X-Git-Url: https://git.lyx.org/gitweb/?a=blobdiff_plain;f=lib%2Fdoc%2FMath.lyx;h=e023438bbaf0ed6570c86d798af456df60635a58;hb=6f04bfaf9601268ac8019d19024b335da3bcdf0a;hp=5ac17d57428bb7c74a53e0df4876a99db6161c22;hpb=4f043fba4dc71647d560babdcaa24dc565f38243;p=lyx.git
diff --git a/lib/doc/Math.lyx b/lib/doc/Math.lyx
index 5ac17d5742..e023438bba 100644
--- a/lib/doc/Math.lyx
+++ b/lib/doc/Math.lyx
@@ -1,38459 +1,38413 @@
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-Syntax Explanation
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-
-\begin_layout Plain Layout
-Centimeter
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-in
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Inch (1
-\begin_inset space \thinspace{}
-\end_inset
-
-in = 2,54
-\begin_inset space \thinspace{}
-\end_inset
-
-cm)
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-pt
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Point (72.27
-\begin_inset space \thinspace{}
-\end_inset
-
-pt = 1
-\begin_inset space \thinspace{}
-\end_inset
-
-in)
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-pc
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-sp
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-scaled point (65536
-\begin_inset space \thinspace{}
-\end_inset
-
-sp = 1
-\begin_inset space \thinspace{}
-\end_inset
-
-pt)
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-bp
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-big point (72
-\begin_inset space \thinspace{}
-\end_inset
-
-bp = 1
-\begin_inset space \thinspace{}
-\end_inset
-
-in)
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-dd
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-cc
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-ex
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Height of letter
-\emph on
-
-\begin_inset Quotes eld
-\end_inset
-
-x
-\emph default
-
-\begin_inset Quotes erd
-\end_inset
-
- in the current font
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-em
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-width of letter
-\begin_inset Quotes eld
-\end_inset
-
-
-\emph on
-M
-\emph default
-
-\begin_inset Quotes erd
-\end_inset
-
- in the current font
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-mu
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-math unit (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
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-Basic Functions
-\end_layout
-
-\begin_layout Subsection
-Exponents
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Exponents
-\end_layout
-
-\end_inset
-
- and Indices
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Indices
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Superscripts|see
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-{
-\end_layout
-
-\end_inset
-
-Exponents
-\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
-Subscripts|see
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-{
-\end_layout
-
-\end_inset
-
-Indices
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Indices are created with an underscore
-\begin_inset Quotes eld
-\end_inset
-
-_
-\begin_inset Quotes erd
-\end_inset
-
- or via the math toolbar button
-\begin_inset Graphics
- filename ../images/math-subscript.png
- scale 85
-
-\end_inset
-
-, exponents with a caret
-\begin_inset Quotes eld
-\end_inset
-
-^
-\begin_inset Quotes erd
-\end_inset
-
- or via the math toolbar button
-\begin_inset Graphics
- filename ../images/math-superscript.png
- scale 85
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-B_V
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $B_{V}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-B^V
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}B^{V}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}B^{A}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-As the caret is in some languages an accent, vowels will be accentuated
- in this case and not set as exponents
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-Depending on the used keyboard settings this can also happen for characters
- other than vowels.
-\end_layout
-
-\end_inset
-
-.
- To get exponents in this case, press
-\family sans
-Space
-\family default
- after the caret as in the last example.
-\end_layout
-
-\begin_layout Subsection
-Fractions
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Fractions"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Fractions
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Fractions are generated with the command
-\series bold
-
-\backslash
-frac
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! F !
-\backslash
-frac
-\end_layout
-
-\end_inset
-
- or via the math toolbar button
-\begin_inset Graphics
- filename ../images/math/frac.png
- scale 50
-
-\end_inset
-
-.
- The font size is adjusted automatically, depending on whether the fraction
- is in an inline or display style formula.
- With the math toolbar button
-\begin_inset Graphics
- filename ../images/math/frac-square.png
- scale 85
-
-\end_inset
-
- you can select different fraction types.
-\end_layout
-
-\begin_layout Standard
-With the command
-\series bold
-
-\backslash
-dfrac
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! D !
-\backslash
-dfrac
-\end_layout
-
-\end_inset
-
- a fraction can be created that always has the size of a display style formula.
- With
-\series bold
-
-\backslash
-tfrac
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! T !
-\backslash
-tfrac
-\end_layout
-
-\end_inset
-
- the fraction appears always with the size of an inline formula.
- An example:
-\end_layout
-
-\begin_layout Standard
-A line with the fraction
-\begin_inset Formula $\frac{1}{2}$
-\end_inset
-
- that was created with the command
-\series bold
-
-\backslash
-frac
-\series default
-.
-\end_layout
-
-\begin_layout Standard
-A line with the fraction
-\begin_inset Formula $\dfrac{1}{2}$
-\end_inset
-
- that was created with the command
-\series bold
-
-\backslash
-dfrac
-\series default
-.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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^
-\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 $\downarrow\downarrow$
-\end_inset
-
-3
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-
-\begin_inset Newpage newpage
-\end_inset
-
-For nested fractions the command
-\series bold
-
-\backslash
-cfrac
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! C !
-\backslash
-cfrac
-\end_layout
-
-\end_inset
-
- can be used.
- Here is an example:
-\begin_inset VSpace -3mm
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Formula
-\begin{align*}
-\textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \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
-The command for the example above is:
-\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
- sets the fraction always in the size of a displayed formula, also when
- it is part of another fraction.
-\end_layout
-
-\begin_layout Standard
-It is possible to specify the alignment of the numerator.
- The command
-\series bold
-
-\backslash
-cfracleft
-\series default
- is used to left align it, the command
-\series bold
-
-\backslash
-cfracright
-\series default
- to right-align it.
-
-\series bold
-
-\backslash
-cfrac
-\series default
- centers the numerator.
- These fractions demonstrate the different alignments:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-\begin_inset Formula
-\[
-\cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
-\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Note Greyedout
-status open
-
-\begin_layout Plain Layout
-
-\series bold
-Note:
-\series default
-
-\series bold
-
-\backslash
-cfracleft
-\series default
- and
-\series bold
-
-\backslash
-cfracright
-\series default
- are no real LaTeX commands but represent the command
-\series bold
-
-\backslash
-cfrac[alignment]{numerator}{denominator}
-\series default
- .
- Therefore you cannot use them in TeX code.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-It is often advantageous to combine
-\series bold
-
-\backslash
-cfrac
-\series default
- and
-\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
-For inline fractions with a sloped fraction stroke you can use the command
-
-\series bold
-
-\backslash
-nicefrac
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! N !
-\backslash
-nicefrac
-\end_layout
-
-\end_inset
-
-:
-\begin_inset Formula $\nicefrac{5}{31}$
-\end_inset
-
- or
-\series bold
-
-\backslash
-unitfrac
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! U !
-\backslash
-unitfrac
-\end_layout
-
-\end_inset
-
-:
-\begin_inset Formula $\unitfrac{5}{31}$
-\end_inset
-
- There is furthermore the command
-\series bold
-
-\backslash
-unitfracthree
-\series default
- that offers to write a fraction in combination with a number:
-\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
-Note:
-\series default
-
-\series bold
-
-\backslash
-unitfracthree
-\series default
- is not a real LaTeX command but the command
-\begin_inset Newline newline
-\end_inset
-
-
-\series bold
-
-\backslash
-unitfrac[number]{numerator}{denominator}
-\series default
- .
- Therefore you cannot use it in TeX code.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-How to define own fractions where the fraction stroke can be changed, is
- explained in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Self-defined-Fractions"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Roots
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Roots
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Square roots are created with
-\series bold
-
-\backslash
-sqrt
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-sqrt
-\end_layout
-
-\end_inset
-
- or the math toolbar button
-\begin_inset Graphics
- filename ../images/math/sqrt.png
- scale 85
-
-\end_inset
-
-, all other roots with the command
-\series bold
-
-\backslash
-root
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-root
-\end_layout
-
-\end_inset
-
- or with the math toolbar button
-\begin_inset Graphics
- filename ../images/math/root.png
- scale 85
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-A square root can also be created with
-\series bold
-
-\backslash
-root
-\series default
- when the root index field is left empty.
-\end_layout
-
-\begin_layout Standard
-With certain indices the distance to the root is too small, like in this
- formula:
-\begin_inset Formula $\sqrt[\beta]{B}$
-\end_inset
-
-
-\begin_inset Newline newline
-\end_inset
-
-The
-\begin_inset Formula $\beta$
-\end_inset
-
- touches the root.
- To avoid this, the commands
-\series bold
-
-\backslash
-leftroot
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! L !
-\backslash
-leftroot
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-uproot
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! U !
-\backslash
-uproot
-\end_layout
-
-\end_inset
-
- are used with the following scheme:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-leftroot{distance}
-\series default
- and
-\series bold
-
-\backslash
-uproot{distance}
-\end_layout
-
-\begin_layout Standard
-Distance is the number of Big Points (unit bp;
-\begin_inset Formula $\mathrm{72\, bp=1\, inch}$
-\end_inset
-
-), that the index should be moved to the left or top, resp..
- The commands are written to the index.
- This way the command
-\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
-produces a correct typeset formula:
-\begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Binomial Coefficients
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Binomial coefficients
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Binomial coefficients are inserted with the command
-\series bold
-
-\backslash
-binom
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! B !
-\backslash
-binom
-\end_layout
-
-\end_inset
-
- or with the submenu of the math toolbar button
-\begin_inset Graphics
- filename ../images/math/frac-square.png
- scale 85
-
-\end_inset
-
-.
- As with fractions (
-\series bold
-
-\backslash
-frac
-\series default
-) in addition to
-\series bold
-
-\backslash
-binom
-\series default
- there are the commands
-\series bold
-
-\backslash
-dbinom
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! D !
-\backslash
-dbinom
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-tbinom
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! T !
-\backslash
-tbinom
-\end_layout
-
-\end_inset
-
-.
- For other brackets around binomial coeficients there are the commands
-\series bold
-
-\backslash
-brace
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! B !
-\backslash
-brace
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-brack
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! B !
-\backslash
-brack
-\end_layout
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Case Differentiations
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Case differentiations
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
-Commands ! C !
-\backslash
-cases
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\begin{cases}
-A & B>0\end{cases}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-cases
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\begin_inset Info
-type "shortcut"
-arg "newline-insert newline"
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\begin{cases}
-A & \textrm{for }x>0\\
-B & \textrm{for }x=0
-\end{cases}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-After inserting
-\series bold
-
-\backslash
-cases
-\series default
- or pressing the math toolbar button
-\begin_inset Graphics
- filename ../images/math/cases.png
- scale 85
-
-\end_inset
-
- you can create new lines with the shortcut
-\begin_inset Info
-type "shortcut"
-arg "newline-insert newline"
-\end_inset
-
- or the table toolbar button
-\begin_inset Graphics
- filename ../images/tabular-feature_append-row.png
- scale 85
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-The command
-\series bold
-
-\backslash
-cases
-\series default
- is also available via the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Cases-Environment
-\family default
-.
-\end_layout
-
-\begin_layout Subsection
-Negations
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Negations
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-By inserting
-\series bold
-
-\backslash
-not
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! N !
-\backslash
-not
-\end_layout
-
-\end_inset
-
- every character can be displayed canceled.
- The characters are quasi accentuated by a slash.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-not=
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\not=$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-not
-\backslash
-le
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\not\le$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-not
-\backslash
-parallel
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\not\parallel$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The last example shows that not all negations look good.
- Therefore there are special commands for some negations (see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Mathematical-Symbols"
-
-\end_inset
-
- and
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Relations"
-
-\end_inset
-
-).
-\end_layout
-
-\begin_layout Subsection
-Placeholders
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Placeholders"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Placeholders
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Chemical characters ! Isotopes
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Isotopes|see
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-{
-\end_layout
-
-\end_inset
-
-Chemical characters
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-When displaying e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-isotopes
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-Typesetting isotopes and chemical symbols is described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Chemical-Symbols-and"
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
- the following problem occurs:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Indices created with sub- and superscripts:
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-correct indices:
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\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
-
-\begin_layout Standard
-The shorter index is by default placed below or above the first character
- of the longer index.
- To avoid this there is the command
-\series bold
-
-\backslash
-phantom
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! P !
-\backslash
-phantom
-\end_layout
-
-\end_inset
-
- or the math toolbar button
-\begin_inset space \thinspace{}
-\end_inset
-
-
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-can be found in the submenu of the toolbar button
-\begin_inset Graphics
- filename ../images/math/space.png
- scale 85
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\begin_inset Graphics
- filename ../images/math/phantom.png
- scale 85
-
-\end_inset
-
- that creates one or more phantom characters.
- When inserting
-\series bold
-
-\backslash
-phantom
-\series default
- a small blue box appears that is superposed with two red arrows.
- The arrows indicate that the complete width and height of the box content
- will be created as placeholder.
- Phantom characters are accordingly placeholders with the size of the characters.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\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 $\to$
-\end_inset
-
-9
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-F
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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 $\to$
-\end_inset
-
-9
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-F
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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 $\to$
-\end_inset
-
-t
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-_MMt
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Furthermore there are the commands
-\series bold
-
-\backslash
-vphantom
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! V !
-\backslash
-vphantom
-\end_layout
-
-\end_inset
-
- (toolbar button
-\begin_inset space ~
-\end_inset
-
-
-\begin_inset Graphics
- filename ../images/math/vphantom.png
- scale 85
-
-\end_inset
-
-) and
-\series bold
-
-\backslash
-hphantom
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! H !
-\backslash
-hphantom
-\end_layout
-
-\end_inset
-
- (toolbar button
-\begin_inset space ~
-\end_inset
-
-
-\begin_inset Graphics
- filename ../images/math/hphantom.png
- scale 85
-
-\end_inset
-
-).
-
-\series bold
-
-\backslash
-hphantom
-\series default
- creates only space for the maximal height of the characters in the box
- but not for its width.
-
-\series bold
-
-\backslash
-vphantom
-\series default
- creates only space for the width of the box content.
- Therefore the boxes of both commands have only one red arrow.
-\end_layout
-
-\begin_layout Standard
-For example the command
-\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
- creates space for the height of the integral sign,
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-The command
-\series bold
-
-\backslash
-int
-\series default
- creates an integral sign, see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Big-Operators"
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
- because this is the larger character.
- An example application is in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Multiline-Brackets"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-Placeholders can also be used for text when they are inserted via the menu
-
-\family sans
-Insert\SpecialChar \menuseparator
-Formatting\SpecialChar \menuseparator
-Phantom
-\family default
-:
-\end_layout
-
-\begin_layout Standard
-This is a sentence.
-\begin_inset Newline newline
-\end_inset
-
-
-\begin_inset Phantom Phantom
-status open
-
-\begin_layout Plain Layout
-This
-\end_layout
-
-\end_inset
-
- is a sentence.
-\end_layout
-
-\begin_layout Subsection
-Lines
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Lines
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! underlined
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\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
-Commands ! O !
-\backslash
-overline
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
-Commands ! U !
-\backslash
-underline
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-In the last example it doesn't matter if first
-\series bold
-
-\backslash
-overline
-\series default
- or
-\series bold
-
-\backslash
-underline
-\series default
- is inserted.
-\end_layout
-
-\begin_layout Standard
-To double underline use
-\series bold
-
-\backslash
-underline
-\series default
- twice.
-\end_layout
-
-\begin_layout Standard
-It is possible to place up to 6 lines above or below characters.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-Custom lines can be created using the command
-\series bold
-
-\backslash
-rule
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-rule
-\end_layout
-
-\end_inset
-
- which has the following scheme:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-rule[vertical offset]{length}{thickness}
-\end_layout
-
-\begin_layout Standard
-The optional vertical offset shifts the line upwards (or downwards, when
- the value is negative).
- The units listed in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "tab:Available-units"
-
-\end_inset
-
- can be used for the values.
- Here are two example lines created with the commands
-\begin_inset Newline newline
-\end_inset
-
-
-\series bold
-
-\backslash
-rule[-2ex]{3cm}{2pt}
-\series default
- and
-\series bold
-
-\backslash
-rule{2cm}{1pt}
-\series default
-:
-\end_layout
-
-\begin_layout Standard
-This is a sentence
-\begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
-\end_inset
-
- with two lines.
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-rule
-\series default
- can also be used for text when a line is inserted via the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Formatting\SpecialChar \menuseparator
-Horizontal
-\begin_inset space ~
-\end_inset
-
-Line
-\family default
-:
-\end_layout
-
-\begin_layout Standard
-This is a sentence
-\begin_inset CommandInset line
-LatexCommand rule
-offset "0.5ex"
-width "3cm"
-height "1pt"
-
-\end_inset
-
- with one line.
-\end_layout
-
-\begin_layout Subsection
-Ellipses
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Ellipses"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Ellipses
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-There are different types of ellipses available.
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-In the math toolbar in the submenu of the button
-\begin_inset Graphics
- filename ../images/math/ldots.png
- scale 85
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
- For listings dots at the baseline are used (
-\series bold
-
-\backslash
-ldots
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! L !
-\backslash
-ldots
-\end_layout
-
-\end_inset
-
-), while for operations dots are needed that are on the same height as the
- operators (
-\series bold
-
-\backslash
-cdots
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! C !
-\backslash
-cdots
-\end_layout
-
-\end_inset
-
-).
- When using the command
-\series bold
-
-\backslash
-dots
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! D !
-\backslash
-dots
-\end_layout
-
-\end_inset
-
-, LaTeX decides on the basis of the next character what type is used.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A_{1},\dots,A_{n}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A_{1}+\dots+A_{n}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A_{1},\ldots,A_{n}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A_{1}+\cdots+A_{n}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-vdots
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\vdots$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-ddots
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\ddots$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-iddots
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\iddots$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-3Ã3
-\begin_inset space \thinspace{}
-\end_inset
-
-matrix with the different dots
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The ellipses available in menu
-\family sans
-Insert\SpecialChar \menuseparator
-Special
-\begin_inset space ~
-\end_inset
-
-Character
-\family default
- are
-\series bold
-
-\backslash
-ldots
-\series default
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-To use
-\series bold
-
-\backslash
-iddots
-\series default
-, one of the options
-\family sans
-Use mathdots package (automatically)
-\family default
- must be set in the document settings under
-\family sans
-Math
-\begin_inset space ~
-\end_inset
-
-Options
-\family default
-.
-\begin_inset Newline newline
-\end_inset
-
-Using the option
-\family sans
-Use mathdots package
-\family default
- will improve the appearance of all dots in the documents if their font
- style or size is not the default.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-Specially for matrices there are ellipses that span over several columns.
- They are created with the command
-\series bold
-
-\backslash
-hdotsfor
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! H !
-\backslash
-hdotsfor
-\end_layout
-
-\end_inset
-
-, that has the following scheme:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-hdotsfor[distance]{number of columns}
-\end_layout
-
-\begin_layout Standard
-The number of columns specifies how many columns should be spanned.
- Distance is a factor for the distance between the dots.
-\end_layout
-
-\begin_layout Standard
-In the following matrix the command
-\series bold
-
-\backslash
-hdotsfor[2]{4}
-\series default
- was inserted in the first box of the second line, to get an ellipsis with
- a dot distance twice as long as with the command
-\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
-
-Note that the matrix fields that should be spanned must be empty, otherwise
- you get LaTeX-errors.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-Furthermore you can fill with the command
-\series bold
-
-\backslash
-dotfill
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! D !
-\backslash
-dotfill
-\end_layout
-
-\end_inset
-
- the rest of a line with dots.
- The effect of these commands is the same as with
-\series bold
-
-\backslash
-hfill
-\series default
-, see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Variable-Space"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-For example the command
-\series bold
-A
-\backslash
-dotfill
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-B
-\series default
- produces
-\end_layout
-
-\begin_layout Standard
-\begin_inset Formula $A\dotfill B$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Similar to
-\series bold
-
-\backslash
-dotfill
-\series default
- there is for a line the command
-\series bold
-
-\backslash
-hrulefill
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! 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
-To use the commands for text, they have to be inserted in TeX-mode.
-\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
-Matrices can be inserted via the math toolbar button
-\begin_inset Graphics
- filename ../images/dialog-show_mathmatrix.png
- scale 85
-
-\end_inset
-
- or the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Matrix
-\family default
-.
- In the matrix dialog you can specify the number of columns and rows, the
- alignment and the decoration.
- The vertical alignment is only of importance for matrices in inline formulas:
-\end_layout
-
-\begin_layout Standard
-The first matrix is top
-\begin_inset Formula $\begin{array}[t]{cccc}
-A & D & G & J\\
-B & E & H & K\\
-C & F & I & L
-\end{array}$
-\end_inset
-
-, the second middle
-\begin_inset Formula $\begin{array}{cccc}
-A & D & G & J\\
-B & E & H & K\\
-C & F & I & L
-\end{array}$
-\end_inset
-
- and the third bottom
-\begin_inset Formula $\begin{array}[b]{cccc}
-A & D & G & J\\
-B & E & H & K\\
-C & F & I & L
-\end{array}$
-\end_inset
-
- aligned.
-\end_layout
-
-\begin_layout Standard
-The horizontal alignment specifies how the column entries should be aligned.
- It is set by entering a letter for every column.
-
-\emph on
-l
-\emph default
- denotes left aligned,
-\emph on
-c
-\emph default
- centered and
-\emph on
-r
-\emph default
- right aligned.
- To create for example a 4
-\series bold
-Ã
-\series default
-4
-\begin_inset space ~
-\end_inset
-
-matrix where the first column is left aligned, the second and third are
- centered and the last one is right aligned, one enters for the horizontal
- alignment
-\series bold
-lccr
-\series default
-.
- Normally in a matrix all columns are centered, therefore the default for
- every column is a
-\series bold
-c
-\series default
-.
-\end_layout
-
-\begin_layout Standard
-Horizontal alignment:
-\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
-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
-To add or delete rows and columns subsequently, the math toolbar buttons
-
-\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.
-\begin_inset space \thinspace{}
-\end_inset
-
-, or the menu
-\family sans
-Edit\SpecialChar \menuseparator
-Rows & Columns
-\family default
- can be used.
- New rows can also be created with
-\begin_inset Info
-type "shortcut"
-arg "newline-insert newline"
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-The
-\family sans
-Decoration
-\family default
- adds parentheses in the selected style around the matrix.
- Alternatively, parentheses can can either be created with the commands
-
-\series bold
-
-\backslash
-left
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! L !
-\backslash
-left
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-right
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-right
-\end_layout
-
-\end_inset
-
- (shortcut
-\family sans
-Alt+M
-\begin_inset space ~
-\end_inset
-
-Parenthesis
-\family default
-), see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Automatic-Bracket-Size"
-
-\end_inset
-
-, or by using the following commands:
-\begin_inset VSpace medskip
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\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
-Ã
-\series default
-2
-\begin_inset space \thinspace{}
-\end_inset
-
-matrix
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\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
-Ã
-\series default
-2
-\begin_inset space \thinspace{}
-\end_inset
-
-matrix
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\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
-Ã
-\series default
-2
-\begin_inset space \thinspace{}
-\end_inset
-
-matrix
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
-Ã
-\series default
-2
-\begin_inset space \thinspace{}
-\end_inset
-
-matrix
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\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
-Ã
-\series default
-2
-\begin_inset space \thinspace{}
-\end_inset
-
-matrix
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\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
-Ã
-\series default
-2
-\begin_inset space \thinspace{}
-\end_inset
-
-matrix
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-When e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-
-\series bold
-
-\backslash
-vmatrix
-\series default
- is inserted, a blue box appears between two vertical lines where the matrix
- is inserted.
-\begin_inset Newline newline
-\end_inset
-
-Note that decorated matrices ignore the vertical alignment.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-As all multiline formulas are matrices, the length
-\series bold
-
-\backslash
-arraycolsep
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! A !
-\backslash
-arraycolsep
-\end_layout
-
-\end_inset
-
- that is described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Column-Separation"
-
-\end_inset
-
- can also be used to change the column separation of matrices.
-\end_layout
-
-\begin_layout Standard
-To change the row separation, the command
-\series bold
-
-\backslash
-arraystretch
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! A !
-\backslash
-arraystretch
-\end_layout
-
-\end_inset
-
- is used.
- It is used as follows:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-renewcommand{
-\backslash
-arraystretch}{stretch factor}
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-renewcommand
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The command
-\series bold
-
-\backslash
-renewcommand
-\series default
- assigns the stretch factor to the predefined command
-\series bold
-
-\backslash
-arraystretch
-\series default
-.
- To double e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-the row separation, use the factor 2.
- This is then used for all following matrices.
- To go back to the original separation, assign the factor 1 to
-\series bold
-
-\backslash
-arraystretch
-\series default
-.
-\end_layout
-
-\begin_layout Standard
-To set matrices into a text line, the command
-\series bold
-
-\backslash
-smallmatrix
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-smallmatrix
-\end_layout
-
-\end_inset
-
- is used.
- When it is inserted a blue box with two dashed lines appears.
- In this box the matrix is inserted.
-\end_layout
-
-\begin_layout Standard
-This is a matrix
-\begin_inset Formula $\left(\begin{smallmatrix}A & B\\
-C & D
-\end{smallmatrix}\right)$
-\end_inset
-
- in a text line.
-\end_layout
-
-\begin_layout Section
-Brackets and Delimiters
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Brackets
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Delimiters
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Vertical Brackets and Delimiters
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Brackets ! vertical
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-(
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $($
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-{
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\{$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-[
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $[$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-langle
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\langle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-lceil
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\lceil$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-lfloor
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\lfloor$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-/
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $/$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-|
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $|$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-)
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $)$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-}
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-]
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $]$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-rangle
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\rangle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-rceil
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\rceil$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-rfloor
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\rfloor$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-
-\backslash
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\backslash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-|
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\|$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-\series medium
-\begin_inset Note Greyedout
-status open
-
-\begin_layout Plain Layout
-
-\series bold
-Note:
-\series default
- In TeX-mode the command
-\series bold
-
-\backslash
-textbackslash
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! T !
-\backslash
-textbackslash
-\end_layout
-
-\end_inset
-
- must be used for the backslash, because the command
-\series bold
-
-\backslash
-
-\backslash
-
-\series default
- produces a line break there.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-For all characters listed above the size can be adjusted with the commands
- described in the following two subsections.
- When using these commands, the characters < and > can directly be used
- instead of the commands
-\series bold
-
-\backslash
-langle
-\series default
- and
-\series bold
-
-\backslash
-rangle
-\series default
-.
-\end_layout
-
-\begin_layout Subsubsection
-Manual Bracket Size
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Manual-Bracket-Size"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Bracket size ! manual
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The bracket size can be specified manually by the LaTeX-commands
-\series bold
-
-\backslash
-big
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! B !
-\backslash
-big
-\end_layout
-
-\end_inset
-
-,
-\series bold
-
-\backslash
-Big
-\series default
-,
-\series bold
-
-\backslash
-bigg
-\series default
- and
-\series bold
-
-\backslash
-Bigg
-\series default
-.
-
-\series bold
-
-\backslash
-big
-\series default
- denotes the smallest and
-\series bold
-
-\backslash
-Bigg
-\series default
- the largest bracket size.
-\end_layout
-
-\begin_layout Standard
-These commands are used to emphasize levels of brackets:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-all brackets in the same size:
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-this looks better:
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\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
-
-\begin_layout Standard
-For the second formula the command
-\series bold
-
-\backslash
-Big((A+B)(A-B)
-\backslash
-Big)^
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-C
-\series default
- has been used.
-\end_layout
-
-\begin_layout Standard
-Here is an overview about all bracket sizes:
-\end_layout
-
-\begin_layout Standard
-\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
-sin(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
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Besides the
-\series bold
-
-\backslash
-big
-\series default
--commands there is the variant
-\series bold
-
-\backslash
-bigm
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! B !
-\backslash
-bigm
-\end_layout
-
-\end_inset
-
- that adds a bit more space between the bracket and its content, and the
- variant
-\series bold
-
-\backslash
-bigl
-\series default
--
-\series bold
-
-\backslash
-bigr
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! B !
-\backslash
-bigl -
-\backslash
-bigr
-\end_layout
-
-\end_inset
-
-, that don't add additional space.
- The
-\emph on
-l
-\emph default
- at the end of the command
-\series bold
-
-\backslash
-bigl
-\series default
- is for a left bracket; for a right bracket this will be replaced by an
-
-\emph on
-r
-\emph default
-.
- A left or right bracket can each be an opening or closing bracket.
-\end_layout
-
-\begin_layout Standard
-In the following table is a comparison of the variants:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-bigl)
-\backslash
-ln(3x)
-\backslash
-bigr(
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsubsection
-Automatic Bracket Size
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Automatic-Bracket-Size"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Bracket size ! automatic
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Brackets with variable size can be inserted with the commands
-\series bold
-
-\backslash
-left
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! L !
-\backslash
-left
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-right
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-right
-\end_layout
-
-\end_inset
-
- or via the math toolbar button
-\begin_inset Graphics
- filename ../images/dialog-show_mathdelimiter.png
- scale 85
-
-\end_inset
-
-.
- Directly behind
-\series bold
-
-\backslash
-left
-\series default
- and
-\series bold
-
-\backslash
-right
-\series default
- the wanted bracket must be inserted.
- The bracket size will then automatically be calculated for the output.
-\end_layout
-
-\begin_layout Standard
-\align center
-normal bracket: The command
-\series bold
-
-\backslash
-ln(
-\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
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-)
-\series default
- creates
-\begin_inset Formula
-\[
-\ln(\frac{A}{C})
-\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\align center
-multiline bracket: The command
-\series bold
-
-\backslash
-ln
-\backslash
-left(
-\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
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\backslash
-right)
-\series default
- creates
-\begin_inset Formula
-\[
-\ln\left(\frac{A}{C}\right)
-\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Instead of
-\series bold
-
-\backslash
-left
-\series default
- and
-\series bold
-
-\backslash
-right
-\series default
- the shortcut
-\family sans
-Alt+M
-\begin_inset space ~
-\end_inset
-
-Bracket
-\family default
- can be used.
- This has the advantage that you can see in LyX immediately the real bracket
- size and that the matching right bracket will be created too.
-\begin_inset Newline newline
-\end_inset
-
-The command for the last example would then be:
-\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
-To omit a left or right bracket, a dot is inserted for the omitted bracket.
- For example the command
-\series bold
-
-\backslash
-left.
-\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
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\backslash
-right}
-\series default
- creates:
-\series bold
-
-\begin_inset Formula
-\[
-\left.\frac{A}{B}\right\}
-\]
-
-\end_inset
-
-
-\series default
-The commands
-\series bold
-
-\backslash
-left
-\series default
- and
-\series bold
-
-\backslash
-right
-\series default
- will be converted by LyX to brackets in the right size when the document
- is reloaded and an omitted bracket will appear as dashed line.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
- the command
-\series bold
-
-\backslash
-middle
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! M !
-\backslash
-middle
-\end_layout
-
-\end_inset
-
- is additionally available for all brackets and limits.
- With this command the height of the following character is adapted to the
- one of the surrounding brackets, what is e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-needed for physical vectors:
-\begin_inset Formula
-\[
-\left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
-\]
-
-\end_inset
-
-For physical vectors there is a special LaTeX-package, described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Physical-Vectors"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Subsection
-Horizontal Brackets
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Brackets ! horizontal
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
-Commands ! O !
-\backslash
-overbrace
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\overbrace{A+B}^{3}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
-Commands ! U !
-\backslash
-underbrace
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\underbrace{A+B}_{5}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-In the last example it doesn't matter if
-\series bold
-
-\backslash
-overbrace
-\series default
- or
-\series bold
-
-\backslash
-underbrace
-\series default
- is inserted at first.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-When brackets are needed that overlap each other, multiline formulas, as
- described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Multiline-Formulas"
-
-\end_inset
-
-, must be used:
-\begin_inset Formula
-\begin{eqnarray*}
-A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
- & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
-\end{eqnarray*}
-
-\end_inset
-
-In the first row the formula is inserted together with the first brace.
- It is hereby important that the space command
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-Space commands are explained in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Predefined-Space"
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
-
-\series bold
-
-\backslash
-:
-\series default
- is inserted before the first
-\begin_inset Formula $d$
-\end_inset
-
-, because the brace that ends behind the
-\begin_inset Formula $q$
-\end_inset
-
- prevents that the following
-\begin_inset Quotes eld
-\end_inset
-
-+
-\begin_inset Quotes erd
-\end_inset
-
- is surrounded by space.
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-because a bracket is not handled as a character, see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Binary-Operators"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
- In the second row the second brace is inserted.
- As it should begin before the
-\begin_inset Formula $b$
-\end_inset
-
-, first the command
-\series bold
-
-\backslash
-hphantom{gggg+
-\backslash
-:}
-\series default
- is inserted.
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-more about
-\series bold
-
-\backslash
-hphantom
-\series default
- see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Placeholders"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
- This space is needed because the
-\begin_inset Quotes eld
-\end_inset
-
-+
-\begin_inset Quotes erd
-\end_inset
-
- is also surrounded by space in the formula.
- The brace is placed under the command
-\series bold
-
-\backslash
-hphantom{bbqq+dddd}
-\series default
-.
-\end_layout
-
-\begin_layout Standard
-It gets more complicated when brackets overlap each other, like in the following
- example:
-\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
-
-The first formula row is the same as the second row of the previous example,
- with the difference that the brace is above.
- The second row contains the formula together with the second brace.
- To avoid that there is space between the upper brace in the first row and
- the formula, the row spacing needs to be reduced.
- This is not easily possible due to a bug in 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
-
-.
- As a solution for the problem, the global formula row separation
-\series bold
-
-\backslash
-jot
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! J !
-\backslash
-jot
-\end_layout
-
-\end_inset
-
- must be changed to -6
-\begin_inset space \thinspace{}
-\end_inset
-
-pt before the formula with the command
-\series bold
-
-\backslash
-setlength{
-\backslash
-jot}{-6pt}
-\series default
- in TeX-mode.
-
-\series bold
-
-\backslash
-jot
-\series default
- is set back after the formula to the standard value of 3
-\begin_inset space \thinspace{}
-\end_inset
-
-pt using the same command.
- More about the row separation in formulas is explained in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Line-Separation"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Section
-Arrows
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Arrows
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Arrows can be inserted via the math toolbar button
-\begin_inset Graphics
- filename ../images/math/leftarrow.png
- scale 85
-
-\end_inset
-
- or the commands listed in the following subsections.
-\end_layout
-
-\begin_layout Subsection
-Horizontal Arrows
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Arrows ! horizontal
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-gets
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\gets$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Leftarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Leftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-longleftarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\longleftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Longleftarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Longleftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-leftharpoonup
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\leftharpoonup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-leftharpoondown
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\leftharpoondown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-hookleftarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\hookleftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-to
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\to$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Rightarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Rightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-longrightarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\longrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Longrightarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Longrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-rightharpoonup
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\rightharpoonup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-rightharpoondown
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\rightharpoondown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-hookrightarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\hookrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-leftrightarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\leftrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Leftrightarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Leftrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-longleftrightarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\longleftrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Longleftrightarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Longleftrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-rightleftharpoons
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\rightleftharpoons$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hspace{}
-\length 25pt
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-mapsto
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\mapsto$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-longmapsto
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\longmapsto$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-leadsto
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\leadsto$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-dasharrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\dasharrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-Arrows used as accents like e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-vector arrows are listed in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Accents"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-Furthermore there are the labeled arrows
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Arrows ! labeled
-\end_layout
-
-\end_inset
-
-
-\series bold
-
-\backslash
-xleftarrow
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! X !
-\backslash
-xleftarrow
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-xrightarrow
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! X !
-\backslash
-xrightarrow
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-vspace{4mm}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-.
- When inserting one of these commands in a formula, an arrow with two blue
- boxes appear where the label can be inserted.
- The length of the arrow adapts to the label width.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Vertical and diagonal Arrows
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Arrows ! diagonal
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Arrows ! vertical
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-uparrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\uparrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Uparrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Uparrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-updownarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\updownarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Updownarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Updownarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Downarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Downarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-downarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\downarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-nearrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\nearrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-searrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\searrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-swarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\swarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-nwarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\nwarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-Vertical arrows can be used also as delimiters together with the commands
- described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Manual-Bracket-Size"
-
-\end_inset
-
- and
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Automatic-Bracket-Size"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Section
-Accents
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Accents"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Accents
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Accents can be inserted via the math toolbar button
-\begin_inset Graphics
- filename ../images/math/hat.png
- scale 85
-
-\end_inset
-
- or the commands listed in the following subsections.
-\end_layout
-
-\begin_layout Subsection
-Accents for one Character
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-texorpdfstring{
-\end_layout
-
-\end_inset
-
-
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-accents in text see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Accents-in-Text"
-
-\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
- is used to avoid that the footnote appears in the PDF-bookmark.
-\end_layout
-
-\begin_layout Plain Layout
-More about
-\series bold
-
-\backslash
-texorpdfstring
-\series default
- is in section
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Formulas-in-Section"
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
-
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Accents-for-one"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Accents ! for one character
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\dot{A}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
-Vectors
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\vec{A}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\bar{A}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\hat{A}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\check{A}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\acute{A}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\grave{A}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\breve{A}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-You can directly insert accents like é to formulas.
- LyX will transform them to the corresponding accent command.
- For umlauts
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Umlauts
-\end_layout
-
-\end_inset
-
- it is better to insert a quotation mark before the vowel.
- These two characters are then treated by LaTeX as
-\emph on
-one
-\emph default
- character when the formula part with the umlaut is marked as German.
- In contrary to
-\series bold
-
-\backslash
-ddot
-\series default
-, with this method
-\begin_inset Quotes eld
-\end_inset
-
-real
-\begin_inset Quotes erd
-\end_inset
-
- umlauts are created as demonstrated in the following example:
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace -2mm
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-
-\series bold
-
-\backslash
-raisebox
-\series default
- and the 0
-\begin_inset space \thinspace{}
-\end_inset
-
-pt space are only used as spacer.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\lang ngerman
-\begin_inset Quotes grd
-\end_inset
-
-i
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset space \hspace{}
-\length 0pt
-\end_inset
-
-
-\lang ngerman
-
-\begin_inset Formula $"i$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Another advantage to
-\series bold
-
-\backslash
-ddot
-\series default
- is that umlauts can directly be converted to mathematical text because
- the accent commands above are
-\emph on
-not allowed
-\emph default
-
-\emph on
-in mathematical text
-\emph default
-.
- To convert an accented character to mathematical text, only the character
- under the accent may be converted.
- This applies also for all other conversions, e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-to italic or bold.
-\end_layout
-
-\begin_layout Standard
-In mathematical text, umlauts and other accented characters can directly
- be inserted.
-\end_layout
-
-\begin_layout Subsection
-Accents for several Characters
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Accents ! for several characters
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-With these commands as many characters as you like can be accented.
- But the accents
-\series bold
-
-\backslash
-widetilde
-\series default
- and
-\series bold
-
-\backslash
-widehat
-\series default
- will only be set in the output with a length of three characters, as shown
- in the following example:
-\begin_inset Formula
-\[
-\widetilde{A+B=C-D}
-\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-With the commands
-\series bold
-
-\backslash
-overset
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! O !
-\backslash
-overset
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-underset
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! U !
-\backslash
-underset
-\end_layout
-
-\end_inset
-
- described in the previous subsection it is also possible to accent several
- characters.
- The command
-\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
- creates:
-\begin_inset Formula
-\[
-\underset{***}{A=B}
-\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-Space
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Space"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Space ! horizontal
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Predefined Space
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Predefined-Space"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Space ! horizontal ! predefined
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Sometimes it is necessary to insert horizontal space into a formula.
- This is done by inserting a protected space (shortcut
-\begin_inset Info
-type "shortcut"
-arg "command-alternatives space-insert protected ; math-space"
-\end_inset
-
-).
- A
-\begin_inset Quotes eld
-\end_inset
-
-
-\color blue
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\color inherit
-
-\begin_inset Quotes erd
-\end_inset
-
- appears and by pressing
-\family sans
-Space
-\family default
- several times one can select one of eight different space sizes.
- The spaces can also be inserted using the math toolbar button
-\begin_inset Graphics
- filename ../images/math/space.png
- scale 85
-
-\end_inset
-
- or special commands.
- Independent from the inserted command, one can select the size again by
- pressing
-\family sans
-Space
-\family default
- afterwards.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset VSpace -5mm
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-,
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-:
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-;
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-quad
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-qquad
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-!
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Number of
-\family sans
-Space
-\family default
- keystrokes after inserting the protected space
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-0
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-1
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-2
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-3
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-4
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-5
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A\, B$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A\: B$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A\; B$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A\quad B$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A\qquad B$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A\! B$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The last size seem to produce no space.
- It is displayed red in LyX contrary to the other sizes, because it is a
- negative space.
- There are two more negative spaces:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-negmedspace
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-negthickspace
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Number of
-\family sans
-Space
-\family default
- keystrokes after inserting the protected space
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-6
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-7
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A\negmedspace B$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A\negthickspace B$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Negative spaces can lead to characters overlapping each other.
- Thus they can be used to enforce ligatures, which are e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-useful for summation operators:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Relations like for example equal signs, are always surrounded by space.
- To suppress this, the equal sign is placed into a TeX-brace.
- The following example demonstrates this:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-normal equation
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A=B$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\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
-
-
-\begin_inset Formula $\raisebox{5mm}{}$
-\end_inset
-
-equation without space
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A{=}B$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\noindent
-The command for the last formula is:
-\series bold
-A
-\backslash
-{=
-\begin_inset Formula $\to$
-\end_inset
-
-B
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-Spaces are needed for physical units, because the space between the value
- and the unit is the smallest one and not a normal space.
- For units in text, the smallest space is inserted via the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Formatting\SpecialChar \menuseparator
-Thin
-\begin_inset space ~
-\end_inset
-
-Space
-\family default
- (shortcut
-\begin_inset Info
-type "shortcut"
-arg "space-insert thin"
-\end_inset
-
-).
-\end_layout
-
-\begin_layout Standard
-An example to visualize the difference:
-\end_layout
-
-\begin_layout Standard
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-24 kW
-\begin_inset Formula $\cdot$
-\end_inset
-
-h
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-space between value and unit
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-smallest space between value and unit
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Variable Space
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-texorpdfstring{
-\end_layout
-
-\end_inset
-
-
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-for vertical space in formulas see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Line-Separation"
-
-\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 is used to avoid that the footnote appears in the PDF-bookmark.
-\end_layout
-
-\begin_layout Plain Layout
-More about
-\backslash
-texorpdfstring is in section
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Formulas-in-Section"
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
-
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Variable-Space"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Space ! horizontal ! variable
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Space with a defined length can be inserted with the command
-\series bold
-
-\backslash
-hspace
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! H !
-\backslash
-hspace
-\end_layout
-
-\end_inset
-
-.
- Then a long
-\begin_inset Quotes eld
-\end_inset
-
-
-\color blue
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\color inherit
-
-\begin_inset Quotes erd
-\end_inset
-
- appears.
- The length can be specified by left-clicking on the
-\begin_inset Quotes eld
-\end_inset
-
-
-\color blue
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\color inherit
-
-\begin_inset Quotes erd
-\end_inset
-
-.
- The length may also be negative.
- To insert as much space as is available, the command
-\series bold
-
-\backslash
-hfill
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! H !
-\backslash
-hfill
-\end_layout
-
-\end_inset
-
- is used.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace -1mm
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command (
-\backslash
-hspace length)
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A=B\hspace{3cm}A\not=C$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A\hspace{-1mm}A\not=A$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A=A\hfill B=B$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-In the last example the available space is given by the longest column entry
- of the table.
- In an inline formula the space depends on the length of the line in which
-
-\series bold
-
-\backslash
-hfill
-\series default
- is inserted.
- Thus, when the line uses the full width, no space will be created.
-
-\series bold
-
-\backslash
-hfill
-\series default
- only has an effect on displayed formulas when the formula style
-\series bold
-Indented
-\series default
- is used.
- (Formula styles are explained in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Formula-Styles"
-
-\end_inset
-
-.)
-\end_layout
-
-\begin_layout Standard
-Besides
-\series bold
-
-\backslash
-hfill
-\series default
-, there are the commands
-\series bold
-
-\backslash
-dotfill
-\series default
- and
-\series bold
-
-\backslash
-hrulefill
-\series default
- that fill the space with a pattern, see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Ellipses"
-
-\end_inset
-
- for an example.
-\end_layout
-
-\begin_layout Standard
-For text, variable space can be inserted via the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Formatting\SpecialChar \menuseparator
-Horizontal
-\begin_inset space ~
-\end_inset
-
-Space
-\family default
-:
-\end_layout
-
-\begin_layout Standard
-This is a line with
-\begin_inset space \hspace{}
-\length 2cm
-\end_inset
-
-2
-\begin_inset space \thinspace{}
-\end_inset
-
-cm space.
-\end_layout
-
-\begin_layout Standard
-This is a line with
-\begin_inset space \hfill{}
-\end_inset
-
-maximum space.
