-#LyX 2.0.0beta2 created this file. For more info see http://www.lyx.org/
-\lyxformat 410
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
\begin_document
\begin_header
\textclass scrartcl
\fi % end if pdflatex is used
-% Folgendes Problem lösen:
-% Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
-% Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
-% die Kapitelnummer geschrieben.
-% Als Lösung wird mehr Platz zwischen Nummer und
-% Überschrift eingefügt.
+% 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}}}}
-\newlength{\abc}
-\settowidth{\abc}{\space}
-\AtBeginDocument{%
-\addto\extrasenglish{
- \renewcommand{\equationautorefname}{\hspace{-\abc}}
+\@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
+\addto\extrasenglish{%
+ \renewcommand*{\equationautorefname}[1]{}
\renewcommand{\sectionautorefname}{sec.\negthinspace}
\renewcommand{\subsectionautorefname}{sec.\negthinspace}
- \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
+ \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}
}
% don't load packages twice
% provides caption formatting
\setkomafont{captionlabel}{\bfseries}
-% used in sec. 23.6
+% used in sec. 24.5
\usepackage[samesize]{cancel}
% enables calculation of values
\usepackage{calc}
-% for multiple columns used in sec. 23.7
+% for multiple columns used in sec. 24.7
\usepackage{multicol}
% needed in sec. 19.4
\use_default_options false
\maintain_unincluded_children false
\language english
+\language_package default
\inputencoding auto
\fontencoding global
\font_roman default
\pdf_colorlinks true
\pdf_backref false
\pdf_pdfusetitle false
-\pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
+\pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
\papersize a4paper
\use_geometry false
\use_amsmath 2
\tracking_changes false
\output_changes false
\html_math_output 0
+\html_css_as_file 0
\html_be_strict false
\end_header
\begin_layout Plain Layout
To export this document to PDF, PS or DVI the LaTeX-packages
\series bold
-braket, cancel, eurosym,
-\series default
-
-\series bold
-mhchem
+braket, cancel, eurosym, mathdots, mhchem
\series default
and
\series bold
was
\series default
should be installed.
- If they are not installed the document can be export anyway but the sections
+ 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 exeption is
+ An exception is
\series bold
mhchem
\series default
\series default
Math
\family default
-, or the
+ or the
\family sans
math
\family default
\family sans
Use AMS math package
\family default
- must be used in the document settings (menu
+ must be checked in the document settings (menu
\family sans
Document\SpecialChar \menuseparator
Settings\SpecialChar \menuseparator
\end_inset
-
+.
\begin_inset Newline newline
\end_inset
\end_inset
- that will appear bigger and in an own paragraph, use one of these shortcuts:
-
+ 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"
\begin_layout Standard
To edit matrices, case differentiations and multiline formulas subsequently,
- the menus
+ use the menus
\family sans
Edit\SpecialChar \menuseparator
Math
\family sans
table toolbar
\family default
- can be used.
+.
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.
.
The text appears black in LyX and can therefore be distinguished from the
- other formula parts that appear blue.
+ other formula parts which appear blue.
In the output mathematical text is set upright, in contrary to other formula
parts.
\end_layout
\end_layout
\begin_layout Standard
-A command starts always with a backslash
+A command always starts with a backslash
\begin_inset Quotes gld
\end_inset
\end_inset
.
- If you add in a formula a left brace to a command name, LyX creates automatical
-ly a TeX-brace.
+ 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
{
\series default
.
- TeX-braces appear red in LyX, in contrary to normal braces that appear
+ 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.
\begin_layout Standard
A protected space is inserted with
\begin_inset Info
-type "shortcut"
-arg "space-insert protected"
+type "shortcuts"
+arg "command-alternatives space-insert protected ; math-space"
\end_inset
.
\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*
\end_inset
- , exponents with a caret
+, exponents with a caret
\begin_inset Quotes eld
\end_inset
status collapsed
\begin_layout Plain Layout
-Depending on the used keyboard settings this can also happen for other character
-s than vowels.
+Depending on the used keyboard settings this can also happen for characters
+ other than vowels.
\end_layout
\end_inset
.
- To get in this case exponents, press
+ To get exponents in this case, press
\family sans
Space
\family default
\end_inset
- a fraction can be created that has in any case the size of a display style
- formula.
