1 #LyX 2.4 created this file. For more info see https://www.lyx.org/
5 \save_transient_properties true
6 \origin /systemlyxdir/doc/
9 % DO NOT ALTER THIS PREAMBLE!!!
11 % This preamble is designed to ensure that the file prints
12 % out as advertised. If you mess with this preamble,
13 % parts of this document may not print out as expected. If you
14 % have problems LaTeXing this file, please contact
15 % the documentation team
16 % email: lyx-docs@lists.lyx.org
18 % solves the following problem:
19 % If the dection number consits of too many numerals the section heading
20 % will be printed in the TOC without a space between it and the section number.
21 % As solution more space between the number and the heading is inserted:
22 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
23 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
25 % increase link area for cross-references and autoname them,
26 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
27 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
28 \@ifpackageloaded{babel}{
29 \addto\extrasenglish{%
30 \renewcommand*{\equationautorefname}[1]{}%
31 \renewcommand{\sectionautorefname}{sec.\negthinspace}%
32 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
33 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
37 % don't load packages twice
38 % see first footnote in sec. 9.3
39 \@ifundefined{textcolor}{\usepackage{color}}{}
41 % the pages of the TOC are numbered roman
42 % and a PDF-bookmark for the TOC is added
44 \let\myTOC\tableofcontents
45 \renewcommand{\tableofcontents}{%
47 \pdfbookmark[1]{\contentsname}{}
50 \pagenumbering{arabic}}
52 % add 0.5 mm vertical space for table rows
53 \@ifundefined{extrarowheight} {\usepackage{array}}{}
54 \setlength{\extrarowheight}{0.5mm}
56 % insert additional vertical space of 1.5 mm between footnotes,
58 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
60 % makes caption labels bold
61 \setkomafont{captionlabel}{\bfseries}
63 % enables calculation of values
66 % for multiple columns used in sec. 24.7
72 % for the Fourier transformation symbol
75 % define a color, used in sec.9.3
76 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
78 % declare operators (see sec. 10.4 and sec. 15.2)
79 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
80 \DeclareMathOperator{\sgn}{sgn}
82 % example definitions for sec. 20.1
83 \newcommand{\gr}{\Longrightarrow}
84 \newcommand{\us}[1]{\underline{#1}}
85 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
86 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
87 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
89 % example macro from sec. 19.4
91 %\def\tagform@#1{\maketag@@@{|#1|}}
94 % ------------------------------------
95 % used to check for needed LaTeX packages
98 % check for package undertilde
99 % used for the command \utilde
100 \newboolean{undertilde}
101 \IfFileExists{undertilde.sty}
102 {\usepackage{undertilde}
103 \setboolean{undertilde}{true}}
104 {\setboolean{undertilde}{false}}
106 % check for package eurosym
107 % used for the Euro symbol
109 \IfFileExists{eurosym.sty}
110 {\usepackage[gennarrow]{eurosym}
111 \setboolean{eurosym}{true}}
112 {\setboolean{eurosym}{false}}
114 % check for package braket
115 % used for physical vectors
117 \IfFileExists{braket.sty}
119 \setboolean{braket}{true}}
120 {\setboolean{braket}{false}}
122 % check for package cancel
124 \IfFileExists{cancel.sty}
126 \setboolean{cancel}{true}}
127 {\setboolean{cancel}{false}}
129 % check for package upgreek
131 \IfFileExists{upgreek.sty}
132 {\usepackage{upgreek}
133 \setboolean{upgreek}{true}}
134 {\setboolean{upgreek}{false}}
136 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
137 \use_default_options false
141 \maintain_unincluded_children no
143 \language_package default
146 \font_roman "lmodern" "default"
147 \font_sans "lmss" "default"
148 \font_typewriter "lmtt" "default"
149 \font_math "auto" "auto"
150 \font_default_family default
151 \use_non_tex_fonts false
153 \font_roman_osf false
155 \font_typewriter_osf false
156 \font_sf_scale 100 100
157 \font_tt_scale 100 100
159 \use_dash_ligatures false
161 \default_output_format pdf2
163 \bibtex_command default
164 \index_command makeindex
165 \float_placement class
166 \float_alignment class
170 \pdf_title "LyX's Math Manual"
171 \pdf_author "LyX Team, Uwe Stöhr"
172 \pdf_subject "LyX-documentation about math"
173 \pdf_keywords "LyX, Mathed"
175 \pdf_bookmarksnumbered true
176 \pdf_bookmarksopen true
177 \pdf_bookmarksopenlevel 1
178 \pdf_breaklinks false
182 \pdf_pdfusetitle false
183 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
186 \use_package amsmath 2
187 \use_package amssymb 2
188 \use_package cancel 1
190 \use_package mathdots 1
191 \use_package mathtools 2
192 \use_package mhchem 1
193 \use_package stackrel 1
194 \use_package stmaryrd 1
195 \use_package undertilde 0
197 \cite_engine_type default
201 \paperorientation portrait
207 \notefontcolor #0000ff
214 \paragraph_separation skip
217 \math_numbering_side default
218 \quotes_style english
222 \paperpagestyle plain
227 \tracking_changes true
228 \output_changes false
230 \postpone_fragile_content false
233 \html_be_strict false
234 \docbook_table_output 0
235 \docbook_mathml_prefix 1
236 \author -563046850 "Jean-Marc LASGOUTTES"
239 \author 47243155 "Jean-Marc"
240 \author 232239728 "Owner"
247 's Detailed Math Manual
251 by the \SpecialChar LyX
256 \begin_layout Plain Layout
258 If you have comments or error corrections, please send them to the \SpecialChar LyX
263 \begin_inset CommandInset href
265 name "lyx-docs@lists.lyx.org"
266 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
278 \begin_inset Note Note
281 \begin_layout Plain Layout
288 \begin_inset Newline newline
292 \begin_inset Newline newline
298 \change_inserted 47243155 1563226038
300 \change_deleted 47243155 1563226038
306 \begin_layout Standard
307 \begin_inset CommandInset toc
308 LatexCommand tableofcontents
315 \begin_layout Standard
316 \begin_inset Note Note
319 \begin_layout Plain Layout
320 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
323 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
330 If they are not installed the document can be exported anyway but the sections
331 where the packages are required will not appear in the output.
336 ; if it is not installed, this file cannot be exported.
339 \begin_layout Plain Layout
340 The latest PDF-version of this document can be found here:
341 \begin_inset Newline newline
346 https://wiki.lyx.org/LyX/Manuals#Math
354 \begin_layout Standard
355 \begin_inset Newpage newpage
361 \begin_layout Section
365 \begin_layout Standard
366 This document details \SpecialChar LyX
367 's math features and the \SpecialChar LaTeX
368 -commands used for mathematical
369 characters and constructs.
370 It is oriented toward the use of commands.
371 The user should read the
379 section of the User's Guide before proceeding.
382 \begin_layout Standard
383 Most of the characters and many constructs explained in this manual are
384 also accessible via the menu
388 \SpecialChar menuseparator
404 But everybody who has to write lots of formulas will notice that it is
405 much faster to use commands instead of the math toolbar.
406 Therefore this manual is focused on commands but also mentions the correspondin
407 g toolbar buttons when available.
410 \begin_layout Standard
411 Unless specially mentioned, math commands are only available within formulas.
412 To be able to use all of the commands explained in this document, the option
417 must be checked in the document settings (menu
419 Document\SpecialChar menuseparator
420 Settings\SpecialChar menuseparator
431 \begin_layout Plain Layout
434 Use AMS math package automatically
440 \begin_layout Plain Layout
449 -math when math constructs are found that are supported by \SpecialChar LyX
458 \begin_layout Standard
459 This document doesn't list all
463 \begin_layout Plain Layout
476 \begin_layout Plain Layout
477 A list containing all
481 \begin_layout Plain Layout
490 -math commands is in the file
493 \begin_inset CommandInset href
496 target "https://www.ctan.org/tex-archive/macros/amstex/doc/amsguide.pdf"
503 , which is part of every \SpecialChar LaTeX
504 standard installation.
509 for lucidity reasons.
512 \begin_layout Section
516 \begin_layout Standard
517 To create an inline formula
518 \begin_inset Index idx
521 \begin_layout Plain Layout
527 that is embedded in a text line, use one of the shortcuts
533 or the toolbar button
540 \begin_inset Newline newline
543 To create a display style formula
544 \begin_inset Index idx
547 \begin_layout Plain Layout
548 Formula ! display style
553 which will appear bigger, has a different format, and will be in a separate
554 paragraph, use one of these shortcuts:
563 \begin_layout Standard
564 To change a display style formula to an inline formula, place the cursor
565 inside the formula and use
566 \change_deleted 5863208 1612729312
570 \change_deleted 5863208 1612729314
574 \change_deleted 5863208 1612729303
582 \change_inserted 5863208 1612729281
586 arg "math-mutate simple"
593 Edit\SpecialChar menuseparator
594 Math\SpecialChar menuseparator
599 \change_inserted 5863208 1612729555
600 Similarly you can use the shortcut
603 arg "math-mutate equation"
606 to change from an inline to a display style formula.
608 \change_deleted 5863208 1612729557
609 The same method is used to change an inline formula to a display style formula.
614 \begin_layout Standard
615 To display parts of an inline formula in the size of a display style formula,
623 \begin_inset Index idx
626 \begin_layout Plain Layout
635 A new blue box will appear in which the desired formula part is inserted.
638 \begin_layout Standard
639 Only inline formulas are allowed inside tables.
642 \begin_layout Standard
644 \change_deleted 232239728 1610897673
649 can be turned on in the menu
651 View\SpecialChar menuseparator
655 When you click there on
656 \begin_inset Quotes eld
660 \begin_inset Quotes erd
663 the toolbar will be shown permanently at the bottom; this state is visualized
668 menu with a checkmark.
669 When you click in this state again on
670 \begin_inset Quotes eld
674 \begin_inset Quotes erd
685 is only shown when the cursor is within a formula; this state is visualized
686 by the renaming of the menu entry from
687 \begin_inset Quotes eld
691 \begin_inset Quotes erd
695 \begin_inset Quotes eld
703 \begin_inset Quotes erd
707 \change_inserted 232239728 1610897478
711 \begin_layout Standard
713 \change_inserted 232239728 1610918987
718 visibility is controlled in the menu
720 View\SpecialChar menuseparator
721 Toolbars\SpecialChar menuseparator
725 Three options will be presented, On, Off, and Automatic.
726 Selecting On will cause the toolbar to be shown permanently at the bottom
728 Selecting Off will disable the toolbar.
729 Selecting Automatic will cause the toolbar to automatically appear when
730 the cursor is located within a formula.
731 The active state of the toolbar is indicated by a checkmark next to the
732 current menu selection.
733 \begin_inset Note Note
736 \begin_layout Plain Layout
738 \change_inserted 232239728 1610897730
739 The menu functionality appears to have changed, I rewrote the paragraph
740 for the current functionality
752 \begin_layout Standard
755 \begin_inset Index idx
758 \begin_layout Plain Layout
765 is invoked by pressing the toolbar button
773 Insert\SpecialChar menuseparator
785 \begin_layout Standard
786 To change the \SpecialChar LaTeX
788 \begin_inset Index idx
791 \begin_layout Plain Layout
800 Document\SpecialChar menuseparator
801 Settings\SpecialChar menuseparator
811 \begin_layout Standard
812 To edit matrices, case differentiations and multiline formulas, use the
815 Edit\SpecialChar menuseparator
820 Edit\SpecialChar menuseparator
822 \begin_inset space \thinspace{}
826 \begin_inset space \thinspace{}
836 When lines and columns are swapped via the menu, the column or line where
837 the cursor is in is exchanged with the column to the right or the line
839 If the cursor is in the last column or row, the exchange is done with the
840 column to the left or the line above.
843 \begin_layout Standard
844 To write text in formulas
848 \begin_layout Plain Layout
849 For multiline formulas the command
856 \begin_inset CommandInset ref
858 reference "subsec:Text-in-multiline"
872 \begin_inset Index idx
875 \begin_layout Plain Layout
882 \begin_inset Index idx
885 \begin_layout Plain Layout
892 This mode is invoked with the shortcut
898 or by the insertion of the command
905 \begin_inset Index idx
908 \begin_layout Plain Layout
917 The text appears black in \SpecialChar LyX
918 and can therefore be distinguished from the
919 other formula parts which appear blue.
920 In the output, mathematical text is set upright contrary to other formula
924 \begin_layout Subsection*
928 \begin_layout Standard
929 Most \SpecialChar LaTeX
930 -commands for math constructs have the following syntax:
933 \begin_layout Standard
949 \begin_layout Standard
950 A command always starts with a backslash
951 \begin_inset Quotes gld
961 \begin_inset Quotes grd
973 s, also omit the associated brackets.
974 The braces around the
982 are referred to in this document as \SpecialChar TeX
984 \begin_inset Index idx
987 \begin_layout Plain Layout
995 If you append a left brace to a command name inside a formula, \SpecialChar LyX
997 creates a right \SpecialChar TeX
999 In all other cases standalone \SpecialChar TeX
1000 braces are created in formulas with the
1008 Normal braces are created by typing
1014 braces appear red in \SpecialChar LyX
1015 , normal braces appear blue.
1017 mode a command is not needed to get \SpecialChar TeX
1020 braces don't appear in the output while normal braces do.
1023 \begin_layout Standard
1024 When commands without arguments, like commands for symbols, are entered
1026 mode, a space character must
1030 be behind the command to end it.
1031 This space doesn't appear in the output.
1032 When the space should appear in the output, the space must be followed
1034 \change_deleted 177693 1654668848
1036 \change_inserted 177693 1654668851
1039 space in normal text.
1042 \begin_layout Standard
1044 \change_deleted 177693 1654668857
1046 \change_inserted 177693 1654668860
1049 space is inserted with
1050 \change_inserted 232239728 1610908934
1052 \change_deleted 5863208 1612729787
1054 \change_inserted 5863208 1612729774
1058 arg "command-alternatives math-space ; space-insert protected"
1062 \change_deleted 232239728 1610908788
1066 arg "command-alternatives space-insert protected; math-space"
1070 \change_inserted 5863208 1612729766
1071 or with the menu selection
1074 \change_inserted 232239728 1610908897
1075 Insert\SpecialChar menuseparator
1076 Formatting\SpecialChar menuseparator
1078 \change_deleted 177693 1654668863
1080 \change_inserted 177693 1654668975
1082 \change_inserted 232239728 1610908897
1086 \change_inserted 5863208 1612729638
1090 \change_deleted 5863208 1612729640
1098 \begin_layout Subsection*
1099 \begin_inset Newpage newpage
1103 \change_deleted 5863208 1612098922
1107 \change_inserted 5863208 1612100879
1108 of Syntax Used in this Manual
1113 \begin_layout Itemize
1115 \begin_inset space \textvisiblespace{}
1118 denotes a space character to be input
1119 \change_inserted 5863208 1612098935
1125 \begin_layout Itemize
1127 \begin_inset Formula $\to$
1130 denotes the usage of the corresponding arrow key on the keyboard.
1135 key can often be used instead of
1136 \begin_inset Formula $\to$
1140 \begin_inset Formula $\downarrow$
1148 \begin_inset Formula $\leftarrow$
1152 \begin_inset Formula $\uparrow$
1158 \begin_layout Subsection*
1162 \begin_layout Standard
1164 \begin_inset Float table
1171 \begin_layout Plain Layout
1173 \begin_inset Caption Standard
1175 \begin_layout Plain Layout
1176 \begin_inset CommandInset label
1178 name "tab:Available-units"
1190 \begin_layout Plain Layout
1192 \begin_inset Tabular
1193 <lyxtabular version="3" rows="13" columns="2">
1194 <features booktabs="true" tabularvalignment="middle">
1195 <column alignment="center" valignment="top">
1196 <column alignment="center" valignment="top" width="0pt">
1198 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1201 \begin_layout Plain Layout
1207 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1210 \begin_layout Plain Layout
1218 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1221 \begin_layout Plain Layout
1227 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1230 \begin_layout Plain Layout
1238 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1241 \begin_layout Plain Layout
1247 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1250 \begin_layout Plain Layout
1258 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1261 \begin_layout Plain Layout
1267 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1270 \begin_layout Plain Layout
1272 \begin_inset space \thinspace{}
1276 \change_deleted 232239728 1610909338
1278 \change_inserted 232239728 1610909338
1282 \begin_inset space \thinspace{}
1292 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1295 \begin_layout Plain Layout
1301 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1304 \begin_layout Plain Layout
1306 \begin_inset space \thinspace{}
1310 \begin_inset space \thinspace{}
1320 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1323 \begin_layout Plain Layout
1329 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1332 \begin_layout Plain Layout
1334 \begin_inset space \thinspace{}
1338 \begin_inset space \thinspace{}
1348 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1351 \begin_layout Plain Layout
1357 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1360 \begin_layout Plain Layout
1362 \begin_inset space \thinspace{}
1366 \begin_inset space \thinspace{}
1376 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1379 \begin_layout Plain Layout
1385 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1388 \begin_layout Plain Layout
1390 \begin_inset space \thinspace{}
1394 \begin_inset space \thinspace{}
1404 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1407 \begin_layout Plain Layout
1413 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1416 \begin_layout Plain Layout
1418 \begin_inset space \thinspace{}
1422 \begin_inset Formula $\approx$
1426 \begin_inset space \thinspace{}
1436 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1439 \begin_layout Plain Layout
1445 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1448 \begin_layout Plain Layout
1450 \begin_inset space \thinspace{}
1454 \begin_inset space \thinspace{}
1464 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1467 \begin_layout Plain Layout
1473 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1476 \begin_layout Plain Layout
1480 \begin_inset Quotes eld
1486 \begin_inset Quotes erd
1496 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1499 \begin_layout Plain Layout
1505 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1508 \begin_layout Plain Layout
1510 \begin_inset Quotes eld
1518 \begin_inset Quotes erd
1528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1531 \begin_layout Plain Layout
1537 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1540 \begin_layout Plain Layout
1542 \begin_inset space \thinspace{}
1546 \begin_inset Formula $\nicefrac{1}{18}$
1550 \begin_inset space \thinspace{}
1571 \begin_layout Section
1575 \begin_layout Subsection
1577 \begin_inset Index idx
1580 \begin_layout Plain Layout
1587 \begin_inset Index idx
1590 \begin_layout Plain Layout
1597 \begin_inset Index idx
1600 \begin_layout Plain Layout
1605 \begin_layout Plain Layout
1616 \begin_layout Plain Layout
1629 \begin_inset Index idx
1632 \begin_layout Plain Layout
1637 \begin_layout Plain Layout
1648 \begin_layout Plain Layout
1663 \begin_layout Standard
1664 Indices are created with an underscore
1665 \begin_inset Quotes eld
1669 \begin_inset Quotes erd
1672 or via the math toolbar button
1675 arg "math-subscript"
1678 , exponents with a caret
1679 \begin_inset Quotes eld
1683 \begin_inset Quotes erd
1686 or via the math toolbar button
1689 arg "math-superscript"
1695 \begin_layout Standard
1697 \begin_inset Tabular
1698 <lyxtabular version="3" rows="4" columns="2">
1699 <features booktabs="true" tabularvalignment="middle">
1700 <column alignment="center" valignment="top" width="0pt">
1701 <column alignment="center" valignment="top" width="0pt">
1703 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1706 \begin_layout Plain Layout
1712 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1715 \begin_layout Plain Layout
1723 <cell alignment="center" valignment="top" usebox="none">
1726 \begin_layout Plain Layout
1732 <cell alignment="center" valignment="top" usebox="none">
1735 \begin_layout Plain Layout
1736 \begin_inset Formula $B_{V}$
1745 <row topspace="1.5mm">
1746 <cell alignment="center" valignment="top" usebox="none">
1749 \begin_layout Plain Layout
1755 <cell alignment="center" valignment="top" usebox="none">
1758 \begin_layout Plain Layout
1759 \begin_inset Formula $B^{V}$
1768 <row topspace="1.5mm">
1769 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1772 \begin_layout Plain Layout
1774 \begin_inset space \textvisiblespace{}
1782 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1785 \begin_layout Plain Layout
1786 \begin_inset Formula $B^{A}$
1802 \begin_layout Standard
1803 As the caret is in some languages an accent, vowels will be accentuated
1804 in this case and not set as exponents
1808 \begin_layout Plain Layout
1809 Depending on the keyboard settings used this can also happen for characters
1816 To get exponents in this case, press
1820 after the caret as in the last example.
1823 \begin_layout Subsection
1825 \begin_inset CommandInset label
1827 name "subsec:Fractions"
1832 \begin_inset Index idx
1835 \begin_layout Plain Layout
1844 \begin_layout Standard
1845 Fractions are generated with the command
1852 \begin_inset Index idx
1855 \begin_layout Plain Layout
1863 or via the math toolbar button
1866 arg "math-insert \\frac"
1870 The font size is adjusted automatically, depending on whether the fraction
1871 is in an inline or display style formula.
1872 With the math toolbar button
1875 arg "math-insert \\frac-square"
1878 you can select different fraction types.
1881 \begin_layout Standard
1889 \begin_inset Index idx
1892 \begin_layout Plain Layout
1900 a fraction can be created that always has the size of a display style formula.
1908 \begin_inset Index idx
1911 \begin_layout Plain Layout
1919 the fraction appears always with the size of an inline formula.
1923 \begin_layout Standard
1924 A line with the fraction
1925 \begin_inset Formula $\frac{1}{2}$
1928 that was created with the command
1937 \begin_layout Standard
1938 A line with the fraction
1939 \begin_inset Formula $\dfrac{1}{2}$
1942 that was created with the command
1951 \begin_layout Standard
1953 \begin_inset Tabular
1954 <lyxtabular version="3" rows="4" columns="2">
1955 <features booktabs="true" tabularvalignment="middle">
1956 <column alignment="center" valignment="top" width="0pt">
1957 <column alignment="center" valignment="top" width="0pt">
1959 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1962 \begin_layout Plain Layout
1968 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1971 \begin_layout Plain Layout
1978 <row topspace="1.5mm">
1979 <cell alignment="center" valignment="top" usebox="none">
1982 \begin_layout Plain Layout
1986 \begin_inset space \textvisiblespace{}
1990 \begin_inset Formula $\downarrow$
1998 <cell alignment="center" valignment="top" usebox="none">
2001 \begin_layout Plain Layout
2002 \begin_inset Formula $\frac{A}{B}$
2011 <row topspace="2mm">
2012 <cell alignment="center" valignment="top" usebox="none">
2015 \begin_layout Plain Layout
2019 \begin_inset space \textvisiblespace{}
2023 \begin_inset Formula $\downarrow$
2031 <cell alignment="center" valignment="top" usebox="none">
2034 \begin_layout Plain Layout
2035 \begin_inset Formula $\dfrac{A}{B}$
2044 <row topspace="2mm" bottomspace="1mm">
2045 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2048 \begin_layout Plain Layout
2052 \begin_inset space \textvisiblespace{}
2058 \begin_inset space \textvisiblespace{}
2062 \begin_inset Formula $\downarrow$
2066 \begin_inset Formula $\downarrow\downarrow$
2074 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2077 \begin_layout Plain Layout
2078 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
2094 \begin_layout Standard
2095 \begin_inset VSpace bigskip
2099 \begin_inset Newpage newpage
2102 For nested fractions the command
2109 \begin_inset Index idx
2112 \begin_layout Plain Layout
2122 \begin_inset VSpace -3mm
2128 \begin_layout Standard
2129 \begin_inset Formula
2131 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2132 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2140 \begin_layout Standard
2141 The command for the example above is:
2144 \begin_layout Standard
2150 \begin_inset space \textvisiblespace{}
2154 \begin_inset Formula $\downarrow$
2160 \begin_inset space \textvisiblespace{}
2166 \begin_inset space \textvisiblespace{}
2170 \begin_inset Formula $\downarrow$
2174 \begin_inset Formula $\downarrow$
2180 \begin_layout Standard
2181 \begin_inset VSpace medskip
2187 \begin_layout Standard
2194 always sets the fraction size to that of a displayed formula, even when
2195 it is part of another fraction.
2198 \begin_layout Standard
2199 It is possible to specify the alignment of the numerator.
2206 is used to left align it, the command
2219 centers the numerator.
2220 These fractions demonstrate the different alignments:
2223 \begin_layout Standard
2226 \begin_inset Formula
2228 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2236 \begin_layout Standard
2237 \begin_inset Note Greyedout
2240 \begin_layout Plain Layout
2257 are not real \SpecialChar LaTeX
2258 commands but represent the command
2262 cfrac[alignment]{numerator}{denominator}
2265 Therefore you cannot use them in \SpecialChar TeX
2274 \begin_layout Standard
2275 \begin_inset VSpace medskip
2278 It is often advantageous to combine
2291 \begin_inset Formula
2293 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2301 \begin_layout Standard
2302 For inline fractions with a sloped fraction stroke you can use the command
2310 \begin_inset Index idx
2313 \begin_layout Plain Layout
2322 \begin_inset Formula $\nicefrac{5}{31}$
2332 \begin_inset Index idx
2335 \begin_layout Plain Layout
2344 \begin_inset Formula $\unitfrac{5}{31}$
2347 There is also the command
2353 which allows you to write a fraction in combination with a number:
2354 \begin_inset Formula $\unitfrac[2]{1}{3}$
2360 \begin_layout Standard
2361 \begin_inset Note Greyedout
2364 \begin_layout Plain Layout
2375 is not a real \SpecialChar LaTeX
2376 command but the command
2377 \begin_inset Newline newline
2384 unitfrac[number]{numerator}{denominator}
2387 Therefore you cannot use it in \SpecialChar TeX
2396 \begin_layout Standard
2397 How to define your own fractions where the fraction stroke can be changed
2399 \begin_inset CommandInset ref
2401 reference "subsec:Self-defined-Fractions"
2408 \begin_layout Standard
2409 Multiline fractions are explained in
2410 \begin_inset CommandInset ref
2412 reference "subsec:Multiline-Fractions"
2419 \begin_layout Subsection
2421 \begin_inset Index idx
2424 \begin_layout Plain Layout
2433 \begin_layout Standard
2434 Square roots are created with
2441 \begin_inset Index idx
2444 \begin_layout Plain Layout
2452 or the math toolbar button
2455 arg "math-insert \\sqrt"
2458 , all other roots with the command
2465 \begin_inset Index idx
2468 \begin_layout Plain Layout
2476 or with the math toolbar button
2479 arg "math-insert \\root"
2485 \begin_layout Standard
2487 \begin_inset Tabular
2488 <lyxtabular version="3" rows="3" columns="2">
2489 <features booktabs="true" tabularvalignment="middle">
2490 <column alignment="center" valignment="top" width="0pt">
2491 <column alignment="center" valignment="top" width="0pt">
2493 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2496 \begin_layout Plain Layout
2502 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2505 \begin_layout Plain Layout
2512 <row topspace="1mm">
2513 <cell alignment="center" valignment="top" usebox="none">
2516 \begin_layout Plain Layout
2520 \begin_inset space \textvisiblespace{}
2528 <cell alignment="center" valignment="top" usebox="none">
2531 \begin_layout Plain Layout
2532 \begin_inset Formula $\sqrt{A-B}$
2541 <row topspace="1mm">
2542 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2545 \begin_layout Plain Layout
2549 \begin_inset space \textvisiblespace{}
2553 \begin_inset Formula $\downarrow$
2561 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2564 \begin_layout Plain Layout
2565 \begin_inset Formula $\sqrt[3]{A-B}$
2581 \begin_layout Standard
2582 A square root can also be created with
2588 when the root index field is left empty.
2591 \begin_layout Standard
2592 With certain indices the distance to the root is too small, like in this
2594 \begin_inset Formula $\sqrt[\beta]{B}$
2598 \begin_inset Newline newline
2602 \begin_inset Formula $\beta$
2606 To avoid this, the commands
2613 \begin_inset Index idx
2616 \begin_layout Plain Layout
2631 \begin_inset Index idx
2634 \begin_layout Plain Layout
2642 are used with the following scheme:
2645 \begin_layout Standard
2659 \begin_layout Standard
2660 Distance is the number of Big Points (unit bp;
2661 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2664 ), that the index should be moved to the left or up, resp..
2665 The commands are written to the index.
2666 This way the command
2667 \begin_inset Newline newline
2677 \begin_inset Formula $\to$
2683 \begin_inset Formula $\to$
2689 \begin_inset space \textvisiblespace{}
2693 \begin_inset Formula $\to$
2697 \begin_inset Newline newline
2702 produces a correct typeset formula:
2703 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2709 \begin_layout Subsection
2710 Binomial Coefficients
2711 \begin_inset Index idx
2714 \begin_layout Plain Layout
2715 Binomial coefficients
2723 \begin_layout Standard
2724 Binomial coefficients are inserted with the command
2731 \begin_inset Index idx
2734 \begin_layout Plain Layout
2742 or with the submenu of the math toolbar button
2745 arg "math-insert \\frac-square"
2761 there are the commands
2768 \begin_inset Index idx
2771 \begin_layout Plain Layout
2786 \begin_inset Index idx
2789 \begin_layout Plain Layout
2798 For other brackets around binomial coefficients there are the commands
2806 \begin_inset Index idx
2809 \begin_layout Plain Layout
2824 \begin_inset Index idx
2827 \begin_layout Plain Layout
2838 \begin_layout Standard
2840 \begin_inset Tabular
2841 <lyxtabular version="3" rows="6" columns="2">
2842 <features booktabs="true" tabularvalignment="middle">
2843 <column alignment="center" valignment="top" width="0pt">
2844 <column alignment="center" valignment="top" width="0pt">
2846 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2849 \begin_layout Plain Layout
2855 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2858 \begin_layout Plain Layout
2865 <row topspace="1mm">
2866 <cell alignment="center" valignment="top" usebox="none">
2869 \begin_layout Plain Layout
2873 \begin_inset space \textvisiblespace{}
2877 \begin_inset Formula $\downarrow$
2885 <cell alignment="center" valignment="top" usebox="none">
2888 \begin_layout Plain Layout
2889 \begin_inset Formula $\binom{A}{B}$
2898 <row topspace="2mm">
2899 <cell alignment="center" valignment="top" usebox="none">
2902 \begin_layout Plain Layout
2906 \begin_inset space \textvisiblespace{}
2910 \begin_inset Formula $\downarrow$
2918 <cell alignment="center" valignment="top" usebox="none">
2921 \begin_layout Plain Layout
2922 \begin_inset Formula $\dbinom{A}{B}$
2931 <row topspace="2mm" bottomspace="0.5mm">
2932 <cell alignment="center" valignment="top" usebox="none">
2935 \begin_layout Plain Layout
2939 \begin_inset space \textvisiblespace{}
2943 \begin_inset Formula $\downarrow$
2951 <cell alignment="center" valignment="top" usebox="none">
2954 \begin_layout Plain Layout
2955 \begin_inset Formula $\tbinom{A}{B}$
2964 <row topspace="1mm">
2965 <cell alignment="center" valignment="top" topline="true" usebox="none">
2968 \begin_layout Plain Layout
2972 \begin_inset space \textvisiblespace{}
2976 \begin_inset Formula $\downarrow$
2984 <cell alignment="center" valignment="top" topline="true" usebox="none">
2987 \begin_layout Plain Layout
2988 \begin_inset Formula ${A \brack B}$
2997 <row topspace="2mm" bottomspace="0.5mm">
2998 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3001 \begin_layout Plain Layout
3005 \begin_inset space \textvisiblespace{}
3009 \begin_inset Formula $\downarrow$
3017 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3020 \begin_layout Plain Layout
3021 \begin_inset Formula ${A \brace B}$
3037 \begin_layout Subsection
3038 Case Differentiations
3039 \begin_inset Index idx
3042 \begin_layout Plain Layout
3043 Case differentiations
3051 \begin_layout Standard
3053 \begin_inset Tabular
3054 <lyxtabular version="3" rows="3" columns="2">
3055 <features booktabs="true" tabularvalignment="middle">
3056 <column alignment="center" valignment="top" width="0pt">
3057 <column alignment="center" valignment="top" width="0pt">
3059 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3062 \begin_layout Plain Layout
3068 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3071 \begin_layout Plain Layout
3079 <cell alignment="center" valignment="top" usebox="none">
3082 \begin_layout Plain Layout
3086 \begin_inset space \textvisiblespace{}
3090 \begin_inset Formula $\to$
3094 \begin_inset Index idx
3097 \begin_layout Plain Layout
3110 <cell alignment="center" valignment="top" usebox="none">
3113 \begin_layout Plain Layout
3114 \begin_inset Formula $\begin{cases}
3124 <row topspace="1.5mm">
3125 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3128 \begin_layout Plain Layout
3132 \begin_inset space \textvisiblespace{}
3138 arg "newline-insert newline"
3146 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3149 \begin_layout Plain Layout
3150 \begin_inset Formula $\begin{cases}
3151 A & \textrm{for }x>0\\
3152 B & \textrm{for }x=0
3169 \begin_layout Standard
3176 or pressing the math toolbar button
3179 arg "math-insert \\cases"
3182 you can create new lines with the shortcut
3185 arg "newline-insert newline"
3188 or the table toolbar button
3191 arg "tabular-feature append-row"
3197 \begin_layout Standard
3204 is also available via the menu
3206 Insert\SpecialChar menuseparator
3207 Math\SpecialChar menuseparator
3213 \begin_layout Subsection
3215 \begin_inset Index idx
3218 \begin_layout Plain Layout
3227 \begin_layout Standard
3235 \begin_inset Index idx
3238 \begin_layout Plain Layout
3246 every character can be displayed canceled.
3247 The characters are quasi accentuated by a slash.
3250 \begin_layout Standard
3252 \begin_inset Tabular
3253 <lyxtabular version="3" rows="4" columns="2">
3254 <features booktabs="true" tabularvalignment="middle">
3255 <column alignment="center" valignment="top" width="0pt">
3256 <column alignment="center" valignment="top" width="0pt">
3258 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3261 \begin_layout Plain Layout
3267 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3270 \begin_layout Plain Layout
3278 <cell alignment="center" valignment="top" usebox="none">
3281 \begin_layout Plain Layout
3289 <cell alignment="center" valignment="top" usebox="none">
3292 \begin_layout Plain Layout
3293 \begin_inset Formula $\not=$
3303 <cell alignment="center" valignment="top" usebox="none">
3306 \begin_layout Plain Layout
3316 <cell alignment="center" valignment="top" usebox="none">
3319 \begin_layout Plain Layout
3320 \begin_inset Formula $\not\le$
3330 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3333 \begin_layout Plain Layout
3343 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3346 \begin_layout Plain Layout
3347 \begin_inset Formula $\not\parallel$
3363 \begin_layout Standard
3364 The last example shows that not all negations look good.
3365 Therefore there are special commands for some negations (see
3366 \begin_inset CommandInset ref
3368 reference "subsec:Mathematical-Symbols"
3373 \begin_inset CommandInset ref
3375 reference "sec:Relations"
3382 \begin_layout Subsection
3384 \begin_inset CommandInset label
3386 name "subsec:Placeholders"
3391 \begin_inset Index idx
3394 \begin_layout Plain Layout
3401 \begin_inset Index idx
3404 \begin_layout Plain Layout
3405 Chemical characters ! Isotopes
3411 \begin_inset Index idx
3414 \begin_layout Plain Layout
3419 \begin_layout Plain Layout
3430 \begin_layout Plain Layout
3445 \begin_layout Standard
3447 \begin_inset space \thinspace{}
3451 \begin_inset space \space{}
3458 \begin_layout Plain Layout
3459 Typesetting isotopes and chemical symbols is described in
3460 \begin_inset CommandInset ref
3462 reference "subsec:Chemical-Symbols-and"
3471 the following problem occurs:
3474 \begin_layout Standard
3476 \begin_inset Tabular
3477 <lyxtabular version="3" rows="2" columns="2">
3478 <features booktabs="true" tabularvalignment="middle">
3479 <column alignment="center" valignment="top" width="0pt">
3480 <column alignment="center" valignment="top" width="0pt">
3482 <cell alignment="center" valignment="top" usebox="none">
3485 \begin_layout Plain Layout
3486 Indices created with sub- and superscripts:
3491 <cell alignment="center" valignment="top" usebox="none">
3494 \begin_layout Plain Layout
3495 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3504 <row topspace="1.5mm">
3505 <cell alignment="center" valignment="top" usebox="none">
3508 \begin_layout Plain Layout
3514 <cell alignment="center" valignment="top" usebox="none">
3517 \begin_layout Plain Layout
3518 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3534 \begin_layout Standard
3535 The shorter index is placed by default below or above the first character
3536 of the longer index.
