.png
        scale 85

\end_inset

 se crean argumentos opcionales.
 El primer argumento no opcional puede transformarse en opcional con el
 botón 
\begin_inset Graphics
        filename ../../images/math-macro-make-optional.png
        scale 85

\end_inset

.
 En el segundo marco azul puede definirse el aspecto de la macro en LyX.
 Normalmente quieres verlo tal como está definido, así que el recuadro se
 deja vacío.
 Pero si has creado una macro que necesita mucho espacio en la pantalla,
 en dicho recuadro puedes insertar, por ejemplo
\begin_inset Newline newline
\end_inset


\series bold
qG: 
\backslash
#1
\series default
 
\series bold
,
\series default
 
\series bold

\backslash
#2
\series default
 
\series bold
,
\series default
 
\series bold

\backslash
#3, 
\backslash
#4
\begin_inset Newline newline
\end_inset


\series default
Para la macro solo los argumentos con el nombre delante de ellos se mostrarán
 en LyX, lo que conlleva una visualización mejor.
 La ecuación aparece en la salida tal como se ha definido en el primer recuadro.
\begin_inset Newline newline
\end_inset

Además, el aspecto de las macros en las ecuaciones puede cambiarse para
 macros individuales situando el cursor en la macro y usando el menú 
\family sans
Ver\SpecialChar \menuseparator
(Des)plegar macro de ecuación.
\end_layout

\begin_layout Standard
Para usar una macro, se inserta el nombre de la misma como comando en una
 ecuación, en nuestro caso 
\series bold

\backslash
qG
\series default
.
 Nuestra macro se muestra en LyX así:
\begin_inset Newline newline
\end_inset


\begin_inset space \hspace*{\fill}
\end_inset


\begin_inset Graphics
        filename ../clipart/macrouse.png

\end_inset


\begin_inset space \hspace*{\fill}
\end_inset


\begin_inset Newline newline
\end_inset

Aquí tenemos nuestro ejemplo de macro con los argumentos 
\begin_inset Formula $x$
\end_inset

, 
\begin_inset Formula $\ln(x)$
\end_inset

, y 
\begin_inset Formula $B$
\end_inset

:
\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\qG x{\ln(x)}B
\]

\end_inset


\end_layout

\begin_layout Standard
LyX ofrece en el menú 
\family sans
Herramientas
\family default
\SpecialChar \menuseparator

\family sans
Preferencias\SpecialChar \menuseparator
Edición\SpecialChar \menuseparator
Control
\family default
 diferentes estilos para editar macros.
 Para encontrar el estilo que más te convenga, elige un estilo y pon el
 cursor en una macro para ver la diferencia.
\end_layout

\begin_layout Standard
Una macro de ecuación se transforma internamente en un comando 
\series bold

\backslash
newcommand
\series default
 cuando se exporta el documento.
 El comando creado 
\series bold

\backslash
newcommand
\series default
 no se coloca en el preámbulo LaTeX, por tanto las macros solo se pueden
 usar en ecuaciones que estén en recuadros de definición de macros en el
 documento.
 
\end_layout

\begin_layout Standard
Las macros de ecuación también pueden crearse directamente a partir de un
 comando
\series bold
 
\backslash
newcommand
\series default
.
 Por ejemplo, escribiendo el comando
\begin_inset Newline newline
\end_inset


\series bold

\backslash
newcommand{
\backslash
larrow}[2]{
\backslash
xleftarrow[#2]{#1}}
\begin_inset Newline newline
\end_inset


\series default
como texto normal en LyX, seleccionándolo completamente y usando a continuación
 el atajo 
\family sans
Ctrl+M
\family default
, el comando se transformará en una macro de ecuación.
 Al emplear este método debes tener cuidado en escribir correctamente el
 comando 
\series bold

\backslash
newcommand
\series default
, de lo contrario la macro defectuosa lleva a obtener errores LaTeX.
 
\end_layout

\begin_layout Standard
Las macros de ecuación todavía tienen el problema de que fórmulas adicionales
 en definiciones de macros se manejan incorrectamente.
 Por eso el ejemplo 
\series bold

\backslash
fb
\series default
 de 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:El-comando-newcommand"

\end_inset

 no puede crearse como macro.
\end_layout

\begin_layout Standard
Cuando el cursor está en un recuadro de definición de macro, verás en LyX
 la barra de herramientas de macros:
\end_layout

\begin_layout Standard
\begin_inset VSpace defskip
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Graphics
        filename ../clipart/MacroToolbar.png

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Macros ! Barra de herramientas
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace defskip
\end_inset


\end_layout

\begin_layout Standard
La barra de herramientas de macros contiene los siguientes botones:
\end_layout

\begin_layout Standard
\begin_inset VSpace defskip
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="9" columns="2">
<features islongtable="true" longtabularalignment="center">
<column alignment="left" valignment="top" width="0">
<column alignment="left" valignment="top" width="85col%">
<row interlinespace="2.5mm">
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Graphics
        filename ../../images/math-macro-remove-param.png
        rotateOrigin center