+ a fraction can be created that always has the size of a display style formula.
With
\series bold
\end_inset
e^
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
\backslash
frac
\begin_inset ERT
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{align*}
+\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_layout
\begin_layout Standard
-\begin_inset Formula $\cfrac[l]{A}{B+C}$
-\end_inset
-,
-\begin_inset Formula $\cfrac{A}{B+C}$
-\end_inset
+\series bold
+\begin_inset Formula
+\[
+\cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
+\]
-,
-\begin_inset Formula $\cfrac[r]{A}{B+C}$
\end_inset
frac
\series default
:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
\]
.
\end_layout
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
\begin_layout Subsection
Roots
\begin_inset Index idx
\end_inset
.
- Analog to fractions (
+ As with fractions (
\series bold
\backslash
frac
\series default
-) there are besides
+) in addition to
\series bold
\backslash
binom
\series default
- the commands
+ there are the commands
\series bold
\backslash
\backslash
cases
\series default
- or the usage of the math toolbar button
+ or pressing the math toolbar button
\begin_inset Graphics
filename ../images/math/cases.png
scale 85
\end_layout
\begin_layout Standard
-By inserting of
+By inserting
\series bold
\backslash
\end_layout
\begin_layout Standard
-The last example shows, that not all negations look good.
- Therefore there are for some negations special commands (see
+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_layout
\begin_layout Standard
-For example creates
+For example the command
\series bold
\backslash
\backslash
int
\series default
- space for the height of the integral sign,
+ creates space for the height of the integral sign,
\begin_inset Foot
status collapsed
\end_layout
\begin_layout Standard
-Placeholders can also be used for text when it is inserted via the menu
+Placeholders can also be used for text when they are inserted via the menu
\family sans
Insert\SpecialChar \menuseparator
\end_layout
\begin_layout Standard
-To double underline e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g.
-\begin_inset space \space{}
-\end_inset
-
-results, one uses
+To double underline use
\series bold
\backslash
dots
\series default
:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\left(\begin{array}{cccc}
A & B & C & D\\
\hdotsfor[2]{4}\\
\end_inset
the rest of a line with dots.
- The effect of these commands is the same like with
+ The effect of these commands is the same as with
\series bold
\backslash
\end_layout
\begin_layout Standard
-Analog to
+Similar to
\series bold
\backslash
.
In the matrix dialog you can specify the number of columns and rows, the
alignment and the decoration.
- The vertical alignment is hereby only of importance for matrices in inline
- formulas:
+ The vertical alignment is only of importance for matrices in inline formulas:
\end_layout
\begin_layout Standard
lccr
\series default
.
- Normally are in a matrix all columns centered, therefore the default is
- for every column is a
+ Normally in a matrix all columns are centered, therefore the default for
+ every column is a
\series bold
c
\series default
\backslash
\series default
- produces there a line break.
+ produces a line break there.
\end_layout
\end_inset
)
\series default
creates
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\ln(\frac{A}{C})
\]
right)
\series default
creates
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\ln\left(\frac{A}{C}\right)
\]
creates:
\series bold
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\left.\frac{A}{B}\right\}
\]
\end_inset
needed for physical vectors:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
\]
\end_inset
, must be used:
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
& & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
\end{eqnarray*}
status collapsed
\begin_layout Plain Layout
-because a bracket is not handled as character, see
+because a bracket is not handled as a character, see
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Binary-Operators"
\end_inset
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
& & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
\end{eqnarray*}
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 need to be reduced.
+ 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
\end_inset
.
- As solution for the problem, the global formula row separation
+ As a solution for the problem, the global formula row separation
\series bold
\backslash
or the commands listed in the following subsections.
\end_layout
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
\begin_layout Subsection
Horizontal Arrows
\begin_inset Index idx
\begin_inset VSpace medskip
\end_inset
-Arrows used as accent like e.
+Arrows used as accents like e.
\begin_inset space \thinspace{}
\end_inset
\begin_inset VSpace medskip
\end_inset
-Vertical arrows can be used also as delimiter together with the commands
+Vertical arrows can be used also as delimiters together with the commands
described in
\begin_inset CommandInset ref
LatexCommand ref
.
\end_layout
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
\begin_layout Section
Accents
\begin_inset CommandInset label
be inserted.