3537 This is corrected using the command
3544 \begin_inset Index idx
3547 \begin_layout Plain Layout
3555 or the math toolbar button
3556 \begin_inset space \thinspace{}
3563 \begin_layout Plain Layout
3564 Found in the submenu of the toolbar button
3567 arg "math-insert \\space"
3581 to create one or more phantom characters.
3582 When inserting phantom characters a small blue box appears that is superposed
3583 with two red arrows.
3584 The arrows indicate the width and height of the box to be created as a
3586 Phantom characters are placeholders with the same character size.
3589 \begin_layout Standard
3591 \begin_inset Tabular
3592 <lyxtabular version="3" rows="4" columns="2">
3593 <features booktabs="true" tabularvalignment="middle">
3594 <column alignment="center" valignment="top" width="0pt">
3595 <column alignment="center" valignment="top" width="0pt">
3597 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3600 \begin_layout Plain Layout
3606 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3609 \begin_layout Plain Layout
3616 <row topspace="1.5mm">
3617 <cell alignment="center" valignment="top" usebox="none">
3620 \begin_layout Plain Layout
3622 \begin_inset space \textvisiblespace{}
3628 \begin_inset space \textvisiblespace{}
3632 \begin_inset Formula $\to$
3636 \begin_inset space \textvisiblespace{}
3640 \change_inserted 5863208 1612176450
3644 \begin_inset space \textvisiblespace{}
3654 <cell alignment="center" valignment="top" usebox="none">
3657 \begin_layout Plain Layout
3658 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3667 <row topspace="1.5mm" bottomspace="0.5mm">
3668 <cell alignment="center" valignment="top" usebox="none">
3671 \begin_layout Plain Layout
3673 \begin_inset space \textvisiblespace{}
3679 \begin_inset space \textvisiblespace{}
3683 \begin_inset Formula $\to$
3687 \begin_inset space \textvisiblespace{}
3691 \change_inserted 5863208 1612707447
3695 \begin_inset space \textvisiblespace{}
3705 <cell alignment="center" valignment="top" usebox="none">
3708 \begin_layout Plain Layout
3709 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3718 <row topspace="1.5mm" bottomspace="0.5mm">
3719 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3722 \begin_layout Plain Layout
3726 \change_inserted 5863208 1612707546
3728 \begin_inset space \textvisiblespace{}
3734 \change_deleted 5863208 1612707563
3736 \begin_inset space \textvisiblespace{}
3744 \begin_inset space \textvisiblespace{}
3748 \begin_inset Formula $\to$
3752 \begin_inset space \textvisiblespace{}
3760 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3763 \begin_layout Plain Layout
3764 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3780 \begin_layout Standard
3781 Furthermore there are the commands
3788 \begin_inset Index idx
3791 \begin_layout Plain Layout
3812 \begin_inset Index idx
3815 \begin_layout Plain Layout
3836 creates only space for the maximal height of the characters in the box
3837 but not for its width.
3844 creates only space for the width of the box content.
3845 Therefore the boxes of both commands have only one red arrow.
3848 \begin_layout Standard
3849 For example the command
3854 \begin_inset space \textvisiblespace{}
3861 creates space for the height of the integral sign,
3865 \begin_layout Plain Layout
3872 creates an integral sign, see
3873 \begin_inset CommandInset ref
3875 reference "subsec:Big-Operators"
3884 because this is the larger character.
3885 An example application is in
3886 \begin_inset CommandInset ref
3888 reference "subsec:Multiline-Brackets"
3895 \begin_layout Standard
3896 Placeholders can also be used for text when they are inserted via the menu
3899 Insert\SpecialChar menuseparator
3900 Formatting\SpecialChar menuseparator
3906 \begin_layout Standard
3908 \begin_inset Newline newline
3912 \begin_inset Phantom Phantom
3915 \begin_layout Plain Layout
3924 \begin_layout Subsection
3926 \begin_inset Index idx
3929 \begin_layout Plain Layout
3936 \begin_inset Index idx
3939 \begin_layout Plain Layout
3940 Formula ! underlined
3948 \begin_layout Standard
3950 \begin_inset Tabular
3951 <lyxtabular version="3" rows="4" columns="2">
3952 <features booktabs="true" tabularvalignment="middle">
3953 <column alignment="center" valignment="top" width="0pt">
3954 <column alignment="center" valignment="top" width="0pt">
3956 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3959 \begin_layout Plain Layout
3965 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3968 \begin_layout Plain Layout
3975 <row topspace="2mm">
3976 <cell alignment="center" valignment="top" usebox="none">
3979 \begin_layout Plain Layout
3983 \begin_inset space \textvisiblespace{}
3987 \begin_inset Index idx
3990 \begin_layout Plain Layout
4003 <cell alignment="center" valignment="top" usebox="none">
4006 \begin_layout Plain Layout
4007 \begin_inset Formula $\overline{A+B}$
4016 <row bottomspace="1mm">
4017 <cell alignment="center" valignment="top" usebox="none">
4020 \begin_layout Plain Layout
4024 \begin_inset space \textvisiblespace{}
4028 \begin_inset Index idx
4031 \begin_layout Plain Layout
4044 <cell alignment="center" valignment="top" usebox="none">
4047 \begin_layout Plain Layout
4048 \begin_inset Formula $\underline{A+B}$
4057 <row topspace="2mm" bottomspace="1mm">
4058 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4061 \begin_layout Plain Layout
4065 \begin_inset space \textvisiblespace{}
4071 \begin_inset space \textvisiblespace{}
4079 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4082 \begin_layout Plain Layout
4083 \begin_inset Formula $\overline{\underline{A+B}}$
4099 \begin_layout Standard
4100 In the last example it doesn't matter if
4115 \begin_layout Standard
4116 To double underline use
4123 \change_deleted 5863208 1612707977
4125 \change_inserted 5863208 1612707993
4126 (or as many times you want).
4131 \begin_layout Standard
4133 \change_deleted 232239728 1610990247
4134 It is possible to place up to 6 lines above or below characters.
4135 \change_deleted 5863208 1612729848
4137 \begin_inset Note Note
4140 \begin_layout Plain Layout
4142 \change_inserted 232239728 1610990434
4143 I put 30 over and under lines in my test so I don't know what the actual
4144 maximum is, but it's greater than 6.
4154 \begin_layout Standard
4155 \begin_inset VSpace bigskip
4158 Custom lines can be created using the command
4165 \begin_inset Index idx
4168 \begin_layout Plain Layout
4176 which has the following scheme:
4179 \begin_layout Standard
4184 rule[vertical offset]{length}{thickness}
4187 \begin_layout Standard
4188 The optional vertical offset shifts the line upwards (or downwards, when
4189 the value is negative).
4191 \begin_inset CommandInset ref
4193 reference "tab:Available-units"
4197 can be used for the values.
4198 Here are two example lines created with the commands
4199 \begin_inset Newline newline
4206 rule[-2ex]{3cm}{2pt}
4217 \begin_layout Standard
4219 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4225 \begin_layout Standard
4232 can also be used for text when a line is inserted via the menu
4234 Insert\SpecialChar menuseparator
4235 Formatting\SpecialChar menuseparator
4237 \begin_inset space ~
4245 \begin_layout Standard
4247 \begin_inset CommandInset line
4258 \begin_layout Subsection
4260 \begin_inset CommandInset label
4262 name "subsec:Ellipses"
4267 \begin_inset Index idx
4270 \begin_layout Plain Layout
4279 \begin_layout Standard
4280 There are different types of ellipses available.
4284 \begin_layout Plain Layout
4285 In the math toolbar in the submenu of the button
4288 arg "math-insert \\ldots"
4296 For listings, dots at the baseline are used (
4303 \begin_inset Index idx
4306 \begin_layout Plain Layout
4314 ), while for operations, dots are needed that are on the same height as
4322 \begin_inset Index idx
4325 \begin_layout Plain Layout
4334 When using the command
4341 \begin_inset Index idx
4344 \begin_layout Plain Layout
4352 , \SpecialChar LaTeX
4353 decides on the basis of the next character what type is used.
4356 \begin_layout Standard
4358 \begin_inset Tabular
4359 <lyxtabular version="3" rows="9" columns="2">
4360 <features booktabs="true" tabularvalignment="middle">
4361 <column alignment="center" valignment="top" width="0pt">
4362 <column alignment="center" valignment="top" width="0pt">
4364 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4367 \begin_layout Plain Layout
4373 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4376 \begin_layout Plain Layout
4384 <cell alignment="center" valignment="top" usebox="none">
4387 \begin_layout Plain Layout
4389 \begin_inset space \textvisiblespace{}
4395 \begin_inset space \textvisiblespace{}
4403 <cell alignment="center" valignment="top" usebox="none">
4406 \begin_layout Plain Layout
4407 \begin_inset Formula $A_{1},\dots,A_{n}$
4417 <cell alignment="center" valignment="top" usebox="none">
4420 \begin_layout Plain Layout
4422 \begin_inset space \textvisiblespace{}
4428 \begin_inset space \textvisiblespace{}
4436 <cell alignment="center" valignment="top" usebox="none">
4439 \begin_layout Plain Layout
4440 \begin_inset Formula $A_{1}+\dots+A_{n}$
4450 <cell alignment="center" valignment="top" usebox="none">
4453 \begin_layout Plain Layout
4455 \begin_inset space \textvisiblespace{}
4461 \begin_inset space \textvisiblespace{}
4469 <cell alignment="center" valignment="top" usebox="none">
4472 \begin_layout Plain Layout
4473 \begin_inset Formula $A_{1},\ldots,A_{n}$
4483 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4486 \begin_layout Plain Layout
4488 \begin_inset space \textvisiblespace{}
4494 \begin_inset space \textvisiblespace{}
4502 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4505 \begin_layout Plain Layout
4506 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4516 <cell alignment="center" valignment="top" usebox="none">
4519 \begin_layout Plain Layout
4527 <cell alignment="center" valignment="top" usebox="none">
4530 \begin_layout Plain Layout
4531 \begin_inset Formula $\vdots$
4541 <cell alignment="center" valignment="top" usebox="none">
4544 \begin_layout Plain Layout
4552 <cell alignment="center" valignment="top" usebox="none">
4555 \begin_layout Plain Layout
4556 \begin_inset Formula $\ddots$
4566 <cell alignment="center" valignment="top" usebox="none">
4569 \begin_layout Plain Layout
4577 <cell alignment="center" valignment="top" usebox="none">
4580 \begin_layout Plain Layout
4581 \begin_inset Formula $\iddots$
4591 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4594 \begin_layout Plain Layout
4596 \begin_inset space \thinspace{}
4599 matrix with the different dots
4604 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4607 \begin_layout Plain Layout
4608 \begin_inset Formula $\begin{array}{ccc}
4609 A_{11} & \cdots & A_{1m}\\
4610 \vdots & \ddots & \vdots\\
4611 A_{n1} & \cdots & A_{nm}
4628 \begin_layout Standard
4629 The ellipses available in menu
4631 Insert\SpecialChar menuseparator
4633 \begin_inset space ~
4647 \begin_layout Standard
4648 \begin_inset VSpace medskip
4659 Use mathdots package (automatically)
4661 must be set in the document settings under
4664 \begin_inset space ~
4670 \begin_inset Newline newline
4675 Use mathdots package
4677 will improve the appearance of all dots in the documents if their font
4678 style or size is not the default.
4681 \begin_layout Standard
4682 \begin_inset VSpace medskip
4685 Specially for matrices there are ellipses that span over several columns.
4686 They are created with the command
4693 \begin_inset Index idx
4696 \begin_layout Plain Layout
4704 and have the following scheme
4705 \change_inserted 5863208 1612709418
4717 \begin_inset space ~
4727 \begin_layout Standard
4732 hdotsfor[distance]{number of columns}
4735 \begin_layout Standard
4736 The number of columns specifies how many columns should be spanned.
4737 Distance is a factor for the distance between the dots.
4740 \begin_layout Standard
4741 In the following matrix the command
4747 was inserted in the first box of the second line to get an ellipsis with
4748 a dot distance twice as long as with the command
4755 \begin_inset Formula
4757 \left(\begin{array}{cccc}
4766 Note that the matrix fields that should be spanned must be empty, otherwise
4767 you get \SpecialChar LaTeX
4771 \begin_layout Standard
4772 \begin_inset VSpace bigskip
4775 Furthermore you can fill with the command
4782 \begin_inset Index idx
4785 \begin_layout Plain Layout
4793 the rest of a line with dots.
4794 The effect of these commands is the same as with
4801 \begin_inset CommandInset ref
4803 reference "subsec:Variable-Space"
4810 \begin_layout Standard
4811 For example the command
4816 \begin_inset space \textvisiblespace{}
4824 \begin_layout Standard
4825 \begin_inset Formula $A\dotfill B$
4831 \begin_layout Standard
4838 there is for a line the command
4845 \begin_inset Index idx
4848 \begin_layout Plain Layout
4859 \begin_layout Standard
4860 \begin_inset Formula $A\hrulefill B$
4866 \begin_layout Standard
4867 To use the commands for text, they have to be inserted in \SpecialChar TeX
4871 \begin_layout Section
4873 \begin_inset CommandInset label
4880 \begin_inset Index idx
4883 \begin_layout Plain Layout
4892 \begin_layout Standard
4893 Matrices can be inserted via the math toolbar button
4896 arg "dialog-show mathmatrix"
4901 Insert\SpecialChar menuseparator
4902 Math\SpecialChar menuseparator
4906 In the matrix dialog you can specify the number of columns and rows, the
4907 alignment and the decoration.
4908 The vertical alignment is only of importance for matrices in inline formulas:
4911 \begin_layout Standard
4912 The first matrix is top
4913 \begin_inset Formula $\begin{array}[t]{cccc}
4921 \begin_inset Formula $\begin{array}{cccc}
4928 and the third bottom
4929 \begin_inset Formula $\begin{array}[b]{cccc}
4939 \begin_layout Standard
4940 The horizontal alignment specifies how the column entries should be aligned.
4941 It is set by entering a letter for every column.
4946 denotes left aligned,
4955 To create for example a 4
4960 \begin_inset space ~
4963 matrix where the first column is left aligned, the second and third are
4964 centered and the last one is right aligned, one enters for the horizontal
4970 Normally in a matrix all columns are centered, therefore the default for
4978 \begin_layout Standard
4979 Horizontal alignment:
4982 \begin_layout Standard
4988 \begin_inset Formula $\begin{array}{lll}
5000 \begin_inset Formula $\begin{array}{ccc}
5012 \begin_inset Formula $\begin{array}{rrr}
5022 \begin_layout Standard
5023 To subsequently add or delete rows and columns, the math toolbar buttons
5027 arg "tabular-feature append-row"
5033 arg "tabular-feature delete-row"
5037 \begin_inset space \thinspace{}
5042 Edit\SpecialChar menuseparator
5046 New rows can also be created with
5049 arg "newline-insert newline"
5055 \begin_layout Standard
5056 \begin_inset VSpace bigskip
5060 \change_deleted 47243155 1563226130
5062 \change_deleted -563046850 1563190969
5066 \change_inserted -563046850 1563190971
5072 \change_deleted -563046850 1563192602
5074 \change_inserted -563046850 1563192607
5077 parentheses in the selected style around the matrix
5078 \change_inserted -563046850 1563192780
5083 style, suitable for an inline matrix like this one
5084 \begin_inset Formula $\bigl(\begin{smallmatrix}0 & \textrm{-}\mathrm{i}\\
5086 \end{smallmatrix}\bigr)$
5093 \change_inserted -563046850 1563192943
5094 Here the parentheses have been added manually using commands
5107 \begin_layout Standard
5109 \change_deleted -563046850 1563192735
5112 Alternatively, parentheses can
5113 \change_deleted -563046850 1563192971
5116 be created with the commands
5123 \begin_inset Index idx
5126 \begin_layout Plain Layout
5141 \begin_inset Index idx
5144 \begin_layout Plain Layout
5155 \begin_inset space ~
5161 \begin_inset CommandInset ref
5163 reference "subsec:Automatic-Bracket-Size"
5167 , or by using the following commands:
5168 \begin_inset VSpace medskip
5174 \begin_layout Standard
5175 \begin_inset space \hfill{}
5179 \begin_inset Tabular
5180 <lyxtabular version="3" rows="4" columns="2">
5181 <features booktabs="true" tabularvalignment="middle">
5182 <column alignment="center" valignment="top" width="0pt">
5183 <column alignment="center" valignment="top">
5185 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5188 \begin_layout Plain Layout
5194 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5197 \begin_layout Plain Layout
5204 <row topspace="1.5mm">
5205 <cell alignment="center" valignment="top" usebox="none">
5208 \begin_layout Plain Layout
5212 \begin_inset space \textvisiblespace{}
5220 \begin_inset space \thinspace{}
5228 <cell alignment="center" valignment="top" usebox="none">
5231 \begin_layout Plain Layout
5232 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
5233 0 & \textrm{-}\mathrm{i}\\
5235 \end{array}\end{bmatrix}$
5244 <row topspace="1.5mm" bottomspace="0.5mm">
5245 <cell alignment="center" valignment="top" usebox="none">
5248 \begin_layout Plain Layout
5252 \begin_inset space \textvisiblespace{}
5260 \begin_inset space \thinspace{}
5268 <cell alignment="center" valignment="top" usebox="none">
5271 \begin_layout Plain Layout
5272 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
5273 0 & \textrm{-}\mathrm{i}\\
5275 \end{array}\end{Bmatrix}$
5285 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5288 \begin_layout Plain Layout
5292 \begin_inset space \textvisiblespace{}
5300 \begin_inset space \thinspace{}
5308 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5311 \begin_layout Plain Layout
5312 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5313 0 & \textrm{-}\mathrm{i}\\
5315 \end{array}\end{pmatrix}$
5329 \begin_inset space \hfill{}
5333 \begin_inset Tabular
5334 <lyxtabular version="3" rows="4" columns="2">
5335 <features booktabs="true" tabularvalignment="middle">
5336 <column alignment="center" valignment="top" width="0pt">
5337 <column alignment="center" valignment="top">
5339 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5342 \begin_layout Plain Layout
5348 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5351 \begin_layout Plain Layout
5358 <row topspace="1.5mm">
5359 <cell alignment="center" valignment="top" usebox="none">
5362 \begin_layout Plain Layout
5366 \begin_inset space \textvisiblespace{}
5374 \begin_inset space \thinspace{}
5382 <cell alignment="center" valignment="top" usebox="none">
5385 \begin_layout Plain Layout
5386 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5387 0 & \textrm{-}\mathrm{i}\\
5389 \end{array}\end{vmatrix}$
5398 <row topspace="1.5mm" bottomspace="0.5mm">
5399 <cell alignment="center" valignment="top" usebox="none">
5402 \begin_layout Plain Layout
5406 \begin_inset space \textvisiblespace{}
5414 \begin_inset space \thinspace{}
5422 <cell alignment="center" valignment="top" usebox="none">
5425 \begin_layout Plain Layout
5426 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5427 0 & \textrm{-}\mathrm{i}\\
5429 \end{array}\end{Vmatrix}$
5439 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5442 \begin_layout Plain Layout
5446 \begin_inset space \textvisiblespace{}
5454 \begin_inset space \thinspace{}
5462 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5465 \begin_layout Plain Layout
5466 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5467 0 & \textrm{-}\mathrm{i}\\
5469 \end{array}\end{matrix}$
5483 \begin_inset space \hfill{}
5489 \begin_layout Standard
5490 \begin_inset VSpace medskip
5494 \begin_inset space \thinspace{}
5498 \begin_inset space \space{}
5507 is inserted, a blue box appears between two vertical lines where the matrix
5509 \begin_inset Newline newline
5512 Note that decorated matrices ignore the vertical alignment.
5515 \begin_layout Standard
5516 \begin_inset VSpace bigskip
5519 As all multiline formulas are matrices, the length
5526 \begin_inset Index idx
5529 \begin_layout Plain Layout
5537 that is described in
5538 \begin_inset CommandInset ref
5540 reference "subsec:Column-Separation"
5544 can also be used to change the column separation of matrices.
5547 \begin_layout Standard
5548 To change the row separation, the command
5555 \begin_inset Index idx
5558 \begin_layout Plain Layout
5569 \begin_layout Standard
5576 arraystretch}{stretch factor}
5577 \begin_inset Index idx
5580 \begin_layout Plain Layout
5591 \begin_layout Standard
5598 assigns the stretch factor to the predefined command
5605 For example to double the row separation, use a stretch factor of 2.
5606 This is then used for all following matrices.
5607 To restore the original separation, assign a stretch factor of 1 to
5616 \begin_layout Standard
5618 \change_inserted 47243155 1563226178
5619 Small inline matrices can also be obtained using
5620 \change_deleted 47243155 1563226182
5621 To set matrices into a text line,
5630 \begin_inset Index idx
5633 \begin_layout Plain Layout
5642 \change_deleted 47243155 1563226186
5646 When it is inserted in a line a blue box with two dashed lines appears.
5647 Adjust the matrix rows and columns as desired.
5650 \begin_layout Standard
5652 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5654 \end{smallmatrix}\right)$
5658 \change_inserted 47243155 1563226243
5659 with automatic delimiters around it
5664 \begin_layout Section
5665 Brackets and Delimiters
5666 \begin_inset Index idx
5669 \begin_layout Plain Layout
5676 \begin_inset Index idx
5679 \begin_layout Plain Layout
5688 \begin_layout Subsection
5689 Vertical Brackets and Delimiters
5690 \begin_inset Index idx
5693 \begin_layout Plain Layout
5702 \begin_layout Standard
5703 \begin_inset space \hfill{}
5707 \begin_inset Tabular
5708 <lyxtabular version="3" rows="9" columns="2">
5709 <features booktabs="true" tabularvalignment="middle">
5710 <column alignment="center" valignment="top" width="0pt">
5711 <column alignment="center" valignment="top" width="0pt">
5713 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5716 \begin_layout Plain Layout
5722 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5725 \begin_layout Plain Layout
5733 <cell alignment="center" valignment="top" usebox="none">
5736 \begin_layout Plain Layout
5742 <cell alignment="center" valignment="top" usebox="none">
5745 \begin_layout Plain Layout
5746 \begin_inset Formula $($
5756 <cell alignment="center" valignment="top" usebox="none">
5759 \begin_layout Plain Layout
5765 <cell alignment="center" valignment="top" usebox="none">
5768 \begin_layout Plain Layout
5769 \begin_inset Formula $\{$
5779 <cell alignment="center" valignment="top" usebox="none">
5782 \begin_layout Plain Layout
5788 <cell alignment="center" valignment="top" usebox="none">
5791 \begin_layout Plain Layout
5792 \begin_inset Formula $[$
5802 <cell alignment="center" valignment="top" usebox="none">
5805 \begin_layout Plain Layout
5813 <cell alignment="center" valignment="top" usebox="none">
5816 \begin_layout Plain Layout
5817 \begin_inset Formula $\langle$
5827 <cell alignment="center" valignment="top" usebox="none">
5830 \begin_layout Plain Layout
5838 <cell alignment="center" valignment="top" usebox="none">
5841 \begin_layout Plain Layout
5842 \begin_inset Formula $\lceil$
5852 <cell alignment="center" valignment="top" usebox="none">
5855 \begin_layout Plain Layout
5863 <cell alignment="center" valignment="top" usebox="none">
5866 \begin_layout Plain Layout
5867 \begin_inset Formula $\lfloor$
5877 <cell alignment="center" valignment="top" usebox="none">
5880 \begin_layout Plain Layout
5886 <cell alignment="center" valignment="top" usebox="none">
5889 \begin_layout Plain Layout
5890 \begin_inset Formula $/$
5900 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5903 \begin_layout Plain Layout
5909 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5912 \begin_layout Plain Layout
5913 \begin_inset Formula $|$
5927 \begin_inset space \hfill{}
5931 \begin_inset Tabular
5932 <lyxtabular version="3" rows="9" columns="2">
5933 <features booktabs="true" tabularvalignment="middle">
5934 <column alignment="center" valignment="top" width="0pt">
5935 <column alignment="center" valignment="top" width="0pt">
5937 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5940 \begin_layout Plain Layout
5946 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5949 \begin_layout Plain Layout
5957 <cell alignment="center" valignment="top" usebox="none">
5960 \begin_layout Plain Layout
5966 <cell alignment="center" valignment="top" usebox="none">
5969 \begin_layout Plain Layout
5970 \begin_inset Formula $)$
5980 <cell alignment="center" valignment="top" usebox="none">
5983 \begin_layout Plain Layout
5989 <cell alignment="center" valignment="top" usebox="none">
5992 \begin_layout Plain Layout
5993 \begin_inset Formula $\}$
6003 <cell alignment="center" valignment="top" usebox="none">
6006 \begin_layout Plain Layout
6012 <cell alignment="center" valignment="top" usebox="none">
6015 \begin_layout Plain Layout
6016 \begin_inset Formula $]$
6026 <cell alignment="center" valignment="top" usebox="none">
6029 \begin_layout Plain Layout
6037 <cell alignment="center" valignment="top" usebox="none">
6040 \begin_layout Plain Layout
6041 \begin_inset Formula $\rangle$
6051 <cell alignment="center" valignment="top" usebox="none">
6054 \begin_layout Plain Layout
6062 <cell alignment="center" valignment="top" usebox="none">
6065 \begin_layout Plain Layout
6066 \begin_inset Formula $\rceil$
6076 <cell alignment="center" valignment="top" usebox="none">
6079 \begin_layout Plain Layout
6087 <cell alignment="center" valignment="top" usebox="none">
6090 \begin_layout Plain Layout
6091 \begin_inset Formula $\rfloor$
6101 <cell alignment="center" valignment="top" usebox="none">
6104 \begin_layout Plain Layout
6114 <cell alignment="center" valignment="top" usebox="none">
6117 \begin_layout Plain Layout
6118 \begin_inset Formula $\backslash$
6128 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6131 \begin_layout Plain Layout
6139 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6142 \begin_layout Plain Layout
6143 \begin_inset Formula $\|$
6157 \begin_inset space \hfill{}
6163 \begin_layout Standard
6166 \begin_inset Note Greyedout
6169 \begin_layout Plain Layout
6182 \begin_inset Index idx
6185 \begin_layout Plain Layout
6193 must be used for the backslash, because the command
6201 produces a line break there.
6209 \begin_layout Standard
6210 For all characters listed above the size can be adjusted with the commands
6211 described in the following two subsections.
6212 When using these commands, the characters < and > can directly be used
6213 instead of the commands
6228 \begin_layout Subsubsection
6230 \begin_inset CommandInset label
6232 name "subsec:Manual-Bracket-Size"
6237 \begin_inset Index idx
6240 \begin_layout Plain Layout
6241 Bracket size ! manual
6249 \begin_layout Standard
6250 The bracket size can be specified manually by the \SpecialChar LaTeX
6258 \begin_inset Index idx
6261 \begin_layout Plain Layout
6294 denotes the smallest and
6300 the largest bracket size.
6303 \begin_layout Standard
6304 These commands are used to emphasize levels of brackets:
6307 \begin_layout Standard
6309 \begin_inset Tabular
6310 <lyxtabular version="3" rows="2" columns="2">
6311 <features booktabs="true" tabularvalignment="middle">
6312 <column alignment="center" valignment="top" width="0pt">
6313 <column alignment="center" valignment="top" width="0pt">
6315 <cell alignment="center" valignment="top" usebox="none">
6318 \begin_layout Plain Layout
6319 All brackets in the same size:
6324 <cell alignment="center" valignment="top" usebox="none">
6327 \begin_layout Plain Layout
6328 \begin_inset Formula $((A+B)(A-B))^{C}$
6337 <row topspace="2mm">
6338 <cell alignment="center" valignment="top" usebox="none">
6341 \begin_layout Plain Layout
6347 <cell alignment="center" valignment="top" usebox="none">
6350 \begin_layout Plain Layout
6351 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6367 \begin_layout Standard
6368 For the second formula the command
6375 \begin_inset space \textvisiblespace{}
6383 \begin_layout Standard
6384 Here is an example containing all bracket sizes:
6387 \begin_layout Standard
6404 \begin_inset space \textvisiblespace{}
6412 \begin_inset space \textvisiblespace{}
6416 \begin_inset space \textvisiblespace{}
6426 \begin_layout Standard
6428 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6434 \begin_layout Standard
6441 -commands there is a variant,
6448 \begin_inset Index idx
6451 \begin_layout Plain Layout
6459 , that adds a bit more space between the bracket and its content.
6473 \begin_inset Index idx
6476 \begin_layout Plain Layout
6486 , don't add additional space.
6491 at the end of the command
6497 is for a left bracket; for a right bracket this is replaced by an
6502 A left or right bracket can each be an opening or closing bracket.
6505 \begin_layout Standard
6506 The following table contains comparisons of the variants:
6509 \begin_layout Standard
6511 \begin_inset Tabular
6512 <lyxtabular version="3" rows="5" columns="2">
6513 <features booktabs="true" tabularvalignment="middle">
6514 <column alignment="center" valignment="top" width="0pt">
6515 <column alignment="center" valignment="middle">
6517 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6520 \begin_layout Plain Layout
6526 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6529 \begin_layout Plain Layout
6536 <row topspace="2mm">
6537 <cell alignment="center" valignment="top" usebox="none">
6540 \begin_layout Plain Layout
6550 \begin_inset space \textvisiblespace{}
6560 <cell alignment="center" valignment="top" usebox="none">
6563 \begin_layout Plain Layout
6564 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6573 <row topspace="2mm">
6574 <cell alignment="center" valignment="top" usebox="none">
6577 \begin_layout Plain Layout
6587 \begin_inset space \textvisiblespace{}
6597 <cell alignment="center" valignment="top" usebox="none">
6600 \begin_layout Plain Layout
6601 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6610 <row topspace="2mm" bottomspace="0.5mm">
6611 <cell alignment="center" valignment="top" usebox="none">
6614 \begin_layout Plain Layout
6624 \begin_inset space \textvisiblespace{}
6634 <cell alignment="center" valignment="top" usebox="none">
6637 \begin_layout Plain Layout
6638 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6647 <row topspace="1.5mm" bottomspace="0.5mm">
6648 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6651 \begin_layout Plain Layout
6663 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6666 \begin_layout Plain Layout
6667 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6683 \begin_layout Subsubsection
6684 Automatic Bracket Size
6685 \begin_inset CommandInset label
6687 name "subsec:Automatic-Bracket-Size"
6692 \begin_inset Index idx
6695 \begin_layout Plain Layout
6696 Bracket size ! automatic
6704 \begin_layout Standard
6705 Variably sized brackets can be inserted with the commands
6712 \begin_inset Index idx
6715 \begin_layout Plain Layout
6730 \begin_inset Index idx
6733 \begin_layout Plain Layout
6741 or via the math toolbar button
6744 arg "dialog-show mathdelimiter"
6748 The desired bracket must be inserted directly behind the
6761 The bracket size will then automatically be calculated for the output.
6764 \begin_layout Standard
6766 normal bracket: The command
6773 \begin_inset space \textvisiblespace{}
6777 \begin_inset Formula $\downarrow$
6781 \begin_inset space \textvisiblespace{}
6787 \begin_inset Formula
6797 \begin_layout Standard
6799 multiline bracket: The command
6808 \begin_inset space \textvisiblespace{}
6812 \begin_inset Formula $\downarrow$
6816 \begin_inset space \textvisiblespace{}
6824 \begin_inset Formula
6826 \ln\left(\frac{A}{C}\right)
6834 \begin_layout Standard
6850 \begin_inset space ~
6856 This has the advantage that you can see in \SpecialChar LyX
6857 immediately the real bracket
6858 size and that the matching right bracket will be created too.
6859 \begin_inset Newline newline
6862 The command for the last example would then be:
6873 \begin_inset space \textvisiblespace{}
6877 \begin_inset Formula $\downarrow$
6883 \begin_layout Standard
6884 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6885 For example the command
6892 \begin_inset space \textvisiblespace{}
6896 \begin_inset Formula $\downarrow$
6900 \begin_inset space \textvisiblespace{}
6910 \begin_inset Formula
6912 \left.\frac{A}{B}\right\}
6931 will be converted by \SpecialChar LyX
6932 to brackets with the correct size when the document
6933 is reloaded and an omitted bracket will appear as dashed line.
6936 \begin_layout Standard
6937 \begin_inset VSpace bigskip
6940 Because all popular \SpecialChar LaTeX
6941 distributions use e\SpecialChar TeX
6942 , an extension to \SpecialChar LaTeX
6951 \begin_inset Index idx
6954 \begin_layout Plain Layout
6962 is available for all brackets and limits.
6963 With this command the height of the following character is adapted to the
6964 one of the surrounding brackets, for example in the case of physical vectors:
6965 \begin_inset Formula
6967 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6972 For physical vectors there is a special \SpecialChar LaTeX
6973 -package, described in
6974 \begin_inset CommandInset ref
6976 reference "subsec:Physical-Vectors"
6983 \begin_layout Subsection
6985 \begin_inset Index idx
6988 \begin_layout Plain Layout
6989 Brackets ! horizontal
6997 \begin_layout Standard
6999 \begin_inset Tabular
7000 <lyxtabular version="3" rows="4" columns="2">
7001 <features booktabs="true" tabularvalignment="middle">
7002 <column alignment="center" valignment="top" width="0pt">
7003 <column alignment="center" valignment="top" width="0pt">
7005 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7008 \begin_layout Plain Layout
7014 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7017 \begin_layout Plain Layout
7025 <cell alignment="center" valignment="top" usebox="none">
7028 \begin_layout Plain Layout
7032 \begin_inset space \textvisiblespace{}
7036 \begin_inset space \textvisiblespace{}
7040 \begin_inset Index idx
7043 \begin_layout Plain Layout
7056 <cell alignment="center" valignment="top" usebox="none">
7059 \begin_layout Plain Layout
7060 \begin_inset Formula $\overbrace{A+B}^{3}$
7069 <row topspace="2mm">
7070 <cell alignment="center" valignment="top" usebox="none">
7073 \begin_layout Plain Layout
7077 \begin_inset space \textvisiblespace{}
7081 \begin_inset space \textvisiblespace{}
7085 \begin_inset Index idx
7088 \begin_layout Plain Layout
7101 <cell alignment="center" valignment="top" usebox="none">
7104 \begin_layout Plain Layout
7105 \begin_inset Formula $\underbrace{A+B}_{5}$
7115 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7118 \begin_layout Plain Layout
7122 \begin_inset space \textvisiblespace{}
7128 \begin_inset space \textvisiblespace{}
7132 \begin_inset space \textvisiblespace{}
7136 \begin_inset space \textvisiblespace{}
7140 \begin_inset space \textvisiblespace{}
7144 \begin_inset space \textvisiblespace{}
7148 \begin_inset space \textvisiblespace{}
7156 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7159 \begin_layout Plain Layout
7160 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7176 \begin_layout Standard
7177 In the last example it doesn't matter if
7192 \begin_layout Standard
7193 \begin_inset VSpace medskip
7199 \begin_layout Standard
7200 If in document settings under
7203 \begin_inset space ~
7208 the option for the package
7213 \begin_inset Index idx
7216 \begin_layout Plain Layout
7217 Packages ! mathtools
7225 \begin_inset space ~
7230 , you will also have access to square brackets:
7233 \begin_layout Standard
7235 \begin_inset Tabular
7236 <lyxtabular version="3" rows="4" columns="2">
7237 <features booktabs="true" tabularvalignment="middle">
7238 <column alignment="center" valignment="top" width="0pt">
7239 <column alignment="center" valignment="top" width="0pt">
7241 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7244 \begin_layout Plain Layout
7250 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7253 \begin_layout Plain Layout
7261 <cell alignment="center" valignment="top" usebox="none">
7264 \begin_layout Plain Layout
7292 \begin_inset space \textvisiblespace{}
7296 \begin_inset Index idx
7299 \begin_layout Plain Layout
7312 <cell alignment="center" valignment="top" usebox="none">
7315 \begin_layout Plain Layout
7316 \begin_inset Formula $\overbracket{A+B}^{3}$
7325 <row topspace="2mm">
7326 <cell alignment="center" valignment="top" usebox="none">
7329 \begin_layout Plain Layout
7357 \begin_inset space \textvisiblespace{}
7361 \begin_inset Index idx
7364 \begin_layout Plain Layout
7389 <cell alignment="center" valignment="top" usebox="none">
7392 \begin_layout Plain Layout
7393 \begin_inset Formula $\underbracket{A+B}_{5}$
7403 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7406 \begin_layout Plain Layout
7412 \begin_inset space \textvisiblespace{}
7416 \begin_inset space \textvisiblespace{}
7420 \begin_inset space \textvisiblespace{}
7424 \begin_inset space \textvisiblespace{}
7428 \change_deleted 5863208 1612711596
7430 \begin_inset space \textvisiblespace{}
7440 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7443 \begin_layout Plain Layout
7444 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7460 \begin_layout Standard
7473 you can change the thickness of the bracket's stroke by specifying the
7474 desired thickness in square brackets behind the command:
7477 \begin_layout Standard
7479 \begin_inset Tabular
7480 <lyxtabular version="3" rows="3" columns="2">
7481 <features booktabs="true" tabularvalignment="middle">
7482 <column alignment="center" valignment="top" width="0pt">
7483 <column alignment="center" valignment="top" width="0pt">
7485 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7488 \begin_layout Plain Layout
7494 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7497 \begin_layout Plain Layout
7505 <cell alignment="center" valignment="top" usebox="none">
7508 \begin_layout Plain Layout
7538 \begin_inset space \textvisiblespace{}
7546 <cell alignment="center" valignment="top" usebox="none">
7549 \begin_layout Plain Layout
7550 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7559 <row topspace="2mm">
7560 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7563 \begin_layout Plain Layout
7593 \begin_inset space \textvisiblespace{}
7601 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7604 \begin_layout Plain Layout
7605 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7621 \begin_layout Standard
7622 \begin_inset VSpace bigskip
7625 When brackets overlap each other, multiline formulas as described in
7626 \begin_inset CommandInset ref
7628 reference "sec:Multiline-Formulas"
7633 \begin_inset Formula
7635 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7636 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7641 In the first row, the formula is inserted together with the first brace.