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Definición de macro\SpecialChar \menuseparator
Quitar último argumento
\end_layout

\end_inset
</cell>
</row>
<row interlinespace="2.5mm">
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Graphics
        filename ../../images/math-macro-add-param.png
        rotateOrigin center

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Definición de macro\SpecialChar \menuseparator
Añadir argumento
\end_layout

\end_inset
</cell>
</row>
<row interlinespace="2.5mm">
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Graphics
        filename ../../images/math-macro-make-optional.png
        rotateOrigin center

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Definición de macro\SpecialChar \menuseparator
Hacer opcional el primer
\begin_inset Newline newline
\end_inset


\begin_inset Phantom HPhantom
status open

\begin_layout Plain Layout

\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Definición de macro\SpecialChar \menuseparator

\end_layout

\end_inset

argumento no opcional
\end_layout

\end_inset
</cell>
</row>
<row interlinespace="2.5mm">
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Graphics
        filename ../../images/math-macro-make-nonoptional.png
        rotateOrigin center

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Definición de macro\SpecialChar \menuseparator
Hacer no opcional el primer
\begin_inset Newline newline
\end_inset


\begin_inset Phantom HPhantom
status open

\begin_layout Plain Layout

\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Definición de macro\SpecialChar \menuseparator

\end_layout

\end_inset

argumento opcional
\end_layout

\end_inset
</cell>
</row>
<row interlinespace="2.5mm">
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Graphics
        filename ../../images/math-macro-remove-optional-param.png
        rotateOrigin center

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Definición de macro\SpecialChar \menuseparator
Quitar argumento opcional
\end_layout

\end_inset
</cell>
</row>
<row interlinespace="2.5mm">
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Graphics
        filename ../../images/math-macro-add-optional-param.png
        rotateOrigin center

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Definición de macro\SpecialChar \menuseparator
Insertar argumento opcional
\end_layout

\end_inset
</cell>
</row>
<row interlinespace="2.5mm">
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Graphics
        filename ../../images/math-macro-remove-greedy-param.png
        rotateOrigin center

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Definición de macro\SpecialChar \menuseparator
Quitar último argumento
\begin_inset Newline newline
\end_inset


\begin_inset Phantom HPhantom
status open

\begin_layout Plain Layout

\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Definición de macro\SpecialChar \menuseparator

\end_layout

\end_inset

yendo hacia la derecha
\end_layout

\end_inset
</cell>
</row>
<row interlinespace="2.5mm">
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Graphics
        filename ../../images/math-macro-append-greedy-param.png
        rotateOrigin center

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Definición de macro\SpecialChar \menuseparator
Añadir argumento comiendo
\begin_inset Newline newline
\end_inset


\begin_inset Phantom HPhantom
status open

\begin_layout Plain Layout

\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Definición de macro\SpecialChar \menuseparator

\end_layout

\end_inset

desde la derecha
\end_layout

\end_inset
</cell>
</row>
<row interlinespace="2.5mm">
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Graphics
        filename ../../images/math-macro-add-greedy-optional-param.png
        rotateOrigin center

\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Definición de macro\SpecialChar \menuseparator
Añadir argumento opcional
\begin_inset Newline newline
\end_inset


\begin_inset Phantom HPhantom
status open

\begin_layout Plain Layout

\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Definición de macro\SpecialChar \menuseparator

\end_layout

\end_inset

comiendo desde la derecha
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Section
Sistema algebraico computacional
\end_layout

\begin_layout Standard
LyX permite el intercambio entre expresiones matemáticas escritas con su
 editor de ecuaciones y aplicaciones externas o guiones definidos por el
 usuario.
 Las aplicaciones soportadas actualmente son 
\family sans
Maple
\family default
, 
\family sans
Mathematica
\family default
, 
\family sans
Maxima
\family default
 y 
\family sans
Octave
\family default
.
 Hay que advertir que el conjunto de estructuras matemáticas soportadas
 se limita a casos muy simples.
\end_layout

\begin_layout Subsection
Utilización
\end_layout

\begin_layout Standard
Escribe alguna expresión en una ecuación, despliega el menú 
\family sans
Editar\SpecialChar \menuseparator
Ecuación\SpecialChar \menuseparator
Usar programa de álgebra
\family default
 y elige la aplicación que esté instalada en tu ordenador.
 Después de eso el resultado de la computación debería mostrarse a la derecha
 de la expresión junto con el operador "=".
\end_layout

\begin_layout Standard
A continuación hay unos ejemplos sencillos (con resultados de 
\family sans
Maxima
\family default
) que muestran qué tipos de computación se pueden realizar:
\end_layout

\begin_layout Itemize
\begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
\end_inset


\end_layout

\begin_layout Itemize
\begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
\end_inset