-\end_layout
-
-\begin_layout Subsection
-Space besides inline Formulas
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Space ! besides inline formulas
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The space that surrounds inline formulas can be adjusted with the length
-
-\series bold
-
-\backslash
-mathsurround
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! M !
-\backslash
-mathsurround
-\end_layout
-
-\end_inset
-
-.
- The value of a length is set with the command
-\series bold
-
-\backslash
-setlength
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-setlength
-\end_layout
-
-\end_inset
-
- which has the following scheme:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-setlength{length name}{value}
-\end_layout
-
-\begin_layout Standard
-To set
-\series bold
-
-\backslash
-mathsurround
-\series default
- to the value 5
-\begin_inset space \thinspace{}
-\end_inset
-
-mm, the command
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-setlength{
-\backslash
-mathsurround}{5mm}
-\end_layout
-
-\begin_layout Standard
-is inserted in TeX-mode.
- 5
-\begin_inset space \thinspace{}
-\end_inset
-
-mm space will now be set around all inline formulas:
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-setlength{
-\backslash
-mathsurround}{5mm}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-This is a line with an inline formula
-\begin_inset Formula $A=B$
-\end_inset
-
- with 5
-\begin_inset space \thinspace{}
-\end_inset
-
-mm surrounding space.
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-setlength{
-\backslash
-mathsurround}{0pt}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To return to the predefined value,
-\series bold
-
-\backslash
-mathsurround
-\series default
- is set to the value 0
-\begin_inset space \thinspace{}
-\end_inset
-
-pt.
-\end_layout
-
-\begin_layout Section
-Boxes and Frames
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Boxes
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Frames | see
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-{
-\end_layout
-
-\end_inset
-
-Boxes
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Boxes for text are described in chapter
-\family typewriter
-Boxes
-\family default
- in the
-\family typewriter
-Embedded
-\begin_inset space ~
-\end_inset
-
-Objects
-\family default
- manual.
-\end_layout
-
-\begin_layout Subsection
-Boxes with Frame
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Boxes-with-Frame"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Boxes ! with frame
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-It is possible to frame a formula or part of one with the commands
-\series bold
-
-\backslash
-fbox
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! F !
-\backslash
-fbox
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-boxed
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! B !
-\backslash
-boxed
-\end_layout
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-When one of these commands is inserted in a formula, a blue box appears
- within a frame to enter formula parts.
- For
-\series bold
-
-\backslash
-fbox
-\series default
- an additional formula has to be created by
-\family sans
-Ctrl+M
-\family default
- within this box, because the box content will otherwise be treated as mathemati
-cal text.
- When
-\series bold
-
-\backslash
-boxed
-\series default
- is used, a new formula is automatically created inside the frame.
-\end_layout
-
-\begin_layout Standard
-The command
-\series bold
-
-\backslash
-fbox
-\series default
- is not suitable to frame displayed formulas because the formula will always
- be set in the size of the text.
-
-\series bold
-
-\backslash
-boxed
-\series default
- is in contrary not suitable to frame inline formulas, because the formula
- will always be set in the size of a displayed formula.
-\end_layout
-
-\begin_layout Standard
-An extension to
-\series bold
-
-\backslash
-fbox
-\series default
- is the command
-\series bold
-
-\backslash
-framebox
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! F !
-\backslash
-framebox
-\end_layout
-
-\end_inset
-
- where additionally the frame width and the alignment can be specified.
-
-\series bold
-
-\backslash
-framebox
-\series default
- is used in the following scheme:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-framebox[frame width][position]{box content}
-\end_layout
-
-\begin_layout Standard
-The position can either be
-\emph on
-l
-\emph default
- or
-\emph on
-r
-\emph default
-.
-
-\emph on
-l
-\emph default
- left aligns,
-\emph on
-r
-\emph default
- right aligns the formula in the box.
- When no position is given, the formula will be centered.
-\begin_inset Newline newline
-\end_inset
-
-If no width is given, also no position can be given.
- In this case the frame width is adjusted to the box content like for
-\series bold
-
-\backslash
-fbox
-\series default
-.
-\end_layout
-
-\begin_layout Standard
-When the command
-\series bold
-
-\backslash
-framebox
-\series default
- is inserted, a box appears containing three blue boxes.
- The first two boxes are surrounded by brackets and denote the two optional
- arguments.
- The third box is for formula parts like for
-\series bold
-
-\backslash
-fbox
-\series default
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The frame thickness can also be adjusted.
- To do this the following commands have to be inserted in TeX-mode before
- the formula
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-fboxrule
-\series default
-
-\series bold
-
-\begin_inset Quotes eld
-\end_inset
-
-thickness
-\begin_inset Quotes erd
-\end_inset
-
-
-\series default
-
-\series bold
-
-\backslash
-fboxsep
-\series default
-
-\series bold
-
-\begin_inset Quotes eld
-\end_inset
-
-distance
-\begin_inset Quotes erd
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Quotes eld
-\end_inset
-
-distance
-\begin_inset Quotes erd
-\end_inset
-
- specifies the minimal distance between the frame and the first character
- in the box.
- An example for this is the following framed formula:
-\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
-
-Before this formula the commands
-\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
-were inserted in TeX-mode.
- The given values are used for all following boxes.
-\end_layout
-
-\begin_layout Standard
-To return to the standard frame size, the command
-\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
-is inserted in TeX-mode before the next formula.
-\end_layout
-
-\begin_layout Subsection
-Boxes without Frame
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Boxes-without-Frame"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Boxes ! without frame
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-For boxes without a frame there are the following box commands:
-\series bold
-
-\backslash
-mbox
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! M !
-\backslash
-mbox
-\end_layout
-
-\end_inset
-
-,
-\series bold
-
-\backslash
-makebox
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! M !
-\backslash
-makebox
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-raisebox
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-raisebox
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-With
-\series bold
-
-\backslash
-raisebox
-\series default
- a box can be super- or subscripted.
- But in contrary to normal super- and subscripting, the characters in the
- box keep their font size.
-
-\series bold
-
-\backslash
-raisebox
-\series default
- is used in the following scheme:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-raisebox{height}{box content}
-\end_layout
-
-\begin_layout Standard
-When the box should contain a formula, an extra formula is needed like for
-
-\series bold
-
-\backslash
-fbox
-\series default
-.
-
-\series medium
-
-\begin_inset Note Greyedout
-status open
-
-\begin_layout Plain Layout
-
-\series bold
-Note:
-\series default
- For
-\series bold
-
-\backslash
-raisebox
-\series default
- this extra formula is created by pressing
-\family sans
-Ctrl+M
-\family default
- twice instead of once because LyX doesn't yet support
-\series bold
-
-\backslash
-raisebox
-\series default
- directly.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $H\raisebox{2mm}{al}lo$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $H\raisebox{-2mm}{al}lo$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-A=
-\backslash
-raisebox{-2mm
-\begin_inset Formula $\to$
-\end_inset
-
-
-\backslash
-{
-\family sans
-Ctrl+M
-\family default
-
-\family sans
-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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The command
-\series bold
-
-\backslash
-mbox
-\series default
- is equivalent to
-\series bold
-
-\backslash
-fbox
-\series default
- and
-\series bold
-
-\backslash
-makebox
-\series default
- is equivalent to
-\series bold
-
-\backslash
-framebox
-\series default
-, with the difference that there is no frame.
-\end_layout
-
-\begin_layout Subsection
-Colored Boxes
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Colored-Boxes"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Boxes ! colored
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To be able to use all commands explained in this section, the LaTeX-package
-
-\series bold
-color
-\series default
-
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-The LaTeX-package
-\series bold
-color
-\series default
- is part of every LaTeX standard installation.
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! color
-\end_layout
-
-\end_inset
-
- has to be loaded in the LaTeX-preamble with the line
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-When text is colored somewhere in the document with a predefined color,
- LyX loads the LaTeX-package
-\series bold
-color
-\series default
- automatically.
- Thus it is possible that the package is loaded twice, but this does not
- cause problems.
-\end_layout
-
-\end_inset
-
-
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
-amble.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-usepackage{color}
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-To color boxes, the command
-\series bold
-
-\backslash
-colorbox
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! C !
-\backslash
-colorbox
-\end_layout
-
-\end_inset
-
- is used in the following scheme:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-colorbox{color}{box content}
-\end_layout
-
-\begin_layout Standard
-The box content can also be a box and a
-\series bold
-
-\backslash
-colorbox
-\series default
- can also be part of another box (see the 2nd and 3rd example).
- When the box should contain a formula, an extra formula has to be created,
- the same way as for
-\series bold
-
-\backslash
-raisebox
-\series default
-.
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-This also applies for the command
-\series bold
-
-\backslash
-fcolorbox
-\series default
-.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-One of the following predefined colors can be chosen:
-\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
- and
-\series bold
-yellow
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-colorbox{yellow
-\begin_inset Formula $\to$
-\end_inset
-
-
-\backslash
-{A=B
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
-\family default
-
-\family sans
-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
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-colorbox
-\series default
- only colors the box but not the characters in the box.
- To color all characters, the whole formula is highlighted and the desired
- color is chosen in the
-\family sans
-Text
-\begin_inset space ~
-\end_inset
-
-Style
-\family default
- dialog.
- The dialog can be called with the toolbar button
-\begin_inset Graphics
- filename ../images/dialog-show_character.png
- scale 85
-
-\end_inset
-
- or the menu
-\family sans
-Edit\SpecialChar \menuseparator
-Text
-\begin_inset space ~
-\end_inset
-
-Style\SpecialChar \menuseparator
-Customized
-\family default
-.
- The formula number then has the same color as the formula.
- When the formula number should get another color than the formula characters,
- the color must be changed within the formula.
-\end_layout
-
-\begin_layout Standard
-An example:
-\end_layout
-
-\begin_layout Standard
-
-\color red
-\begin_inset Formula
-\begin{equation}
-\int A=B\label{eq:red}
-\end{equation}
-
-\end_inset
-
-
-\color green
-
-\begin_inset Formula
-\begin{equation}
-\textcolor{red}{\int A=B}\label{eq:redgreen}
-\end{equation}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Formula
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:red"
-
-\end_inset
-
- is completely colored red.
-\begin_inset Newline newline
-\end_inset
-
-Formula
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:redgreen"
-
-\end_inset
-
- was first completely colored green to set the color for the formula number.
- Subsequently the formula characters were colored red.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-To color the frame different than the rest of the box, the command
-\series bold
-
-\backslash
-fcolorbox
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! F !
-\backslash
-fcolorbox
-\end_layout
-
-\end_inset
-
- is used in the following scheme:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-fcolorbox{frame color}{color}{box content}
-\end_layout
-
-\begin_layout Standard
-So
-\series bold
-
-\backslash
-fcolorbox
-\series default
- is an extension of the command
-\series bold
-
-\backslash
-colorbox
-\series default
-.
- The frame width is set, like for
-\series bold
-
-\backslash
-framebox
-\series default
-, with
-\series bold
-
-\backslash
-fboxrule
-\series default
- and
-\series bold
-
-\backslash
-fboxsep
-\series default
-.
- An example:
-\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
-
-
-\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
-This formula was created with the command
-\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
-\series default
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-To use other colors than the predefined ones, they have to be defined first.
-\end_layout
-
-\begin_layout Standard
-One can for example define the color
-\begin_inset Quotes eld
-\end_inset
-
-
-\series bold
-darkgreen
-\series default
-
-\begin_inset Quotes erd
-\end_inset
-
- with the LaTeX-preamble line:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-definecolor{darkgreen}{cmyk}{0.5,
-\series default
-
-\series bold
-0,
-\series default
-
-\series bold
-1,
-\series default
-
-\series bold
-0.5}
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! D !
-\backslash
-definecolor
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-cmyk
-\series default
- is the color space that denotes the colors
-\series bold
-cyan
-\series default
-,
-\series bold
-magenta
-\series default
-,
-\series bold
-yellow
-\series default
- and
-\series bold
-black
-\series default
-.
- The four comma separated numbers are the portion factor for the corresponding
- colors of the color space.
- The factors can be in the range of 0
-\begin_inset space \thinspace{}
-\end_inset
-
--
-\begin_inset space \thinspace{}
-\end_inset
-
-1.
- Instead of
-\series bold
-cmyk
-\series default
- also the color space
-\series bold
-rgb
-\series default
- can be used for definitions.
-
-\series bold
-rgb
-\series default
- denotes
-\series bold
-red
-\series default
-,
-\series bold
-green
-\series default
- and
-\series bold
-blue
-\series default
-, so that there are in this case three portion factors for the corresponding
- colors.
- Furthermore there is the color space
-\series bold
-gray
-\series default
- with one portion factor for the gray value.
-\end_layout
-
-\begin_layout Standard
-As example a framed box with the new defined color
-\series bold
-darkgreen
-\series default
- where the characters have been colored
-\series bold
-yellow
-\series default
-:
-\begin_inset Formula
-\begin{equation}
-\colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
-\end{equation}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Self-defined colors can also be used for text with the help of the command
-
-\series bold
-
-\backslash
-textcolor
-\series default
-:
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Text ! colored
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-textcolor{darkgreen}{
-\end_layout
-
-\end_inset
-
-This sentence is
-\begin_inset Quotes eld
-\end_inset
-
-darkgreen
-\begin_inset Quotes erd
-\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
-Commands ! T !
-\backslash
-textcolor
-\end_layout
-
-\end_inset
-
- is used in the scheme
-\series bold
-
-\backslash
-textcolor{color}{characters to color}
-\series default
-.
-\end_layout
-
-\begin_layout Subsection
-Paragraph Boxes
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Paragraph-Boxes"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Boxes ! as paragraph
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-A box that can contain several lines and paragraphs, a so-called paragraph
- box (parbox), can be created with the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Box
-\family default
- or the toolbar button
-\begin_inset Graphics
- filename ../images/box-insert.png
- scale 85
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-The following example shows a framed parbox in a line:
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-This is a line
-\begin_inset Box Boxed
-position "c"
-hor_pos "c"
-has_inner_box 1
-inner_pos "t"
-use_parbox 1
-use_makebox 0
-width "5cm"
-special "none"
-height "1in"
-height_special "totalheight"
-status open
-
-\begin_layout Plain Layout
-This is a paragraph box.
- It is exactly 5
-\begin_inset space \thinspace{}
-\end_inset
-
-cm long and can also contain formulas:
-\begin_inset Formula $\int A\,\mathrm{d}s=C$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
- with a parbox.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Such a box is created by right-clicking on the gray box inset.
- A dialog pops up showing the box properties.
- In our case set:
-\emph on
-Decoration
-\emph default
-: Rectangular box,
-\emph on
-Inner Box
-\emph default
-: Parbox,
-\emph on
-Width
-\emph default
-: 5
-\begin_inset space \thinspace{}
-\end_inset
-
-cm,
-\emph on
-Vertical Box Alignment
-\emph default
-: Middle
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-In LaTeX a parbox is created with the command
-\series bold
-
-\backslash
-parbox
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! P !
-\backslash
-parbox
-\end_layout
-
-\end_inset
-
- which has the following scheme:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-parbox[position]{width}{box content}
-\end_layout
-
-\begin_layout Standard
-The positions
-\emph on
-b
-\emph default
- and
-\emph on
-t
-\emph default
- are possible.
-
-\emph on
-b
-\emph default
- for
-\begin_inset Quotes eld
-\end_inset
-
-bottom
-\begin_inset Quotes erd
-\end_inset
-
- means that the box is aligned within the surrounding text with its last
- line.
- With
-\emph on
-t
-\emph default
- for
-\begin_inset Quotes eld
-\end_inset
-
-top
-\begin_inset Quotes erd
-\end_inset
-
- this is done with the first line.
- When no position is given, the box will be vertically centered, see section
-
-\emph on
-Boxes
-\emph default
- of the
-\emph on
-Embedded
-\begin_inset space ~
-\end_inset
-
-Objects
-\emph default
- manual for examples.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-To frame formulas completely, including the formula number, the formula
- must be set into a parbox.
- To do this, the command
-\series bold
-
-\backslash
-fbox{
-\backslash
-parbox{
-\backslash
-linewidth-2
-\backslash
-fboxsep-2
-\backslash
-fboxrule}{
-\series default
- is inserted in TeX-mode before the formula.
-
-\series bold
-
-\backslash
-linewidth
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! L !
-\backslash
-linewidth
-\end_layout
-
-\end_inset
-
- is hereby the line width set for the document.
- Because the frame is outside the parbox, 2
-\begin_inset space \thinspace{}
-\end_inset
-
-times the frame separation and the frame thickness must be subtracted from
- the line width.
- As this is not automatically done by LyX due to a bug
-\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
-
-, TeX-mode has to be used.
- To be able to multiply and subtract in arguments, the 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 LaTeX standard installation.
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! calc
-\end_layout
-
-\end_inset
-
- must be loaded in the 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 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 "sub:User-defined-Numbering"
-
-\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 TeX-mode because 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 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"
-
-\end_inset
-
-)
-\end_layout
-
-\end_inset
-
- Then the description follows as normal text and finally
-\series bold
-}}
-\backslash
-]
-\series default
- is inserted in TeX-mode.
- The commands
-\series bold
-
-\backslash
-[
-\series default
- and
-\series bold
-
-\backslash
-]
-\series default
- hereby 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
-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 "sub:Big-Operators"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Operators ! big
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Sums
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Integrals
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To be able to use all integral operators listed here, the option
-\family sans
-Use esint package automatically
-\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
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-int
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! I !
-\backslash
-int
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\int$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-oint
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\oint$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-ointctrclockwise
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\ointctrclockwise$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-ointclockwise
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\ointclockwise$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sqint
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\sqint$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-fint
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\begin_inset Formula $\fint$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-landupint
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\begin_inset Formula $\landupint$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-landdownint
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\begin_inset Formula $\landdownint$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-bigcap
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\bigcap$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-bigcup
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\bigcup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sum
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-sum
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\sum$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-prod
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! P !
-\backslash
-prod
-\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 Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\prod$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-coprod
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\coprod$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-bigodot
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\bigodot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-bigotimes
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\bigotimes$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-bigoplus
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\bigoplus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-bigwedge
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\bigwedge$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-bigvee
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\bigvee$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-bigsqcup
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\bigsqcup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-biguplus
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\biguplus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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 Graphics
- filename ../images/math/intop.png
- scale 85
-
-\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 are different from
-\series bold
-
-\backslash
-int
-\series default
- etc.
-\begin_inset space \space{}
-\end_inset
-
-in the style the operator limits are displayed, see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Operator-Limits"
-
-\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 therefore 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 "sub:Font-Styles"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-.
- Finally 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
-For multiple integrals there are the following commands:
-\begin_inset VSpace medskip
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-iint
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-oiint
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sqiint
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-iiint
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-iiiint
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-dotsint
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Operator Limits
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Operator-Limits"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Operators ! Limits
-\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
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Limits of inline formulas are set right beside the operator.
- Limits in displayed formulas are set above or below the operator, except
- for integral limits.
-\end_layout
-
-\begin_layout Standard
-To force that the limits are set beside the operator, the cursor is set
- 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 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 was 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 are by default set beside the operator.
- But for multiple integrals the limits are often set below the operator.
- In the following example the limits type was therefore 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
-
-
-\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
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-subarray
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-substack
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-substack
-\end_layout
-
-\end_inset
-
- are used.
- To create for example this expression
-\begin_inset Formula
-\begin{equation}
-\sum_{\begin{subarray}{c}
-0
-
-
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-+
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $+$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
--
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $-$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-pm
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\pm$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-mp
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\mp$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-cdot
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\cdot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-times
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\times$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-div
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\div$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $*$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-star
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\star$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-circ
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\circ$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-diamond
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\diamond$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-bullet
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\bullet$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-nabla
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\nabla$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-bigtriangledown
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\bigtriangledown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-bigtriangleup
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\bigtriangleup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Box
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Box$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-cap
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\cap$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-cup
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\cup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-dagger
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\dagger$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-ddagger
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\ddagger$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-wr
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\wr$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-bigcirc
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\bigcirc$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-wedge
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\wedge$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-vee
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\vee$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-oplus
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\oplus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-ominus
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\ominus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-otimes
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\otimes$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-oslash
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\oslash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-odot
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\odot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-amalg
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\amalg$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-uplus
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\uplus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-setminus
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\setminus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sqcap
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\sqcap$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sqcup
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\sqcup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-triangleleft
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\triangleleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-triangleright
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\triangleright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-All binary operators can also be inserted via the math toolbar button
-\begin_inset Graphics
- filename ../images/math/pm.png
- scale 85
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-To typeset the Laplace operator also
-\series bold
-
-\backslash
-Delta
-\series default
- or
-\series bold
-
-\backslash
-nabla
-\series default
-^
-\series bold
-2
-\series default
- (
-\begin_inset Formula $\nabla^{2}$
-\end_inset
-
-) can be used instead of
-\series bold
-
-\backslash
-bigtriangleup
-\series default
- .
-\end_layout
-
-\begin_layout Standard
-The character
-\family sans
-Menu Separator
-\family default
- from the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Special Character
-\family default
- is the operator
-\series bold
-
-\backslash
-triangleright
-\series default
-.
-\end_layout
-
-\begin_layout Subsection
-Self-defined Operators
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Self-defined-Operators"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Operators ! self-defined
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-With the help of the command
-\series bold
-
-\backslash
-DeclareMathOperator
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! D !
-\backslash
-dbinom@
-\backslash
-DeclareMathOperator
-\end_layout
-
-\end_inset
-
- custom operators can be defined in the LaTeX-preamble.
- Its command scheme is:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-DeclareMathOperator{new command}{display}
-\end_layout
-
-\begin_layout Standard
-Display can be characters or symbols that define how the operator looks
- in the output.
- To define a big operator a * is set behind the command.
- All self-defined big operators can have limits as described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Operator-Limits"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-For example the LaTeX-preamble line
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-DeclareMathOperator*{
-\backslash
-Lozenge}{
-\backslash
-blacklozenge}
-\end_layout
-
-\begin_layout Standard
-defines the command
-\series bold
-
-\backslash
-Lozenge
-\series default
-, that inserts a big operator consisting of the lozenge symbol from
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Miscellaneous-Symbols"
-
-\end_inset
-
-:
-\begin_inset Formula
-\[
-\Lozenge_{n=1}^{\infty}
-\]
-
-\end_inset
-
-The command for this formula is:
-\series bold
-
-\backslash
-Lozenge
-\series default
-^
-\series bold
-
-\backslash
-infty
-\begin_inset Formula $\to$
-\end_inset
-
-_n=1
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-When self-defined operators are not used several times in the document,
- they can also be defined with the commands
-\series bold
-
-\backslash
-mathop
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! M !
-\backslash
-mathop
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-mathbin
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! M !
-\backslash
-mathbin
-\end_layout
-
-\end_inset
-
-, which have the following scheme:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-mathop{display}
-\series default
- and
-\series bold
-
-\backslash
-mathbin{display}
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-mathop
-\series default
- defines big operators,
-\series bold
-
-\backslash
-mathbin
-\series default
- binary operators.
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-mathop
-\series default
- can e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-be used to use one limit for several operators:
-\end_layout
-
-\begin_layout Standard
-\begin_inset Formula
-\[
-\mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
-\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The command for the formula above is:
-\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
-Fonts
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Fonts
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Font Styles
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Font-Styles"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Font ! style
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Latin letters in formulas can be set in one of the following font styles:
-\begin_inset VSpace -2mm
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-shortcut
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\mathbb{ABC}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Info
-type "shortcuts"
-arg "font-noun"
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\mathbf{AbC}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Info
-type "shortcuts"
-arg "font-bold"
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\boldsymbol{AbC}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Info
-type "shortcuts"
-arg "font-boldsymbol"
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\mathcal{ABC}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Info
-type "shortcuts"
-arg "font-emph"
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\mathfrak{AbC}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
--
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\mathscr{AbC}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
--
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-shortcut
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\mathit{AbC}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
--
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\mathrm{AbC}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Info
-type "shortcuts"
-arg "font-roman"
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\mathsf{AbC}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Info
-type "shortcuts"
-arg "font-sans"
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\mathtt{AbC}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Info
-type "shortcuts"
-arg "font-typewriter"
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Note Greyedout
-status open
-
-\begin_layout Plain Layout
-
-\series bold
-Note:
-\series default
- The styles
-\series bold
-
-\backslash
-mathbb
-\series default
- and
-\series bold
-
-\backslash
-mathcal
-\series default
- can only be used for big letters.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Predefined is the style
-\series bold
-
-\backslash
-mathnormal
-\series default
-.
-\end_layout
-
-\begin_layout Standard
-The style commands work also for letters in mathematical constructs:
-\begin_inset Formula
-\[
-\mathfrak{A=\frac{b}{C}}
-\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Characters in mathematical text don't appear in a math font style but in
- the text font style
-\series bold
-
-\backslash
-textrm
-\series default
-.
- That their style can't be set correctly via the text style dialog is a
- bug in LyX.
-\begin_inset Foot
-status collapsed
-
-\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
-Instead of the style commands the dialog
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Text Style
-\family default
- or the toolbar button
-\begin_inset Graphics
- filename ../images/math/font.png
- scale 85
-
-\end_inset
-
- can be used.
-\end_layout
-
-\begin_layout Subsection
-Bold Formulas
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Bold-Formulas"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! bold
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To make a complete formula bold, the command
-\series bold
-
-\backslash
-mathbf
-\series default
- from the previous subsection cannot be used, because it doesn't work for
- small Greek letters.
- Furthermore it prints Latin letters always upright, like in the following
- equation:
-\end_layout
-
-\begin_layout Standard
-\begin_inset Formula
-\[
-\mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
-\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To display the formula correctly, the command
-\series bold
-
-\backslash
-boldsymbol
-\series default
- is used:
-\begin_inset Formula
-\[
-\boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
-\]
-
-\end_inset
-
-It is also possible to set the formula in a
-\series bold
-boldmath environment
-\series default
-.
- This environment is created by inserting the command
-\series bold
-
-\backslash
-boldmath
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! B !
-\backslash
-boldmath
-\end_layout
-
-\end_inset
-
- in TeX-mode.
- To end the environment, the command
-\series bold
-
-\backslash
-unboldmath
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! U !
-\backslash
-unboldmath
-\end_layout
-
-\end_inset
-
- is inserted in TeX-mode.
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-boldmath
-\end_layout
-
-\end_inset
-
-
-\begin_inset Formula
-\[
-\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
-\]
-
-\end_inset
-
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-unboldmath
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Colored Formulas
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! colored
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Formulas can be colored like normal text: Highlight a formula or a formula
- part and use the
-\family sans
-Text Style
-\family default
- dialog.
- Here is a formula in magenta:
-\begin_inset Formula
-\[
-{\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
-\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-You can also define your own colors as described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Colored-Boxes"
-
-\end_inset
-
-.
- They can be used with the TeX code command
-\series bold
-
-\backslash
-textcolor
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! T !
-\backslash
-textcolor
-\end_layout
-
-\end_inset
-
- in the scheme
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-textcolor{color}{characters or formula}
-\end_layout
-
-\begin_layout Standard
-The following example was colored completely dark green and partly red:
-\end_layout
-
-\begin_layout Standard
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-textcolor{darkgreen}{
-\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
-Due to a bug in LyX only complete formulas can be colored with self-defined
- colors.
-\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
-Font Sizes
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Font-Sizes"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Font ! size
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-For characters in formulas there are, analog to characters in text, the
- following size commands:
-\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
- and
-\series bold
-
-\backslash
-tiny
-\end_layout
-
-\begin_layout Standard
-The size produced by the commands depends on the document font size, which
- corresponds to the command
-\series bold
-
-\backslash
-normalsize
-\series default
-.
- The other commands produce smaller or larger sizes than
-\series bold
-
-\backslash
-normalsize
-\series default
-.
- The font size can however not exceed a certain value.
- Is for example the document font size 12
-\begin_inset space \thinspace{}
-\end_inset
-
-pt, the command
-\series bold
-
-\backslash
-Huge
-\series default
- switches to the same size as
-\series bold
-
-\backslash
-huge
-\series default
-.
-
-\end_layout
-
-\begin_layout Standard
-A size command is inserted in TeX-mode before the formula and sets the size
- for all following formula and text characters.
- To switch back to the initial size, the command
-\series bold
-
-\backslash
-normalsize
-\series default
- is inserted behind the formula in TeX-mode.
-\end_layout
-
-\begin_layout Standard
-Within a formula the size can be changed using the following size commands:
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-displaystyle
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! D !
-\backslash
-displaystyle
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-textstyle
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-scriptstyle
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-scriptscriptstyle
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-After entering these commands, a blue box appears in which the formula parts
- are inserted.
-\end_layout
-
-\begin_layout Standard
-There is a further method to change the font size, that though only works
- for symbols or letters in mathematical text.
- To use it, one of the above text size commands is inserted in mathematical
- text.
- All following characters until the end of the mathematical text or until
- another size command will have the selected size.
- Two examples:
-\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
-
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-normalsize
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-Before both formulas the command
-\series bold
-
-\backslash
-huge
-\series default
- was inserted.
- The command for the second formula is:
-\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
-\series default
-
-\series bold
-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
-If a symbol cannot be displayed in different sizes, it will always be displayed
- in the default size.
-\end_layout
-
-\begin_layout Section
-Greek Letters
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Greek letters
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Greek letters can also be inserted via the toolbar button
-\begin_inset Graphics
- filename ../images/math/alpha.png
- scale 85
-
-\end_inset
-
-.
- All international typesetting norms purport that Greek letters in math
- have to be typeset italic/slanted.
- In some languages, like French or Russian, they are nevertheless sometimes
- typeset upright.
-\end_layout
-
-\begin_layout Subsection
-Small Letters
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Greek letters ! small
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-alpha
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\alpha$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-beta
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\beta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-gamma
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\gamma$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-delta
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\delta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-epsilon
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\epsilon$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-varepsilon
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\varepsilon$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-zeta
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\zeta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-eta
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\eta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-theta
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\theta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-vartheta
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\vartheta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-iota
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\iota$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-kappa
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\kappa$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-varkappa
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\varkappa$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-lambda
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\lambda$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-mu
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\mu$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-nu
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\nu$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-xi
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\xi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-o
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $o$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-pi
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\pi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-varpi
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\varpi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-rho
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\rho$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-varrho
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\varrho$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sigma
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\sigma$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-varsigma
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\varsigma$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-tau
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\tau$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-upsilon
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\upsilon$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-phi
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\phi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-varphi
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\varphi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-chi
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\chi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-psi
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\psi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-omega
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\omega$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-How to create special upright Greek letters is explained in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Upright-small-Greek"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Subsection
-Big Letters
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Greek letters ! big
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Gamma
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Gamma$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Delta
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Delta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Theta
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Theta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Lambda
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Lambda$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Xi
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Xi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Pi
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Pi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Sigma
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Sigma$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Upsilon
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Upsilon$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Phi
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Phi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Psi
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Psi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Omega
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Omega$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-That the big Greek letters appear upright is caused by a design bug when
- TeX was developed.
- To get correct italic big letters, begin every command with
-\series bold
-var
-\series default
-.
- For example the command
-\series bold
-
-\backslash
-varGamma
-\series default
- produces
-\begin_inset Formula $\varGamma$
-\end_inset
-
-.
- Another way is to load the package
-\series bold
-fixmath
-\series default
-
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-
-\series bold
-fixmath
-\series default
- is part of the LaTeX-package
-\series bold
-was
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! 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
-Packages ! fixmath
-\end_layout
-
-\end_inset
-
- with the LaTeX-preamble line
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-usepackage{fixmath}
-\end_layout
-
-\begin_layout Standard
-Then all big Greek letters in a document will automatically be typeset italic.
-\end_layout
-
-\begin_layout Subsection
-Bold Letters
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Greek letters ! bold
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Greek letters cannot be set with different font styles like Latin letters.
- They can only be made bold with the command
-\series bold
-
-\backslash
-boldsymbol
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! B !
-\backslash
-boldsymbol
-\end_layout
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Upsilon
-\backslash
-boldsymbol
-\backslash
-Upsilon
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-theta
-\backslash
-boldsymbol
-\backslash
-theta
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\theta\boldsymbol{\theta}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-Symbols
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-texorpdfstring{
-\end_layout
-
-\end_inset
-
-
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-A list with all symbols of most of the LaTeX-packages can be found in
-\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 is used to avoid that the footnote appears in the PDF-bookmark.
-\end_layout
-
-\begin_layout Plain Layout
-More about
-\backslash
-texorpdfstring is in section
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Formulas-in-Section"
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Symbols
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Many of the symbols listed in this section can also be inserted via the
- toolbar buttons
-\begin_inset Graphics
- filename ../images/math/nabla.png
- scale 85
-
-\end_inset
-
- and
-\begin_inset Graphics
- filename ../images/math/digamma.png
- scale 85
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Subsection
-Mathematical Symbols
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Mathematical-Symbols"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Symbols ! mathematical
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-neg
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\neg$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Im
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Im$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Re
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Re$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-aleph
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\aleph$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-partial
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\partial$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-infty
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\infty$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-wp
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\wp$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-imath
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\imath$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-jmath
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\jmath$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-forall
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\forall$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-exists
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\exists$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-nexists
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\nexists$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-emptyset
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\emptyset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-varnothing
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\varnothing$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-dag
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\dag$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-ddag
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\ddag$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-complement
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
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-\end_inset
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-\end_layout
-
-\end_inset
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-
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-
-\end_inset
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-
-\begin_inset Tabular
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-
-
-
-
-
-\begin_inset Text
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-\begin_layout Plain Layout
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-
-\end_inset
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-
-\begin_inset Text
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-\begin_layout Plain Layout
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-\end_inset
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-
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-
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-
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-
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-\begin_inset Text
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-
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-
-\end_inset
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-\begin_inset Text
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-\begin_inset Formula $\spadesuit$
-\end_inset
-
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-
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-
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-\begin_inset Text
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-
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-\end_inset
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-\begin_inset Formula $\bigstar$
-\end_inset
-
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-\end_layout
-
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-
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-\begin_inset Text
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-
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-
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-
-\begin_inset Text
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-\begin_layout Plain Layout
-\begin_inset Formula $\blacklozenge$
-\end_inset
-
-
-\end_layout
-
-\end_inset
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-
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-\begin_inset Text
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-
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-
-\end_inset
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-
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-\begin_inset Formula $\blacktriangle$
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-
-
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-
-\end_inset
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-
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-\begin_inset Text
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-
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-
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- |
-
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-
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-\begin_inset Formula $\blacktriangledown$
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-
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-\end_layout
-
-\end_inset
- |
-
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-\begin_inset Text
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-\begin_layout Plain Layout
-
-\backslash
-bullet
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-
-\end_inset
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-
-\begin_inset Text
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-\begin_layout Plain Layout
-\begin_inset Formula $\bullet$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
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-\begin_inset Text
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-\begin_layout Plain Layout
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-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
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-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
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-
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-\begin_inset Text
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-
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-
-\begin_inset Text
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-
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-
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-
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-
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-
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-\begin_inset Formula $\Diamond$
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-
-
-\end_layout
-
-\end_inset
- |
-
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-\begin_inset Text
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-
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-
-\end_inset
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-
-\begin_inset Text
-
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-\begin_inset Formula $\heartsuit$
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-
-
-\end_layout
-
-\end_inset
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-
-
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-\begin_inset Text
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-
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-P
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-
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-
-\begin_inset Text
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-
-
-\end_layout
-
-\end_inset
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-
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-
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-\begin_inset Text
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-\begin_inset Formula $\copyright$
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-
-
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-
-\end_inset
- |
-
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-
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-
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-
-
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-
-\end_inset
- |
-
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-
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-
-
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-
-\end_inset
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-
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-
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-
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-
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-
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-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
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-
-More symbols are listed in
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-LatexCommand ref
-reference "sub:Miscellaneous-special-Characters"
-
-\end_inset
-
-.
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-
-\begin_layout Standard
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-LatexCommand ref
-reference "sub:Font-Sizes"
-
-\end_inset
-
-.
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-
-\begin_layout Subsection
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-
-\begin_layout Plain Layout
-Symbols ! Euro-symbol
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-
-\end_inset
-
-
-\begin_inset Index idx
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-
-\begin_layout Plain Layout
-
-\backslash
-@
-\begin_inset ERT
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-
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-
-
-\backslash
-officialeuro
-\end_layout
-
-\end_inset
-
-
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-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To use the Euro symbol in formulas, the LaTeX-package
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-eurosym
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! eurosym
-\end_layout
-
-\end_inset
-
- must be installed and loaded with the LaTeX-preamble line
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-usepackage[gennarrow]{eurosym}
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-
-\begin_layout Standard
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-
-\backslash
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-\series default
-
-\begin_inset Index idx
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-
-\begin_layout Plain Layout
-Commands ! E !
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-
-\end_inset
-
-.
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-
-\begin_layout Standard
-The Euro symbol can directly be inserted with the ⬠key in mathematical
- text, without having
-\series bold
-eurosym
-\series default
- installed.
- When
-\series bold
-eurosym
-\series default
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-\series bold
-
-\backslash
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-\series default
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- The official currency symbol can then be inserted with the command
-\series bold
-
-\backslash
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-\series default
-
-\begin_inset Index idx
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-
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-Commands ! O !
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-
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-
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-
-\begin_layout Standard
-\begin_inset ERT
-status collapsed
-
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-
-
-\backslash
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-\end_layout
-
-\end_inset
-
-
-\begin_inset Note Note
-status open
-
-\begin_layout Plain Layout
-The following table will only be displayed when the LaTeX-package
-\series bold
-eurosym
-\series default
- is installed.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-An overview about the different Euro symbols:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
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-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
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-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-formula
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
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-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\euro$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-mathematical text
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-â¬
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\mbox{â¬}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-TeX-mode
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-officialeuro
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\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
-The following will be displayed when the LaTeX-package
-\series bold
-eurosym
-\series default
- is not installed:
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-You need to install the LaTeX-package
-\series bold
-eurosym
-\series default
- to see the rest of this subsection in the output.
-\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
-Relations
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Relations"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Relations
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Comparisons|see
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-{
-\end_layout
-
-\end_inset
-
-Relations
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-All relations can also be inserted via the toolbar button
-\begin_inset Graphics
- filename ../images/math/leq.png
- scale 85
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-<
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $<$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-le
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\le$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-ll
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\ll$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-prec
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\prec$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-preceq
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\preceq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-subset
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\subset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-subseteq
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\subseteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sqsubseteq
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\sqsubseteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-in
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\in$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-vdash
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\vdash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-smile
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\smile$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-lhd
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\lhd$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-unlhd
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\unlhd$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-gtrless
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\gtrless$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-mid
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\mid$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-nmid
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\nmid$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-=
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $=$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-not=
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\not=$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-equiv
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\equiv$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sim
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\sim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-simeq
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\simeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-approx
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\approx$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-cong
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\cong$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-bowtie
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\bowtie$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-notin
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\notin$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-perp
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\perp$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-propto
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\propto$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-asymp
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\asymp$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-doteq
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\doteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-circeq
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\circeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-models
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\models$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-widehat=
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\widehat{=}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
->
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $>$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-ge
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\ge$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-gg
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\gg$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-succ
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\succ$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-succeq
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\succeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-supset
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\supset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-supseteq
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\supseteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sqsupseteq
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\sqsupseteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-ni
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\ni$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-dashv
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\dashv$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-frown
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\frown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-rhd
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\rhd$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-unrhd
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\unrhd$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-lessgtr
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\lessgtr$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-parallel
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\parallel$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-nparallel
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\nparallel$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-The characters
-\series bold
-
-\backslash
-lhd
-\series default
- and
-\series bold
-
-\backslash
-rhd
-\series default
- are bigger than the equal looking operators
-\series bold
-
-\backslash
-triangleleft
-\series default
- and
-\series bold
-
-\backslash
-triangleright
-\series default
-, respectively.
-\end_layout
-
-\begin_layout Standard
-Relations are, in contrary to symbols, always surrounded by space.
-\end_layout
-
-\begin_layout Standard
-Relations with labels can be created with the command
-\series bold
-
-\backslash
-stackrel
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-stackrel
-\end_layout
-
-\end_inset
-
-:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-Functions
-\end_layout
-
-\begin_layout Subsection
-Predefined Functions
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Predefined-Functions"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Functions ! predefined
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-In general, variables are set
-\emph on
-italic
-\emph default
- in mathematical expressions, but not function names, because
-\begin_inset Formula $sin$
-\end_inset
-
- could be misunderstood as
-\begin_inset Formula $s\cdot i\cdot n$
-\end_inset
-
-.
- Therefore there are predefined functionswhich are additionally a bit separated
- from prefactors.
- They are inserted as commands starting with a backslash before their name.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Asin(x)+B
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $Asin(x)+B$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-A
-\backslash
-sin(x)+B
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A\sin(x)+B$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The following functions are predefined:
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace -2mm
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sin
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sinh
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-arcsin
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sup
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-cos
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-cosh
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-arccos
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-inf
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-tan
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-tanh
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-arctan
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-lim
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-cot
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-coth
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-arg
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-liminf
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-sec
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-min
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-deg
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-limsup
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-csc
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-max
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-det
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Pr
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-ln
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-exp
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-dim
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-hom
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-lg
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-log
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-ker
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-gcd
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-They can also be inserted with the math toolbar button
-\begin_inset Graphics
- filename ../images/math/functions.png
- scale 85
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Subsection
-Self-defined Functions
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Functions ! self-defined
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To use a function that is not predefined, like for example the sign function
- sgn(x), there are two possibilities:
-\end_layout
-
-\begin_layout Itemize
-Define the function by inserting the following line to the LaTeX-preamble
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-For more about
-\series bold
-
-\backslash
-DeclareMathOperator
-\series default
- see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Self-defined-Operators"
-
-\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
-Commands ! 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
-
-Now the new defined function can be called with the command
-\series bold
-
-\backslash
-sgn
-\series default
-.
-\end_layout
-
-\begin_layout Itemize
-Write the formula as usual, mark the formula name, in our example the letters
-
-\emph on
-sgn
-\emph default
-, and change it to mathematical text.
- Finally, a space is inserted between prefactor and function.
-\end_layout
-
-\begin_layout Standard
-The result is the same with both methods as with a predefined function
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-In LyX self-defined functions are displayed red, predefined ones black.
-\end_layout
-
-\end_inset
-
-:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-A
-\backslash
-sgn(x)+B
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A\sgn(x)+B$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-A
-\backslash
-,
-\begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
-\end_inset
-
-(x)+B
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A\,\textrm{sgn}(x)+B$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The first method is more suitable when the self-defined function should
- be used several times.
-\end_layout
-
-\begin_layout Subsection
-Limits
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Limits
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-For limits, in addition to the commands
-\series bold
-
-\backslash
-lim
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! L !
-\backslash
-lim
-\end_layout
-
-\end_inset
-
-,
-\series bold
-
-\backslash
-liminf
-\series default
- and
-\series bold
-
-\backslash
-limsup
-\series default
- the following functions are defined:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-varliminf
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\varliminf$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-varlimsup
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\varlimsup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-varprojlim
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\varprojlim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-varinjlim
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-The limit is created by inserting a subscript.
- It is set right beside the function in an inline formula:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset space \hspace{}
-\length 1cm
-\end_inset
-
-Result
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-The space and
-\series bold
-
-\backslash
-raisebox
-\series default
- are used here as spacer.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-In a displayed formula the limit is set below the formula, as usual:
-\begin_inset Formula
-\[
-\lim_{x\to A}x=B
-\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Modulo-Functions
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Functions ! modulo-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The modulo-function is special, because it exists in four variants.
- The variants in a displayed formula are:
-\begin_inset Formula
-\begin{align*}
-\underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
-\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
-
-
-\end_layout
-
-\begin_layout Standard
-In an inline formula less space is set before the function names for all
- variants.
- By default the modulo-functions take only the first following character
- into account.
- To use more than one character, one has to put them into TeX-braces:
-\begin_inset Formula
-\begin{align*}
-\underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
-\mathrm{a\backslash pod\textrm{\spce}bcd} & & a\pod bcd\\
-\mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
-\end{align*}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-Special Characters
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Special characters
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Special Characters in Mathematical Text
-\end_layout
-
-\begin_layout Standard
-The following commands can only be used in mathematical text or in TeX-mode:
-\end_layout
-
-\begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-oe
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\textrm{Å}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-OE
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\textrm{Å}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-ae
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\textrm{æ}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-AE
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\textrm{Ã}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-aa
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\textrm{\aa}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\textrm{â«}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-i
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\textrm{ı}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-command
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-The space of 0
-\begin_inset space \thinspace{}
-\end_inset
-
-mm is used for separation, because otherwise the output will be ¡ and ¿
- respectively.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-o
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\textrm{ø}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-O
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\textrm{Ã}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-l
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\textrm{Å}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-L
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\textrm{Å}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\textrm{!`}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\textrm{?`}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-j
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\textrm{È·}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The characters
-\begin_inset Formula $\textrm{\textrm{Ã
}}$
-\end_inset
-
- and
-\begin_inset Formula $\textrm{\textrm{Ã}}$
-\end_inset
-
- can also be inserted via the math toolbar button
-\begin_inset Graphics
- filename ../images/math/digamma.png
- scale 85
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-An exception are the commands
-\series bold
-!
