+
+
+\end_layout
+
+\end_inset
+
+ is the line width set for the document.
+ Because the frame is outside the parbox,
+ two times the frame separation and the frame thickness must be subtracted from the line width.
+ To be able to multiply and subtract in arguments,
+ the \SpecialChar LaTeX
+-package
+\series bold
+calc
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+calc
+\series default
+ is part of every \SpecialChar LaTeX
+ standard installation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+calc
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ must be loaded in the \SpecialChar LaTeX
+-preamble with the line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{calc}
+\end_layout
+
+\begin_layout Standard
+Behind the formula both boxes are closed by entering
+\series bold
+}}
+\series default
+ in \SpecialChar TeX
+ mode.
+ Here is an example:
+\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
+
+
+\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
+
+As a parbox is used as the argument of
+\series bold
+
+\backslash
+fbox
+\series default
+,
+ there is in this case no difference between
+\series bold
+
+\backslash
+fbox
+\series default
+ and
+\series bold
+
+\backslash
+boxed
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Paragraph boxes are very useful to comment formulas directly.
+ To do this,
+
+\series bold
+
+\backslash
+parbox
+\series default
+ is used in combination with the command
+\series bold
+
+\backslash
+tag
+\series default
+.
+ (more about
+\series bold
+
+\backslash
+tag
+\series default
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:User-defined-Numbering"
+nolink "false"
+
+\end_inset
+
+)
+\end_layout
+
+\begin_layout Standard
+An example of a formula commented with
+\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
+
+This is a description.
+ It is distinctly separated from the formula and multiline.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}}
+\backslash
+]
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Such a formula must be inserted completely in \SpecialChar TeX
+ mode because \SpecialChar LyX
+ does not yet support the command
+\series bold
+
+\backslash
+parbox
+\series default
+ in formulas.
+ The formula is created with the following command sequence:
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+[5x-7b=3b
+\backslash
+tag*
+\backslash
+{
+\backslash
+parbox{5cm}{
+\series default
+ is inserted in \SpecialChar TeX
+ mode.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+When the formula style
+\series bold
+Indented
+\series default
+ is used,
+
+\series bold
+
+\backslash
+tag*
+\backslash
+{
+\series default
+ can also be replaced by
+\series bold
+
+\backslash
+hfill
+\series default
+.
+ (formula styles see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Formula-Styles"
+nolink "false"
+
+\end_inset
+
+)
+\end_layout
+
+\end_inset
+
+ Then the description follows as normal text and finally
+\series bold
+}}
+\backslash
+]
+\series default
+ is inserted in \SpecialChar TeX
+ mode.
+ The commands
+\series bold
+
+\backslash
+[
+\series default
+ and
+\series bold
+
+\backslash
+]
+\series default
+ create a displayed formula.
+\end_layout
+
+\begin_layout Standard
+The advantages of
+\series bold
+
+\backslash
+parbox
+\series default
+ can be seen in this example that was
+\begin_inset Quotes eld
+\end_inset
+
+commented
+\begin_inset Quotes erd
+\end_inset
+
+ using the mathematical textmode:
+\begin_inset Formula
+\[
+5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Operators
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Operators
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Big Operators
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Big-Operators"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Operators
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+big
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Sums
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Integrals
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To be able to use all of the integral operators listed here,
+ the
+\family sans
+Load automatically
+\family default
+ option for the
+\family sans
+ esint package
+\family default
+ must be set in the document settings under
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="11" columns="2">
+<features booktabs="true" 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
+Command
+\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
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+int
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+I
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+int
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\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 $\int$
+\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
+oint
+\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 $\oint$
+\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
+ointctrclockwise
+\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 $\ointctrclockwise$
+\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
+ointclockwise
+\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 $\ointclockwise$
+\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
+sqint
+\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 $\sqint$
+\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
+fint
+\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 $\fint$
+\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
+landupint
+\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 $\landupint$
+\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
+landdownint
+\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 $\landdownint$
+\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
+bigcap
+\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 $\bigcap$
+\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
+bigcup
+\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 $\bigcup$
+\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 booktabs="true" 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
+Command
+\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
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sum
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+sum
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\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 $\sum$
+\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
+prod
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+P
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+prod
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\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 $\prod$
+\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
+coprod
+\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 $\coprod$
+\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
+bigodot
+\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 $\bigodot$
+\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
+bigotimes
+\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 $\bigotimes$
+\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
+bigoplus
+\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 $\bigoplus$
+\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
+bigwedge
+\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 $\bigwedge$
+\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
+bigvee
+\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 $\bigvee$
+\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
+bigsqcup
+\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 $\bigsqcup$
+\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
+biguplus
+\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 $\biguplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+All big operators can also be inserted via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\intop"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The operators are called big because they are bigger than the sometimes equal looking binary operators.