7642 It is important that the space command
7646 \begin_layout Plain Layout
7647 Space commands are explained in
7648 \begin_inset CommandInset ref
7650 reference "subsec:Predefined-Space"
7665 is inserted before the first
7666 \begin_inset Formula $d$
7669 because the brace that ends behind the
7670 \begin_inset Formula $q$
7673 prevents the following
7674 \begin_inset Quotes eld
7678 \begin_inset Quotes erd
7681 from being surrounded by spaces.
7685 \begin_layout Plain Layout
7686 Because a bracket is not handled as a character, see
7687 \begin_inset CommandInset ref
7689 reference "subsec:Binary-Operators"
7698 The second brace is inserted in the second row.
7699 As it should begin before the
7700 \begin_inset Formula $b$
7715 \begin_layout Plain Layout
7723 \begin_inset CommandInset ref
7725 reference "subsec:Placeholders"
7734 This space is needed because the
7735 \begin_inset Quotes eld
7739 \begin_inset Quotes erd
7742 is surrounded by spaces in the formula.
7743 The brace is placed under the command
7752 \begin_layout Standard
7753 It gets more complicated when brackets overlap each other above and under
7754 the formula as in the following example:
7758 \begin_layout Plain Layout
7770 \begin_inset Formula
7772 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7773 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7782 \begin_layout Plain Layout
7793 The first formula row is the same as the second row of the previous example,
7794 with the difference that the brace is above.
7795 The second row contains the formula together with the second brace.
7796 To avoid the space between the upper brace in the first row and the formula,
7797 the row spacing needs to be reduced.
7798 This is not easily done due to a bug in \SpecialChar LyX
7803 \begin_layout Plain Layout
7804 \begin_inset CommandInset href
7806 name "LyX-bug #1505"
7807 target "https://www.lyx.org/trac/ticket/1505"
7817 As a solution for the problem, the global formula row separation
7824 \begin_inset Index idx
7827 \begin_layout Plain Layout
7835 must be changed to -6
7836 \begin_inset space \thinspace{}
7839 pt before the formula with the command
7855 is set back after the formula to the standard value of 3
7856 \begin_inset space \thinspace{}
7859 pt using the same command.
7860 More about the row separation in formulas is explained in
7861 \begin_inset CommandInset ref
7863 reference "subsec:Line-Separation"
7870 \begin_layout Section
7872 \begin_inset Index idx
7875 \begin_layout Plain Layout
7884 \begin_layout Standard
7885 Arrows can be inserted via the math toolbar button
7888 arg "math-insert \\leftarrow"
7891 or the commands listed in the following subsections.
7894 \begin_layout Subsection
7896 \begin_inset Index idx
7899 \begin_layout Plain Layout
7908 \begin_layout Standard
7909 \begin_inset space \hfill{}
7913 \begin_inset Tabular
7914 <lyxtabular version="3" rows="8" columns="2">
7915 <features booktabs="true" tabularvalignment="middle">
7916 <column alignment="center" valignment="top" width="0pt">
7917 <column alignment="center" valignment="top" width="0pt">
7919 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7922 \begin_layout Plain Layout
7928 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7931 \begin_layout Plain Layout
7939 <cell alignment="center" valignment="top" usebox="none">
7942 \begin_layout Plain Layout
7950 <cell alignment="center" valignment="top" usebox="none">
7953 \begin_layout Plain Layout
7954 \begin_inset Formula $\gets$
7964 <cell alignment="center" valignment="top" usebox="none">
7967 \begin_layout Plain Layout
7975 <cell alignment="center" valignment="top" usebox="none">
7978 \begin_layout Plain Layout
7979 \begin_inset Formula $\Leftarrow$
7989 <cell alignment="center" valignment="top" usebox="none">
7992 \begin_layout Plain Layout
8000 <cell alignment="center" valignment="top" usebox="none">
8003 \begin_layout Plain Layout
8004 \begin_inset Formula $\longleftarrow$
8014 <cell alignment="center" valignment="top" usebox="none">
8017 \begin_layout Plain Layout
8025 <cell alignment="center" valignment="top" usebox="none">
8028 \begin_layout Plain Layout
8029 \begin_inset Formula $\Longleftarrow$
8039 <cell alignment="center" valignment="top" usebox="none">
8042 \begin_layout Plain Layout
8050 <cell alignment="center" valignment="top" usebox="none">
8053 \begin_layout Plain Layout
8054 \begin_inset Formula $\leftharpoonup$
8064 <cell alignment="center" valignment="top" usebox="none">
8067 \begin_layout Plain Layout
8075 <cell alignment="center" valignment="top" usebox="none">
8078 \begin_layout Plain Layout
8079 \begin_inset Formula $\leftharpoondown$
8089 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8092 \begin_layout Plain Layout
8100 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8103 \begin_layout Plain Layout
8104 \begin_inset Formula $\hookleftarrow$
8118 \begin_inset space \hfill{}
8122 \begin_inset Tabular
8123 <lyxtabular version="3" rows="8" columns="2">
8124 <features booktabs="true" tabularvalignment="middle">
8125 <column alignment="center" valignment="top" width="0pt">
8126 <column alignment="center" valignment="top" width="0pt">
8128 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8131 \begin_layout Plain Layout
8137 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8140 \begin_layout Plain Layout
8148 <cell alignment="center" valignment="top" usebox="none">
8151 \begin_layout Plain Layout
8159 <cell alignment="center" valignment="top" usebox="none">
8162 \begin_layout Plain Layout
8163 \begin_inset Formula $\to$
8173 <cell alignment="center" valignment="top" usebox="none">
8176 \begin_layout Plain Layout
8184 <cell alignment="center" valignment="top" usebox="none">
8187 \begin_layout Plain Layout
8188 \begin_inset Formula $\Rightarrow$
8198 <cell alignment="center" valignment="top" usebox="none">
8201 \begin_layout Plain Layout
8209 <cell alignment="center" valignment="top" usebox="none">
8212 \begin_layout Plain Layout
8213 \begin_inset Formula $\longrightarrow$
8223 <cell alignment="center" valignment="top" usebox="none">
8226 \begin_layout Plain Layout
8234 <cell alignment="center" valignment="top" usebox="none">
8237 \begin_layout Plain Layout
8238 \begin_inset Formula $\Longrightarrow$
8248 <cell alignment="center" valignment="top" usebox="none">
8251 \begin_layout Plain Layout
8259 <cell alignment="center" valignment="top" usebox="none">
8262 \begin_layout Plain Layout
8263 \begin_inset Formula $\rightharpoonup$
8273 <cell alignment="center" valignment="top" usebox="none">
8276 \begin_layout Plain Layout
8284 <cell alignment="center" valignment="top" usebox="none">
8287 \begin_layout Plain Layout
8288 \begin_inset Formula $\rightharpoondown$
8298 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8301 \begin_layout Plain Layout
8309 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8312 \begin_layout Plain Layout
8313 \begin_inset Formula $\hookrightarrow$
8327 \begin_inset space \hfill{}
8333 \begin_layout Standard
8334 \begin_inset space \hfill{}
8338 \begin_inset Tabular
8339 <lyxtabular version="3" rows="6" columns="2">
8340 <features booktabs="true" tabularvalignment="middle">
8341 <column alignment="center" valignment="top" width="0pt">
8342 <column alignment="center" valignment="top" width="0pt">
8344 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8347 \begin_layout Plain Layout
8353 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8356 \begin_layout Plain Layout
8364 <cell alignment="center" valignment="top" usebox="none">
8367 \begin_layout Plain Layout
8375 <cell alignment="center" valignment="top" usebox="none">
8378 \begin_layout Plain Layout
8379 \begin_inset Formula $\leftrightarrow$
8389 <cell alignment="center" valignment="top" usebox="none">
8392 \begin_layout Plain Layout
8400 <cell alignment="center" valignment="top" usebox="none">
8403 \begin_layout Plain Layout
8404 \begin_inset Formula $\Leftrightarrow$
8414 <cell alignment="center" valignment="top" usebox="none">
8417 \begin_layout Plain Layout
8425 <cell alignment="center" valignment="top" usebox="none">
8428 \begin_layout Plain Layout
8429 \begin_inset Formula $\longleftrightarrow$
8439 <cell alignment="center" valignment="top" usebox="none">
8442 \begin_layout Plain Layout
8450 <cell alignment="center" valignment="top" usebox="none">
8453 \begin_layout Plain Layout
8454 \begin_inset Formula $\Longleftrightarrow$
8464 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8467 \begin_layout Plain Layout
8475 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8478 \begin_layout Plain Layout
8479 \begin_inset Formula $\rightleftharpoons$
8493 \begin_inset space \hspace{}
8498 \begin_inset space \hfill{}
8502 \begin_inset Tabular
8503 <lyxtabular version="3" rows="5" columns="2">
8504 <features booktabs="true" tabularvalignment="middle">
8505 <column alignment="center" valignment="top" width="0pt">
8506 <column alignment="center" valignment="top" width="0pt">
8508 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8511 \begin_layout Plain Layout
8517 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8520 \begin_layout Plain Layout
8528 <cell alignment="center" valignment="top" usebox="none">
8531 \begin_layout Plain Layout
8539 <cell alignment="center" valignment="top" usebox="none">
8542 \begin_layout Plain Layout
8543 \begin_inset Formula $\mapsto$
8553 <cell alignment="center" valignment="top" usebox="none">
8556 \begin_layout Plain Layout
8564 <cell alignment="center" valignment="top" usebox="none">
8567 \begin_layout Plain Layout
8568 \begin_inset Formula $\longmapsto$
8578 <cell alignment="center" valignment="top" usebox="none">
8581 \begin_layout Plain Layout
8589 <cell alignment="center" valignment="top" usebox="none">
8592 \begin_layout Plain Layout
8593 \begin_inset Formula $\leadsto$
8603 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8606 \begin_layout Plain Layout
8614 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8617 \begin_layout Plain Layout
8618 \begin_inset Formula $\dasharrow$
8632 \begin_inset space \hfill{}
8638 \begin_layout Standard
8639 \begin_inset VSpace medskip
8642 Arrows used as accents such as vector arrows are listed in
8643 \begin_inset CommandInset ref
8645 reference "sec:Accents"
8652 \begin_layout Standard
8653 \begin_inset VSpace bigskip
8657 \begin_inset Index idx
8660 \begin_layout Plain Layout
8666 are also available using the commands
8673 \begin_inset Index idx
8676 \begin_layout Plain Layout
8691 \begin_inset Index idx
8694 \begin_layout Plain Layout
8701 \begin_layout Plain Layout
8716 When inserting one of these commands in a formula, an arrow with two blue
8717 boxes appears indicating where the labels can be inserted.
8718 The length of the arrow adapts to the label width.
8721 \begin_layout Standard
8723 \begin_inset Tabular
8724 <lyxtabular version="3" rows="3" columns="2">
8725 <features booktabs="true" tabularvalignment="middle">
8726 <column alignment="center" valignment="top" width="0pt">
8727 <column alignment="center" valignment="top" width="0pt">
8729 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8732 \begin_layout Plain Layout
8738 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8741 \begin_layout Plain Layout
8749 <cell alignment="center" valignment="top" usebox="none">
8752 \begin_layout Plain Layout
8756 \begin_inset space \textvisiblespace{}
8760 \begin_inset Formula $\downarrow$
8764 \begin_inset Formula $\to$
8772 <cell alignment="center" valignment="top" usebox="none">
8775 \begin_layout Plain Layout
8776 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8785 <row topspace="2mm">
8786 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8789 \begin_layout Plain Layout
8793 \begin_inset space \textvisiblespace{}
8797 \begin_inset Formula $\downarrow$
8801 \begin_inset Formula $\to$
8809 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8812 \begin_layout Plain Layout
8813 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8829 \begin_layout Standard
8830 \begin_inset VSpace medskip
8836 \begin_layout Standard
8837 If in the document settings under
8840 \begin_inset space ~
8850 \begin_inset Index idx
8853 \begin_layout Plain Layout
8854 Packages ! mathtools
8862 \begin_inset space ~
8867 is set, you will have access to the following labeled arrows:
8870 \begin_layout Standard
8871 \begin_inset Newpage newpage
8877 \begin_layout Standard
8879 \begin_inset space \hspace*{\fill}
8883 \begin_inset Tabular
8884 <lyxtabular version="3" rows="7" columns="2">
8885 <features booktabs="true" tabularvalignment="middle">
8886 <column alignment="center" valignment="top" width="0pt">
8887 <column alignment="center" valignment="top" width="0pt">
8889 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8892 \begin_layout Plain Layout
8898 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8901 \begin_layout Plain Layout
8909 <cell alignment="center" valignment="top" usebox="none">
8912 \begin_layout Plain Layout
8932 <cell alignment="center" valignment="top" usebox="none">
8935 \begin_layout Plain Layout
8936 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8945 <row topspace="2mm">
8946 <cell alignment="center" valignment="top" usebox="none">
8949 \begin_layout Plain Layout
8969 <cell alignment="center" valignment="top" usebox="none">
8972 \begin_layout Plain Layout
8973 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8982 <row topspace="2mm">
8983 <cell alignment="center" valignment="top" usebox="none">
8986 \begin_layout Plain Layout
9006 <cell alignment="center" valignment="top" usebox="none">
9009 \begin_layout Plain Layout
9010 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
9019 <row topspace="2mm">
9020 <cell alignment="center" valignment="top" usebox="none">
9023 \begin_layout Plain Layout
9043 <cell alignment="center" valignment="top" usebox="none">
9046 \begin_layout Plain Layout
9047 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
9056 <row topspace="2mm">
9057 <cell alignment="center" valignment="top" usebox="none">
9060 \begin_layout Plain Layout
9080 <cell alignment="center" valignment="top" usebox="none">
9083 \begin_layout Plain Layout
9084 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
9093 <row topspace="2mm">
9094 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9097 \begin_layout Plain Layout
9117 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9120 \begin_layout Plain Layout
9121 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
9135 \begin_inset space \hspace*{\fill}
9139 \begin_inset Tabular
9140 <lyxtabular version="3" rows="7" columns="2">
9141 <features booktabs="true" tabularvalignment="middle">
9142 <column alignment="center" valignment="top" width="0pt">
9143 <column alignment="center" valignment="top" width="0pt">
9145 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9148 \begin_layout Plain Layout
9154 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9157 \begin_layout Plain Layout
9165 <cell alignment="center" valignment="top" usebox="none">
9168 \begin_layout Plain Layout
9188 <cell alignment="center" valignment="top" usebox="none">
9191 \begin_layout Plain Layout
9192 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
9201 <row topspace="2mm">
9202 <cell alignment="center" valignment="top" usebox="none">
9205 \begin_layout Plain Layout
9225 <cell alignment="center" valignment="top" usebox="none">
9228 \begin_layout Plain Layout
9229 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
9238 <row topspace="2mm">
9239 <cell alignment="center" valignment="top" usebox="none">
9242 \begin_layout Plain Layout
9262 <cell alignment="center" valignment="top" usebox="none">
9265 \begin_layout Plain Layout
9266 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
9275 <row topspace="2mm">
9276 <cell alignment="center" valignment="top" usebox="none">
9279 \begin_layout Plain Layout
9299 <cell alignment="center" valignment="top" usebox="none">
9302 \begin_layout Plain Layout
9303 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9312 <row topspace="2mm">
9313 <cell alignment="center" valignment="top" usebox="none">
9316 \begin_layout Plain Layout
9336 <cell alignment="center" valignment="top" usebox="none">
9339 \begin_layout Plain Layout
9340 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9349 <row topspace="2mm">
9350 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9353 \begin_layout Plain Layout
9373 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9376 \begin_layout Plain Layout
9377 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9391 \begin_inset space \hspace*{\fill}
9397 \begin_layout Standard
9398 The command scheme for all of these arrows is:
9401 \begin_layout Standard
9403 \begin_inset Tabular
9404 <lyxtabular version="3" rows="2" columns="2">
9405 <features booktabs="true" tabularvalignment="middle">
9406 <column alignment="center" valignment="top" width="0pt">
9407 <column alignment="center" valignment="top" width="0pt">
9409 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9412 \begin_layout Plain Layout
9418 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9421 \begin_layout Plain Layout
9428 <row bottomspace="0.5mm">
9429 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9432 \begin_layout Plain Layout
9435 xleftrightarrow[x=a]
9438 \begin_inset Formula $\to$
9446 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9449 \begin_layout Plain Layout
9450 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9466 \begin_layout Subsection
9467 Vertical and Diagonal Arrows
9468 \begin_inset Index idx
9471 \begin_layout Plain Layout
9478 \begin_inset Index idx
9481 \begin_layout Plain Layout
9490 \begin_layout Standard
9491 \begin_inset space \hfill{}
9495 \begin_inset Tabular
9496 <lyxtabular version="3" rows="7" columns="2">
9497 <features booktabs="true" tabularvalignment="middle">
9498 <column alignment="center" valignment="top" width="0pt">
9499 <column alignment="center" valignment="top" width="0pt">
9501 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9504 \begin_layout Plain Layout
9510 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9513 \begin_layout Plain Layout
9521 <cell alignment="center" valignment="top" usebox="none">
9524 \begin_layout Plain Layout
9532 <cell alignment="center" valignment="top" usebox="none">
9535 \begin_layout Plain Layout
9536 \begin_inset Formula $\uparrow$
9546 <cell alignment="center" valignment="top" usebox="none">
9549 \begin_layout Plain Layout
9557 <cell alignment="center" valignment="top" usebox="none">
9560 \begin_layout Plain Layout
9561 \begin_inset Formula $\Uparrow$
9571 <cell alignment="center" valignment="top" usebox="none">
9574 \begin_layout Plain Layout
9582 <cell alignment="center" valignment="top" usebox="none">
9585 \begin_layout Plain Layout
9586 \begin_inset Formula $\updownarrow$
9596 <cell alignment="center" valignment="top" usebox="none">
9599 \begin_layout Plain Layout
9607 <cell alignment="center" valignment="top" usebox="none">
9610 \begin_layout Plain Layout
9611 \begin_inset Formula $\Updownarrow$
9621 <cell alignment="center" valignment="top" usebox="none">
9624 \begin_layout Plain Layout
9632 <cell alignment="center" valignment="top" usebox="none">
9635 \begin_layout Plain Layout
9636 \begin_inset Formula $\Downarrow$
9646 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9649 \begin_layout Plain Layout
9657 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9660 \begin_layout Plain Layout
9661 \begin_inset Formula $\downarrow$
9675 \begin_inset space \hfill{}
9679 \begin_inset Tabular
9680 <lyxtabular version="3" rows="5" columns="2">
9681 <features booktabs="true" tabularvalignment="middle">
9682 <column alignment="center" valignment="top" width="0pt">
9683 <column alignment="center" valignment="top" width="0pt">
9685 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9688 \begin_layout Plain Layout
9694 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9697 \begin_layout Plain Layout
9705 <cell alignment="center" valignment="top" usebox="none">
9708 \begin_layout Plain Layout
9716 <cell alignment="center" valignment="top" usebox="none">
9719 \begin_layout Plain Layout
9720 \begin_inset Formula $\nearrow$
9730 <cell alignment="center" valignment="top" usebox="none">
9733 \begin_layout Plain Layout
9741 <cell alignment="center" valignment="top" usebox="none">
9744 \begin_layout Plain Layout
9745 \begin_inset Formula $\searrow$
9755 <cell alignment="center" valignment="top" usebox="none">
9758 \begin_layout Plain Layout
9766 <cell alignment="center" valignment="top" usebox="none">
9769 \begin_layout Plain Layout
9770 \begin_inset Formula $\swarrow$
9780 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9783 \begin_layout Plain Layout
9791 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9794 \begin_layout Plain Layout
9795 \begin_inset Formula $\nwarrow$
9809 \begin_inset space \hfill{}
9815 \begin_layout Standard
9816 \begin_inset VSpace medskip
9819 Vertical arrows can also be used as delimiters together with the commands
9821 \begin_inset CommandInset ref
9823 reference "subsec:Manual-Bracket-Size"
9828 \begin_inset CommandInset ref
9830 reference "subsec:Automatic-Bracket-Size"
9837 \begin_layout Section
9839 \begin_inset CommandInset label
9846 \begin_inset Index idx
9849 \begin_layout Plain Layout
9858 \begin_layout Standard
9859 Accents can be inserted via the math toolbar button
9862 arg "math-insert \\hat"
9865 or the commands listed in the following subsections.
9868 \begin_layout Subsection
9869 Accents for One Character
9873 \begin_layout Plain Layout
9886 \begin_layout Plain Layout
9887 For accents in text see
9888 \begin_inset CommandInset ref
9890 reference "subsec:Accents-in-Text"
9903 \begin_layout Plain Layout
9911 \begin_inset Note Note
9914 \begin_layout Plain Layout
9921 is used to avoid that the footnote appears in the PDF-bookmark.
9924 \begin_layout Plain Layout
9932 \begin_inset CommandInset ref
9934 reference "subsec:Formulas-in-Section"
9944 \begin_inset CommandInset label
9946 name "subsec:Accents-for-one"
9951 \begin_inset Index idx
9954 \begin_layout Plain Layout
9955 Accents ! for one character
9963 \begin_layout Standard
9964 \begin_inset space \hfill{}
9968 \begin_inset Tabular
9969 <lyxtabular version="3" rows="8" columns="2">
9970 <features booktabs="true" tabularvalignment="middle">
9971 <column alignment="center" valignment="top" width="0pt">
9972 <column alignment="center" valignment="top" width="0pt">
9974 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9977 \begin_layout Plain Layout
9983 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9986 \begin_layout Plain Layout
9993 <row topspace="1.5mm">
9994 <cell alignment="center" valignment="top" usebox="none">
9997 \begin_layout Plain Layout
10001 \begin_inset space \textvisiblespace{}
10009 <cell alignment="center" valignment="top" usebox="none">
10012 \begin_layout Plain Layout
10013 \begin_inset Formula $\dot{A}$
10022 <row topspace="1.5mm">
10023 <cell alignment="center" valignment="top" usebox="none">
10026 \begin_layout Plain Layout
10030 \begin_inset space \textvisiblespace{}
10038 <cell alignment="center" valignment="top" usebox="none">
10041 \begin_layout Plain Layout
10042 \begin_inset Formula $\ddot{A}$
10051 <row topspace="1.5mm">
10052 <cell alignment="center" valignment="top" usebox="none">
10055 \begin_layout Plain Layout
10059 \begin_inset space \textvisiblespace{}
10067 <cell alignment="center" valignment="top" usebox="none">
10070 \begin_layout Plain Layout
10071 \begin_inset Formula $\dddot{A}$
10080 <row topspace="1.5mm">
10081 <cell alignment="center" valignment="top" usebox="none">
10084 \begin_layout Plain Layout
10088 \begin_inset space \textvisiblespace{}
10096 <cell alignment="center" valignment="top" usebox="none">
10099 \begin_layout Plain Layout
10100 \begin_inset Formula $\ddddot{A}$
10109 <row topspace="1.5mm">
10110 <cell alignment="center" valignment="top" usebox="none">
10113 \begin_layout Plain Layout
10117 \begin_inset space \textvisiblespace{}
10121 \begin_inset Index idx
10124 \begin_layout Plain Layout
10135 <cell alignment="center" valignment="top" usebox="none">
10138 \begin_layout Plain Layout
10139 \begin_inset Formula $\vec{A}$
10148 <row topspace="1.5mm">
10149 <cell alignment="center" valignment="top" usebox="none">
10152 \begin_layout Plain Layout
10156 \begin_inset space \textvisiblespace{}
10164 <cell alignment="center" valignment="top" usebox="none">
10167 \begin_layout Plain Layout
10168 \begin_inset Formula $\bar{A}$
10177 <row topspace="1.5mm">
10178 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10181 \begin_layout Plain Layout
10185 \begin_inset space \textvisiblespace{}
10193 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10196 \begin_layout Plain Layout
10197 \begin_inset Formula $\mathring{A}$
10211 \begin_inset space \hfill{}
10215 \begin_inset Tabular
10216 <lyxtabular version="3" rows="7" columns="2">
10217 <features booktabs="true" tabularvalignment="middle">
10218 <column alignment="center" valignment="top" width="0pt">
10219 <column alignment="center" valignment="top" width="0pt">
10221 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10224 \begin_layout Plain Layout
10230 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10233 \begin_layout Plain Layout
10240 <row topspace="1.5mm">
10241 <cell alignment="center" valignment="top" usebox="none">
10244 \begin_layout Plain Layout
10248 \begin_inset space \textvisiblespace{}
10256 <cell alignment="center" valignment="top" usebox="none">
10259 \begin_layout Plain Layout
10260 \begin_inset Formula $\tilde{A}$
10269 <row topspace="1.5mm">
10270 <cell alignment="center" valignment="top" usebox="none">
10273 \begin_layout Plain Layout
10277 \begin_inset space \textvisiblespace{}
10285 <cell alignment="center" valignment="top" usebox="none">
10288 \begin_layout Plain Layout
10289 \begin_inset Formula $\hat{A}$
10298 <row topspace="1.5mm">
10299 <cell alignment="center" valignment="top" usebox="none">
10302 \begin_layout Plain Layout
10306 \begin_inset space \textvisiblespace{}
10314 <cell alignment="center" valignment="top" usebox="none">
10317 \begin_layout Plain Layout
10318 \begin_inset Formula $\check{A}$
10327 <row topspace="1.5mm">
10328 <cell alignment="center" valignment="top" usebox="none">
10331 \begin_layout Plain Layout
10335 \begin_inset space \textvisiblespace{}
10343 <cell alignment="center" valignment="top" usebox="none">
10346 \begin_layout Plain Layout
10347 \begin_inset Formula $\acute{A}$
10356 <row topspace="1.5mm">
10357 <cell alignment="center" valignment="top" usebox="none">
10360 \begin_layout Plain Layout
10364 \begin_inset space \textvisiblespace{}
10372 <cell alignment="center" valignment="top" usebox="none">
10375 \begin_layout Plain Layout
10376 \begin_inset Formula $\grave{A}$
10385 <row topspace="1.5mm">
10386 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10389 \begin_layout Plain Layout
10393 \begin_inset space \textvisiblespace{}
10401 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10404 \begin_layout Plain Layout
10405 \begin_inset Formula $\breve{A}$
10419 \begin_inset space \hfill{}
10425 \begin_layout Standard
10426 \begin_inset VSpace bigskip
10432 \begin_layout Standard
10433 You can directly insert accents such as é in formulas.
10435 will transform them to the corresponding accent command.
10437 \begin_inset Index idx
10440 \begin_layout Plain Layout
10446 however it is better to insert a quotation mark before the vowel.
10447 These two characters are then treated by \SpecialChar LaTeX
10452 character when the formula part with the umlaut is marked as German.
10460 \begin_inset Quotes eld
10464 \begin_inset Quotes erd
10467 umlauts are created as demonstrated in the following example:
10470 \begin_layout Standard
10471 \begin_inset VSpace -2mm
10477 \begin_layout Standard
10479 \begin_inset Tabular
10480 <lyxtabular version="3" rows="3" columns="2">
10481 <features booktabs="true" tabularvalignment="middle">
10482 <column alignment="center" valignment="top" width="0pt">
10483 <column alignment="center" valignment="top">
10485 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10488 \begin_layout Plain Layout
10494 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10497 \begin_layout Plain Layout
10505 <cell alignment="center" valignment="top" usebox="none">
10508 \begin_layout Plain Layout
10509 \begin_inset Quotes grd
10517 <cell alignment="center" valignment="top" usebox="none">
10520 \begin_layout Plain Layout
10521 \begin_inset space \hspace{}
10528 \begin_inset Formula $"i$
10537 <row topspace="1.5mm">
10538 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10541 \begin_layout Plain Layout
10545 \begin_inset space \textvisiblespace{}
10553 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10556 \begin_layout Plain Layout
10557 \begin_inset Formula $\ddot{i}$
10573 \begin_layout Standard
10580 is that umlauts can be directly converted to mathematical text because
10581 the accent commands above are
10587 in mathematical text
10590 To convert an accented character to mathematical text, only the character
10591 under the accent may be converted.
10592 This applies for all conversions, e.
10593 \begin_inset space \thinspace{}
10597 \begin_inset space \space{}
10603 \begin_layout Standard
10604 \begin_inset VSpace bigskip
10610 \begin_layout Standard
10612 also supports a tilde under the character if the \SpecialChar LaTeX
10618 \begin_inset Index idx
10621 \begin_layout Plain Layout
10622 Packages ! undertilde
10627 is installed on your system:
10630 \begin_layout Standard
10634 \begin_layout Plain Layout
10644 \begin_inset Note Note
10647 \begin_layout Plain Layout
10648 The following table will only be displayed when the \SpecialChar LaTeX
10661 \begin_layout Standard
10664 \begin_inset Tabular
10665 <lyxtabular version="3" rows="2" columns="2">
10666 <features booktabs="true" tabularvalignment="middle">
10667 <column alignment="center" valignment="top" width="0pt">
10668 <column alignment="center" valignment="top" width="0pt">
10670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10673 \begin_layout Plain Layout
10679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10682 \begin_layout Plain Layout
10690 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10693 \begin_layout Plain Layout
10697 \begin_inset space \textvisiblespace{}
10705 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10708 \begin_layout Plain Layout
10709 \begin_inset Formula $\utilde{A}$
10725 \begin_layout Standard
10729 \begin_layout Plain Layout
10739 \begin_inset Note Note
10742 \begin_layout Plain Layout
10743 The following will be displayed when the \SpecialChar LaTeX
10756 \begin_layout Standard
10757 You need to install the \SpecialChar LaTeX
10762 to see the rest of this subsection in the output.
10765 \begin_layout Standard
10769 \begin_layout Plain Layout
10781 \begin_layout Subsection
10782 Accents for Several Characters
10783 \begin_inset Index idx
10786 \begin_layout Plain Layout
10787 Accents ! for several characters
10795 \begin_layout Standard
10796 \begin_inset space \hfill{}
10800 \begin_inset Tabular
10801 <lyxtabular version="3" rows="5" columns="2">
10802 <features booktabs="true" tabularvalignment="middle">
10803 <column alignment="center" valignment="top" width="0pt">
10804 <column alignment="center" valignment="top" width="0pt">
10806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10809 \begin_layout Plain Layout
10815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10818 \begin_layout Plain Layout
10825 <row topspace="1.5mm">
10826 <cell alignment="center" valignment="top" usebox="none">
10829 \begin_layout Plain Layout
10833 \begin_inset space \textvisiblespace{}
10841 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10844 \begin_layout Plain Layout
10845 \begin_inset Formula $\overleftarrow{A=B}$
10854 <row topspace="1.5mm">
10855 <cell alignment="center" valignment="top" usebox="none">
10858 \begin_layout Plain Layout
10862 \begin_inset space \textvisiblespace{}
10870 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10873 \begin_layout Plain Layout
10874 \begin_inset Formula $\underleftarrow{A=B}$
10883 <row topspace="1.5mm">
10884 <cell alignment="center" valignment="top" usebox="none">
10887 \begin_layout Plain Layout
10891 \begin_inset space \textvisiblespace{}
10899 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10902 \begin_layout Plain Layout
10903 \begin_inset Formula $\overleftrightarrow{A=B}$
10912 <row topspace="1.5mm" bottomspace="1mm">
10913 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10916 \begin_layout Plain Layout
10919 underleftrightarrow
10920 \begin_inset space \textvisiblespace{}
10928 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10931 \begin_layout Plain Layout
10932 \begin_inset Formula $\underleftrightarrow{A=B}$
10946 \begin_inset space \hfill{}
10950 \begin_inset Tabular
10951 <lyxtabular version="3" rows="5" columns="2">
10952 <features booktabs="true" tabularvalignment="middle">
10953 <column alignment="center" valignment="top" width="0pt">
10954 <column alignment="center" valignment="top" width="0pt">
10956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10959 \begin_layout Plain Layout
10965 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10968 \begin_layout Plain Layout
10975 <row topspace="1.5mm">
10976 <cell alignment="center" valignment="top" usebox="none">
10979 \begin_layout Plain Layout
10983 \begin_inset space \textvisiblespace{}
10991 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10994 \begin_layout Plain Layout
10995 \begin_inset Formula $\overrightarrow{A=B}$
11004 <row topspace="1.5mm">
11005 <cell alignment="center" valignment="top" usebox="none">
11008 \begin_layout Plain Layout
11012 \begin_inset space \textvisiblespace{}
11020 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11023 \begin_layout Plain Layout
11024 \begin_inset Formula $\underrightarrow{A=B}$
11033 <row topspace="1.5mm">
11034 <cell alignment="center" valignment="top" usebox="none">
11037 \begin_layout Plain Layout
11041 \begin_inset space \textvisiblespace{}
11049 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11052 \begin_layout Plain Layout
11053 \begin_inset Formula $\widetilde{A=B}$
11062 <row topspace="1.5mm" bottomspace="1mm">
11063 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11066 \begin_layout Plain Layout
11070 \begin_inset space \textvisiblespace{}
11078 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11081 \begin_layout Plain Layout
11082 \begin_inset Formula $\widehat{A=B}$
11096 \begin_inset space \hfill{}
11102 \begin_layout Standard
11103 \begin_inset VSpace medskip
11106 Using these commands you can accent as many characters as you like.
11119 will only be set in the output with a length of three characters, as shown
11120 in the following example:
11121 \begin_inset Formula
11123 \widetilde{A+B=C-D}
11131 \begin_layout Standard
11132 It is also possible to accent several characters using the commands
11139 \begin_inset Index idx
11142 \begin_layout Plain Layout
11157 \begin_inset Index idx
11160 \begin_layout Plain Layout
11168 described in the previous subsection.