-\begin_inset space \hspace{}
-\length 0mm
-\end_inset
-
-`
-\series default
- and
-\series bold
-?
-\begin_inset space \hspace{}
-\length 0mm
-\end_inset
-
-`
-\series default
-, because they can be inserted in LyX directly to text.
-\end_layout
-
-\begin_layout Subsection
-Accents in Text
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Accents-in-Text"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Accents ! in text
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-With the following commands all letters can be accented.
- The commands must be inserted in TeX-mode.
-\end_layout
-
-\begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-
-\begin_inset Quotes grd
-\end_inset
-
-e
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-`e
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-=e
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-'e
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-.e
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-With the command
-\series bold
-
-\backslash
-t
-\series default
- also two different characters can be accented.
- The command
-\series bold
-
-\backslash
-t
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-sz
-\series default
- creates:
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-t sz
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The accents
-\series bold
-`
-\series default
- ,
-\series bold
-'
-\series default
- and
-\series bold
-^
-\series default
- can in combination with vowels directly be inserted with the keyboard without
- using TeX-mode.
- The same applies for the tilde
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-This only applies for keyboards where the tilde is defined as accent.
-\end_layout
-
-\end_inset
-
-
-\series bold
-~
-\series default
- in combination with
-\emph on
-a
-\emph default
- ,
-\emph on
-n
-\emph default
- , or
-\emph on
-o
-\emph default
-.
-\end_layout
-
-\begin_layout Standard
-The commands
-\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
- and accents that are inserted directly with the keyboard are also available
- in mathematical text.
- For the other accents there are special math commands to be used in formulas,
- see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Accents-for-one"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-Furthermore, with the command
-\series bold
-
-\backslash
-textcircled
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! T !
-\backslash
-textcircled
-\end_layout
-
-\end_inset
-
- all numbers and letters can be set into a circle, quasi accented with a
- circle, similar to the copyright symbol.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-textcircled{w}
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Large
-\backslash
-textcircled{
-\backslash
-normalsize
-\backslash
-protect
-\backslash
-raisebox{-1.5pt}{W}}
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-One has to take care that the character fits in the circle.
-
-\series bold
-
-\backslash
-Large
-\series default
-
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Font-Sizes"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
- specifies thereby the size of the circle.
- With the help of
-\series bold
-
-\backslash
-raisebox
-\series default
-
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Boxes-without-Frame"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
- the character can be centered.
-\end_layout
-
-\begin_layout Subsection
-Old-style Figures
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Old-style Figures
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Old-style figures (also known as old-style numerals) are created with the
- command
-\series bold
-
-\backslash
-oldstylenums
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! O !
-\backslash
-oldstylenums
-\end_layout
-
-\end_inset
-
-.
- The command can be used in formulas and in TeX-mode.
- The command scheme is:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-oldstylenums{number}
-\end_layout
-
-\begin_layout Standard
-The command
-\series bold
-
-\backslash
-oldstylenums{0123456789
-\series default
- produces:
-\begin_inset Formula $\oldstylenums{0123456789}$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Miscellaneous special Characters
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Miscellaneous-special-Characters"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Special characters ! miscellaneous
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The following characters can only be inserted to formulas by using commands:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\mathcircumflex$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-_
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\_$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $^{\circ}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
- contains the following line
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-More about this is described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Text-Characters-in"
-
-\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
-Formula Styles
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Formula-Styles"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! styles
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Itemize
-There are two different alignment styles:
-\end_layout
-
-\begin_deeper
-\begin_layout Description
-Centered is the predefined standard
-\end_layout
-
-\begin_layout Description
-Indented for this the option
-\series bold
-fleqn
-\series default
- must be inserted in the menu
-\family sans
-Document\SpecialChar \menuseparator
-Settings
-\family default
- under
-\family sans
-Document
-\begin_inset space ~
-\end_inset
-
-Class
-\end_layout
-
-\begin_layout Standard
-When
-\series bold
-Indented
-\series default
- is used, the indentation can be adjusted with the length
-\series bold
-
-\backslash
-mathindent
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! M !
-\backslash
-mathindent
-\end_layout
-
-\end_inset
-
-.
- Should the distance be 15
-\begin_inset space \thinspace{}
-\end_inset
-
-mm, the following command line is inserted in the LaTeX-preamble
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-setlength{
-\backslash
-mathindent}{15mm}
-\end_layout
-
-\begin_layout Standard
-When no length is specified, the predefined value of 30
-\begin_inset space \thinspace{}
-\end_inset
-
-pt will be used.
-\end_layout
-
-\end_deeper
-\begin_layout Itemize
-And two different numbering styles:
-\end_layout
-
-\begin_deeper
-\begin_layout Description
-Right is the predefined standard
-\end_layout
-
-\begin_layout Description
-Left for this the option
-\series bold
-leqno
-\series default
- must be inserted in the menu
-\family sans
-Document\SpecialChar \menuseparator
-Settings
-\family default
- under
-\family sans
-Document
-\begin_inset space ~
-\end_inset
-
-Class
-\end_layout
-
-\end_deeper
-\begin_layout Standard
-
-\series bold
-fleqn
-\series default
- and
-\series bold
-leqno
-\series default
- can also be used together.
- In this case both options are inserted, separated by a comma.
-\end_layout
-
-\begin_layout Standard
-The chosen styles are used for all displayed formulas of the document.
- When both, centered and indented formulas should be created in a document,
- the style
-\series bold
-Centered
-\series default
- is used.
- The indented formulas are then set in a flalign environment, see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Flalign-Environment"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Section
-Multiline Formulas
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Multiline-Formulas"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-General
-\end_layout
-
-\begin_layout Standard
-In LyX multiline formulas are created by pressing
-\series bold
-
-\begin_inset Info
-type "shortcut"
-arg "newline-insert newline"
-\end_inset
-
-
-\series default
- inside a formula.
- This creates either an
-\series bold
-eqnarray environment
-\series default
- that is described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Eqnarray-Environment"
-
-\end_inset
-
- or, when the option
-\family sans
-Use AMS math package
-\family default
- in the document settings is selected, an
-\series bold
-align environment
-\series default
- that is described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Standard-align-Environment"
-
-\end_inset
-
-.
- The align environment is recommended because it provides in any case a
- typographically correct output.
-\end_layout
-
-\begin_layout Standard
-There are other multiline formula environments that can be created via the
- menu
-\family sans
-Insert\SpecialChar \menuseparator
-Math
-\family default
-.
- These environments are described in the following sections.
-\end_layout
-
-\begin_layout Standard
-In all multiline formula environments a new line is created by pressing
-
-\begin_inset Info
-type "shortcut"
-arg "newline-insert newline"
-\end_inset
-
-.
- To add or delete lines, the math toolbar buttons
-\begin_inset Graphics
- filename ../images/tabular-feature_append-row.png
- scale 85
-
-\end_inset
-
- or
-\begin_inset Graphics
- filename ../images/tabular-feature_delete-row.png
- scale 85
-
-\end_inset
-
-, respectively, or the menu
-\family sans
-Edit\SpecialChar \menuseparator
-Rows & Columns
-\family default
- can be used.
-\end_layout
-
-\begin_layout Subsubsection
-Line Separation
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Line-Separation"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! Line separation
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-There is sometimes not enough space in multiline formulas between the lines:
-\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
-
-
-\end_layout
-
-\begin_layout Standard
-In LaTeX additional line space is specified as optional argument of the
- new line command.
- This is not yet possible in LyX
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-see
-\begin_inset CommandInset href
-LatexCommand href
-name "LyX-bug #1505"
-target "http://www.lyx.org/trac/ticket/1505"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-, therefore the whole formula must be inserted in TeX-mode.
- To add in our example space, the command
-\series bold
-
-\backslash
-
-\backslash
-[3mm]
-\series default
- is inserted at the end of the first line.
- One gets:
-\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
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-To set the line separation for all lines in a formula, the length
-\series bold
-
-\backslash
-jot
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! J !
-\backslash
-jot
-\end_layout
-
-\end_inset
-
- is changed.
- The definition is:
-\begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
-\end_inset
-
-.
- Predefined for
-\series bold
-
-\backslash
-jot
-\series default
- is the value 3
-\begin_inset space \thinspace{}
-\end_inset
-
-pt.
- To create 3
-\begin_inset space \thinspace{}
-\end_inset
-
-mm additional line separation as in the previous example, the command
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-setlength{
-\backslash
-jot}{3mm+3pt}
-\end_layout
-
-\begin_layout Standard
-is inserted in TeX-mode before the formula.
- This requires that the 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 LaTeX standard installation.
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! calc
-\end_layout
-
-\end_inset
-
- was loaded in LaTeX-preamble with the line
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-usepackage{calc}
-\end_layout
-
-\begin_layout Standard
-One gets:
-\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
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-setlength{
-\backslash
-jot}{3pt}
-\end_layout
-
-\end_inset
-
- To get back to the predefined distance,
-\series bold
-
-\backslash
-jot
-\series default
- is set to the value 3
-\begin_inset space \thinspace{}
-\end_inset
-
-pt.
-\end_layout
-
-\begin_layout Subsubsection
-Column Separation
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Column-Separation"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! Column separation
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Multiline formulas form a matrix.
- A formula in the eqnarray environment is for example a matrix with three
- columns.
- By changing the column separation in this environment, the space beside
- the relation sign can be changed.
-\end_layout
-
-\begin_layout Standard
-The column separation is specified with the length
-\series bold
-
-\backslash
-arraycolsep
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! A !
-\backslash
-arraycolsep
-\end_layout
-
-\end_inset
-
- according to:
-\begin_inset Newline newline
-\end_inset
-
-column separation = 2
-\begin_inset space \thinspace{}
-\end_inset
-
-
-\series bold
-
-\backslash
-arraycolsep
-\series default
-
-\begin_inset Newline newline
-\end_inset
-
-Thus, the command
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-setlength{
-\backslash
-arraycolsep}{1cm}
-\end_layout
-
-\begin_layout Standard
-inserted in TeX-mode, sets for all following formulas a column separation
- of 2
-\begin_inset space \thinspace{}
-\end_inset
-
-cm.
- To get back to the predefined distance,
-\series bold
-
-\backslash
-arraycolsep
-\series default
- is set to 5
-\begin_inset space \thinspace{}
-\end_inset
-
-pt.
-\end_layout
-
-\begin_layout Standard
-A formula with 2
-\begin_inset space \thinspace{}
-\end_inset
-
-cm column separation:
-\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
-
-A formula with the predefined column separation for matrices of 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
-Long Formulas
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! long
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Long formulas can be typeset using these methods:
-\end_layout
-
-\begin_layout Itemize
-When one side of the equation is much shorter than the line width, this
- one is chosen for the left side and the right side is typeset over two
- lines:
-\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:shortlong}
-\end{eqnarray}
-
-\end_inset
-
-The minus sign at the beginning of the second line does normally not appear
- as an operator because it is the first character of the line.
- Thus it would not be surrounded by space and could not be distinguished
- from the fraction bar.
- To avoid this, 3
-\begin_inset space \thinspace{}
-\end_inset
-
-pt space was inserted behind the minus sign with the command
-\series bold
-
-\backslash
-hspace
-\series default
-.
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-for more about
-\series bold
-
-\backslash
-hspace
-\series default
- see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Variable-Space"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! H !
-\backslash
-hspace
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Itemize
-When both sides of the equation are too long, the command
-\series bold
-
-\backslash
-lefteqn
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! L !
-\backslash
-lefteqn
-\end_layout
-
-\end_inset
-
- is used.
- It is inserted in the first column of the first line and causes all further
- insertions to overwrite the following columns:
-\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
-
-After the insertion of
-\series bold
-
-\backslash
-lefteqn
-\series default
-, the cursor is in a purple box that is a bit shifted to the left from the
- blue one.
- In this the formula is inserted.
-\begin_inset Newline newline
-\end_inset
-
-The content of the further lines is inserted to the second or another formula
- column.
- The greater the column number where it was inserted, the larger the indentation.
-\begin_inset VSpace medskip
-\end_inset
-
-
-\begin_inset Newline newline
-\end_inset
-
-
-\begin_inset Note Greyedout
-status open
-
-\begin_layout Plain Layout
-Note the following when using
-\series bold
-
-\backslash
-lefteqn
-\series default
-:
-\end_layout
-
-\begin_layout Itemize
-The formula doesn't use the full page width.
- When e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-the term
-\begin_inset Formula $-B^{2}$
-\end_inset
-
- is added to the first line in the above example, it would have been outside
- the page margin.
- To better use the width, negative space can be inserted at the beginning
- of the first line.
-\end_layout
-
-\begin_layout Itemize
-Due to a bug in LyX the cursor cannot be set with the mouse into the first
- line.
-\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
-
- One can only set the cursor at the beginning of the line and move it with
- the arrow keys.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Itemize
-Other methods to set long formulas are offered by the environments described
- in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Multline-Environment"
-
-\end_inset
-
- and
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Multiline-Formula-Parts"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Subsubsection
-Multiline Brackets
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Multiline-Brackets"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Brackets ! for multiline expressions
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-For brackets spanning multiple lines the following problem occurs:
-\begin_inset Formula
-\begin{eqnarray*}
-A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
- & & \left.\cdots+B-D\right]
-\end{eqnarray*}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The closing bracket is smaller than the opening bracket because brackets
- with variable size may not span multiple lines.
-\end_layout
-
-\begin_layout Standard
-To set the bracket size for the second line correctly, the first line is
- ended with
-\series bold
-
-\backslash
-right.
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-right
-\end_layout
-
-\end_inset
-
- and the second line with
-\series bold
-
-\backslash
-left.
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-for more about
-\series bold
-
-\backslash
-left
-\series default
- and
-\series bold
-
-\backslash
-right
-\series default
- see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Automatic-Bracket-Size"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! L !
-\backslash
-left
-\end_layout
-
-\end_inset
-
-.
- After
-\series bold
-
-\backslash
-left.
-
-\series default
- the command
-\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
-Commands ! V !
-\backslash
-vphantom
-\end_layout
-
-\end_inset
-
- is inserted, because the multiplication operator with its limits is the
- largest symbol in the first line and this should be the size for the bracket
- in the second line.
-\end_layout
-
-\begin_layout Standard
-The result is this:
-\begin_inset Formula
-\begin{eqnarray*}
-A & = & \sin(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
-Align Environments
-\end_layout
-
-\begin_layout Standard
-Align environments can be used for every kind of multiline formulas.
- They are especially useful to set several formulas side by side.
-\end_layout
-
-\begin_layout Standard
-Align environments consist of columns.
- The odd columns are right aligned, the even ones left aligned.
- Every line in an Align environment can be numbered.
-\end_layout
-
-\begin_layout Standard
-Align environments are created via the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Math
-\family default
-.
- With the menu
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Change Formula Type
-\family default
- already existing formulas can be converted to Align environments.
-\end_layout
-
-\begin_layout Standard
-To add or delete columns, the math toolbar buttons
-\begin_inset Graphics
- filename ../images/tabular-feature_append-column.png
- scale 85
-
-\end_inset
-
- or
-\begin_inset Graphics
- filename ../images/tabular-feature_delete-column.png
- scale 85
-
-\end_inset
-
-, respectively, or the menu
-\family sans
-Edit\SpecialChar \menuseparator
-Rows & Columns
-\family default
- can be used.
-\end_layout
-
-\begin_layout Subsubsection
-Standard align Environment
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Standard-align-Environment"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! align environment
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-This Align environment is created by pressing
-\begin_inset Info
-type "shortcut"
-arg "newline-insert newline"
-\end_inset
-
- in a formula or by the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-AMS align Environment
-\family default
-.
-\end_layout
-
-\begin_layout Standard
-An example for two formulas set side by side, that are created with a four
- column align environment:
-\begin_inset Formula
-\begin{align*}
-A & =\sin(B) & C & =D\\
-C & \ne A & B & \ne D
-\end{align*}
-
-\end_inset
-
-As it can be seen, the formulas in this environment are placed so as if
- there would be a
-\series bold
-
-\backslash
-hfill
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-more about
-\series bold
-
-\backslash
-hfill
-\series default
- see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Variable-Space"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\series default
- before the first and after every even column.
- When the formula style
-\series bold
-Indented
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-formula styles see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Formula-Styles"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\series default
- is used, the formula is set without the
-\series bold
-
-\backslash
-hfill
-\series default
- before the first column.
-\end_layout
-
-\begin_layout Subsubsection
-Alignat Environment
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! alignat environment
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The alignat environment has no predefined column separation.
- It can be inserted manually with the spaces that are described
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Space"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-The above example in the alignat environment where 1
-\begin_inset space \thinspace{}
-\end_inset
-
-cm space was inserted at the beginning of the second formula:
-\begin_inset Formula
-\begin{alignat*}{2}
-A & =\sin(B) & \hspace{1cm}C & =D\\
-C & \ne A & B & \ne D
-\end{alignat*}
-
-\end_inset
-
-Because the column separation can be set separately for every column, this
- environment is especially suitable to set three and more formulas side
- by side.
-\end_layout
-
-\begin_layout Subsubsection
-Flalign Environment
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Flalign-Environment"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! flalign environment
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-In this environment the first two columns are always set as much as possible
- to the left and the last two ones to the right.
- An example:
-\begin_inset Formula
-\begin{flalign*}
-A & =1 & B & =2 & C & =3\\
-X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
-\end{flalign*}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-By creating a flalign environment with an odd number of columns where an
- empty TeX-brace is inserted to the last column, several formulas in a document
- can be set to the left, although the formula style
-\series bold
-Centered
-\series default
- is used.
- As example the indented formula
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:VolInt"
-
-\end_inset
-
-:
-\begin_inset Formula
-\begin{flalign}
-\hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
-\end{flalign}
-
-\end_inset
-
-The first two columns contain the formula.
- To indent it as with the formula style
-\series bold
-Indented
-\series default
-, 30
-\begin_inset space \thinspace{}
-\end_inset
-
-pt space was inserted at the beginning of the first column.
-\end_layout
-
-\begin_layout Subsection
-Eqnarray Environment
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Eqnarray-Environment"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! eqnarray environment
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-When this environment has been created, three blue boxes appear.
- The content of the first box is right aligned, the content of the last
- one left aligned.
- The content of the middle box appears centered and a bit smaller, because
- it is designed to insert there only relation characters.
-\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
-Gather Environment
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! gather environment
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-This environment consists of only one centered column.
- Every line can be numbered.
-\begin_inset Formula
-\begin{gather}
-A=1\\
-X=\textrm{-}1
-\end{gather}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Multline Environment
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Multline-Environment"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! multline environment
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The multline environment consists, like the gather environment, of only
- one column.
- But the first line is left aligned, the last one right aligned.
- All other lines are centered.
- Therefore this environment is suitable for long formulas.
- As example formula
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:lefteqn"
-
-\end_inset
-
- in the multline environment:
-\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
-
-
-\end_layout
-
-\begin_layout Standard
-In the output only the last (first) line of a multline environment appears
- numbered when the document numbering is right (left).
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-numbering styles see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Formula-Styles"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-With the commands
-\series bold
-
-\backslash
-shoveright
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-shoveright
-\end_layout
-
-\end_inset
-
- and
-\series bold
-
-\backslash
-shoveleft
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-shoveleft
-\end_layout
-
-\end_inset
-
- a centered line can be right or left aligned, respectively.
- The commands are used as follows:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-shoveright{line content}
-\series default
- and
-\series bold
-
-\backslash
-shoveleft{line content}
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-The length
-\series bold
-
-\backslash
-multlinegap
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! M !
-\backslash
-multlinegap
-\end_layout
-
-\end_inset
-
- specifies the distance of the first line from the left page margin.
- Predefined is the length 0
-\begin_inset space \thinspace{}
-\end_inset
-
-pt.
-\end_layout
-
-\begin_layout Standard
-As example the above formula where the command
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-setlength{
-\backslash
-multlinegap}{2cm}
-\end_layout
-
-\begin_layout Standard
-was inserted in TeX-mode before:
-\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
-
-The second line was left aligned using
-\series bold
-
-\backslash
-shoveleft
-\series default
-.
-\end_layout
-
-\begin_layout Subsection
-Multiline Formula Parts
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Multiline-Formula-Parts"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! formula parts
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To display only parts of a formula with multiple lines, one of the following
- environments is used:
-\series bold
-aligned
-\series default
-,
-\series bold
-alignedat
-\series default
-,
-\series bold
-gathered
-\series default
- or
-\series bold
-split
-\series default
-.
- They can be inserted via the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Math
-\family default
- or by using the commands described in this section.
-\end_layout
-
-\begin_layout Standard
-The first three have the same properties as the corresponding multiline
- formula environments, but it is possible to set further formula parts beside
- them.
- An example:
-\begin_inset Formula
-\[
-\left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
-\Delta E\Delta t & \ge\frac{\hbar}{2}
-\end{aligned}
-\right\} \textrm{Uncertainty relations}
-\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To get this formula, a displayed formula is created where the command
-\series bold
-
-\backslash
-aligned
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! A !
-\backslash
-aligned
-\end_layout
-
-\end_inset
-
- is inserted.
- A purple box appears around the blue formula box where now columns and
- lines can be added.
- Outside the multiline environment other formula parts can be set, like
- the brace.
-\end_layout
-
-\begin_layout Standard
-The aligned environment is also suitable for long formulas whose lines are
- horizontally aligned.
- Using aligned in a displayed formula has the advantage that the formula
- number is vertically centered behind the lines.
- As example formula
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:shortlong"
-
-\end_inset
-
- in the aligned environment:
-\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
-
-
-\end_layout
-
-\begin_layout Standard
-To use the environments
-\series bold
-alignedat
-\series default
-,
-\series bold
-gathered
-\series default
-, or
-\series bold
-split
-\series default
-, the command
-\series bold
-
-\backslash
-alignedat
-\series default
-,
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! A !
-\backslash
-alignedat
-\end_layout
-
-\end_inset
-
-
-\series bold
-
-\backslash
-gathered
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! G !
-\backslash
-gathered
-\end_layout
-
-\end_inset
-
-, or
-\series bold
-
-\backslash
-split
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-split
-\end_layout
-
-\end_inset
-
- are inserted, respectively.
- The split environment has the same properties as the aligned environment
- but it can only have two columns.
-\end_layout
-
-\begin_layout Subsection
-Text in multiline Formulas
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Text-in-multiline"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Text ! in formulas
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! multiline ! text
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-In the Align environments, and the multline and gather environment, text
- can be inserted that will appear in a separate line and doesn't affect
- the column alignment.
- To do this, the command
-\series bold
-
-\backslash
-intertext
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! I !
-\backslash
-intertext
-\end_layout
-
-\end_inset
-
- is used in the following scheme:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-intertext{text}
-\end_layout
-
-\begin_layout Standard
-The text should not be longer than a line because it cannot be hyphenated.
- As LyX doesn't yet support
-\series bold
-
-\backslash
-intertext
-\series default
- directly, the text is written as mathematical text.
-
-\series bold
-
-\backslash
-intertext
-\series default
- must hereby be at the beginning of a line and appears in the output above
- this line.
- An example where the text was inserted at the beginning of the second line:
-\begin_inset Formula
-\begin{align}
-I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
-\intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
-\end{align}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-Formula Numbering
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula numbering
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! numbering|see
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-{
-\end_layout
-
-\end_inset
-
-Formula numbering
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-General
-\end_layout
-
-\begin_layout Standard
-Numbered formulas can be created with the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Numbered
-\begin_inset space ~
-\end_inset
-
-Formula
-\family default
- (shortcut
-\family sans
-Ctrl+Alt
-\begin_inset space ~
-\end_inset
-
-N
-\family default
-).
- Existing formulas can be numbered with the menu
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Toggle
-\begin_inset space ~
-\end_inset
-
-Numbering
-\family default
- (shortcut
-\begin_inset Info
-type "shortcut"
-arg "math-number-toggle"
-\end_inset
-
-).
- The formula number is displayed in LyX behind the formula as a number sign
- in parentheses.
- The number sign is replaced in the output by the formula number.
-\end_layout
-
-\begin_layout Standard
-When numbering is turned on in multiline formulas, all lines will be numbered.
- But the numbering can be controlled with the menu
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Toggle
-\begin_inset space ~
-\end_inset
-
-Numbering
-\begin_inset space ~
-\end_inset
-
-of
-\begin_inset space ~
-\end_inset
-
-Line
-\family default
- (shortcut
-\begin_inset Info
-type "shortcut"
-arg "math-number-line-toggle"
-\end_inset
-
-) for every line.
-\end_layout
-
-\begin_layout Standard
-Except for inline formulas, all formulas can be numbered with two different
- styles, see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Formula-Styles"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Subsection
-Cross-References
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Cross-references ! to formulas
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-All labeled formulas can be cross-referenced.
- A label is added by the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Label
-\family default
- or the toolbar button
-\begin_inset Graphics
- filename ../images/label-insert.png
- scale 85
-
-\end_inset
-
-.
- The cursor must hereby be inside a displayed formula.
- Alternatively you can right-click on the formula and choose
-\family sans
-Equation Label
-\family default
-.
- A dialog pops up displaying the prefix
-\series bold
-eq:
-\series default
- in a text field.
- The label is inserted there behind the prefix.
- The predefined prefix means
-\begin_inset Quotes eld
-\end_inset
-
-equation
-\begin_inset Quotes erd
-\end_inset
-
- and makes it easier to find labels in large documents because it marks
- it as formula label to divide it from e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-section labels.
- To change a label, the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Label
-\family default
- is used again or you right-click on a formula and then on
-\family sans
-Equation Label
-\family default
-.
-\end_layout
-
-\begin_layout Standard
-The name of the label is displayed in LyX within two parentheses behind
- formula.
- A formula with a label is always numbered.
-\end_layout
-
-\begin_layout Standard
-Cross-references are inserted via the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Cross-Reference
-\family default
- or with the toolbar button
-\begin_inset Graphics
- filename ../images/dialog-show-new-inset_ref.png
- scale 85
-
-\end_inset
-
-.
- A formula cross-reference appears in the output as formula number.
- When in the cross-reference dialog window the format
-\series bold
-()
-\series default
- is chosen, the cross-reference appears in the output as formula number
- in parentheses.
-\begin_inset Newline newline
-\end_inset
-
-By right-clicking on a cross-reference in LyX, one jumps to the formula
- that is referenced.
-\end_layout
-
-\begin_layout Standard
-Here are as examples cross-references to formulas of the following subsections:
-\begin_inset Note Note
-status open
-
-\begin_layout Plain Layout
-Note the different cross-reference types.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The equations
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:tag"
-
-\end_inset
-
- and
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:c"
-
-\end_inset
-
- are equivalent.
- In (
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "eq:Lat"
-
-\end_inset
-
-) big Latin letters are used for the numbering in contrary to (
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "eq:Rom"
-
-\end_inset
-
-).
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-When the argument of
-\series bold
-
-\backslash
-tag
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-
-\series bold
-
-\backslash
-tag
-\series default
- is described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:User-defined-Numbering"
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
-
-\series default
- contains a box like in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Paragraph-Boxes"
-
-\end_inset
-
-, the formula cannot be referenced.
-\end_layout
-
-\begin_layout Subsection
-Subnumbering
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula numbering ! subnumbering
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-With the help of the commands
-\series bold
-
-\backslash
-begin{subequations}
-\series default
- and
-\series bold
-
-\backslash
-end{subequations}
-\series default
- formulas can be subnumbered.
- Both commands are inserted in TeX-mode.
-\end_layout
-
-\begin_layout Standard
-An example:
-\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
-To create the example, the following is done:
-\end_layout
-
-\begin_layout Enumerate
-first formula is inserted
-\end_layout
-
-\begin_layout Enumerate
-
-\series bold
-
-\backslash
-addtocounter{equation}{-1}
-\backslash
-begin{subequations}
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! A !
-\backslash
-addtocounter
-\end_layout
-
-\end_inset
-
-
-\begin_inset Newline newline
-\end_inset
-
-
-\series default
-is inserted after the first formula
-\end_layout
-
-\begin_layout Enumerate
-second formula is inserted
-\end_layout
-
-\begin_layout Enumerate
-third formula is inserted
-\end_layout
-
-\begin_layout Enumerate
-
-\series bold
-
-\backslash
-end{subequations}
-\series default
- is inserted after the third formula
-\end_layout
-
-\begin_layout Standard
-Every formula between the commands
-\series bold
-
-\backslash
-begin
-\series default
- and
-\series bold
-
-\backslash
-end
-\series default
- is subnumbered as a, b,
-\begin_inset Newline linebreak
-\end_inset
-
-c, \SpecialChar \ldots{}
- For multiline formulas every line will be subnumbered.
- All subnumbered formulas are treated as
-\emph on
-one
-\emph default
- numbered formula.
- But as every numbered formula increases the counter
-\series bold
-equation
-\series default
- by one, the command
-\series bold
-
-\backslash
-addtocounter
-\series default
- is needed to decrease it.
- Otherwise the formulas
-\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
-
- would be numbered as
-\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
-By inserting the commands in TeX-mode, a space is created between the first
- two formulas.
- To revert this -5
-\begin_inset space \thinspace{}
-\end_inset
-
-mm vertical space is inserted after the command
-\series bold
-
-\backslash
-begin{subequations}
-\series default
-.
- When the formula style
-\series bold
-Indented
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-formula styles see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Formula-Styles"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\series default
- is used, -7
-\begin_inset space \thinspace{}
-\end_inset
-
-mm space is inserted instead.
-\end_layout
-
-\begin_layout Standard
-Here is an example for a multiline formula where the numbering was turned
- off for the second line:
-\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
-User-defined Numbering
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:User-defined-Numbering"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula numbering ! user-defined
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula numbering ! self-defined delimiters
-\end_layout
-
-\end_inset
-
-With the standard numbering parentheses are set around the formula number.
- To replace the parentheses for example by vertical bars, the following
- line is added to the LaTeX-preamble:
-\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
-This macro is already declared in the LaTeX-preamble for testing.
- To activate it, remove the percent sign at the beginning.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To use other characters, the vertical bars besides the
-\series bold
-#1
-\series default
- are replaced by one ore more characters.
- To get only the formula number the vertical bars are omitted.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-When there should be an expression of your choice instead of the consecutive
- formula number in parentheses behind the formula, the command
-\series bold
-
-\backslash
-tag
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! T !
-\backslash
-tag
-\end_layout
-
-\end_inset
-
- is used:
-\begin_inset Formula
-\begin{equation}
-A+B=C\tag{something}\label{eq:tag}
-\end{equation}
-
-\end_inset
-
-In this example the command
-\series bold
-
-\backslash
-tag
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-something
-\series default
- was inserted in the formula.
-\end_layout
-
-\begin_layout Standard
-When the command
-\series bold
-
-\backslash
-tag*
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-something
-\series default
- is inserted instead, the star prevents the parentheses around the expression:
-\begin_inset Formula
-\[
-A+B=C\tag*{something}
-\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-To restart the formula numbering with new document parts or sections, the
- following command is used:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-@addtoreset{equation}{part}
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands !
-\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
-
-resp.
-\begin_inset Newline newline
-\end_inset
-
-
-\series bold
-
-\backslash
-@addtoreset{equation}{section}
-\end_layout
-
-\begin_layout Standard
-To be able to use these commands in TeX-mode, the
-\begin_inset Quotes eld
-\end_inset
-
-@
-\begin_inset Quotes erd
-\end_inset
-
- character has to be made
-\begin_inset Quotes eld
-\end_inset
-
-active
-\begin_inset Quotes erd
-\end_inset
-
- for LaTeX using the command
-\series bold
-
-\backslash
-makeatletter.
-
-\series default
- The command
-\series bold
-
-\backslash
-makeatother
-\series default
- reverts this.
- So the command sequence in TeX-mode is:
-\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
-In the LaTeX-preamble
-\series bold
-
-\backslash
-makeatletter
-\series default
- and
-\series bold
-
-\backslash
-makeatother
-\series default
- can be omitted as they are automatically internally inserted by LyX.
-\end_layout
-
-\begin_layout Standard
-To revert
-\series bold
-
-\backslash
-@addtoreset
-\series default
-, the file
-\series bold
-remreset.sty
-\series default
-
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-
-\series bold
-remreset
-\series default
- is part of the LaTeX-package
-\series bold
-carlisle
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! carlisle
-\end_layout
-
-\end_inset
-
- that is part of every LaTeX standard installation.
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! remreset
-\end_layout
-
-\end_inset
-
- has to be loaded in the LaTeX-preamble with the line
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-usepackage{remreset}
-\end_layout
-
-\begin_layout Standard
-Then the command
-\series bold
-
-\backslash
-@removefromreset
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands !
-\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
-
- can be used with the same scheme as
-\series bold
-
-\backslash
-@addtoreset
-\series default
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-Sometimes formulas should be numbered in the following form:
-\end_layout
-
-\begin_layout Standard
-
-\family typewriter
-(section number.formula number)
-\end_layout
-
-\begin_layout Standard
-The formula number should start with every section with
-\begin_inset Quotes eld
-\end_inset
-
-1
-\begin_inset Quotes erd
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-For this case there is the command
-\series bold
-
-\backslash
-numberwithin
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! N !
-\backslash
-numberwithin
-\end_layout
-
-\end_inset
-
-, which is used with the following scheme:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-numberwithin{counter}{sectioning}
-\end_layout
-
-\begin_layout Standard
-Counter denotes what kind of numbering is affected, sectioning denotes what
- number is before the dot.
-\end_layout
-
-\begin_layout Standard
-Thus in our case the following LaTeX-preamble or TeX code line is used:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-numberwithin{equation}{section}
-\end_layout
-
-\begin_layout Standard
-This is the result:
-\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
-To number e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-tables so that the number of the part is the sectioning,
-\begin_inset Newline newline
-\end_inset
-
-
-\series bold
-
-\backslash
-numberwithin{table}{part}
-\series default
- is used.
-\end_layout
-
-\begin_layout Standard
-To go back to the standard numbering or to prevent this kind of numbering
- when it is defined by the document class, the following command is inserted
- as TeX code or to the LaTeX-preamble:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-renewcommand{
-\backslash
-theequation}{
-\backslash
-arabic{equation}}
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! 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
-or
-\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
- uses internally the command
-\series bold
-
-\backslash
-@addtoreset
-\series default
-, described above, that also needs to be reverted.
-\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
-Numbering with Roman Numbers and Letters
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula numbering ! with letters
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula numbering ! with Roman numbers
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Formulas can also be numbered with Roman numbers and Latin letters.
- To number for example with small Roman numbers, the command
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-renewcommand{
-\backslash
-theequation}{
-\backslash
-roman{equation}}
-\end_layout
-
-\begin_layout Standard
-is inserted before the formula in TeX-mode.
-
-\series bold
-
-\backslash
-renewcommand
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-renewcommand
-\end_layout
-
-\end_inset
-
- redefines the predefined command
-\series bold
-
-\backslash
-theequation
-\series default
- to the command
-\series bold
-
-\backslash
-roman{equation}
-\series default
-.
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-The command
-\series bold
-
-\backslash
-renewcommand
-\series default
- has the same scheme like the command
-\series bold
-
-\backslash
-newcommand
-\series default
- that is described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:The-Command-newcommand"
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
-
-\series bold
-equation
-\series default
- is the formula counter.
- When the command
-\series bold
-
-\backslash
-the
-\series default
- is used as prefix for a counter, the value of the counter is output as
- Arabic number.
- When a formula is numbered, LaTeX sets internally the command
-\series bold
-
-\backslash
-theequation
-\series default
- behind the formula.
-
-\series bold
-
-\backslash
-roman{equation}
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-roman
-\end_layout
-
-\end_inset
-
-
-\series default
- outputs the counter as small Roman number.
-\end_layout
-
-\begin_layout Standard
-All formulas behind the command
-\series bold
-
-\backslash
-renew
-\series default
-c
-\series bold
-ommand
-\series default
- are now numbered Roman.
- To switch to numbering with big Roman numbers, the command is inserted
- again, but
-\series bold
-
-\backslash
-roman
-\series default
- is replaced by
-\series bold
-
-\backslash
-Roman
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! R !
-\backslash
-roman@
-\backslash
-Roman
-\end_layout
-
-\end_inset
-
-.
- To
-\begin_inset Quotes eld
-\end_inset
-
-number
-\begin_inset Quotes erd
-\end_inset
-
- with small Latin letters there is the command
-\series bold
-
-\backslash
-alph
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! A !
-\backslash
-alph
-\end_layout
-
-\end_inset
-
-, for big ones there is the command
-\series bold
-
-\backslash
-Alph
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! 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
-\color none
-Note:
-\series default
- Only maximal 26
-\begin_inset space ~
-\end_inset
-
-formulas can be numbered with Latin letters in one document.
-\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
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Formula
-\begin{equation}
-A=\textrm{small roman}
-\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{big Roman}\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{small Latin}
-\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{big Latin}\label{eq:Lat}
-\end{equation}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To switch back to the default numbering, insert the command:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-renewcommand{
-\backslash
-theequation}{
-\backslash
-arabic{equation}}
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! 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=\textrm{Arabic}
-\end{equation}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-As you see, formulas are numbered serially independent from the numbering
- style.
- When then numbering should start with
-\begin_inset Quotes eld
-\end_inset
-
-1
-\begin_inset Quotes erd
-\end_inset
-
- when the style is changed, new equation counters have to be defined.
- A description about this can be found in the file
-\begin_inset CommandInset href
-LatexCommand href
-name "Formula-numbering.lyx"
-target "run:Formula-numbering.lyx"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-Chemical Symbols and Equations
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Chemical-Symbols-and"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Chemical characters ! Symbols
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Chemical equations
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Symbols ! chemical
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-An example text from chemistry:
-\end_layout
-
-\begin_layout Quote
-The
-\begin_inset Formula $\mathrm{SO_{4}^{2-}}$
-\end_inset
-
--ion reacts with two
-\begin_inset Formula $\mathrm{Na^{+}}$
-\end_inset
-
--ions to sodium sulfate
-\begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
-\end_inset
-
-.
- The chemical equation for this is:
-\begin_inset Formula
-\begin{equation}
-\mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
-\end{equation}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-This chemical equation can directly be created as formula.
- To avoid that the symbols appear italic, everything is highlighted and
- changed by the shortcut
-\begin_inset Info
-type "shortcut"
-arg "font-roman"
-\end_inset
-
- to the upright font style.
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-font styles
-\series bold
-
-\series default
-see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Font-Styles"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-A more convenient way to typeset chemical formulas is to use the command
-
-\series bold
-
-\backslash
-ce
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! C !
-\backslash
-ce
-\end_layout
-
-\end_inset
-
- that is available when the LaTeX-package
-\series bold
-mhchem
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! mhchem
-\end_layout
-
-\end_inset
-
- is installed.
- After inserting
-\series bold
-
-\backslash
-ce
-\series default
- to a formula a new blue box appears where chemical formulas can be inserted
- in an intuitive way.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
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-
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-C
-\begin_inset ERT
-status collapsed
-
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-
-
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-
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-\end_inset
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-
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-\begin_inset Text
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-\begin_layout Plain Layout
-
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-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
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-status collapsed
-
-\begin_layout Plain Layout
-
-
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-\end_layout
-
-\end_inset
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-+
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
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-C
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
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-
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-
-->[
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-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
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-\end_layout
-
-\end_inset
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-2CO}
-\end_layout
-
-\end_inset
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-
-\begin_inset Text
-
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-\begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
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-
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-
-
-
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-
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-status open
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-\begin_layout Plain Layout
-
-\series bold
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-Note:
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-\backslash
-ce
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-\color inherit
-
-\begin_inset Foot
-status collapsed
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-\begin_inset CommandInset href
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-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\color none
- In this case TeX code has to be used like for
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-
-\backslash
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-\series default
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-\begin_inset ERT
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-
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-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Note Greyedout
-status open
-
-\begin_layout Plain Layout
-
-\series bold
-\color none
-Note:
-\series default
- It is not possible in LyX to use the character ^ to get an up-arrow as
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-\series bold
-mhchem
-\series default
- manual.
- One instead uses a negative thin space followed by the command
-\series bold
-
-\backslash
-uparrow
-\series default
-:
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-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Using
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-
-\backslash
-ce
-\series default
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-\begin_inset space ~
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-
-
-\begin_inset CommandInset ref
-LatexCommand eqref
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-
-\end_inset
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- is:
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-
-
-\series bold
-
-\backslash
-ce
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
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-\end_layout
-
-\end_inset
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-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
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-Na2SO4
-\end_layout
-
-\begin_layout Standard
-To create multiline chemical equations first a multiline formula is created
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-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Multiline-Formulas"
-
-\end_inset
-
-.
- Afterwards the command
-\series bold
-
-\backslash
-ce
-\series default
- is used in every small blue box of the formula.
-
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:TEOS-reaction-1"
-
-\end_inset
-
- and
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:TEOS-reaction-2"
-
-\end_inset
-
- are an example of a multi-stage chemical reaction where every equation
- has its own number.
-\begin_inset Formula
-\begin{eqnarray}
-\ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
-\ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
-\end{eqnarray}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Besides
-\series bold
-
-\backslash
-ce
-\series default
- the
-\series bold
-mhchem
-\series default
- package provides the command
-\series bold
-
-\backslash
-cf
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! C !
-\backslash
-cf
-\end_layout
-
-\end_inset
-
- that has to be used for special cases.
- For more information about
-\series bold
-
-\backslash
-cf
-\series default
- and more examples have a look at the documentation of
-\series bold
-mhchem
-\series default
-,
-\begin_inset CommandInset citation
-LatexCommand cite
-key "mhchem"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Section
-Diagrams
-\end_layout
-
-\begin_layout Standard
-LyX supports two types of commutative diagrams:
-\series bold
-amscd
-\series default
- and
-\series bold
-xymatrix
-\series default
- that are explained in the following.
-\end_layout
-
-\begin_layout Subsection
-Amscd Diagrams
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Diagrams ! amscd
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Diagrams of this type visualize relations by vertical and horizontal lines
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-\begin_inset Formula
-\[
-\begin{CD}A@>>>B@>>>C\\
-@AAA@.@VVV\\
-F@<<>>
-\series default
- a right arrow and
-\series bold
-@=
-\series default
- a long equal sign
-\end_layout
-
-\begin_layout Itemize
-
-\series bold
-@AAA
-\series default
- creates an up arrow,
-\series bold
-@VVV
-\series default
- a down arrow and
-\series bold
-@|
-\series default
- a vertical equal sign
-\end_layout
-
-\begin_layout Itemize
-
-\series bold
-@.
-
-\series default
- is a placeholder for non-existent relations
-\end_layout
-
-\begin_layout Standard
-All arrows can be labeled as follows:
-\end_layout
-
-\begin_layout Itemize
-If text inserted between the first and second < or >, resp., it is placed
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- When it is inserted between the second and third one, it appears under
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-\end_layout
-
-\begin_layout Itemize
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- If the text contains an A or V, these letters must be set into a TeX-brace.
-\end_layout
-
-\begin_layout Standard
-As example a diagram with all possible relations:
-\end_layout
-
-\begin_layout Standard
-\begin_inset Formula
-\[
-\begin{CD}A@>j>>B@>>k>C@=F\\
-@AmAA@.@VV{V}V@|\\
-D@<k>>F@=C
-\end{CD}
-\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The command for this is:
-\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+Return
-\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+Return
-\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@<k>>F@=C
-\end_layout
-
-\begin_layout Subsection
-Xymatrix Diagrams
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Diagrams ! xymatrix
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To be able to use xymatrices, the LaTeX-package
-\series bold
-xypic
-\series default
- must be installed.
- A xymatrix is created by inserting the command
-\series bold
-
-\backslash
-xymatrix
-\series default
- in a formula.
- Then you are able to add new matrix columns and rows like for normal matrices,
- see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Matrices"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
- and much more.
- All possibilities to create commutative diagrams and decorations are explained
- in detail in the
-\emph on
-XY-pic manual
-\emph default
- that you find in the menu
-\family sans
-Help\SpecialChar \menuseparator
-Specific
-\begin_inset space ~
-\end_inset
-
-Manuals
-\family default
-.
-\end_layout
-
-\begin_layout Subsection
-
-\noun on
-Feynman
-\noun default
- Diagrams
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Diagrams ! Feynman
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To be able to use
-\noun on
-Feynman
-\noun default
--diagrams, the LaTeX-package
-\series bold
-feyn
-\series default
- must be installed.
- A
-\noun on
-Feynman
-\noun default
--diagram is created by inserting the command
-\series bold
-
-\backslash
-Diagram
-\series default
- in a formula.
- Then you are able to add new matrix columns and rows like for normal matrices,
- see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Matrices"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-Examples how to create
-\noun on
-Feynman-
-\noun default
-diagrams in LyX is given in the
-\emph on
-Feynman-diagram manual
-\emph default
- that you find in the menu
-\family sans
-Help\SpecialChar \menuseparator
-Specific
-\begin_inset space ~
-\end_inset
-
-Manuals
-\family default
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-User-defined Commands
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-User-defined commands
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Note Greyedout
-status open
-
-\begin_layout Plain Layout
-
-\series bold
-Note:
-\series default
- The names of user-defined commands and macros may only consist of Latin
- letters.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-The Command
-\backslash
-newcommand
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:The-Command-newcommand"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-User-defined commands !