+ All big operators can have limits as described in the next subsection.
+\end_layout
+
+\begin_layout Standard
+For all integral operators there is a second version available,
+ ending in
+\series bold
+op
+\series default
+:
+
+\series bold
+
+\backslash
+intop
+\series default
+,
+
+\series bold
+
+\backslash
+ointop
+\series default
+ etc.
+ These operators differ in the style the operator limits are displayed,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Operator-Limits"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsubsection*
+Advice for Integrals
+\end_layout
+
+\begin_layout Standard
+The letter
+\emph on
+d
+\emph default
+ in an integral is an operator that has to be set upright.
+ This is done by highlighting the
+\emph on
+d
+\emph default
+ and using the keyboard shortcut
+\begin_inset Info
+type "shortcut"
+arg "font-roman"
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+Font styles
+\series bold
+
+\series default
+see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Font-Styles"
+nolink "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ Also the smallest space is inserted before the
+\emph on
+d
+\emph default
+,
+ as this is usual for operators.
+ An example:
+\end_layout
+
+\begin_layout Standard
+incorrect:
+
+\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
+
+correct:
+
+\begin_inset Formula $\int A(x)\,\mathrm{d}x$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The following commands exist for multiple integrals:
+\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 booktabs="true" 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
+Command
+\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
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomspace="1mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+iint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\iint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomspace="1mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+oiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\oiint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomspace="1mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sqiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sqiint$
+\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 booktabs="true" 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
+Command
+\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
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomspace="1mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+iiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\iiint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomspace="1mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+iiiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\iiiint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomspace="1mm">
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dotsint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\dotsint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Operator Limits
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Operator-Limits"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Operators
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+Limits
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Limits are created by super- and subscripts:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features booktabs="true" 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
+Command
+\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
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+prod^
+\backslash
+infty
+\begin_inset space \textvisiblespace{}
+\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" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\prod_{0}^{\infty}A(x)$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Limits of inline formulas are set on the right side of the operator.
+ Limits in displayed formulas are set above or below the operator,
+ except for integral limits.
+\end_layout
+
+\begin_layout Standard
+To force the limits to be set beside the operator,
+ the cursor is placed directly behind the operator and the limits type is changed with the menu
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Change Limits Type
+\family default
+ to
+\family sans
+\series bold
+Inline
+\family default
+\series default
+ (shortcut
+\begin_inset Info
+type "shortcut"
+arg "math-limits"
+\end_inset
+
+).
+ An example:
+\end_layout
+
+\begin_layout Standard
+The default displayed formulas limits type is this:
+\begin_inset Formula
+\[
+\sum_{x=0}^{\infty}\frac{1}{x^{2}}
+\]
+
+\end_inset
+
+This is how it looks when the limits type is changed to
+\family sans
+\series bold
+Inline
+\family default
+\series default
+:
+\begin_inset Formula
+\[
+\sum\nolimits_{x=0}^{\infty}\frac{1}{x^{2}}
+\]
+
+\end_inset
+
+For integrals,
+ except those ending with
+\series bold
+op
+\series default
+ like
+\series bold
+
+\backslash
+intop
+\series default
+,
+
+\series bold
+
+\backslash
+ointop
+\series default
+ etc.,
+ the limits by default are set beside the operator.