\end_layout

\begin_layout Itemize
\begin_inset Formula $\int_{1}^{2}\sen(x)dx=\cos1-\cos2$
\end_inset


\end_layout

\begin_layout Itemize
\begin_inset Formula $\det\left[\begin{array}{ccc}
1 & 6 & 7\\
2 & 5 & 8\\
3 & 4 & 17
\end{array}\right]=-56$
\end_inset


\end_layout

\begin_layout Itemize
\begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
\end_inset


\end_layout

\begin_layout Subsection
Atajos de teclado
\end_layout

\begin_layout Standard
Actualmente no hay atajos de teclado para ejecutar las aplicaciones de álgebra.
 Se puede vincular fácilmente una combinación de teclas a la función 
\family sans
math-extern
\family default
 de Lyx (véase el manual 
\emph on
Funciones de LyX
\emph default
).
 Por ejemplo, para vincular la tecla 
\family sans
Entrar
\family default
 en el editor de ecuaciones a 
\family sans
Maxima
\family default
 se podría usar este comando para definir el atajo de teclado:
\end_layout

\begin_layout Standard

\series bold
command-alternatives break-paragraph;math-extern maxima
\end_layout

\begin_layout Section
Consejos prácticos
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Consejos prácticos
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Números negativos
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Numeros@Números ! negativos
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Los números negativos a veces se ven feos en las ecuaciones porque el signo
 menos delante del número tiene la misma longitud que el operador signo
 menos.
 Si se escribe el número negativo en texto normal el signo menos aparece
 correctamente.
\end_layout

\begin_layout Standard
Así pues, el problema desaparece si se convierte el signo menos a texto
 matemático.
\end_layout

\begin_layout Standard
Un ejemplo para visualizar el problema:
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
texto normal:
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
x = -2
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
ecuación:
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $x=-2$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
solución:
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $x=\mbox{-}2$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Subsection
Coma como separador decimal
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Coma decimal
\end_layout

\end_inset


\end_layout

\begin_layout Standard
En LaTeX, de acuerdo con la convención inglesa, se usa la coma como separador
 de grupos numéricos.
 Entonces en las fórmulas habrá un espacio añadido detrás de todas las comas.
\end_layout

\begin_layout Standard
Para evitarlo, se selecciona la coma y se cambia a texto matemático (atajo
 
\family sans
Ctrl+M
\family default
).
\end_layout

\begin_layout Standard
Para usar las comas en todas las fórmulas del documento como separador decimal,
 se carga el archivo 
\series bold
icomma.sty
\series default

\begin_inset Foot
status collapsed

\begin_layout Plain Layout

\series bold
icomma
\series default
 forma parte del paquete LaTeX 
\series bold
was
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Paquetes ! was
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
vspace{4mm}
\end_layout

\end_inset


\end_layout

\end_inset

.
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Paquetes ! icomma
\end_layout

\end_inset

 en el preámbulo LaTeX con la línea: 
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage{icomma}
\end_layout

\begin_layout Subsection
Vectores cuánticos y notación bra-ket
\begin_inset CommandInset label
LatexCommand label
name "sub:Vectores-cuánticos"

\end_inset


\begin_inset Index idx
status open

\begin_layout Plain Layout
Vectores cuánticos
\end_layout

\end_inset


\begin_inset Index idx
status open

\begin_layout Plain Layout
Notación bra-ket
\end_layout

\end_inset


\end_layout

\begin_layout Standard
El paquete LaTeX 
\series bold
braket
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Paquetes ! braket
\end_layout

\end_inset

 suministra comandos para escribir paréntesis angulares que se usan en mecánica
 cuántica: la notación 
\begin_inset Quotes fld
\end_inset

bra-ket
\begin_inset Quotes frd
\end_inset

; se carga con la línea de preámbulo LaTeX:
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage{braket}
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ifbraket 
\end_layout

\end_inset


\begin_inset Note Note
status open

\begin_layout Plain Layout
El cuadro siguiente sólo se mostrará en la salida si el paquete LaTeX 
\series bold
braket
\series default
 está instalado.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Están definidos los siguientes comandos:
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Bra{
\backslash
psi
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Bra{\psi}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Ket{
\backslash
psi
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Ket{\psi}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
Braket{
\backslash
psi|
\backslash
phi
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Braket{\psi|\phi}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
El comando 
\series bold

\backslash
Braket
\series default
 asegura que todas las barras verticales tienen el tamaño de los delimitadores
 circundantes:
\begin_inset Formula 
\[
\Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
\]

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
else
\end_layout

\end_inset


\begin_inset Note Note
status open

\begin_layout Plain Layout
Lo que sigue se verá en la salida si el paquete LaTeX 
\series bold
braket
\series default
 no está instalado:
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Debes instalar el paquete LaTeX 
\series bold
braket
\series default
 para ver en la salida el resto de esta subsección.
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
fi
\end_layout