-\backslash
-newcommand
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! N !
-\backslash
-newcommand
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Many LaTeX-commands are too long to be used frequently.
- But it is possible to define with the command
-\series bold
-
-\backslash
-newcommand
-\series default
- new shorter commands.
-\end_layout
-
-\begin_layout Standard
-The command scheme of
-\series bold
-
-\backslash
-newcommand
-\series default
- is:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-newcommand{new command name}[number of arguments][optional
-\series default
-
-\series bold
-value]
-\begin_inset Newline newline
-\end_inset
-
-
-\begin_inset Phantom HPhantom
-status open
-
-\begin_layout Plain Layout
-
-\series bold
-
-\backslash
-newcommand
-\end_layout
-
-\end_inset
-
-{command definition}
-\end_layout
-
-\begin_layout Standard
-\begin_inset Note Greyedout
-status open
-
-\begin_layout Plain Layout
-
-\series bold
-Note:
-\series default
- Assure that the name of the new command is not already used in your document
- or by LaTeX-packages that you use.
- When you for example define the command
-\series bold
-
-\backslash
-le
-\series default
- for
-\series bold
-
-\backslash
-Leftarrow
-\series default
-, you get an error message because
-\series bold
-
-\backslash
-le
-\series default
- is already defined as command for
-\begin_inset Quotes eld
-\end_inset
-
-
-\begin_inset Formula $\le$
-\end_inset
-
-
-\begin_inset Quotes erd
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The number of arguments is an integer in the range 0
-\begin_inset space \thinspace{}
-\end_inset
-
--
-\begin_inset space \thinspace{}
-\end_inset
-
-9 and specifies how many arguments the new command should have.
- With the optional value a value for an optional argument can be predefined.
- When this is done, the
-\emph on
-first
-\emph default
-
-\emph on
-a
-\emph default
-rgument of the new command is automatically an optional one.
-\end_layout
-
-\begin_layout Standard
-Here are some examples:
-\end_layout
-
-\begin_layout Itemize
-To define the command
-\series bold
-
-\backslash
-gr
-\series default
- for
-\series bold
-
-\backslash
-Longrightarrow
-\series default
-, the LaTeX-preamble line is:
-\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
-To define the command
-\series bold
-
-\backslash
-us
-\series default
- for
-\series bold
-
-\backslash
-underline
-\series default
-, the argument (that should be underlined) must be taken into account.
- For this the preamble line is:
-\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
-
-The character
-\series bold
-#
-\series default
- acts as argument placeholder, the
-\series bold
-1
-\series default
- behind it denotes that it is the placeholder for the first argument.
-\end_layout
-
-\begin_layout Itemize
-For
-\series bold
-
-\backslash
-framebox
-\series default
- one can e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-define the command
-\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
-
-The two Dollar signs creates the extra formula needed for
-\series bold
-
-\backslash
-framebox
-\series default
-, see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Boxes-with-Frame"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Itemize
-To create a new command for
-\series bold
-
-\backslash
-fcolorbox
-\series default
- where the color for the box need not be specified, the argument for the
- color is defined optional:
-\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
-
-When the color is not specified when using
-\series bold
-
-\backslash
-cb
-\series default
-, the predefined color
-\series bold
-white
-\series default
- will be used.
-\end_layout
-
-\begin_layout Standard
-A test of the new defined commands:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\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
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $A\gr B$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-us{ABcd
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Math Macros
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-User-defined commands! Math macros
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Macros
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-User-defined commands are especially convenient for complex expressions.
- When you are for example dealing with a document that has quadratic equations,
- the same solution type occurs several times.
- The general form of a quadratic equation is
-\begin_inset Formula
-\[
-0=\lambda^{2}+p\lambda+q
-\]
-
-\end_inset
-
-The general form of the solution is
-\begin_inset Formula
-\[
-\lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
-\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To define a command for the solution formula where only the three parameters
-
-\begin_inset Formula $\lambda$
-\end_inset
-
-,
-\begin_inset Formula $p$
-\end_inset
-
- and
-\begin_inset Formula $q$
-\end_inset
-
- need to be specified and the index of
-\begin_inset Formula $\lambda$
-\end_inset
-
- can be given optionally, the LaTeX-preamble line is
-\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
-To create with this the solution formula, the command
-\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
- is inserted to a formula
-\series bold
-.
-\end_layout
-
-\begin_layout Standard
-The definition of the new command is unintuitive because one has to know
- the schemes of all used LaTeX commands, e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-that a fraction is inserted in LaTeX as
-\series bold
-
-\backslash
-frac{numerator}{denominator}
-\series default
-.
- Furthermore one can easily forget a brace in the definition and cannot
- see in LyX what the new command is doing.
- To avoid these problems LyX offers the possibility to use math macros instead
- of the command
-\series bold
-
-\backslash
-newcommand
-\series default
-.
-\end_layout
-
-\begin_layout Standard
-A math macro is created by using the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Macro
-\family default
- or the toolbar button
-\begin_inset Graphics
- filename ../images/math-macro_newmacroname_newcommand.png
- scale 85
-
-\end_inset
-
-.
- The math macro toolbar appears together with the following box where the
- macro is defined:
-\begin_inset Newline newline
-\end_inset
-
-
-\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 is the default name of the macro that should be changed to
- something sensible.
- The wanted formula is inserted in the first blue box.
- An argument placeholder is inserted with the command
-\series bold
-
-\backslash
-#argumentnumber
-\series default
-, e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g
-\begin_inset space \space{}
-\end_inset
-
-
-\series bold
-
-\backslash
-#1
-\series default
- or by using the macro toolbar button
-\begin_inset Graphics
- filename ../images/math-macro-add-param.png
- scale 85
-
-\end_inset
-
-.
- Argument placeholders are displayed red.
- A maximum of 9
-\begin_inset space ~
-\end_inset
-
-arguments are possible.
- Optional arguments are created with the toolbar button
-\begin_inset Graphics
- filename ../images/math-macro-add-optional-param.png
- scale 85
-
-\end_inset
-
-.
- The first non-optional argument can be transformed to an optional one with
- the toolbar button
-\begin_inset Graphics
- filename ../images/math-macro-make-optional.png
- scale 85
-
-\end_inset
-
-.
- In the second blue box the appearance of the macro in LyX can be defined.
- Normally you want to see it as it is defined, so the box is kept empty.
- But when you have created a macro that needs lot of space on the screen,
- you can insert in the box for example
-\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
-For the macro only the arguments with the macro name in front of them will
- then be displayed in LyX, leading to a better overview.
- The formula appears in the output as defined in the first box.
-\begin_inset Newline newline
-\end_inset
-
-The appearance of macros in formulas can furthermore be changed for single
- macros by setting the cursor in the macro and using the menu
-\family sans
-View\SpecialChar \menuseparator
-(Un)fold
-\begin_inset space ~
-\end_inset
-
-Math
-\begin_inset space ~
-\end_inset
-
-Macro
-\family default
-.
-\end_layout
-
-\begin_layout Standard
-To use a macro, the macro name is inserted as command to a formula, in our
- case
-\series bold
-
-\backslash
-qG
-\series default
-.
- Our macro looks in LyX like this:
-\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
-
-Here is our macro example with the arguments
-\begin_inset Formula $x$
-\end_inset
-
-,
-\begin_inset Formula $\ln(x)$
-\end_inset
-
- and
-\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 offers in the menu
-\family sans
-Tools\SpecialChar \menuseparator
-Preferences\SpecialChar \menuseparator
-Editing\SpecialChar \menuseparator
-Control
-\family default
- different styles to edit macros.
- To find the style that suits you the most, choose a style and set the cursor
- in a macro formula to see the difference.
-\end_layout
-
-\begin_layout Standard
-A math macro is transformed internally to a
-\series bold
-
-\backslash
-newcommand
-\series default
- command when exporting the document.
- The created
-\series bold
-
-\backslash
-newcommand
-\series default
- command is not placed in the LaTeX-preamble, therefore macros can only
- be used in formulas that are in the document below the macro definition
- box.
-\end_layout
-
-\begin_layout Standard
-Math macros can also be directly created from a
-\series bold
-
-\backslash
-newcommand
-\series default
- command.
- When writing for example the command
-\series bold
-
-\begin_inset Newline newline
-\end_inset
-
-
-\backslash
-newcommand{
-\backslash
-larrow}[2]{
-\backslash
-xleftarrow[#2]{#1}}
-\begin_inset Newline newline
-\end_inset
-
-
-\series default
-in LyX as normal text, highlighting it completely and using then the shortcut
-
-\family sans
-Ctrl+M
-\family default
-, the command will be transformed to a math macro.
- Using this method you need to be careful that the
-\series bold
-
-\backslash
-newcommand
-\series default
- command is typed correctly, otherwise you get a faulty macro leading to
- LaTeX errors.
-\end_layout
-
-\begin_layout Standard
-Math macros currently have the problem that further formulas in macro definition
-s are handled wrongly.
- Therefore the example
-\series bold
-
-\backslash
-fb
-\series default
- from
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:The-Command-newcommand"
-
-\end_inset
-
- cannot be created as macro.
-\end_layout
-
-\begin_layout Standard
-When the cursor is in a macro definition box, you will see the macro toolbar
- in LyX:
-\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 ! Toolbar
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace defskip
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The macro toolbar contains from left to right the following buttons:
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace defskip
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Tabular
-
-
-
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Macro
-\begin_inset space ~
-\end_inset
-
-Definition\SpecialChar \menuseparator
-Remove Last Argument
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Macro
-\begin_inset space ~
-\end_inset
-
-Definition\SpecialChar \menuseparator
-Append Argument
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Macro
-\begin_inset space ~
-\end_inset
-
-Definition\SpecialChar \menuseparator
-Make First Non-Optional into
-\begin_inset Newline newline
-\end_inset
-
-
-\begin_inset Phantom HPhantom
-status open
-
-\begin_layout Plain Layout
-
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Macro
-\begin_inset space ~
-\end_inset
-
-Definition\SpecialChar \menuseparator
-
-\end_layout
-
-\end_inset
-
-Optional Argument
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Macro
-\begin_inset space ~
-\end_inset
-
-Definition\SpecialChar \menuseparator
-Make Last Optional into
-\begin_inset Newline newline
-\end_inset
-
-
-\begin_inset Phantom HPhantom
-status open
-
-\begin_layout Plain Layout
-
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Macro
-\begin_inset space ~
-\end_inset
-
-Definition\SpecialChar \menuseparator
-
-\end_layout
-
-\end_inset
-
-Non-Optional Argument
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Macro
-\begin_inset space ~
-\end_inset
-
-Definition\SpecialChar \menuseparator
-Remove Optional Argument
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Macro
-\begin_inset space ~
-\end_inset
-
-Definition\SpecialChar \menuseparator
-Insert Optional Argument
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Macro
-\begin_inset space ~
-\end_inset
-
-Definition\SpecialChar \menuseparator
-Remove Last Argument
-\begin_inset Newline newline
-\end_inset
-
-
-\begin_inset Phantom HPhantom
-status open
-
-\begin_layout Plain Layout
-
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Macro
-\begin_inset space ~
-\end_inset
-
-Definition\SpecialChar \menuseparator
-
-\end_layout
-
-\end_inset
-
-Spitting Out To The Right
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Macro
-\begin_inset space ~
-\end_inset
-
-Definition\SpecialChar \menuseparator
-Append Argument
-\begin_inset Newline newline
-\end_inset
-
-
-\begin_inset Phantom HPhantom
-status open
-
-\begin_layout Plain Layout
-
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Macro
-\begin_inset space ~
-\end_inset
-
-Definition\SpecialChar \menuseparator
-
-\end_layout
-
-\end_inset
-
-Eating From The Right
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Macro
-\begin_inset space ~
-\end_inset
-
-Definition\SpecialChar \menuseparator
-Append Optional Argument
-\begin_inset Newline newline
-\end_inset
-
-
-\begin_inset Phantom HPhantom
-status open
-
-\begin_layout Plain Layout
-
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Macro
-\begin_inset space ~
-\end_inset
-
-Definition\SpecialChar \menuseparator
-
-\end_layout
-
-\end_inset
-
-Eating From The Right
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-Computer Algebra Systems
-\end_layout
-
-\begin_layout Standard
-LyX offers the exchange between mathematical expressions written in LyX's
- math editor and external applications or user defined scripts.
- Currently supported applications are
-\family sans
-Maple
-\family default
-,
-\family sans
-Mathematica
-\family default
-,
-\family sans
-Maxima
-\family default
- and
-\family sans
-Octave
-\family default
-.
- Note that the set of supported mathematical constructs is limited only
- to very simple cases.
-\end_layout
-
-\begin_layout Subsection
-Usage
-\end_layout
-
-\begin_layout Standard
-Write some expression in a formula, go to the
-\family sans
-Edit\SpecialChar \menuseparator
-Math\SpecialChar \menuseparator
-Use Computer Algebra System
-\family default
- menu and choose the application you have installed on the computer.
- After that the result of computation should show on the right side of the
- expression together with the
-\begin_inset Quotes eld
-\end_inset
-
-=
-\begin_inset Quotes erd
-\end_inset
-
- operator.
-\end_layout
-
-\begin_layout Standard
-Here are few simple examples (with results from
-\family typewriter
-Maxima
-\family default
-) to show what kind of computations can be performed:
-\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 $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
-\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
-Keyboard shortcut
-\end_layout
-
-\begin_layout Standard
-Currently there is no keyboard shortcut for calling the algebra applications.
- One can easily bind a shortcut to the
-\family sans
-math-extern
-\family default
- LyX function (see the
-\family sans
-\emph on
-LyX Functions
-\family default
-\emph default
- manual).
- One could e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-bind the
-\family sans
-Return
-\family default
- key inside the math editor.
- To bind it to
-\family typewriter
-Maxima
-\family default
- one would use this shortcut definition command:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-command-alternatives break-paragraph;math-extern maxima
-\end_layout
-
-\begin_layout Section
-Miscellaneous
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Miscellaneous
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Negative Numbers
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Numbers ! negative
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Negative numbers often look ugly in formulas because the minus sign before
- the number is set with the same length as the minus operator sign.
- When writing the negative number in normal text, the minus sign appears
- correctly.
-\end_layout
-
-\begin_layout Standard
-Thus, the problem disappears when converting the minus sign to mathematical
- text.
-\end_layout
-
-\begin_layout Standard
-An example to visualize the problem:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-normal text:
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-x = -2
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-formula:
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $x=-2$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-solution:
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $x=\textrm{-}2$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Comma as decimal Separator
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Comma
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-In LaTeX a comma inside a formula is used, according to the English convention,
- as number group separator.
- So there will be space added behind all commas in formulas.
-\end_layout
-
-\begin_layout Standard
-To avoid this, the comma is highlighted and changed to mathematical text
- (shortcut
-\begin_inset Info
-type "shortcut"
-arg "math-mode"
-\end_inset
-
-).
-\end_layout
-
-\begin_layout Standard
-To use all formula commas in the document as decimal separator, the file
-
-\series bold
-icomma.sty
-\series default
-
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-
-\series bold
-icomma
-\series default
- is part of the LaTeX-package
-\series bold
-was
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! 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
-Packages ! icomma
-\end_layout
-
-\end_inset
-
- is loaded with the LaTeX-preamble line
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-usepackage{icomma}
-\end_layout
-
-\begin_layout Subsection
-Physical Vectors
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Physical-Vectors"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Vectors ! physical
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Predefined vectors are offered by the LaTeX-package
-\series bold
-braket
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! braket
-\end_layout
-
-\end_inset
-
- that is loaded with the LaTeX-preamble line
-\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
-The following table will only be displayed when the LaTeX-package
-\series bold
-braket
-\series default
- is installed.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The following commands are defined:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Bra{
-\backslash
-psi
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Bra{\psi}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Ket{
-\backslash
-psi
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Ket{\psi}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-Braket{
-\backslash
-psi|
-\backslash
-phi
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\Braket{\psi|\phi}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The command
-\series bold
-
-\backslash
-Braket
-\series default
- assures that all vertical bars are set in the size of the surrounding brackets:
-\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
-The following will be displayed when the LaTeX-package
-\series bold
-braket
-\series default
- is not installed:
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-You need to install the LaTeX-package
-\series bold
-braket
-\series default
- to see the rest of this subsection in the output.
-\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
-The effect of
-\series bold
-
-\backslash
-Braket
-\series default
- can also be achieved using the command
-\series bold
-
-\backslash
-middle
-\series default
-, that is described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Automatic-Bracket-Size"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Subsection
-Self-defined Fractions
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Self-defined-Fractions"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Fractions ! self-defined
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To define custom commands for fractions, the command
-\series bold
-
-\backslash
-genfrac
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! G !
-\backslash
-genfrac
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-vspace{4mm}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
- is used in the following scheme:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-genfrac{left
-\series default
-
-\series bold
-bracket}{right
-\series default
-
-\series bold
-bracket}{fraction bar thickness}{style}
-\begin_inset Newline newline
-\end_inset
-
-
-\begin_inset Phantom HPhantom
-status open
-
-\begin_layout Plain Layout
-
-\series bold
-
-\backslash
-genfrac
-\end_layout
-
-\end_inset
-
-{numerator}{denominator}
-\end_layout
-
-\begin_layout Standard
-The style is a number in the range of 0
-\begin_inset space \thinspace{}
-\end_inset
-
--
-\begin_inset space \thinspace{}
-\end_inset
-
-3.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Number
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Style (Size)
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-0
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-display style formula
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-1
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-inline formula
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-2
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-small
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-3
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-tiny
-\end_layout
-
-\end_inset
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-When no style is given, the size is adjusted to the surrounding environment
- like for the command
-\series bold
-
-\backslash
-frac
-\series default
-.
-\end_layout
-
-\begin_layout Standard
-When no fraction bar thickness is given, the predefined value of 0.4
-\begin_inset space \thinspace{}
-\end_inset
-
-pt will be used.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-For example, the commands
-\series bold
-
-\backslash
-dfrac
-\series default
- and
-\series bold
-
-\backslash
-tbinom
-\series default
- from
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Fractions"
-
-\end_inset
-
- are defined with the commands
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-newcommand{
-\backslash
-dfrac}[2]{
-\backslash
-genfrac{}{}{}{0}{#1}{#2}}
-\end_layout
-
-\begin_layout Standard
-and
-\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
-
-To define a fraction where the fraction bar thickness can be given as optional
- argument, the following line is inserted to the LaTeX-preamble:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-newcommand{
-\backslash
-fracS}[3][]{
-\backslash
-genfrac{}{}{#1}{}{#2}{#3}}
-\end_layout
-
-\begin_layout Standard
-A test:
-\begin_inset Formula
-\begin{align*}
-\text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
-\text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
-\end{align*}
-
-\end_inset
-
-As one can see, the distance of the numerator and the denominator to the
- fraction bar is round about three times the bar thickness.
-\end_layout
-
-\begin_layout Subsection
-Canceled Formulas
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! canceled
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To cancel formulas or formula parts, the LaTeX-package
-\series bold
-cancel
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! cancel
-\end_layout
-
-\end_inset
-
- has to be loaded with the LaTeX-preamble line
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-usepackage{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
-The following table will only be displayed when the LaTeX-package
-\series bold
-cancel
-\series default
- is installed.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-There are four ways to cancel formulas:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Result
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-The space and
-\series bold
-
-\backslash
-raisebox
-\series default
- are used here as spacer.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\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
- |
-
-\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
- |
-
-
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-cancelto
-\series default
- is especially suitable to visualize the reduction of fractions within formulas:
-\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
-To change the size of
-\series bold
-
-\backslash
-cancelto
-\series default
-'s
-\begin_inset Quotes eld
-\end_inset
-
-subscript
-\begin_inset Quotes erd
-\end_inset
-
- value one can load the package
-\series bold
-cancel
-\series default
- with either the option
-\series bold
-samesize
-\series default
- which leads to the same size as for the canceled value or with the option
-
-\series bold
-Smaller
-\series default
- which makes is it a bit smaller than the size one gets without using a
- package option.
- In this document
-\series bold
-cancel
-\series default
- was loaded with this line:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-usepackage[samesize]{cancel}
-\end_layout
-
-\begin_layout Standard
-To color the cancellation bar one adds this command as TeX code:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-renewcommand{
-\backslash
-CancelColor}{
-\backslash
-color{red}}
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-red
-\series default
- can be replaced by a color of your choice.
-\end_layout
-
-\begin_layout Standard
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-renewcommand{
-\backslash
-CancelColor}{
-\backslash
-color{red}}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\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
-renewcommand{
-\backslash
-CancelColor}{
-\backslash
-color{black}}
-\end_layout
-
-\end_inset
-
-
-\begin_inset Note Note
-status open
-
-\begin_layout Plain Layout
-reset the color
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-For further customizations, see the documentation of the package
-\series bold
-cancel
-\series default
-,
-\begin_inset CommandInset citation
-LatexCommand cite
-key "cancel"
-
-\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
-The following will be displayed when the LaTeX-package
-\series bold
-cancel
-\series default
- is not installed:
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-You need to install the LaTeX-package
-\series bold
-cancel
-\series default
- to see the rest of this subsection in the output.
-\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
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Formulas in Section Headings
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Formulas-in-Section"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! in section headings
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-When formulas are used in section headings, the following has to be taken
- into account:
-\end_layout
-
-\begin_layout Standard
-\begin_inset Note Greyedout
-status open
-
-\begin_layout Plain Layout
-When
-\series bold
-hyperref
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! hyperref
-\end_layout
-
-\end_inset
-
- support is enabled in the document settings dialog under
-\family sans
-PDF
-\begin_inset space ~
-\end_inset
-
-Properties
-\family default
-, PDF-bookmarks are created for every section heading in the table of contents.
- If a section heading contains formulas, they are incorrectly displayed
- in the bookmark text, because formulas in bookmarks infringe the PDF convention
-s.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Both problems can be solved by inserting at the end of the section heading
- a short title with the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Short
-\begin_inset space ~
-\end_inset
-
-Title
-\family default
-.
- Short titles are used as alternative for multiline section headings to
- keep the table of contents clearly arranged.
- Only the short title appears in the table of contents and therefore also
- in the PDF-bookmark.
-\end_layout
-
-\begin_layout Standard
-When formulas should be used in the table of contents but
-\series bold
-hyperref
-\series default
- is used, one can use the following command in TeX-mode:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-texorpdfstring{part}{alternative}
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! T !
-\backslash
-texorpdfstring
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Part is the part of the heading that shouldn't appear in the PDF-bookmark.
- This can be characters, formulas, footnotes, but also cross-references.
- The alternative is used instead of the part for the bookmark.
-\end_layout
-
-\begin_layout Standard
-Here are two example headings:
-\begin_inset VSpace -3mm
-\end_inset
-
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-boldmath
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsubsection
-Heading without formula in table of contents
-\begin_inset Formula $\sqrt{-1}=\mathrm{i}$
-\end_inset
-
-
-\begin_inset Argument 1
-status collapsed
-
-\begin_layout Plain Layout
-Heading without formula in table of contents
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsubsection
-Heading with formula in table of contents
-\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
-
-In the first heading a short title was used, in the second one
-\series bold
-
-\backslash
-texorpdfstring
-\series default
-.
-\end_layout
-
-\begin_layout Standard
-To get the same formatting as for the other headings, the complete heading
- was set into a
-\series bold
-boldmath
-\series default
- environment
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Bold-Formulas"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Subsection
-Formulas in multi-column Text
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! in multi-column text
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Formulas in multi-column text are often too wide to fit into a column and
- thus need to be set over the whole page width.
- This is done by using the LaTeX-package
-\series bold
-multicol
-\series default
-
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-
-\series bold
-multicol
-\series default
- is part of every LaTeX standard installation.
-\end_layout
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! multicol
-\end_layout
-
-\end_inset
-
-, that is loaded with the LaTeX-preamble line
-\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
-Note that in this case the setting
-\family sans
-Two-column
-\begin_inset space ~
-\end_inset
-
-document
-\family default
- in the menu
-\family sans
-Document\SpecialChar \menuseparator
-Settings
-\family default
- under
-\family sans
-Text
-\begin_inset space ~
-\end_inset
-
-Layout
-\family default
-\emph on
-
-\emph default
-must
-\emph on
-not
-\emph default
- be selected.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Before the multi-column text the command
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-begin{multicols}{column number}
-\end_layout
-
-\begin_layout Standard
-is written in TeX-mode.
- The column number is a number in the range of 2
-\begin_inset space \thinspace{}
-\end_inset
-
--
-\begin_inset space \thinspace{}
-\end_inset
-
-10.
- Before the formula the multi-column text is ended by inserting the command
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-end{multicols}
-\end_layout
-
-\begin_layout Standard
-in TeX-mode.
-\end_layout
-
-\begin_layout Standard
-Due to the command some space is automatically added before the formula.
- To revert this, -6
-\begin_inset space \thinspace{}
-\end_inset
-
-mm vertical space is inserted before the formula.
- When the formula style
-\series bold
-Indented
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-formula styles see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Formula-Styles"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\series default
- is used, -9
-\begin_inset space \thinspace{}
-\end_inset
-
-mm space is inserted instead.
-\end_layout
-
-\begin_layout Standard
-As example a multi-column text with a displayed formula:
-\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 auÃer 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
-Formulas with Description of Variables
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Formula ! with description of variables
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-To describe variables within a formula, like in formula
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:within"
-
-\end_inset
-
-, a 2
-\series bold
-Ã
-\series default
-
-\begin_inset Formula $n$
-\end_inset
-
-
-\begin_inset space ~
-\end_inset
-
-matrix is used with left aligned columns for the
-\begin_inset Formula $n$
-\end_inset
-
- used variables.
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-matrices see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Matrices"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
- To set the description in a smaller size, before the matrix e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-the command
-\series bold
-
-\backslash
-footnotesize
-\series default
- is inserted.
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-font sizes see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Font-Sizes"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-When the formula style
-\series bold
-Indented
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-formula styles see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Formula-Styles"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\series default
- is used, a
-\series bold
-
-\backslash
-hfill
-\series default
-
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-
-\series bold
-
-\backslash
-hfill
-\series default
- only works in formulas with the style
-\series bold
-Indented
-\series default
-, see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Variable-Space"
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
- is inserted before and after the matrix to have the same separation of
- the matrix from the equation and the side margin.
-\end_layout
-
-\begin_layout Standard
-When the formula style
-\series bold
-Centered
-\series default
- is used, the method described in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Flalign-Environment"
-
-\end_inset
-
- is used to indent formulas.
- Formula
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:within"
-
-\end_inset
-
- consists of five columns where in the first two columns contain the equation,
- the third the matrix and the last one an empty TeX-brace.
-\begin_inset Formula
-\begin{flalign}
-\hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
-\rho & \textrm{density}\\
-V & \textrm{volume}\\
-g & \textrm{gravitational acceleration}
-\end{array} & & {}\label{eq:within}
-\end{flalign}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Upright small Greek Letters
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Upright-small-Greek"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Greek letters ! upright
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Most of the math fonts only provide italic small Greek letters.
- But for symbols of elementary particles like pions and neutrinos, upright
- Greek letters are needed.
- The file
-\series bold
-upgreek.sty
-\series default
-
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-
-\series bold
-upgreek
-\series default
- is part of the LaTeX-package
-\series bold
-was
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Packages ! 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
-Packages ! upgreek
-\end_layout
-
-\end_inset
-
- that is loaded with the LaTeX-preamble line
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-usepackage{upgreek}
-\end_layout
-
-\begin_layout Standard
-provides them.
-
-\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
-The following table will only be displayed when the LaTeX-package
-\series bold
-upgreek
-\series default
- is installed:
-\end_layout
-
-\end_inset
-
- They are created when the command for a small Greek letter is started with
-
-\series bold
-up
-\series default
-.
- For example the command
-\series bold
-
-\backslash
-uptau
-\series default
- creates this:
-\begin_inset Formula $\uptau$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-With these commands reactions of elementary particles can be typeset:
-\begin_inset Formula
-\[
-\uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
-\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The upright letters are more bold and wider than the italic ones.
- They should therefore not be used for units like
-\begin_inset Quotes eld
-\end_inset
-
-µm
-\begin_inset Quotes erd
-\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
-The following will be displayed when the LaTeX-package
-\series bold
-upgreek
-\series default
- is not installed:
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-You need to install the LaTeX-package
-\series bold
-upgreek
-\series default
- to see the rest of this subsection in the output.
-\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
-Text Characters in Formulas
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Text-Characters-in"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Text ! in formulas
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-In some cases you might want to insert text characters directly into formulas.
- When for example the centered dot · is often used in formulas like
-\begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
-\end_inset
-
-, one would have to insert the command
-\series bold
-
-\backslash
-cdot
-\series default
-
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Binary-Operators"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
- all the time, because this character is defined in all encodings as text
- character.
- But the encoding can be changed by this LaTeX-preamble line:
-\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
-The character encoding (menu
-\family sans
-Document\SpecialChar \menuseparator
-Settings\SpecialChar \menuseparator
-Language
-\family default
-) specifies what character appears when a keyboard key is pressed.
- When the key for the character '·' is pressed, internally the command
-\series bold
-
-\backslash
-textperiodcentered
-\series default
- is used.
- But this command is not available in a formula so that you would get LaTeX-erro
-rs.
- With the changed encoding the right command is chosen automatically, depending
- on if the character was inserted into a formula or not.
-\end_layout
-
-\begin_layout Standard
-The encoding of several characters is saved in definition files.
- For example the encoding
-\series bold
-latin9
-\series default
- is defined in the file
-\series bold
-latin9.def
-\series default
- which is in the installation folder of LaTeX.
- Encodings should only be changed via the LaTeX-preamble and not in the
- definition files.
- Otherwise documents could not be edited by other LyX users working on other
- computers.
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-Besides the centered dot, in this document the degree sign ° is defined
- with the following LaTeX-preamble line so that it can be directly inserted
- into a formula:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-DeclareInputtext{176}{
-\backslash
-ifmmode^
-\backslash
-circ
-\backslash
-else
-\backslash
-textdegree
-\backslash
-f\SpecialChar \textcompwordmark{}
-i}
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-\start_of_appendix
-Typographic Advice
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Typographic advice
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-This section is a summary of the most important typographic rules, listed
- in ISO norms.
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-This collection was partly taken from the German semi-official dictionary
- called
-\begin_inset Quotes eld
-\end_inset
-
-Duden
-\begin_inset Quotes erd
-\end_inset
-
-
-\begin_inset CommandInset citation
-LatexCommand cite
-key "Duden"
-
-\end_inset
-
- that lists some of the ISO rules.
- More rules are listed in
-\begin_inset CommandInset citation
-LatexCommand cite
-key "Checklist"
-
-\end_inset
-
-.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Itemize
-Physical units are
-\emph on
-always
-\emph default
- set upright
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-done with font styles, see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Font-Styles"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-, no matter if they appear in italic text: 30
-\begin_inset space \thinspace{}
-\end_inset
-
-km/h
-\begin_inset Newline newline
-\end_inset
-
-Between the value and the unit is the smallest space, see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Predefined-Space"
-
-\end_inset
-
-.
-\begin_inset Newline newline
-\end_inset
-
-This convention is automatically fulfilled when the command
-\series bold
-
-\backslash
-unittwo
-\series default
- is used.
- When it is entered to a formula, two boxes appear.
- In the first one the value is inserted, in the second one the unit, and
- one gets as above:
-\begin_inset Formula $\unit[30]{km/h}$
-\end_inset
-
-
-\begin_inset space \thinspace{}
-\end_inset
-
-.
- Note that
-\series bold
-
-\backslash
-unittwo
-\series default
- is not a real LaTeX command but the command
-\series bold
-
-\backslash
-unit[value]{unit}
-\series default
-, therefore you cannot use it in TeX code.
-\end_layout
-
-\begin_layout Itemize
-Percent and perthousand signs are set like physical units:
-\begin_inset Newline newline
-\end_inset
-
-1.2
-\begin_inset space \thinspace{}
-\end_inset
-
-â° alcohol in blood
-\end_layout
-
-\begin_layout Itemize
-The degree sign follows directly on the value: 15°, but not when it is used
- in units: 15
-\begin_inset space \thinspace{}
-\end_inset
-
-°C
-\end_layout
-
-\begin_layout Itemize
-In numbers with more than four digits the smallest space is inserted before
- every third digit to group them:
-\family roman
-\series medium
-\shape up
-\size normal
-\emph off
-\bar no
-\noun off
-\color none
-18
-\begin_inset space \thinspace{}
-\end_inset
-
-473
-\begin_inset space \thinspace{}
-\end_inset
-
-588
-\end_layout
-
-\begin_layout Itemize
-For dimensions like 120Ã90Ã40
-\begin_inset space \thinspace{}
-\end_inset
-
-cm the multiplication sign
-\begin_inset Quotes eld
-\end_inset
-
-Ã
-\begin_inset Quotes erd
-\end_inset
-
- is used.
- It is available either via the command
-\series bold
-
-\backslash
-times
-\series default
- or via the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Special Character\SpecialChar \menuseparator
-Symbols
-\family default
-.
-\end_layout
-
-\begin_layout Itemize
-Functions with names consisting of several letters are set upright to avoid
- confusions, see
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Predefined-Functions"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Itemize
-Indices consisting of several letters, are set upright:
-\begin_inset Formula $E_{\mathrm{kin}}$
-\end_inset
-
-
-\begin_inset Newline newline
-\end_inset
-
-Components of matrices are set italic:
-\begin_inset Formula $\hat{H}_{kl}$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Itemize
-The differentiation/integration operator 'd', the Euler's number 'e' and
- the imaginary unit 'i' should be set upright, to avoid mixing them up with
- other variables.
-\end_layout
-
-\begin_layout Itemize
-The character that denotes a
-\noun on
-Fourier
-\noun default
- transformation is inserted either by the command
-\series bold
-
-\backslash
-mathscr
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-F
-\series default
- or via the menu
-\family sans
-Insert\SpecialChar \menuseparator
-Special Character\SpecialChar \menuseparator
-Symbols\SpecialChar \menuseparator
-Letterlike
-\begin_inset space ~
-\end_inset
-
-Symbols
-\family default
-:
-\begin_inset Formula $\mathscr{F}$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
-\begin_layout Section
-Synonyms
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Synonyms
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-Some characters and symbols can be created with several commands.
- Here is a list of the synonym commands:
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\begin_inset Tabular
-
-
-
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-Command
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-equivalent to
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-ast
-\end_layout
-
-\end_inset
- |
-
-\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
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-choose
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-binom
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-geq
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-ge
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-lbrace
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-{
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-lbracket
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-[
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-leftarrow
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-gets
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-leq
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-le
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-lor
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-vee
-\end_layout
-
-\end_inset
- |
-
-
-
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\backslash
-neq
-\end_layout
-
-\end_inset
- |
-
-\begin_inset Text
-
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+#LyX 2.1 created this file. For more info see http://www.lyx.org/
+\lyxformat 474
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+\begin_header
+\textclass scrartcl
+\begin_preamble
+% DO NOT ALTER THIS PREAMBLE!!!
+%
+% This preamble is designed to ensure that the file prints
+% out as advertised. If you mess with this preamble,
+% parts of this document may not print out as expected. If you
+% have problems LaTeXing this file, please contact
+% the documentation team
+% email: lyx-docs@lists.lyx.org
+
+% if pdflatex is used
+\usepackage{ifpdf}
+\ifpdf
+
+% set fonts for nicer pdf view
+\IfFileExists{lmodern.sty}
+ {\usepackage{lmodern}}{}
+
+\fi % end if pdflatex is used
+
+% solves the following problem:
+% If the dection number consits of too many numerals the section heading
+% will be printed in the TOC without a space between it and the section number.
+% As solution more space between the number and the heading is inserted:
+\renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
+\renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
+
+% increase link area for cross-references and autoname them,
+\AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
+\@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
+\addto\extrasenglish{%
+ \renewcommand*{\equationautorefname}[1]{}%
+ \renewcommand{\sectionautorefname}{sec.\negthinspace}%
+ \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
+ \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
+}
+
+% don't load packages twice
+% see first footnote in sec. 9.3
+\@ifundefined{textcolor}{\usepackage{color}}{}
+
+% the pages of the TOC are numbered roman
+% and a PDF-bookmark for the TOC is added
+\pagenumbering{roman}
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+\renewcommand{\tableofcontents}{%
+ \vspace{1cm}
+ \pdfbookmark[1]{\contentsname}{}
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+% insert additional vertical space of 1.5 mm between footnotes,
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+
+% provides caption formatting
+\setkomafont{captionlabel}{\bfseries}
+
+% enables calculation of values
+\usepackage{calc}
+
+% for multiple columns used in sec. 24.7
+\usepackage{multicol}
+
+% needed in sec. 19.4
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+
+% for the Fourier transformation symbol
+\usepackage{mathrsfs}
+
+% define a color, used in sec.9.3
+\definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
+
+% declare operators (see sec. 10.4 and sec. 15.2)
+\DeclareMathOperator*{\Lozenge}{\blacklozenge}
+\DeclareMathOperator{\sgn}{sgn}
+
+% example definitions for sec. 20.1
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+
+% example macro from sec. 19.4
+%\def\tagform@#1{\maketag@@@{|#1|}}
+
+
+% ------------------------------------
+% used to check for needed LaTeX packages
+\usepackage{ifthen}
+
+% check for package undertilde
+% used for the command \utilde
+\newboolean{undertilde}
+\IfFileExists{undertilde.sty}
+ {\usepackage{undertilde}
+ \setboolean{undertilde}{true}}
+ {\setboolean{undertilde}{false}}
+
+% check for package eurosym
+% used for the Euro symbol
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+\IfFileExists{eurosym.sty}
+ {\usepackage[gennarrow]{eurosym}
+ \setboolean{eurosym}{true}}
+ {\setboolean{eurosym}{false}}
+
+% check for package braket
+% used for physical vectors
+\newboolean{braket}
+\IfFileExists{braket.sty}
+ {\usepackage{braket}
+ \setboolean{braket}{true}}
+ {\setboolean{braket}{false}}
+
+% check for package cancel
+\newboolean{cancel}
+\IfFileExists{cancel.sty}
+ {\usepackage{cancel}
+ \setboolean{cancel}{true}}
+ {\setboolean{cancel}{false}}
+
+% check for package upgreek
+\newboolean{upgreek}
+\IfFileExists{upgreek.sty}
+ {\usepackage{upgreek}
+ \setboolean{upgreek}{true}}
+ {\setboolean{upgreek}{false}}
+\end_preamble
+\options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
+\use_default_options false
+\maintain_unincluded_children false
+\language english
+\language_package default
+\inputencoding auto
+\fontencoding global
+\font_roman default
+\font_sans default
+\font_typewriter default
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+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+\graphics default
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+\spacing single
+\use_hyperref true
+\pdf_title "LyX's Math Manual"
+\pdf_author "LyX Team, Uwe Stöhr"
+\pdf_subject "LyX-documentation about math"
+\pdf_keywords "LyX, Mathed"
+\pdf_bookmarks true
+\pdf_bookmarksnumbered true
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+\papersize a4paper
+\use_geometry false
+\use_package amsmath 2
+\use_package amssymb 2
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+\cite_engine basic
+\cite_engine_type default
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+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 0
+\notefontcolor #0000ff
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\secnumdepth 4
+\tocdepth 3
+\paragraph_separation skip
+\defskip medskip
+\quotes_language english
+\papercolumns 1
+\papersides 2
+\paperpagestyle plain
+\bullet 1 0 6 -1
+\bullet 2 2 35 -1
+\bullet 3 2 7 -1
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Title
+LyX's detailed Math manual
+\end_layout
+
+\begin_layout Author
+by the LyX Team
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+\noindent
+If you have comments or error corrections, please send them to the LyX Documenta
+tion mailing list:
+\family typewriter
+
+\begin_inset CommandInset href
+LatexCommand href
+name "lyx-docs@lists.lyx.org"
+target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
+type "mailto:"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+author: Uwe Stöhr
+\end_layout
+
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
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+
+\family sans
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+\end_layout
+
+\begin_layout Standard
+\begin_inset CommandInset toc
+LatexCommand tableofcontents
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+To export this document to PDF, PS or DVI the LaTeX-packages
+\series bold
+braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
+\series default
+ and
+\series bold
+was
+\series default
+ should be installed.
+ If they are not installed the document can be exported anyway but the sections
+ where the packages are required will not appear in the output.
+ An exception is
+\series bold
+mhchem
+\series default
+; if it is not installed, this file cannot be exported.
+\end_layout
+
+\begin_layout Plain Layout
+The latest PDF-version of this document can be found here:
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Introduction
+\end_layout
+
+\begin_layout Standard
+This document explains LyX's math features and is furthermore a collection
+ of LaTeX-commands used for mathematical characters and constructs.
+ The explanations are designed for the usage of commands.
+ It is therefore required that you have read the section
+\family typewriter
+Mathematical
+\begin_inset space ~
+\end_inset
+
+Formulas
+\family default
+ of the User's Guide.
+\end_layout
+
+\begin_layout Standard
+Most of the characters and many constructs explained in this manual are
+ also accessible via the menu
+\family sans
+Insert
+\series bold
+\SpecialChar \menuseparator
+
+\series default
+Math
+\family default
+ or the
+\family sans
+math
+\family default
+\series bold
+
+\family sans
+\series default
+toolbar
+\family default
+.
+ But everybody who has to write lots of formulas will notice that it is
+ much faster to use commands instead of the math toolbar.
+ Therefore this manual is focused on commands but also mentions the correspondin
+g toolbar buttons when available.
+\end_layout
+
+\begin_layout Standard
+If not specially mentioned the commands are only available within formulas.
+ To be able to use all commands explained in this document, the option
+\family sans
+Use AMS math package
+\family default
+ must be checked in the document settings (menu
+\family sans
+Document\SpecialChar \menuseparator
+Settings\SpecialChar \menuseparator
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+).
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+The option
+\family sans
+Use AMS math package automatically
+\family default
+ only uses
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+AmS
+\end_layout
+
+\end_inset
+
+-math when math constructs are found that are supported by LyX.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This document doesn't list all
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+AmS
+\end_layout
+
+\end_inset
+
+-math commands
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+A list with all
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+AmS
+\end_layout
+
+\end_inset
+
+-math commands is in the file
+\family sans
+
+\begin_inset CommandInset href
+LatexCommand href
+name "amsguide.ps"
+target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
+
+\end_inset
+
+
+\family default
+, which is part of every LaTeX standard installation.
+\end_layout
+
+\end_inset
+
+ for lucidity reasons.
+\end_layout
+
+\begin_layout Section
+General Instructions
+\end_layout
+
+\begin_layout Standard
+To create an inline formula
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! inline
+\end_layout
+
+\end_inset
+
+ that is embedded into a text line, use one of the shortcuts
+\begin_inset Info
+type "shortcuts"
+arg "math-mode"
+\end_inset
+
+ or the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-mode"
+\end_inset
+
+.
+\begin_inset Newline newline
+\end_inset
+
+To create a display style formula
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! display style
+\end_layout
+
+\end_inset
+
+ which will appear bigger, has a different format, and will be in a separate
+ paragraph, use one of these shortcuts:
+\begin_inset Info
+type "shortcuts"
+arg "math-display"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+To change a display style formula to an inline formula, set the cursor into
+ the formula and use one of the shortcuts
+\begin_inset Info
+type "shortcuts"
+arg "math-mode"
+\end_inset
+
+ or the menu
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Change formula type
+\family default
+.
+ The same way is used to change an inline formula to a display style formula.
+\end_layout
+
+\begin_layout Standard
+To display parts of an inline formula in the size of a display style formula,
+ enter the command
+\series bold
+
+\backslash
+displaystyle
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! D !
+\backslash
+displaystyle
+\end_layout
+
+\end_inset
+
+ to a formula.
+ Then a new blue box appears in which the desired formula part is inserted.
+\end_layout
+
+\begin_layout Standard
+Only inline formulas are allowed inside tables.
+\end_layout
+
+\begin_layout Standard
+The
+\family sans
+math toolbar
+\family default
+ can be turned on in the menu
+\family sans
+View\SpecialChar \menuseparator
+Toolbars
+\family default
+.
+ When you click there on
+\begin_inset Quotes eld
+\end_inset
+
+Math
+\begin_inset Quotes erd
+\end_inset
+
+ the toolbar will be shown permanently at the bottom; this state is visualized
+ in the
+\family sans
+Toolbars
+\family default
+ menu with a checkmark.