11174 \begin_inset space \textvisiblespace{}
11178 \begin_inset Formula $\downarrow$
11184 \begin_inset Formula
11186 \underset{***}{A=B}
11194 \begin_layout Section
11196 \begin_inset CommandInset label
11198 name "subsec:Space"
11203 \begin_inset Index idx
11206 \begin_layout Plain Layout
11215 \begin_layout Subsection
11217 \begin_inset CommandInset label
11219 name "subsec:Predefined-Space"
11224 \begin_inset Index idx
11227 \begin_layout Plain Layout
11228 Space ! horizontal ! predefined
11236 \begin_layout Standard
11237 Sometimes it is necessary to insert horizontal space into a formula.
11238 This is done by inserting a
11239 \change_deleted 177693 1654668870
11241 \change_inserted 177693 1654668872
11245 \change_inserted 5863208 1612729962
11249 arg "command-alternatives math-space ; space-insert protected"
11253 \change_deleted 5863208 1612729965
11257 arg "command-alternatives space-insert protected ; math-space"
11261 \begin_inset Note Note
11264 \begin_layout Plain Layout
11266 \change_inserted 232239728 1611160593
11267 What is intended here?
11278 \begin_inset Quotes eld
11284 \begin_inset space \textvisiblespace{}
11290 \begin_inset Quotes erd
11293 appears and by pressing
11297 several times one can select one of eight different space sizes.
11298 The spaces can also be inserted using the math toolbar button
11301 arg "math-insert \\space"
11304 or special commands.
11305 The size can be adjusted at any time by positioning the cursor on the
11308 arg "math-insert \\space"
11315 until the desired size is achieved.
11318 \begin_layout Standard
11321 \begin_inset Tabular
11322 <lyxtabular version="3" rows="6" columns="3">
11323 <features booktabs="true" tabularvalignment="middle">
11324 <column alignment="center" valignment="top">
11325 <column alignment="center" valignment="top" width="15col%">
11326 <column alignment="center" valignment="top">
11328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11331 \begin_layout Plain Layout
11337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11340 \begin_layout Plain Layout
11350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11353 \begin_layout Plain Layout
11361 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11364 \begin_layout Plain Layout
11372 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11375 \begin_layout Plain Layout
11381 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11384 \begin_layout Plain Layout
11385 \begin_inset Formula $A\,B$
11395 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11398 \begin_layout Plain Layout
11406 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11409 \begin_layout Plain Layout
11415 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11418 \begin_layout Plain Layout
11419 \begin_inset Formula $A\:B$
11429 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11432 \begin_layout Plain Layout
11440 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11443 \begin_layout Plain Layout
11449 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11452 \begin_layout Plain Layout
11453 \begin_inset Formula $A\;B$
11463 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11466 \begin_layout Plain Layout
11474 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11477 \begin_layout Plain Layout
11483 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11486 \begin_layout Plain Layout
11487 \begin_inset Formula $A\quad B$
11497 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11500 \begin_layout Plain Layout
11508 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11511 \begin_layout Plain Layout
11517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11520 \begin_layout Plain Layout
11521 \begin_inset Formula $A\qquad B$
11535 \begin_inset space \hfill{}
11539 \begin_inset Tabular
11540 <lyxtabular version="3" rows="6" columns="3">
11541 <features booktabs="true" tabularvalignment="middle">
11542 <column alignment="center" valignment="top">
11543 <column alignment="center" valignment="top" width="15col%">
11544 <column alignment="center" valignment="top">
11546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11549 \begin_layout Plain Layout
11555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11558 \begin_layout Plain Layout
11568 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11571 \begin_layout Plain Layout
11579 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11582 \begin_layout Plain Layout
11590 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11593 \begin_layout Plain Layout
11599 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11602 \begin_layout Plain Layout
11603 \begin_inset Formula $A\hfill B$
11613 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11616 \begin_layout Plain Layout
11624 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11627 \begin_layout Plain Layout
11633 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11636 \begin_layout Plain Layout
11637 \begin_inset Formula $A\hspace*{1em}B$
11647 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11650 \begin_layout Plain Layout
11658 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11661 \begin_layout Plain Layout
11667 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11670 \begin_layout Plain Layout
11671 \begin_inset Formula $A\hspace{1em}B$
11681 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11684 \begin_layout Plain Layout
11688 \begin_inset space \textvisiblespace{}
11696 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11699 \begin_layout Plain Layout
11705 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11708 \begin_layout Plain Layout
11709 \begin_inset Formula $A\ B$
11719 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11722 \begin_layout Plain Layout
11730 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11733 \begin_layout Plain Layout
11739 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11742 \begin_layout Plain Layout
11743 \begin_inset Formula $A\!B$
11759 \begin_layout Standard
11761 \begin_inset space ~
11765 \begin_inset space \thinspace{}
11769 \begin_inset space \thinspace{}
11772 7 are variable spaces which are explained in
11773 \begin_inset CommandInset ref
11775 reference "subsec:Variable-Space"
11781 \begin_inset space ~
11784 9 appears to produce no space.
11785 It is displayed red in \SpecialChar LyX
11786 contrary to the other sizes, because it is a negative
11788 There are two more negative spaces:
11791 \begin_layout Standard
11793 \begin_inset Tabular
11794 <lyxtabular version="3" rows="3" columns="3">
11795 <features booktabs="true" tabularvalignment="middle">
11796 <column alignment="center" valignment="middle" width="6.8cm">
11797 <column alignment="center" valignment="top" width="0pt">
11798 <column alignment="center" valignment="top" width="0pt">
11800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11803 \begin_layout Plain Layout
11809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11812 \begin_layout Plain Layout
11820 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11823 \begin_layout Plain Layout
11833 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11836 \begin_layout Plain Layout
11841 keystrokes after inserting the
11842 \change_deleted 177693 1654668881
11844 \change_inserted 177693 1654668883
11852 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11855 \begin_layout Plain Layout
11861 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11864 \begin_layout Plain Layout
11872 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11875 \begin_layout Plain Layout
11881 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11884 \begin_layout Plain Layout
11885 \begin_inset Formula $A\negmedspace B$
11893 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11896 \begin_layout Plain Layout
11897 \begin_inset Formula $A\negthickspace B$
11913 \begin_layout Standard
11914 Negative spaces can lead to characters overlapping each other.
11915 Thus they can be used to enforce ligatures, which are useful for things
11916 such as summation operators:
11919 \begin_layout Standard
11921 \begin_inset Tabular
11922 <lyxtabular version="3" rows="3" columns="2">
11923 <features booktabs="true" tabularvalignment="middle">
11924 <column alignment="center" valignment="top" width="0pt">
11925 <column alignment="center" valignment="top">
11927 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11930 \begin_layout Plain Layout
11936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11939 \begin_layout Plain Layout
11947 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11950 \begin_layout Plain Layout
11956 \begin_inset space \textvisiblespace{}
11964 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11967 \begin_layout Plain Layout
11968 \begin_inset Formula $\sum\sum f_{kl}$
11978 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11981 \begin_layout Plain Layout
11989 \begin_inset space \textvisiblespace{}
11997 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12000 \begin_layout Plain Layout
12001 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
12017 \begin_layout Standard
12019 \begin_inset VSpace medskip
12025 \begin_layout Standard
12027 Relational operators, for example equal or less than signs, are always surrounde
12029 To suppress this, the operator is placed into a \SpecialChar TeX
12031 The following example demonstrates this:
12034 \begin_layout Standard
12036 \begin_inset Tabular
12037 <lyxtabular version="3" rows="2" columns="2">
12038 <features tabularvalignment="middle">
12039 <column alignment="center" valignment="top" width="0pt">
12040 <column alignment="center" valignment="top" width="0pt">
12042 <cell alignment="center" valignment="top" usebox="none">
12045 \begin_layout Plain Layout
12051 <cell alignment="center" valignment="top" usebox="none">
12054 \begin_layout Plain Layout
12055 \begin_inset Formula $A=B$
12065 <cell alignment="center" valignment="top" usebox="none">
12068 \begin_layout Plain Layout
12069 Equation without space
12074 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
12077 \begin_layout Plain Layout
12078 \begin_inset Formula $A{=}B$
12094 \begin_layout Standard
12096 The command for the last formula is:
12101 \begin_inset Formula $\to$
12107 \begin_layout Standard
12108 \begin_inset VSpace bigskip
12114 \begin_layout Standard
12115 Another example of controlled spaces is physical units.
12116 The space between a value and its unit is smaller than a normal space,
12117 typically a thin space is used.
12118 For units in text, the smaller space is inserted via the menu
12120 Insert\SpecialChar menuseparator
12121 Formatting\SpecialChar menuseparator
12123 \begin_inset space ~
12131 arg "space-insert thin"
12137 \begin_layout Standard
12138 An example to visualize the difference:
12141 \begin_layout Standard
12142 \begin_inset Tabular
12143 <lyxtabular version="3" rows="2" columns="2">
12144 <features tabularvalignment="middle">
12145 <column alignment="left" valignment="top">
12146 <column alignment="left" valignment="top">
12148 <cell alignment="center" valignment="top" usebox="none">
12151 \begin_layout Plain Layout
12153 \begin_inset Formula $\cdot$
12161 <cell alignment="center" valignment="top" usebox="none">
12164 \begin_layout Plain Layout
12165 Space between value and unit
12172 <cell alignment="center" valignment="top" usebox="none">
12175 \begin_layout Plain Layout
12177 \begin_inset space \thinspace{}
12181 \begin_inset Formula $\cdot$
12189 <cell alignment="center" valignment="top" usebox="none">
12192 \begin_layout Plain Layout
12193 Thin space between value and unit
12206 \begin_layout Subsection
12211 \begin_layout Plain Layout
12224 \begin_layout Plain Layout
12225 For vertical space in formulas see
12226 \begin_inset CommandInset ref
12228 reference "subsec:Line-Separation"
12241 \begin_layout Plain Layout
12249 \begin_inset Note Note
12252 \begin_layout Plain Layout
12255 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12258 \begin_layout Plain Layout
12261 texorpdfstring is in section
12262 \begin_inset CommandInset ref
12264 reference "subsec:Formulas-in-Section"
12274 \begin_inset CommandInset label
12276 name "subsec:Variable-Space"
12281 \begin_inset Index idx
12284 \begin_layout Plain Layout
12285 Space ! horizontal ! variable
12293 \begin_layout Standard
12294 Space with a defined length can be inserted with the command
12301 \begin_inset Index idx
12304 \begin_layout Plain Layout
12314 \begin_inset Quotes eld
12320 \begin_inset space \textvisiblespace{}
12326 \begin_inset Quotes erd
12329 will appear, the length of which can be specified by left-clicking on the
12331 \begin_inset Quotes eld
12337 \begin_inset space \textvisiblespace{}
12343 \begin_inset Quotes erd
12347 The length may also be negative.
12348 If the space is the first character in a line, it will ordinarily be omitted.
12349 To force its output use the command
12361 or left-click on the
12362 \begin_inset Quotes eld
12368 \begin_inset space \textvisiblespace{}
12374 \begin_inset Quotes erd
12377 and check the option
12382 \begin_inset Newline newline
12385 To insert as much space as is available, the command
12392 \begin_inset Index idx
12395 \begin_layout Plain Layout
12406 \begin_layout Standard
12408 \begin_inset Tabular
12409 <lyxtabular version="3" rows="4" columns="2">
12410 <features booktabs="true" tabularvalignment="middle">
12411 <column alignment="center" valignment="top" width="0pt">
12412 <column alignment="center" valignment="top">
12414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12417 \begin_layout Plain Layout
12425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12428 \begin_layout Plain Layout
12436 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12439 \begin_layout Plain Layout
12443 \begin_inset space \textvisiblespace{}
12449 \begin_inset space \thinspace{}
12457 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12460 \begin_layout Plain Layout
12461 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12471 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12474 \begin_layout Plain Layout
12478 \begin_inset space \textvisiblespace{}
12484 \begin_inset space \thinspace{}
12492 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12495 \begin_layout Plain Layout
12496 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12509 \begin_layout Plain Layout
12513 \begin_inset space \textvisiblespace{}
12521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12524 \begin_layout Plain Layout
12525 \begin_inset Formula $A=A\hfill B=B$
12541 \begin_layout Standard
12542 In the last example the available space is given by the longest column entry
12544 In an inline formula the space depends on the length of the line in which
12552 Thus, when the line uses the full width, no space will be created.
12559 only has an effect on displayed formulas when the formula style
12564 (Formula styles are explained in
12565 \begin_inset CommandInset ref
12567 reference "sec:Formula-Styles"
12574 \begin_layout Standard
12581 , there are also commands,
12593 that fill the space with a pattern.
12595 \begin_inset CommandInset ref
12597 reference "subsec:Ellipses"
12604 \begin_layout Standard
12605 For text, variable space can be inserted via the menu
12607 Insert\SpecialChar menuseparator
12608 Formatting\SpecialChar menuseparator
12610 \begin_inset space ~
12618 \begin_layout Standard
12619 This is a line with
12620 \begin_inset space \hspace{}
12625 \begin_inset space \thinspace{}
12631 \begin_layout Standard
12632 This is a line with
12633 \begin_inset space \hfill{}
12639 \begin_layout Subsection
12640 Space Besides Inline Formulas
12641 \begin_inset Index idx
12644 \begin_layout Plain Layout
12645 Space ! besides inline formulas
12653 \begin_layout Standard
12654 The space that surrounds inline formulas can be adjusted with the length
12662 \begin_inset Index idx
12665 \begin_layout Plain Layout
12674 The value of a length is set with the command
12681 \begin_inset Index idx
12684 \begin_layout Plain Layout
12692 which has the following scheme:
12695 \begin_layout Standard
12700 setlength{length name}{value}
12703 \begin_layout Standard
12711 \begin_inset space \thinspace{}
12717 \begin_layout Standard
12727 \begin_layout Standard
12728 is inserted in \SpecialChar TeX
12731 \begin_inset space \thinspace{}
12734 mm space will now be set around all inline formulas:
12738 \begin_layout Plain Layout
12752 \begin_layout Standard
12753 This is a line with an inline formula
12754 \begin_inset Formula $A=B$
12758 \begin_inset space \thinspace{}
12761 mm surrounding space.
12765 \begin_layout Plain Layout
12779 \begin_layout Standard
12780 To return to the predefined value,
12786 is set to the value 0
12787 \begin_inset space \thinspace{}
12793 \begin_layout Section
12795 \begin_inset Index idx
12798 \begin_layout Plain Layout
12805 \begin_inset Index idx
12808 \begin_layout Plain Layout
12813 \begin_layout Plain Layout
12824 \begin_layout Plain Layout
12839 \begin_layout Standard
12840 Boxes for text are described in chapter
12847 \begin_inset space ~
12855 \begin_layout Subsection
12857 \begin_inset CommandInset label
12859 name "subsec:Boxes-with-Frame"
12864 \begin_inset Index idx
12867 \begin_layout Plain Layout
12876 \begin_layout Standard
12877 It is possible to frame a formula or part of one with the commands
12884 \begin_inset Index idx
12887 \begin_layout Plain Layout
12902 \begin_inset Index idx
12905 \begin_layout Plain Layout
12916 \begin_layout Standard
12917 When one of these commands is inserted in a formula, a blue box appears
12918 within a frame to enter formula parts.
12925 an additional formula has to be created by
12929 within this box, because the box content will otherwise be treated as mathemati
12937 is used, a new formula is automatically created inside the frame.
12940 \begin_layout Standard
12947 is not suitable to frame displayed formulas because the formula will always
12948 be set in the size of the documents text.
12955 is not suitable to frame inline formulas because the formula will always
12956 be set in the size of a displayed formula.
12959 \begin_layout Standard
12973 \begin_inset Index idx
12976 \begin_layout Plain Layout
12984 with which the frame width and the alignment can be specified.
12991 is used in the following scheme:
12994 \begin_layout Standard
12999 framebox[frame width][position]{box content}
13002 \begin_layout Standard
13003 The position can either be
13020 right aligns the formula in the box.
13021 If no position is given the formula will be centered.
13022 \begin_inset Newline newline
13025 If width is not given then position can not be given.
13026 In this case the frame width is adjusted to the box content like for
13035 \begin_layout Standard
13042 is inserted, a box appears containing three blue boxes.
13043 The first two boxes are surrounded by brackets and denote the two optional
13045 The third box is for formula parts like for
13054 \begin_layout Standard
13056 \begin_inset Tabular
13057 <lyxtabular version="3" rows="5" columns="2">
13058 <features booktabs="true" tabularvalignment="middle">
13059 <column alignment="center" valignment="top" width="0pt">
13060 <column alignment="center" valignment="top">
13062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13065 \begin_layout Plain Layout
13071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13074 \begin_layout Plain Layout
13081 <row topspace="1.5mm">
13082 <cell alignment="center" valignment="top" usebox="none">
13085 \begin_layout Plain Layout
13089 \begin_inset space \textvisiblespace{}
13099 \begin_inset space \textvisiblespace{}
13107 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13110 \begin_layout Plain Layout
13111 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
13120 <row topspace="1.5mm">
13121 <cell alignment="center" valignment="top" usebox="none">
13124 \begin_layout Plain Layout
13128 \begin_inset space \textvisiblespace{}
13134 \begin_inset space \textvisiblespace{}
13142 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13145 \begin_layout Plain Layout
13146 \begin_inset Formula $\boxed{\int A=B}$
13155 <row topspace="1.5mm">
13156 <cell alignment="center" valignment="top" usebox="none">
13159 \begin_layout Plain Layout
13163 \begin_inset space \textvisiblespace{}
13171 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13174 \begin_layout Plain Layout
13175 \begin_inset Formula $A+\fbox{B}$
13184 <row topspace="1.5mm" bottomspace="1mm">
13185 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13188 \begin_layout Plain Layout
13192 \begin_inset space \textvisiblespace{}
13196 \begin_inset Formula $\to$
13200 \begin_inset Formula $\to$
13210 \begin_inset space \textvisiblespace{}
13214 \begin_inset Formula $\downarrow$
13222 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13225 \begin_layout Plain Layout
13226 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13242 \begin_layout Standard
13243 To adjust the frame thickness the following commands are inserted in \SpecialChar TeX
13245 before the formula:
13248 \begin_layout Standard
13258 \begin_inset Quotes eld
13262 \begin_inset Quotes erd
13276 \begin_inset Quotes eld
13280 \begin_inset Quotes erd
13286 \begin_layout Standard
13287 \begin_inset Quotes eld
13291 \begin_inset Quotes erd
13294 specifies the minimum distance between the frame and the first character
13296 An example of this is given in the following framed formula:
13300 \begin_layout Plain Layout
13312 \begin_inset Formula
13319 Before this formula the commands
13322 \begin_layout Standard
13344 \begin_layout Standard
13345 were inserted in \SpecialChar TeX
13347 These values are then used for all following boxes.
13350 \begin_layout Standard
13351 To return to the standard frame size, the command
13354 \begin_layout Standard
13379 \begin_layout Plain Layout
13393 \begin_layout Standard
13394 is inserted in \SpecialChar TeX
13395 mode before the next formula.
13398 \begin_layout Subsection
13399 Boxes Without Frame
13400 \begin_inset CommandInset label
13402 name "subsec:Boxes-without-Frame"
13407 \begin_inset Index idx
13410 \begin_layout Plain Layout
13411 Boxes ! without frame
13419 \begin_layout Standard
13420 For boxes without a frame the following box commands:
13427 \begin_inset Index idx
13430 \begin_layout Plain Layout
13445 \begin_inset Index idx
13448 \begin_layout Plain Layout
13463 \begin_inset Index idx
13466 \begin_layout Plain Layout
13477 \begin_layout Standard
13484 a box can be super- or subscripted.
13485 But in contrary to normal super- and subscripting, the characters in the
13486 box keep their font size.
13493 is used in the following scheme:
13496 \begin_layout Standard
13501 raisebox{height}{box content}
13504 \begin_layout Standard
13505 When the box contains a formula, an extra formula is needed like for
13514 \begin_layout Standard
13517 \begin_inset Note Greyedout
13520 \begin_layout Plain Layout
13531 this extra formula is created by pressing
13535 twice instead of once because \SpecialChar LyX
13536 doesn't yet support
13550 \begin_layout Standard
13552 \begin_inset Tabular
13553 <lyxtabular version="3" rows="4" columns="2">
13554 <features booktabs="true" tabularvalignment="middle">
13555 <column alignment="center" valignment="top" width="0pt">
13556 <column alignment="center" valignment="top">
13558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13561 \begin_layout Plain Layout
13567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13570 \begin_layout Plain Layout
13578 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13581 \begin_layout Plain Layout
13585 \begin_inset Formula $\to$
13591 \begin_inset Formula $\to$
13599 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13602 \begin_layout Plain Layout
13603 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13613 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13616 \begin_layout Plain Layout
13620 \begin_inset Formula $\to$
13626 \begin_inset Formula $\to$
13634 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13637 \begin_layout Plain Layout
13638 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13651 \begin_layout Plain Layout
13655 \begin_inset Formula $\to$
13671 \begin_inset space \textvisiblespace{}
13679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13682 \begin_layout Plain Layout
13683 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13699 \begin_layout Standard
13724 , except that there is no frame.
13727 \begin_layout Subsection
13729 \begin_inset CommandInset label
13731 name "subsec:Colored-Boxes"
13736 \begin_inset Index idx
13739 \begin_layout Plain Layout
13748 \begin_layout Standard
13749 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13758 \begin_layout Plain Layout
13759 The \SpecialChar LaTeX
13764 is part of every \SpecialChar LaTeX
13765 standard installation.
13771 \begin_inset Index idx
13774 \begin_layout Plain Layout
13780 must be loaded in the \SpecialChar LaTeX
13781 -preamble with the line
13785 \begin_layout Plain Layout
13786 When text is colored somewhere in the document with a predefined color,
13788 loads the \SpecialChar LaTeX
13794 Thus it is possible that the package is loaded twice, but this does not
13801 \begin_inset Note Note
13804 \begin_layout Plain Layout
13805 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13814 \begin_layout Standard
13822 \begin_layout Standard
13823 \begin_inset VSpace medskip
13826 To create color boxes, the command
13833 \begin_inset Index idx
13836 \begin_layout Plain Layout
13844 is used in the following scheme:
13847 \begin_layout Standard
13852 colorbox{color}{box content}
13855 \begin_layout Standard
13856 The box content can also be a box and a
13862 can also be part of another box (see the 2nd and 3rd example).
13863 When the box should contain a formula, an extra formula has to be created,
13864 the same way as for
13874 \begin_layout Plain Layout
13875 This also applies for the command
13889 \begin_layout Standard
13890 One of the following predefined colors can be chosen:
13893 \begin_layout Standard
13925 \begin_inset VSpace smallskip
13931 \begin_layout Standard
13933 \begin_inset Tabular
13934 <lyxtabular version="3" rows="4" columns="2">
13935 <features booktabs="true" tabularvalignment="middle">
13936 <column alignment="center" valignment="top" width="0pt">
13937 <column alignment="center" valignment="top">
13939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13942 \begin_layout Plain Layout
13948 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13951 \begin_layout Plain Layout
13959 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13962 \begin_layout Plain Layout
13966 \begin_inset Formula $\to$
13976 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13979 \begin_layout Plain Layout
13980 \begin_inset Formula $\colorbox{yellow}{A=B}$
13989 <row topspace="1.5mm">
13990 <cell alignment="center" valignment="top" usebox="none">
13993 \begin_layout Plain Layout
13997 \begin_inset Formula $\to$
14005 \begin_inset space \textvisiblespace{}
14009 \change_inserted 232239728 1611182042
14011 \begin_inset Formula $\gets\gets$
14021 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14024 \begin_layout Plain Layout
14025 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
14034 <row topspace="1.5mm" bottomspace="1mm">
14035 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
14038 \begin_layout Plain Layout
14042 \begin_inset space \textvisiblespace{}
14046 \change_inserted 232239728 1611182036
14048 \begin_inset Formula $\gets\gets$
14056 \begin_inset Formula $\to$
14072 \begin_inset space \textvisiblespace{}
14080 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
14083 \begin_layout Plain Layout
14084 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
14098 \begin_inset VSpace smallskip
14104 \begin_layout Standard
14111 only colors the box background, not the characters in the box.
14112 To color all characters, the whole formula is highlighted and the desired
14113 color is chosen in the
14116 \begin_inset space ~
14122 The dialog can be called with the toolbar button
14125 arg "dialog-show character"
14130 Edit\SpecialChar menuseparator
14132 \begin_inset space ~
14135 Properties\SpecialChar menuseparator
14139 The formula number will have the same color as the formula.
14140 If a different color for the formula number is desired, the color must
14141 be changed within the formula.
14144 \begin_layout Standard
14148 \begin_layout Standard
14151 \begin_inset Formula
14153 \int A=B\label{eq:red}
14161 \begin_inset Formula
14163 \textcolor{red}{\int A=B}\label{eq:redgreen}
14171 \begin_layout Standard
14173 \begin_inset CommandInset ref
14179 is completely colored red.
14180 \begin_inset Newline newline
14184 \begin_inset CommandInset ref
14186 reference "eq:redgreen"
14190 was first completely colored green to set the color for the formula number.
14191 Subsequently the formula characters were colored red.
14194 \begin_layout Standard
14195 \begin_inset VSpace bigskip
14198 To color the frame different than the rest of the box, the command
14205 \begin_inset Index idx
14208 \begin_layout Plain Layout
14216 is used in the following scheme:
14219 \begin_layout Standard
14224 fcolorbox{frame color}{color}{box content}
14227 \begin_layout Standard
14234 is an extension of the command
14241 The frame width is set, like for
14264 \begin_layout Plain Layout
14276 \begin_inset Formula
14278 \fcolorbox{cyan}{magenta}{A=B}
14287 \begin_layout Plain Layout
14301 \begin_layout Standard
14302 This formula was created with the command
14303 \begin_inset Newline newline
14311 \begin_inset Formula $\to$
14317 \begin_inset Formula $\to$
14327 \begin_layout Standard
14328 \begin_inset VSpace bigskip
14331 To use colors other than predefined ones, they must be defined first.
14334 \begin_layout Standard
14335 One can for example define the color
14336 \begin_inset Quotes eld
14344 \begin_inset Quotes erd
14347 with the \SpecialChar LaTeX
14351 \begin_layout Standard
14356 definecolor{darkgreen}{cmyk}{0.5,
14371 \begin_inset Index idx
14374 \begin_layout Plain Layout
14385 \begin_layout Standard
14390 is the color space denoting the colors
14407 The four comma separated numbers are the portion factors for the corresponding
14408 colors of the color space.
14409 The factors can be in the range of 0
14410 \begin_inset space \thinspace{}
14414 \begin_inset space \thinspace{}
14426 can also be used for definitions.
14443 , so there are three portion factors for the corresponding colors.
14444 Furthermore there is the color space
14448 with one portion factor for the gray value.
14451 \begin_layout Standard
14452 As an example here is a framed box with the newly defined color
14456 where the characters have been colored
14461 \begin_inset Formula
14463 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14471 \begin_layout Standard
14472 Self-defined colors can also be used for text with the help of the command
14480 \begin_inset Index idx
14483 \begin_layout Plain Layout
14492 \begin_layout Standard
14496 \begin_layout Plain Layout
14500 textcolor{darkgreen}{
14506 \begin_inset Quotes eld
14510 \begin_inset Quotes erd
14517 \begin_layout Plain Layout
14527 \begin_layout Standard
14535 \begin_inset Index idx
14538 \begin_layout Plain Layout
14546 is used in the scheme
14550 textcolor{color}{characters to color}
14555 \begin_layout Subsection
14557 \begin_inset CommandInset label
14559 name "subsec:Paragraph-Boxes"
14564 \begin_inset Index idx
14567 \begin_layout Plain Layout
14568 Boxes ! as paragraph
14576 \begin_layout Standard
14577 A box that can contain several lines and paragraphs, a so-called paragraph
14578 box (parbox), can be created with the menu
14580 Insert\SpecialChar menuseparator
14583 or the toolbar button
14592 \begin_layout Standard
14593 The following example shows a framed parbox in a line:
14596 \begin_layout Standard
14597 \begin_inset VSpace medskip
14601 \begin_inset Box Boxed
14611 height_special "totalheight"
14616 backgroundcolor "none"
14619 \begin_layout Plain Layout
14620 This is a paragraph box.
14622 \begin_inset space \thinspace{}
14625 cm long and can also contain formulas:
14626 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14637 \begin_layout Standard
14638 \begin_inset VSpace medskip
14644 \begin_layout Standard
14645 Such a box is created by right-clicking on the gray box inset.
14646 A dialog pops up showing the box properties.
14660 \begin_inset space \thinspace{}
14665 Vertical Box Alignment
14670 \begin_layout Standard
14671 \begin_inset VSpace medskip
14674 In \SpecialChar LaTeX
14675 a parbox is created with the command
14682 \begin_inset Index idx
14685 \begin_layout Plain Layout
14693 which has the following scheme:
14696 \begin_layout Standard
14701 parbox[position]{width}{box content}
14704 \begin_layout Standard
14719 \begin_inset Quotes eld
14723 \begin_inset Quotes erd
14726 means that the box is aligned within the surrounding text with its last
14733 \begin_inset Quotes eld
14737 \begin_inset Quotes erd
14740 this is done with the first line.
14741 When no position is given, the box will be vertically centered, see section
14749 \begin_inset space ~
14754 manual for examples.
14757 \begin_layout Standard
14758 \begin_inset VSpace bigskip
14761 To frame formulas completely, including the formula number, the formula
14762 must be set into a parbox.
14763 To do this, the command
14777 is inserted in \SpecialChar TeX
14778 mode before the formula.
14786 \begin_inset Index idx
14789 \begin_layout Plain Layout
14797 is the line width set for the document.
14798 Because the frame is outside the parbox, two times the frame separation
14799 and the frame thickness must be subtracted from the line width.
14800 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14809 \begin_layout Plain Layout
14814 is part of every \SpecialChar LaTeX
14815 standard installation.
14821 \begin_inset Index idx
14824 \begin_layout Plain Layout
14830 must be loaded in the \SpecialChar LaTeX
14831 -preamble with the line
14834 \begin_layout Standard
14842 \begin_layout Standard
14843 Behind the formula both boxes are closed by entering
14847 in \SpecialChar TeX
14849 Here is an example:
14853 \begin_layout Plain Layout
14867 \begin_layout Standard
14871 \begin_layout Plain Layout
14889 \begin_inset Formula
14891 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14900 \begin_layout Plain Layout
14911 \begin_layout Plain Layout
14925 \begin_layout Standard
14926 \begin_inset VSpace medskip
14929 As a parbox is used as the argument of
14935 , there is in this case no difference between
14950 \begin_layout Standard
14951 \begin_inset VSpace bigskip
14954 Paragraph boxes are very useful to comment formulas directly.
14961 is used in combination with the command
14975 \begin_inset CommandInset ref
14977 reference "subsec:User-defined-Numbering"
14984 \begin_layout Standard
14985 An example of a formula commented with
14994 \begin_layout Standard
14998 \begin_layout Plain Layout
15011 This is a description.
15012 It is distinctly separated from the formula and multiline.
15016 \begin_layout Plain Layout
15028 \begin_layout Standard
15029 Such a formula must be inserted completely in \SpecialChar TeX
15030 mode because \SpecialChar LyX
15032 support the command
15039 The formula is created with the following command sequence:
15042 \begin_layout Standard
15055 is inserted in \SpecialChar TeX
15060 \begin_layout Plain Layout
15061 When the formula style
15073 can also be replaced by
15080 (formula styles see
15081 \begin_inset CommandInset ref
15083 reference "sec:Formula-Styles"
15092 Then the description follows as normal text and finally
15098 is inserted in \SpecialChar TeX
15112 create a displayed formula.
15115 \begin_layout Standard
15122 can be seen in this example that was
15123 \begin_inset Quotes eld
15127 \begin_inset Quotes erd
15130 using the mathematical textmode:
15131 \begin_inset Formula
15133 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
15141 \begin_layout Section
15143 \begin_inset Index idx
15146 \begin_layout Plain Layout
15155 \begin_layout Subsection
15157 \begin_inset CommandInset label
15159 name "subsec:Big-Operators"
15164 \begin_inset Index idx
15167 \begin_layout Plain Layout
15174 \begin_inset Index idx
15177 \begin_layout Plain Layout
15184 \begin_inset Index idx
15187 \begin_layout Plain Layout
15196 \begin_layout Standard
15197 To be able to use all of the integral operators listed here, the
15205 must be set in the document settings under
15208 \begin_inset space ~
15216 \begin_layout Standard
15217 \begin_inset space \hfill{}
15221 \begin_inset Tabular
15222 <lyxtabular version="3" rows="11" columns="2">
15223 <features booktabs="true" tabularvalignment="middle">
15224 <column alignment="center" valignment="top" width="0pt">
15225 <column alignment="center" valignment="top" width="0pt">
15227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15230 \begin_layout Plain Layout
15236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15239 \begin_layout Plain Layout
15247 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15250 \begin_layout Plain Layout
15254 \begin_inset Index idx
15257 \begin_layout Plain Layout
15270 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15273 \begin_layout Plain Layout
15274 \begin_inset Formula $\int$
15284 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15287 \begin_layout Plain Layout
15295 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15298 \begin_layout Plain Layout
15299 \begin_inset Formula $\oint$
15309 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15312 \begin_layout Plain Layout
15320 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15323 \begin_layout Plain Layout
15324 \begin_inset Formula $\ointctrclockwise$
15334 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15337 \begin_layout Plain Layout
15345 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15348 \begin_layout Plain Layout
15349 \begin_inset Formula $\ointclockwise$
15359 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15362 \begin_layout Plain Layout
15370 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15373 \begin_layout Plain Layout
15374 \begin_inset Formula $\sqint$
15384 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15387 \begin_layout Plain Layout
15395 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15398 \begin_layout Plain Layout
15400 \begin_inset Formula $\fint$
15410 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15413 \begin_layout Plain Layout
15421 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15424 \begin_layout Plain Layout
15426 \begin_inset Formula $\landupint$
15436 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15439 \begin_layout Plain Layout
15447 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15450 \begin_layout Plain Layout
15452 \begin_inset Formula $\landdownint$
15462 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15465 \begin_layout Plain Layout
15473 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15476 \begin_layout Plain Layout
15477 \begin_inset Formula $\bigcap$
15487 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15490 \begin_layout Plain Layout
15498 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15501 \begin_layout Plain Layout
15502 \begin_inset Formula $\bigcup$
15516 \begin_inset space \hfill{}
15520 \begin_inset Tabular
15521 <lyxtabular version="3" rows="11" columns="2">
15522 <features booktabs="true" tabularvalignment="middle">
15523 <column alignment="center" valignment="top" width="0pt">
15524 <column alignment="center" valignment="top" width="0pt">
15526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15529 \begin_layout Plain Layout
15535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15538 \begin_layout Plain Layout
15546 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15549 \begin_layout Plain Layout
15553 \begin_inset Index idx
15556 \begin_layout Plain Layout
15569 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15572 \begin_layout Plain Layout
15573 \begin_inset Formula $\sum$
15583 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15586 \begin_layout Plain Layout
15590 \begin_inset Index idx
15593 \begin_layout Plain Layout
15600 \begin_layout Plain Layout
15619 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15622 \begin_layout Plain Layout
15623 \begin_inset Formula $\prod$
15633 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15636 \begin_layout Plain Layout
15644 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15647 \begin_layout Plain Layout
15648 \begin_inset Formula $\coprod$
15658 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15661 \begin_layout Plain Layout
15669 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15672 \begin_layout Plain Layout
15673 \begin_inset Formula $\bigodot$
15683 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15686 \begin_layout Plain Layout
15694 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15697 \begin_layout Plain Layout
15698 \begin_inset Formula $\bigotimes$
15708 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15711 \begin_layout Plain Layout
15719 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15722 \begin_layout Plain Layout
15723 \begin_inset Formula $\bigoplus$
15733 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15736 \begin_layout Plain Layout
15744 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15747 \begin_layout Plain Layout
15748 \begin_inset Formula $\bigwedge$
15758 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15761 \begin_layout Plain Layout
15769 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15772 \begin_layout Plain Layout
15773 \begin_inset Formula $\bigvee$
15783 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15786 \begin_layout Plain Layout
15794 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15797 \begin_layout Plain Layout
15798 \begin_inset Formula $\bigsqcup$
15808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15811 \begin_layout Plain Layout
15819 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15822 \begin_layout Plain Layout
15823 \begin_inset Formula $\biguplus$
15837 \begin_inset space \hfill{}
15843 \begin_layout Standard
15844 All big operators can also be inserted via the math toolbar button
15847 arg "math-insert \\intop"
15853 \begin_layout Standard
15854 The operators are called big because they are bigger than the sometimes
15855 equal looking binary operators.