\end_inset


\end_layout

\begin_layout Standard
El efecto de 
\series bold

\backslash
Braket
\series default
 también se puede conseguir con el comando 
\series bold

\backslash
middle
\series default
, que se describe en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Tamaño-automático-de"

\end_inset

.
\end_layout

\begin_layout Subsection
Fracciones definidas por el usuario
\begin_inset CommandInset label
LatexCommand label
name "sub:Fracciones-personalizadas"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Fracciones ! personalizadas
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para definir comandos personalizados para fracciones, se usa el comando
 
\series bold

\backslash
genfrac
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! G ! 
\backslash
genfrac
\end_layout

\end_inset

 con el siguiente esquema:
\end_layout

\begin_layout Standard

\series bold

\backslash
genfrac{delimitador izquierdo}{delimitador derecho}
\begin_inset Newline newline
\end_inset


\begin_inset Phantom HPhantom
status open

\begin_layout Plain Layout

\series bold

\backslash
genfrac
\end_layout

\end_inset

{grosor raya de fracción}{estilo}{numerador}{denominador}
\end_layout

\begin_layout Standard
El estilo es un número en el rango 0
\begin_inset space \thinspace{}
\end_inset

-
\begin_inset space \thinspace{}
\end_inset

3.
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Número
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Estilo (tamaño)
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
ecuación presentada
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
ecuación en línea
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
2
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
pequeño
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
3
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
muy pequeño
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Si no se pone estilo el tamaño se ajusta al entorno, como con el comando
 
\series bold

\backslash
frac
\series default
.
\end_layout

\begin_layout Standard
Si no se pone grosor de la raya de fracción se usará el valor predefinido
 de 0.4
\begin_inset space \thinspace{}
\end_inset

pt.
\end_layout

\begin_layout Standard
Por ejemplo, los comandos 
\series bold

\backslash
dfrac
\series default
 y 
\series bold

\backslash
tbinom
\series default
 de la 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Fracciones"

\end_inset

 se definen con los comandos:
\end_layout

\begin_layout Standard

\series bold

\backslash
newcommand{
\backslash
dfrac}[2]{
\backslash
genfrac{}{}{}{0}{#1}{#2}}
\end_layout

\begin_layout Standard
y
\end_layout

\begin_layout Standard

\series bold

\backslash
newcommand{
\backslash
tbinom}[2]{
\backslash
genfrac{(}{)}{0pt}{1}{#1}{#2}}
\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
Para definir una fracción en la que el grosor de la raya se pueda definir
 como argumento opcional, se inserta la siguiente línea en el preámbulo
 LaTeX:
\end_layout

\begin_layout Standard

\series bold

\backslash
newcommand{
\backslash
fracS}[3][]{
\backslash
genfrac{}{}{#1}{}{#2}{#3}}
\end_layout

\begin_layout Standard
Un ensayo:
\begin_inset Formula 
\begin{align*}
\text{Comando} &  & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} &  & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
\text{Resultado} &  & \fracS[1mm]{A}{B} &  & \fracS[5mm]{A}{B}
\end{align*}

\end_inset

Como se puede ver, la distancia del numerador y el denominador a la raya
 de fracción se redondea a unas tres veces el grosor de la raya.
\end_layout

\begin_layout Subsection
Ecuaciones canceladas
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! cancelada
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para cancelar ecuaciones o partes de ellas hay que cargar el paquete LaTeX
 
\series bold
cancel
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Paquetes ! cancel
\end_layout

\end_inset

 con la línea de preámbulo LaTeX
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage[samesize]{cancel}
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ifcancel 
\end_layout

\end_inset


\begin_inset Note Note
status open

\begin_layout Plain Layout
El cuadro siguiente sólo se mostrará en la salida si el paquete LaTeX 
\series bold
cancel
\series default
 está instalado.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Hay cuatro formas de cancelar ecuaciones:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comando
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Resultado
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout
El
\series bold
 
\series default
espacio y 
\series bold

\backslash
raisebox
\series default
 se usa sólo como espaciador
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
cancel{
\backslash
int
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
bcancel{
\backslash
int
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
xcancel{
\backslash
int
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\backslash
cancelto{1
\begin_inset Formula $\to$
\end_inset


\backslash
{
\backslash
int
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard

\series bold

\backslash
cancelto
\series default
 es especialmente apropiada para visualizar la simplificación de fracciones
 en una ecuación:
\begin_inset Formula 
\[
\frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
else
\end_layout

\end_inset


\begin_inset Note Note
status open

\begin_layout Plain Layout
Lo que sigue se verá en la salida si el paquete LaTeX 
\series bold
cancel
\series default
 no está instalado:
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Debes instalar el paquete LaTeX 
\series bold
cancel
\series default
 para ver en la salida el resto de esta subsección.
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
fi
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Ecuaciones en encabezados de sección
\begin_inset CommandInset label
LatexCommand label
name "sub:Ecuaciones-en-encabezados"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! en encabezados de sección
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Si se quiere poner una ecuación en un encabezado de sección hay que tener
 en cuenta lo siguiente:
\end_layout