+ When you click in this state again on
+\begin_inset Quotes eld
+\end_inset
+
+Math
+\begin_inset Quotes erd
+\end_inset
+
+ in the
+\family sans
+Toolbars
+\family default
+ menu, the
+\family sans
+math toolbar
+\family default
+ is only shown when the cursor is within a formula; this state is visualized
+ by the renaming of the menu entry from
+\begin_inset Quotes eld
+\end_inset
+
+Math
+\begin_inset Quotes erd
+\end_inset
+
+ to
+\begin_inset Quotes eld
+\end_inset
+
+Math
+\begin_inset space ~
+\end_inset
+
+(auto)
+\begin_inset Quotes erd
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The TeX-mode
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+T@TeX-mode
+\end_layout
+
+\end_inset
+
+ is invoked by pressing the toolbar button
+\begin_inset Info
+type "icon"
+arg "ert-insert"
+\end_inset
+
+ or by using the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Te
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+{}
+\end_layout
+
+\end_inset
+
+X Code
+\family default
+ (shortcut
+\begin_inset Info
+type "shortcut"
+arg "ert-insert"
+\end_inset
+
+).
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+In LyX there are three
+\begin_inset Quotes eld
+\end_inset
+
+proper names
+\begin_inset Quotes erd
+\end_inset
+
+ that appear in the output with sub- and superscript letters: TeX, LaTeX
+ and LyX
+\end_layout
+
+\begin_layout Plain Layout
+To avoid that these names are recognized as proper names, a TeX-brace pair
+ is inserted.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To change the LaTeX-preamble
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+L@LaTeX-preamble
+\end_layout
+
+\end_inset
+
+, use the menu
+\family sans
+Document\SpecialChar \menuseparator
+Settings\SpecialChar \menuseparator
+LaT
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+{}
+\end_layout
+
+\end_inset
+
+eX
+\family default
+
+\family sans
+Preamble
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+To edit matrices, case differentiations and multiline formulas subsequently,
+ use the menus
+\family sans
+Edit\SpecialChar \menuseparator
+Math
+\family default
+ and
+\family sans
+Edit\SpecialChar \menuseparator
+Rows
+\begin_inset space \thinspace{}
+\end_inset
+
+&
+\begin_inset space \thinspace{}
+\end_inset
+
+Columns,
+\family default
+ or the
+\family sans
+table toolbar
+\family default
+.
+ When lines and columns are swapped via the menu, the column or line where
+ the cursor is in is exchanged with the column to the right or the line
+ below, respectively.
+ Is the cursor in the last column or row, the exchange is done with the
+ column to the left or the line above.
+\end_layout
+
+\begin_layout Standard
+To write text in formulas
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+For multiline formulas the command
+\series bold
+
+\backslash
+intertext
+\series default
+ is used, see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Text-in-multiline"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\emph on
+mathematical text
+\emph default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Text ! in formulas
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Mathematical text
+\end_layout
+
+\end_inset
+
+ is used.
+ This mode is invoked with the shortcut
+\begin_inset Info
+type "shortcut"
+arg "font-default"
+\end_inset
+
+ or by the insertion of the command
+\series bold
+
+\backslash
+text
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! T !
+\backslash
+text
+\end_layout
+
+\end_inset
+
+.
+ The text appears black in LyX and can therefore be distinguished from the
+ other formula parts which appear blue.
+ In the output mathematical text is set upright, in contrary to other formula
+ parts.
+\end_layout
+
+\begin_layout Subsection*
+Command Scheme
+\end_layout
+
+\begin_layout Standard
+Most of the LaTeX-commands for math constructs have the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+commandname[optional
+\series default
+
+\series bold
+argument]{required
+\series default
+
+\series bold
+argument}
+\end_layout
+
+\begin_layout Standard
+A command always starts with a backslash
+\begin_inset Quotes gld
+\end_inset
+
+
+\series bold
+
+\backslash
+
+\series default
+
+\begin_inset Quotes grd
+\end_inset
+
+.
+ To omit optional arguments, also omit the associated brackets.
+ The braces around the required arguments are named in this document as
+ TeX-braces
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+T@TeX-braces
+\end_layout
+
+\end_inset
+
+.
+ If you add in a formula a left brace to a command name, LyX automatically
+ creates a TeX-brace.
+ In all other cases TeX-braces are created in formulas with the command
+
+\series bold
+
+\backslash
+{
+\series default
+.
+ TeX-braces appear red in LyX, in contrary to normal braces which appear
+ blue.
+ In TeX-mode no command is needed to get TeX-braces.
+ TeX-braces don't appear in the output.
+\end_layout
+
+\begin_layout Standard
+When commands without arguments, like commands for symbols are entered in
+ TeX-mode, a space character must
+\emph on
+always
+\emph default
+ be behind the command to end it.
+ This space doesn't appear in the output.
+ When the space should appear in the output, the space must be followed
+ by a protected space in normal text.
+\end_layout
+
+\begin_layout Standard
+A protected space is inserted with
+\begin_inset Info
+type "shortcuts"
+arg "command-alternatives space-insert protected ; math-space"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection*
+\begin_inset Newpage newpage
+\end_inset
+
+Syntax Explanation
+\end_layout
+
+\begin_layout Itemize
+The symbol
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+ denotes a space character to be input.
+\end_layout
+
+\begin_layout Itemize
+An arrow like
+\begin_inset Formula $\to$
+\end_inset
+
+ denotes the usage of the corresponding arrow key on the keyboard.
+ The
+\family sans
+Tab
+\family default
+ key can often be used instead of
+\begin_inset Formula $\to$
+\end_inset
+
+ and
+\begin_inset Formula $\downarrow$
+\end_inset
+
+, and
+\family sans
+Shift+Tab
+\family default
+ instead of
+\begin_inset Formula $\leftarrow$
+\end_inset
+
+ and
+\begin_inset Formula $\uparrow$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection*
+Available units
+\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 Standard
+
+\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "tab:Available-units"
+
+\end_inset
+
+Available units
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Unit
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Name / Description
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+mm
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Millimeter
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+cm
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Centimeter
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+in
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Inch (1
+\begin_inset space \thinspace{}
+\end_inset
+
+in = 2,54
+\begin_inset space \thinspace{}
+\end_inset
+
+cm)
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+pt
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Point (72.27
+\begin_inset space \thinspace{}
+\end_inset
+
+pt = 1
+\begin_inset space \thinspace{}
+\end_inset
+
+in)
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+pc
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+sp
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+scaled point (65536
+\begin_inset space \thinspace{}
+\end_inset
+
+sp = 1
+\begin_inset space \thinspace{}
+\end_inset
+
+pt)
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+bp
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+big point (72
+\begin_inset space \thinspace{}
+\end_inset
+
+bp = 1
+\begin_inset space \thinspace{}
+\end_inset
+
+in)
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+dd
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+cc
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+ex
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Height of letter
+\emph on
+
+\begin_inset Quotes eld
+\end_inset
+
+x
+\emph default
+
+\begin_inset Quotes erd
+\end_inset
+
+ in the current font
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+em
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+width of letter
+\begin_inset Quotes eld
+\end_inset
+
+
+\emph on
+M
+\emph default
+
+\begin_inset Quotes erd
+\end_inset
+
+ in the current font
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+mu
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+math unit (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
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Basic Functions
+\end_layout
+
+\begin_layout Subsection
+Exponents
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Exponents
+\end_layout
+
+\end_inset
+
+ and Indices
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Indices
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Superscripts|see
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+{
+\end_layout
+
+\end_inset
+
+Exponents
+\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
+Subscripts|see
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+{
+\end_layout
+
+\end_inset
+
+Indices
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Indices are created with an underscore
+\begin_inset Quotes eld
+\end_inset
+
+_
+\begin_inset Quotes erd
+\end_inset
+
+ or via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-subscript"
+\end_inset
+
+, exponents with a caret
+\begin_inset Quotes eld
+\end_inset
+
+^
+\begin_inset Quotes erd
+\end_inset
+
+ or via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-superscript"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+B_V
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $B_{V}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+B^V
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}B^{V}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+B^
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}B^{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+As the caret is in some languages an accent, vowels will be accentuated
+ in this case and not set as exponents
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+Depending on the used keyboard settings this can also happen for characters
+ other than vowels.
+\end_layout
+
+\end_inset
+
+.
+ To get exponents in this case, press
+\family sans
+Space
+\family default
+ after the caret as in the last example.
+\end_layout
+
+\begin_layout Subsection
+Fractions
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Fractions"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Fractions
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Fractions are generated with the command
+\series bold
+
+\backslash
+frac
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! F !
+\backslash
+frac
+\end_layout
+
+\end_inset
+
+ or via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\frac"
+\end_inset
+
+.
+ The font size is adjusted automatically, depending on whether the fraction
+ is in an inline or display style formula.
+ With the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\frac-square"
+\end_inset
+
+ you can select different fraction types.
+\end_layout
+
+\begin_layout Standard
+With the command
+\series bold
+
+\backslash
+dfrac
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! D !
+\backslash
+dfrac
+\end_layout
+
+\end_inset
+
+ a fraction can be created that always has the size of a display style formula.
+ With
+\series bold
+
+\backslash
+tfrac
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! T !
+\backslash
+tfrac
+\end_layout
+
+\end_inset
+
+ the fraction appears always with the size of an inline formula.
+ An example:
+\end_layout
+
+\begin_layout Standard
+A line with the fraction
+\begin_inset Formula $\frac{1}{2}$
+\end_inset
+
+ that was created with the command
+\series bold
+
+\backslash
+frac
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+A line with the fraction
+\begin_inset Formula $\dfrac{1}{2}$
+\end_inset
+
+ that was created with the command
+\series bold
+
+\backslash
+dfrac
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+frac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dfrac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dfrac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+e^
+\backslash
+frac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+1
+\begin_inset Formula $\downarrow$
+\end_inset
+
+2
+\begin_inset Formula $\downarrow\downarrow$
+\end_inset
+
+3
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\begin_inset Newpage newpage
+\end_inset
+
+For nested fractions the command
+\series bold
+
+\backslash
+cfrac
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! C !
+\backslash
+cfrac
+\end_layout
+
+\end_inset
+
+ can be used.
+ Here is an example:
+\begin_inset VSpace -3mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\begin{align*}
+\textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \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
+The command for the example above is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+cfrac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B+
+\backslash
+cfrac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+C+
+\backslash
+cfrac
+\begin_inset space \textvisiblespace{}
+\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
+ sets the fraction always in the size of a displayed formula, also when
+ it is part of another fraction.
+\end_layout
+
+\begin_layout Standard
+It is possible to specify the alignment of the numerator.
+ The command
+\series bold
+
+\backslash
+cfracleft
+\series default
+ is used to left align it, the command
+\series bold
+
+\backslash
+cfracright
+\series default
+ to right-align it.
+
+\series bold
+
+\backslash
+cfrac
+\series default
+ centers the numerator.
+ These fractions demonstrate the different alignments:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+\begin_inset Formula
+\[
+\cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+\series default
+
+\series bold
+
+\backslash
+cfracleft
+\series default
+ and
+\series bold
+
+\backslash
+cfracright
+\series default
+ are no real LaTeX commands but represent the command
+\series bold
+
+\backslash
+cfrac[alignment]{numerator}{denominator}
+\series default
+ .
+ Therefore you cannot use them in TeX code.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+It is often advantageous to combine
+\series bold
+
+\backslash
+cfrac
+\series default
+ and
+\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
+For inline fractions with a sloped fraction stroke you can use the command
+
+\series bold
+
+\backslash
+nicefrac
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! N !
+\backslash
+nicefrac
+\end_layout
+
+\end_inset
+
+:
+\begin_inset Formula $\nicefrac{5}{31}$
+\end_inset
+
+ or
+\series bold
+
+\backslash
+unitfrac
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! U !
+\backslash
+unitfrac
+\end_layout
+
+\end_inset
+
+:
+\begin_inset Formula $\unitfrac{5}{31}$
+\end_inset
+
+ There is furthermore the command
+\series bold
+
+\backslash
+unitfracthree
+\series default
+ that offers to write a fraction in combination with a number:
+\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
+Note:
+\series default
+
+\series bold
+
+\backslash
+unitfracthree
+\series default
+ is not a real LaTeX command but the command
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+unitfrac[number]{numerator}{denominator}
+\series default
+ .
+ Therefore you cannot use it in TeX code.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+How to define own fractions where the fraction stroke can be changed, is
+ explained in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Self-defined-Fractions"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Multiline fractions are explained in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Multiline-Fractions"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Roots
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Roots
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Square roots are created with
+\series bold
+
+\backslash
+sqrt
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! S !
+\backslash
+sqrt
+\end_layout
+
+\end_inset
+
+ or the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\sqrt"
+\end_inset
+
+, all other roots with the command
+\series bold
+
+\backslash
+root
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! R !
+\backslash
+root
+\end_layout
+
+\end_inset
+
+ or with the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\root"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sqrt
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A-B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+root
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+3
+\begin_inset Formula $\downarrow$
+\end_inset
+
+A-B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+A square root can also be created with
+\series bold
+
+\backslash
+root
+\series default
+ when the root index field is left empty.
+\end_layout
+
+\begin_layout Standard
+With certain indices the distance to the root is too small, like in this
+ formula:
+\begin_inset Formula $\sqrt[\beta]{B}$
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+The
+\begin_inset Formula $\beta$
+\end_inset
+
+ touches the root.
+ To avoid this, the commands
+\series bold
+
+\backslash
+leftroot
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! L !
+\backslash
+leftroot
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+uproot
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! U !
+\backslash
+uproot
+\end_layout
+
+\end_inset
+
+ are used with the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+leftroot{distance}
+\series default
+ and
+\series bold
+
+\backslash
+uproot{distance}
+\end_layout
+
+\begin_layout Standard
+Distance is the number of Big Points (unit bp;
+\begin_inset Formula $\mathrm{72\, bp=1\, inch}$
+\end_inset
+
+), that the index should be moved to the left or top, resp..
+ The commands are written to the index.
+ This way the command
+\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 space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+B
+\begin_inset Newline newline
+\end_inset
+
+
+\series default
+produces a correct typeset formula:
+\begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Binomial Coefficients
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Binomial coefficients
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Binomial coefficients are inserted with the command
+\series bold
+
+\backslash
+binom
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! B !
+\backslash
+binom
+\end_layout
+
+\end_inset
+
+ or with the submenu of the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\frac-square"
+\end_inset
+
+.
+ As with fractions (
+\series bold
+
+\backslash
+frac
+\series default
+) in addition to
+\series bold
+
+\backslash
+binom
+\series default
+ there are the commands
+\series bold
+
+\backslash
+dbinom
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! D !
+\backslash
+dbinom
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+tbinom
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! T !
+\backslash
+tbinom
+\end_layout
+
+\end_inset
+
+.
+ For other brackets around binomial coeficients there are the commands
+\series bold
+
+\backslash
+brace
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! B !
+\backslash
+brace
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+brack
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! B !
+\backslash
+brack
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+binom
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dbinom
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+tbinom
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+brack
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+brace
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Case Differentiations
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Case differentiations
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cases
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\to$
+\end_inset
+
+B>0
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! C !
+\backslash
+cases
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\begin{cases}
+A & B>0\end{cases}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cases
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\begin{cases}
+A & \textrm{for }x>0\\
+B & \textrm{for }x=0
+\end{cases}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+After inserting
+\series bold
+
+\backslash
+cases
+\series default
+ or pressing the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\cases"
+\end_inset
+
+ you can create new lines with the shortcut
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+ or the table toolbar button
+\begin_inset Info
+type "icon"
+arg "inset-modify tabular append-row"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+cases
+\series default
+ is also available via the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Cases-Environment
+\family default
+.
+\end_layout
+
+\begin_layout Subsection
+Negations
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Negations
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+By inserting
+\series bold
+
+\backslash
+not
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! N !
+\backslash
+not
+\end_layout
+
+\end_inset
+
+ every character can be displayed canceled.
+ The characters are quasi accentuated by a slash.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+not=
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\not=$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+not
+\backslash
+le
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\not\le$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+not
+\backslash
+parallel
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\not\parallel$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The last example shows that not all negations look good.
+ Therefore there are special commands for some negations (see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Mathematical-Symbols"
+
+\end_inset
+
+ and
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Relations"
+
+\end_inset
+
+).
+\end_layout
+
+\begin_layout Subsection
+Placeholders
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Placeholders"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Placeholders
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Chemical characters ! Isotopes
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Isotopes|see
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+{
+\end_layout
+
+\end_inset
+
+Chemical characters
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+When displaying e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+isotopes
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+Typesetting isotopes and chemical symbols is described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Chemical-Symbols-and"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ the following problem occurs:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Indices created with sub- and superscripts:
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+correct indices:
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\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
+
+\begin_layout Standard
+The shorter index is by default placed below or above the first character
+ of the longer index.
+ To avoid this there is the command
+\series bold
+
+\backslash
+phantom
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! P !
+\backslash
+phantom
+\end_layout
+
+\end_inset
+
+ or the math toolbar button
+\begin_inset space \thinspace{}
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+can be found in the submenu of the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\space"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Graphics
+ filename ../images/math/phantom.png
+ scale 85
+
+\end_inset
+
+ that creates one or more phantom characters.
+ When inserting
+\series bold
+
+\backslash
+phantom
+\series default
+ a small blue box appears that is superposed with two red arrows.
+ The arrows indicate that the complete width and height of the box content
+ will be created as placeholder.
+ Phantom characters are accordingly placeholders with the size of the characters.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+^19
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_
+\backslash
+phantom
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+1
+\begin_inset Formula $\to$
+\end_inset
+
+9
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+F
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+^235
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_
+\backslash
+phantom
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+23
+\begin_inset Formula $\to$
+\end_inset
+
+9
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+F
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Lambda^
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+phantom
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+ii
+\begin_inset Formula $\to$
+\end_inset
+
+t
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_MMt
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Furthermore there are the commands
+\series bold
+
+\backslash
+vphantom
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! V !
+\backslash
+vphantom
+\end_layout
+
+\end_inset
+
+ (toolbar button
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset Graphics
+ filename ../images/math/vphantom.png
+ scale 85
+
+\end_inset
+
+) and
+\series bold
+
+\backslash
+hphantom
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! H !
+\backslash
+hphantom
+\end_layout
+
+\end_inset
+
+ (toolbar button
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset Graphics
+ filename ../images/math/hphantom.png
+ scale 85
+
+\end_inset
+
+).
+
+\series bold
+
+\backslash
+hphantom
+\series default
+ creates only space for the maximal height of the characters in the box
+ but not for its width.
+
+\series bold
+
+\backslash
+vphantom
+\series default
+ creates only space for the width of the box content.
+ Therefore the boxes of both commands have only one red arrow.
+\end_layout
+
+\begin_layout Standard
+For example the command
+\series bold
+
+\backslash
+vphantom
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+a
+\backslash
+int
+\series default
+ creates space for the height of the integral sign,
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+The command
+\series bold
+
+\backslash
+int
+\series default
+ creates an integral sign, see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Big-Operators"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ because this is the larger character.
+ An example application is in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Multiline-Brackets"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Placeholders can also be used for text when they are inserted via the menu
+
+\family sans
+Insert\SpecialChar \menuseparator
+Formatting\SpecialChar \menuseparator
+Phantom
+\family default
+:
+\end_layout
+
+\begin_layout Standard
+This is a sentence.
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom Phantom
+status open
+
+\begin_layout Plain Layout
+This
+\end_layout
+
+\end_inset
+
+ is a sentence.
+\end_layout
+
+\begin_layout Subsection
+Lines
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Lines
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! underlined
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+overline
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A+B
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! O !
+\backslash
+overline
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+underline
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A+B
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! U !
+\backslash
+underline
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+overline
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+underline
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A+B
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In the last example it doesn't matter if first
+\series bold
+
+\backslash
+overline
+\series default
+ or
+\series bold
+
+\backslash
+underline
+\series default
+ is inserted.
+\end_layout
+
+\begin_layout Standard
+To double underline use
+\series bold
+
+\backslash
+underline
+\series default
+ twice.
+\end_layout
+
+\begin_layout Standard
+It is possible to place up to 6 lines above or below characters.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Custom lines can be created using the command
+\series bold
+
+\backslash
+rule
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! R !
+\backslash
+rule
+\end_layout
+
+\end_inset
+
+ which has the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+rule[vertical offset]{length}{thickness}
+\end_layout
+
+\begin_layout Standard
+The optional vertical offset shifts the line upwards (or downwards, when
+ the value is negative).
+ The units listed in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "tab:Available-units"
+
+\end_inset
+
+ can be used for the values.
+ Here are two example lines created with the commands
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+rule[-2ex]{3cm}{2pt}
+\series default
+ and
+\series bold
+
+\backslash
+rule{2cm}{1pt}
+\series default
+:
+\end_layout
+
+\begin_layout Standard
+This is a sentence
+\begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
+\end_inset
+
+ with two lines.
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+rule
+\series default
+ can also be used for text when a line is inserted via the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Formatting\SpecialChar \menuseparator
+Horizontal
+\begin_inset space ~
+\end_inset
+
+Line
+\family default
+:
+\end_layout
+
+\begin_layout Standard
+This is a sentence
+\begin_inset CommandInset line
+LatexCommand rule
+offset "0.5ex"
+width "3cm"
+height "1pt"
+
+\end_inset
+
+ with one line.
+\end_layout
+
+\begin_layout Subsection
+Ellipses
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Ellipses"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Ellipses
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+There are different types of ellipses available.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+In the math toolbar in the submenu of the button
+\begin_inset Info
+type "icon"
+arg "math-insert \\ldots"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ For listings dots at the baseline are used (
+\series bold
+
+\backslash
+ldots
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! L !
+\backslash
+ldots
+\end_layout
+
+\end_inset
+
+), while for operations dots are needed that are on the same height as the
+ operators (
+\series bold
+
+\backslash
+cdots
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! C !
+\backslash
+cdots
+\end_layout
+
+\end_inset
+
+).
+ When using the command
+\series bold
+
+\backslash
+dots
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! D !
+\backslash
+dots
+\end_layout
+
+\end_inset
+
+, LaTeX decides on the basis of the next character what type is used.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+A_1
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+,
+\backslash
+dots
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+,A_n
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A_{1},\dots,A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+A_1
+\begin_inset space \textvisiblespace{}
+\end_inset
+
++
+\backslash
+dots
+\begin_inset space \textvisiblespace{}
+\end_inset
+
++A_n
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A_{1}+\dots+A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+A_1
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+,
+\backslash
+ldots
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+,A_n
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A_{1},\ldots,A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+A_1
+\begin_inset space \textvisiblespace{}
+\end_inset
+
++
+\backslash
+cdots
+\begin_inset space \textvisiblespace{}
+\end_inset
+
++A_n
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A_{1}+\cdots+A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+vdots
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\vdots$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ddots
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ddots$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+iddots
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\iddots$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+3Ã3
+\begin_inset space \thinspace{}
+\end_inset
+
+matrix with the different dots
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The ellipses available in menu
+\family sans
+Insert\SpecialChar \menuseparator
+Special
+\begin_inset space ~
+\end_inset
+
+Character
+\family default
+ are
+\series bold
+
+\backslash
+ldots
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+To use
+\series bold
+
+\backslash
+iddots
+\series default
+, one of the options
+\family sans
+Use mathdots package (automatically)
+\family default
+ must be set in the document settings under
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+.
+\begin_inset Newline newline
+\end_inset
+
+Using the option
+\family sans
+Use mathdots package
+\family default
+ will improve the appearance of all dots in the documents if their font
+ style or size is not the default.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Specially for matrices there are ellipses that span over several columns.
+ They are created with the command
+\series bold
+
+\backslash
+hdotsfor
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! H !
+\backslash
+hdotsfor
+\end_layout
+
+\end_inset
+
+, that has the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+hdotsfor[distance]{number of columns}
+\end_layout
+
+\begin_layout Standard
+The number of columns specifies how many columns should be spanned.
+ Distance is a factor for the distance between the dots.
+\end_layout
+
+\begin_layout Standard
+In the following matrix the command
+\series bold
+
+\backslash
+hdotsfor[2]{4}
+\series default
+ was inserted in the first box of the second line, to get an ellipsis with
+ a dot distance twice as long as with the command
+\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
+
+Note that the matrix fields that should be spanned must be empty, otherwise
+ you get LaTeX-errors.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Furthermore you can fill with the command
+\series bold
+
+\backslash
+dotfill
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! D !
+\backslash
+dotfill
+\end_layout
+
+\end_inset
+
+ the rest of a line with dots.
+ The effect of these commands is the same as with
+\series bold
+
+\backslash
+hfill
+\series default
+, see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Variable-Space"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+For example the command
+\series bold
+A
+\backslash
+dotfill
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+B
+\series default
+ produces
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $A\dotfill B$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Similar to
+\series bold
+
+\backslash
+dotfill
+\series default
+ there is for a line the command
+\series bold
+
+\backslash
+hrulefill
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! 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
+To use the commands for text, they have to be inserted in TeX-mode.
+\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
+Matrices can be inserted via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "dialog-show mathmatrix"
+\end_inset
+
+ or the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Matrix
+\family default
+.
+ In the matrix dialog you can specify the number of columns and rows, the
+ alignment and the decoration.
+ The vertical alignment is only of importance for matrices in inline formulas:
+\end_layout
+
+\begin_layout Standard
+The first matrix is top
+\begin_inset Formula $\begin{array}[t]{cccc}
+A & D & G & J\\
+B & E & H & K\\
+C & F & I & L
+\end{array}$
+\end_inset
+
+, the second middle
+\begin_inset Formula $\begin{array}{cccc}
+A & D & G & J\\
+B & E & H & K\\
+C & F & I & L
+\end{array}$
+\end_inset
+
+ and the third bottom
+\begin_inset Formula $\begin{array}[b]{cccc}
+A & D & G & J\\
+B & E & H & K\\
+C & F & I & L
+\end{array}$
+\end_inset
+
+ aligned.
+\end_layout
+
+\begin_layout Standard
+The horizontal alignment specifies how the column entries should be aligned.
+ It is set by entering a letter for every column.
+
+\emph on
+l
+\emph default
+ denotes left aligned,
+\emph on
+c
+\emph default
+ centered and
+\emph on
+r
+\emph default
+ right aligned.
+ To create for example a 4
+\series bold
+Ã
+\series default
+4
+\begin_inset space ~
+\end_inset
+
+matrix where the first column is left aligned, the second and third are
+ centered and the last one is right aligned, one enters for the horizontal
+ alignment
+\series bold
+lccr
+\series default
+.
+ Normally in a matrix all columns are centered, therefore the default for
+ every column is a
+\series bold
+c
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+Horizontal alignment:
+\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
+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
+To add or delete rows and columns subsequently, the math toolbar buttons
+
+\begin_inset Info
+type "icon"
+arg "inset-modify tabular append-row"
+\end_inset
+
+,
+\begin_inset Info
+type "icon"
+arg "inset-modify tabular delete-row"
+\end_inset
+
+, etc.
+\begin_inset space \thinspace{}
+\end_inset
+
+, or the menu
+\family sans
+Edit\SpecialChar \menuseparator
+Rows & Columns
+\family default
+ can be used.
+ New rows can also be created with
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+The
+\family sans
+Decoration
+\family default
+ adds parentheses in the selected style around the matrix.
+ Alternatively, parentheses can can either be created with the commands
+
+\series bold
+
+\backslash
+left
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! L !
+\backslash
+left
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+right
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! R !
+\backslash
+right
+\end_layout
+
+\end_inset
+
+ (shortcut
+\family sans
+Alt+M
+\begin_inset space ~
+\end_inset
+
+Parenthesis
+\family default
+), see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Automatic-Bracket-Size"
+
+\end_inset
+
+, or by using the following commands:
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bmatrix
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2
+\series bold
+Ã
+\series default
+2
+\begin_inset space \thinspace{}
+\end_inset
+
+matrix
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Bmatrix
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2
+\series bold
+Ã
+\series default
+2
+\begin_inset space \thinspace{}
+\end_inset
+
+matrix
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+pmatrix
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2
+\series bold
+Ã
+\series default
+2
+\begin_inset space \thinspace{}
+\end_inset
+
+matrix
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+vmatrix
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2
+\series bold
+Ã
+\series default
+2
+\begin_inset space \thinspace{}
+\end_inset
+
+matrix
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Vmatrix
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2
+\series bold
+Ã
+\series default
+2
+\begin_inset space \thinspace{}
+\end_inset
+
+matrix
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+matrix
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2
+\series bold
+Ã
+\series default
+2
+\begin_inset space \thinspace{}
+\end_inset
+
+matrix
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+When e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+
+\series bold
+
+\backslash
+vmatrix
+\series default
+ is inserted, a blue box appears between two vertical lines where the matrix
+ is inserted.
+\begin_inset Newline newline
+\end_inset
+
+Note that decorated matrices ignore the vertical alignment.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+As all multiline formulas are matrices, the length
+\series bold
+
+\backslash
+arraycolsep
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! A !
+\backslash
+arraycolsep
+\end_layout
+
+\end_inset
+
+ that is described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Column-Separation"
+
+\end_inset
+
+ can also be used to change the column separation of matrices.
+\end_layout
+
+\begin_layout Standard
+To change the row separation, the command
+\series bold
+
+\backslash
+arraystretch
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! A !
+\backslash
+arraystretch
+\end_layout
+
+\end_inset
+
+ is used.
+ It is used as follows:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+arraystretch}{stretch factor}
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! R !
+\backslash
+renewcommand
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+renewcommand
+\series default
+ assigns the stretch factor to the predefined command
+\series bold
+
+\backslash
+arraystretch
+\series default
+.
+ To double e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+the row separation, use the factor 2.
+ This is then used for all following matrices.
+ To go back to the original separation, assign the factor 1 to
+\series bold
+
+\backslash
+arraystretch
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+To set matrices into a text line, the command
+\series bold
+
+\backslash
+smallmatrix
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! S !
+\backslash
+smallmatrix
+\end_layout
+
+\end_inset
+
+ is used.
+ When it is inserted a blue box with two dashed lines appears.
+ In this box the matrix is inserted.
+\end_layout
+
+\begin_layout Standard
+This is a matrix
+\begin_inset Formula $\left(\begin{smallmatrix}A & B\\
+C & D
+\end{smallmatrix}\right)$
+\end_inset
+
+ in a text line.
+\end_layout
+
+\begin_layout Section
+Brackets and Delimiters
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Brackets
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Delimiters
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Vertical Brackets and Delimiters
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Brackets ! vertical
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+(
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $($
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+{
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\{$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+[
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $[$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+langle
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\langle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lceil
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\lceil$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lfloor
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\lfloor$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+/
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $/$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+|
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $|$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+)
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $)$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+}
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+]
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $]$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rangle
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\rangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rceil
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\rceil$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rfloor
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\rfloor$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\backslash
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\backslash$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+|
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\|$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series medium
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+\series default
+ In TeX-mode the command
+\series bold
+
+\backslash
+textbackslash
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! T !
+\backslash
+textbackslash
+\end_layout
+
+\end_inset
+
+ must be used for the backslash, because the command
+\series bold
+
+\backslash
+
+\backslash
+
+\series default
+ produces a line break there.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For all characters listed above the size can be adjusted with the commands
+ described in the following two subsections.
+ When using these commands, the characters < and > can directly be used
+ instead of the commands
+\series bold
+
+\backslash
+langle
+\series default
+ and
+\series bold
+
+\backslash
+rangle
+\series default
+.
+\end_layout
+
+\begin_layout Subsubsection
+Manual Bracket Size
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Manual-Bracket-Size"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Bracket size ! manual
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The bracket size can be specified manually by the LaTeX-commands
+\series bold
+
+\backslash
+big
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! B !
+\backslash
+big
+\end_layout
+
+\end_inset
+
+,
+\series bold
+
+\backslash
+Big
+\series default
+,
+\series bold
+
+\backslash
+bigg
+\series default
+ and
+\series bold
+
+\backslash
+Bigg
+\series default
+.
+
+\series bold
+
+\backslash
+big
+\series default
+ denotes the smallest and
+\series bold
+
+\backslash
+Bigg
+\series default
+ the largest bracket size.
+\end_layout
+
+\begin_layout Standard
+These commands are used to emphasize levels of brackets:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+all brackets in the same size:
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+this looks better:
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\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
+
+\begin_layout Standard
+For the second formula the command
+\series bold
+
+\backslash
+Big((A+B)(A-B)
+\backslash
+Big)^
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+C
+\series default
+ has been used.
+\end_layout
+
+\begin_layout Standard
+Here is an overview about all bracket sizes:
+\end_layout
+
+\begin_layout Standard
+\align center
+
+\backslash
+Bigg(
+\backslash
+exp
+\backslash
+bigg<
+\backslash
+Big[
+\backslash
+big{
+\backslash
+ln(3x)
+\backslash
+big}^2
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+sin(x)
+\backslash
+Big]^
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+bigg>
+\backslash
+Bigg)^0,5
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Besides the
+\series bold
+
+\backslash
+big
+\series default
+-commands there is the variant
+\series bold
+
+\backslash
+bigm
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! B !
+\backslash
+bigm
+\end_layout
+
+\end_inset
+
+ that adds a bit more space between the bracket and its content, and the
+ variant
+\series bold
+
+\backslash
+bigl
+\series default
+-
+\series bold
+
+\backslash
+bigr
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! B !
+\backslash
+bigl -
+\backslash
+bigr
+\end_layout
+
+\end_inset
+
+, that don't add additional space.
+ The
+\emph on
+l
+\emph default
+ at the end of the command
+\series bold
+
+\backslash
+bigl
+\series default
+ is for a left bracket; for a right bracket this will be replaced by an
+
+\emph on
+r
+\emph default
+.
+ A left or right bracket can each be an opening or closing bracket.
+\end_layout
+
+\begin_layout Standard
+In the following table is a comparison of the variants:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Bigm(
+\backslash
+bigm(
+\backslash
+ln(3x)
+\backslash
+bigm)^2
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+Bigm)
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Big(
+\backslash
+big(
+\backslash
+ln(3x)
+\backslash
+big)^2
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+Big)
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Bigl(
+\backslash
+bigl(
+\backslash
+ln(3x)
+\backslash
+bigr)^2
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+Bigr)
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigl)
+\backslash
+ln(3x)
+\backslash
+bigr(
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Automatic Bracket Size
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Automatic-Bracket-Size"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Bracket size ! automatic
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Brackets with variable size can be inserted with the commands
+\series bold
+
+\backslash
+left
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! L !
+\backslash
+left
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+right
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! R !
+\backslash
+right
+\end_layout
+
+\end_inset
+
+ or via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "dialog-show mathdelimiter"
+\end_inset
+
+.
+ Directly behind
+\series bold
+
+\backslash
+left
+\series default
+ and
+\series bold
+
+\backslash
+right
+\series default
+ the wanted bracket must be inserted.
+ The bracket size will then automatically be calculated for the output.
+\end_layout
+
+\begin_layout Standard
+\align center
+normal bracket: The command
+\series bold
+
+\backslash
+ln(
+\backslash
+frac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+C
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+)
+\series default
+ creates
+\begin_inset Formula
+\[
+\ln(\frac{A}{C})
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+multiline bracket: The command
+\series bold
+
+\backslash
+ln
+\backslash
+left(
+\backslash
+frac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+C
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+right)
+\series default
+ creates
+\begin_inset Formula
+\[
+\ln\left(\frac{A}{C}\right)
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Instead of
+\series bold
+
+\backslash
+left
+\series default
+ and
+\series bold
+
+\backslash
+right
+\series default
+ the shortcut
+\family sans
+Alt+M
+\begin_inset space ~
+\end_inset
+
+Bracket
+\family default
+ can be used.
+ This has the advantage that you can see in LyX immediately the real bracket
+ size and that the matching right bracket will be created too.
+\begin_inset Newline newline
+\end_inset
+
+The command for the last example would then be:
+\series bold
+
+\backslash
+ln Alt+M
+\series default
+
+\series bold
+(
+\backslash
+frac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+C
+\end_layout
+
+\begin_layout Standard
+To omit a left or right bracket, a dot is inserted for the omitted bracket.
+ For example the command
+\series bold
+
+\backslash
+left.
+\backslash
+frac
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+right}
+\series default
+ creates:
+\series bold
+
+\begin_inset Formula
+\[
+\left.\frac{A}{B}\right\}
+\]
+
+\end_inset
+
+
+\series default
+The commands
+\series bold
+
+\backslash
+left
+\series default
+ and
+\series bold
+
+\backslash
+right
+\series default
+ will be converted by LyX to brackets in the right size when the document
+ is reloaded and an omitted bracket will appear as dashed line.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
+ the command
+\series bold
+
+\backslash
+middle
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! M !
+\backslash
+middle
+\end_layout
+
+\end_inset
+
+ is additionally available for all brackets and limits.
+ With this command the height of the following character is adapted to the
+ one of the surrounding brackets, what is e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+needed for physical vectors:
+\begin_inset Formula
+\[
+\left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
+\]
+
+\end_inset
+
+For physical vectors there is a special LaTeX-package, described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Physical-Vectors"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Horizontal Brackets
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Brackets ! horizontal
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\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
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\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 space \textvisiblespace{}
+\end_inset
+
+A+B
+\begin_inset space \textvisiblespace{}
+\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
+Commands ! O !
+\backslash
+overbrace
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\overbrace{A+B}^{3}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\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 space \textvisiblespace{}
+\end_inset
+
+A+B
+\begin_inset space \textvisiblespace{}
+\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
+Commands ! U !
+\backslash
+underbrace
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\underbrace{A+B}_{5}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+overbrace
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+underbrace
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A+B_w
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_7
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+^
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+C
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In the last example it doesn't matter if
+\series bold
+
+\backslash
+overbrace
+\series default
+ or
+\series bold
+
+\backslash
+underbrace
+\series default
+ is inserted at first.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+If you set 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
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! mathtools
+\end_layout
+
+\end_inset
+
+ the option
+\family sans
+Load
+\begin_inset space ~
+\end_inset
+
+always
+\family default
+, you have access to square backets:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\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
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\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
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+overbracket
+\family default
+\series default
+\shape default
+\size default
+\emph default
+\bar default
+\strikeout default
+\uuline default
+\uwave default
+\noun default
+\color inherit
+{A+B
+\begin_inset space \textvisiblespace{}
+\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
+Commands ! O !
+\backslash
+overbracket
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\overbracket{A+B}^{3}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\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
+under
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+bracket
+\family default
+\series default
+\shape default
+\size default
+\emph default
+\bar default
+\strikeout default
+\uuline default
+\uwave default
+\noun default
+\color inherit
+{A+B
+\begin_inset space \textvisiblespace{}
+\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
+Commands ! U !
+\backslash
+under
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+bracket
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\underbracket{A+B}_{5}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+overbracket{
+\backslash
+underbracket{A+B_w
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_7
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+^
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+C
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For
+\series bold
+
+\backslash
+overbracket
+\series default
+ and
+\series bold
+
+\backslash
+underbracket
+\series default
+ you can change the thickness of the bracket's stroke by specifying the
+ desired thickness in square brackets behind the command:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\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
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\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
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+overbracket
+\family default
+\series default
+\shape default
+\size default
+\emph default
+\bar default
+\strikeout default
+\uuline default
+\uwave default
+\noun default
+\color inherit
+[3pt]
+\backslash
+{A+B
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+^3
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\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
+under
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+bracket
+\family default
+\series default
+\shape default
+\size default
+\emph default
+\bar default
+\strikeout default
+\uuline default
+\uwave default
+\noun default
+\color inherit
+[1pt]
+\backslash
+{A+B
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_5
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+When brackets should overlap each other, multiline formulas, as described
+ in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Multiline-Formulas"
+
+\end_inset
+
+, must be used:
+\begin_inset Formula
+\begin{eqnarray*}
+A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
+ & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
+\end{eqnarray*}
+
+\end_inset
+
+In the first row the formula is inserted together with the first brace.
+ It is hereby important that the space command
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+Space commands are explained in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Predefined-Space"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+:
+\series default
+ is inserted before the first
+\begin_inset Formula $d$
+\end_inset
+
+, because the brace that ends behind the
+\begin_inset Formula $q$
+\end_inset
+
+ prevents that the following
+\begin_inset Quotes eld
+\end_inset
+
++
+\begin_inset Quotes erd
+\end_inset
+
+ is surrounded by space.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+because a bracket is not handled as a character, see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Binary-Operators"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ In the second row the second brace is inserted.
+ As it should begin before the
+\begin_inset Formula $b$
+\end_inset
+
+, first the command
+\series bold
+
+\backslash
+hphantom{gggg+
+\backslash
+:}
+\series default
+ is inserted.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+more about
+\series bold
+
+\backslash
+hphantom
+\series default
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Placeholders"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ This space is needed because the
+\begin_inset Quotes eld
+\end_inset
+
++
+\begin_inset Quotes erd
+\end_inset
+
+ is also surrounded by space in the formula.
+ The brace is placed under the command
+\series bold
+
+\backslash
+hphantom{bbqq+dddd}
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+It gets more complicated when brackets overlap each other above and under
+ the formula, like in the following example:
+\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
+
+The first formula row is the same as the second row of the previous example,
+ with the difference that the brace is above.
+ The second row contains the formula together with the second brace.
+ To avoid that there is space between the upper brace in the first row and
+ the formula, the row spacing needs to be reduced.
+ This is not easily possible due to a bug in 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
+
+ As a solution for the problem, the global formula row separation
+\series bold
+
+\backslash
+jot
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! J !
+\backslash
+jot
+\end_layout
+
+\end_inset
+
+ must be changed to -6
+\begin_inset space \thinspace{}
+\end_inset
+
+pt before the formula with the command
+\series bold
+
+\backslash
+setlength{
+\backslash
+jot}{-6pt}
+\series default
+ in TeX-mode.
+
+\series bold
+
+\backslash
+jot
+\series default
+ is set back after the formula to the standard value of 3
+\begin_inset space \thinspace{}
+\end_inset
+
+pt using the same command.
+ More about the row separation in formulas is explained in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Line-Separation"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Arrows
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Arrows
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Arrows can be inserted via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\leftarrow"
+\end_inset
+
+ or the commands listed in the following subsections.
+\end_layout
+
+\begin_layout Subsection
+Horizontal Arrows
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Arrows ! horizontal
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+gets
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\gets$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Leftarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Leftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+longleftarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\longleftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Longleftarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Longleftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+leftharpoonup
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\leftharpoonup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+leftharpoondown
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\leftharpoondown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+hookleftarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\hookleftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+to
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\to$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Rightarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Rightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+longrightarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\longrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Longrightarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Longrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rightharpoonup
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\rightharpoonup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rightharpoondown
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\rightharpoondown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+hookrightarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\hookrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+leftrightarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\leftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Leftrightarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Leftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+longleftrightarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\longleftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Longleftrightarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Longleftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rightleftharpoons
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\rightleftharpoons$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hspace{}
+\length 25pt
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mapsto
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mapsto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+longmapsto
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\longmapsto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+leadsto
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\leadsto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dasharrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\dasharrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Arrows used as accents like e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+vector arrows are listed in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Accents"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Furthermore there are the labeled arrows
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Arrows ! labeled
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+xleftarrow
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! X !
+\backslash
+xleftarrow
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+xrightarrow
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! X !
+\backslash
+xrightarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+vspace{4mm}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ When inserting one of these commands in a formula, an arrow with two blue
+ boxes appear where the label can be inserted.
+ The length of the arrow adapts to the label width.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+F(a)
+\backslash
+xleftarrow
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+x=a
+\begin_inset Formula $\downarrow$
+\end_inset
+
+x>0
+\begin_inset Formula $\to$
+\end_inset
+
+F(x)
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5.5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+F(x)
+\backslash
+xrightarrow
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+x=a
+\begin_inset Formula $\downarrow$
+\end_inset
+
+x>0
+\begin_inset Formula $\to$
+\end_inset
+
+F(a)
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5.5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+If you set 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
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! mathtools
+\end_layout
+
+\end_inset
+
+ the option
+\family sans
+Load
+\begin_inset space ~
+\end_inset
+
+always
+\family default
+, you have access to the following labeled arrows:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset space \hspace*{\fill}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Example
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+
+\backslash
+xleftrightarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\xleftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+
+\backslash
+xLeftarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\xLeftarrow[x=a]{x>0}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xRightarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\xRightarrow[x=a]{x>0}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xLeftrightarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\xLeftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+
+\backslash
+xhookleftarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\xhookleftarrow[x=a]{x>0}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+
+\backslash
+xhookrightarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\xhookrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hspace*{\fill}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Example
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xleftharpoondown
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\xleftharpoondown[x=a]{x>0}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xleftharpoonup
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\xleftharpoonup[x=a]{x>0}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xrightharpoondown
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\xrightharpoondown[x=a]{x>0}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xrightharpoonup
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\xrightharpoonup[x=a]{x>0}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xleftrightharpoons
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\xleftrightharpoons[x=a]{x>0}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xrightleftharpoons
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\xrightleftharpoons[x=a]{x>0}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hspace*{\fill}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command scheme is for all these arrows:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+F(a)
+\backslash
+xleftrightarrow[x=a]
+\backslash
+{x>0
+\begin_inset Formula $\to$
+\end_inset
+
+F(x)
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}F(a)\xleftrightarrow[x=a]{x>0}F(x)\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Vertical and diagonal Arrows
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Arrows ! diagonal
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Arrows ! vertical
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+uparrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\uparrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Uparrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Uparrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+updownarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\updownarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Updownarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Updownarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Downarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Downarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+downarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\downarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+nearrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\nearrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+searrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\searrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+swarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\swarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+nwarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\nwarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Vertical arrows can be used also as delimiters together with the commands
+ described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Manual-Bracket-Size"
+
+\end_inset
+
+ and
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Automatic-Bracket-Size"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Accents
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Accents"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Accents
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Accents can be inserted via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\hat"
+\end_inset
+
+ or the commands listed in the following subsections.