\end_layout
-\begin_layout Subsection
-Accents for Operators
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Accents ! for operators
-\end_layout
-
-\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
-
- characters can be placed above or below an operator, respectively, to accent
- it.
- With the command
-\series bold
-
-\backslash
-sideset
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! S !
-\backslash
-sideset
-\end_layout
-
-\end_inset
-
- characters can be set before and behind an operator.
- The command scheme is:
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-sideset{character
-\series default
-
-\series bold
-before}{character
-\series default
-
-\series bold
-behind}
-\end_layout
-
-\begin_layout Standard
-
-\series bold
-
-\backslash
-sideset
-\series default
- must always be before the operator that should be accented.
- You can accent with several characters and even with other operators and
- symbols.
- To place with
-\series bold
-
-\backslash
-sideset
-\series default
- for example only characters behind an operator, write nothing between the
- first braces but don't omit the braces.
-\end_layout
-
-\begin_layout Standard
-For example the command
-\series bold
-
-\backslash
-sideset{
-\begin_inset Formula $\to$
-\end_inset
-
-
-\backslash
-{
-\series default
-'
-\series bold
-
-\begin_inset Formula $\to$
-\end_inset
-
-
-\backslash
-sum_k=1
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series default
-^
-\series bold
-n
-\series default
- produces:
-\begin_inset Formula \[
-\sideset{}{'}\sum_{k=1}^{n}
-\]
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The command
-\series bold
-
-\backslash
-overset
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\backslash
-maltese
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-spce
-\end_layout
-
-\end_inset
-
-
-\series default
-
-\begin_inset Formula $\uparrow$
-\end_inset
-
-
-\series bold
-a
-\series default
- produces:
-\begin_inset Formula \[
-\overset{a}{\maltese}
-\]
-
-\end_inset
-
-As seen in the last example, with
-\series bold
-
-\backslash
-overset
-\series default
- and
-\series bold
-
-\backslash
-underset
-\series default
- also symbols and characters can be accented; with
-\series bold
-
-\backslash
-sideset
-\series default
- this is not possible.
-\end_layout
-
\begin_layout Subsection
Accents for several Characters
\begin_inset Index idx
\series default
will only be set in the output with a length of three characters, as shown
in the following example:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\widetilde{A+B=C-D}
\]
***
\series default
creates:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\underset{***}{A=B}
\]
\end_inset
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
\end_layout
\begin_layout Section
\end_layout
\begin_layout Standard
-Sometimes it is necessary to insert horizontal space to a formula.
+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 "space-insert protected"
+arg "command-alternatives space-insert protected ; math-space"
\end_inset
).
\begin_layout Standard
Negative spaces can lead to characters overlapping each other.
- Thus they can be used to enforce ligatures, what is e.
+ Thus they can be used to enforce ligatures, which are e.
\begin_inset space \thinspace{}
\end_inset
\begin_inset space \space{}
\end_inset
-useful for summation operators:
+useful for summation operators:
\end_layout
\begin_layout Standard
.
The length may also be negative.
- To insert so many space that the formula uses all available space, the
- command
+ To insert as much space as is available, the command
\series bold
\backslash
\end_inset
- that has the following scheme:
+ which has the following scheme:
\end_layout
\begin_layout Standard
\end_layout
\begin_layout Standard
-It is possible to frame formulas or parts of it with the commands
+It is possible to frame a formula or part of one with the commands
\series bold
\backslash
\end_layout
\begin_layout Standard
-When one of these commands is inserted to a formula, a blue box appears
+When one of these commands is inserted in a formula, a blue box appears
within a frame to enter formula parts.
For
\series bold
\end_layout
\begin_layout Standard
-As extension to
+An extension to
\series bold
\backslash
fbox
\series default
- there is the command
+ is the command
\series bold
\backslash
\begin_inset Newline newline
\end_inset
-Is no width given, also no position can be given.
+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
.
\end_layout
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
\begin_layout Standard
\align center
\begin_inset Tabular
\end_inset
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\boxed{A+B=C}
\]
color
\series default
automatically.
- Thus it is possible that the package is loaded twice, but this doesn't
- arise problems.
+ Thus it is possible that the package is loaded twice, but this does not
+ cause problems.
\end_layout
\end_inset
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 wanted
+ To color all characters, the whole formula is highlighted and the desired
color is chosen in the
\family sans
Text
Customized
\family default
.