\begin_layout Standard
\begin_inset Note Greyedout
status open

\begin_layout Plain Layout
Si el soporte para 
\series bold
hyperref
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Paquetes ! hyperref
\end_layout

\end_inset

 está activado en la configuración del documento, 
\family sans
Propiedades
\begin_inset space ~
\end_inset


\family default
PDF, se generan marcadores PDF para cada encabezado de sección en el índice.
 Si el encabezado contiene ecuaciones, se muestran incorrectamente en el
 texto del marcador, porque se infringen las convenciones PDF.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Estos problemas se pueden solucionar insertando al final del encabezado
 un título breve con el menú 
\family sans
Insertar\SpecialChar \menuseparator
Título
\begin_inset space ~
\end_inset

breve
\family default
.
 Los títulos breves se usan como alternativa para encabezados de sección
 con más de una línea para mantener el buen aspecto del índice.
 En éste sólo aparece el título breve y por tanto también en los marcadores.
\end_layout

\begin_layout Standard
Si hay que poner ecuaciones en el índice y se usa 
\series bold
hyperref
\series default
, se puede insertar el siguiente comando en modo TeX:
\end_layout

\begin_layout Standard

\series bold

\backslash
texorpdfstring{parte}{alternativa}
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! T ! 
\backslash
texorpdfstring
\end_layout

\end_inset


\end_layout

\begin_layout Standard
parte se refiere a la parte del encabezado que no debería aparecer en el
 marcador PDF.
 Puede ser caracteres, ecuaciones, notas al pie, y también referencias cruzadas.
 La alternativa se usa para el marcador en vez de la parte.
\end_layout

\begin_layout Standard
Aquí hay dos ejemplos de encabezados con ecuación:
\end_layout

\begin_layout Standard
\begin_inset VSpace -3mm
\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
boldmath 
\end_layout

\end_inset


\end_layout

\begin_layout Subsubsection
Encabezado sin ecuación en el índice 
\begin_inset Formula $\sqrt{-1}=\mathrm{i}$
\end_inset


\begin_inset Argument
status collapsed

\begin_layout Plain Layout
Encabezado sin ecuación en el índice
\end_layout

\end_inset


\end_layout

\begin_layout Subsubsection
Encabezado con ecuación en el índice
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
texorpdfstring{
\end_layout

\end_inset

 
\begin_inset Formula $\sqrt{-1}=\mathrm{i}$
\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout

}{}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
unboldmath 
\end_layout

\end_inset

En el primer encabezado se ha puesto un título breve, en el segundo un 
\series bold

\backslash
texorpdfstring
\series default
.
\end_layout

\begin_layout Standard
Para obtener el mismo formato que en los demás encabezados se han puesto
 ambos en un entorno 
\series bold
boldmath
\series default
.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
véase 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Ecuaciones-en-negrita"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Ecuaciones en texto multicolumna
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! en texto multicolumna
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Las ecuaciones en texto multicolumna son con frecuencia demasiado anchas
 para ajustarse a la columna y entonces es preciso abarcar la anchura total
 de la página.
 Esto se hace usando el paquete LaTeX 
\series bold
multicol
\series default
,
\begin_inset Foot
status collapsed

\begin_layout Plain Layout

\series bold
multicol
\series default
 forma parte de las distribuciones LaTeX estándar.
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Paquetes ! multicol
\end_layout

\end_inset

 que se carga en el preámbulo LaTeX con la línea
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage{multicol}
\end_layout

\begin_layout Standard
\begin_inset Note Greyedout
status open

\begin_layout Plain Layout
Ten en cuenta que la opción 
\family sans
Documento
\begin_inset space ~
\end_inset

con
\begin_inset space ~
\end_inset

dos
\begin_inset space ~
\end_inset

caras
\family default
, bajo 
\family sans
Diseño
\begin_inset space ~
\end_inset

de
\begin_inset space ~
\end_inset

página 
\family default
en el menú 
\family sans
Documento\SpecialChar \menuseparator
Configuración
\family default
 
\emph on
debe
\emph default
 estar desmarcada.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Antes del texto multicolumna se inserta en modo TeX el comando
\end_layout

\begin_layout Standard

\series bold

\backslash
begin{multicols}{número de columnas}
\end_layout

\begin_layout Standard
El número de columnas está en el rango 2-10.
 Antes de la ecuación, se finaliza el texto multicolumna insertando en modo
 TeX el comando
\end_layout

\begin_layout Standard

\series bold

\backslash
end{multicols}
\end_layout

\begin_layout Standard
Debido al comando se añade automáticamente algún espacio delante de la ecuación.
 Para quitarlo se inserta un espacio vertical de -6
\begin_inset space \thinspace{}
\end_inset

mm antes de la ecuación.
 Si se usa el estilo 
\series bold
Sangrado
\series default
,
\begin_inset Foot
status open