+ But for multiple integrals the limits are often set below the operator.
+ In the following example the limits type was set to
+\series bold
+Display
+\series default
+ and so set below the integrals:
+\begin_inset Formula
+\begin{equation}
+\iiint\limits_{V}X\,\mathrm{d}V=U\label{eq:VolInt}
+\end{equation}
+
+\end_inset
+
+
+\change_deleted 5863208 1612725771
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+
+\change_inserted 232239728 1611193306
+This integral did not have its limits set to Display in the original document
+\change_unchanged
+
+\end_layout
+
+\end_inset
+
+
+\change_unchanged
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+To specify conditions for limits,
+ the commands
+\series bold
+
+\backslash
+subarray
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+subarray
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+substack
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+substack
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ are used.
+ To create this expression
+\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
+
+
+\end_layout
+
+\begin_layout Standard
+the following must be done:
+\begin_inset Newline newline
+\end_inset
+
+First the command
+\series bold
+
+\backslash
+sum
+\series default
+^
+\series bold
+n
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_
+\series default
+ is typed in.
+ The cursor is now in a blue box under the summation operator.
+ Insert the command
+\series bold
+
+\backslash
+subarray
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+.
+ The blue box is now within a purple box and now multiple limit lines can be written.
+ A new line is created by inserting a line break (
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+).
+ When
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+0<k<1000 Ctrl+Return
+\begin_inset Newline newline
+\end_inset
+
+
+\series default
+is typed in,
+ a new box appears below for the new limit line.
+\end_layout
+
+\begin_layout Standard
+The alignment of the lines can be changed to left aligned with the
+\family sans
+table
+\family default
+
+\family sans
+toolbar
+\family default
+ or the menu
+\family sans
+Edit\SpecialChar menuseparator
+Rows &Columns
+\family default
+.
+ To get right alignment,
+
+\series bold
+
+\backslash
+hfill
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+ is inserted at the beginning of the line.
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+substack
+\series default
+ is equivalent to
+\series bold
+
+\backslash
+subarray
+\series default
+ with the difference that the lines are always centered.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+As in formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:substack"
+nolink "false"
+
+\end_inset
+
+ there can be too much space beside an operator.
+ This occurs because the characters following the operator are set beside the limits.
+ To avoid this the command
+\series bold
+
+\backslash
+smashoperator
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+smashoperator
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ can be used.
+ To use it,
+ set the package
+\series bold
+mathtools
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+mathtools
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ in the document settings under
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+ to
+\family sans
+Load
+\begin_inset space ~
+\end_inset
+
+always
+\family default
+.
+
+\series bold
+
+\backslash
+smashoperator
+\series default
+ sets the space besides the operator to 0
+\begin_inset space \thinspace{}
+\end_inset
+
+pt.
+\begin_inset Newline newline
+\end_inset
+
+Applied on formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:substack"
+nolink "false"
+
+\end_inset
+
+,
+ one uses the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+smashoperator{
+\end_layout
+
+\begin_layout Standard
+and inserts the operator with its limits into the braces.
+ Behind the brace one continues the formula:
+\begin_inset Formula
+\[
+\smashoperator{\sum_{\begin{subarray}{c}
+0<k<1000\\
+\\k\,\in\,\mathbb{N}
+\end{subarray}}^{n}}k^{-2}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+It is possible to set the space of only one side of the operator to 0
+\begin_inset space \thinspace{}
+\end_inset
+
+pt.
+ To do this write either
+\series bold
+[l]
+\series default
+ or
+\series bold
+[r]
+\series default
+ between
+\series bold
+
+\backslash
+smashoperator
+\series default
+ and its brace.
+
+\series bold
+l
+\series default
+ stands for the left and
+\series bold
+r
+\series default
+ for the right side of the operator.