- The formula number has then the same color as the formula.
+ 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
\color red
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
\int A=B\label{eq:red}
\end{equation}
\color green
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
\textcolor{red}{\int A=B}\label{eq:redgreen}
\end{equation}
\end_inset
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\fcolorbox{cyan}{magenta}{A=B}
\]
yellow
\series default
:
-\begin_inset Formula \begin{equation}
+\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_layout
\begin_layout Standard
-A box that can contain several lines and paragraphs, a so called paragraph
+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
\emph on
Decoration
\emph default
-: Recangular box,
+: Rectangular box,
\emph on
Inner Box
\emph default
\end_inset
- that has the following scheme:
+ which has the following scheme:
\end_layout
\begin_layout Standard
\emph on
b
\emph default
- for bottom means that the box is aligned within the surrounding text with
- its last line.
+ 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 top this is done with the first line.
+ 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
\end_inset
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
\end{equation}
\begin_inset VSpace medskip
\end_inset
-As a parbox is used as argument of
+As a parbox is used as the argument of
\series bold
\backslash
\end_inset
using the mathematical textmode:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
\]
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
\begin_layout Standard
-For all integral operators there is a second version available, ending on
+For all integral operators there is a second version available, ending in
\series bold
op
\end_inset
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
\end_layout
\begin_layout Subsection
\begin_layout Standard
The default limits type is this:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\sum_{x=0}^{\infty}\frac{1}{x^{2}}
\]
\family default
\series default
:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
\]
Display
\series default
and so set below the integrals:
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
\iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
\end{equation}
are used.
To create for example this expression
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
\sum_{\begin{subarray}{c}
0<k<1000\\
\\
\begin_layout Standard
to create the lower limit.
The summand is now directly behind the summation operator:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\sum_{\mathclap{\substack{0<k<1000\\
\\
k\,\in\,\mathbb{N}
.
\end_layout
+\begin_layout Subsection
+Decoration for Operators
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Operators ! Decoration
+\end_layout
+
+\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
+
+ characters can be placed above or below an operator, respectively.
+ With the command
+\series bold
+
+\backslash
+sideset
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! S !
+\backslash
+sideset
+\end_layout
+
+\end_inset
+
+ characters can be set before and behind a big operator.
+ The command scheme is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+sideset{character
+\series default
+
+\series bold
+before}{character
+\series default
+
+\series bold
+behind}
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+sideset
+\series default
+ must always be before the operator.
+ You can decorate with several characters and even with other operators
+ and symbols.
+ To place for example only characters behind a big operator, write nothing
+ between the first braces but don't omit the braces.
+\end_layout
+
+\begin_layout Standard
+For example the command
+\series bold
+
+\backslash
+sideset{
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\series default
+'
+\series bold
+
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+sum_k=1
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+^
+\series bold
+n
+\series default
+ produces:
+\begin_inset Formula
+\[
+\sideset{}{'}\sum_{k=1}^{n}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+\backslash
+sideset
+\series default
+ can only be used to decorate big operators, binary operators are not allowed.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+overset
+\series default
+ and
+\series bold
+
+\backslash
+underset
+\series default
+ can also be used to decorate symbols and characters.
+ For example, the command
+\series bold
+
+\backslash
+overset
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+maltese
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+
+\begin_inset Formula $\uparrow$
+\end_inset
+
+
+\series bold
+a
+\series default
+ produces:
+\begin_inset Formula
+\[
+\overset{a}{\maltese}
+\]
+
+\end_inset
+
+
+\end_layout
+
\begin_layout Subsection
Binary Operators
\begin_inset CommandInset label
\begin_layout Standard
Binary operators are surrounded by space when there is a character before
- and behind them.
+ and after them.
\begin_inset VSpace medskip
\end_inset
\end_inset
:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\Lozenge_{n=1}^{\infty}
\]
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
\]
\begin_layout Standard
The style commands work also for letters in mathematical constructs:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\mathfrak{A=\frac{b}{C}}
\]
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
\]
boldsymbol
\series default
is used:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
\]
\end_inset
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
\]
\family default
dialog.
Here is a formula in magenta:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
{\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
\]
\end_inset
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
\]
\end_layout
\begin_layout Standard
-The size produced by the commands depends on the document font size, that
- corresponds with the command
+The size produced by the commands depends on the document font size, which
+ corresponds to the command
\series bold
\backslash
is inserted behind the formula in TeX-mode.