\begin_layout Plain Layout
véase estilos de ecuación en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Estilos-de-ecuación"

\end_inset


\end_layout

\end_inset

 se inserta un espacio de -9
\begin_inset space \thinspace{}
\end_inset

mm.
\end_layout

\begin_layout Standard
Un ejemplo de texto multicolumna con una ecuación en modo presentación:
\end_layout

\begin_layout Standard

\lang german
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
begin{multicols}{2}
\end_layout

\end_inset

Das Spektrum wird fouriertransformiert.
 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
, Lösungsmittel) zu trennen.
 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
 nun das Aussehen des Ausgangssignals.
 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
 über alle Phasen integrieren muss.
 Sei nun 
\begin_inset Formula $S$
\end_inset

 unser normiertes Ausgangssignal und 
\begin_inset Formula $P$
\end_inset

 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
end{multicols}
\end_layout

\end_inset


\begin_inset VSpace -6mm
\end_inset


\begin_inset Formula 
\begin{equation}
S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
\end{equation}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
begin{multicols}{2}
\end_layout

\end_inset

wobei 
\begin_inset Formula $S_{0}$
\end_inset

 das Signal ohne Gradient ist und die Normierungsbedingung 
\begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
\end_inset

 gilt.
 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
 Direkt nach dem 
\begin_inset Formula $\nicefrac{\pi}{2}$
\end_inset


\begin_inset space \thinspace{}
\end_inset

-rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
 das Signal zusätzlich abschwächt.
 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
 
\begin_inset Formula $T_{2}$
\end_inset

-Zeit.
\end_layout

\begin_layout Standard

\lang german
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
end{multicols}
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Ecuaciones con descripción de variables
\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Ecuación ! con descripción de variables
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Para describir variables en una ecuación, como en la fórmula 
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:within"

\end_inset

, se inserta una matriz 2×
\begin_inset Formula $n$
\end_inset

 con columnas alineadas a la izquierda para las 
\emph on

\begin_inset Formula $n$
\end_inset


\emph default
 variables usadas.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
véase matrices en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Matrices"

\end_inset


\end_layout

\end_inset

 Para poner la descripción en tamaño más pequeño se inserta, por ejemplo,
 el comando 
\series bold

\backslash
footnotesize
\series default
 antes de la matriz.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
véase tamaños de tipografías en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Tamaños-de-tipografías"

\end_inset

.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Si se usa el estilo 
\series bold
Sangrado
\series default
,
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
véase estilos de ecuación en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Estilos-de-ecuación"

\end_inset


\end_layout

\end_inset

 se inserta un 
\series bold

\backslash
hfill
\series default

\begin_inset Foot
status collapsed

\begin_layout Plain Layout

\series bold

\backslash
hfill
\series default
 sólo funciona en ecuaciones en estilo 
\series bold
Sangrado
\series default
, véase 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Espacio-variable"

\end_inset


\end_layout

\end_inset

 delante y detrás de la matriz para que tenga la misma separación con la
 ecuación y con el margen.
\end_layout

\begin_layout Standard
Si se usa el estilo 
\series bold
Centrado
\series default
 se emplea el método descrito en la 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Entorno-flalign"

\end_inset

 para sangrar la ecuación.
 La ecuación 
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:within"

\end_inset

 consta de cinco columnas ya que las dos primeras contienen la fórmula,
 la tercera la matriz y la última una llave TeX vacía.
\begin_inset Formula 
\begin{flalign}
\hspace{30pt} & F_{A}=\rho\cdot V\cdot g & \footnotesize\begin{array}{ll}
\rho & \mbox{densidad}\\
V & \mbox{volumen}\\
g & \mbox{aceleración gravitatoria}
\end{array} &  & {}\label{eq:within}
\end{flalign}

\end_inset


\end_layout

\begin_layout Subsection
Letras griegas minúsculas en redonda
\begin_inset CommandInset label
LatexCommand label
name "sub:Griegas-en-redonda"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Letras griegas ! en redonda
\end_layout

\end_inset


\end_layout

\begin_layout Standard
La mayoría de las tipografías sólo suministran letras griegas minúsculas
 en cursiva.
 Pero para símbolos de partículas elementales como piones y neutrinos hacen
 falta letras griegas en redonda.
 El archivo 
\series bold
upgreek.sty
\series default

\begin_inset Foot
status collapsed

\begin_layout Plain Layout

\series bold
upgreek
\series default
 forma parte del paquete LaTeX 
\series bold
was
\series default

\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Paquetes ! was
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
vspace{4mm}
\end_layout

\end_inset


\end_layout

\end_inset

.
\end_layout

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Paquetes ! upgreek
\end_layout

\end_inset

, que se carga en el preámbulo LaTeX con la línea
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage{upgreek}
\end_layout