+\end_layout
+
+\begin_layout Subsection
+Accents for one Character
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+accents in text see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Accents-in-Text"
+
+\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
+ is used to avoid that the footnote appears in the PDF-bookmark.
+\end_layout
+
+\begin_layout Plain Layout
+More about
+\series bold
+
+\backslash
+texorpdfstring
+\series default
+ is in section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Formulas-in-Section"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Accents-for-one"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Accents ! for one character
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dot
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\dot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ddot
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dddot
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ddddot
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+vec
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Vectors
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\vec{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bar
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\bar{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathring
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+tilde
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+hat
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\hat{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+check
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\check{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+acute
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\acute{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+grave
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\grave{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+breve
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\breve{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You can directly insert accents like é to formulas.
+ LyX will transform them to the corresponding accent command.
+ For umlauts
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Umlauts
+\end_layout
+
+\end_inset
+
+ it is better to insert a quotation mark before the vowel.
+ These two characters are then treated by LaTeX as
+\emph on
+one
+\emph default
+ character when the formula part with the umlaut is marked as German.
+ In contrary to
+\series bold
+
+\backslash
+ddot
+\series default
+, with this method
+\begin_inset Quotes eld
+\end_inset
+
+real
+\begin_inset Quotes erd
+\end_inset
+
+ umlauts are created as demonstrated in the following example:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ and the 0
+\begin_inset space \thinspace{}
+\end_inset
+
+pt space are only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\lang ngerman
+\begin_inset Quotes grd
+\end_inset
+
+i
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset space \hspace{}
+\length 0pt
+\end_inset
+
+
+\lang ngerman
+
+\begin_inset Formula $"i$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ddot
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+i
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Another advantage to
+\series bold
+
+\backslash
+ddot
+\series default
+ is that umlauts can directly be converted to mathematical text because
+ the accent commands above are
+\emph on
+not allowed
+\emph default
+
+\emph on
+in mathematical text
+\emph default
+.
+ To convert an accented character to mathematical text, only the character
+ under the accent may be converted.
+ This applies also for all other conversions, e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+to italic or bold.
+\end_layout
+
+\begin_layout Standard
+In mathematical text, umlauts and other accented characters can directly
+ be inserted.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+LyX also supports a tilde under the character if the LaTeX-package
+\series bold
+undertilde
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! undertilde
+\end_layout
+
+\end_inset
+
+ is installed on your system:
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+ifundertilde
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+The following table will only be displayed when the LaTeX-package
+\series bold
+undertilde
+\series default
+ is installed.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+utilde
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\utilde{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\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
+The following will be displayed when the LaTeX-package
+\series bold
+undertilde
+\series default
+ is not installed:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You need to install the LaTeX-package
+\series bold
+undertilde
+\series default
+ to see the rest of this subsection in the output.
+\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
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Accents for several Characters
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Accents ! for several characters
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+overleftarrow
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+underleftarrow
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+overleftrightarrow
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+underleftrightarrow
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+overrightarrow
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+underrightarrow
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+widetilde
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+widehat
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+With these commands as many characters as you like can be accented.
+ But the accents
+\series bold
+
+\backslash
+widetilde
+\series default
+ and
+\series bold
+
+\backslash
+widehat
+\series default
+ will only be set in the output with a length of three characters, as shown
+ in the following example:
+\begin_inset Formula
+\[
+\widetilde{A+B=C-D}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With the commands
+\series bold
+
+\backslash
+overset
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! O !
+\backslash
+overset
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+underset
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! U !
+\backslash
+underset
+\end_layout
+
+\end_inset
+
+ described in the previous subsection it is also possible to accent several
+ characters.
+ The command
+\series bold
+
+\backslash
+underset
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\begin_inset Formula $\downarrow$
+\end_inset
+
+***
+\series default
+ creates:
+\begin_inset Formula
+\[
+\underset{***}{A=B}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Space
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Space"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Space ! horizontal
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Predefined Space
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Predefined-Space"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Space ! horizontal ! predefined
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Sometimes it is necessary to insert horizontal space into a formula.
+ This is done by inserting a protected space (shortcut
+\begin_inset Info
+type "shortcut"
+arg "command-alternatives space-insert protected ; math-space"
+\end_inset
+
+).
+ A
+\begin_inset Quotes eld
+\end_inset
+
+
+\color blue
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\color inherit
+
+\begin_inset Quotes erd
+\end_inset
+
+ appears and by pressing
+\family sans
+Space
+\family default
+ several times one can select one of eight different space sizes.
+ The spaces can also be inserted using the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\space"
+\end_inset
+
+ or special commands.
+ Independent from the inserted command, one can select the size again by
+ pressing
+\family sans
+Space
+\family default
+ afterwards.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Number of
+\family sans
+Space
+\family default
+ keystrokes
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+,
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+0
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\, B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+:
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+1
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\: B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+;
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+2
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\; B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+quad
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+3
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\quad B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+qquad
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+4
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\qquad B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Number of
+\family sans
+Space
+\family default
+ keystrokes
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+hfill
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+5
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\hfill B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+hspace*{1em}
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+6
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\hspace*{1em}B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+hspace{1em}
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+7
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\hspace{1em}B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+8
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\ B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+!
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+9
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\! B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Space
+\begin_inset space ~
+\end_inset
+
+5
+\begin_inset space \thinspace{}
+\end_inset
+
+--
+\begin_inset space \thinspace{}
+\end_inset
+
+7 are variable spaces which are explained in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Variable-Space"
+
+\end_inset
+
+.
+ Space
+\begin_inset space ~
+\end_inset
+
+9 seems to produce no space.
+ It is displayed red in LyX contrary to the other sizes, because it is a
+ negative space.
+ There are two more negative spaces:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+negmedspace
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+negthickspace
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Number of
+\family sans
+Space
+\family default
+ keystrokes after inserting the protected space
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+10
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+11
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\negmedspace B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\negthickspace B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Negative spaces can lead to characters overlapping each other.
+ Thus they can be used to enforce ligatures, which are e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+useful for summation operators:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sum
+\backslash
+sum
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+f_kl
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sum
+\backslash
+negmedspace
+\backslash
+sum
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+f_kl
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+Relations like for example equal signs, are always surrounded by space.
+ To suppress this, the equal sign is placed into a TeX-brace.
+ The following example demonstrates this:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+normal equation
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A=B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\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
+
+
+\begin_inset Formula $\raisebox{5mm}{}$
+\end_inset
+
+equation without space
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A{=}B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+The command for the last formula is:
+\series bold
+A
+\backslash
+{=
+\begin_inset Formula $\to$
+\end_inset
+
+B
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Spaces are needed for physical units, because the space between the value
+ and the unit is the smallest one and not a normal space.
+ For units in text, the smallest space is inserted via the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Formatting\SpecialChar \menuseparator
+Thin
+\begin_inset space ~
+\end_inset
+
+Space
+\family default
+ (shortcut
+\begin_inset Info
+type "shortcut"
+arg "space-insert thin"
+\end_inset
+
+).
+\end_layout
+
+\begin_layout Standard
+An example to visualize the difference:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+24 kW
+\begin_inset Formula $\cdot$
+\end_inset
+
+h
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+space between value and unit
+\end_layout
+
+\end_inset
+ |
+
+
+
+\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
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+smallest space between value and unit
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Variable Space
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+for vertical space in formulas see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Line-Separation"
+
+\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 is used to avoid that the footnote appears in the PDF-bookmark.
+\end_layout
+
+\begin_layout Plain Layout
+More about
+\backslash
+texorpdfstring is in section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Formulas-in-Section"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Variable-Space"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Space ! horizontal ! variable
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Space with a defined length can be inserted with the command
+\series bold
+
+\backslash
+hspace
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! H !
+\backslash
+hspace
+\end_layout
+
+\end_inset
+
+.
+ Then a long
+\begin_inset Quotes eld
+\end_inset
+
+
+\color blue
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\color inherit
+
+\begin_inset Quotes erd
+\end_inset
+
+ appears.
+ The length can be specified by left-clicking on the
+\begin_inset Quotes eld
+\end_inset
+
+
+\color blue
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\color inherit
+
+\begin_inset Quotes erd
+\end_inset
+
+.
+ The length may also be negative.
+ When a space would be the first character in a line it would be omitted.
+ To force its output use the command
+\series bold
+
+\backslash
+hspace*
+\series default
+ instead of
+\series bold
+
+\backslash
+hspace
+\series default
+ or left-click on the
+\begin_inset Quotes eld
+\end_inset
+
+
+\color blue
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\color inherit
+
+\begin_inset Quotes erd
+\end_inset
+
+ and check the option
+\family sans
+Protect
+\family default
+.
+\begin_inset Newline newline
+\end_inset
+
+To insert as much space as is available, the command
+\series bold
+
+\backslash
+hfill
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! H !
+\backslash
+hfill
+\end_layout
+
+\end_inset
+
+ is used.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace -1mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command (
+\backslash
+hspace length)
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+A=B
+\backslash
+hspace
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\backslash
+not=C (3
+\begin_inset space \thinspace{}
+\end_inset
+
+cm)
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A=B\hspace{3cm}A\not=C$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+A
+\backslash
+hspace
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\backslash
+not=A (-1
+\begin_inset space \thinspace{}
+\end_inset
+
+mm)
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\hspace{-1mm}A\not=A$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+A=A
+\backslash
+hfill
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+B=B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A=A\hfill B=B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In the last example the available space is given by the longest column entry
+ of the table.
+ In an inline formula the space depends on the length of the line in which
+
+\series bold
+
+\backslash
+hfill
+\series default
+ is inserted.
+ Thus, when the line uses the full width, no space will be created.
+
+\series bold
+
+\backslash
+hfill
+\series default
+ only has an effect on displayed formulas when the formula style
+\series bold
+Indented
+\series default
+ is used.
+ (Formula styles are explained in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Formula-Styles"
+
+\end_inset
+
+.)
+\end_layout
+
+\begin_layout Standard
+Besides
+\series bold
+
+\backslash
+hfill
+\series default
+, there are the commands
+\series bold
+
+\backslash
+dotfill
+\series default
+ and
+\series bold
+
+\backslash
+hrulefill
+\series default
+ that fill the space with a pattern, see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Ellipses"
+
+\end_inset
+
+ for an example.
+\end_layout
+
+\begin_layout Standard
+For text, variable space can be inserted via the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Formatting\SpecialChar \menuseparator
+Horizontal
+\begin_inset space ~
+\end_inset
+
+Space
+\family default
+:
+\end_layout
+
+\begin_layout Standard
+This is a line with
+\begin_inset space \hspace{}
+\length 2cm
+\end_inset
+
+2
+\begin_inset space \thinspace{}
+\end_inset
+
+cm space.
+\end_layout
+
+\begin_layout Standard
+This is a line with
+\begin_inset space \hfill{}
+\end_inset
+
+maximum space.
+\end_layout
+
+\begin_layout Subsection
+Space besides inline Formulas
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Space ! besides inline formulas
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The space that surrounds inline formulas can be adjusted with the length
+
+\series bold
+
+\backslash
+mathsurround
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! M !
+\backslash
+mathsurround
+\end_layout
+
+\end_inset
+
+.
+ The value of a length is set with the command
+\series bold
+
+\backslash
+setlength
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! S !
+\backslash
+setlength
+\end_layout
+
+\end_inset
+
+ which has the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{length name}{value}
+\end_layout
+
+\begin_layout Standard
+To set
+\series bold
+
+\backslash
+mathsurround
+\series default
+ to the value 5
+\begin_inset space \thinspace{}
+\end_inset
+
+mm, the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+mathsurround}{5mm}
+\end_layout
+
+\begin_layout Standard
+is inserted in TeX-mode.
+ 5
+\begin_inset space \thinspace{}
+\end_inset
+
+mm space will now be set around all inline formulas:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+setlength{
+\backslash
+mathsurround}{5mm}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This is a line with an inline formula
+\begin_inset Formula $A=B$
+\end_inset
+
+ with 5
+\begin_inset space \thinspace{}
+\end_inset
+
+mm surrounding space.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+setlength{
+\backslash
+mathsurround}{0pt}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To return to the predefined value,
+\series bold
+
+\backslash
+mathsurround
+\series default
+ is set to the value 0
+\begin_inset space \thinspace{}
+\end_inset
+
+pt.
+\end_layout
+
+\begin_layout Section
+Boxes and Frames
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Boxes
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Frames | see
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+{
+\end_layout
+
+\end_inset
+
+Boxes
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Boxes for text are described in chapter
+\family typewriter
+Boxes
+\family default
+ in the
+\family typewriter
+Embedded
+\begin_inset space ~
+\end_inset
+
+Objects
+\family default
+ manual.
+\end_layout
+
+\begin_layout Subsection
+Boxes with Frame
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Boxes-with-Frame"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Boxes ! with frame
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+It is possible to frame a formula or part of one with the commands
+\series bold
+
+\backslash
+fbox
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! F !
+\backslash
+fbox
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+boxed
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! B !
+\backslash
+boxed
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+When one of these commands is inserted in a formula, a blue box appears
+ within a frame to enter formula parts.
+ For
+\series bold
+
+\backslash
+fbox
+\series default
+ an additional formula has to be created by
+\family sans
+Ctrl+M
+\family default
+ within this box, because the box content will otherwise be treated as mathemati
+cal text.
+ When
+\series bold
+
+\backslash
+boxed
+\series default
+ is used, a new formula is automatically created inside the frame.
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+fbox
+\series default
+ is not suitable to frame displayed formulas because the formula will always
+ be set in the size of the text.
+
+\series bold
+
+\backslash
+boxed
+\series default
+ is in contrary not suitable to frame inline formulas, because the formula
+ will always be set in the size of a displayed formula.
+\end_layout
+
+\begin_layout Standard
+An extension to
+\series bold
+
+\backslash
+fbox
+\series default
+ is the command
+\series bold
+
+\backslash
+framebox
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! F !
+\backslash
+framebox
+\end_layout
+
+\end_inset
+
+ where additionally the frame width and the alignment can be specified.
+
+\series bold
+
+\backslash
+framebox
+\series default
+ is used in the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+framebox[frame width][position]{box content}
+\end_layout
+
+\begin_layout Standard
+The position can either be
+\emph on
+l
+\emph default
+ or
+\emph on
+r
+\emph default
+.
+
+\emph on
+l
+\emph default
+ left aligns,
+\emph on
+r
+\emph default
+ right aligns the formula in the box.
+ When no position is given, the formula will be centered.
+\begin_inset Newline newline
+\end_inset
+
+If no width is given, also no position can be given.
+ In this case the frame width is adjusted to the box content like for
+\series bold
+
+\backslash
+fbox
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+When the command
+\series bold
+
+\backslash
+framebox
+\series default
+ is inserted, a box appears containing three blue boxes.
+ The first two boxes are surrounded by brackets and denote the two optional
+ arguments.
+ The third box is for formula parts like for
+\series bold
+
+\backslash
+fbox
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+fbox
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\family sans
+Ctrl+M
+\family default
+
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+boxed
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+A+
+\backslash
+fbox
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+framebox
+\begin_inset space \textvisiblespace{}
+\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 space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The frame thickness can also be adjusted.
+ To do this the following commands have to be inserted in TeX-mode before
+ the formula
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fboxrule
+\series default
+
+\series bold
+
+\begin_inset Quotes eld
+\end_inset
+
+thickness
+\begin_inset Quotes erd
+\end_inset
+
+
+\series default
+
+\series bold
+
+\backslash
+fboxsep
+\series default
+
+\series bold
+
+\begin_inset Quotes eld
+\end_inset
+
+distance
+\begin_inset Quotes erd
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Quotes eld
+\end_inset
+
+distance
+\begin_inset Quotes erd
+\end_inset
+
+ specifies the minimal distance between the frame and the first character
+ in the box.
+ An example for this is the following framed formula:
+\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
+
+Before this formula the commands
+\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
+were inserted in TeX-mode.
+ The given values are used for all following boxes.
+\end_layout
+
+\begin_layout Standard
+To return to the standard frame size, the command
+\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
+is inserted in TeX-mode before the next formula.
+\end_layout
+
+\begin_layout Subsection
+Boxes without Frame
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Boxes-without-Frame"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Boxes ! without frame
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For boxes without a frame there are the following box commands:
+\series bold
+
+\backslash
+mbox
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! M !
+\backslash
+mbox
+\end_layout
+
+\end_inset
+
+,
+\series bold
+
+\backslash
+makebox
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! M !
+\backslash
+makebox
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+raisebox
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! R !
+\backslash
+raisebox
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With
+\series bold
+
+\backslash
+raisebox
+\series default
+ a box can be super- or subscripted.
+ But in contrary to normal super- and subscripting, the characters in the
+ box keep their font size.
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is used in the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox{height}{box content}
+\end_layout
+
+\begin_layout Standard
+When the box should contain a formula, an extra formula is needed like for
+
+\series bold
+
+\backslash
+fbox
+\series default
+.
+
+\series medium
+
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+\series default
+ For
+\series bold
+
+\backslash
+raisebox
+\series default
+ this extra formula is created by pressing
+\family sans
+Ctrl+M
+\family default
+ twice instead of once because LyX doesn't yet support
+\series bold
+
+\backslash
+raisebox
+\series default
+ directly.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\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
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $H\raisebox{2mm}{al}lo$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\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
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $H\raisebox{-2mm}{al}lo$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+A=
+\backslash
+raisebox{-2mm
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\family sans
+Ctrl+M
+\family default
+
+\family sans
+Ctrl+M
+\family default
+
+\backslash
+sqrt
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+mbox
+\series default
+ is equivalent to
+\series bold
+
+\backslash
+fbox
+\series default
+ and
+\series bold
+
+\backslash
+makebox
+\series default
+ is equivalent to
+\series bold
+
+\backslash
+framebox
+\series default
+, with the difference that there is no frame.
+\end_layout
+
+\begin_layout Subsection
+Colored Boxes
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Colored-Boxes"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Boxes ! colored
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To be able to use all commands explained in this section, the LaTeX-package
+
+\series bold
+color
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+The LaTeX-package
+\series bold
+color
+\series default
+ is part of every LaTeX standard installation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! color
+\end_layout
+
+\end_inset
+
+ has to be loaded in the LaTeX-preamble with the line
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+When text is colored somewhere in the document with a predefined color,
+ LyX loads the LaTeX-package
+\series bold
+color
+\series default
+ automatically.
+ Thus it is possible that the package is loaded twice, but this does not
+ cause problems.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
+amble.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{color}
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+To color boxes, the command
+\series bold
+
+\backslash
+colorbox
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! C !
+\backslash
+colorbox
+\end_layout
+
+\end_inset
+
+ is used in the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+colorbox{color}{box content}
+\end_layout
+
+\begin_layout Standard
+The box content can also be a box and a
+\series bold
+
+\backslash
+colorbox
+\series default
+ can also be part of another box (see the 2nd and 3rd example).
+ When the box should contain a formula, an extra formula has to be created,
+ the same way as for
+\series bold
+
+\backslash
+raisebox
+\series default
+.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+This also applies for the command
+\series bold
+
+\backslash
+fcolorbox
+\series default
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+One of the following predefined colors can be chosen:
+\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
+ and
+\series bold
+yellow
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+colorbox{yellow
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{A=B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+colorbox{green
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+fbox
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+fbox
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+colorbox{green
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\family sans
+Ctrl+M
+\family default
+
+\family sans
+Ctrl+M
+\family default
+
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+C=D
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+colorbox
+\series default
+ only colors the box but not the characters in the box.
+ To color all characters, the whole formula is highlighted and the desired
+ color is chosen in the
+\family sans
+Text
+\begin_inset space ~
+\end_inset
+
+Style
+\family default
+ dialog.
+ The dialog can be called with the toolbar button
+\begin_inset Info
+type "icon"
+arg "dialog-show character"
+\end_inset
+
+ or the menu
+\family sans
+Edit\SpecialChar \menuseparator
+Text
+\begin_inset space ~
+\end_inset
+
+Style\SpecialChar \menuseparator
+Customized
+\family default
+.
+ The formula number then has the same color as the formula.
+ When the formula number should get another color than the formula characters,
+ the color must be changed within the formula.
+\end_layout
+
+\begin_layout Standard
+An example:
+\end_layout
+
+\begin_layout Standard
+
+\color red
+\begin_inset Formula
+\begin{equation}
+\int A=B\label{eq:red}
+\end{equation}
+
+\end_inset
+
+
+\color green
+
+\begin_inset Formula
+\begin{equation}
+\textcolor{red}{\int A=B}\label{eq:redgreen}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:red"
+
+\end_inset
+
+ is completely colored red.
+\begin_inset Newline newline
+\end_inset
+
+Formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:redgreen"
+
+\end_inset
+
+ was first completely colored green to set the color for the formula number.
+ Subsequently the formula characters were colored red.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+To color the frame different than the rest of the box, the command
+\series bold
+
+\backslash
+fcolorbox
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! F !
+\backslash
+fcolorbox
+\end_layout
+
+\end_inset
+
+ is used in the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fcolorbox{frame color}{color}{box content}
+\end_layout
+
+\begin_layout Standard
+So
+\series bold
+
+\backslash
+fcolorbox
+\series default
+ is an extension of the command
+\series bold
+
+\backslash
+colorbox
+\series default
+.
+ The frame width is set, like for
+\series bold
+
+\backslash
+framebox
+\series default
+, with
+\series bold
+
+\backslash
+fboxrule
+\series default
+ and
+\series bold
+
+\backslash
+fboxsep
+\series default
+.
+ An example:
+\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
+
+
+\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
+This formula was created with the command
+\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
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+To use other colors than the predefined ones, they have to be defined first.
+\end_layout
+
+\begin_layout Standard
+One can for example define the color
+\begin_inset Quotes eld
+\end_inset
+
+
+\series bold
+darkgreen
+\series default
+
+\begin_inset Quotes erd
+\end_inset
+
+ with the LaTeX-preamble line:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+definecolor{darkgreen}{cmyk}{0.5,
+\series default
+
+\series bold
+0,
+\series default
+
+\series bold
+1,
+\series default
+
+\series bold
+0.5}
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! D !
+\backslash
+definecolor
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+cmyk
+\series default
+ is the color space that denotes the colors
+\series bold
+cyan
+\series default
+,
+\series bold
+magenta
+\series default
+,
+\series bold
+yellow
+\series default
+ and
+\series bold
+black
+\series default
+.
+ The four comma separated numbers are the portion factor for the corresponding
+ colors of the color space.
+ The factors can be in the range of 0
+\begin_inset space \thinspace{}
+\end_inset
+
+-
+\begin_inset space \thinspace{}
+\end_inset
+
+1.
+ Instead of
+\series bold
+cmyk
+\series default
+ also the color space
+\series bold
+rgb
+\series default
+ can be used for definitions.
+
+\series bold
+rgb
+\series default
+ denotes
+\series bold
+red
+\series default
+,
+\series bold
+green
+\series default
+ and
+\series bold
+blue
+\series default
+, so that there are in this case three portion factors for the corresponding
+ colors.
+ Furthermore there is the color space
+\series bold
+gray
+\series default
+ with one portion factor for the gray value.
+\end_layout
+
+\begin_layout Standard
+As example a framed box with the new defined color
+\series bold
+darkgreen
+\series default
+ where the characters have been colored
+\series bold
+yellow
+\series default
+:
+\begin_inset Formula
+\begin{equation}
+\colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Self-defined colors can also be used for text with the help of the command
+
+\series bold
+
+\backslash
+textcolor
+\series default
+:
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Text ! colored
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+textcolor{darkgreen}{
+\end_layout
+
+\end_inset
+
+This sentence is
+\begin_inset Quotes eld
+\end_inset
+
+darkgreen
+\begin_inset Quotes erd
+\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
+Commands ! T !
+\backslash
+textcolor
+\end_layout
+
+\end_inset
+
+ is used in the scheme
+\series bold
+
+\backslash
+textcolor{color}{characters to color}
+\series default
+.
+\end_layout
+
+\begin_layout Subsection
+Paragraph Boxes
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Paragraph-Boxes"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Boxes ! as paragraph
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+A box that can contain several lines and paragraphs, a so-called paragraph
+ box (parbox), can be created with the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Box
+\family default
+ or the toolbar button
+\begin_inset Info
+type "icon"
+arg "box-insert"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The following example shows a framed parbox in a line:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+This is a line
+\begin_inset Box Boxed
+position "c"
+hor_pos "c"
+has_inner_box 1
+inner_pos "t"
+use_parbox 1
+use_makebox 0
+width "5cm"
+special "none"
+height "1in"
+height_special "totalheight"
+status open
+
+\begin_layout Plain Layout
+This is a paragraph box.
+ It is exactly 5
+\begin_inset space \thinspace{}
+\end_inset
+
+cm long and can also contain formulas:
+\begin_inset Formula $\int A\,\mathrm{d}s=C$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ with a parbox.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Such a box is created by right-clicking on the gray box inset.
+ A dialog pops up showing the box properties.
+ In our case set:
+\emph on
+Decoration
+\emph default
+: Rectangular box,
+\emph on
+Inner Box
+\emph default
+: Parbox,
+\emph on
+Width
+\emph default
+: 5
+\begin_inset space \thinspace{}
+\end_inset
+
+cm,
+\emph on
+Vertical Box Alignment
+\emph default
+: Middle
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+In LaTeX a parbox is created with the command
+\series bold
+
+\backslash
+parbox
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! P !
+\backslash
+parbox
+\end_layout
+
+\end_inset
+
+ which has the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+parbox[position]{width}{box content}
+\end_layout
+
+\begin_layout Standard
+The positions
+\emph on
+b
+\emph default
+ and
+\emph on
+t
+\emph default
+ are possible.
+
+\emph on
+b
+\emph default
+ for
+\begin_inset Quotes eld
+\end_inset
+
+bottom
+\begin_inset Quotes erd
+\end_inset
+
+ means that the box is aligned within the surrounding text with its last
+ line.
+ With
+\emph on
+t
+\emph default
+ for
+\begin_inset Quotes eld
+\end_inset
+
+top
+\begin_inset Quotes erd
+\end_inset
+
+ this is done with the first line.
+ When no position is given, the box will be vertically centered, see section
+
+\emph on
+Boxes
+\emph default
+ of the
+\emph on
+Embedded
+\begin_inset space ~
+\end_inset
+
+Objects
+\emph default
+ manual for examples.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+To frame formulas completely, including the formula number, the formula
+ must be set into a parbox.
+ To do this, the command
+\series bold
+
+\backslash
+fbox{
+\backslash
+parbox{
+\backslash
+linewidth-2
+\backslash
+fboxsep-2
+\backslash
+fboxrule}{
+\series default
+ is inserted in TeX-mode before the formula.
+
+\series bold
+
+\backslash
+linewidth
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! L !
+\backslash
+linewidth
+\end_layout
+
+\end_inset
+
+ is hereby the line width set for the document.
+ Because the frame is outside the parbox, 2
+\begin_inset space \thinspace{}
+\end_inset
+
+times the frame separation and the frame thickness must be subtracted from
+ the line width.
+ As this is not automatically done by LyX due to a bug
+\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
+
+, TeX-mode has to be used.
+ To be able to multiply and subtract in arguments, the 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 LaTeX standard installation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! calc
+\end_layout
+
+\end_inset
+
+ must be loaded in the 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 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 "sub:User-defined-Numbering"
+
+\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 TeX-mode because 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 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"
+
+\end_inset
+
+)
+\end_layout
+
+\end_inset
+
+ Then the description follows as normal text and finally
+\series bold
+}}
+\backslash
+]
+\series default
+ is inserted in TeX-mode.
+ The commands
+\series bold
+
+\backslash
+[
+\series default
+ and
+\series bold
+
+\backslash
+]
+\series default
+ hereby 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
+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 "sub:Big-Operators"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Operators ! big
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Sums
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Integrals
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To be able to use all integral operators listed here, the option
+\family sans
+Use esint package automatically
+\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
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+int
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! I !
+\backslash
+int
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\int$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+oint
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ointctrclockwise
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ointctrclockwise$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ointclockwise
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ointclockwise$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sqint
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sqint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+fint
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\begin_inset Formula $\fint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+landupint
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\begin_inset Formula $\landupint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+landdownint
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\begin_inset Formula $\landdownint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigcap
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigcap$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
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+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigcup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
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+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! S !
+\backslash
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+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sum$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! P !
+\backslash
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+\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 Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\prod$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+coprod
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\coprod$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigodot
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigodot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigotimes
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigotimes$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
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+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigoplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigwedge
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigwedge$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigvee
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigvee$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigsqcup
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigsqcup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+biguplus
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\biguplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\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 are different from
+\series bold
+
+\backslash
+int
+\series default
+ etc.
+\begin_inset space \space{}
+\end_inset
+
+in the style the operator limits are displayed, see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Operator-Limits"
+
+\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 therefore 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 "sub:Font-Styles"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ Finally 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
+For multiple integrals there are the following commands:
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+iint
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+oiint
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sqiint
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+iiint
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+iiiint
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dotsint
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Operator Limits
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Operator-Limits"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Operators ! Limits
+\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
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\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
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Limits of inline formulas are set right beside the operator.
+ Limits in displayed formulas are set above or below the operator, except
+ for integral limits.
+\end_layout
+
+\begin_layout Standard
+To force that the limits are set beside the operator, the cursor is set
+ 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 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 was 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 are by default set beside the operator.
+ But for multiple integrals the limits are often set below the operator.
+ In the following example the limits type was therefore 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
+
+
+\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
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! S !
+\backslash
+subarray
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+substack
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! S !
+\backslash
+substack
+\end_layout
+
+\end_inset
+
+ are used.
+ To create for example this expression
+\begin_inset Formula
+\begin{equation}
+\sum_{\begin{subarray}{c}
+0
+
+
+
+
+
+\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
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
++
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $+$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+-
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $-$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+pm
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\pm$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mp
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cdot
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\cdot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+times
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\times$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+div
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\div$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\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
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $*$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+star
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\star$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+circ
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\circ$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+diamond
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\diamond$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bullet
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bullet$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+nabla
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\nabla$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigtriangledown
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigtriangledown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigtriangleup
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigtriangleup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Box
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Box$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cap
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\cap$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cup
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\cup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dagger
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\dagger$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ddagger
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ddagger$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+wr
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\wr$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bigcirc
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigcirc$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+wedge
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\wedge$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+vee
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\vee$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+oplus
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\oplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ominus
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ominus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+otimes
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\otimes$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+oslash
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\oslash$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+odot
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\odot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+amalg
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\amalg$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+uplus
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\uplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+setminus
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\setminus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sqcap
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sqcap$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sqcup
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sqcup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+triangleleft
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\triangleleft$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+triangleright
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\triangleright$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+All binary operators can also be inserted via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\pm"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+To typeset the Laplace operator also
+\series bold
+
+\backslash
+Delta
+\series default
+ or
+\series bold
+
+\backslash
+nabla
+\series default
+^
+\series bold
+2
+\series default
+ (
+\begin_inset Formula $\nabla^{2}$
+\end_inset
+
+) can be used instead of
+\series bold
+
+\backslash
+bigtriangleup
+\series default
+ .
+\end_layout
+
+\begin_layout Standard
+The character
+\family sans
+Menu Separator
+\family default
+ from the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Special Character
+\family default
+ is the operator
+\series bold
+
+\backslash
+triangleright
+\series default
+.
+\end_layout
+
+\begin_layout Subsection
+Self-defined Operators
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Self-defined-Operators"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Operators ! self-defined
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With the help of the command
+\series bold
+
+\backslash
+DeclareMathOperator
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! D !
+\backslash
+dbinom@
+\backslash
+DeclareMathOperator
+\end_layout
+
+\end_inset
+
+ custom operators can be defined in the LaTeX-preamble.
+ Its command scheme is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareMathOperator{new command}{display}
+\end_layout
+
+\begin_layout Standard
+Display can be characters or symbols that define how the operator looks
+ in the output.
+ To define a big operator a * is set behind the command.
+ All self-defined big operators can have limits as described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Operator-Limits"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+For example the LaTeX-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareMathOperator*{
+\backslash
+Lozenge}{
+\backslash
+blacklozenge}
+\end_layout
+
+\begin_layout Standard
+defines the command
+\series bold
+
+\backslash
+Lozenge
+\series default
+, that inserts a big operator consisting of the lozenge symbol from
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Miscellaneous-Symbols"
+
+\end_inset
+
+:
+\begin_inset Formula
+\[
+\Lozenge_{n=1}^{\infty}
+\]
+
+\end_inset
+
+The command for this formula is:
+\series bold
+
+\backslash
+Lozenge
+\series default
+^
+\series bold
+
+\backslash
+infty
+\begin_inset Formula $\to$
+\end_inset
+
+_n=1
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+When self-defined operators are not used several times in the document,
+ they can also be defined with the commands
+\series bold
+
+\backslash
+mathop
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! M !
+\backslash
+mathop
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+mathbin
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! M !
+\backslash
+mathbin
+\end_layout
+
+\end_inset
+
+, which have the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+mathop{display}
+\series default
+ and
+\series bold
+
+\backslash
+mathbin{display}
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+mathop
+\series default
+ defines big operators,
+\series bold
+
+\backslash
+mathbin
+\series default
+ binary operators.
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+mathop
+\series default
+ can e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+be used to use one limit for several operators:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\[
+\mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command for the formula above is:
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+mathop{
+\backslash
+sum
+\backslash
+negmedspace
+\backslash
+sum
+\series default
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series bold
+
+\begin_inset Formula $\to$
+\end_inset
+
+^N
+\series default
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series bold
+_i,j=1
+\end_layout
+
+\begin_layout Section
+Fonts
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Fonts
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Font Styles
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Font-Styles"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Font ! style
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Latin letters in formulas can be set in one of the following font styles:
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+shortcut
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathbb
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+ABC
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathbb{ABC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "shortcuts"
+arg "font-noun"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathbf
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathbf{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "shortcuts"
+arg "font-bold"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+boldsymbol
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\boldsymbol{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "shortcuts"
+arg "font-boldsymbol"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathcal
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+ABC
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathcal{ABC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "shortcuts"
+arg "font-emph"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathfrak
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathfrak{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+-
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathscr
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathscr{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+-
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+shortcut
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathit
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathit{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+-
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathrm
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathrm{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "shortcuts"
+arg "font-roman"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathsf
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathsf{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "shortcuts"
+arg "font-sans"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mathtt
+\series bold
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathtt{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "shortcuts"
+arg "font-typewriter"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+\series default
+ The styles
+\series bold
+
+\backslash
+mathbb
+\series default
+ and
+\series bold
+
+\backslash
+mathcal
+\series default
+ can only be used for big letters.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Predefined is the style
+\series bold
+
+\backslash
+mathnormal
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+The style commands work also for letters in mathematical constructs:
+\begin_inset Formula
+\[
+\mathfrak{A=\frac{b}{C}}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Characters in mathematical text don't appear in a math font style but in
+ the text font style
+\series bold
+
+\backslash
+textrm
+\series default
+.
+ That their style can't be set correctly via the text style dialog is a
+ bug in LyX.
+\begin_inset Foot
+status collapsed
+
+\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
+Instead of the style commands the dialog
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Text Style
+\family default
+ or the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\font"
+\end_inset
+
+ can be used.
+\end_layout
+
+\begin_layout Subsection
+Bold Formulas
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Bold-Formulas"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! bold
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To make a complete formula bold, the command
+\series bold
+
+\backslash
+mathbf
+\series default
+ from the previous subsection cannot be used, because it doesn't work for
+ small Greek letters.
+ Furthermore it prints Latin letters always upright, like in the following
+ equation:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\[
+\mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To display the formula correctly, the command
+\series bold
+
+\backslash
+boldsymbol
+\series default
+ is used:
+\begin_inset Formula
+\[
+\boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
+\]
+
+\end_inset
+
+It is also possible to set the formula in a
+\series bold
+boldmath environment
+\series default
+.
+ This environment is created by inserting the command
+\series bold
+
+\backslash
+boldmath
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! B !
+\backslash
+boldmath
+\end_layout
+
+\end_inset
+
+ in TeX-mode.
+ To end the environment, the command
+\series bold
+
+\backslash
+unboldmath
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! U !
+\backslash
+unboldmath
+\end_layout
+
+\end_inset
+
+ is inserted in TeX-mode.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+boldmath
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\[
+\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
+\]
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+unboldmath
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Colored Formulas
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! colored
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Formulas can be colored like normal text: Highlight a formula or a formula
+ part and use the
+\family sans
+Text Style
+\family default
+ dialog.
+ Here is a formula in magenta:
+\begin_inset Formula
+\[
+{\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You can also define your own colors as described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Colored-Boxes"
+
+\end_inset
+
+.
+ They can be used with the TeX code command
+\series bold
+
+\backslash
+textcolor
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! T !
+\backslash
+textcolor
+\end_layout
+
+\end_inset
+
+ in the scheme
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+textcolor{color}{characters or formula}
+\end_layout
+
+\begin_layout Standard
+The following example was colored completely dark green and partly red:
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+textcolor{darkgreen}{
+\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
+Due to a bug in LyX only complete formulas can be colored with self-defined
+ colors.
+\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
+Font Sizes
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Font-Sizes"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Font ! size
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For characters in formulas there are, analog to characters in text, the
+ following size commands:
+\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
+ and
+\series bold
+
+\backslash
+tiny
+\end_layout
+
+\begin_layout Standard
+The size produced by the commands depends on the document font size, which
+ corresponds to the command
+\series bold
+
+\backslash
+normalsize
+\series default
+.
+ The other commands produce smaller or larger sizes than
+\series bold
+
+\backslash
+normalsize
+\series default
+.
+ The font size can however not exceed a certain value.
+ Is for example the document font size 12
+\begin_inset space \thinspace{}
+\end_inset
+
+pt, the command
+\series bold
+
+\backslash
+Huge
+\series default
+ switches to the same size as
+\series bold
+
+\backslash
+huge
+\series default
+.
+
+\end_layout
+
+\begin_layout Standard
+A size command is inserted in TeX-mode before the formula and sets the size
+ for all following formula and text characters.
+ To switch back to the initial size, the command
+\series bold
+
+\backslash
+normalsize
+\series default
+ is inserted behind the formula in TeX-mode.
+\end_layout
+
+\begin_layout Standard
+Within a formula the size can be changed using the following size commands
+ or the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\style"
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+displaystyle
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! D !
+\backslash
+displaystyle
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+textstyle
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+scriptstyle
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+scriptscriptstyle
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+After entering these commands, a blue box appears in which the formula parts
+ are inserted.
+\end_layout
+
+\begin_layout Standard
+There is a further method to change the font size, that though only works
+ for symbols or letters in mathematical text.
+ To use it, one of the above text size commands is inserted in mathematical
+ text.
+ All following characters until the end of the mathematical text or until
+ another size command will have the selected size.
+ Two examples:
+\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
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+normalsize
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Before both formulas the command
+\series bold
+
+\backslash
+huge
+\series default
+ was inserted.
+ The command for the second formula is:
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+maltese
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A Alt+M M
+\backslash
+Large
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+maltese
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+textit
+\begin_inset space \textvisiblespace{}
+\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
+\series default
+
+\series bold
+M
+\backslash
+tiny
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+maltese
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+textit
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\end_layout
+
+\begin_layout Standard
+If a symbol cannot be displayed in different sizes, it will always be displayed
+ in the default size.
+\end_layout
+
+\begin_layout Section
+Greek Letters
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Greek letters
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Greek letters can also be inserted via the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\alpha"
+\end_inset
+
+.
+ All international typesetting norms purport that Greek letters in math
+ have to be typeset italic/slanted.
+ In some languages, like French or Russian, they are nevertheless sometimes
+ typeset upright.
+\end_layout
+
+\begin_layout Subsection
+Small Letters
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Greek letters ! small
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+alpha
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\alpha$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+beta
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\beta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+gamma
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\gamma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+delta
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\delta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+epsilon
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\epsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varepsilon
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varepsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+zeta
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\zeta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+eta
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\eta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+theta
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\theta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+vartheta
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\vartheta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+iota
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\iota$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+kappa
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\kappa$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varkappa
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varkappa$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lambda
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\lambda$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mu
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mu$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+nu
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\nu$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+xi
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\xi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+o
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $o$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+pi
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\pi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varpi
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varpi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rho
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\rho$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varrho
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varrho$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sigma
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sigma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varsigma
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varsigma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+tau
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\tau$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+upsilon
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\upsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+phi
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\phi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varphi
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varphi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+chi
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\chi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+psi
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\psi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+omega
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\omega$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+How to create special upright Greek letters is explained in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Upright-small-Greek"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Big Letters
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Greek letters ! big
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Gamma
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Gamma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Delta
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Delta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Theta
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Theta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Lambda
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Lambda$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Xi
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Xi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Pi
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Pi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Sigma
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Sigma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Upsilon
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Upsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Phi
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Phi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Psi
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Psi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Omega
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Omega$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+That the big Greek letters appear upright is caused by a design bug when
+ TeX was developed.
+ To get correct italic big letters, begin every command with
+\series bold
+var
+\series default
+.
+ For example the command
+\series bold
+
+\backslash
+varGamma
+\series default
+ produces
+\begin_inset Formula $\varGamma$
+\end_inset
+
+.
+ Another way is to load the package
+\series bold
+fixmath
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+fixmath
+\series default
+ is part of the LaTeX-package
+\series bold
+was
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! 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
+Packages ! fixmath
+\end_layout
+
+\end_inset
+
+ with the LaTeX-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{fixmath}
+\end_layout
+
+\begin_layout Standard
+Then all big Greek letters in a document will automatically be typeset italic.
+\end_layout
+
+\begin_layout Subsection
+Bold Letters
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Greek letters ! bold
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Greek letters cannot be set with different font styles like Latin letters.
+ They can only be made bold with the command
+\series bold
+
+\backslash
+boldsymbol
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! B !
+\backslash
+boldsymbol
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Upsilon
+\backslash
+boldsymbol
+\backslash
+Upsilon
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+theta
+\backslash
+boldsymbol
+\backslash
+theta
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\theta\boldsymbol{\theta}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Symbols
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+A list with all symbols of most of the LaTeX-packages can be found in
+\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 is used to avoid that the footnote appears in the PDF-bookmark.
+\end_layout
+
+\begin_layout Plain Layout
+More about
+\backslash
+texorpdfstring is in section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Formulas-in-Section"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Symbols
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Many of the symbols listed in this section can also be inserted via the
+ toolbar buttons
+\begin_inset Info
+type "icon"
+arg "math-insert \\nabla"
+\end_inset
+
+ and
+\begin_inset Info
+type "icon"
+arg "math-insert \\digamma"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Mathematical Symbols
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Mathematical-Symbols"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Symbols ! mathematical
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+neg
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\neg$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Im
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Im$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Re
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Re$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+aleph
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\aleph$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+partial
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\partial$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+infty
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\infty$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+wp
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\wp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+imath
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\imath$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+jmath
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\jmath$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+forall
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\forall$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+exists
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\exists$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+nexists
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\nexists$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+emptyset
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\emptyset$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varnothing
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varnothing$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dag
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\dag$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ddag
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ddag$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+complement
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Bbbk
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Bbbk$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+prime
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\prime$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+backprime
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\backprime$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mho
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mho$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+triangle
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\triangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+angle
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\angle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+measuredangle
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\measuredangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sphericalangle
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sphericalangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+top
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\top$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
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+
+\end_inset
+ |
+
+\begin_inset Text
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+\end_inset
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+
+\end_layout
+
+\end_inset
+ |
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+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Miscellaneous Symbols
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Miscellaneous-Symbols"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Symbols ! miscellaneous
+\end_layout
+
+\end_inset
+
+
+\end_layout
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+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Tabular
+
+
+
+
+
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+\begin_inset Text
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+\begin_layout Plain Layout
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+\end_inset
+ |
+
+\begin_inset Text
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+\begin_layout Plain Layout
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+
+\end_inset
+ |
+
+
+
+\begin_inset Text
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+\begin_layout Plain Layout
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+\backslash
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+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\flat$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\backslash
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+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\natural$
+\end_inset
+
+
+\end_layout
+
+\end_inset
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+
+
+\begin_inset Text
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+\begin_layout Plain Layout
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+\backslash
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+\end_layout
+
+\end_inset
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+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sharp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
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+
+\end_inset
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+\begin_inset Text
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+\end_inset
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+
+\end_layout
+
+\end_inset
+ |
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+
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\checkmark$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
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+
+
+\begin_inset Text
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+
+\end_inset
+ |
+
+\begin_inset Text
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+\end_layout
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+\end_inset
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+\begin_layout Plain Layout
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+\end_layout
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+\end_inset
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+\begin_inset Text
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+\begin_layout Plain Layout
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+
+\end_inset
+ |
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+\begin_inset Text
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+\begin_layout Plain Layout
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+\end_inset
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+
+\end_layout
+
+\end_inset
+ |
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+
+
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
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+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
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+\begin_layout Plain Layout
+
+\backslash
+hbar
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\hbar$
+\end_inset
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+
+\end_layout
+
+\end_inset
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+
+
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+\begin_layout Plain Layout
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+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\hslash$
+\end_inset
+
+
+\end_layout
+
+\end_inset
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+
+
+\begin_inset Text
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+\begin_layout Plain Layout
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+\backslash
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+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\clubsuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
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+
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+\begin_inset Text
+
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+
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+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\spadesuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
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+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bigstar$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
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+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\blacklozenge$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
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+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\backslash
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+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\blacktriangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
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+
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+\begin_inset Text
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+\end_layout
+
+\end_inset
+ |
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+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\blacktriangledown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
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+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
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+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bullet$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+diamondsuit
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\diamondsuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
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+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Diamond$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
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+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\heartsuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+P
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\P$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+copyright
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\copyright$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+circledR
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\circledR$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
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+
+\backslash
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+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\maltese$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+diagup
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\diagup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
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+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\diagdown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Some symbols can be displayed in different sizes, see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Font-Sizes"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+The Euro-Symbol â¬
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Symbols ! Euro-symbol
+\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
+To use the Euro symbol in formulas, the LaTeX-package
+\series bold
+eurosym
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! eurosym
+\end_layout
+
+\end_inset
+
+ must be installed and loaded with the LaTeX-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage[gennarrow]{eurosym}
+\end_layout
+
+\begin_layout Standard
+The Euro symbol can now be inserted with the command
+\series bold
+
+\backslash
+euro
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! E !