15856 All big operators can have limits as described in the next subsection.
15859 \begin_layout Standard
15860 For all integral operators there is a second version available, ending in
15878 These operators differ in the style the operator limits are displayed,
15880 \begin_inset CommandInset ref
15882 reference "subsec:Operator-Limits"
15889 \begin_layout Subsubsection*
15890 Advice for Integrals
15893 \begin_layout Standard
15898 in an integral is an operator that has to be set upright.
15899 This is done by highlighting the
15903 and using the keyboard shortcut
15913 \begin_layout Plain Layout
15919 \begin_inset CommandInset ref
15921 reference "subsec:Font-Styles"
15931 Also the smallest space is inserted before the
15935 , as this is usual for operators.
15939 \begin_layout Standard
15941 \begin_inset Formula $\int A(x)dx$
15945 \begin_inset Newline newline
15949 \begin_inset Phantom HPhantom
15952 \begin_layout Plain Layout
15959 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15965 \begin_layout Standard
15966 The following commands exist for multiple integrals:
15967 \begin_inset VSpace medskip
15973 \begin_layout Standard
15974 \begin_inset space \hfill{}
15978 \begin_inset Tabular
15979 <lyxtabular version="3" rows="4" columns="2">
15980 <features booktabs="true" tabularvalignment="middle">
15981 <column alignment="center" valignment="top" width="0pt">
15982 <column alignment="center" valignment="top" width="0pt">
15984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15987 \begin_layout Plain Layout
15993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15996 \begin_layout Plain Layout
16003 <row bottomspace="1mm">
16004 <cell alignment="center" valignment="top" usebox="none">
16007 \begin_layout Plain Layout
16015 <cell alignment="center" valignment="top" usebox="none">
16018 \begin_layout Plain Layout
16019 \begin_inset Formula $\iint$
16028 <row bottomspace="1mm">
16029 <cell alignment="center" valignment="top" usebox="none">
16032 \begin_layout Plain Layout
16040 <cell alignment="center" valignment="top" usebox="none">
16043 \begin_layout Plain Layout
16044 \begin_inset Formula $\oiint$
16053 <row bottomspace="1mm">
16054 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16057 \begin_layout Plain Layout
16065 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16068 \begin_layout Plain Layout
16069 \begin_inset Formula $\sqiint$
16083 \begin_inset space \hfill{}
16087 \begin_inset Tabular
16088 <lyxtabular version="3" rows="4" columns="2">
16089 <features booktabs="true" tabularvalignment="middle">
16090 <column alignment="center" valignment="top" width="0pt">
16091 <column alignment="center" valignment="top" width="0pt">
16093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16096 \begin_layout Plain Layout
16102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16105 \begin_layout Plain Layout
16112 <row bottomspace="1mm">
16113 <cell alignment="center" valignment="top" usebox="none">
16116 \begin_layout Plain Layout
16124 <cell alignment="center" valignment="top" usebox="none">
16127 \begin_layout Plain Layout
16128 \begin_inset Formula $\iiint$
16137 <row bottomspace="1mm">
16138 <cell alignment="center" valignment="top" usebox="none">
16141 \begin_layout Plain Layout
16149 <cell alignment="center" valignment="top" usebox="none">
16152 \begin_layout Plain Layout
16153 \begin_inset Formula $\iiiint$
16162 <row bottomspace="1mm">
16163 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16166 \begin_layout Plain Layout
16174 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16177 \begin_layout Plain Layout
16178 \begin_inset Formula $\dotsint$
16192 \begin_inset space \hfill{}
16198 \begin_layout Subsection
16200 \begin_inset CommandInset label
16202 name "subsec:Operator-Limits"
16207 \begin_inset Index idx
16210 \begin_layout Plain Layout
16219 \begin_layout Standard
16220 Limits are created by super- and subscripts:
16223 \begin_layout Standard
16225 \begin_inset Tabular
16226 <lyxtabular version="3" rows="2" columns="2">
16227 <features booktabs="true" tabularvalignment="middle">
16228 <column alignment="center" valignment="top" width="0pt">
16229 <column alignment="center" valignment="top" width="0pt">
16231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16234 \begin_layout Plain Layout
16240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16243 \begin_layout Plain Layout
16251 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16254 \begin_layout Plain Layout
16260 \begin_inset space \textvisiblespace{}
16264 \begin_inset Formula $\to$
16268 \begin_inset Formula $\to$
16276 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16279 \begin_layout Plain Layout
16280 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
16296 \begin_layout Standard
16297 Limits of inline formulas are set on the right side of the operator.
16298 Limits in displayed formulas are set above or below the operator, except
16299 for integral limits.
16302 \begin_layout Standard
16303 To force the limits to be set beside the operator, the cursor is placed
16304 directly behind the operator and the limits type is changed with the menu
16307 Edit\SpecialChar menuseparator
16308 Math\SpecialChar menuseparator
16327 \begin_layout Standard
16328 The default displayed formulas limits type is this:
16329 \begin_inset Formula
16331 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16336 This is how it looks when the limits type is changed to
16343 \begin_inset Formula
16345 \sum\nolimits_{x=0}^{\infty}\frac{1}{x^{2}}
16350 For integrals, except those ending with
16366 etc., the limits by default are set beside the operator.
16367 But for multiple integrals the limits are often set below the operator.
16368 In the following example the limits type was set to
16372 and so set below the integrals:
16373 \begin_inset Formula
16375 \iiint\limits_{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16381 \change_deleted 5863208 1612725771
16383 \begin_inset Note Note
16386 \begin_layout Plain Layout
16388 \change_inserted 232239728 1611193306
16389 This integral did not have its limits set to Display in the original document
16401 \begin_layout Standard
16402 \begin_inset VSpace medskip
16405 To specify conditions for limits, the commands
16412 \begin_inset Index idx
16415 \begin_layout Plain Layout
16430 \begin_inset Index idx
16433 \begin_layout Plain Layout
16442 To create this expression
16443 \begin_inset Formula
16445 \sum_{\begin{subarray}{c}
16449 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16457 \begin_layout Standard
16458 the following must be done:
16459 \begin_inset Newline newline
16471 \begin_inset space \textvisiblespace{}
16477 The cursor is now in a blue box under the summation operator.
16483 \begin_inset space \textvisiblespace{}
16489 The blue box is now within a purple box and now multiple limit lines can
16491 A new line is created by inserting a line break (
16494 arg "newline-insert newline"
16499 \begin_inset Newline newline
16504 0<k<1000 Ctrl+Return
16505 \begin_inset Newline newline
16510 is typed in, a new box appears below for the new limit line.
16513 \begin_layout Standard
16514 The alignment of the lines can be changed to left aligned with the
16524 Edit\SpecialChar menuseparator
16528 To get right alignment,
16533 \begin_inset space \textvisiblespace{}
16538 is inserted at the beginning of the line.
16541 \begin_layout Standard
16554 with the difference that the lines are always centered.
16557 \begin_layout Standard
16558 \begin_inset VSpace bigskip
16562 \begin_inset CommandInset ref
16564 reference "eq:substack"
16568 there can be too much space beside an operator.
16569 This occurs because the characters following the operator are set beside
16571 To avoid this the command
16578 \begin_inset Index idx
16581 \begin_layout Plain Layout
16590 To use it, set the package
16595 \begin_inset Index idx
16598 \begin_layout Plain Layout
16599 Packages ! mathtools
16604 in the document settings under
16607 \begin_inset space ~
16615 \begin_inset space ~
16627 sets the space besides the operator to 0
16628 \begin_inset space \thinspace{}
16632 \begin_inset Newline newline
16636 \begin_inset CommandInset ref
16638 reference "eq:substack"
16642 , one uses the command
16645 \begin_layout Standard
16653 \begin_layout Standard
16654 and inserts the operator with its limits into the braces.
16655 Behind the brace one continues the formula:
16656 \begin_inset Formula
16658 \smashoperator{\sum_{\begin{subarray}{c}
16662 \end{subarray}}^{n}}k^{-2}
16670 \begin_layout Standard
16671 It is possible to set the space of only one side of the operator to 0
16672 \begin_inset space \thinspace{}
16676 To do this write either
16695 stands for the left and
16699 for the right side of the operator.
16700 Here is an example of the possible
16709 \begin_layout Standard
16710 \begin_inset Formula
16712 Y\smashoperator{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}=Y\smashoperator[l]{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}=Y\smashoperator[r]{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}
16720 \begin_layout Standard
16721 \begin_inset VSpace bigskip
16727 \begin_layout Standard
16728 When several consecutive operators have limits the typesetting of the limits
16729 looks often imperfect in the output, for example:
16730 \begin_inset Formula
16732 \text{a)}\lim_{n\to\infty}\max_{p\ge n}\quad\text{b)}\lim_{n\to\infty}\max_{p^{2}\ge n}\quad\text{c)}\lim_{n\to\infty}\sup_{p^{2}\ge nK}\quad\text{d)}\limsup_{n\to\infty}\max_{p\ge n}
16737 To improve the typesetting, in the document settings under
16740 \begin_inset space ~
16750 \begin_inset Index idx
16753 \begin_layout Plain Layout
16754 Packages ! mathtools
16759 , set the option to
16762 \begin_inset space ~
16768 Then insert the command
16775 \begin_inset Index idx
16778 \begin_layout Plain Layout
16786 directly before the first operator.
16787 The example will then look like this:
16788 \begin_inset Formula
16790 \text{a)}\adjustlimits\lim_{n\to\infty}\max_{p\ge n}\quad\text{b)}\adjustlimits\lim_{n\to\infty}\max_{p^{2}\ge n}\quad\text{c)}\adjustlimits\lim_{n\to\infty}\sup_{p^{2}\ge nK}\quad\text{d)}\adjustlimits\limsup_{n\to\infty}\max_{p\ge n}
16798 \begin_layout Standard
16799 \begin_inset VSpace bigskip
16802 How to use one limit for several operators is described in
16803 \begin_inset CommandInset ref
16805 reference "subsec:Self-defined-Operators"
16812 \begin_layout Subsection
16813 Decoration for Operators
16814 \begin_inset Index idx
16817 \begin_layout Plain Layout
16818 Operators ! Decoration
16826 \begin_layout Standard
16834 \begin_inset Index idx
16837 \begin_layout Plain Layout
16852 \begin_inset Index idx
16855 \begin_layout Plain Layout
16863 characters can be placed above or below an operator respectively.
16871 \begin_inset Index idx
16874 \begin_layout Plain Layout
16882 characters can be set before and behind a big operator.
16885 \begin_layout Standard
16887 \begin_inset space ~
16899 \begin_layout Itemize
16906 is used to set characters at the corners of the operator
16909 \begin_layout Itemize
16916 is used to set characters before and/or behind the operator (this variant
16917 represents \SpecialChar LaTeX
16927 \begin_layout Itemize
16934 is used to set characters at the left corners and/or behind the operator
16937 \begin_layout Itemize
16944 is used to set characters at the right corners and/or before the operator
16947 \begin_layout Standard
16948 For example the command
16953 \begin_inset space \textvisiblespace{}
16959 \begin_inset space \textvisiblespace{}
16963 \begin_inset Formula $\to$
16967 \begin_inset Formula $\to$
16971 \begin_inset space \textvisiblespace{}
16981 \begin_inset Formula
16983 \sideset{}{'}\sum_{k=1}^{n}
16991 \begin_layout Standard
16992 \begin_inset Note Greyedout
16995 \begin_layout Plain Layout
17002 can only be used to decorate big operators, binary operators are not allowed.
17010 \begin_layout Standard
17023 can also be used to decorate symbols and characters.
17024 For example, the command
17029 \begin_inset space \textvisiblespace{}
17035 \begin_inset space \textvisiblespace{}
17041 \begin_inset Formula $\uparrow$
17049 \begin_inset Formula
17051 \overset{a}{\maltese}
17059 \begin_layout Subsection
17061 \begin_inset CommandInset label
17063 name "subsec:Binary-Operators"
17068 \begin_inset Index idx
17071 \begin_layout Plain Layout
17080 \begin_layout Standard
17081 Binary operators are surrounded by space when there is a character before
17083 \begin_inset VSpace medskip
17089 \begin_layout Standard
17090 \begin_inset Tabular
17091 <lyxtabular version="3" rows="13" columns="2">
17092 <features booktabs="true" tabularvalignment="middle">
17093 <column alignment="center" valignment="top" width="0pt">
17094 <column alignment="center" valignment="top" width="0pt">
17096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17099 \begin_layout Plain Layout
17101 \begin_inset Note Note
17104 \begin_layout Plain Layout
17111 is only used as spacer.
17121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17124 \begin_layout Plain Layout
17132 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17135 \begin_layout Plain Layout
17141 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17144 \begin_layout Plain Layout
17145 \begin_inset Formula $+$
17155 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17158 \begin_layout Plain Layout
17164 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17167 \begin_layout Plain Layout
17168 \begin_inset Formula $-$
17178 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17181 \begin_layout Plain Layout
17189 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17192 \begin_layout Plain Layout
17193 \begin_inset Formula $\pm$
17203 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17206 \begin_layout Plain Layout
17214 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17217 \begin_layout Plain Layout
17218 \begin_inset Formula $\mp$
17228 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17231 \begin_layout Plain Layout
17239 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17242 \begin_layout Plain Layout
17243 \begin_inset Formula $\cdot$
17253 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17256 \begin_layout Plain Layout
17264 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17267 \begin_layout Plain Layout
17268 \begin_inset Formula $\times$
17278 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17281 \begin_layout Plain Layout
17289 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17292 \begin_layout Plain Layout
17293 \begin_inset Formula $\div$
17303 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17306 \begin_layout Plain Layout
17310 \begin_layout Plain Layout
17323 \begin_layout Plain Layout
17335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17338 \begin_layout Plain Layout
17339 \begin_inset Formula $*$
17349 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17352 \begin_layout Plain Layout
17360 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17363 \begin_layout Plain Layout
17364 \begin_inset Formula $\star$
17374 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17377 \begin_layout Plain Layout
17385 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17388 \begin_layout Plain Layout
17389 \begin_inset Formula $\circ$
17399 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17402 \begin_layout Plain Layout
17410 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17413 \begin_layout Plain Layout
17414 \begin_inset Formula $\diamond$
17424 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17427 \begin_layout Plain Layout
17435 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17438 \begin_layout Plain Layout
17439 \begin_inset Formula $\bullet$
17453 \begin_inset space \hfill{}
17457 \begin_inset Tabular
17458 <lyxtabular version="3" rows="13" columns="2">
17459 <features booktabs="true" tabularvalignment="middle">
17460 <column alignment="center" valignment="top" width="0pt">
17461 <column alignment="center" valignment="top" width="0pt">
17463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17466 \begin_layout Plain Layout
17472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17475 \begin_layout Plain Layout
17483 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17486 \begin_layout Plain Layout
17494 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17497 \begin_layout Plain Layout
17498 \begin_inset Formula $\nabla$
17508 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17511 \begin_layout Plain Layout
17519 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17522 \begin_layout Plain Layout
17523 \begin_inset Formula $\bigtriangledown$
17533 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17536 \begin_layout Plain Layout
17544 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17547 \begin_layout Plain Layout
17548 \begin_inset Formula $\bigtriangleup$
17558 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17561 \begin_layout Plain Layout
17569 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17572 \begin_layout Plain Layout
17573 \begin_inset Formula $\Box$
17583 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17586 \begin_layout Plain Layout
17594 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17597 \begin_layout Plain Layout
17598 \begin_inset Formula $\cap$
17608 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17611 \begin_layout Plain Layout
17619 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17622 \begin_layout Plain Layout
17623 \begin_inset Formula $\cup$
17633 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17636 \begin_layout Plain Layout
17644 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17647 \begin_layout Plain Layout
17648 \begin_inset Formula $\dagger$
17658 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17661 \begin_layout Plain Layout
17669 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17672 \begin_layout Plain Layout
17673 \begin_inset Formula $\ddagger$
17683 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17686 \begin_layout Plain Layout
17694 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17697 \begin_layout Plain Layout
17698 \begin_inset Formula $\wr$
17708 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17711 \begin_layout Plain Layout
17719 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17722 \begin_layout Plain Layout
17723 \begin_inset Formula $\bigcirc$
17733 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17736 \begin_layout Plain Layout
17744 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17747 \begin_layout Plain Layout
17748 \begin_inset Formula $\wedge$
17758 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17761 \begin_layout Plain Layout
17769 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17772 \begin_layout Plain Layout
17773 \begin_inset Formula $\vee$
17787 \begin_inset space \hfill{}
17791 \begin_inset Tabular
17792 <lyxtabular version="3" rows="13" columns="2">
17793 <features booktabs="true" tabularvalignment="middle">
17794 <column alignment="center" valignment="top" width="0pt">
17795 <column alignment="center" valignment="top" width="0pt">
17797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17800 \begin_layout Plain Layout
17806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17809 \begin_layout Plain Layout
17817 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17820 \begin_layout Plain Layout
17828 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17831 \begin_layout Plain Layout
17832 \begin_inset Formula $\oplus$
17842 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17845 \begin_layout Plain Layout
17853 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17856 \begin_layout Plain Layout
17857 \begin_inset Formula $\ominus$
17867 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17870 \begin_layout Plain Layout
17878 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17881 \begin_layout Plain Layout
17882 \begin_inset Formula $\otimes$
17892 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17895 \begin_layout Plain Layout
17903 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17906 \begin_layout Plain Layout
17907 \begin_inset Formula $\oslash$
17917 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17920 \begin_layout Plain Layout
17928 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17931 \begin_layout Plain Layout
17932 \begin_inset Formula $\odot$
17942 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17945 \begin_layout Plain Layout
17953 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17956 \begin_layout Plain Layout
17957 \begin_inset Formula $\amalg$
17967 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17970 \begin_layout Plain Layout
17978 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17981 \begin_layout Plain Layout
17982 \begin_inset Formula $\uplus$
17992 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17995 \begin_layout Plain Layout
18003 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18006 \begin_layout Plain Layout
18007 \begin_inset Formula $\setminus$
18017 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18020 \begin_layout Plain Layout
18028 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18031 \begin_layout Plain Layout
18032 \begin_inset Formula $\sqcap$
18042 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18045 \begin_layout Plain Layout
18053 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18056 \begin_layout Plain Layout
18057 \begin_inset Formula $\sqcup$
18067 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18070 \begin_layout Plain Layout
18078 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18081 \begin_layout Plain Layout
18082 \begin_inset Formula $\triangleleft$
18092 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18095 \begin_layout Plain Layout
18103 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18106 \begin_layout Plain Layout
18107 \begin_inset Formula $\triangleright$
18123 \begin_layout Standard
18124 All binary operators can also be inserted via the math toolbar button
18127 arg "math-insert \\pm"
18133 \begin_layout Standard
18134 To typeset the Laplace operator,
18151 \begin_inset Formula $\nabla^{2}$
18154 ) can also be used instead of
18163 \begin_layout Standard
18170 Insert\SpecialChar menuseparator
18182 \begin_layout Subsection
18183 Self-defined Operators
18184 \begin_inset CommandInset label
18186 name "subsec:Self-defined-Operators"
18191 \begin_inset Index idx
18194 \begin_layout Plain Layout
18195 Operators ! self-defined
18203 \begin_layout Standard
18204 With the help of the command
18208 DeclareMathOperator
18211 \begin_inset Index idx
18214 \begin_layout Plain Layout
18219 DeclareMathOperator
18224 , custom operators can be defined in the \SpecialChar LaTeX
18226 Its command scheme is:
18229 \begin_layout Standard
18234 DeclareMathOperator{new command}{display}
18237 \begin_layout Standard
18238 Display can be characters or symbols that define how the operator looks
18240 To define a big operator a * is set behind the command.
18241 All self-defined big operators can have limits as described in
18242 \begin_inset CommandInset ref
18244 reference "subsec:Operator-Limits"
18251 \begin_layout Standard
18252 For example the \SpecialChar LaTeX
18256 \begin_layout Standard
18261 DeclareMathOperator*{
18268 \begin_layout Standard
18269 defines the command
18275 , that inserts a big operator consisting of the black lozenge symbol from
18277 \begin_inset CommandInset ref
18279 reference "subsec:Miscellaneous-Symbols"
18284 \begin_inset Formula
18286 \Lozenge_{n=1}^{\infty}
18291 The command for this formula is:
18302 \begin_inset Formula $\to$
18308 \begin_layout Standard
18309 \begin_inset VSpace bigskip
18312 When self-defined operators are not used several times in the document,
18313 they can also be defined with the commands
18320 \begin_inset Index idx
18323 \begin_layout Plain Layout
18338 \begin_inset Index idx
18341 \begin_layout Plain Layout
18349 , which have the following scheme:
18352 \begin_layout Standard
18366 \begin_layout Standard
18373 defines big operators,
18382 \begin_layout Standard
18389 can be used to use one limit for several operators:
18392 \begin_layout Standard
18393 \begin_inset Formula
18395 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18403 \begin_layout Standard
18404 The command for the formula above is:
18405 \begin_inset Newline newline
18421 \begin_inset space \textvisiblespace{}
18427 \begin_inset Formula $\to$
18433 \begin_inset space \textvisiblespace{}
18441 \begin_layout Section
18443 \begin_inset Index idx
18446 \begin_layout Plain Layout
18455 \begin_layout Subsection
18457 \begin_inset CommandInset label
18459 name "subsec:Font-Styles"
18464 \begin_inset Index idx
18467 \begin_layout Plain Layout
18476 \begin_layout Standard
18477 Latin letters in formulas can be set in one of the following font styles:
18480 \begin_layout Standard
18482 \begin_inset Tabular
18483 <lyxtabular version="3" rows="6" columns="3">
18484 <features booktabs="true" tabularvalignment="middle">
18485 <column alignment="center" valignment="top" width="0pt">
18486 <column alignment="center" valignment="top">
18487 <column alignment="center" valignment="top">
18489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18492 \begin_layout Plain Layout
18498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18501 \begin_layout Plain Layout
18507 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18510 \begin_layout Plain Layout
18518 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18521 \begin_layout Plain Layout
18527 \begin_inset space \textvisiblespace{}
18537 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18540 \begin_layout Plain Layout
18541 \begin_inset Formula $\mathbb{ABC}$
18549 <cell alignment="center" valignment="top" usebox="none">
18552 \begin_layout Plain Layout
18560 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18563 \begin_layout Plain Layout
18569 \begin_inset space \textvisiblespace{}
18579 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18582 \begin_layout Plain Layout
18583 \begin_inset Formula $\mathbf{AbC}$
18591 <cell alignment="center" valignment="top" usebox="none">
18594 \begin_layout Plain Layout
18607 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18610 \begin_layout Plain Layout
18616 \begin_inset space \textvisiblespace{}
18626 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18629 \begin_layout Plain Layout
18630 \begin_inset Formula $\boldsymbol{AbC}$
18638 <cell alignment="center" valignment="top" usebox="none">
18641 \begin_layout Plain Layout
18644 arg "font-boldsymbol"
18654 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18657 \begin_layout Plain Layout
18663 \begin_inset space \textvisiblespace{}
18673 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18676 \begin_layout Plain Layout
18677 \begin_inset Formula $\mathcal{ABC}$
18685 <cell alignment="center" valignment="top" usebox="none">
18688 \begin_layout Plain Layout
18696 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18699 \begin_layout Plain Layout
18705 \begin_inset space \textvisiblespace{}
18715 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18718 \begin_layout Plain Layout
18719 \begin_inset Formula $\mathfrak{AbC}$
18727 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18730 \begin_layout Plain Layout
18744 \begin_layout Standard
18746 \begin_inset Tabular
18747 <lyxtabular version="3" rows="6" columns="3">
18748 <features booktabs="true" tabularvalignment="middle">
18749 <column alignment="center" valignment="top" width="0pt">
18750 <column alignment="center" valignment="top">
18751 <column alignment="center" valignment="top">
18753 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18756 \begin_layout Plain Layout
18762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18765 \begin_layout Plain Layout
18771 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18774 \begin_layout Plain Layout
18782 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18785 \begin_layout Plain Layout
18791 \begin_inset space \textvisiblespace{}
18801 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18804 \begin_layout Plain Layout
18805 \begin_inset Formula $\mathit{AbC}$
18813 <cell alignment="center" valignment="top" usebox="none">
18816 \begin_layout Plain Layout
18824 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18827 \begin_layout Plain Layout
18833 \begin_inset space \textvisiblespace{}
18843 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18846 \begin_layout Plain Layout
18847 \begin_inset Formula $\mathrm{AbC}$
18855 <cell alignment="center" valignment="top" usebox="none">
18858 \begin_layout Plain Layout
18871 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18874 \begin_layout Plain Layout
18880 \begin_inset space \textvisiblespace{}
18890 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18893 \begin_layout Plain Layout
18894 \begin_inset Formula $\mathsf{AbC}$
18902 <cell alignment="center" valignment="top" usebox="none">
18905 \begin_layout Plain Layout
18918 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18921 \begin_layout Plain Layout
18927 \begin_inset space \textvisiblespace{}
18937 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18940 \begin_layout Plain Layout
18941 \begin_inset Formula $\mathtt{AbC}$
18949 <cell alignment="center" valignment="top" usebox="none">
18952 \begin_layout Plain Layout
18955 arg "font-typewriter"
18965 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18968 \begin_layout Plain Layout
18974 \begin_inset space \textvisiblespace{}
18984 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18987 \begin_layout Plain Layout
18988 \begin_inset Formula $\mathscr{ABC}$
18996 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18999 \begin_layout Plain Layout
19013 \begin_layout Standard
19014 \begin_inset Note Greyedout
19017 \begin_layout Plain Layout
19040 can only be used for big letters.
19048 \begin_layout Standard
19058 \begin_layout Standard
19059 The style commands also work for letters in mathematical constructs:
19060 \begin_inset Formula
19062 \mathfrak{A=\frac{b}{C}}
19070 \begin_layout Standard
19071 Characters in mathematical text don't appear in a math font style but in
19072 the text font style
19079 Note that their style can't be set correctly via the text style dialog.
19080 This is a known bug in \SpecialChar LyX
19085 \begin_layout Plain Layout
19086 \begin_inset CommandInset href
19088 name "LyX-bug #4629"
19089 target "https://www.lyx.org/trac/ticket/4629"
19102 \begin_layout Standard
19103 Instead of the style commands,
19105 Edit\SpecialChar menuseparator
19106 Math\SpecialChar menuseparator
19109 dialog, or the toolbar button,
19112 arg "math-insert \\font"
19118 \begin_layout Subsection
19120 \begin_inset CommandInset label
19122 name "subsec:Bold-Formulas"
19127 \begin_inset Index idx
19130 \begin_layout Plain Layout
19139 \begin_layout Standard
19140 To make a complete formula bold, the command
19146 from the previous subsection cannot be used because it doesn't work for
19147 small Greek letters.
19148 Additionally it always prints Latin letters upright, as in the following
19152 \begin_layout Standard
19153 \begin_inset Formula
19155 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
19163 \begin_layout Standard
19164 To display the formula correctly, the command
19171 \begin_inset Formula
19173 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
19178 It is also possible to set the formula in a
19180 boldmath environment
19183 This environment is created by inserting the command
19190 \begin_inset Index idx
19193 \begin_layout Plain Layout
19201 in \SpecialChar TeX
19203 To end the environment, the command
19210 \begin_inset Index idx
19213 \begin_layout Plain Layout
19221 is inserted in \SpecialChar TeX
19226 \begin_layout Plain Layout
19236 \begin_inset Formula
19238 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
19247 \begin_layout Plain Layout
19259 \begin_layout Subsection
19261 \begin_inset Index idx
19264 \begin_layout Plain Layout
19273 \begin_layout Standard
19274 Formulas can be colored like normal text: Highlight a formula or a formula
19280 Here is a formula in magenta:
19281 \begin_inset Formula
19283 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19291 \begin_layout Standard
19292 You can also define your own colors as described in
19293 \begin_inset CommandInset ref
19295 reference "subsec:Colored-Boxes"
19300 They can be used with the \SpecialChar TeX
19308 \begin_inset Index idx
19311 \begin_layout Plain Layout
19322 \begin_layout Standard
19327 textcolor{color}{characters or formula}
19330 \begin_layout Standard
19331 The following example was colored completely dark green and partly red:
19334 \begin_layout Standard
19338 \begin_layout Plain Layout
19342 textcolor{darkgreen}{
19348 \begin_inset Formula
19350 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19359 \begin_layout Plain Layout
19369 \begin_layout Standard
19370 Due to a bug in \SpecialChar LyX
19371 only complete formulas can be colored with self-defined
19376 \begin_layout Plain Layout
19377 \begin_inset CommandInset href
19379 name "LyX-bug #5269"
19380 target "https://www.lyx.org/trac/ticket/5269"
19393 \begin_layout Subsection
19395 \begin_inset CommandInset label
19397 name "subsec:Font-Sizes"
19402 \begin_inset Index idx
19405 \begin_layout Plain Layout
19414 \begin_layout Standard
19415 As with characters in text, the following size commands are available for
19416 formula characters:
19419 \begin_layout Standard
19463 \begin_inset Newline newline
19485 \begin_layout Standard
19486 The font size produced by the commands depends on the document's original
19487 font size, which corresponds to the command
19494 The other commands produce character sizes smaller or larger than
19501 There are however limits to how small or large the font size can be changed.
19502 If for example the document font size is 12
19503 \begin_inset space \thinspace{}
19512 switches to the same size as
19521 \begin_layout Standard
19522 A size command is inserted in \SpecialChar TeX
19523 mode before a formula and sets the size for
19524 all of the following formulas and text characters.
19525 To switch back to the initial size, the command
19531 is inserted behind the formula, again in \SpecialChar TeX
19535 \begin_layout Standard
19536 Size can also be changed within a formula using the following size commands
19537 or the toolbar button
19540 arg "math-insert \\style"
19546 \begin_layout Standard
19549 \begin_inset Tabular
19550 <lyxtabular version="3" rows="5" columns="2">
19551 <features booktabs="true" tabularvalignment="middle">
19552 <column alignment="center" valignment="top" width="0pt">
19553 <column alignment="center" valignment="top">
19555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19558 \begin_layout Plain Layout
19564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19567 \begin_layout Plain Layout
19575 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19578 \begin_layout Plain Layout
19582 \begin_inset Index idx
19585 \begin_layout Plain Layout
19598 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19601 \begin_layout Plain Layout
19602 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19611 <row topspace="1mm">
19612 <cell alignment="center" valignment="top" usebox="none">
19615 \begin_layout Plain Layout
19623 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19626 \begin_layout Plain Layout
19627 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19637 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19640 \begin_layout Plain Layout
19648 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19651 \begin_layout Plain Layout
19652 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19662 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19665 \begin_layout Plain Layout
19673 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19676 \begin_layout Plain Layout
19677 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19693 \begin_layout Standard
19694 After entering these commands, a blue box appears in which the formula parts
19698 \begin_layout Standard
19699 There is another method for changing the font size, although it only works
19700 for symbols or letters in mathematical text.
19701 To use it, one of the above text size commands is inserted into mathematical
19703 All characters until the end of the mathematical text or until another
19704 size command will have the selected size.
19706 \begin_inset VSpace -2mm
19712 \begin_layout Standard
19716 \begin_layout Plain Layout
19726 \begin_inset Formula
19728 A=\frac{B}{c}\cdot\maltese
19734 \begin_inset Formula
19736 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19745 \begin_layout Plain Layout
19755 \begin_inset VSpace medskip
19758 Before the first formula the command
19765 The command for the second formula is:
19766 \begin_inset Newline newline
19774 \begin_inset space \textvisiblespace{}
19780 \begin_inset space \textvisiblespace{}
19786 \begin_inset space \textvisiblespace{}
19792 \begin_inset space \textvisiblespace{}
19796 \begin_inset Formula $\to$
19800 \begin_inset Formula $\to$
19804 \begin_inset Newline newline
19808 \begin_inset space \hspace*{}
19819 \begin_inset space \textvisiblespace{}
19825 \begin_inset space \textvisiblespace{}
19831 \begin_inset space \textvisiblespace{}
19837 \begin_layout Standard
19838 If a symbol cannot be displayed in different sizes, it will always be displayed
19839 in the default size.
19842 \begin_layout Section
19844 \begin_inset Index idx
19847 \begin_layout Plain Layout
19856 \begin_layout Standard
19857 Greek letters can be inserted via the toolbar button
19860 arg "math-insert \\alpha"
19863 as well as by command.
19864 All international typesetting norms purport that Greek letters in math
19865 have to be typeset italic/slanted.