\begin_layout Standard
las suministra.
 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
ifupgreek 
\end_layout

\end_inset


\begin_inset Note Note
status open

\begin_layout Plain Layout
Lo siguiente sólo se podrá ver si está instalado el paquete LaTeX 
\series bold
upgreek
\series default
:
\end_layout

\end_inset

 Se imprimen con el comando de la letra correspondiente precedido de 
\series bold
up
\series default
.
 Por ejemplo, el comando 
\series bold

\backslash
uptau
\series default
 genera: 
\begin_inset Formula $\uptau$
\end_inset


\end_layout

\begin_layout Standard
Con estos comandos se pueden escribir reacciones entre partículas elementales:
\begin_inset Formula 
\[
\uppi^{+}\rightarrow\upmu^{+}+\upnu_{\upmu}
\]

\end_inset


\end_layout

\begin_layout Standard
Las letras en redonda son más remarcadas y más grandes que las correspondientes
 en cursiva.
 Por tanto no deberían emplearse para unidades como 
\begin_inset Quotes fld
\end_inset

µm
\begin_inset Quotes frd
\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
else 
\end_layout

\end_inset


\begin_inset Note Note
status open

\begin_layout Plain Layout
Lo siguiente se mostrará si el paquete LaTeX 
\series bold
upgreek
\series default
 no está instalado:
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Debes instalar el paquete LaTeX 
\series bold
upgreek
\series default
 para ver en la salida el resto de esta subsección.
 
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
fi
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Caracteres de texto en ecuaciones
\begin_inset CommandInset label
LatexCommand label
name "sub:Caracteres-de-texto"

\end_inset


\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Texto ! en ecuaciones
\end_layout

\end_inset


\end_layout

\begin_layout Standard
En algunos casos podrías querer insertar caracteres de texto directamente
 en ecuaciones.
 Por ejemplo, cuando se usa con frecuencia el punto centrado 
\begin_inset Formula $\cdot$
\end_inset

 en expresiones como 
\begin_inset Formula $v=5\cdot10^{5}\,\mathrm{Hz}$
\end_inset

, habría que insertar el comando 
\series bold

\backslash
cdot
\series default

\begin_inset Foot
status collapsed

\begin_layout Plain Layout
véase 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Operadores-binarios"

\end_inset


\end_layout

\end_inset

 continuamente, porque este carácter está definido en todas las codificaciones
 como carácter de texto.
 Pero la codificación se puede cambiar con la línea de preámbulo LaTeX:
\end_layout

\begin_layout Standard

\series bold

\backslash
Declare Inputtext{183}{
\backslash
ifmmode
\backslash
cdot
\backslash
else
\backslash
textperiodcentered
\backslash
f\SpecialChar \textcompwordmark{}
i}
\end_layout

\begin_layout Standard
La codificación de caracteres (menú 
\family sans
Documento\SpecialChar \menuseparator
Configuración\SpecialChar \menuseparator
Idioma
\family default
) especifica el carácter que se muestra al pulsar una tecla.
 Si se pulsa la tecla para el carácter '·', se usa internamente el comando
 
\series bold

\backslash
textperiodcentered
\series default
.
 Pero este comando no está disponible en ecuaciones así que obtendrías errores
 de LaTeX.
 Con la codificación cambiada se escoge automáticamente el comando correcto,
 dependiendo de si el carácter se ha insertado en una ecuación o no.
\end_layout

\begin_layout Standard
La codificación de diversos caracteres se guarda en archivos de definición.
 Por ejemplo la codificación 
\series bold
latin9
\series default
 se define en el archivo 
\series bold
latin9.def
\series default
 que está en el directorio de LaTeX.
 La codificación sólo debería cambiarse en el preámbulo LaTeX y no en el
 archivo de definición, de lo contrario nuestros documentos no podrían ser
 editados en otros ordenadores.
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
Además del punto centrado, en este documento se ha definido el símbolo grado
 ° con la siguiente línea de preámbulo LaTeX, para que se pueda insertar
 directamente en una fórmula:
\end_layout

\begin_layout Standard

\series bold

\backslash
DeclareInputtext{176}{
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circ
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textdegree
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f\SpecialChar \textcompwordmark{}
i}
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Section
\start_of_appendix
Notas sobre tipografía
\begin_inset Index idx
status open

\begin_layout Plain Layout
Tipografía, normas
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Esta sección es un resumen de las normas tipográficas ISO más importantes.
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
Este compendio se ha tomado parcialmente del diccionario semi-oficial alemán
 
\begin_inset Quotes fld
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Duden
\begin_inset Quotes frd
\end_inset

 
\begin_inset CommandInset citation
LatexCommand cite
key "Duden"

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, que incluye algunas de las normas ISO.
 