+\backslash
+euro
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The Euro symbol can directly be inserted with the ⬠key in mathematical
+ text, without having
+\series bold
+eurosym
+\series default
+ installed.
+ When
+\series bold
+eurosym
+\series default
+ is installed,
+\series bold
+
+\backslash
+euro
+\series default
+ can also be inserted in TeX-mode.
+ The official currency symbol can then be inserted with the command
+\series bold
+
+\backslash
+officialeuro
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! O !
+\backslash
+officialeuro
+\end_layout
+
+\end_inset
+
+, that is only available in TeX-mode.
+\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 open
+
+\begin_layout Plain Layout
+The following table will only be displayed when the LaTeX-package
+\series bold
+eurosym
+\series default
+ is installed.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+An overview about the different Euro symbols:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+formula
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+euro
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\euro$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+mathematical text
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+â¬
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mbox{â¬}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+TeX-mode
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+officialeuro
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\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
+The following will be displayed when the LaTeX-package
+\series bold
+eurosym
+\series default
+ is not installed:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You need to install the LaTeX-package
+\series bold
+eurosym
+\series default
+ to see the rest of this subsection in the output.
+\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
+Relations
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Relations"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Relations
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Comparisons|see
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+{
+\end_layout
+
+\end_inset
+
+Relations
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+All following relations can also be inserted via the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\leq"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+<
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $<$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+le
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\le$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ll
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ll$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+prec
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\prec$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+preceq
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\preceq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+subset
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\subset$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+subseteq
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\subseteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sqsubseteq
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sqsubseteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+in
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\in$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+vdash
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\vdash$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+smile
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\smile$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lhd
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\lhd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+unlhd
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\unlhd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+gtrless
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\gtrless$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+mid
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mid$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+nmid
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\nmid$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+=
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $=$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+not=
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\not=$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+equiv
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\equiv$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sim
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sim$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+simeq
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\simeq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+approx
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\approx$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cong
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\cong$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bowtie
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\bowtie$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+notin
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\notin$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+perp
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\perp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+propto
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\propto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+asymp
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\asymp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+doteq
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\doteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+circeq
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\circeq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+models
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\models$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+widehat=
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\widehat{=}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+>
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $>$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ge
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ge$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+gg
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\gg$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+succ
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\succ$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+succeq
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\succeq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+supset
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\supset$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+supseteq
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\supseteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sqsupseteq
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sqsupseteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ni
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\ni$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dashv
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\dashv$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+frown
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\frown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rhd
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\rhd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+unrhd
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\unrhd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lessgtr
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\lessgtr$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+parallel
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\parallel$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+nparallel
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\nparallel$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+The characters
+\series bold
+
+\backslash
+lhd
+\series default
+ and
+\series bold
+
+\backslash
+rhd
+\series default
+ are bigger than the equal looking operators
+\series bold
+
+\backslash
+triangleleft
+\series default
+ and
+\series bold
+
+\backslash
+triangleright
+\series default
+, respectively.
+\end_layout
+
+\begin_layout Standard
+LyX supports also many special relations.
+ Use the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\leqq"
+\end_inset
+
+ to see a list of these relations.
+\end_layout
+
+\begin_layout Standard
+Relations are, in contrary to symbols, always surrounded by space.
+\end_layout
+
+\begin_layout Standard
+Relations with labels can be created with the command
+\series bold
+
+\backslash
+stackrel
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! S !
+\backslash
+stackrel
+\end_layout
+
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+A(r)
+\backslash
+stackrel
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+r
+\backslash
+to
+\backslash
+infty
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset Formula $\downarrow$
+\end_inset
+
+
+\backslash
+approx
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Functions
+\end_layout
+
+\begin_layout Subsection
+Predefined Functions
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Predefined-Functions"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Functions ! predefined
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In general, variables are set
+\emph on
+italic
+\emph default
+ in mathematical expressions, but not function names, because
+\begin_inset Formula $sin$
+\end_inset
+
+ could be misunderstood as
+\begin_inset Formula $s\cdot i\cdot n$
+\end_inset
+
+.
+ Therefore there are predefined functionswhich are additionally a bit separated
+ from prefactors.
+ They are inserted as commands starting with a backslash before their name.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Asin(x)+B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $Asin(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+A
+\backslash
+sin(x)+B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\sin(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The following functions are predefined:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sin
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sinh
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+arcsin
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sup
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cos
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cosh
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+arccos
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+inf
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+tan
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+tanh
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+arctan
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lim
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cot
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+coth
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+arg
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+liminf
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+sec
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+min
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+deg
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+limsup
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+csc
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+max
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+det
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Pr
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ln
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+exp
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dim
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+hom
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lg
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+log
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ker
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+gcd
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+They can also be inserted with the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\functions"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Self-defined Functions
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Functions ! self-defined
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To use a function that is not predefined, like for example the sign function
+ sgn(x), there are two possibilities:
+\end_layout
+
+\begin_layout Itemize
+Define the function by inserting the following line to the LaTeX-preamble
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+For more about
+\series bold
+
+\backslash
+DeclareMathOperator
+\series default
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Self-defined-Operators"
+
+\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
+Commands ! 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
+
+Now the new defined function can be called with the command
+\series bold
+
+\backslash
+sgn
+\series default
+.
+\end_layout
+
+\begin_layout Itemize
+Write the formula as usual, mark the formula name, in our example the letters
+
+\emph on
+sgn
+\emph default
+, and change it to mathematical text.
+ Finally, a space is inserted between prefactor and function.
+\end_layout
+
+\begin_layout Standard
+The result is the same with both methods as with a predefined function
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+In LyX self-defined functions are displayed red, predefined ones black.
+\end_layout
+
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+A
+\backslash
+sgn(x)+B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\sgn(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+A
+\backslash
+,
+\begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
+\end_inset
+
+(x)+B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\,\textrm{sgn}(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The first method is more suitable when the self-defined function should
+ be used several times.
+\end_layout
+
+\begin_layout Subsection
+Limits
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Limits
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For limits, in addition to the commands
+\series bold
+
+\backslash
+lim
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! L !
+\backslash
+lim
+\end_layout
+
+\end_inset
+
+,
+\series bold
+
+\backslash
+liminf
+\series default
+ and
+\series bold
+
+\backslash
+limsup
+\series default
+ the following functions are defined:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varliminf
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varliminf$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varlimsup
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varlimsup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varprojlim
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\varprojlim$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+varinjlim
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+The limit is created by inserting a subscript.
+ It is set right beside the function in an inline formula:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset space \hspace{}
+\length 1cm
+\end_inset
+
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+The space and
+\series bold
+
+\backslash
+raisebox
+\series default
+ are used here as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lim_x
+\backslash
+to
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+x=B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In a displayed formula the limit is set below the formula, as usual:
+\begin_inset Formula
+\[
+\lim_{x\to A}x=B
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+How to adjust the typesetting of the limits see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Operator-Limits"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Modulo-Functions
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Functions ! modulo-
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The modulo-function is special, because it exists in four variants.
+ The variants in a displayed formula are:
+\begin_inset Formula
+\begin{align*}
+\underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
+\mathrm{a\backslash mod\textrm{â£}b} & & a\mod b\\
+\mathrm{a\backslash pmod\textrm{â£}b} & & a\pmod b\\
+\mathrm{a\backslash bmod\textrm{â£}b} & & a\bmod b\\
+\mathrm{a\backslash pod\textrm{â£}b} & & a\pod b
+\end{align*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In an inline formula less space is set before the function names for all
+ variants.
+ By default the modulo-functions take only the first following character
+ into account.
+ To use more than one character, one has to put them into TeX-braces:
+\begin_inset Formula
+\begin{align*}
+\underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
+\mathrm{a\backslash pod\textrm{â£}bcd} & & a\pod bcd\\
+\mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
+\end{align*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Special Characters
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Special characters
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The characters ^ and _ would normally create a superscript and subscript,
+ respectively.
+ To get these characters you have to insert them with a leading
+\backslash
+:
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+^
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mathcircumflex$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+_
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\_$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Special Characters in Mathematical Text
+\end_layout
+
+\begin_layout Standard
+The following commands can only be used in mathematical text or in TeX-mode:
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+oe
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{Å}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+OE
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{Å}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ae
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{æ}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+AE
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{Ã}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+aa
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{\aa}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\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
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{â«}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+i
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{ı}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+command
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+The space of 0
+\begin_inset space \thinspace{}
+\end_inset
+
+mm is used for separation, because otherwise the output will be ¡ and ¿
+ respectively.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+o
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{ø}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+O
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{Ã}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+l
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{Å}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+L
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{Å}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+!
+\begin_inset space \hspace{}
+\length 0mm
+\end_inset
+
+`
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{!`}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+?
+\begin_inset space \hspace{}
+\length 0mm
+\end_inset
+
+`
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{?`}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+j
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\textrm{È·}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The characters
+\begin_inset Formula $\textrm{\textrm{Ã
}}$
+\end_inset
+
+ and
+\begin_inset Formula $\textrm{\textrm{Ã}}$
+\end_inset
+
+ can also be inserted via the math toolbar button
+\begin_inset Info
+type "icon"
+arg "math-insert \\digamma"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+An exception are the commands
+\series bold
+!
+\begin_inset space \hspace{}
+\length 0mm
+\end_inset
+
+`
+\series default
+ and
+\series bold
+?
+\begin_inset space \hspace{}
+\length 0mm
+\end_inset
+
+`
+\series default
+, because they can be inserted in LyX directly to text.
+\end_layout
+
+\begin_layout Subsection
+Accents in Text
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Accents-in-Text"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Accents ! in text
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With the following commands all letters can be accented.
+ The commands must be inserted in TeX-mode.
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\begin_inset Quotes grd
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+`e
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+^
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+=e
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+u
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+b
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+t
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+ee
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+H
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+'e
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\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
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+.e
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+v
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+d
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+c
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+With the command
+\series bold
+
+\backslash
+t
+\series default
+ also two different characters can be accented.
+ The command
+\series bold
+
+\backslash
+t
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+sz
+\series default
+ creates:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+t sz
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The accents
+\series bold
+`
+\series default
+ ,
+\series bold
+'
+\series default
+ and
+\series bold
+^
+\series default
+ can in combination with vowels directly be inserted with the keyboard without
+ using TeX-mode.
+ The same applies for the tilde
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+This only applies for keyboards where the tilde is defined as accent.
+\end_layout
+
+\end_inset
+
+
+\series bold
+~
+\series default
+ in combination with
+\emph on
+a
+\emph default
+ ,
+\emph on
+n
+\emph default
+ , or
+\emph on
+o
+\emph default
+.
+\end_layout
+
+\begin_layout Standard
+The commands
+\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
+ and accents that are inserted directly with the keyboard are also available
+ in mathematical text.
+ For the other accents there are special math commands to be used in formulas,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Accents-for-one"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Furthermore, with the command
+\series bold
+
+\backslash
+textcircled
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! T !
+\backslash
+textcircled
+\end_layout
+
+\end_inset
+
+ all numbers and letters can be set into a circle, quasi accented with a
+ circle, similar to the copyright symbol.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+textcircled{w}
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Large
+\backslash
+textcircled{
+\backslash
+normalsize
+\backslash
+protect
+\backslash
+raisebox{-1.5pt}{W}}
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+One has to take care that the character fits in the circle.
+
+\series bold
+
+\backslash
+Large
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Font-Sizes"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ specifies thereby the size of the circle.
+ With the help of
+\series bold
+
+\backslash
+raisebox
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Boxes-without-Frame"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ the character can be centered.
+\end_layout
+
+\begin_layout Subsection
+Old-style Figures
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Old-style Figures
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Old-style figures (also known as old-style numerals) are created with the
+ command
+\series bold
+
+\backslash
+oldstylenums
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! O !
+\backslash
+oldstylenums
+\end_layout
+
+\end_inset
+
+.
+ The command can be used in formulas and in TeX-mode.
+ The command scheme is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+oldstylenums{number}
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+oldstylenums{0123456789
+\series default
+ produces:
+\begin_inset Formula $\oldstylenums{0123456789}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Formula Styles
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Formula-Styles"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! styles
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+There are two different alignment styles:
+\end_layout
+
+\begin_deeper
+\begin_layout Description
+Centered is the predefined standard
+\end_layout
+
+\begin_layout Description
+Indented for this the option
+\series bold
+fleqn
+\series default
+ must be inserted in the menu
+\family sans
+Document\SpecialChar \menuseparator
+Settings
+\family default
+ under
+\family sans
+Document
+\begin_inset space ~
+\end_inset
+
+Class
+\end_layout
+
+\begin_layout Standard
+When
+\series bold
+Indented
+\series default
+ is used, the indentation can be adjusted with the length
+\series bold
+
+\backslash
+mathindent
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! M !
+\backslash
+mathindent
+\end_layout
+
+\end_inset
+
+.
+ Should the distance be 15
+\begin_inset space \thinspace{}
+\end_inset
+
+mm, the following command line is inserted in the LaTeX-preamble
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+mathindent}{15mm}
+\end_layout
+
+\begin_layout Standard
+When no length is specified, the predefined value of 30
+\begin_inset space \thinspace{}
+\end_inset
+
+pt will be used.
+\end_layout
+
+\end_deeper
+\begin_layout Itemize
+And two different numbering styles:
+\end_layout
+
+\begin_deeper
+\begin_layout Description
+Right is the predefined standard
+\end_layout
+
+\begin_layout Description
+Left for this the option
+\series bold
+leqno
+\series default
+ must be inserted in the menu
+\family sans
+Document\SpecialChar \menuseparator
+Settings
+\family default
+ under
+\family sans
+Document
+\begin_inset space ~
+\end_inset
+
+Class
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+
+\series bold
+fleqn
+\series default
+ and
+\series bold
+leqno
+\series default
+ can also be used together.
+ In this case both options are inserted, separated by a comma.
+\end_layout
+
+\begin_layout Standard
+The chosen styles are used for all displayed formulas of the document.
+ When both, centered and indented formulas should be created in a document,
+ the style
+\series bold
+Centered
+\series default
+ is used.
+ The indented formulas are then set in a flalign environment, see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Flalign-Environment"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Multiline Formulas
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Multiline-Formulas"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! multiline
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+General
+\end_layout
+
+\begin_layout Standard
+In LyX multiline formulas are created by pressing
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+ inside a formula.
+ This creates either an
+\series bold
+eqnarray environment
+\series default
+ that is described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Eqnarray-Environment"
+
+\end_inset
+
+ or, when the option
+\family sans
+Use AMS math package
+\family default
+ in the document settings is selected, an
+\series bold
+align environment
+\series default
+ that is described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Standard-align-Environment"
+
+\end_inset
+
+.
+ The align environment is recommended because it provides in any case a
+ typographically correct output.
+\end_layout
+
+\begin_layout Standard
+There are other multiline formula environments that can be created via the
+ menu
+\family sans
+Insert\SpecialChar \menuseparator
+Math
+\family default
+.
+ These environments are described in the following sections.
+\end_layout
+
+\begin_layout Standard
+In all multiline formula environments a new line is created by pressing
+
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+.
+ To add or delete lines, the math toolbar buttons
+\begin_inset Info
+type "icon"
+arg "inset-modify tabular append-row"
+\end_inset
+
+ or
+\begin_inset Info
+type "icon"
+arg "inset-modify tabular delete-row"
+\end_inset
+
+, respectively, or the menu
+\family sans
+Edit\SpecialChar \menuseparator
+Rows & Columns
+\family default
+ can be used.
+\end_layout
+
+\begin_layout Subsubsection
+Line Separation
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Line-Separation"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! multiline ! Line separation
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+There is sometimes not enough space in multiline formulas between the lines:
+\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
+
+
+\end_layout
+
+\begin_layout Standard
+In LaTeX additional line space is specified as optional argument of the
+ new line command.
+ This is not yet possible in LyX
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+see
+\begin_inset CommandInset href
+LatexCommand href
+name "LyX-bug #1505"
+target "http://www.lyx.org/trac/ticket/1505"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+, therefore the whole formula must be inserted in TeX-mode.
+ To add in our example space, the command
+\series bold
+
+\backslash
+
+\backslash
+[3mm]
+\series default
+ is inserted at the end of the first line.
+ One gets:
+\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
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+To set the line separation for all lines in a formula, the length
+\series bold
+
+\backslash
+jot
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! J !
+\backslash
+jot
+\end_layout
+
+\end_inset
+
+ is changed.
+ The definition is:
+\begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
+\end_inset
+
+.
+ Predefined for
+\series bold
+
+\backslash
+jot
+\series default
+ is the value 3
+\begin_inset space \thinspace{}
+\end_inset
+
+pt.
+ To create 3
+\begin_inset space \thinspace{}
+\end_inset
+
+mm additional line separation as in the previous example, the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+jot}{3mm+3pt}
+\end_layout
+
+\begin_layout Standard
+is inserted in TeX-mode before the formula.
+ This requires that the 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 LaTeX standard installation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! calc
+\end_layout
+
+\end_inset
+
+ was loaded in LaTeX-preamble with the line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{calc}
+\end_layout
+
+\begin_layout Standard
+One gets:
+\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
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+setlength{
+\backslash
+jot}{3pt}
+\end_layout
+
+\end_inset
+
+ To get back to the predefined distance,
+\series bold
+
+\backslash
+jot
+\series default
+ is set to the value 3
+\begin_inset space \thinspace{}
+\end_inset
+
+pt.
+\end_layout
+
+\begin_layout Subsubsection
+Column Separation
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Column-Separation"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! multiline ! Column separation
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Multiline formulas form a matrix.
+ A formula in the eqnarray environment is for example a matrix with three
+ columns.
+ By changing the column separation in this environment, the space beside
+ the relation sign can be changed.
+\end_layout
+
+\begin_layout Standard
+The column separation is specified with the length
+\series bold
+
+\backslash
+arraycolsep
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! A !
+\backslash
+arraycolsep
+\end_layout
+
+\end_inset
+
+ according to:
+\begin_inset Newline newline
+\end_inset
+
+column separation = 2
+\begin_inset space \thinspace{}
+\end_inset
+
+
+\series bold
+
+\backslash
+arraycolsep
+\series default
+
+\begin_inset Newline newline
+\end_inset
+
+Thus, the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+arraycolsep}{1cm}
+\end_layout
+
+\begin_layout Standard
+inserted in TeX-mode, sets for all following formulas a column separation
+ of 2
+\begin_inset space \thinspace{}
+\end_inset
+
+cm.
+ To get back to the predefined distance,
+\series bold
+
+\backslash
+arraycolsep
+\series default
+ is set to 5
+\begin_inset space \thinspace{}
+\end_inset
+
+pt.
+\end_layout
+
+\begin_layout Standard
+A formula with 2
+\begin_inset space \thinspace{}
+\end_inset
+
+cm column separation:
+\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
+
+A formula with the predefined column separation for matrices of 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
+Long Formulas
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! long
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Long formulas can be typeset using these methods:
+\end_layout
+
+\begin_layout Itemize
+When one side of the equation is much shorter than the line width, this
+ one is chosen for the left side and the right side is typeset over two
+ lines:
+\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:shortlong}
+\end{eqnarray}
+
+\end_inset
+
+The minus sign at the beginning of the second line does normally not appear
+ as an operator because it is the first character of the line.
+ Thus it would not be surrounded by space and could not be distinguished
+ from the fraction bar.
+ To avoid this, 3
+\begin_inset space \thinspace{}
+\end_inset
+
+pt space was inserted behind the minus sign with the command
+\series bold
+
+\backslash
+hspace
+\series default
+.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+for more about
+\series bold
+
+\backslash
+hspace
+\series default
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Variable-Space"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! H !
+\backslash
+hspace
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+When both sides of the equation are too long, the command
+\series bold
+
+\backslash
+lefteqn
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! L !
+\backslash
+lefteqn
+\end_layout
+
+\end_inset
+
+ is used.
+ It is inserted in the first column of the first line and causes all further
+ insertions to overwrite the following columns:
+\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
+
+After the insertion of
+\series bold
+
+\backslash
+lefteqn
+\series default
+, the cursor is in a purple box that is a bit shifted to the left from the
+ blue one.
+ In this the formula is inserted.
+\begin_inset Newline newline
+\end_inset
+
+The content of the further lines is inserted to the second or another formula
+ column.
+ The greater the column number where it was inserted, the larger the indentation.
+\begin_inset VSpace medskip
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+Note the following when using
+\series bold
+
+\backslash
+lefteqn
+\series default
+:
+\end_layout
+
+\begin_layout Itemize
+The formula doesn't use the full page width.
+ When e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+the term
+\begin_inset Formula $-B^{2}$
+\end_inset
+
+ is added to the first line in the above example, it would have been outside
+ the page margin.
+ To better use the width, negative space can be inserted at the beginning
+ of the first line.
+\end_layout
+
+\begin_layout Itemize
+Due to a bug in LyX the cursor cannot be set with the mouse into the first
+ line.
+\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
+
+ One can only set the cursor at the beginning of the line and move it with
+ the arrow keys.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Other methods to set long formulas are offered by the environments described
+ in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Multline-Environment"
+
+\end_inset
+
+ and
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Multiline-Formula-Parts"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsubsection
+Multiline Fractions
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Multiline-Fractions"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Fractions ! multiline
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+There are cases where the denominator and/or the numerator of a fraction
+ is so long that the fraction does not fit into one line.
+ It is then necessary to add a line break within the fraction.
+ This can be done using the command
+\series bold
+
+\backslash
+splitfrac
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! S !
+\backslash
+splitfrac
+\end_layout
+
+\end_inset
+
+.
+ To activate it, set 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
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! mathtools
+\end_layout
+
+\end_inset
+
+ the option
+\family sans
+Load
+\begin_inset space ~
+\end_inset
+
+always
+\family default
+.
+
+\series bold
+
+\backslash
+splitfrac
+\series default
+ has the scheme
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+splitfrac{first line}{second line}
+\end_layout
+
+\begin_layout Standard
+and is used as denominator and/or numerator:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\[
+a=\frac{\splitfrac{xy+xy+xy+xy+xy}{+wy+wy+wy+wy}}{z}\ne\frac{\splitdfrac{xy+\frac{xy}{z}+xy+xy+xy}{+xy+xy+xy+xy}}{z}
+\]
+
+\end_inset
+
+The command for the first numerator above is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+splitfrac{xy+xy+xy+xy+xy
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+{+wy+wy+wy+wy
+\end_layout
+
+\begin_layout Subsubsection
+Multiline Brackets
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Multiline-Brackets"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Brackets ! for multiline expressions
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For brackets spanning multiple lines the following problem occurs:
+\begin_inset Formula
+\begin{eqnarray*}
+A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
+ & & \left.\cdots+B-D\right]
+\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The closing bracket is smaller than the opening bracket because brackets
+ with variable size may not span multiple lines.
+\end_layout
+
+\begin_layout Standard
+To set the bracket size for the second line correctly, the first line is
+ ended with
+\series bold
+
+\backslash
+right.
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! R !
+\backslash
+right
+\end_layout
+
+\end_inset
+
+ and the second line with
+\series bold
+
+\backslash
+left.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+for more about
+\series bold
+
+\backslash
+left
+\series default
+ and
+\series bold
+
+\backslash
+right
+\series default
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Automatic-Bracket-Size"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! L !
+\backslash
+left
+\end_layout
+
+\end_inset
+
+.
+ After
+\series bold
+
+\backslash
+left.
+
+\series default
+ the command
+\series bold
+
+\backslash
+vphantom
+\series default
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series bold
+
+\backslash
+prod
+\series default
+^
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series bold
+
+\backslash
+infty
+\series default
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series bold
+
+\begin_inset Formula $\downarrow$
+\end_inset
+
+_R=1}
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! V !
+\backslash
+vphantom
+\end_layout
+
+\end_inset
+
+ is inserted, because the multiplication operator with its limits is the
+ largest symbol in the first line and this should be the size for the bracket
+ in the second line.
+\end_layout
+
+\begin_layout Standard
+The result is this:
+\begin_inset Formula
+\begin{eqnarray*}
+A & = & \sin(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
+Align Environments
+\end_layout
+
+\begin_layout Standard
+Align environments can be used for every kind of multiline formulas.
+ They are especially useful to set several formulas side by side.
+\end_layout
+
+\begin_layout Standard
+Align environments consist of columns.
+ The odd columns are right aligned, the even ones left aligned.
+ Every line in an Align environment can be numbered.
+\end_layout
+
+\begin_layout Standard
+Align environments are created via the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Math
+\family default
+.
+ With the menu
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Change Formula Type
+\family default
+ already existing formulas can be converted to Align environments.
+\end_layout
+
+\begin_layout Standard
+To add or delete columns, the math toolbar buttons
+\begin_inset Info
+type "icon"
+arg "inset-modify tabular append-column"
+\end_inset
+
+ or
+\begin_inset Info
+type "icon"
+arg "inset-modify tabular delete-column"
+\end_inset
+
+, respectively, or the menu
+\family sans
+Edit\SpecialChar \menuseparator
+Rows & Columns
+\family default
+ can be used.
+\end_layout
+
+\begin_layout Subsubsection
+Standard align Environment
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Standard-align-Environment"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! multiline ! align environment
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This Align environment is created by pressing
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+ in a formula or by the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+AMS align Environment
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+An example for two formulas set side by side, that are created with a four
+ column align environment:
+\begin_inset Formula
+\begin{align*}
+A & =\sin(B) & C & =D\\
+C & \ne A & B & \ne D
+\end{align*}
+
+\end_inset
+
+As it can be seen, the formulas in this environment are placed so as if
+ there would be a
+\series bold
+
+\backslash
+hfill
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+more about
+\series bold
+
+\backslash
+hfill
+\series default
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Variable-Space"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ before the first and after every even column.
+ When the formula style
+\series bold
+Indented
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+formula styles see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Formula-Styles"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ is used, the formula is set without the
+\series bold
+
+\backslash
+hfill
+\series default
+ before the first column.
+\end_layout
+
+\begin_layout Subsubsection
+Alignat Environment
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! multiline ! alignat environment
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The alignat environment has no predefined column separation.
+ It can be inserted manually with the spaces that are described
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Space"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The above example in the alignat environment where 1
+\begin_inset space \thinspace{}
+\end_inset
+
+cm space was inserted at the beginning of the second formula:
+\begin_inset Formula
+\begin{alignat*}{2}
+A & =\sin(B) & \hspace{1cm}C & =D\\
+C & \ne A & B & \ne D
+\end{alignat*}
+
+\end_inset
+
+Because the column separation can be set separately for every column, this
+ environment is especially suitable to set three and more formulas side
+ by side.
+\end_layout
+
+\begin_layout Subsubsection
+Flalign Environment
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Flalign-Environment"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! multiline ! flalign environment
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In this environment the first two columns are always set as much as possible
+ to the left and the last two ones to the right.
+ An example:
+\begin_inset Formula
+\begin{flalign*}
+A & =1 & B & =2 & C & =3\\
+X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
+\end{flalign*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+By creating a flalign environment with an odd number of columns where an
+ empty TeX-brace is inserted to the last column, several formulas in a document
+ can be set to the left, although the formula style
+\series bold
+Centered
+\series default
+ is used.
+ As example the indented formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:VolInt"
+
+\end_inset
+
+:
+\begin_inset Formula
+\begin{flalign}
+\hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
+\end{flalign}
+
+\end_inset
+
+The first two columns contain the formula.
+ To indent it as with the formula style
+\series bold
+Indented
+\series default
+, 30
+\begin_inset space \thinspace{}
+\end_inset
+
+pt space was inserted at the beginning of the first column.
+\end_layout
+
+\begin_layout Subsection
+Eqnarray Environment
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Eqnarray-Environment"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! multiline ! eqnarray environment
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+When this environment has been created, three blue boxes appear.
+ The content of the first box is right aligned, the content of the last
+ one left aligned.
+ The content of the middle box appears centered and a bit smaller, because
+ it is designed to insert there only relation characters.
+\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
+Gather Environment
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! multiline ! gather environment
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This environment consists of only one centered column.
+ Every line can be numbered.
+\begin_inset Formula
+\begin{gather}
+A=1\\
+X=\textrm{-}1
+\end{gather}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Multline Environment
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Multline-Environment"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! multiline ! multline environment
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The multline environment consists, like the gather environment, of only
+ one column.
+ But the first line is left aligned, the last one right aligned.
+ All other lines are centered.
+ Therefore this environment is suitable for long formulas.
+ As example formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:lefteqn"
+
+\end_inset
+
+ in the multline environment:
+\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
+
+
+\end_layout
+
+\begin_layout Standard
+In the output only the last (first) line of a multline environment appears
+ numbered when the document numbering is right (left).
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+numbering styles see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Formula-Styles"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With the commands
+\series bold
+
+\backslash
+shoveright
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! S !
+\backslash
+shoveright
+\end_layout
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+shoveleft
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! S !
+\backslash
+shoveleft
+\end_layout
+
+\end_inset
+
+ a centered line can be right or left aligned, respectively.
+ The commands are used as follows:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+shoveright{line content}
+\series default
+ and
+\series bold
+
+\backslash
+shoveleft{line content}
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+The length
+\series bold
+
+\backslash
+multlinegap
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! M !
+\backslash
+multlinegap
+\end_layout
+
+\end_inset
+
+ specifies the distance of the first line from the left page margin.
+ Predefined is the length 0
+\begin_inset space \thinspace{}
+\end_inset
+
+pt.
+\end_layout
+
+\begin_layout Standard
+As example the above formula where the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+multlinegap}{2cm}
+\end_layout
+
+\begin_layout Standard
+was inserted in TeX-mode before:
+\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
+
+The second line was left aligned using
+\series bold
+
+\backslash
+shoveleft
+\series default
+.
+\end_layout
+
+\begin_layout Subsection
+Multiline Formula Parts
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Multiline-Formula-Parts"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! multiline ! formula parts
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To display only parts of a formula with multiple lines, one of the following
+ environments is used:
+\series bold
+aligned
+\series default
+,
+\series bold
+alignedat
+\series default
+,
+\series bold
+gathered
+\series default
+ or
+\series bold
+split
+\series default
+.
+ They can be inserted via the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Math
+\family default
+ or by using the commands described in this section.
+\end_layout
+
+\begin_layout Standard
+The first three have the same properties as the corresponding multiline
+ formula environments, but it is possible to set further formula parts beside
+ them.
+ An example:
+\begin_inset Formula
+\[
+\left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
+\Delta E\Delta t & \ge\frac{\hbar}{2}
+\end{aligned}
+\right\} \textrm{Uncertainty relations}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To get this formula, a displayed formula is created where the command
+\series bold
+
+\backslash
+aligned
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! A !
+\backslash
+aligned
+\end_layout
+
+\end_inset
+
+ is inserted.
+ A purple box appears around the blue formula box where now columns and
+ lines can be added.
+ Outside the multiline environment other formula parts can be set, like
+ the brace.
+\end_layout
+
+\begin_layout Standard
+The aligned environment is also suitable for long formulas whose lines are
+ horizontally aligned.
+ Using aligned in a displayed formula has the advantage that the formula
+ number is vertically centered behind the lines.
+ As example formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:shortlong"
+
+\end_inset
+
+ in the aligned environment:
+\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
+
+
+\end_layout
+
+\begin_layout Standard
+To use the environments
+\series bold
+alignedat
+\series default
+,
+\series bold
+gathered
+\series default
+, or
+\series bold
+split
+\series default
+, the command
+\series bold
+
+\backslash
+alignedat
+\series default
+,
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! A !
+\backslash
+alignedat
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+gathered
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! G !
+\backslash
+gathered
+\end_layout
+
+\end_inset
+
+, or
+\series bold
+
+\backslash
+split
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! S !
+\backslash
+split
+\end_layout
+
+\end_inset
+
+ are inserted, respectively.
+ The split environment has the same properties as the aligned environment
+ but it can only have two columns.
+\end_layout
+
+\begin_layout Subsection
+Text in multiline Formulas
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Text-in-multiline"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Text ! in formulas
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! multiline ! text
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In the Align environments, and the multline and gather environment, text
+ can be inserted that will appear in a separate line and doesn't affect
+ the column alignment.
+ To do this, the command
+\series bold
+
+\backslash
+intertext
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! I !
+\backslash
+intertext
+\end_layout
+
+\end_inset
+
+ is used in the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+intertext{text}
+\end_layout
+
+\begin_layout Standard
+The text should not be longer than a line because it cannot be hyphenated.
+ As LyX doesn't yet support
+\series bold
+
+\backslash
+intertext
+\series default
+ directly, the text is written as mathematical text.
+
+\series bold
+
+\backslash
+intertext
+\series default
+ must hereby be at the beginning of a line and appears in the output above
+ this line.
+ An example where the text was inserted at the beginning of the second line:
+\begin_inset Formula
+\begin{align}
+I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
+\intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
+\end{align}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+intertext
+\series default
+ always creates some vertical space between the text and the formula lines.
+ To avoid this space, set 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
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! mathtools
+\end_layout
+
+\end_inset
+
+ the option
+\family sans
+Load
+\begin_inset space ~
+\end_inset
+
+always
+\family default
+.
+ Then you can use the command
+\series bold
+
+\backslash
+shortintertext
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! S !
+\backslash
+shortintertext
+\end_layout
+
+\end_inset
+
+ instead of
+\series bold
+
+\backslash
+intertext
+\series default
+:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\begin{align}
+I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
+\shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
+\end{align}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Formula Numbering
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula numbering
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! numbering|see
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+{
+\end_layout
+
+\end_inset
+
+Formula numbering
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+General
+\end_layout
+
+\begin_layout Standard
+Numbered formulas can be created with the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Numbered
+\begin_inset space ~
+\end_inset
+
+Formula
+\family default
+ (shortcut
+\family sans
+Ctrl+Alt
+\begin_inset space ~
+\end_inset
+
+N
+\family default
+).
+ Existing formulas can be numbered with the menu
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Toggle
+\begin_inset space ~
+\end_inset
+
+Numbering
+\family default
+ (shortcut
+\begin_inset Info
+type "shortcut"
+arg "math-number-toggle"
+\end_inset
+
+).
+ The formula number is displayed in LyX behind the formula as a number sign
+ in parentheses.
+ The number sign is replaced in the output by the formula number.
+\end_layout
+
+\begin_layout Standard
+When numbering is turned on in multiline formulas, all lines will be numbered.
+ But the numbering can be controlled with the menu
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Toggle
+\begin_inset space ~
+\end_inset
+
+Numbering
+\begin_inset space ~
+\end_inset
+
+of
+\begin_inset space ~
+\end_inset
+
+Line
+\family default
+ (shortcut
+\begin_inset Info
+type "shortcut"
+arg "math-number-line-toggle"
+\end_inset
+
+) for every line.
+\end_layout
+
+\begin_layout Standard
+Except for inline formulas, all formulas can be numbered with two different
+ styles, see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Formula-Styles"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Cross-References
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Cross-references ! to formulas
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+All labeled formulas can be cross-referenced.
+ A label is added by the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Label
+\family default
+ or the toolbar button
+\begin_inset Info
+type "icon"
+arg "label-insert"
+\end_inset
+
+.
+ The cursor must hereby be inside a displayed formula.
+ Alternatively you can right-click on the formula and choose
+\family sans
+Equation Label
+\family default
+.
+ A dialog pops up displaying the prefix
+\series bold
+eq:
+\series default
+ in a text field.
+ The label is inserted there behind the prefix.
+ The predefined prefix means
+\begin_inset Quotes eld
+\end_inset
+
+equation
+\begin_inset Quotes erd
+\end_inset
+
+ and makes it easier to find labels in large documents because it marks
+ it as formula label to divide it from e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+section labels.
+ To change a label, the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Label
+\family default
+ is used again or you right-click on a formula and then on
+\family sans
+Equation Label
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+The name of the label is displayed in LyX within two parentheses behind
+ formula.
+ A formula with a label is always numbered.
+\end_layout
+
+\begin_layout Standard
+Cross-references are inserted via the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Cross-Reference
+\family default
+ or with the toolbar button
+\begin_inset Info
+type "icon"
+arg "dialog-show-new-inset ref"
+\end_inset
+
+.
+ A formula cross-reference appears in the output as formula number.
+ When in the cross-reference dialog window the format
+\series bold
+()
+\series default
+ is chosen, the cross-reference appears in the output as formula number
+ in parentheses.
+\begin_inset Newline newline
+\end_inset
+
+By right-clicking on a cross-reference in LyX, one jumps to the formula
+ that is referenced.
+\end_layout
+
+\begin_layout Standard
+Here are as examples cross-references to formulas of the following subsections:
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+Note the different cross-reference types.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The equations
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:tag"
+
+\end_inset
+
+ and
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:c"
+
+\end_inset
+
+ are equivalent.
+ In (
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:Lat"
+
+\end_inset
+
+) big Latin letters are used for the numbering in contrary to (
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:Rom"
+
+\end_inset
+
+).
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+When the argument of
+\series bold
+
+\backslash
+tag
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+tag
+\series default
+ is described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:User-defined-Numbering"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\series default
+ contains a box like in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Paragraph-Boxes"
+
+\end_inset
+
+, the formula cannot be referenced.
+\end_layout
+
+\begin_layout Subsection
+Subnumbering
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula numbering ! subnumbering
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With the help of the commands
+\series bold
+
+\backslash
+begin{subequations}
+\series default
+ and
+\series bold
+
+\backslash
+end{subequations}
+\series default
+ formulas can be subnumbered.
+ Both commands are inserted in TeX-mode.
+\end_layout
+
+\begin_layout Standard
+An example:
+\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
+To create the example, the following is done:
+\end_layout
+
+\begin_layout Enumerate
+first formula is inserted
+\end_layout
+
+\begin_layout Enumerate
+
+\series bold
+
+\backslash
+addtocounter{equation}{-1}
+\backslash
+begin{subequations}
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! A !
+\backslash
+addtocounter
+\end_layout
+
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+
+\series default
+is inserted after the first formula
+\end_layout
+
+\begin_layout Enumerate
+second formula is inserted
+\end_layout
+
+\begin_layout Enumerate
+third formula is inserted
+\end_layout
+
+\begin_layout Enumerate
+
+\series bold
+
+\backslash
+end{subequations}
+\series default
+ is inserted after the third formula
+\end_layout
+
+\begin_layout Standard
+Every formula between the commands
+\series bold
+
+\backslash
+begin
+\series default
+ and
+\series bold
+
+\backslash
+end
+\series default
+ is subnumbered as a, b,
+\begin_inset Newline linebreak
+\end_inset
+
+c, \SpecialChar \ldots{}
+ For multiline formulas every line will be subnumbered.
+ All subnumbered formulas are treated as
+\emph on
+one
+\emph default
+ numbered formula.
+ But as every numbered formula increases the counter
+\series bold
+equation
+\series default
+ by one, the command
+\series bold
+
+\backslash
+addtocounter
+\series default
+ is needed to decrease it.
+ Otherwise the formulas
+\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
+
+ would be numbered as
+\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
+By inserting the commands in TeX-mode, a space is created between the first
+ two formulas.
+ To revert this -5
+\begin_inset space \thinspace{}
+\end_inset
+
+mm vertical space is inserted after the command
+\series bold
+
+\backslash
+begin{subequations}
+\series default
+.
+ When the formula style
+\series bold
+Indented
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+formula styles see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Formula-Styles"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ is used, -7
+\begin_inset space \thinspace{}
+\end_inset
+
+mm space is inserted instead.
+\end_layout
+
+\begin_layout Standard
+Here is an example for a multiline formula where the numbering was turned
+ off for the second line:
+\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
+User-defined Numbering
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:User-defined-Numbering"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula numbering ! user-defined
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula numbering ! self-defined delimiters
+\end_layout
+
+\end_inset
+
+With the standard numbering parentheses are set around the formula number.
+ To replace the parentheses for example by vertical bars, the following
+ line is added to the LaTeX-preamble:
+\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
+This macro is already declared in the LaTeX-preamble for testing.
+ To activate it, remove the percent sign at the beginning.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To use other characters, the vertical bars besides the
+\series bold
+#1
+\series default
+ are replaced by one ore more characters.
+ To get only the formula number the vertical bars are omitted.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+When there should be an expression of your choice instead of the consecutive
+ formula number in parentheses behind the formula, the command
+\series bold
+
+\backslash
+tag
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! T !
+\backslash
+tag
+\end_layout
+
+\end_inset
+
+ is used:
+\begin_inset Formula
+\begin{equation}
+A+B=C\tag{something}\label{eq:tag}
+\end{equation}
+
+\end_inset
+
+In this example the command
+\series bold
+
+\backslash
+tag
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+something
+\series default
+ was inserted in the formula.
+\end_layout
+
+\begin_layout Standard
+When the command
+\series bold
+
+\backslash
+tag*
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+something
+\series default
+ is inserted instead, the star prevents the parentheses around the expression:
+\begin_inset Formula
+\[
+A+B=C\tag*{something}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+To restart the formula numbering with new document parts or sections, the
+ following command is used:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+@addtoreset{equation}{part}
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands !
+\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
+
+resp.
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+@addtoreset{equation}{section}
+\end_layout
+
+\begin_layout Standard
+To be able to use these commands in TeX-mode, the
+\begin_inset Quotes eld
+\end_inset
+
+@
+\begin_inset Quotes erd
+\end_inset
+
+ character has to be made
+\begin_inset Quotes eld
+\end_inset
+
+active
+\begin_inset Quotes erd
+\end_inset
+
+ for LaTeX using the command
+\series bold
+
+\backslash
+makeatletter.
+
+\series default
+ The command
+\series bold
+
+\backslash
+makeatother
+\series default
+ reverts this.
+ So the command sequence in TeX-mode is:
+\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
+In the LaTeX-preamble
+\series bold
+
+\backslash
+makeatletter
+\series default
+ and
+\series bold
+
+\backslash
+makeatother
+\series default
+ can be omitted as they are automatically internally inserted by LyX.
+\end_layout
+
+\begin_layout Standard
+To revert
+\series bold
+
+\backslash
+@addtoreset
+\series default
+, the file
+\series bold
+remreset.sty
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+remreset
+\series default
+ is part of the LaTeX-package
+\series bold
+carlisle
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! carlisle
+\end_layout
+
+\end_inset
+
+ that is part of every LaTeX standard installation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! remreset
+\end_layout
+
+\end_inset
+
+ has to be loaded in the LaTeX-preamble with the line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{remreset}
+\end_layout
+
+\begin_layout Standard
+Then the command
+\series bold
+
+\backslash
+@removefromreset
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands !
+\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
+
+ can be used with the same scheme as
+\series bold
+
+\backslash
+@addtoreset
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Sometimes formulas should be numbered in the following form:
+\end_layout
+
+\begin_layout Standard
+
+\family typewriter
+(section number.formula number)
+\end_layout
+
+\begin_layout Standard
+The formula number should start with every section with
+\begin_inset Quotes eld
+\end_inset
+
+1
+\begin_inset Quotes erd
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+For this case there is the command
+\series bold
+
+\backslash
+numberwithin
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! N !
+\backslash
+numberwithin
+\end_layout
+
+\end_inset
+
+, which is used with the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+numberwithin{counter}{sectioning}
+\end_layout
+
+\begin_layout Standard
+Counter denotes what kind of numbering is affected, sectioning denotes what
+ number is before the dot.