19866 In some languages, like French or Russian, they are nevertheless sometimes
19870 \begin_layout Subsection
19872 \begin_inset Index idx
19875 \begin_layout Plain Layout
19876 Greek letters ! small
19884 \begin_layout Standard
19885 \begin_inset space \hfill{}
19889 \begin_inset Tabular
19890 <lyxtabular version="3" rows="11" columns="2">
19891 <features booktabs="true" tabularvalignment="middle">
19892 <column alignment="center" valignment="top" width="0pt">
19893 <column alignment="center" valignment="top" width="0pt">
19895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19898 \begin_layout Plain Layout
19904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19907 \begin_layout Plain Layout
19915 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19918 \begin_layout Plain Layout
19926 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19929 \begin_layout Plain Layout
19930 \begin_inset Formula $\alpha$
19940 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19943 \begin_layout Plain Layout
19951 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19954 \begin_layout Plain Layout
19955 \begin_inset Formula $\beta$
19965 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19968 \begin_layout Plain Layout
19976 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19979 \begin_layout Plain Layout
19980 \begin_inset Formula $\gamma$
19990 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19993 \begin_layout Plain Layout
20001 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20004 \begin_layout Plain Layout
20005 \begin_inset Formula $\delta$
20015 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20018 \begin_layout Plain Layout
20026 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20029 \begin_layout Plain Layout
20030 \begin_inset Formula $\epsilon$
20040 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20043 \begin_layout Plain Layout
20051 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20054 \begin_layout Plain Layout
20055 \begin_inset Formula $\varepsilon$
20065 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20068 \begin_layout Plain Layout
20076 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20079 \begin_layout Plain Layout
20080 \begin_inset Formula $\zeta$
20090 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20093 \begin_layout Plain Layout
20101 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20104 \begin_layout Plain Layout
20105 \begin_inset Formula $\eta$
20115 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20118 \begin_layout Plain Layout
20126 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20129 \begin_layout Plain Layout
20130 \begin_inset Formula $\theta$
20140 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20143 \begin_layout Plain Layout
20151 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20154 \begin_layout Plain Layout
20155 \begin_inset Formula $\vartheta$
20169 \begin_inset space \hfill{}
20173 \begin_inset Tabular
20174 <lyxtabular version="3" rows="12" columns="2">
20175 <features booktabs="true" tabularvalignment="middle">
20176 <column alignment="center" valignment="top" width="0pt">
20177 <column alignment="center" valignment="top" width="0pt">
20179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20182 \begin_layout Plain Layout
20188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20191 \begin_layout Plain Layout
20199 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20202 \begin_layout Plain Layout
20210 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20213 \begin_layout Plain Layout
20214 \begin_inset Formula $\iota$
20224 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20227 \begin_layout Plain Layout
20235 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20238 \begin_layout Plain Layout
20239 \begin_inset Formula $\kappa$
20249 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20252 \begin_layout Plain Layout
20260 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20263 \begin_layout Plain Layout
20264 \begin_inset Formula $\varkappa$
20274 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20277 \begin_layout Plain Layout
20285 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20288 \begin_layout Plain Layout
20289 \begin_inset Formula $\lambda$
20299 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20302 \begin_layout Plain Layout
20310 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20313 \begin_layout Plain Layout
20314 \begin_inset Formula $\mu$
20324 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20327 \begin_layout Plain Layout
20335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20338 \begin_layout Plain Layout
20339 \begin_inset Formula $\nu$
20349 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20352 \begin_layout Plain Layout
20360 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20363 \begin_layout Plain Layout
20364 \begin_inset Formula $\xi$
20374 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20377 \begin_layout Plain Layout
20383 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20386 \begin_layout Plain Layout
20387 \begin_inset Formula $o$
20397 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20400 \begin_layout Plain Layout
20408 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20411 \begin_layout Plain Layout
20412 \begin_inset Formula $\pi$
20422 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20425 \begin_layout Plain Layout
20433 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20436 \begin_layout Plain Layout
20437 \begin_inset Formula $\varpi$
20447 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20450 \begin_layout Plain Layout
20458 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20461 \begin_layout Plain Layout
20462 \begin_inset Formula $\rho$
20476 \begin_inset space \hfill{}
20480 \begin_inset Tabular
20481 <lyxtabular version="3" rows="11" columns="2">
20482 <features booktabs="true" tabularvalignment="middle">
20483 <column alignment="center" valignment="top" width="0pt">
20484 <column alignment="center" valignment="top" width="0pt">
20486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20489 \begin_layout Plain Layout
20495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20498 \begin_layout Plain Layout
20506 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20509 \begin_layout Plain Layout
20517 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20520 \begin_layout Plain Layout
20521 \begin_inset Formula $\varrho$
20531 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20534 \begin_layout Plain Layout
20542 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20545 \begin_layout Plain Layout
20546 \begin_inset Formula $\sigma$
20556 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20559 \begin_layout Plain Layout
20567 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20570 \begin_layout Plain Layout
20571 \begin_inset Formula $\varsigma$
20581 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20584 \begin_layout Plain Layout
20592 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20595 \begin_layout Plain Layout
20596 \begin_inset Formula $\tau$
20606 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20609 \begin_layout Plain Layout
20617 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20620 \begin_layout Plain Layout
20621 \begin_inset Formula $\upsilon$
20631 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20634 \begin_layout Plain Layout
20642 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20645 \begin_layout Plain Layout
20646 \begin_inset Formula $\phi$
20656 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20659 \begin_layout Plain Layout
20667 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20670 \begin_layout Plain Layout
20671 \begin_inset Formula $\varphi$
20681 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20684 \begin_layout Plain Layout
20692 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20695 \begin_layout Plain Layout
20696 \begin_inset Formula $\chi$
20706 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20709 \begin_layout Plain Layout
20717 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20720 \begin_layout Plain Layout
20721 \begin_inset Formula $\psi$
20731 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20734 \begin_layout Plain Layout
20742 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20745 \begin_layout Plain Layout
20746 \begin_inset Formula $\omega$
20760 \begin_inset space \hfill{}
20766 \begin_layout Standard
20767 \begin_inset VSpace medskip
20773 \begin_layout Standard
20774 Creating upright Greek letters is explained in
20775 \begin_inset CommandInset ref
20777 reference "subsec:Upright-small-Greek"
20784 \begin_layout Subsection
20786 \begin_inset Index idx
20789 \begin_layout Plain Layout
20790 Greek letters ! big
20798 \begin_layout Standard
20799 \begin_inset space \hfill{}
20803 \begin_inset Tabular
20804 <lyxtabular version="3" rows="7" columns="2">
20805 <features booktabs="true" tabularvalignment="middle">
20806 <column alignment="center" valignment="top" width="0pt">
20807 <column alignment="center" valignment="top" width="0pt">
20809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20812 \begin_layout Plain Layout
20818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20821 \begin_layout Plain Layout
20829 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20832 \begin_layout Plain Layout
20840 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20843 \begin_layout Plain Layout
20844 \begin_inset Formula $\Gamma$
20854 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20857 \begin_layout Plain Layout
20865 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20868 \begin_layout Plain Layout
20869 \begin_inset Formula $\Delta$
20879 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20882 \begin_layout Plain Layout
20890 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20893 \begin_layout Plain Layout
20894 \begin_inset Formula $\Theta$
20904 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20907 \begin_layout Plain Layout
20915 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20918 \begin_layout Plain Layout
20919 \begin_inset Formula $\Lambda$
20929 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20932 \begin_layout Plain Layout
20940 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20943 \begin_layout Plain Layout
20944 \begin_inset Formula $\Xi$
20954 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20957 \begin_layout Plain Layout
20965 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20968 \begin_layout Plain Layout
20969 \begin_inset Formula $\Pi$
20983 \begin_inset space \hfill{}
20987 \begin_inset Tabular
20988 <lyxtabular version="3" rows="6" columns="2">
20989 <features booktabs="true" tabularvalignment="middle">
20990 <column alignment="center" valignment="top" width="0pt">
20991 <column alignment="center" valignment="top" width="0pt">
20993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20996 \begin_layout Plain Layout
21002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21005 \begin_layout Plain Layout
21013 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21016 \begin_layout Plain Layout
21024 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21027 \begin_layout Plain Layout
21028 \begin_inset Formula $\Sigma$
21038 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21041 \begin_layout Plain Layout
21049 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21052 \begin_layout Plain Layout
21053 \begin_inset Formula $\Upsilon$
21063 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21066 \begin_layout Plain Layout
21074 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21077 \begin_layout Plain Layout
21078 \begin_inset Formula $\Phi$
21088 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21091 \begin_layout Plain Layout
21099 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21102 \begin_layout Plain Layout
21103 \begin_inset Formula $\Psi$
21113 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21116 \begin_layout Plain Layout
21124 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21127 \begin_layout Plain Layout
21128 \begin_inset Formula $\Omega$
21142 \begin_inset space \hfill{}
21148 \begin_layout Standard
21149 \begin_inset VSpace medskip
21152 The big Greek letters appearing upright is caused by a design bug in \SpecialChar TeX
21154 To create correct italic big letters, begin every command with
21159 For example the command
21166 \begin_inset Formula $\varGamma$
21170 Another way is to load the package
21178 \begin_layout Plain Layout
21183 is part of the \SpecialChar LaTeX
21189 \begin_inset Index idx
21192 \begin_layout Plain Layout
21197 \begin_layout Plain Layout
21217 \begin_inset Index idx
21220 \begin_layout Plain Layout
21226 with the \SpecialChar LaTeX
21230 \begin_layout Standard
21235 usepackage{fixmath}
21238 \begin_layout Standard
21239 Then all big Greek letters in a document will automatically be typeset italic.
21242 \begin_layout Subsection
21244 \begin_inset Index idx
21247 \begin_layout Plain Layout
21248 Greek letters ! bold
21256 \begin_layout Standard
21257 Greek letters cannot be set with different font styles like Latin letters.
21258 They can only be made bold with the command
21265 \begin_inset Index idx
21268 \begin_layout Plain Layout
21279 \begin_layout Standard
21281 \begin_inset Tabular
21282 <lyxtabular version="3" rows="3" columns="2">
21283 <features booktabs="true" tabularvalignment="middle">
21284 <column alignment="center" valignment="top" width="0pt">
21285 <column alignment="center" valignment="top">
21287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21290 \begin_layout Plain Layout
21296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21299 \begin_layout Plain Layout
21307 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21310 \begin_layout Plain Layout
21322 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21325 \begin_layout Plain Layout
21326 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21336 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21339 \begin_layout Plain Layout
21351 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21354 \begin_layout Plain Layout
21355 \begin_inset Formula $\theta\boldsymbol{\theta}$
21371 \begin_layout Section
21376 \begin_layout Plain Layout
21389 \begin_layout Plain Layout
21390 A list with all symbols of most of the \SpecialChar LaTeX
21391 -packages can be found in
21392 \begin_inset CommandInset citation
21408 \begin_layout Plain Layout
21416 \begin_inset Note Note
21419 \begin_layout Plain Layout
21422 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21425 \begin_layout Plain Layout
21428 texorpdfstring is in section
21429 \begin_inset CommandInset ref
21431 reference "subsec:Formulas-in-Section"
21441 \begin_inset Index idx
21444 \begin_layout Plain Layout
21453 \begin_layout Standard
21454 Many of the symbols listed in this section can also be inserted via the
21458 arg "math-insert \\nabla"
21464 arg "math-insert \\digamma"
21470 \begin_layout Subsection
21471 Mathematical Symbols
21472 \begin_inset CommandInset label
21474 name "subsec:Mathematical-Symbols"
21479 \begin_inset Index idx
21482 \begin_layout Plain Layout
21483 Symbols ! mathematical
21491 \begin_layout Standard
21492 \begin_inset Tabular
21493 <lyxtabular version="3" rows="10" columns="2">
21494 <features booktabs="true" tabularvalignment="middle">
21495 <column alignment="center" valignment="top" width="0pt">
21496 <column alignment="center" valignment="top" width="0pt">
21498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21501 \begin_layout Plain Layout
21507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21510 \begin_layout Plain Layout
21518 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21521 \begin_layout Plain Layout
21529 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21532 \begin_layout Plain Layout
21533 \begin_inset Formula $\neg$
21543 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21546 \begin_layout Plain Layout
21554 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21557 \begin_layout Plain Layout
21558 \begin_inset Formula $\Im$
21568 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21571 \begin_layout Plain Layout
21579 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21582 \begin_layout Plain Layout
21583 \begin_inset Formula $\Re$
21593 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21596 \begin_layout Plain Layout
21604 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21607 \begin_layout Plain Layout
21608 \begin_inset Formula $\aleph$
21618 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21621 \begin_layout Plain Layout
21629 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21632 \begin_layout Plain Layout
21633 \begin_inset Formula $\partial$
21643 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21646 \begin_layout Plain Layout
21654 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21657 \begin_layout Plain Layout
21658 \begin_inset Formula $\infty$
21668 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21671 \begin_layout Plain Layout
21679 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21682 \begin_layout Plain Layout
21683 \begin_inset Formula $\wp$
21693 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21696 \begin_layout Plain Layout
21704 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21707 \begin_layout Plain Layout
21708 \begin_inset Formula $\imath$
21718 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21721 \begin_layout Plain Layout
21729 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21732 \begin_layout Plain Layout
21733 \begin_inset Formula $\jmath$
21747 \begin_inset space \hfill{}
21751 \begin_inset Tabular
21752 <lyxtabular version="3" rows="10" columns="2">
21753 <features booktabs="true" tabularvalignment="middle">
21754 <column alignment="center" valignment="top" width="0pt">
21755 <column alignment="center" valignment="top" width="0pt">
21757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21760 \begin_layout Plain Layout
21766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21769 \begin_layout Plain Layout
21771 \begin_inset Note Note
21774 \begin_layout Plain Layout
21781 is only used as spacer.
21793 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21796 \begin_layout Plain Layout
21804 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21807 \begin_layout Plain Layout
21808 \begin_inset Formula $\forall$
21818 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21821 \begin_layout Plain Layout
21829 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21832 \begin_layout Plain Layout
21833 \begin_inset Formula $\exists$
21843 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21846 \begin_layout Plain Layout
21854 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21857 \begin_layout Plain Layout
21858 \begin_inset Formula $\nexists$
21868 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21871 \begin_layout Plain Layout
21879 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21882 \begin_layout Plain Layout
21883 \begin_inset Formula $\emptyset$
21893 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21896 \begin_layout Plain Layout
21904 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21907 \begin_layout Plain Layout
21908 \begin_inset Formula $\varnothing$
21918 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21921 \begin_layout Plain Layout
21929 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21932 \begin_layout Plain Layout
21933 \begin_inset Formula $\dag$
21943 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21946 \begin_layout Plain Layout
21954 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21957 \begin_layout Plain Layout
21958 \begin_inset Formula $\ddag$
21968 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21971 \begin_layout Plain Layout
21979 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21982 \begin_layout Plain Layout
21986 \begin_layout Plain Layout
21996 \begin_inset Formula $\complement$
22003 \begin_layout Plain Layout
22017 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22020 \begin_layout Plain Layout
22028 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22031 \begin_layout Plain Layout
22032 \begin_inset Formula $\Bbbk$
22046 \begin_inset space \hfill{}
22050 \begin_inset Tabular
22051 <lyxtabular version="3" rows="10" columns="2">
22052 <features booktabs="true" tabularvalignment="middle">
22053 <column alignment="center" valignment="top" width="0pt">
22054 <column alignment="center" valignment="top" width="0pt">
22056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22059 \begin_layout Plain Layout
22065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22068 \begin_layout Plain Layout
22076 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22079 \begin_layout Plain Layout
22087 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22090 \begin_layout Plain Layout
22091 \begin_inset Formula $\prime$
22101 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22104 \begin_layout Plain Layout
22112 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22115 \begin_layout Plain Layout
22116 \begin_inset Formula $\backprime$
22126 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22129 \begin_layout Plain Layout
22137 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22140 \begin_layout Plain Layout
22141 \begin_inset Formula $\mho$
22151 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22154 \begin_layout Plain Layout
22162 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22165 \begin_layout Plain Layout
22166 \begin_inset Formula $\triangle$
22176 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22179 \begin_layout Plain Layout
22187 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22190 \begin_layout Plain Layout
22191 \begin_inset Formula $\angle$
22201 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22204 \begin_layout Plain Layout
22212 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22215 \begin_layout Plain Layout
22216 \begin_inset Formula $\measuredangle$
22226 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22229 \begin_layout Plain Layout
22237 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22240 \begin_layout Plain Layout
22241 \begin_inset Formula $\sphericalangle$
22251 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22254 \begin_layout Plain Layout
22262 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22265 \begin_layout Plain Layout
22266 \begin_inset Formula $\top$
22276 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22279 \begin_layout Plain Layout
22287 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22290 \begin_layout Plain Layout
22291 \begin_inset Formula $\bot$
22307 \begin_layout Subsection
22308 Miscellaneous Symbols
22309 \begin_inset CommandInset label
22311 name "subsec:Miscellaneous-Symbols"
22316 \begin_inset Index idx
22319 \begin_layout Plain Layout
22320 Symbols ! miscellaneous
22328 \begin_layout Standard
22331 \begin_inset Tabular
22332 <lyxtabular version="3" rows="10" columns="2">
22333 <features booktabs="true" tabularvalignment="middle">
22334 <column alignment="center" valignment="top" width="0pt">
22335 <column alignment="center" valignment="top" width="0pt">
22337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22340 \begin_layout Plain Layout
22346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22349 \begin_layout Plain Layout
22357 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22360 \begin_layout Plain Layout
22368 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22371 \begin_layout Plain Layout
22372 \begin_inset Formula $\flat$
22382 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22385 \begin_layout Plain Layout
22393 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22396 \begin_layout Plain Layout
22397 \begin_inset Formula $\natural$
22407 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22410 \begin_layout Plain Layout
22418 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22421 \begin_layout Plain Layout
22422 \begin_inset Formula $\sharp$
22432 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22435 \begin_layout Plain Layout
22443 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22446 \begin_layout Plain Layout
22447 \begin_inset Formula $\surd$
22457 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22460 \begin_layout Plain Layout
22468 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22471 \begin_layout Plain Layout
22472 \begin_inset Formula $\checkmark$
22482 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22485 \begin_layout Plain Layout
22493 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22496 \begin_layout Plain Layout
22497 \begin_inset Formula $\yen$
22507 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22510 \begin_layout Plain Layout
22518 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22521 \begin_layout Plain Layout
22522 \begin_inset Formula $\pounds$
22532 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22535 \begin_layout Plain Layout
22541 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22544 \begin_layout Plain Layout
22545 \begin_inset Formula $\$$
22555 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22558 \begin_layout Plain Layout
22564 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22567 \begin_layout Plain Layout
22568 \begin_inset Formula $§$
22582 \begin_inset space \hfill{}
22586 \begin_inset Tabular
22587 <lyxtabular version="3" rows="10" columns="2">
22588 <features booktabs="true" tabularvalignment="middle">
22589 <column alignment="center" valignment="top" width="0pt">
22590 <column alignment="center" valignment="top">
22592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22595 \begin_layout Plain Layout
22601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22604 \begin_layout Plain Layout
22612 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22615 \begin_layout Plain Layout
22623 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22626 \begin_layout Plain Layout
22627 \begin_inset Formula $\hbar$
22637 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22640 \begin_layout Plain Layout
22648 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22651 \begin_layout Plain Layout
22652 \begin_inset Formula $\hslash$
22662 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22665 \begin_layout Plain Layout
22673 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22676 \begin_layout Plain Layout
22677 \begin_inset Formula $\clubsuit$
22687 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22690 \begin_layout Plain Layout
22698 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22701 \begin_layout Plain Layout
22702 \begin_inset Formula $\spadesuit$
22712 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22715 \begin_layout Plain Layout
22723 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22726 \begin_layout Plain Layout
22727 \begin_inset Formula $\bigstar$
22737 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22740 \begin_layout Plain Layout
22748 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22751 \begin_layout Plain Layout
22752 \begin_inset Formula $\blacklozenge$
22762 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22765 \begin_layout Plain Layout
22773 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22776 \begin_layout Plain Layout
22777 \begin_inset Formula $\blacktriangle$
22787 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22790 \begin_layout Plain Layout
22798 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22801 \begin_layout Plain Layout
22802 \begin_inset Formula $\blacktriangledown$
22812 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22815 \begin_layout Plain Layout
22823 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22826 \begin_layout Plain Layout
22827 \begin_inset Formula $\bullet$
22841 \begin_inset space \hfill{}
22845 \begin_inset Tabular
22846 <lyxtabular version="3" rows="10" columns="2">
22847 <features booktabs="true" tabularvalignment="middle">
22848 <column alignment="center" valignment="top" width="0pt">
22849 <column alignment="center" valignment="top" width="0pt">
22851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22854 \begin_layout Plain Layout
22860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22863 \begin_layout Plain Layout
22871 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22874 \begin_layout Plain Layout
22882 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22885 \begin_layout Plain Layout
22886 \begin_inset Formula $\diamondsuit$
22896 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22899 \begin_layout Plain Layout
22907 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22910 \begin_layout Plain Layout
22911 \begin_inset Formula $\Diamond$
22921 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22924 \begin_layout Plain Layout
22932 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22935 \begin_layout Plain Layout
22936 \begin_inset Formula $\heartsuit$
22946 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22949 \begin_layout Plain Layout
22957 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22960 \begin_layout Plain Layout
22961 \begin_inset Formula $\P$
22971 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22974 \begin_layout Plain Layout
22982 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22985 \begin_layout Plain Layout
22986 \begin_inset Formula $\copyright$
22996 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22999 \begin_layout Plain Layout
23007 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23010 \begin_layout Plain Layout
23011 \begin_inset Formula $\circledR$
23021 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23024 \begin_layout Plain Layout
23032 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23035 \begin_layout Plain Layout
23036 \begin_inset Formula $\maltese$
23046 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23049 \begin_layout Plain Layout
23057 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23060 \begin_layout Plain Layout
23061 \begin_inset Formula $\diagup$
23071 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23074 \begin_layout Plain Layout
23082 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23085 \begin_layout Plain Layout
23086 \begin_inset Formula $\diagdown$
23102 \begin_layout Standard
23103 \begin_inset VSpace medskip
23109 \begin_layout Standard
23110 Some symbols can be displayed in different sizes, see
23111 \begin_inset CommandInset ref
23113 reference "subsec:Font-Sizes"
23120 \begin_layout Subsection
23122 \begin_inset Index idx
23125 \begin_layout Plain Layout
23126 Symbols ! Euro-symbol
23132 \begin_inset Index idx
23135 \begin_layout Plain Layout
23142 \begin_layout Plain Layout
23159 \begin_layout Standard
23160 To use the Euro symbol in formulas, the \SpecialChar LaTeX
23166 \begin_inset Index idx
23169 \begin_layout Plain Layout
23175 must be installed and loaded with the \SpecialChar LaTeX
23179 \begin_layout Standard
23184 usepackage[gennarrow]{eurosym}
23187 \begin_layout Standard
23188 The Euro symbol can now be inserted with the command
23195 \begin_inset Index idx
23198 \begin_layout Plain Layout
23209 \begin_layout Standard
23210 The Euro symbol can directly be inserted with the € key in mathematical
23211 text, without having
23226 can also be inserted in \SpecialChar TeX
23228 The official currency symbol can then be inserted with the command
23235 \begin_inset Index idx
23238 \begin_layout Plain Layout
23246 , which is also only available in \SpecialChar TeX
23250 \begin_layout Standard
23254 \begin_layout Plain Layout
23264 \begin_inset Note Note
23267 \begin_layout Plain Layout
23268 The following table will only be displayed when the \SpecialChar LaTeX
23281 \begin_layout Standard
23282 An overview about the different Euro symbols:
23285 \begin_layout Standard
23287 \begin_inset Tabular
23288 <lyxtabular version="3" rows="4" columns="3">
23289 <features booktabs="true" tabularvalignment="middle">
23290 <column alignment="center" valignment="top" width="0pt">
23291 <column alignment="center" valignment="top" width="0pt">
23292 <column alignment="center" valignment="top" width="0pt">
23294 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
23297 \begin_layout Plain Layout
23301 \begin_layout Plain Layout
23305 cmidrule[0.08em]{2-3}
23315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23318 \begin_layout Plain Layout
23324 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23327 \begin_layout Plain Layout
23335 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23338 \begin_layout Plain Layout
23344 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23347 \begin_layout Plain Layout
23355 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23358 \begin_layout Plain Layout
23359 \begin_inset Formula $\euro$
23369 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23372 \begin_layout Plain Layout
23378 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23381 \begin_layout Plain Layout
23387 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23390 \begin_layout Plain Layout
23391 \begin_inset Formula $\mbox{€}$
23401 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23404 \begin_layout Plain Layout
23411 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23414 \begin_layout Plain Layout
23422 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23425 \begin_layout Plain Layout
23429 \begin_layout Plain Layout
23449 \begin_inset Note Note
23452 \begin_layout Plain Layout
23459 is used here only for table borders.
23469 manual for details.
23477 \begin_layout Standard
23481 \begin_layout Plain Layout
23491 \begin_inset Note Note
23494 \begin_layout Plain Layout
23495 The following will be displayed when the \SpecialChar LaTeX
23508 \begin_layout Standard
23509 You need to install the \SpecialChar LaTeX
23514 to see the rest of this subsection in the output.
23517 \begin_layout Standard
23521 \begin_layout Plain Layout
23533 \begin_layout Section
23535 \begin_inset CommandInset label
23537 name "sec:Relations"
23542 \begin_inset Index idx
23545 \begin_layout Plain Layout
23552 \begin_inset Index idx
23555 \begin_layout Plain Layout
23560 \begin_layout Plain Layout
23571 \begin_layout Plain Layout
23586 \begin_layout Standard
23587 All of the following relations can also be inserted via the toolbar button
23591 arg "math-insert \\leq"
23597 \begin_layout Standard
23598 \begin_inset Tabular
23599 <lyxtabular version="3" rows="17" columns="2">
23600 <features booktabs="true" tabularvalignment="middle">
23601 <column alignment="center" valignment="top" width="0pt">
23602 <column alignment="center" valignment="top" width="0pt">
23604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23607 \begin_layout Plain Layout
23613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23616 \begin_layout Plain Layout
23624 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23627 \begin_layout Plain Layout
23633 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23636 \begin_layout Plain Layout
23637 \begin_inset Formula $<$
23647 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23650 \begin_layout Plain Layout
23658 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23661 \begin_layout Plain Layout
23662 \begin_inset Formula $\le$
23672 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23675 \begin_layout Plain Layout
23683 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23686 \begin_layout Plain Layout
23687 \begin_inset Formula $\ll$
23697 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23700 \begin_layout Plain Layout
23708 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23711 \begin_layout Plain Layout
23712 \begin_inset Formula $\prec$
23722 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23725 \begin_layout Plain Layout
23733 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23736 \begin_layout Plain Layout
23737 \begin_inset Formula $\preceq$
23747 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23750 \begin_layout Plain Layout
23758 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23761 \begin_layout Plain Layout
23762 \begin_inset Formula $\subset$
23772 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23775 \begin_layout Plain Layout
23783 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23786 \begin_layout Plain Layout
23787 \begin_inset Formula $\subseteq$
23797 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23800 \begin_layout Plain Layout
23808 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23811 \begin_layout Plain Layout
23812 \begin_inset Formula $\sqsubseteq$
23822 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23825 \begin_layout Plain Layout
23833 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23836 \begin_layout Plain Layout
23837 \begin_inset Formula $\in$
23847 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23850 \begin_layout Plain Layout
23858 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23861 \begin_layout Plain Layout
23862 \begin_inset Formula $\vdash$
23872 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23875 \begin_layout Plain Layout
23883 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23886 \begin_layout Plain Layout
23887 \begin_inset Formula $\smile$
23897 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23900 \begin_layout Plain Layout
23908 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23911 \begin_layout Plain Layout
23912 \begin_inset Formula $\lhd$
23922 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23925 \begin_layout Plain Layout
23933 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23936 \begin_layout Plain Layout
23937 \begin_inset Formula $\unlhd$
23947 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23950 \begin_layout Plain Layout
23958 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23961 \begin_layout Plain Layout
23962 \begin_inset Formula $\gtrless$
23972 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23975 \begin_layout Plain Layout
23983 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23986 \begin_layout Plain Layout
23987 \begin_inset Formula $\mid$
23997 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24000 \begin_layout Plain Layout
24008 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24011 \begin_layout Plain Layout
24012 \begin_inset Formula $\nmid$
24026 \begin_inset space \hfill{}
24030 \begin_inset Tabular
24031 <lyxtabular version="3" rows="17" columns="2">
24032 <features booktabs="true" tabularvalignment="middle">
24033 <column alignment="center" valignment="top" width="0pt">
24034 <column alignment="center" valignment="top" width="0pt">
24036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24039 \begin_layout Plain Layout
24045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24048 \begin_layout Plain Layout
24056 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24059 \begin_layout Plain Layout
24065 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24068 \begin_layout Plain Layout
24069 \begin_inset Formula $=$
24079 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24082 \begin_layout Plain Layout
24090 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24093 \begin_layout Plain Layout
24094 \begin_inset Formula $\not=$
24104 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24107 \begin_layout Plain Layout
24115 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24118 \begin_layout Plain Layout
24119 \begin_inset Formula $\equiv$
24129 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24132 \begin_layout Plain Layout
24140 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24143 \begin_layout Plain Layout
24144 \begin_inset Formula $\sim$
24154 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24157 \begin_layout Plain Layout
24165 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24168 \begin_layout Plain Layout
24169 \begin_inset Formula $\simeq$
24179 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24182 \begin_layout Plain Layout
24190 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24193 \begin_layout Plain Layout
24194 \begin_inset Formula $\approx$
24204 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24207 \begin_layout Plain Layout
24215 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24218 \begin_layout Plain Layout
24219 \begin_inset Formula $\cong$
24229 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24232 \begin_layout Plain Layout
24240 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24243 \begin_layout Plain Layout
24244 \begin_inset Formula $\bowtie$
24254 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24257 \begin_layout Plain Layout
24265 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24268 \begin_layout Plain Layout
24269 \begin_inset Formula $\notin$
24279 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24282 \begin_layout Plain Layout
24290 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24293 \begin_layout Plain Layout
24294 \begin_inset Formula $\perp$
24304 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24307 \begin_layout Plain Layout
24315 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24318 \begin_layout Plain Layout
24319 \begin_inset Formula $\propto$
24329 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24332 \begin_layout Plain Layout
24340 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24343 \begin_layout Plain Layout
24344 \begin_inset Formula $\asymp$
24354 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24357 \begin_layout Plain Layout
24365 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24368 \begin_layout Plain Layout
24369 \begin_inset Formula $\doteq$
24379 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24382 \begin_layout Plain Layout
24390 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24393 \begin_layout Plain Layout
24394 \begin_inset Formula $\circeq$
24404 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24407 \begin_layout Plain Layout
24415 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24418 \begin_layout Plain Layout
24419 \begin_inset Formula $\models$
24429 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24432 \begin_layout Plain Layout
24440 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24443 \begin_layout Plain Layout
24444 \begin_inset Formula $\widehat{=}$
24458 \begin_inset space \hfill{}
24462 \begin_inset Tabular
24463 <lyxtabular version="3" rows="17" columns="2">
24464 <features booktabs="true" tabularvalignment="middle">
24465 <column alignment="center" valignment="top" width="0pt">
24466 <column alignment="center" valignment="top" width="0pt">
24468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24471 \begin_layout Plain Layout
24477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24480 \begin_layout Plain Layout
24488 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24491 \begin_layout Plain Layout
24497 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24500 \begin_layout Plain Layout
24501 \begin_inset Formula $>$
24511 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24514 \begin_layout Plain Layout
24522 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24525 \begin_layout Plain Layout
24526 \begin_inset Formula $\ge$
24536 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24539 \begin_layout Plain Layout
24547 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24550 \begin_layout Plain Layout
24551 \begin_inset Formula $\gg$
24561 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24564 \begin_layout Plain Layout
24572 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24575 \begin_layout Plain Layout
24576 \begin_inset Formula $\succ$
24586 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24589 \begin_layout Plain Layout
24597 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24600 \begin_layout Plain Layout
24601 \begin_inset Formula $\succeq$
24611 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24614 \begin_layout Plain Layout
24622 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24625 \begin_layout Plain Layout
24626 \begin_inset Formula $\supset$
24636 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24639 \begin_layout Plain Layout
24647 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24650 \begin_layout Plain Layout
24651 \begin_inset Formula $\supseteq$
24661 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24664 \begin_layout Plain Layout
24672 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24675 \begin_layout Plain Layout
24676 \begin_inset Formula $\sqsupseteq$
24686 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24689 \begin_layout Plain Layout
24697 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24700 \begin_layout Plain Layout
24701 \begin_inset Formula $\ni$
24711 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24714 \begin_layout Plain Layout
24722 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24725 \begin_layout Plain Layout
24726 \begin_inset Formula $\dashv$
24736 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24739 \begin_layout Plain Layout
24747 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24750 \begin_layout Plain Layout
24751 \begin_inset Formula $\frown$
24761 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24764 \begin_layout Plain Layout
24772 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24775 \begin_layout Plain Layout
24776 \begin_inset Formula $\rhd$
24786 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24789 \begin_layout Plain Layout
24797 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24800 \begin_layout Plain Layout
24801 \begin_inset Formula $\unrhd$
24811 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24814 \begin_layout Plain Layout
24822 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24825 \begin_layout Plain Layout
24826 \begin_inset Formula $\lessgtr$
24836 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24839 \begin_layout Plain Layout
24847 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24850 \begin_layout Plain Layout
24851 \begin_inset Formula $\parallel$
24861 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24864 \begin_layout Plain Layout
24872 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24875 \begin_layout Plain Layout
24876 \begin_inset Formula $\nparallel$
24892 \begin_layout Standard
24893 \begin_inset VSpace medskip
24908 are bigger than the equal looking operators
24923 \begin_layout Standard
24925 supports also many special relations.
24926 Use the toolbar button
24929 arg "math-insert \\leqq"
24932 to see a list of these relations.
24935 \begin_layout Standard
24936 Contrary to symbols, relations are always surrounded by space.
24939 \begin_layout Standard
24940 Relations with labels can be created with the command
24947 \begin_inset Index idx
24950 \begin_layout Plain Layout
24961 \begin_layout Standard
24963 \begin_inset Tabular
24964 <lyxtabular version="3" rows="2" columns="2">
24965 <features booktabs="true" tabularvalignment="middle">
24966 <column alignment="center" valignment="top" width="0pt">
24967 <column alignment="center" valignment="top">
24969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24972 \begin_layout Plain Layout
24978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24981 \begin_layout Plain Layout
24988 <row topspace="1.5mm">
24989 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24992 \begin_layout Plain Layout
24996 \begin_inset space \textvisiblespace{}
25004 \begin_inset space \textvisiblespace{}
25008 \begin_inset Formula $\downarrow$
25014 \begin_inset space \textvisiblespace{}
25018 \begin_inset space \textvisiblespace{}
25026 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25029 \begin_layout Plain Layout
25030 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
25046 \begin_layout Section
25050 \begin_layout Subsection
25051 Predefined Functions
25052 \begin_inset CommandInset label
25054 name "subsec:Predefined-Functions"
25059 \begin_inset Index idx
25062 \begin_layout Plain Layout
25063 Functions ! predefined
25071 \begin_layout Standard
25072 In general, variables are set
25076 in mathematical expressions, but not function names, because
25077 \begin_inset Formula $sin$
25080 could be misunderstood as
25081 \begin_inset Formula $s\cdot i\cdot n$
25085 Also predefined functions are separated a bit from the character in front
25087 They are inserted as commands starting with a backslash before their name.
25090 \begin_layout Standard
25092 \begin_inset Tabular
25093 <lyxtabular version="3" rows="2" columns="2">
25094 <features booktabs="true" tabularvalignment="middle">
25095 <column alignment="center" valignment="top" width="0pt">
25096 <column alignment="center" valignment="top" width="0pt">
25098 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
25101 \begin_layout Plain Layout
25107 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
25110 \begin_layout Plain Layout
25118 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25121 \begin_layout Plain Layout
25127 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
25130 \begin_layout Plain Layout
25131 \begin_inset Formula $Asin(x)+B$
25145 \begin_inset space \quad{}
25149 \begin_inset Tabular
25150 <lyxtabular version="3" rows="2" columns="2">
25151 <features booktabs="true" tabularvalignment="middle">
25152 <column alignment="center" valignment="top" width="0pt">
25153 <column alignment="center" valignment="top" width="0pt">
25155 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
25158 \begin_layout Plain Layout
25164 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
25167 \begin_layout Plain Layout
25175 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25178 \begin_layout Plain Layout
25186 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25189 \begin_layout Plain Layout
25190 \begin_inset Formula $A\sin(x)+B$
25206 \begin_layout Standard
25207 The following functions are predefined:
25210 \begin_layout Standard
25211 \begin_inset VSpace -2mm
25217 \begin_layout Standard
25219 \begin_inset Tabular
25220 <lyxtabular version="3" rows="9" columns="4">
25221 <features booktabs="true" tabularvalignment="middle">
25222 <column alignment="center" valignment="top" width="0pt">
25223 <column alignment="center" valignment="top" width="0pt">
25224 <column alignment="center" valignment="top" width="0pt">
25225 <column alignment="center" valignment="top" width="0pt">
25227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25230 \begin_layout Plain Layout
25236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25239 \begin_layout Plain Layout
25245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25248 \begin_layout Plain Layout
25254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25257 \begin_layout Plain Layout
25265 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25268 \begin_layout Plain Layout
25276 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25279 \begin_layout Plain Layout
25287 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25290 \begin_layout Plain Layout
25298 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25301 \begin_layout Plain Layout
25311 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25314 \begin_layout Plain Layout
25322 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25325 \begin_layout Plain Layout
25333 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25336 \begin_layout Plain Layout
25344 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25347 \begin_layout Plain Layout
25357 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25360 \begin_layout Plain Layout
25368 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25371 \begin_layout Plain Layout
25379 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25382 \begin_layout Plain Layout
25390 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25393 \begin_layout Plain Layout
25403 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25406 \begin_layout Plain Layout
25414 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25417 \begin_layout Plain Layout
25425 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25428 \begin_layout Plain Layout
25436 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25439 \begin_layout Plain Layout
25449 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25452 \begin_layout Plain Layout
25460 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25463 \begin_layout Plain Layout
25471 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25474 \begin_layout Plain Layout
25482 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25485 \begin_layout Plain Layout
25495 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25498 \begin_layout Plain Layout
25506 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25509 \begin_layout Plain Layout
25517 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25520 \begin_layout Plain Layout
25528 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25531 \begin_layout Plain Layout
25541 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25544 \begin_layout Plain Layout
25552 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25555 \begin_layout Plain Layout
25563 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25566 \begin_layout Plain Layout
25574 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25577 \begin_layout Plain Layout
25587 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25590 \begin_layout Plain Layout
25598 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25601 \begin_layout Plain Layout
25609 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25612 \begin_layout Plain Layout
25620 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25623 \begin_layout Plain Layout
25639 \begin_layout Standard
25640 They can also be inserted with the math toolbar button
25643 arg "math-insert \\functions"
25649 \begin_layout Subsection
25650 Self-defined Functions
25651 \begin_inset Index idx
25654 \begin_layout Plain Layout
25655 Functions ! self-defined
25663 \begin_layout Standard
25664 To use a function that is not predefined, for instance the sign function
25665 sgn(x), there are two possibilities:
25668 \begin_layout Itemize
25669 Define the function by inserting the following line in the \SpecialChar LaTeX
25674 \begin_layout Plain Layout
25679 DeclareMathOperator
25682 \begin_inset CommandInset ref
25684 reference "subsec:Self-defined-Operators"
25694 \begin_inset Newline newline
25698 \begin_inset VSpace -3mm
25702 \begin_inset Newline newline
25709 DeclareMathOperator{
25714 \begin_inset Index idx
25717 \begin_layout Plain Layout
25722 DeclareMathOperator
25728 \begin_inset Newline newline
25732 \begin_inset VSpace -2mm
25736 \begin_inset Newline newline
25739 Now the newly defined function can be called with the command
25748 \begin_layout Itemize
25749 Write the formula as usual, mark the formula name, in our example the letters
25754 , and change it to mathematical text.