\end_layout
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
\begin_layout Standard
Within a formula the size can be changed using the following size commands:
\end_layout
\end_inset
-\begin_inset Formula \[
+\begin_inset Formula
+\[
A=\frac{B}{c}\cdot\maltese
\]
\end_inset
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
\]
in the default size.
\end_layout
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
\begin_layout Section
Greek Letters
\begin_inset Index idx
\end_inset
.
- Therefore there are predefined functions, that are additionally a bit separated
+ 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
sgn
\emph default
, and change it to mathematical text.
- At last a space is inserted between prefactor and function.
+ Finally, a space is inserted between prefactor and function.
\end_layout
\begin_layout Standard
\end_layout
\begin_layout Standard
-For limits there are defined besides
+For limits, in addition to the commands
\series bold
\backslash
\backslash
limsup
\series default
- furthermore the following functions:
+ the following functions are defined:
\end_layout
\begin_layout Standard
\begin_layout Standard
In a displayed formula the limit is set below the formula, as usual:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\lim_{x\to A}x=B
\]
\begin_layout Standard
The modulo-function is special, because it exists in four variants.
-\end_layout
-
-\begin_layout Standard
-The variants in a displayed formula:
-\begin_inset Formula \begin{align*}
+ 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\\
\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
\end_layout
\begin_layout Subsection
-Minuscule Numbers
+Old-style Figures
\begin_inset Index idx
status collapsed
\begin_layout Plain Layout
-Minuscule numbers
+Old-style Figures
\end_layout
\end_inset
\end_layout
\begin_layout Standard
-Minuscule numbers are created with the command
+Old-style figures (also known as old-style numerals) are created with the
+ command
\series bold
\backslash
\end_inset
.
+ The align environment is recommended because it provides in any case a
+ typographically correct output.
\end_layout
\begin_layout Standard
\begin_layout Standard
There is sometimes not enough space in multiline formulas between the lines:
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\
4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0
\end{eqnarray*}
\end_inset
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\
4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0
\end{eqnarray*}
\end_inset
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
A & = & B\\
C & \ne & A
\end{eqnarray*}
\end_inset
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
A & = & B\\
C & \ne & A
\end{eqnarray*}
\end_layout
\begin_layout Itemize
-When one side of the equation is much shorther than the line width, this
+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}
+\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 operator because it is the first character of the line.
+ 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
status collapsed
\begin_layout Plain Layout
-more about
+for more about
\series bold
\backslash
\end_inset
is used.
- It is inserted to the first column of the first line and effects that all
- further insertions overwrite the following columns:
-\begin_inset Formula \begin{eqnarray}
+ 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}
\begin_layout Standard
For brackets spanning multiple lines the following problem occurs:
-\begin_inset Formula \begin{eqnarray*}
+\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*}
\begin_layout Standard
The result is this:
-\begin_inset Formula \begin{eqnarray*}
+\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*}
\begin_layout Standard
Align environments can be used for every kind of multiline formulas.
- They are specially useful to set several formulas side by side.
+ They are especially useful to set several formulas side by side.
\end_layout
\begin_layout Standard
\end_layout
\begin_layout Standard
-This Align environment is created by presssing
+This Align environment is created by pressing
\begin_inset Info
type "shortcut"
arg "newline-insert newline"
\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*}
+\begin_inset Formula
+\begin{align*}
A & =\sin(B) & C & =D\\
C & \ne A & B & \ne D
\end{align*}
\end_inset
cm space was inserted at the beginning of the second formula:
-\begin_inset Formula \begin{alignat*}{2}
+\begin_inset Formula
+\begin{alignat*}{2}
A & =\sin(B) & \hspace{1cm}C & =D\\
C & \ne A & B & \ne D
\end{alignat*}
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*}
+\begin_inset Formula
+\begin{flalign*}
A & =1 & B & =2 & C & =3\\
X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
\end{flalign*}
\end_inset
:
-\begin_inset Formula \begin{flalign}
+\begin_inset Formula
+\begin{flalign}
\hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
\end{flalign}
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*}
+\begin_inset Formula
+\begin{eqnarray*}
\frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
AB & AB & AB\\
A & = & A
\begin_layout Standard
This environment consists of only one centered column.