+\end_layout
+
+\begin_layout Standard
+Thus in our case the following LaTeX-preamble or TeX code line is used:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+numberwithin{equation}{section}
+\end_layout
+
+\begin_layout Standard
+This is the result:
+\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
+To number e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+tables so that the number of the part is the sectioning,
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+numberwithin{table}{part}
+\series default
+ is used.
+\end_layout
+
+\begin_layout Standard
+To go back to the standard numbering or to prevent this kind of numbering
+ when it is defined by the document class, the following command is inserted
+ as TeX code or to the LaTeX-preamble:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+arabic{equation}}
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! 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
+or
+\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
+ uses internally the command
+\series bold
+
+\backslash
+@addtoreset
+\series default
+, described above, that also needs to be reverted.
+\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
+Numbering with Roman Numbers and Letters
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula numbering ! with letters
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula numbering ! with Roman numbers
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Formulas can also be numbered with Roman numbers and Latin letters.
+ To number for example with small Roman numbers, the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+roman{equation}}
+\end_layout
+
+\begin_layout Standard
+is inserted before the formula in TeX-mode.
+
+\series bold
+
+\backslash
+renewcommand
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! R !
+\backslash
+renewcommand
+\end_layout
+
+\end_inset
+
+ redefines the predefined command
+\series bold
+
+\backslash
+theequation
+\series default
+ to the command
+\series bold
+
+\backslash
+roman{equation}
+\series default
+.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+The command
+\series bold
+
+\backslash
+renewcommand
+\series default
+ has the same scheme like the command
+\series bold
+
+\backslash
+newcommand
+\series default
+ that is described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:The-Command-newcommand"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\series bold
+equation
+\series default
+ is the formula counter.
+ When the command
+\series bold
+
+\backslash
+the
+\series default
+ is used as prefix for a counter, the value of the counter is output as
+ Arabic number.
+ When a formula is numbered, LaTeX sets internally the command
+\series bold
+
+\backslash
+theequation
+\series default
+ behind the formula.
+
+\series bold
+
+\backslash
+roman{equation}
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! R !
+\backslash
+roman
+\end_layout
+
+\end_inset
+
+
+\series default
+ outputs the counter as small Roman number.
+\end_layout
+
+\begin_layout Standard
+All formulas behind the command
+\series bold
+
+\backslash
+renew
+\series default
+c
+\series bold
+ommand
+\series default
+ are now numbered Roman.
+ To switch to numbering with big Roman numbers, the command is inserted
+ again, but
+\series bold
+
+\backslash
+roman
+\series default
+ is replaced by
+\series bold
+
+\backslash
+Roman
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! R !
+\backslash
+roman@
+\backslash
+Roman
+\end_layout
+
+\end_inset
+
+.
+ To
+\begin_inset Quotes eld
+\end_inset
+
+number
+\begin_inset Quotes erd
+\end_inset
+
+ with small Latin letters there is the command
+\series bold
+
+\backslash
+alph
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! A !
+\backslash
+alph
+\end_layout
+
+\end_inset
+
+, for big ones there is the command
+\series bold
+
+\backslash
+Alph
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! 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
+\color none
+Note:
+\series default
+ Only maximal 26
+\begin_inset space ~
+\end_inset
+
+formulas can be numbered with Latin letters in one document.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\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
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\begin{equation}
+A=\textrm{small roman}
+\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{big Roman}\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{small Latin}
+\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{big Latin}\label{eq:Lat}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To switch back to the default numbering, insert the command:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+arabic{equation}}
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! 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=\textrm{Arabic}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+As you see, formulas are numbered serially independent from the numbering
+ style.
+ When then numbering should start with
+\begin_inset Quotes eld
+\end_inset
+
+1
+\begin_inset Quotes erd
+\end_inset
+
+ when the style is changed, new equation counters have to be defined.
+ A description about this can be found in the file
+\begin_inset CommandInset href
+LatexCommand href
+name "Formula-numbering.lyx"
+target "run:Formula-numbering.lyx"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Chemical Symbols and Equations
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Chemical-Symbols-and"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Chemical characters ! Symbols
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Chemical equations
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Symbols ! chemical
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+An example text from chemistry:
+\end_layout
+
+\begin_layout Quote
+The
+\begin_inset Formula $\mathrm{SO_{4}^{2-}}$
+\end_inset
+
+-ion reacts with two
+\begin_inset Formula $\mathrm{Na^{+}}$
+\end_inset
+
+-ions to sodium sulfate
+\begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
+\end_inset
+
+.
+ The chemical equation for this is:
+\begin_inset Formula
+\begin{equation}
+\mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This chemical equation can directly be created as formula.
+ To avoid that the symbols appear italic, everything is highlighted and
+ changed by the shortcut
+\begin_inset Info
+type "shortcut"
+arg "font-roman"
+\end_inset
+
+ to the upright font style.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+font styles
+\series bold
+
+\series default
+see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Font-Styles"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+A more convenient way to typeset chemical formulas is to use the command
+
+\series bold
+
+\backslash
+ce
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! C !
+\backslash
+ce
+\end_layout
+
+\end_inset
+
+ that is available when the LaTeX-package
+\series bold
+mhchem
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! mhchem
+\end_layout
+
+\end_inset
+
+ is installed.
+ After inserting
+\series bold
+
+\backslash
+ce
+\series default
+ to a formula a new blue box appears where chemical formulas can be inserted
+ in an intuitive way.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+H2CO3
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+SO4^2-
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+(NH4)2S
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+KCr(SO4)2.12H2O
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A-B
+\backslash
+dbond
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+C
+\backslash
+tbond
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+D
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+^227
+\begin_inset Formula $\downarrow$
+\end_inset
+
+_90
+\begin_inset Formula $\to$
+\end_inset
+
+Th+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+CO2
+\begin_inset space \textvisiblespace{}
+\end_inset
+
++
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+C
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+<=>
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2CO
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+CO2
+\begin_inset space \textvisiblespace{}
+\end_inset
+
++
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+C
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+->[
+\backslash
+alpha][
+\backslash
+beta]
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2CO}
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+\color none
+Note:
+\series default
+ Inserting a formula to a
+\series bold
+
+\backslash
+ce
+\series default
+ box will lead to LaTeX errors due to a LyX bug.
+\color inherit
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+\begin_inset CommandInset href
+LatexCommand href
+name "LyX-bug #8566"
+target "http://www.lyx.org/trac/ticket/8566"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\color none
+ In this case TeX code has to be used like for
+\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
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+\color none
+Note:
+\series default
+ It is not possible in LyX to use the character ^ to get an up-arrow as
+ described in the
+\series bold
+mhchem
+\series default
+ manual.
+ One instead uses a negative thin space followed by the command
+\series bold
+
+\backslash
+uparrow
+\series default
+:
+\begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Using
+\series bold
+
+\backslash
+ce
+\series default
+ the command for equation
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:chem-reaction"
+
+\end_inset
+
+ is:
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+ce
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2Na+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
++
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+SO4^2-
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+->
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+Na2SO4
+\end_layout
+
+\begin_layout Standard
+To create multiline chemical equations first a multiline formula is created
+ as described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Multiline-Formulas"
+
+\end_inset
+
+.
+ Afterwards the command
+\series bold
+
+\backslash
+ce
+\series default
+ is used in every small blue box of the formula.
+
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:TEOS-reaction-1"
+
+\end_inset
+
+ and
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:TEOS-reaction-2"
+
+\end_inset
+
+ are an example of a multi-stage chemical reaction where every equation
+ has its own number.
+\begin_inset Formula
+\begin{eqnarray}
+\ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
+\ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
+\end{eqnarray}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Besides
+\series bold
+
+\backslash
+ce
+\series default
+ the
+\series bold
+mhchem
+\series default
+ package provides the command
+\series bold
+
+\backslash
+cf
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! C !
+\backslash
+cf
+\end_layout
+
+\end_inset
+
+ that has to be used for special cases.
+ For more information about
+\series bold
+
+\backslash
+cf
+\series default
+ and more examples have a look at the documentation of
+\series bold
+mhchem
+\series default
+,
+\begin_inset CommandInset citation
+LatexCommand cite
+key "mhchem"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Diagrams
+\end_layout
+
+\begin_layout Standard
+LyX supports two types of commutative diagrams:
+\series bold
+amscd
+\series default
+ and
+\series bold
+xymatrix
+\series default
+ that are explained in the following.
+\end_layout
+
+\begin_layout Subsection
+Amscd Diagrams
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Diagrams ! amscd
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Diagrams of this type visualize relations by vertical and horizontal lines
+ or arrows:
+\begin_inset Formula
+\[
+\begin{CD}A@>>>B@>>>C\\
+@AAA@.@VVV\\
+F@<<>>
+\series default
+ a right arrow and
+\series bold
+@=
+\series default
+ a long equal sign
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+@AAA
+\series default
+ creates an up arrow,
+\series bold
+@VVV
+\series default
+ a down arrow and
+\series bold
+@|
+\series default
+ a vertical equal sign
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+@.
+
+\series default
+ is a placeholder for non-existent relations
+\end_layout
+
+\begin_layout Standard
+All arrows can be labeled as follows:
+\end_layout
+
+\begin_layout Itemize
+If text inserted between the first and second < or >, resp., it is placed
+ above the arrow.
+ When it is inserted between the second and third one, it appears under
+ the arrow.
+\end_layout
+
+\begin_layout Itemize
+When text for vertical arrows is inserted between the first and second A
+ or V, resp., it is placed left beside the arrow.
+ When it is inserted between the second and third one, it appears right
+ beside the arrow.
+ If the text contains an A or V, these letters must be set into a TeX-brace.
+\end_layout
+
+\begin_layout Standard
+As example a diagram with all possible relations:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula
+\[
+\begin{CD}A@>j>>B@>>k>C@=F\\
+@AmAA@.@VV{V}V@|\\
+D@<k>>F@=C
+\end{CD}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command for this is:
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+CD
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A@>j>>B@>>k>C@=F Ctrl+Return
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+CD
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+@AmAA@.@VV
+\backslash
+{V
+\series default
+
+\begin_inset Formula $\to$
+\end_inset
+
+
+\series bold
+V@| Ctrl+Return
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+CD
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+D@<k>>F@=C
+\end_layout
+
+\begin_layout Subsection
+Xymatrix Diagrams
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Diagrams ! xymatrix
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To be able to use xymatrices, the LaTeX-package
+\series bold
+xypic
+\series default
+ must be installed.
+ A xymatrix is created by inserting the command
+\series bold
+
+\backslash
+xymatrix
+\series default
+ in a formula.
+ Then you are able to add new matrix columns and rows like for normal matrices,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Matrices"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
+ and much more.
+ All possibilities to create commutative diagrams and decorations are explained
+ in detail in the
+\emph on
+XY-pic manual
+\emph default
+ that you find in the menu
+\family sans
+Help\SpecialChar \menuseparator
+Specific
+\begin_inset space ~
+\end_inset
+
+Manuals
+\family default
+.
+\end_layout
+
+\begin_layout Subsection
+
+\noun on
+Feynman
+\noun default
+ Diagrams
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Diagrams ! Feynman
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To be able to use
+\noun on
+Feynman
+\noun default
+-diagrams, the LaTeX-package
+\series bold
+feyn
+\series default
+ must be installed.
+ A
+\noun on
+Feynman
+\noun default
+-diagram is created by inserting the command
+\series bold
+
+\backslash
+Diagram
+\series default
+ in a formula.
+ Then you are able to add new matrix columns and rows like for normal matrices,
+ see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Matrices"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Examples how to create
+\noun on
+Feynman-
+\noun default
+diagrams in LyX is given in the
+\emph on
+Feynman-diagram manual
+\emph default
+ that you find in the menu
+\family sans
+Help\SpecialChar \menuseparator
+Specific
+\begin_inset space ~
+\end_inset
+
+Manuals
+\family default
+.
+\end_layout
+
+\begin_layout Section
+User-defined Commands
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+User-defined commands
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+\series default
+ The names of user-defined commands and macros may only consist of Latin
+ letters.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+The Command
+\backslash
+newcommand
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:The-Command-newcommand"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+User-defined commands !
+\backslash
+newcommand
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! N !
+\backslash
+newcommand
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Many LaTeX-commands are too long to be used frequently.
+ But it is possible to define with the command
+\series bold
+
+\backslash
+newcommand
+\series default
+ new shorter commands.
+\end_layout
+
+\begin_layout Standard
+The command scheme of
+\series bold
+
+\backslash
+newcommand
+\series default
+ is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{new command name}[number of arguments][optional
+\series default
+
+\series bold
+value]
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+newcommand
+\end_layout
+
+\end_inset
+
+{command definition}
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+\series default
+ Assure that the name of the new command is not already used in your document
+ or by LaTeX-packages that you use.
+ When you for example define the command
+\series bold
+
+\backslash
+le
+\series default
+ for
+\series bold
+
+\backslash
+Leftarrow
+\series default
+, you get an error message because
+\series bold
+
+\backslash
+le
+\series default
+ is already defined as command for
+\begin_inset Quotes eld
+\end_inset
+
+
+\begin_inset Formula $\le$
+\end_inset
+
+
+\begin_inset Quotes erd
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The number of arguments is an integer in the range 0
+\begin_inset space \thinspace{}
+\end_inset
+
+-
+\begin_inset space \thinspace{}
+\end_inset
+
+9 and specifies how many arguments the new command should have.
+ With the optional value a value for an optional argument can be predefined.
+ When this is done, the
+\emph on
+first
+\emph default
+
+\emph on
+a
+\emph default
+rgument of the new command is automatically an optional one.
+\end_layout
+
+\begin_layout Standard
+Here are some examples:
+\end_layout
+
+\begin_layout Itemize
+To define the command
+\series bold
+
+\backslash
+gr
+\series default
+ for
+\series bold
+
+\backslash
+Longrightarrow
+\series default
+, the LaTeX-preamble line is:
+\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
+To define the command
+\series bold
+
+\backslash
+us
+\series default
+ for
+\series bold
+
+\backslash
+underline
+\series default
+, the argument (that should be underlined) must be taken into account.
+ For this the preamble line is:
+\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
+
+The character
+\series bold
+#
+\series default
+ acts as argument placeholder, the
+\series bold
+1
+\series default
+ behind it denotes that it is the placeholder for the first argument.
+\end_layout
+
+\begin_layout Itemize
+For
+\series bold
+
+\backslash
+framebox
+\series default
+ one can e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+define the command
+\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
+
+The two Dollar signs creates the extra formula needed for
+\series bold
+
+\backslash
+framebox
+\series default
+, see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Boxes-with-Frame"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+To create a new command for
+\series bold
+
+\backslash
+fcolorbox
+\series default
+ where the color for the box need not be specified, the argument for the
+ color is defined optional:
+\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
+
+When the color is not specified when using
+\series bold
+
+\backslash
+cb
+\series default
+, the predefined color
+\series bold
+white
+\series default
+ will be used.
+\end_layout
+
+\begin_layout Standard
+A test of the new defined commands:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+A
+\backslash
+gr
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\gr B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+us{ABcd
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\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 space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cb{red
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cb[green]
+\backslash
+{red
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Math Macros
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+User-defined commands! Math macros
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Macros
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+User-defined commands are especially convenient for complex expressions.
+ When you are for example dealing with a document that has quadratic equations,
+ the same solution type occurs several times.
+ The general form of a quadratic equation is
+\begin_inset Formula
+\[
+0=\lambda^{2}+p\lambda+q
+\]
+
+\end_inset
+
+The general form of the solution is
+\begin_inset Formula
+\[
+\lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To define a command for the solution formula where only the three parameters
+
+\begin_inset Formula $\lambda$
+\end_inset
+
+,
+\begin_inset Formula $p$
+\end_inset
+
+ and
+\begin_inset Formula $q$
+\end_inset
+
+ need to be specified and the index of
+\begin_inset Formula $\lambda$
+\end_inset
+
+ can be given optionally, the LaTeX-preamble line is
+\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
+To create with this the solution formula, the command
+\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
+ is inserted to a formula
+\series bold
+.
+\end_layout
+
+\begin_layout Standard
+The definition of the new command is unintuitive because one has to know
+ the schemes of all used LaTeX commands, e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+that a fraction is inserted in LaTeX as
+\series bold
+
+\backslash
+frac{numerator}{denominator}
+\series default
+.
+ Furthermore one can easily forget a brace in the definition and cannot
+ see in LyX what the new command is doing.
+ To avoid these problems LyX offers the possibility to use math macros instead
+ of the command
+\series bold
+
+\backslash
+newcommand
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+A math macro is created by using the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\family default
+ or the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-macro newmacroname_newcommand"
+\end_inset
+
+.
+ The math macro toolbar appears together with the following box where the
+ macro is defined:
+\begin_inset Newline newline
+\end_inset
+
+
+\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 is the default name of the macro that should be changed to
+ something sensible.
+ The wanted formula is inserted in the first blue box.
+ An argument placeholder is inserted with the command
+\series bold
+
+\backslash
+#argumentnumber
+\series default
+, e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g
+\begin_inset space \space{}
+\end_inset
+
+
+\series bold
+
+\backslash
+#1
+\series default
+ or by using the macro toolbar button
+\begin_inset Info
+type "icon"
+arg "math-macro-add-param"
+\end_inset
+
+.
+ Argument placeholders are displayed red.
+ A maximum of 9
+\begin_inset space ~
+\end_inset
+
+arguments are possible.
+ Optional arguments are created with the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-macro-add-optional-param"
+\end_inset
+
+.
+ The first non-optional argument can be transformed to an optional one with
+ the toolbar button
+\begin_inset Info
+type "icon"
+arg "math-macro-make-optional"
+\end_inset
+
+.
+ In the second blue box the appearance of the macro in LyX can be defined.
+ Normally you want to see it as it is defined, so the box is kept empty.
+ But when you have created a macro that needs lot of space on the screen,
+ you can insert in the box for example
+\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
+For the macro only the arguments with the macro name in front of them will
+ then be displayed in LyX, leading to a better overview.
+ The formula appears in the output as defined in the first box.
+\begin_inset Newline newline
+\end_inset
+
+The appearance of macros in formulas can furthermore be changed for single
+ macros by setting the cursor in the macro and using the menu
+\family sans
+View\SpecialChar \menuseparator
+(Un)fold
+\begin_inset space ~
+\end_inset
+
+Math
+\begin_inset space ~
+\end_inset
+
+Macro
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+To use a macro, the macro name is inserted as command to a formula, in our
+ case
+\series bold
+
+\backslash
+qG
+\series default
+.
+ Our macro looks in LyX like this:
+\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
+
+Here is our macro example with the arguments
+\begin_inset Formula $x$
+\end_inset
+
+,
+\begin_inset Formula $\ln(x)$
+\end_inset
+
+ and
+\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 offers in the menu
+\family sans
+Tools\SpecialChar \menuseparator
+Preferences\SpecialChar \menuseparator
+Editing\SpecialChar \menuseparator
+Control
+\family default
+ different styles to edit macros.
+ To find the style that suits you the most, choose a style and set the cursor
+ in a macro formula to see the difference.
+\end_layout
+
+\begin_layout Standard
+A math macro is transformed internally to a
+\series bold
+
+\backslash
+newcommand
+\series default
+ command when exporting the document.
+ The created
+\series bold
+
+\backslash
+newcommand
+\series default
+ command is not placed in the LaTeX-preamble, therefore macros can only
+ be used in formulas that are in the document below the macro definition
+ box.
+\end_layout
+
+\begin_layout Standard
+Math macros can also be directly created from a
+\series bold
+
+\backslash
+newcommand
+\series default
+ command.
+ When writing for example the command
+\series bold
+
+\begin_inset Newline newline
+\end_inset
+
+
+\backslash
+newcommand{
+\backslash
+larrow}[2]{
+\backslash
+xleftarrow[#2]{#1}}
+\begin_inset Newline newline
+\end_inset
+
+
+\series default
+in LyX as normal text, highlighting it completely and using then the shortcut
+
+\family sans
+Ctrl+M
+\family default
+, the command will be transformed to a math macro.
+ Using this method you need to be careful that the
+\series bold
+
+\backslash
+newcommand
+\series default
+ command is typed correctly, otherwise you get a faulty macro leading to
+ LaTeX errors.
+\end_layout
+
+\begin_layout Standard
+Math macros currently have the problem that further formulas in macro definition
+s are handled wrongly.
+ Therefore the example
+\series bold
+
+\backslash
+fb
+\series default
+ from
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:The-Command-newcommand"
+
+\end_inset
+
+ cannot be created as macro.
+\end_layout
+
+\begin_layout Standard
+When the cursor is in a macro definition box, you will see the macro toolbar
+ in LyX:
+\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 ! Toolbar
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace defskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The macro toolbar contains from left to right the following buttons:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace defskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "icon"
+arg "math-macro-remove-param"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+Remove Last Argument
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "icon"
+arg "math-macro-add-param"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+Append Argument
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "icon"
+arg "math-macro-make-optional"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+Transform First Non-Optional to
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+
+\end_layout
+
+\end_inset
+
+Optional Argument
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "icon"
+arg "math-macro-make-nonoptional"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+Transform Last Optional to
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+
+\end_layout
+
+\end_inset
+
+Non-Optional Argument
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "icon"
+arg "math-macro-remove-optional-param"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+Remove Optional Argument
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "icon"
+arg "math-macro-add-optional-param"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+Insert Optional Argument
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "icon"
+arg "math-macro-remove-greedy-param"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+Remove Last Argument
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+
+\end_layout
+
+\end_inset
+
+Spitting Out To The Right
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "icon"
+arg "math-macro-append-greedy-param"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+Append Argument
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+
+\end_layout
+
+\end_inset
+
+Eating From The Right
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Info
+type "icon"
+arg "math-macro-add-greedy-optional-param"
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+Append Optional Argument
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+
+\end_layout
+
+\end_inset
+
+Eating From The Right
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Computer Algebra Systems
+\end_layout
+
+\begin_layout Standard
+LyX offers the exchange between mathematical expressions written in LyX's
+ math editor and external applications or user defined scripts.
+ Currently supported applications are
+\family sans
+Maple
+\family default
+,
+\family sans
+Mathematica
+\family default
+,
+\family sans
+Maxima
+\family default
+ and
+\family sans
+Octave
+\family default
+.
+ Note that the set of supported mathematical constructs is limited only
+ to very simple cases.
+\end_layout
+
+\begin_layout Subsection
+Usage
+\end_layout
+
+\begin_layout Standard
+Write some expression in a formula, go to the
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Use Computer Algebra System
+\family default
+ menu and choose the application you have installed on the computer.
+ After that the result of computation should show on the right side of the
+ expression together with the
+\begin_inset Quotes eld
+\end_inset
+
+=
+\begin_inset Quotes erd
+\end_inset
+
+ operator.
+\end_layout
+
+\begin_layout Standard
+Here are few simple examples (with results from
+\family typewriter
+Maxima
+\family default
+) to show what kind of computations can be performed:
+\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 $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
+\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
+Keyboard shortcut
+\end_layout
+
+\begin_layout Standard
+Currently there is no keyboard shortcut for calling the algebra applications.
+ One can easily bind a shortcut to the
+\family sans
+math-extern
+\family default
+ LyX function (see the
+\family sans
+\emph on
+LyX Functions
+\family default
+\emph default
+ manual).
+ One could e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+bind the
+\family sans
+Return
+\family default
+ key inside the math editor.
+ To bind it to
+\family typewriter
+Maxima
+\family default
+ one would use this shortcut definition command:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+command-alternatives paragraph-break;math-extern maxima
+\end_layout
+
+\begin_layout Section
+Miscellaneous
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Miscellaneous
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Negative Numbers
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Numbers ! negative
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Negative numbers often look ugly in formulas because the minus sign before
+ the number is set with the same length as the minus operator sign.
+ When writing the negative number in normal text, the minus sign appears
+ correctly.
+\end_layout
+
+\begin_layout Standard
+Thus, the problem disappears when converting the minus sign to mathematical
+ text.
+\end_layout
+
+\begin_layout Standard
+An example to visualize the problem:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+normal text:
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+x = -2
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+formula:
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $x=-2$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+solution:
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $x=\textrm{-}2$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Comma as decimal Separator
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Comma
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In LaTeX a comma inside a formula is used, according to the English convention,
+ as number group separator.
+ So there will be space added behind all commas in formulas.
+\end_layout
+
+\begin_layout Standard
+To avoid this, the comma is highlighted and changed to mathematical text
+ (shortcut
+\begin_inset Info
+type "shortcut"
+arg "math-mode"
+\end_inset
+
+).
+\end_layout
+
+\begin_layout Standard
+To use all formula commas in the document as decimal separator, the file
+
+\series bold
+icomma.sty
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+icomma
+\series default
+ is part of the LaTeX-package
+\series bold
+was
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! 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
+Packages ! icomma
+\end_layout
+
+\end_inset
+
+ is loaded with the LaTeX-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{icomma}
+\end_layout
+
+\begin_layout Subsection
+Physical Vectors
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Physical-Vectors"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Vectors ! physical
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Predefined vectors are offered by the LaTeX-package
+\series bold
+braket
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! braket
+\end_layout
+
+\end_inset
+
+ that is loaded with the LaTeX-preamble line
+\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
+The following table will only be displayed when the LaTeX-package
+\series bold
+braket
+\series default
+ is installed.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The following commands are defined:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Bra{
+\backslash
+psi
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Bra{\psi}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Ket{
+\backslash
+psi
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Ket{\psi}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Braket{
+\backslash
+psi|
+\backslash
+phi
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Braket{\psi|\phi}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+Braket
+\series default
+ assures that all vertical bars are set in the size of the surrounding brackets:
+\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
+The following will be displayed when the LaTeX-package
+\series bold
+braket
+\series default
+ is not installed:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You need to install the LaTeX-package
+\series bold
+braket
+\series default
+ to see the rest of this subsection in the output.
+\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
+The effect of
+\series bold
+
+\backslash
+Braket
+\series default
+ can also be achieved using the command
+\series bold
+
+\backslash
+middle
+\series default
+, that is described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Automatic-Bracket-Size"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Self-defined Fractions
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Self-defined-Fractions"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Fractions ! self-defined
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To define custom commands for fractions, the command
+\series bold
+
+\backslash
+genfrac
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! G !
+\backslash
+genfrac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+vspace{4mm}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ is used in the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+genfrac{left
+\series default
+
+\series bold
+bracket}{right
+\series default
+
+\series bold
+bracket}{fraction bar thickness}{style}
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Phantom HPhantom
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+genfrac
+\end_layout
+
+\end_inset
+
+{numerator}{denominator}
+\end_layout
+
+\begin_layout Standard
+The style is a number in the range of 0
+\begin_inset space \thinspace{}
+\end_inset
+
+-
+\begin_inset space \thinspace{}
+\end_inset
+
+3.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Number
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Style (Size)
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+0
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+display style formula
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+1
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+inline formula
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+2
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+small
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+3
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+tiny
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+When no style is given, the size is adjusted to the surrounding environment
+ like for the command
+\series bold
+
+\backslash
+frac
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+When no fraction bar thickness is given, the predefined value of 0.4
+\begin_inset space \thinspace{}
+\end_inset
+
+pt will be used.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+For example, the commands
+\series bold
+
+\backslash
+dfrac
+\series default
+ and
+\series bold
+
+\backslash
+tbinom
+\series default
+ from
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Fractions"
+
+\end_inset
+
+ are defined with the commands
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+dfrac}[2]{
+\backslash
+genfrac{}{}{}{0}{#1}{#2}}
+\end_layout
+
+\begin_layout Standard
+and
+\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
+
+To define a fraction where the fraction bar thickness can be given as optional
+ argument, the following line is inserted to the LaTeX-preamble:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+fracS}[3][]{
+\backslash
+genfrac{}{}{#1}{}{#2}{#3}}
+\end_layout
+
+\begin_layout Standard
+A test:
+\begin_inset Formula
+\begin{align*}
+\text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
+\text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
+\end{align*}
+
+\end_inset
+
+As one can see, the distance of the numerator and the denominator to the
+ fraction bar is round about three times the bar thickness.
+\end_layout
+
+\begin_layout Subsection
+Canceled Formulas
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! canceled
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+There are four ways to cancel formulas or parts of formulas:
+\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
+The following table will only be displayed when the LaTeX-package
+\series bold
+cancel
+\series default
+ is installed.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+The space and
+\series bold
+
+\backslash
+raisebox
+\series default
+ are used here as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cancel
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+bcancel
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+xcancel
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+cancelto
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+int
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+A=B
+\begin_inset Formula $\to$
+\end_inset
+
+1
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+cancelto
+\series default
+ is especially suitable to visualize the reduction of fractions within formulas:
+\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
+To change the size of
+\series bold
+
+\backslash
+cancelto
+\series default
+'s
+\begin_inset Quotes eld
+\end_inset
+
+subscript
+\begin_inset Quotes erd
+\end_inset
+
+ value one can add the LaTeX-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+PassOptionsToPackage{option}{cancel}
+\end_layout
+
+\begin_layout Standard
+where
+\series bold
+option
+\series default
+ is either
+\series bold
+samesize
+\series default
+ which leads to the same size as for the canceled value, or
+\series bold
+Smaller
+\series default
+ which makes is it a bit smaller than normal.
+\end_layout
+
+\begin_layout Standard
+To color the cancellation bar one adds this command as TeX code:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+CancelColor}{
+\backslash
+color{red}}
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+red
+\series default
+ can be replaced by a color of your choice.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+renewcommand{
+\backslash
+CancelColor}{
+\backslash
+color{red}}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\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
+renewcommand{
+\backslash
+CancelColor}{
+\backslash
+color{black}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+reset the color
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For further customizations, see the documentation of the package
+\series bold
+cancel
+\series default
+,
+\begin_inset CommandInset citation
+LatexCommand cite
+key "cancel"
+
+\end_inset
+
+.
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! cancel
+\end_layout
+
+\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
+The following will be displayed when the LaTeX-package
+\series bold
+cancel
+\series default
+ is not installed:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You need to install the LaTeX-package
+\series bold
+cancel
+\series default
+ to see the rest of this subsection in the output.
+\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
+Formulas in Section Headings
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Formulas-in-Section"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! in section headings
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+When formulas are used in section headings, the following has to be taken
+ into account:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+When
+\series bold
+hyperref
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! hyperref
+\end_layout
+
+\end_inset
+
+ support is enabled in the document settings dialog under
+\family sans
+PDF
+\begin_inset space ~
+\end_inset
+
+Properties
+\family default
+, PDF-bookmarks are created for every section heading in the table of contents.
+ If a section heading contains formulas, they are incorrectly displayed
+ in the bookmark text, because formulas in bookmarks infringe the PDF convention
+s.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Both problems can be solved by inserting at the end of the section heading
+ a short title with the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Short
+\begin_inset space ~
+\end_inset
+
+Title
+\family default
+.
+ Short titles are used as alternative for multiline section headings to
+ keep the table of contents clearly arranged.
+ Only the short title appears in the table of contents and therefore also
+ in the PDF-bookmark.
+\end_layout
+
+\begin_layout Standard
+When formulas should be used in the table of contents but
+\series bold
+hyperref
+\series default
+ is used, one can use the following command in TeX-mode:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+texorpdfstring{part}{alternative}
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! T !
+\backslash
+texorpdfstring
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Part is the part of the heading that shouldn't appear in the PDF-bookmark.
+ This can be characters, formulas, footnotes, but also cross-references.
+ The alternative is used instead of the part for the bookmark.
+\end_layout
+
+\begin_layout Standard
+Here are two example headings:
+\begin_inset VSpace -3mm
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+boldmath
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Heading without formula in table of contents
+\begin_inset Formula $\sqrt{-1}=\mathrm{i}$
+\end_inset
+
+
+\begin_inset Argument 1
+status collapsed
+
+\begin_layout Plain Layout
+Heading without formula in table of contents
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Heading with formula in table of contents
+\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
+
+In the first heading a short title was used, in the second one
+\series bold
+
+\backslash
+texorpdfstring
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+To get the same formatting as for the other headings, the complete heading
+ was set into a
+\series bold
+boldmath
+\series default
+ environment
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Bold-Formulas"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Formulas in multi-column Text
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! in multi-column text
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Formulas in multi-column text are often too wide to fit into a column and
+ thus need to be set over the whole page width.
+ This is done by using the LaTeX-package
+\series bold
+multicol
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+multicol
+\series default
+ is part of every LaTeX standard installation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! multicol
+\end_layout
+
+\end_inset
+
+, that is loaded with the LaTeX-preamble line
+\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
+Note that in this case the setting
+\family sans
+Two-column
+\begin_inset space ~
+\end_inset
+
+document
+\family default
+ in the menu
+\family sans
+Document\SpecialChar \menuseparator
+Settings
+\family default
+ under
+\family sans
+Text
+\begin_inset space ~
+\end_inset
+
+Layout
+\family default
+\emph on
+
+\emph default
+must
+\emph on
+not
+\emph default
+ be selected.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Before the multi-column text the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+begin{multicols}{column number}
+\end_layout
+
+\begin_layout Standard
+is written in TeX-mode.
+ The column number is a number in the range of 2
+\begin_inset space \thinspace{}
+\end_inset
+
+-
+\begin_inset space \thinspace{}
+\end_inset
+
+10.
+ Before the formula the multi-column text is ended by inserting the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+end{multicols}
+\end_layout
+
+\begin_layout Standard
+in TeX-mode.
+\end_layout
+
+\begin_layout Standard
+Due to the command some space is automatically added before the formula.
+ To revert this, -6
+\begin_inset space \thinspace{}
+\end_inset
+
+mm vertical space is inserted before the formula.
+ When the formula style
+\series bold
+Indented
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+formula styles see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Formula-Styles"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ is used, -9
+\begin_inset space \thinspace{}
+\end_inset
+
+mm space is inserted instead.
+\end_layout
+
+\begin_layout Standard
+As example a multi-column text with a displayed formula:
+\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 auÃer 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
+Formulas with Description of Variables
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Formula ! with description of variables
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To describe variables within a formula, like in formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:within"
+
+\end_inset
+
+, a 2
+\series bold
+Ã
+\series default
+
+\begin_inset Formula $n$
+\end_inset
+
+
+\begin_inset space ~
+\end_inset
+
+matrix is used with left aligned columns for the
+\begin_inset Formula $n$
+\end_inset
+
+ used variables.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+matrices see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Matrices"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ To set the description in a smaller size, before the matrix e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+the command
+\series bold
+
+\backslash
+footnotesize
+\series default
+ is inserted.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+font sizes see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Font-Sizes"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+When the formula style
+\series bold
+Indented
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+formula styles see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Formula-Styles"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ is used, a
+\series bold
+
+\backslash
+hfill
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+hfill
+\series default
+ only works in formulas with the style
+\series bold
+Indented
+\series default
+, see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Variable-Space"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ is inserted before and after the matrix to have the same separation of
+ the matrix from the equation and the side margin.
+\end_layout
+
+\begin_layout Standard
+When the formula style
+\series bold
+Centered
+\series default
+ is used, the method described in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Flalign-Environment"
+
+\end_inset
+
+ is used to indent formulas.
+ Formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:within"
+
+\end_inset
+
+ consists of five columns where in the first two columns contain the equation,
+ the third the matrix and the last one an empty TeX-brace.
+\begin_inset Formula
+\begin{flalign}
+\hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
+\rho & \textrm{density}\\
+V & \textrm{volume}\\
+g & \textrm{gravitational acceleration}
+\end{array} & & {}\label{eq:within}
+\end{flalign}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Upright small Greek Letters
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Upright-small-Greek"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Greek letters ! upright
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Most of the math fonts only provide italic small Greek letters.
+ But for symbols of elementary particles like pions and neutrinos, upright
+ Greek letters are needed.
+ The file
+\series bold
+upgreek.sty
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+upgreek
+\series default
+ is part of the LaTeX-package
+\series bold
+was
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! 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
+Packages ! upgreek
+\end_layout
+
+\end_inset
+
+ that is loaded with the LaTeX-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{upgreek}
+\end_layout
+
+\begin_layout Standard
+provides them.
+
+\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
+The following table will only be displayed when the LaTeX-package
+\series bold
+upgreek
+\series default
+ is installed:
+\end_layout
+
+\end_inset
+
+ They are created when the command for a small Greek letter is started with
+
+\series bold
+up
+\series default
+.
+ For example the command
+\series bold
+
+\backslash
+uptau
+\series default
+ creates this:
+\begin_inset Formula $\uptau$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With these commands reactions of elementary particles can be typeset:
+\begin_inset Formula
+\[
+\uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The upright letters are more bold and wider than the italic ones.
+ They should therefore not be used for units like
+\begin_inset Quotes eld
+\end_inset
+
+µm
+\begin_inset Quotes erd
+\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
+The following will be displayed when the LaTeX-package
+\series bold
+upgreek
+\series default
+ is not installed:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You need to install the LaTeX-package
+\series bold
+upgreek
+\series default
+ to see the rest of this subsection in the output.
+\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
+Text Characters in Formulas
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Text ! in formulas
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In some cases you might want to insert text characters directly into formulas.
+ When for example the centered dot · is often used in formulas like
+\begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
+\end_inset
+
+, one would have to insert the command
+\series bold
+
+\backslash
+cdot
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Binary-Operators"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ all the time, because this character is defined in all encodings as text
+ character.
+ But the encoding can be changed by this LaTeX-preamble line:
+\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
+The character encoding (menu
+\family sans
+Document\SpecialChar \menuseparator
+Settings\SpecialChar \menuseparator
+Language
+\family default
+) specifies what character appears when a keyboard key is pressed.
+ When the key for the character '·' is pressed, internally the command
+\series bold
+
+\backslash
+textperiodcentered
+\series default
+ is used.
+ But this command is not available in a formula so that you would get LaTeX-erro
+rs.
+ With the changed encoding the right command is chosen automatically, depending
+ on if the character was inserted into a formula or not.
+\end_layout
+
+\begin_layout Standard
+The encoding of several characters is saved in definition files.
+ For example the encoding
+\series bold
+latin9
+\series default
+ is defined in the file
+\series bold
+latin9.def
+\series default
+ which is in the installation folder of LaTeX.
+ Encodings should only be changed via the LaTeX-preamble and not in the
+ definition files.
+ Otherwise documents could not be edited by other LyX users working on other
+ computers.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Besides the centered dot, in this document the degree sign ° is defined
+ with the following LaTeX-preamble line so that it can be directly inserted
+ into a formula:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareInputtext{176}{
+\backslash
+ifmmode^
+\backslash
+circ
+\backslash
+else
+\backslash
+textdegree
+\backslash
+f\SpecialChar \textcompwordmark{}
+i}
+\end_layout
+
+\begin_layout Subsection
+LaTeX-comments in formulas
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+LaTeX-comments
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In text you can insert a comment that will only be visible in the LaTeX
+ source code of your file with the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Note\SpecialChar \menuseparator
+Comment
+\family default
+.
+ This is not possible in a formula but you can insert LaTeX-comments with
+ the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+%
+\end_layout
+
+\begin_layout Standard
+This creates a box in which you can write your comment.
+ Due to a bug in LyX
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+\begin_inset CommandInset href
+LatexCommand href
+name "LyX-bug #9002"
+target "http://www.lyx.org/trac/ticket/9002"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ you cannot write normal text inside the comment, even when you use mathematical
+ text, you will see its LaTeX-commands in the LaTeX-output.
+\begin_inset Newline newline
+\end_inset
+
+This a formula with a LaTeX-comment:
+\begin_inset Formula
+\[
+A=B%\text{This is the comment}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+\start_of_appendix
+Typographic Advice
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Typographic advice
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This section is a summary of the most important typographic rules, listed
+ in ISO norms.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+This collection was partly taken from the German semi-official dictionary
+ called
+\begin_inset Quotes eld
+\end_inset
+
+Duden
+\begin_inset Quotes erd
+\end_inset
+
+
+\begin_inset CommandInset citation
+LatexCommand cite
+key "Duden"
+
+\end_inset
+
+ that lists some of the ISO rules.
+ More rules are listed in
+\begin_inset CommandInset citation
+LatexCommand cite
+key "Checklist"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Physical units are
+\emph on
+always
+\emph default
+ set upright
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+done with font styles, see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Font-Styles"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+, no matter if they appear in italic text: 30
+\begin_inset space \thinspace{}
+\end_inset
+
+km/h
+\begin_inset Newline newline
+\end_inset
+
+Between the value and the unit is the smallest space, see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Predefined-Space"
+
+\end_inset
+
+.
+\begin_inset Newline newline
+\end_inset
+
+This convention is automatically fulfilled when the command
+\series bold
+
+\backslash
+unittwo
+\series default
+ is used.
+ When it is entered to a formula, two boxes appear.
+ In the first one the value is inserted, in the second one the unit, and
+ one gets as above:
+\begin_inset Formula $\unit[30]{km/h}$
+\end_inset
+
+
+\begin_inset space \thinspace{}
+\end_inset
+
+.
+ Note that
+\series bold
+
+\backslash
+unittwo
+\series default
+ is not a real LaTeX command but the command
+\series bold
+
+\backslash
+unit[value]{unit}
+\series default
+, therefore you cannot use it in TeX code.
+\end_layout
+
+\begin_layout Itemize
+Percent and perthousand signs are set like physical units:
+\begin_inset Newline newline
+\end_inset
+
+1.2
+\begin_inset space \thinspace{}
+\end_inset
+
+â° alcohol in blood
+\end_layout
+
+\begin_layout Itemize
+The degree sign follows directly on the value: 15°, but not when it is used
+ in units: 15
+\begin_inset space \thinspace{}
+\end_inset
+
+°C
+\end_layout
+
+\begin_layout Itemize
+In numbers with more than four digits the smallest space is inserted before
+ every third digit to group them:
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+18
+\begin_inset space \thinspace{}
+\end_inset
+
+473
+\begin_inset space \thinspace{}
+\end_inset
+
+588
+\end_layout
+
+\begin_layout Itemize
+For dimensions like 120Ã90Ã40
+\begin_inset space \thinspace{}
+\end_inset
+
+cm the multiplication sign
+\begin_inset Quotes eld
+\end_inset
+
+Ã
+\begin_inset Quotes erd
+\end_inset
+
+ is used.
+ It is available either via the command
+\series bold
+
+\backslash
+times
+\series default
+ or via the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Special Character\SpecialChar \menuseparator
+Symbols
+\family default
+.
+\end_layout
+
+\begin_layout Itemize
+Functions with names consisting of several letters are set upright to avoid
+ confusions, see
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Predefined-Functions"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+Indices consisting of several letters, are set upright:
+\begin_inset Formula $E_{\mathrm{kin}}$
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+Components of matrices are set italic:
+\begin_inset Formula $\hat{H}_{kl}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+The differentiation/integration operator 'd', the Euler's number 'e' and
+ the imaginary unit 'i' should be set upright, to avoid mixing them up with
+ other variables.
+\end_layout
+
+\begin_layout Itemize
+The character that denotes a
+\noun on
+Fourier
+\noun default
+ transformation is inserted either by the command
+\series bold
+
+\backslash
+mathscr
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+F
+\series default
+ or via the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Special Character\SpecialChar \menuseparator
+Symbols\SpecialChar \menuseparator
+Letterlike
+\begin_inset space ~
+\end_inset
+
+Symbols
+\family default
+:
+\begin_inset Formula $\mathscr{F}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Synonyms
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Synonyms
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Some characters and symbols can be created with several commands.
+ Here is a list of the synonym commands:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+equivalent to
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ast
+\end_layout
+
+\end_inset
+ |
+
+\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
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+choose
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+binom
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+geq
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ge
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lbrace
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+{
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lbracket
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+[
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+leftarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+gets
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+leq
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+le
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lor
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+vee
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+neq
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+not=
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+slash
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+/
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+vert
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+|
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+
+
+
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+equivalent to
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+backslash
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+
+\backslash
+
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dasharrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dashrightarrow
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+land
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+wedge
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rbrace
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+}
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rbracket
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+]
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rightarrow
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+to
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+lnot
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+neg
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ne
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+not=
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+owns
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+ni
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+square
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Box
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+Vert
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+|
+\end_layout
+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+key "TLC2"
+
+\end_inset
+
+
+\shape smallcaps
+Mittelbach, F.
+ ; Goossens, M.
+\shape default
+:
+\shape italic
+The LaTeX Companion
+\shape default
+.
+ Addison Wesley, 2004
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+key "Mathmode"
+
+\end_inset
+
+
+\begin_inset CommandInset href
+LatexCommand href
+name "Description"
+target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
+
+\end_inset
+
+ of LaTeX's math abilities
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+key "AMS"
+
+\end_inset
+
+
+\begin_inset CommandInset href
+LatexCommand href
+name "Description"
+target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
+
+\end_inset
+
+ of
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+AmS
+\end_layout
+
+\end_inset
+
+-LaTeX
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+key "Symbols"
+
+\end_inset
+
+
+\begin_inset CommandInset href
+LatexCommand href
+name "List"
+target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
+
+\end_inset
+
+ of all symbols available with LaTeX-packages
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
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