25755 Finally, insert a space between the prefactor and function.
25758 \begin_layout Standard
25759 The result is the same with both methods as with a predefined function
25763 \begin_layout Plain Layout
25764 In \SpecialChar LyX
25765 self-defined functions are displayed red, predefined ones black.
25773 \begin_layout Standard
25775 \begin_inset Tabular
25776 <lyxtabular version="3" rows="3" columns="2">
25777 <features booktabs="true" tabularvalignment="middle">
25778 <column alignment="center" valignment="top" width="0pt">
25779 <column alignment="center" valignment="top" width="0pt">
25781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25784 \begin_layout Plain Layout
25790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25793 \begin_layout Plain Layout
25801 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25804 \begin_layout Plain Layout
25812 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25815 \begin_layout Plain Layout
25816 \begin_inset Formula $A\sgn(x)+B$
25826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25829 \begin_layout Plain Layout
25833 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25844 \begin_layout Plain Layout
25845 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25861 \begin_layout Standard
25862 The first method is more suitable when the self-defined function will be
25863 used several times.
25866 \begin_layout Subsection
25868 \begin_inset Index idx
25871 \begin_layout Plain Layout
25880 \begin_layout Standard
25881 For limits, in addition to the commands
25888 \begin_inset Index idx
25891 \begin_layout Plain Layout
25911 the following functions are defined:
25914 \begin_layout Standard
25916 \begin_inset Tabular
25917 <lyxtabular version="3" rows="5" columns="2">
25918 <features booktabs="true" tabularvalignment="middle">
25919 <column alignment="center" valignment="top" width="0pt">
25920 <column alignment="center" valignment="top" width="0pt">
25922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25925 \begin_layout Plain Layout
25931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25934 \begin_layout Plain Layout
25942 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25945 \begin_layout Plain Layout
25953 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25956 \begin_layout Plain Layout
25957 \begin_inset Formula $\varliminf$
25966 <row topspace="1.5mm">
25967 <cell alignment="center" valignment="top" usebox="none">
25970 \begin_layout Plain Layout
25978 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25981 \begin_layout Plain Layout
25982 \begin_inset Formula $\varlimsup$
25991 <row topspace="1.5mm">
25992 <cell alignment="center" valignment="top" usebox="none">
25995 \begin_layout Plain Layout
26003 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26006 \begin_layout Plain Layout
26007 \begin_inset Formula $\varprojlim$
26016 <row topspace="1.5mm" bottomspace="1mm">
26017 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
26020 \begin_layout Plain Layout
26028 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26031 \begin_layout Plain Layout
26032 \begin_inset Formula $\varinjlim$
26048 \begin_layout Standard
26049 \begin_inset VSpace medskip
26052 The limit is created by inserting a subscript.
26053 It is set right beside the function in an inline formula:
26056 \begin_layout Standard
26058 \begin_inset Tabular
26059 <lyxtabular version="3" rows="2" columns="2">
26060 <features booktabs="true" tabularvalignment="middle">
26061 <column alignment="center" valignment="top" width="0pt">
26062 <column alignment="center" valignment="top" width="0pt">
26064 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
26067 \begin_layout Plain Layout
26073 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
26076 \begin_layout Plain Layout
26084 <cell alignment="center" valignment="top" usebox="none">
26087 \begin_layout Plain Layout
26093 \begin_inset space \textvisiblespace{}
26097 \begin_inset space \textvisiblespace{}
26105 <cell alignment="center" valignment="top" usebox="none">
26108 \begin_layout Plain Layout
26109 \begin_inset Formula $\lim_{x\to A}x=B$
26125 \begin_layout Standard
26126 In a displayed formula the limit is set below the formula, as usual:
26127 \begin_inset Formula
26137 \begin_layout Standard
26138 \begin_inset VSpace medskip
26144 \begin_layout Standard
26145 How to adjust the typesetting of the limits see
26146 \begin_inset CommandInset ref
26148 reference "subsec:Operator-Limits"
26155 \begin_layout Subsection
26157 \begin_inset Index idx
26160 \begin_layout Plain Layout
26161 Functions ! modulo-
26169 \begin_layout Standard
26170 The modulo-function is special, because it exists in four variants.
26171 The variants in a displayed formula are:
26172 \begin_inset Formula
26174 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26175 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
26176 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
26177 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
26178 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
26186 \begin_layout Standard
26187 In an inline formula less space is set before the function names for all
26189 By default the modulo-functions take only the first character following
26190 the command into account.
26191 To use more than one character, put them in \SpecialChar TeX
26193 \begin_inset Formula
26195 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26196 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
26197 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26205 \begin_layout Section
26207 \begin_inset Index idx
26210 \begin_layout Plain Layout
26219 \begin_layout Standard
26220 The characters ^ and _ would normally create a superscript and subscript,
26222 To get these characters you have to insert them with a leading
26227 \begin_layout Standard
26230 \begin_inset Tabular
26231 <lyxtabular version="3" rows="3" columns="2">
26232 <features booktabs="true" tabularvalignment="middle">
26233 <column alignment="left" valignment="top" width="0pt">
26234 <column alignment="block" valignment="top">
26236 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26239 \begin_layout Plain Layout
26245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26248 \begin_layout Plain Layout
26256 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26259 \begin_layout Plain Layout
26263 \begin_inset space \textvisiblespace{}
26271 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26274 \begin_layout Plain Layout
26275 \begin_inset Formula $\mathcircumflex$
26285 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26288 \begin_layout Plain Layout
26296 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26299 \begin_layout Plain Layout
26300 \begin_inset Formula $\_$
26316 \begin_layout Subsection
26317 Special Characters in Mathematical Text
26320 \begin_layout Standard
26321 The following commands can only be used in mathematical text or in \SpecialChar TeX
26325 \begin_layout Standard
26326 \begin_inset space \hfill{}
26330 \begin_inset Tabular
26331 <lyxtabular version="3" rows="8" columns="2">
26332 <features booktabs="true" tabularvalignment="middle">
26333 <column alignment="left" valignment="top" width="0pt">
26334 <column alignment="block" valignment="top">
26336 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26339 \begin_layout Plain Layout
26345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26348 \begin_layout Plain Layout
26356 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26359 \begin_layout Plain Layout
26367 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26370 \begin_layout Plain Layout
26371 \begin_inset Formula $\textrm{œ}$
26381 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26384 \begin_layout Plain Layout
26392 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26395 \begin_layout Plain Layout
26396 \begin_inset Formula $\textrm{Œ}$
26406 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26409 \begin_layout Plain Layout
26417 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26420 \begin_layout Plain Layout
26421 \begin_inset Formula $\textrm{æ}$
26431 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26434 \begin_layout Plain Layout
26442 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26445 \begin_layout Plain Layout
26446 \begin_inset Formula $\textrm{Æ}$
26456 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26459 \begin_layout Plain Layout
26467 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26470 \begin_layout Plain Layout
26471 \begin_inset Formula $\textrm{å}$
26481 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26484 \begin_layout Plain Layout
26492 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26495 \begin_layout Plain Layout
26496 \begin_inset Formula $\textrm{Å}$
26506 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26509 \begin_layout Plain Layout
26517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26520 \begin_layout Plain Layout
26521 \begin_inset Formula $\textrm{ı}$
26535 \begin_inset space \hfill{}
26539 \begin_inset Tabular
26540 <lyxtabular version="3" rows="8" columns="2">
26541 <features booktabs="true" tabularvalignment="middle">
26542 <column alignment="left" valignment="top" width="0pt">
26543 <column alignment="center" valignment="top">
26545 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26548 \begin_layout Plain Layout
26550 \begin_inset Note Note
26553 \begin_layout Plain Layout
26555 \begin_inset space \thinspace{}
26558 mm is used for separation, because otherwise the output will be ¡ and ¿
26569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26572 \begin_layout Plain Layout
26580 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26583 \begin_layout Plain Layout
26591 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26594 \begin_layout Plain Layout
26595 \begin_inset Formula $\textrm{ø}$
26605 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26608 \begin_layout Plain Layout
26616 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26619 \begin_layout Plain Layout
26620 \begin_inset Formula $\textrm{Ø}$
26630 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26633 \begin_layout Plain Layout
26641 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26644 \begin_layout Plain Layout
26645 \begin_inset Formula $\textrm{ł}$
26655 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26658 \begin_layout Plain Layout
26666 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26669 \begin_layout Plain Layout
26670 \begin_inset Formula $\textrm{Ł}$
26680 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26683 \begin_layout Plain Layout
26685 \begin_inset space \hspace{}
26690 \begin_inset space \textvisiblespace{}
26698 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26701 \begin_layout Plain Layout
26702 \begin_inset Formula $\textrm{!`}$
26712 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26715 \begin_layout Plain Layout
26717 \begin_inset space \hspace{}
26722 \begin_inset space \textvisiblespace{}
26730 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26733 \begin_layout Plain Layout
26734 \begin_inset Formula $\textrm{?`}$
26744 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26747 \begin_layout Plain Layout
26755 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26758 \begin_layout Plain Layout
26759 \begin_inset Formula $\textrm{ȷ}$
26773 \begin_inset space \hfill{}
26779 \begin_layout Standard
26781 \begin_inset Formula $\textrm{Å}$
26785 \begin_inset Formula $\textrm{Ø}$
26788 can also be inserted via the math toolbar button
26791 arg "math-insert \\digamma"
26797 \begin_layout Standard
26801 \begin_inset space \hspace{}
26810 \begin_inset space \hspace{}
26816 are exceptions because they can be inserted in \SpecialChar LyX
26820 \begin_layout Subsection
26822 \begin_inset CommandInset label
26824 name "subsec:Accents-in-Text"
26829 \begin_inset Index idx
26832 \begin_layout Plain Layout
26841 \begin_layout Standard
26842 Any letter can be accented with the following commands.
26843 The commands must be inserted in \SpecialChar TeX
26847 \begin_layout Standard
26848 \begin_inset space \hfill{}
26852 \begin_inset Tabular
26853 <lyxtabular version="3" rows="8" columns="2">
26854 <features booktabs="true" tabularvalignment="middle">
26855 <column alignment="left" valignment="top" width="0pt">
26856 <column alignment="block" valignment="top">
26858 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26861 \begin_layout Plain Layout
26867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26870 \begin_layout Plain Layout
26878 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26881 \begin_layout Plain Layout
26885 \begin_inset Quotes grd
26893 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26896 \begin_layout Plain Layout
26900 \begin_layout Plain Layout
26916 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26919 \begin_layout Plain Layout
26927 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26930 \begin_layout Plain Layout
26934 \begin_layout Plain Layout
26950 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26953 \begin_layout Plain Layout
26957 \begin_inset space \textvisiblespace{}
26965 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26968 \begin_layout Plain Layout
26972 \begin_layout Plain Layout
26988 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26991 \begin_layout Plain Layout
26999 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27002 \begin_layout Plain Layout
27006 \begin_layout Plain Layout
27022 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27025 \begin_layout Plain Layout
27029 \begin_inset space \textvisiblespace{}
27037 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27040 \begin_layout Plain Layout
27044 \begin_layout Plain Layout
27060 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27063 \begin_layout Plain Layout
27067 \begin_inset space \textvisiblespace{}
27075 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27078 \begin_layout Plain Layout
27082 \begin_layout Plain Layout
27098 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
27101 \begin_layout Plain Layout
27105 \begin_inset space \textvisiblespace{}
27113 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27116 \begin_layout Plain Layout
27120 \begin_layout Plain Layout
27140 \begin_inset space \hfill{}
27144 \begin_inset Tabular
27145 <lyxtabular version="3" rows="8" columns="2">
27146 <features booktabs="true" tabularvalignment="middle">
27147 <column alignment="left" valignment="top" width="0pt">
27148 <column alignment="center" valignment="top">
27150 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27153 \begin_layout Plain Layout
27159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27162 \begin_layout Plain Layout
27170 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27173 \begin_layout Plain Layout
27177 \begin_inset space \textvisiblespace{}
27185 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27188 \begin_layout Plain Layout
27192 \begin_layout Plain Layout
27208 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27211 \begin_layout Plain Layout
27219 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27222 \begin_layout Plain Layout
27226 \begin_layout Plain Layout
27242 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27245 \begin_layout Plain Layout
27249 \begin_inset Index idx
27252 \begin_layout Plain Layout
27263 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27266 \begin_layout Plain Layout
27270 \begin_layout Plain Layout
27286 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27289 \begin_layout Plain Layout
27297 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27300 \begin_layout Plain Layout
27304 \begin_layout Plain Layout
27320 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27323 \begin_layout Plain Layout
27327 \begin_inset space \textvisiblespace{}
27335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27338 \begin_layout Plain Layout
27342 \begin_layout Plain Layout
27358 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27361 \begin_layout Plain Layout
27365 \begin_inset space \textvisiblespace{}
27373 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27376 \begin_layout Plain Layout
27380 \begin_layout Plain Layout
27396 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27399 \begin_layout Plain Layout
27403 \begin_inset space \textvisiblespace{}
27411 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27414 \begin_layout Plain Layout
27418 \begin_layout Plain Layout
27438 \begin_inset space \hfill{}
27444 \begin_layout Standard
27445 \begin_inset VSpace medskip
27454 also two different characters can be accented.
27460 \begin_inset space \textvisiblespace{}
27469 \begin_layout Plain Layout
27481 \begin_layout Standard
27494 can in combination with vowels be directly inserted with the keyboard without
27495 using \SpecialChar TeX
27497 The same applies for the tilde
27501 \begin_layout Plain Layout
27502 This only applies for keyboards where the tilde is defined as accent.
27511 in combination with
27526 \begin_layout Standard
27569 and accents that are inserted directly with the keyboard are also available
27570 in mathematical text.
27571 For the other accents there are special math commands used in formulas,
27573 \begin_inset CommandInset ref
27575 reference "subsec:Accents-for-one"
27582 \begin_layout Standard
27583 \begin_inset VSpace bigskip
27593 \begin_inset Index idx
27596 \begin_layout Plain Layout
27604 any number or letter can be set into a circle, quasi accented with a circle,
27605 similar to the copyright symbol.
27608 \begin_layout Standard
27610 \begin_inset Tabular
27611 <lyxtabular version="3" rows="3" columns="2">
27612 <features booktabs="true" tabularvalignment="middle">
27613 <column alignment="center" valignment="top" width="0pt">
27614 <column alignment="center" valignment="top">
27616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27619 \begin_layout Plain Layout
27625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27628 \begin_layout Plain Layout
27636 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27639 \begin_layout Plain Layout
27647 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27650 \begin_layout Plain Layout
27654 \begin_layout Plain Layout
27669 <row topspace="1mm">
27670 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27673 \begin_layout Plain Layout
27684 raisebox{-1.5pt}{W}}
27689 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27692 \begin_layout Plain Layout
27696 \begin_layout Plain Layout
27726 \begin_layout Standard
27727 One has to take care that the character fits into the circle.
27738 \begin_layout Plain Layout
27740 \begin_inset CommandInset ref
27742 reference "subsec:Font-Sizes"
27751 specifies the size of the circle.
27762 \begin_layout Plain Layout
27764 \begin_inset CommandInset ref
27766 reference "subsec:Boxes-without-Frame"
27775 the character can be centered.
27778 \begin_layout Subsection
27780 \begin_inset Index idx
27783 \begin_layout Plain Layout
27792 \begin_layout Standard
27793 Old-style figures (also known as old-style numerals) are created with the
27801 \begin_inset Index idx
27804 \begin_layout Plain Layout
27813 The command can be used in formulas and in \SpecialChar TeX
27815 The command scheme is:
27818 \begin_layout Standard
27823 oldstylenums{number}
27826 \begin_layout Standard
27831 oldstylenums{0123456789}
27834 \begin_inset Formula $\oldstylenums{0123456789}$
27840 \begin_layout Section
27842 \begin_inset CommandInset label
27844 name "sec:Formula-Styles"
27849 \begin_inset Index idx
27852 \begin_layout Plain Layout
27861 \begin_layout Itemize
27862 There are two different alignment styles:
27866 \begin_layout Description
27867 Centered is the predefined standard.
27870 \begin_layout Description
27871 Indented can be set using the menu
27873 Document\SpecialChar menuseparator
27879 \begin_inset space ~
27885 \begin_layout Standard
27890 is used, the indentation can be adjusted.
27891 The default value depends on the document class.
27895 \begin_layout Itemize
27896 Two different numbering styles are available in the menu
27898 Document\SpecialChar menuseparator
27904 \begin_inset space ~
27913 \begin_layout Description
27914 Right is in most cases the default.
27917 \begin_layout Description
27922 \begin_layout Standard
27923 The chosen styles are used for all displayed formulas of the document.
27924 When both, centered and indented formulas should be created in a document,
27930 The indented formulas are then set in a flalign environment, see
27931 \begin_inset CommandInset ref
27933 reference "subsec:Flalign-Environment"
27940 \begin_layout Section
27942 \begin_inset CommandInset label
27944 name "sec:Multiline-Formulas"
27949 \begin_inset Index idx
27952 \begin_layout Plain Layout
27953 Formula ! multiline
27961 \begin_layout Subsection
27965 \begin_layout Standard
27966 In \SpecialChar LyX
27967 , multiline formulas are created by pressing
27970 arg "newline-insert newline"
27974 This creates either an
27978 that is described in
27979 \begin_inset CommandInset ref
27981 reference "subsec:Standard-align-Environment"
27985 or, when automatically loading of the package
27989 is disabled in the document settings, an
27991 eqnarray environment
27993 that is described in
27994 \begin_inset CommandInset ref
27996 reference "subsec:Eqnarray-Environment"
28001 The align environment is recommended as it provides a typographically correct
28002 output in all cases.
28005 \begin_layout Standard
28006 There are other multiline formula environments that can be created via the
28009 Insert\SpecialChar menuseparator
28013 These environments are described in the following sections.
28016 \begin_layout Standard
28017 In all multiline formula environments a new line is created by pressing
28021 arg "newline-insert newline"
28025 To add or delete lines, use the math toolbar buttons
28028 arg "tabular-feature append-row"
28034 arg "tabular-feature delete-row"
28037 respectively, or the menu option
28039 Edit\SpecialChar menuseparator
28045 \begin_layout Subsubsection
28047 \begin_inset CommandInset label
28049 name "subsec:Line-Separation"
28054 \begin_inset Index idx
28057 \begin_layout Plain Layout
28058 Formula ! multiline ! Line separation
28066 \begin_layout Standard
28067 Sometimes there is not enough space in multiline formulas between the lines:
28068 \begin_inset Formula
28070 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}\\
28071 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
28079 \begin_layout Standard
28080 In \SpecialChar LaTeX
28081 additional line space is specified as an optional argument of the new
28083 This is not yet possible in \SpecialChar LyX
28088 \begin_layout Plain Layout
28090 \begin_inset CommandInset href
28092 name "LyX-bug #1505"
28093 target "https://www.lyx.org/trac/ticket/1505"
28103 , therefore the whole formula must be inserted in \SpecialChar TeX
28105 To add in our example space, the command
28113 is inserted at the end of the first line.
28118 \begin_layout Plain Layout
28125 \begin_layout Plain Layout
28127 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28130 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28137 \begin_layout Plain Layout
28141 left(B^{2}+x_{0}^{2}
28149 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28154 \begin_layout Plain Layout
28166 \begin_layout Standard
28167 \begin_inset VSpace bigskip
28170 To set the line separation for all lines in a formula, the length of
28177 \begin_inset Index idx
28180 \begin_layout Plain Layout
28190 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
28201 \begin_inset space \thinspace{}
28206 \begin_inset space \thinspace{}
28209 mm of additional line separation as in the previous example, the command
28212 \begin_layout Standard
28222 \begin_layout Standard
28223 is inserted in \SpecialChar TeX
28224 mode before the formula.
28225 This requires that the \SpecialChar LaTeX
28234 \begin_layout Plain Layout
28239 is part of every \SpecialChar LaTeX
28240 standard installation.
28246 \begin_inset Index idx
28249 \begin_layout Plain Layout
28255 was loaded in \SpecialChar LaTeX
28256 -preamble with the line
28259 \begin_layout Standard
28267 \begin_layout Standard
28272 \begin_layout Plain Layout
28284 \begin_inset Formula
28286 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}\\
28287 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
28295 \begin_layout Standard
28299 \begin_layout Plain Layout
28316 to its original value,
28322 is set to the value 3
28323 \begin_inset space \thinspace{}
28329 \begin_layout Subsubsection
28331 \begin_inset CommandInset label
28333 name "subsec:Column-Separation"
28338 \begin_inset Index idx
28341 \begin_layout Plain Layout
28342 Formula ! multiline ! Column separation
28350 \begin_layout Standard
28351 Multiline formulas form a matrix.
28352 A formula in the eqnarray environment for example is a matrix with three
28354 By changing the column separation in this environment, the space beside
28355 the relation sign can be changed.
28358 \begin_layout Standard
28359 The column separation is specified with the length
28366 \begin_inset Index idx
28369 \begin_layout Plain Layout
28377 according to the formula: column separation = 2
28378 \begin_inset space \thinspace{}
28386 \change_deleted 5863208 1612730022
28390 \begin_inset Note Note
28393 \begin_layout Plain Layout
28395 \change_inserted 232239728 1611406079
28396 How does units play into this? (cm/in/pt) Is the 2 unitless and the result
28397 takes on the units of the input value?
28407 \begin_inset Newline newline
28413 \begin_layout Standard
28423 \begin_layout Standard
28424 inserted in \SpecialChar TeX
28425 mode, sets all following formula column separations to 2
28426 \begin_inset space \thinspace{}
28430 To return to the predefined distance,
28437 \begin_inset space \thinspace{}
28443 \begin_layout Standard
28445 \begin_inset space \thinspace{}
28448 cm column separation:
28452 \begin_layout Plain Layout
28464 \begin_inset Formula
28472 A formula with the predefined column separation for matrices of 10
28473 \begin_inset space \thinspace{}
28480 \begin_layout Plain Layout
28492 \begin_inset Formula
28503 \begin_layout Standard
28504 \begin_inset Newpage newpage
28510 \begin_layout Subsubsection
28512 \begin_inset Index idx
28515 \begin_layout Plain Layout
28524 \begin_layout Standard
28525 Long formulas can be typeset using these methods:
28528 \begin_layout Itemize
28529 If one side of an equation is much shorter than the line width, this is
28530 chosen for the left side and the right side is typeset over two lines:
28531 \begin_inset Formula
28533 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 \\
28534 & & -\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}
28539 The minus sign at the beginning of the second line does normally not appear
28540 as an operator because it is the first character of the line.
28541 Thus it would not be surrounded by space and could not be distinguished
28542 from the fraction bar.
28544 \begin_inset space \thinspace{}
28547 pt space was inserted behind the minus sign with the command
28557 \begin_layout Plain Layout
28565 \begin_inset CommandInset ref
28567 reference "subsec:Variable-Space"
28577 \begin_inset Index idx
28580 \begin_layout Plain Layout
28591 \begin_layout Itemize
28592 When both sides of the equation are long, the command
28599 \begin_inset Index idx
28602 \begin_layout Plain Layout
28611 It is inserted in the first column of the first line and causes all further
28612 insertions to overwrite the following columns:
28613 \begin_inset Formula
28615 \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 \\
28616 & & -\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 \\
28617 & & =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}
28622 After the insertion of
28628 , the cursor is in a purple box that is shifted a bit to the left from the
28630 The formula is inserted there.
28631 \begin_inset Newline newline
28634 The content of additional lines is inserted in the second or another formula
28636 The greater the insertion column number , the larger the indentation.
28637 \begin_inset VSpace medskip
28641 \begin_inset Newline newline
28645 \begin_inset Note Greyedout
28648 \begin_layout Plain Layout
28649 Note the following when using
28658 \begin_layout Itemize
28659 The formula doesn't use the full page width.
28661 \begin_inset space \thinspace{}
28665 \begin_inset space \space{}
28669 \begin_inset Formula $-B^{2}$
28672 is added to the first line in the above example, it would have been outside
28674 To better use the width, negative space can be inserted at the beginning
28678 \begin_layout Itemize
28679 Due to a bug in \SpecialChar LyX
28680 the cursor cannot be set with the mouse in the first line.
28684 \begin_layout Plain Layout
28685 \begin_inset CommandInset href
28687 name "LyX-bug #1429"
28688 target "https://www.lyx.org/trac/ticket/1429"
28698 One can only set the cursor at the beginning of the line and move it with
28707 \begin_layout Itemize
28708 Other methods to set long formulas are offered by the environments described
28710 \begin_inset CommandInset ref
28712 reference "subsec:Multline-Environment"
28717 \begin_inset CommandInset ref
28719 reference "subsec:Multiline-Formula-Parts"
28726 \begin_layout Subsubsection
28727 Multiline Fractions
28728 \begin_inset CommandInset label
28730 name "subsec:Multiline-Fractions"
28735 \begin_inset Index idx
28738 \begin_layout Plain Layout
28739 Fractions ! multiline
28747 \begin_layout Standard
28748 There are cases where the denominator and/or the numerator of a fraction
28749 is so long that the fraction does not fit on one line.
28750 It is then necessary to add a line break within the fraction.
28751 This can be done using the command
28758 \begin_inset Index idx
28761 \begin_layout Plain Layout
28770 To activate it, go to the document settings under
28773 \begin_inset space ~
28783 \begin_inset Index idx
28786 \begin_layout Plain Layout
28787 Packages ! mathtools
28792 and set its option to
28795 \begin_inset space ~
28810 \begin_layout Standard
28815 splitfrac{first line}{second line}
28818 \begin_layout Standard
28819 and is used for either the denominator or numerator:
28822 \begin_layout Standard
28823 \begin_inset Formula
28825 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}
28830 The command for the first numerator above is:
28833 \begin_layout Standard
28838 splitfrac{xy+xy+xy+xy+xy
28839 \begin_inset space \textvisiblespace{}
28847 \begin_layout Subsubsection
28849 \begin_inset CommandInset label
28851 name "subsec:Multiline-Brackets"
28856 \begin_inset Index idx
28859 \begin_layout Plain Layout
28860 Brackets ! for multiline expressions
28868 \begin_layout Standard
28869 For brackets spanning multiple lines the following problem occurs:
28870 \begin_inset Formula
28872 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28873 & & \left.\cdots+B-D\right]
28881 \begin_layout Standard
28882 The closing bracket is smaller than the opening bracket because brackets
28883 with variable size may not span multiple lines.
28886 \begin_layout Standard
28887 To set the bracket size for the second line correctly, the first line is
28895 \begin_inset Index idx
28898 \begin_layout Plain Layout
28906 and the second line with
28914 \begin_layout Plain Layout
28928 \begin_inset CommandInset ref
28930 reference "subsec:Automatic-Bracket-Size"
28942 \begin_inset Index idx
28945 \begin_layout Plain Layout
28968 \begin_inset space \textvisiblespace{}
28978 \begin_inset space \textvisiblespace{}
28988 \begin_inset space \textvisiblespace{}
28994 \begin_inset Formula $\downarrow$
29000 \begin_inset Index idx
29003 \begin_layout Plain Layout
29011 is inserted, because the multiplication operator with its limits is the
29012 largest symbol in the first line and this should be the size for the bracket
29013 in the second line.
29016 \begin_layout Standard
29017 The result is this:
29018 \begin_inset Formula
29020 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29021 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29029 \begin_layout Subsection
29033 \begin_layout Standard
29034 Align environments can be used for every kind of multiline formulas.
29035 They are especially useful to set several formulas side by side.
29038 \begin_layout Standard
29039 Align environments consist of columns.
29040 The odd columns are right aligned, the even ones left aligned.
29041 Every line in an Align environment can be numbered.
29044 \begin_layout Standard
29045 Align environments are created via the menu
29047 Insert\SpecialChar menuseparator
29053 Edit\SpecialChar menuseparator
29054 Math\SpecialChar menuseparator
29055 Change Formula Type
29057 pre-existing formulas can be converted to Align environments.
29060 \begin_layout Standard
29061 To add or delete columns, use the math toolbar buttons
29064 arg "tabular-feature append-column"
29070 arg "tabular-feature delete-column"
29073 respectively, or the menu option
29075 Edit\SpecialChar menuseparator
29081 \begin_layout Subsubsection
29082 Standard Align Environment
29083 \begin_inset CommandInset label
29085 name "subsec:Standard-align-Environment"
29090 \begin_inset Index idx
29093 \begin_layout Plain Layout
29094 Formula ! multiline ! align environment
29102 \begin_layout Standard
29103 This align environment is created by pressing
29106 arg "newline-insert newline"
29109 in a formula or by the menu
29111 Insert\SpecialChar menuseparator
29112 Math\SpecialChar menuseparator
29113 AMS align Environment
29118 \begin_layout Standard
29119 An example for two formulas set side by side, that are created with a four
29120 column align environment:
29121 \begin_inset Formula
29123 A & =\sin(B) & C & =D\\
29124 C & \ne A & B & \ne D
29129 As it can be seen, the formulas in this environment are placed so as if
29138 \begin_layout Plain Layout
29146 \begin_inset CommandInset ref
29148 reference "subsec:Variable-Space"
29159 before the first and after every even column.
29160 When the formula style
29166 \begin_layout Plain Layout
29167 For formula styles see
29168 \begin_inset CommandInset ref
29170 reference "sec:Formula-Styles"
29181 is used, the formula is set without the
29187 before the first column.
29190 \begin_layout Subsubsection
29191 Alignat Environment
29192 \begin_inset Index idx
29195 \begin_layout Plain Layout
29196 Formula ! multiline ! alignat environment
29204 \begin_layout Standard
29205 The alignat environment has no predefined column separation.
29206 It can be inserted manually with the spaces that are described in
29207 \begin_inset CommandInset ref
29209 reference "subsec:Space"
29216 \begin_layout Standard
29217 The above example is shown in the alignat environment where 1
29218 \begin_inset space \thinspace{}
29221 cm space was inserted at the beginning of the second formula:
29222 \begin_inset Formula
29223 \begin{alignat*}{2}
29224 A & =\sin(B) & \hspace{1cm}C & =D\\
29225 C & \ne A & B & \ne D
29230 Because the column separation can be set separately for every column, this
29231 environment is especially suitable to set three or more formulas side by
29235 \begin_layout Subsubsection
29236 Flalign Environment
29237 \begin_inset CommandInset label
29239 name "subsec:Flalign-Environment"
29244 \begin_inset Index idx
29247 \begin_layout Plain Layout
29248 Formula ! multiline ! flalign environment
29256 \begin_layout Standard
29257 In this environment the first column is always set to the left as much as
29258 possible and the last one to the right.
29260 \begin_inset Formula
29262 A & =1 & B & =2 & C & =3\\
29263 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29271 \begin_layout Standard
29272 By creating a flalign environment with an odd number of columns where an
29273 empty \SpecialChar TeX
29274 brace is inserted in the last column, several formulas in a document
29275 can be set to the left, although the formula style
29280 As example the indented formula
29281 \begin_inset CommandInset ref
29283 reference "eq:VolInt"
29288 \begin_inset Formula
29290 \hspace{30pt}\iiint_{V}X\,\mathrm{d}V & =U & {}
29295 The first two columns contain the formula.
29296 To indent it as with the formula style
29301 \begin_inset space \thinspace{}
29304 pt space was inserted at the beginning of the first column.
29307 \begin_layout Subsection
29308 Eqnarray Environment
29309 \begin_inset CommandInset label
29311 name "subsec:Eqnarray-Environment"
29316 \begin_inset Index idx
29319 \begin_layout Plain Layout
29320 Formula ! multiline ! eqnarray environment
29328 \begin_layout Standard
29329 When this environment is created, three blue boxes appear.
29330 The content of the first box is right aligned, the content of the last
29332 The content of the middle box appears centered and a bit smaller because
29333 it is intended for relational characters only.
29334 \begin_inset Formula
29336 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29346 \begin_layout Subsection
29348 \begin_inset Index idx
29351 \begin_layout Plain Layout
29352 Formula ! multiline ! gather environment
29360 \begin_layout Standard
29361 This environment consists of one centered column.
29362 Every line can be numbered.
29363 \begin_inset Formula
29374 \begin_layout Subsection
29375 Multline Environment
29376 \begin_inset CommandInset label
29378 name "subsec:Multline-Environment"
29383 \begin_inset Index idx
29386 \begin_layout Plain Layout
29387 Formula ! multiline ! multline environment
29395 \begin_layout Standard
29396 The multline environment consists, like the gather environment, of one column.
29397 But the first line is left aligned, the last one right aligned.
29398 All other lines are centered.
29399 Therefore this environment is suitable for long formulas.
29400 Using example formula
29401 \begin_inset CommandInset ref
29403 reference "eq:lefteqn"
29407 in the multline environment:
29408 \begin_inset Formula
29410 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}\\
29411 -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}\\
29412 =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}}
29420 \begin_layout Standard
29421 In the output, only the last line of a multline environment appears numbered
29422 when the document numbering is on the right .
29423 If the document numbering is on the left then only the first line will
29428 \begin_layout Plain Layout
29429 For numbering styles see
29430 \begin_inset CommandInset ref
29432 reference "sec:Formula-Styles"
29444 \begin_layout Standard
29452 \begin_inset Index idx
29455 \begin_layout Plain Layout
29470 \begin_inset Index idx
29473 \begin_layout Plain Layout
29481 a centered line can be right or left aligned, respectively.
29482 The commands are used as follows:
29485 \begin_layout Standard
29490 shoveright{line content}
29496 shoveleft{line content}
29499 \begin_layout Standard
29500 \begin_inset VSpace medskip
29510 \begin_inset Index idx
29513 \begin_layout Plain Layout
29521 specifies the distance of the first line from the left page margin.
29522 Predefined is the length 0
29523 \begin_inset space \thinspace{}
29529 \begin_layout Standard
29530 As example the above formula where the command
29533 \begin_layout Standard
29543 \begin_layout Standard
29544 was inserted in \SpecialChar TeX
29549 \begin_layout Plain Layout
29561 \begin_inset Formula
29563 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}\\
29564 \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}}\\
29565 =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}}
29574 \begin_layout Plain Layout
29585 The second line was left aligned using
29594 \begin_layout Subsection
29595 Multiline Formula Parts
29596 \begin_inset CommandInset label
29598 name "subsec:Multiline-Formula-Parts"
29603 \begin_inset Index idx
29606 \begin_layout Plain Layout
29607 Formula ! multiline ! formula parts
29615 \begin_layout Standard
29616 To display only parts of a formula with multiple lines, one of the following
29617 environments is used:
29634 They can be inserted via the menu
29636 Insert\SpecialChar menuseparator
29639 or by using the commands described in this section.
29642 \begin_layout Standard
29643 The first three have the same properties as the corresponding multiline
29644 formula environments, but it is possible to set additional formula parts
29647 \begin_inset Formula
29649 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29650 \Delta E\Delta t & \ge\frac{\hbar}{2}
29652 \right\} \textrm{Uncertainty relations}
29660 \begin_layout Standard
29661 To get this formula, a displayed formula is created where the command
29668 \begin_inset Index idx
29671 \begin_layout Plain Layout
29680 A purple box appears around the blue formula box where now columns and
29681 lines can be added.
29682 Outside the multiline environment other formula parts can be set, like
29686 \begin_layout Standard
29687 The aligned environment is also suitable for long formulas whose lines are
29688 horizontally aligned.
29689 Using aligned in a displayed formula has the advantage that the formula
29690 number is vertically centered behind the lines.
29691 For example here is formula
29692 \begin_inset CommandInset ref
29694 reference "eq:shortlong"
29698 in the aligned environment:
29699 \begin_inset Formula
29701 \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}|}\\
29702 & -\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}|}
29711 \begin_layout Standard
29712 To use the environments
29731 \begin_inset Index idx
29734 \begin_layout Plain Layout
29749 \begin_inset Index idx
29752 \begin_layout Plain Layout
29767 \begin_inset Index idx
29770 \begin_layout Plain Layout
29778 are inserted, respectively.
29779 The split environment has the same properties as the aligned environment
29780 but it can only have two columns.
29783 \begin_layout Subsection
29784 Text in Multiline Formulas
29785 \begin_inset CommandInset label
29787 name "subsec:Text-in-multiline"
29792 \begin_inset Index idx
29795 \begin_layout Plain Layout
29802 \begin_inset Index idx
29805 \begin_layout Plain Layout
29806 Formula ! multiline ! text
29814 \begin_layout Standard
29815 In the align environments as well as the multline and gather environment,
29816 text can be inserted that will appear in a separate line and doesn't affect
29817 the column alignment.