Every line can be numbered.
-\begin_inset Formula \begin{gather}
+\begin_inset Formula
+\begin{gather}
A=1\\
X=\textrm{-}1
\end{gather}
\end_inset
in the multline environment:
-\begin_inset Formula \begin{multline}
+\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_inset
-\begin_inset Formula \begin{multline}
+\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}}
\begin_layout Standard
To display only parts of a formula with multiple lines, one of the following
- environments are used:
+ environments is used:
\series bold
aligned
\series default
formula environments, but it is possible to set further formula parts beside
them.
An example:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
\Delta E\Delta t & \ge\frac{\hbar}{2}
\end{aligned}
\end_inset
in the aligned environment:
-\begin_inset Formula \begin{equation}
+\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}
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}
+\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
).
- The formula number is displayed in LyX behind the formula as number sign
+ 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
Line
\family default
- (shortcut
+ (shortcut
\begin_inset Info
type "shortcut"
arg "math-number-line-toggle"
.
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:
Insert\SpecialChar \menuseparator
Label
\family default
- is used again.
+ is used again or you right-click on a formula and then on
+\family sans
+Equation Label
+\family default
+.
\end_layout
\begin_layout Standard
\begin_layout Standard
An example:
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
A=C-B\label{eq:a}
\end{equation}
\end_inset
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
B=C-A\label{eq:b}
\end{equation}
\end_inset
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
C=A+B\label{eq:c}
\end{equation}
\end_inset
-\begin_inset Formula \begin{eqnarray}
+\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_inset
is used:
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
A+B=C\tag{something}\label{eq:tag}
\end{equation}
something
\series default
- was inserted to the formula.
+ was inserted in the formula.
\end_layout
\begin_layout Standard
something
\series default
is inserted instead, the star prevents the parentheses around the expression:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
A+B=C\tag*{something}
\]
\end_layout
\begin_layout Standard
-Thus in our case the following LaTeX-preamble or TeX-Code line is used:
+Thus in our case the following LaTeX-preamble or TeX code line is used:
\end_layout
\begin_layout Standard
\end_inset
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
A+B=C
\end{equation}
\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:
+ as TeX code or to the LaTeX-preamble:
\end_layout
\begin_layout Standard
\begin_layout Plain Layout
\series bold
+\color none
Note:
\series default
- Only maximal 26 formulas can be numbered with Latin letters in one document.
+ 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 Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
A=\textrm{small roman}
\end{equation}
\end_inset
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
B=\textrm{big Roman}\label{eq:Rom}
\end{equation}
\end_inset
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
C=\textrm{small Latin}
\end{equation}
\end_inset
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
D=\textrm{big Latin}\label{eq:Lat}
\end{equation}
\end_inset
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
E=\textrm{Arabic}
\end{equation}
.
\end_layout
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
\begin_layout Section
Chemical Symbols and Equations
\begin_inset CommandInset label
.
The chemical equation for this is:
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
\mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
\end{equation}
\begin_layout Plain Layout
\series bold
+\color none
Note:
\series default
Inserting a formula to a
\backslash
ce
\series default
- box will lead to LaTeX errors.
+ 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
\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
are an example of a multi-stage chemical reaction where every equation
has its own number.
-\begin_inset Formula \begin{eqnarray}
+\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_layout
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
\begin_layout Section
Diagrams
\end_layout
\begin_layout Standard
Diagrams of this type visualize relations by vertical and horizontal lines
or arrows:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\begin{CD}A@>>>B@>>>C\\
@AAA@.@VVV\\
F@<<<E@<<<D
\series bold
@VVV
\series default
- an down arrow and
+ a down arrow and
\series bold
@|
\series default
\end_layout
\begin_layout Itemize
-Is text inserted between the first and second < or >, resp., it is placed
+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 Standard
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\begin{CD}A@>j>>B@>>k>C@=F\\
@AmAA@.@VV{V}V@|\\
D@<<j<E@>k>>F@=C
.
\end_layout
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
\begin_layout Section
User-defined Commands
\begin_inset Index idx
\backslash
fcolorbox
\series default
- where the color for the box needn't to be specified, the argument for the
+ 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_layout Standard
User-defined commands are especially convenient for complex expressions.