\begin_inset Newline newline
\end_inset

(
\emph on
N.
\begin_inset space \thinspace{}
\end_inset

del t.
\emph default
: Para documentación en español sobre el tema, véase 
\begin_inset CommandInset citation
LatexCommand cite
key "Bezos"

\end_inset

.)
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Las unidades físicas se escriben 
\emph on
siempre 
\emph default
en redonda
\begin_inset Foot
status collapsed

\begin_layout Plain Layout
véase estilos de tipografías en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Estilos-de-tipografías"

\end_inset


\end_layout

\end_inset

, aunque aparezcan en un texto en cursiva: 30
\begin_inset space \thinspace{}
\end_inset

km/h
\begin_inset Newline newline
\end_inset

Entre el valor y la unidad hay un espacio delgado, véase 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Espacio-predefinido"

\end_inset

.
\begin_inset Newline newline
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Esta norma la cumple automáticamente el comando 
\series bold

\backslash
unittwo
\series default
.
 Si se introduce en una fórmula aparecen dos marcos.
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 como antes, 
\begin_inset Formula $\unit[30]{km/h}$
\end_inset


\begin_inset space \thinspace{}
\end_inset

.
 Ten en cuenta que 
\series bold

\backslash
unittwo
\series default
 no es un auténtico comando LaTeX, sino el comando 
\series bold

\backslash
unit[value]{unit}
\series default
, por tanto no lo puedes usar en código TeX.
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\begin_layout Itemize
Los signos por ciento y por mil se escriben como las unidades físicas:
\begin_inset Newline newline
\end_inset

1,2
\begin_inset space \thinspace{}
\end_inset

‰ de alcohol en sangre.
\end_layout

\begin_layout Itemize
El símbolo grado sigue directamente al valor: 15°, excepto si acompaña a
 otra unidad: 15
\begin_inset space \thinspace{}
\end_inset

°C
\end_layout

\begin_layout Itemize
En números con más de cuatro dígitos se inserta un espacio delgado para
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\begin_inset space \thinspace{}
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473
\begin_inset space \thinspace{}
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588
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Para dimensiones como 120×90×40
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cm se usa el aspa de multiplicar 
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×
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.
 Está disponible en el menú 
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Insertar\SpecialChar \menuseparator
Carácter especial
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\SpecialChar \menuseparator

\family sans
Símbolos
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 o bien mediante el comando 
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\backslash
times
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.
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\begin_layout Itemize
Las funciones con nombres que constan de varias letras se escriben en redonda
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LatexCommand ref
reference "sub:Funciones-predefinidas"

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.
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Los componentes de una matriz se escriben en cursiva: 
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\begin_layout Itemize
El operador de diferenciación/integración 'd', el número de Euler 'e' y
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El carácter que indica una transformación 
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Fourier
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\backslash
mathscr
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
spce 
\end_layout

\end_inset

F
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 o mediante el menú
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 Insertar\SpecialChar \menuseparator
Carácter especial
\family default
\SpecialChar \menuseparator

\family sans
Símbolos\SpecialChar \menuseparator
Símbolos de letra
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\begin_inset Newpage newpage
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Sinónimos
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Sinónimos
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Algunos caracteres y símbolos se pueden componer con varios comandos sinónimos
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\begin_layout Plain Layout
véase también 
\begin_inset CommandInset ref
LatexCommand ref
reference "fn:sinónimos"

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.
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\begin_inset Text

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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
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<row>
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\begin_layout Standard
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\begin_inset CommandInset bibitem
LatexCommand bibitem
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\shape smallcaps
Mittelbach, F.
 ; Goossens, M.
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: 
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The LaTeX Companion
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.
 Addison Wesley, 2004
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\begin_inset CommandInset href
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 de habilidades matemáticas de LaTeX
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\begin_inset CommandInset href
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 de 
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\begin_layout Plain Layout


\backslash
AmS
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-LaTeX
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LatexCommand bibitem
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\begin_inset CommandInset href
LatexCommand href
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 del paquete LaTeX 
\series bold
hyperref
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 del paquete LaTeX 
\series bold
mhchem
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Paquetes ! mhchem
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\begin_inset CommandInset href
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 del comando 
\series bold

\backslash
mathclap
\series default
, descrito en 
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Límites-de-operadores"

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\begin_inset Index idx
status collapsed

\begin_layout Plain Layout
Comandos ! M ! 
\backslash
mathclap
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\begin_layout Bibliography
\labelwidthstring Referencias
\begin_inset CommandInset bibitem
LatexCommand bibitem
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\emph on
Duden Band 1
\emph default
.
 22.
 Auflage, Duden 2001
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 del estilo 
\series bold
spanish
\family sans
\series default
 
\family default
incluido en el paquete 
\series bold
babel
\end_layout

\begin_layout Bibliography
\labelwidthstring Referencias
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "Bezos"

\end_inset


\begin_inset CommandInset href
LatexCommand href
name "Documento"
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 sobre ortotipografía y notaciones matemáticas en español
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