+ Here is an example of the possible
+\series bold
+
+\backslash
+smashoperator
+\series default
+ forms:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\[
+Y\smashoperator{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}=Y\smashoperator[l]{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}=Y\smashoperator[r]{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+When several consecutive operators have limits the typesetting of the limits looks often imperfect in the output,
+ for example:
+\begin_inset Formula
+\[
+\text{a)}\lim_{n\to\infty}\max_{p\ge n}\quad\text{b)}\lim_{n\to\infty}\max_{p^{2}\ge n}\quad\text{c)}\lim_{n\to\infty}\sup_{p^{2}\ge nK}\quad\text{d)}\limsup_{n\to\infty}\max_{p\ge n}
+\]
+
+\end_inset
+
+To improve the typesetting,
+ in the document settings under
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+ for the package
+\series bold
+mathtools
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Packages
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+mathtools
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+,
+ set the option to
+\family sans
+ Load
+\begin_inset space ~
+\end_inset
+
+always
+\family default
+.
+ Then insert the command
+\series bold
+
+\backslash
+adjustlimits
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+A
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+adjustlimits
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ directly before the first operator.
+ The example will then look like this:
+\begin_inset Formula
+\[
+\text{a)}\adjustlimits\lim_{n\to\infty}\max_{p\ge n}\quad\text{b)}\adjustlimits\lim_{n\to\infty}\max_{p^{2}\ge n}\quad\text{c)}\adjustlimits\lim_{n\to\infty}\sup_{p^{2}\ge nK}\quad\text{d)}\adjustlimits\limsup_{n\to\infty}\max_{p\ge n}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+How to use one limit for several operators is described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Self-defined-Operators"
+nolink "false"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Decoration for Operators
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Operators
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+Decoration
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With the commands
+\series bold
+
+\backslash
+overset
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+O
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+overset
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+underset
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+U
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+underset
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ characters can be placed above or below an operator respectively.
+ With the command
+\series bold
+
+\backslash
+sideset
+\series default
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Commands
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+
+
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+sideset
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ characters can be set before and behind a big operator.
+\end_layout
+
+\begin_layout Standard
+There are 4
+\begin_inset space ~
+\end_inset
+
+variants of
+\series bold
+
+\backslash
+sideset
+\series default
+:
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+
+\backslash
+sideset
+\series default
+ is used to set characters at the corners of the operator
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+
+\backslash
+sidesetn
+\series default
+ is used to set characters before and/or behind the operator (this variant represents \SpecialChar LaTeX
+'s original
+\series bold
+
+\backslash
+sideset
+\series default
+ command)
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+
+\backslash
+sidesetl
+\series default
+ is used to set characters at the left corners and/or behind the operator
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+
+\backslash
+sidesetr
+\series default
+ is used to set characters at the right corners and/or before the operator
+\end_layout
+
+\begin_layout Standard
+For example the command
+\series bold
+
+\backslash
+sidesetn
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+sum
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+'
+\begin_inset Formula $\to$
+\end_inset
+
+_k=1
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+^
+\series bold
+n
+\series default
+ produces:
+\begin_inset Formula
+\[
+\sideset{}{'}\sum_{k=1}^{n}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+
+\backslash
+sideset
+\series default
+ can only be used to decorate big operators,
+ binary operators are not allowed.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+overset
+\series default
+ and
+\series bold
+
+\backslash
+underset
+\series default
+ can also be used to decorate symbols and characters.
+ For example,
+ the command
+\series bold
+
+\backslash
+overset
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+maltese
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+
+\begin_inset Formula $\uparrow$
+\end_inset
+
+
+\series bold
+a
+\series default
+ produces:
+\begin_inset Formula
+\[
+\overset{a}{\maltese}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Binary Operators
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Binary-Operators"
+
+\end_inset
+
+
+\begin_inset Index idx
+range none
+pageformat default
+status collapsed
+
+\begin_layout Plain Layout
+Operators
+\begin_inset IndexMacro subentry
+status open
+
+\begin_layout Plain Layout
+binary
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Binary operators are surrounded by space when there is a character before and after them.
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="13" columns="2">
+<features booktabs="true" 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
+Command
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\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
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
++
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text