- When you are for example dealing in a document with quadratic equations,
+ 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 \[
+\begin_inset Formula
+\[
0=\lambda^{2}+p\lambda+q
\]
\end_inset
The general form of the solution is
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
\]
.
Argument placeholders are displayed red.
- Maximum 9 arguments are possible.
+ 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
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\qG x{\ln(x)}B
\]
\end_layout
\begin_layout Standard
-Math macros can also be directly be created from a
+Math macros can also be directly created from a
\series bold
\backslash
\end_layout
\begin_layout Standard
-Math macros currently yet have the problem that further formulas in macro
- definitions are handled wrongly.
+Math macros currently have the problem that further formulas in macro definition
+s are handled wrongly.
Therefore the example
\series bold
\end_layout
+\begin_layout Section
+Computer Algebra Systems
+\end_layout
+
\begin_layout Standard
-\begin_inset Newpage newpage
+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
-Tips
+Miscellaneous
\begin_inset Index idx
status collapsed
\begin_layout Plain Layout
-Tips
+Miscellaneous
\end_layout
\end_inset
Braket
\series default
assures that all vertical bars are set in the size of the surrounding brackets:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
\]
Commands ! G !
\backslash
genfrac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+vspace{4mm}
+\end_layout
+
+\end_inset
+
+
\end_layout
\end_inset
\begin_layout Standard
A test:
-\begin_inset Formula \begin{align*}
+\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*}
\series bold
\backslash
-usepackage[samesize]{cancel}
+usepackage{cancel}
\end_layout
\begin_layout Standard
cancelto
\series default
is especially suitable to visualize the reduction of fractions within formulas:
-\begin_inset Formula \[
+\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_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
\end_inset
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
\end_layout
\begin_layout Subsection
status open
\begin_layout Plain Layout
-Note herby that the setting
+Note that in this case the setting
\family sans
Two-column
\begin_inset space ~
\end_inset
-\begin_inset Formula \begin{equation}
+\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
- consists of five columns whereas in the first two columns contain the equation,
+ 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}
+\begin_inset Formula
+\begin{flalign}
\hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
\rho & \textrm{density}\\
V & \textrm{volume}\\
\end_inset
- They are created when the command for a small Greek letters is started
- with
+ They are created when the command for a small Greek letter is started with
+
\series bold
up
\series default
\begin_layout Standard
With these commands reactions of elementary particles can be typeset:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
\]
\begin_layout Standard
The encoding of several characters is saved in definition files.
- Fore example the encoding
+ For example the encoding
\series bold
latin9
\series default
\series bold
latin9.def
\series default
- that is in the installation folder of LaTeX.
+ which is in the installation folder of LaTeX.
Encodings should only be changed via the LaTeX-preamble and not in the
definition files.
- Otherwise own documents could not be edited by other LyX users working
- on other computers.
+ Otherwise documents could not be edited by other LyX users working on other
+ computers.
\end_layout
\begin_layout Standard
\end_inset
Besides the centered dot, in this document the degree sign ° is defined
- with the following LaTeX-preamble line so that it can directly be inserted
- to a formula:
+ with the following LaTeX-preamble line so that it can be directly inserted
+ into a formula:
\end_layout
\begin_layout Standard
\end_layout
\begin_layout Bibliography
-\labelwidthstring References
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "TLC2"
\end_layout
\begin_layout Bibliography
-\labelwidthstring References
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "Mathmode"
\end_layout
\begin_layout Bibliography
-\labelwidthstring References
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "AMS"
\end_layout
\begin_layout Bibliography
-\labelwidthstring References
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "Symbols"
\end_layout
\begin_layout Bibliography
-\labelwidthstring References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+key "cancel"
+
+\end_inset
+
+
+\begin_inset CommandInset href
+LatexCommand href
+name "Documentation"
+target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
+
+\end_inset
+
+ of the LaTeX-package
+\series bold
+cancel
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! cancel
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "hyperref"
\end_layout
\begin_layout Bibliography
-\labelwidthstring References
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "mhchem"
\end_layout
\begin_layout Bibliography
-\labelwidthstring References
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "Mathclap"
\end_layout
\begin_layout Bibliography
-\labelwidthstring References
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "Duden"
\end_layout
\begin_layout Bibliography
-\labelwidthstring References
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "Checklist"
projects / lyx.git / blobdiff