29818 To do this, the command
29825 \begin_inset Index idx
29828 \begin_layout Plain Layout
29836 is used in the following scheme:
29839 \begin_layout Standard
29847 \begin_layout Standard
29848 The text should not be longer than a line because it cannot be hyphenated.
29849 As \SpecialChar LyX
29850 doesn't yet support
29856 directly, the text is written as mathematical text.
29863 must be at the beginning of a line and will appear in the output above
29865 An example where the text was inserted at the beginning of the second line:
29866 \begin_inset Formula
29868 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29869 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29877 \begin_layout Standard
29884 always creates some vertical space between the text and the formula lines.
29885 To avoid this space, in the document settings under
29888 \begin_inset space ~
29898 \begin_inset Index idx
29901 \begin_layout Plain Layout
29902 Packages ! mathtools
29910 \begin_inset space ~
29916 Then you can use the command
29923 \begin_inset Index idx
29926 \begin_layout Plain Layout
29943 \begin_layout Standard
29944 \begin_inset Formula
29946 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29947 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29955 \begin_layout Section
29957 \begin_inset Index idx
29960 \begin_layout Plain Layout
29967 \begin_inset Index idx
29970 \begin_layout Plain Layout
29971 Formula ! numbering|see
29975 \begin_layout Plain Layout
29986 \begin_layout Plain Layout
30001 \begin_layout Subsection
30005 \begin_layout Standard
30006 Numbered formulas can be created with the menu
30008 Insert\SpecialChar menuseparator
30009 Math\SpecialChar menuseparator
30011 \begin_inset space ~
30019 arg "command-sequence math-display; math-number-toggle;"
30023 Existing formulas can be numbered with the menu
30025 Edit\SpecialChar menuseparator
30026 Math\SpecialChar menuseparator
30028 \begin_inset space ~
30032 \begin_inset space ~
30040 arg "math-number-toggle"
30044 The formula number is displayed in \SpecialChar LyX
30045 behind the formula as a number in parenthes
30048 \change_deleted 232239728 1611410645
30049 The number sign is replaced in the output by the formula number.
30050 \change_deleted 5863208 1612727075
30052 \begin_inset Note Note
30055 \begin_layout Plain Layout
30057 \change_inserted 232239728 1611410697
30058 LyX appears to put the actual formula number in the raw file now
30070 \begin_layout Standard
30071 When numbering is turned on in multiline formulas, all formulas will be
30073 But the numbering can be controlled with the menu
30075 Edit\SpecialChar menuseparator
30076 Math\SpecialChar menuseparator
30078 \begin_inset space ~
30082 \begin_inset space ~
30090 arg "math-number-line-toggle"
30093 ) for every formula.
30096 \begin_layout Standard
30097 Except for inline formulas, all formulas can be numbered with two different
30099 \begin_inset CommandInset ref
30101 reference "sec:Formula-Styles"
30108 \begin_layout Subsection
30110 \begin_inset Index idx
30113 \begin_layout Plain Layout
30114 Cross-references ! to formulas
30122 \begin_layout Standard
30123 All labeled formulas can be cross-referenced.
30124 A label is added with the menu
30126 Insert\SpecialChar menuseparator
30129 or the toolbar button
30136 The cursor must be inside a displayed formula.
30137 Alternatively you can right-click on the formula and choose
30142 A dialog pops up displaying the prefix
30147 The label is inserted behind the prefix.
30148 The predefined prefix means
30149 \begin_inset Quotes eld
30153 \begin_inset Quotes erd
30156 and makes it easier to find labels in large documents because it marks
30157 it as a formula label to distinguish it from e.
30158 \begin_inset space \thinspace{}
30162 \begin_inset space \space{}
30166 To change a label, the menu
30168 Insert\SpecialChar menuseparator
30171 is used again or you can right-click on a formula and then on
30178 \begin_layout Standard
30179 The name of the label is displayed in \SpecialChar LyX
30180 within parentheses behind the formula
30182 A formula with a label is always numbered.
30185 \begin_layout Standard
30186 Cross-references are inserted via the menu
30188 Insert\SpecialChar menuseparator
30191 or with the toolbar button
30194 arg "dialog-show-new-inset ref"
30198 A formula cross-reference appears in the output as formula number.
30199 When in the cross-reference dialog window the format
30203 is chosen, the cross-reference appears in the output as formula number
30205 \begin_inset Newline newline
30208 By right-clicking on a cross-reference in \SpecialChar LyX
30209 , one jumps to the formula that
30213 \begin_layout Standard
30214 Here are as examples cross-references to formulas of the following subsections:
30215 \begin_inset Note Note
30218 \begin_layout Plain Layout
30219 Note the different cross-reference types.
30227 \begin_layout Standard
30229 \begin_inset CommandInset ref
30236 \begin_inset CommandInset ref
30244 \begin_inset CommandInset ref
30250 ) big Latin letters are used for the numbering in contrary to (
30251 \begin_inset CommandInset ref
30260 \begin_layout Standard
30261 \begin_inset VSpace medskip
30264 When the argument of
30272 \begin_layout Plain Layout
30280 \begin_inset CommandInset ref
30282 reference "subsec:User-defined-Numbering"
30293 contains a box like in
30294 \begin_inset CommandInset ref
30296 reference "subsec:Paragraph-Boxes"
30300 , the formula cannot be referenced.
30303 \begin_layout Subsection
30305 \begin_inset Index idx
30308 \begin_layout Plain Layout
30309 Formula numbering ! subnumbering
30317 \begin_layout Standard
30318 Formulas can be numbered as subequations.
30319 To activate this feature, add the module
30323 to the document in the menu
30325 Document\SpecialChar menuseparator
30326 Settings\SpecialChar menuseparator
30330 To insert subequations use the menu
30332 Insert\SpecialChar menuseparator
30333 Custom Insets\SpecialChar menuseparator
30339 \begin_layout Standard
30340 The equations to be subnumbered are put into the
30346 \begin_inset Formula
30354 \begin_inset VSpace -5mm
30358 \begin_inset Flex Subequations
30361 \begin_layout Plain Layout
30362 \begin_inset Formula
30370 \begin_inset Formula
30385 \begin_layout Standard
30386 Every formula in the
30390 inset will be subnumbered with a, b, c, \SpecialChar ldots
30392 For multiline formulas every line will be subnumbered.
30395 \begin_layout Standard
30396 Referencing subequations works like normal equations:
30397 \begin_inset CommandInset ref
30404 \begin_inset CommandInset ref
30411 If you want to reference the subequations collectively, insert a label
30412 as first thing in the
30418 \begin_inset CommandInset ref
30420 reference "eq:Here-is-an"
30430 \begin_layout Standard
30431 When inserting subequations, vertical space is added before the equation.
30432 To remove this, insert -5
30433 \begin_inset space \thinspace{}
30436 mm vertical space right before the
30441 If the formula style
30447 \begin_layout Plain Layout
30448 For formula styles see
30449 \begin_inset CommandInset ref
30451 reference "sec:Formula-Styles"
30463 \begin_inset space \thinspace{}
30469 \begin_layout Standard
30470 To get another subnumber instead of small Latin letters, insert this command
30471 as \SpecialChar TeX
30472 code before the equations in the
30479 \begin_layout Standard
30488 theparentequation -
30493 \begin_layout Standard
30500 creates the parent number and
30506 adds a small Roman number as subnumber.
30507 For more information about the customization of the numbering, see
30508 \begin_inset CommandInset ref
30510 reference "subsec:Numbering-with-Roman"
30517 \begin_layout Standard
30518 Here is an example of a multiline formula where the numbering is customized
30519 and turned off for the second line:
30520 \begin_inset Flex Subequations
30523 \begin_layout Plain Layout
30524 \begin_inset CommandInset label
30526 name "eq:Here-is-an"
30534 \begin_layout Plain Layout
30542 theparentequation -
30550 \begin_inset Formula
30552 A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
30553 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30554 & = & B^{2}-2BZ+Z^{2}
30567 \begin_layout Subsection
30568 Numbering with Roman Numbers and Letters
30569 \begin_inset CommandInset label
30571 name "subsec:Numbering-with-Roman"
30576 \begin_inset Index idx
30579 \begin_layout Plain Layout
30580 Formula numbering ! with letters
30586 \begin_inset Index idx
30589 \begin_layout Plain Layout
30590 Formula numbering ! with Roman numbers
30598 \begin_layout Standard
30599 Formulas can also be numbered with Roman numbers and Latin letters.
30600 To number with small Roman numbers, the command
30603 \begin_layout Standard
30615 \begin_layout Standard
30616 is inserted before the formula in \SpecialChar TeX
30625 \begin_inset Index idx
30628 \begin_layout Plain Layout
30636 redefines the predefined command
30652 \begin_layout Plain Layout
30659 has the same scheme as the command
30666 \begin_inset CommandInset ref
30668 reference "subsec:The-Command-newcommand"
30681 is the formula counter.
30688 is used as prefix for a counter, the value of the counter is output as
30690 When a formula is numbered, \SpecialChar LaTeX
30691 sets internally the command
30697 behind the formula.
30703 \begin_inset Index idx
30706 \begin_layout Plain Layout
30716 outputs the counter as small Roman number.
30719 \begin_layout Standard
30720 All formulas behind the command
30730 are now numbered Roman.
30731 To switch to numbering with big Roman numbers, the command is inserted
30745 \begin_inset Index idx
30748 \begin_layout Plain Layout
30760 \begin_inset Quotes eld
30764 \begin_inset Quotes erd
30767 with small Latin letters there is the command
30774 \begin_inset Index idx
30777 \begin_layout Plain Layout
30785 , for big ones there is the command
30792 \begin_inset Index idx
30795 \begin_layout Plain Layout
30808 \begin_layout Standard
30809 \begin_inset Note Greyedout
30812 \begin_layout Plain Layout
30817 Only a maximum of 26
30818 \begin_inset space ~
30821 formulas can be numbered with Latin letters in one document.
30829 \begin_layout Standard
30833 \begin_layout Plain Layout
30849 \begin_layout Standard
30850 \begin_inset Formula
30852 A=\textrm{small roman}
30861 \begin_layout Plain Layout
30875 \begin_inset Formula
30877 B=\textrm{big Roman}\label{eq:Rom}
30886 \begin_layout Plain Layout
30900 \begin_inset Formula
30902 C=\textrm{small Latin}
30911 \begin_layout Plain Layout
30925 \begin_inset Formula
30927 D=\textrm{big Latin}\label{eq:Lat}
30935 \begin_layout Standard
30936 To switch back to the default numbering, insert the command:
30939 \begin_layout Standard
30949 \begin_inset Index idx
30952 \begin_layout Plain Layout
30963 \begin_layout Standard
30967 \begin_layout Plain Layout
30981 \begin_inset Formula
30991 \begin_layout Standard
30992 \begin_inset VSpace medskip
30995 As you see, formulas are numbered serially independent from the numbering
30997 When then numbering should start with
30998 \begin_inset Quotes eld
31002 \begin_inset Quotes erd
31005 when the style is changed, new equation counters have to be defined.
31006 A description of this can be found in the file
31007 \begin_inset CommandInset href
31009 name "Formula-numbering.lyx"
31010 target "run:Formula-numbering.lyx"
31018 \begin_layout Subsection
31019 User-defined Numbering
31020 \begin_inset CommandInset label
31022 name "subsec:User-defined-Numbering"
31027 \begin_inset Index idx
31030 \begin_layout Plain Layout
31031 Formula numbering ! user-defined
31039 \begin_layout Standard
31040 \begin_inset Note Greyedout
31043 \begin_layout Plain Layout
31048 If the document language is a right-to-left language such as Arabic, you
31049 must add this to the to the \SpecialChar LaTeX
31050 -preamble to be able to use the commands described
31052 \begin_inset Newline newline
31060 \begin_inset Newline newline
31064 \begin_inset Phantom HPhantom
31067 \begin_layout Plain Layout
31070 \begin_inset space ~
31096 \begin_layout Standard
31097 \begin_inset Index idx
31100 \begin_layout Plain Layout
31101 Formula numbering ! self-defined delimiters
31106 With standard numbering, parentheses are set around a formula number.
31107 To replace the parentheses for example with vertical bars, the following
31108 line is added to the \SpecialChar LaTeX
31112 \begin_layout Standard
31118 \begin_inset Newline newline
31122 \begin_inset Phantom HPhantom
31125 \begin_layout Plain Layout
31128 \begin_inset space ~
31142 maketag@@@{|#1|}} }
31145 \begin_inset Note Note
31148 \begin_layout Plain Layout
31149 This macro is already declared in the \SpecialChar LaTeX
31150 -preamble for testing.
31151 To activate it, remove the percent signs at the beginning.
31159 \begin_layout Standard
31160 To use other characters, the vertical bars besides the
31164 are replaced by one or more characters.
31165 To display only the formula number the vertical bars are omitted.
31168 \begin_layout Standard
31169 \begin_inset VSpace bigskip
31172 When there should be an expression of your choice instead of the consecutive
31173 formula number in parentheses behind the formula, the command
31180 \begin_inset Index idx
31183 \begin_layout Plain Layout
31192 \begin_inset Formula
31194 A+B=C\tag{something}\label{eq:tag}
31199 In this example the command
31204 \begin_inset space \textvisiblespace{}
31209 was inserted in the formula.
31212 \begin_layout Standard
31218 \begin_inset space \textvisiblespace{}
31223 is inserted instead, the parentheses are removed:
31224 \begin_inset Formula
31226 A+B=C\tag*{something}
31234 \begin_layout Standard
31235 \begin_inset VSpace bigskip
31238 To restart the formula numbering with new document parts or sections, the
31239 following command is used:
31242 \begin_layout Standard
31247 @addtoreset{equation}{part}
31250 \begin_inset Index idx
31253 \begin_layout Plain Layout
31258 \begin_layout Plain Layout
31269 \begin_layout Plain Layout
31282 \begin_layout Plain Layout
31293 \begin_layout Plain Layout
31306 \begin_inset Newline newline
31310 \begin_inset Newline newline
31317 @addtoreset{equation}{section}
31320 \begin_layout Standard
31321 To be able to use these commands in \SpecialChar TeX
31323 \begin_inset Quotes eld
31327 \begin_inset Quotes erd
31330 character has to be made
31331 \begin_inset Quotes eld
31335 \begin_inset Quotes erd
31338 for \SpecialChar LaTeX
31353 So the command sequence in \SpecialChar TeX
31357 \begin_layout Standard
31363 \begin_inset Newline newline
31368 @addtoreset{equation}{section}
31369 \begin_inset Newline newline
31377 \begin_layout Standard
31378 In the \SpecialChar LaTeX
31391 can be omitted as they are automatically internally inserted by \SpecialChar LyX
31395 \begin_layout Standard
31410 \begin_layout Plain Layout
31415 is part of the \SpecialChar LaTeX
31421 \begin_inset Index idx
31424 \begin_layout Plain Layout
31425 Packages ! carlisle
31430 that is part of every \SpecialChar LaTeX
31431 standard installation.
31437 \begin_inset Index idx
31440 \begin_layout Plain Layout
31441 Packages ! remreset
31446 has to be loaded in the \SpecialChar LaTeX
31447 -preamble with the line
31450 \begin_layout Standard
31455 usepackage{remreset}
31458 \begin_layout Standard
31466 \begin_inset Index idx
31469 \begin_layout Plain Layout
31474 \begin_layout Plain Layout
31485 \begin_layout Plain Layout
31498 \begin_layout Plain Layout
31509 \begin_layout Plain Layout
31521 can be used with the same scheme as
31530 \begin_layout Standard
31531 \begin_inset VSpace bigskip
31534 Sometimes formulas should be numbered in the following form:
31537 \begin_layout Standard
31540 (section number.formula number)
31543 \begin_layout Standard
31544 The formula number should start with every section with
31545 \begin_inset Quotes eld
31549 \begin_inset Quotes erd
31555 \begin_layout Standard
31556 For this case there is the command
31563 \begin_inset Index idx
31566 \begin_layout Plain Layout
31574 , which is used with the following scheme:
31577 \begin_layout Standard
31582 numberwithin{counter}{sectioning}
31585 \begin_layout Standard
31586 Counter denotes what kind of numbering is affected, sectioning denotes what
31587 the number before the dot is.
31590 \begin_layout Standard
31591 Thus in our case the following \SpecialChar LaTeX
31592 preamble or \SpecialChar TeX
31596 \begin_layout Standard
31601 numberwithin{equation}{section}
31604 \begin_layout Standard
31605 This is the result:
31609 \begin_layout Plain Layout
31613 numberwithin{equation}{section}
31619 \begin_inset Formula
31629 \begin_layout Standard
31631 \begin_inset space \thinspace{}
31635 \begin_inset space \space{}
31638 tables so that the number of the part is the sectioning,
31639 \begin_inset Newline newline
31646 numberwithin{table}{part}
31651 \begin_layout Standard
31652 To go back to the standard numbering or to prevent this kind of numbering
31653 when it is defined by the document class, the following command is inserted
31654 as \SpecialChar TeX
31655 code or to the \SpecialChar LaTeX
31659 \begin_layout Standard
31669 \begin_inset Index idx
31672 \begin_layout Plain Layout
31686 \begin_layout Plain Layout
31702 \begin_inset Newline newline
31710 \begin_inset Newline newline
31722 \begin_layout Standard
31729 internally uses the command
31735 , described above, and would also need to be reverted.
31739 \begin_layout Plain Layout
31746 \begin_layout Plain Layout
31750 @removefromreset{equation}{section}
31753 \begin_layout Plain Layout
31765 \begin_layout Section
31766 Chemical Symbols and Equations
31767 \begin_inset CommandInset label
31769 name "subsec:Chemical-Symbols-and"
31774 \begin_inset Index idx
31777 \begin_layout Plain Layout
31778 Chemical characters ! Symbols
31784 \begin_inset Index idx
31787 \begin_layout Plain Layout
31794 \begin_inset Index idx
31797 \begin_layout Plain Layout
31806 \begin_layout Standard
31807 An example text from chemistry:
31810 \begin_layout Quote
31812 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31815 -ion reacts with two
31816 \begin_inset Formula $\mathrm{Na^{+}}$
31819 -ions to sodium sulfate
31820 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31824 The chemical equation for this is:
31825 \begin_inset Formula
31827 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31835 \begin_layout Standard
31836 Chemical equations can be created as formulas.
31837 To avoid the symbols appearing in italic, everything is highlighted and
31838 changed by the shortcut
31844 to the upright font style.
31848 \begin_layout Plain Layout
31854 \begin_inset CommandInset ref
31856 reference "subsec:Font-Styles"
31868 \begin_layout Standard
31869 A more convenient way to typeset chemical formulas is to use the command
31877 \begin_inset Index idx
31880 \begin_layout Plain Layout
31888 which is available when the \SpecialChar LaTeX
31894 \begin_inset Index idx
31897 \begin_layout Plain Layout
31910 in a formula a new blue box appears where chemical formulas can be inserted
31911 in an intuitive way.
31914 \begin_layout Standard
31916 \begin_inset Tabular
31917 <lyxtabular version="3" rows="10" columns="2">
31918 <features booktabs="true" tabularvalignment="middle">
31919 <column alignment="center" valignment="top" width="0pt">
31920 <column alignment="center" valignment="top">
31922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31925 \begin_layout Plain Layout
31931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31934 \begin_layout Plain Layout
31942 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31945 \begin_layout Plain Layout
31949 \begin_inset space \textvisiblespace{}
31957 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31960 \begin_layout Plain Layout
31961 \begin_inset Formula $\ce{H2CO3}$
31970 <row topspace="1.5mm">
31971 <cell alignment="center" valignment="top" usebox="none">
31974 \begin_layout Plain Layout
31978 \begin_inset space \textvisiblespace{}
31986 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31989 \begin_layout Plain Layout
31990 \begin_inset Formula $\ce{SO4^{2-}}$
31999 <row topspace="1.5mm">
32000 <cell alignment="center" valignment="top" usebox="none">
32003 \begin_layout Plain Layout
32007 \begin_inset space \textvisiblespace{}
32015 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32018 \begin_layout Plain Layout
32019 \begin_inset Formula $\ce{(NH4)2S}$
32028 <row topspace="1.5mm">
32029 <cell alignment="center" valignment="top" usebox="none">
32032 \begin_layout Plain Layout
32036 \begin_inset space \textvisiblespace{}
32044 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32047 \begin_layout Plain Layout
32048 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
32057 <row topspace="1.5mm">
32058 <cell alignment="center" valignment="top" usebox="none">
32061 \begin_layout Plain Layout
32065 \begin_inset space \textvisiblespace{}
32071 \begin_inset space \textvisiblespace{}
32077 \begin_inset space \textvisiblespace{}
32085 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32088 \begin_layout Plain Layout
32089 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
32098 <row topspace="1.5mm">
32099 <cell alignment="center" valignment="top" usebox="none">
32102 \begin_layout Plain Layout
32106 \begin_inset space \textvisiblespace{}
32110 \begin_inset Formula $\downarrow$
32114 \begin_inset Formula $\to$
32122 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32125 \begin_layout Plain Layout
32126 \begin_inset Formula $\ce{_{90}^{227}Th+}$
32136 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32139 \begin_layout Plain Layout
32143 \begin_inset space \textvisiblespace{}
32149 \begin_inset space \textvisiblespace{}
32155 \begin_inset space \textvisiblespace{}
32163 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32166 \begin_layout Plain Layout
32167 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
32177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32180 \begin_layout Plain Layout
32184 \begin_inset space \textvisiblespace{}
32188 \begin_inset space \textvisiblespace{}
32192 \begin_inset space \textvisiblespace{}
32196 \begin_inset space \textvisiblespace{}
32200 \begin_inset space \textvisiblespace{}
32208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32211 \begin_layout Plain Layout
32212 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
32221 <row topspace="1.5mm">
32222 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
32225 \begin_layout Plain Layout
32229 \begin_inset space \textvisiblespace{}
32233 \begin_inset space \textvisiblespace{}
32237 \begin_inset space \textvisiblespace{}
32241 \begin_inset space \textvisiblespace{}
32249 \begin_inset space \textvisiblespace{}
32257 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
32260 \begin_layout Plain Layout
32261 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
32277 \begin_layout Standard
32278 \begin_inset Note Greyedout
32281 \begin_layout Plain Layout
32286 It is not possible in \SpecialChar LyX
32287 to use the character ^ to get an up-arrow as described
32293 One instead uses a negative thin space followed by the command
32300 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32311 \begin_layout Standard
32318 the command for equation
32319 \begin_inset space ~
32323 \begin_inset CommandInset ref
32325 reference "eq:chem-reaction"
32330 \begin_inset Newline newline
32338 \begin_inset space \textvisiblespace{}
32342 \begin_inset space \textvisiblespace{}
32346 \begin_inset space \textvisiblespace{}
32350 \begin_inset space \textvisiblespace{}
32354 \begin_inset space \textvisiblespace{}
32358 \begin_inset space \textvisiblespace{}
32364 \begin_layout Standard
32365 To create multiline chemical equations first a multiline formula is created
32367 \begin_inset CommandInset ref
32369 reference "sec:Multiline-Formulas"
32374 Afterwards the command
32380 is used in every small blue box of the formula.
32382 \begin_inset CommandInset ref
32384 reference "eq:TEOS-reaction-1"
32389 \begin_inset CommandInset ref
32391 reference "eq:TEOS-reaction-2"
32395 are an example of a multi-stage chemical reaction where every equation
32396 has its own number.
32397 \begin_inset Formula
32399 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32400 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32408 \begin_layout Standard
32419 package provides the command
32426 \begin_inset Index idx
32429 \begin_layout Plain Layout
32437 that is used for special cases.
32438 For more information about
32444 and more examples have a look at the documentation of
32449 \begin_inset CommandInset citation
32459 \begin_layout Section
32463 \begin_layout Standard
32465 supports two types of commutative diagrams:
32473 and are explained below.
32476 \begin_layout Subsection
32478 \begin_inset Index idx
32481 \begin_layout Plain Layout
32490 \begin_layout Standard
32491 Diagrams of this type visualize relations by vertical and horizontal lines
32493 \begin_inset Formula
32495 \begin{CD}A@>>>B@>>>C\\
32506 \begin_layout Standard
32507 To create them, the command
32512 \begin_inset Index idx
32515 \begin_layout Plain Layout
32525 is inserted to a formula.
32526 A blue box appears with two dashed lines where additional commands can
32531 arg "newline-insert newline"
32534 a new line is created.
32535 Horizontal relations are inserted in odd formula lines, vertical in even
32539 \begin_layout Standard
32540 To create the relations use the following commands:
32543 \begin_layout Itemize
32548 creates a left arrow,
32559 \begin_layout Itemize
32564 creates an up arrow,
32572 a vertical equal sign
32575 \begin_layout Itemize
32581 is a placeholder for non-existent relations
32584 \begin_layout Standard
32585 All arrows can be labeled as follows:
32588 \begin_layout Itemize
32589 If text inserted between the first and second < or >, resp., it is placed
32591 When it is inserted between the second and third one, it appears under
32595 \begin_layout Itemize
32596 When text for vertical arrows is inserted between the first and second A
32597 or V, resp., it is placed left beside the arrow.
32598 When it is inserted between the second and third one, it appears right
32600 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32604 \begin_layout Standard
32605 As example a diagram with all possible relations:
32608 \begin_layout Standard
32609 \begin_inset Formula
32611 \begin{CD}A@>j>>B@>>k>C@=F\\
32622 \begin_layout Standard
32623 The command for this is:
32624 \begin_inset Newline newline
32632 \begin_inset space \textvisiblespace{}
32635 A@>j>>B@>>k>C@=F Ctrl+Return
32636 \begin_inset Newline newline
32640 \begin_inset Phantom HPhantom
32643 \begin_layout Plain Layout
32649 \begin_inset space \textvisiblespace{}
32662 \begin_inset Formula $\to$
32668 \begin_inset Newline newline
32672 \begin_inset Phantom HPhantom
32675 \begin_layout Plain Layout
32681 \begin_inset space \textvisiblespace{}
32692 \begin_layout Subsection
32694 \begin_inset Index idx
32697 \begin_layout Plain Layout
32698 Diagrams ! xymatrix
32706 \begin_layout Standard
32707 To be able to use xymatrices, the \SpecialChar LaTeX
32713 A xymatrix is created by inserting the command
32720 Then you are able to add new matrix columns and rows like for normal matrices,
32722 \begin_inset CommandInset ref
32724 reference "sec:Matrices"
32731 \begin_layout Standard
32732 Contrary to amscd diagrams, xymatrices support diagonal and curved arrows,
32734 The commands used to create commutative diagrams and decorations are explained
32741 Help\SpecialChar menuseparator
32743 \begin_inset space ~
32751 \begin_layout Subsection
32757 \begin_inset Index idx
32760 \begin_layout Plain Layout
32769 \begin_layout Standard
32774 -diagrams, the \SpecialChar LaTeX
32784 -diagram is created by inserting the command
32791 Then you will be able to add new matrix columns and rows like for normal
32793 \begin_inset CommandInset ref
32795 reference "sec:Matrices"
32802 \begin_layout Standard
32803 Examples of how to create
32807 diagrams in \SpecialChar LyX
32812 manual that you find in the menu
32814 Help\SpecialChar menuseparator
32816 \begin_inset space ~
32824 \begin_layout Section
32825 User-defined Commands
32826 \begin_inset Index idx
32829 \begin_layout Plain Layout
32830 User-defined commands
32838 \begin_layout Standard
32839 \begin_inset Note Greyedout
32842 \begin_layout Plain Layout
32847 The names of user-defined commands and macros may only consist of Latin
32856 \begin_layout Subsection
32860 \begin_inset CommandInset label
32862 name "subsec:The-Command-newcommand"
32867 \begin_inset Index idx
32870 \begin_layout Plain Layout
32871 User-defined commands !
32879 \begin_inset Index idx
32882 \begin_layout Plain Layout
32893 \begin_layout Standard
32894 Many \SpecialChar LaTeX
32895 -commands are too long to be used frequently.
32896 But it is possible to define with the command
32902 new shorter commands.
32905 \begin_layout Standard
32906 The command scheme of
32915 \begin_layout Standard
32920 newcommand{new command name}[number of arguments][optional
32925 \begin_inset Newline newline
32929 \begin_inset Phantom HPhantom
32932 \begin_layout Plain Layout
32942 {command definition}
32945 \begin_layout Standard
32946 \begin_inset Note Greyedout
32949 \begin_layout Plain Layout
32954 Verify that the name of the new command is not already used in your document
32955 or by the \SpecialChar LaTeX
32956 -packages that you use.
32957 If you for example define the command
32969 , you will get an error message because
32975 is already defined as command for
32976 \begin_inset Quotes eld
32980 \begin_inset Formula $\le$
32984 \begin_inset Quotes erd
32995 \begin_layout Standard
32996 The number of arguments is an integer in the range 0
32997 \begin_inset space \thinspace{}
33001 \begin_inset space \thinspace{}
33004 9 and specifies how many arguments the new command should have.
33005 With the optional value a value for an optional argument can be predefined.
33006 When this is done, the
33014 rgument of the new command is automatically an optional one.
33017 \begin_layout Standard
33018 Here are some examples:
33021 \begin_layout Itemize
33022 To define the command
33034 , the \SpecialChar LaTeX
33036 \begin_inset VSpace medskip
33040 \begin_inset Newline newline
33054 \begin_layout Itemize
33055 To define the command
33067 , the argument (that should be underlined) must be taken into account.
33068 For this the preamble line is:
33069 \begin_inset VSpace medskip
33073 \begin_inset Newline newline
33087 \begin_inset VSpace medskip
33091 \begin_inset Newline newline
33098 acts as argument placeholder, the
33102 behind it denotes that it is the placeholder for the first argument.
33105 \begin_layout Itemize
33113 \begin_inset space \thinspace{}
33117 \begin_inset space \space{}
33127 \begin_inset VSpace medskip
33131 \begin_inset Newline newline
33142 framebox#1#2{$#3$}}
33145 \begin_inset VSpace medskip
33149 \begin_inset Newline newline
33152 The two Dollar signs creates the extra formula needed for
33159 \begin_inset CommandInset ref
33161 reference "subsec:Boxes-with-Frame"
33168 \begin_layout Itemize
33169 To create a new command for
33175 where the color for the box need not be specified, the argument for the
33176 color is defined optional:
33177 \begin_inset VSpace medskip
33181 \begin_inset Newline newline
33192 fcolorbox{#2}{#1}{$#3$}}
33195 \begin_inset VSpace medskip
33199 \begin_inset Newline newline
33202 When the color is not specified when using
33208 , the predefined color
33215 \begin_layout Standard
33216 A test of the new defined commands:
33219 \begin_layout Standard
33221 \begin_inset Tabular
33222 <lyxtabular version="3" rows="6" columns="2">
33223 <features booktabs="true" tabularvalignment="middle">
33224 <column alignment="center" valignment="top" width="0pt">
33225 <column alignment="center" valignment="top">
33227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33230 \begin_layout Plain Layout
33236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33239 \begin_layout Plain Layout
33247 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33250 \begin_layout Plain Layout
33254 \begin_inset space \textvisiblespace{}
33262 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33265 \begin_layout Plain Layout
33266 \begin_inset Formula $A\gr B$
33276 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33279 \begin_layout Plain Layout
33287 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33290 \begin_layout Plain Layout
33291 \begin_inset Formula $\us{ABcd}$
33300 <row topspace="1mm">
33301 <cell alignment="center" valignment="top" usebox="none">
33304 \begin_layout Plain Layout
33308 \begin_inset Formula $\to$
33314 \begin_inset Formula $\to$
33322 \begin_inset space \textvisiblespace{}
33330 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33333 \begin_layout Plain Layout
33334 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33343 <row topspace="1.5mm">
33344 <cell alignment="center" valignment="top" usebox="none">
33347 \begin_layout Plain Layout
33351 \begin_inset Formula $\to$
33359 \begin_inset space \textvisiblespace{}
33367 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33370 \begin_layout Plain Layout
33371 \begin_inset Formula $\cb{red}{\int A=B}$
33380 <row topspace="1.5mm" bottomspace="1mm">
33381 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33384 \begin_layout Plain Layout
33390 \begin_inset Formula $\to$
33398 \begin_inset space \textvisiblespace{}
33406 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33409 \begin_layout Plain Layout
33410 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33426 \begin_layout Subsection
33428 \begin_inset Index idx
33431 \begin_layout Plain Layout
33432 User-defined commands! Math macros
33438 \begin_inset Index idx
33441 \begin_layout Plain Layout
33450 \begin_layout Standard
33451 User-defined commands are especially convenient for complex expressions.
33452 For example if you are dealing with a document that has quadratic equations,
33453 the same solution type occurs several times.
33454 The general form of a quadratic equation is
33455 \begin_inset Formula
33457 0=\lambda^{2}+p\lambda+q
33462 The general form of the solution is
33463 \begin_inset Formula
33465 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33473 \begin_layout Standard
33474 To define a command for the solution formula where only the three parameters
33476 \begin_inset Formula $\lambda$
33480 \begin_inset Formula $p$
33484 \begin_inset Formula $q$
33487 need to be specified and the index of
33488 \begin_inset Formula $\lambda$
33491 can be given optionally, the \SpecialChar LaTeX
33493 \begin_inset Newline newline
33509 \begin_inset Newline newline
33513 \begin_inset Phantom HPhantom
33516 \begin_layout Plain Layout
33530 frac{#3^{2}}{4}-#4}}
33533 \begin_layout Standard
33534 To create with this the solution formula, the command
33535 \begin_inset Newline newline
33545 \begin_inset Formula $\to$
33551 \begin_inset Formula $\to$
33558 is inserted to a formula
33563 \begin_layout Standard
33564 The definition of the new command is unintuitive because one has to know
33565 the schemes of all used \SpecialChar LaTeX
33567 \begin_inset space \thinspace{}
33571 \begin_inset space \space{}
33574 that a fraction is inserted in \SpecialChar LaTeX
33579 frac{numerator}{denominator}
33582 Furthermore one can easily forget a brace in the definition and cannot
33583 see in \SpecialChar LyX
33584 what the new command is doing.
33585 To avoid these problems \SpecialChar LyX
33586 offers the possibility to use math macros instead
33596 \begin_layout Standard
33597 A math macro is created by using the menu
33599 Insert\SpecialChar menuseparator
33600 Math\SpecialChar menuseparator
33603 or the toolbar button
33606 arg "math-macro newmacroname_newcommand"
33610 The math macro toolbar appears together with the following box where the
33612 \begin_inset Newline newline
33616 \begin_inset space \hspace*{\fill}
33620 \begin_inset Graphics
33621 filename clipart/macrobox.png
33627 \begin_inset space \hspace*{\fill}
33631 \begin_inset Newline newline
33635 \begin_inset FormulaMacro
33636 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33641 newmacroname is the default name of the macro that should be changed to
33642 something sensible.
33643 The wanted formula is inserted in the first blue box.
33644 An argument placeholder is inserted with the command
33651 \begin_inset space \thinspace{}
33655 \begin_inset space \space{}
33664 or by using the macro toolbar button
33667 arg "math-macro-add-param"
33671 Argument placeholders are displayed red.
33673 \begin_inset space ~
33676 arguments are possible.
33677 Optional arguments are created with the toolbar button
33680 arg "math-macro-add-optional-param"
33684 The first non-optional argument can be transformed to an optional one with
33688 arg "math-macro-make-optional"
33692 In the second blue box the appearance of the macro in \SpecialChar LyX
33694 Normally you want to see it as it is defined, so the box is kept empty.
33695 But when you have created a macro that needs lot of space on the screen,
33696 you can insert in the box for example
33697 \begin_inset Newline newline
33727 \begin_inset Newline newline
33732 For the macro only the arguments with the macro name in front of them will
33733 then be displayed in \SpecialChar LyX
33734 , leading to a better overview.
33735 The formula appears in the output as defined in the first box.
33736 \begin_inset Newline newline
33739 The appearance of macros in formulas can furthermore be changed for single
33740 macros by setting the cursor in the macro and using the menu
33742 View\SpecialChar menuseparator
33744 \begin_inset space ~
33748 \begin_inset space ~
33756 \begin_layout Standard
33757 To use a macro, the macro name is inserted as command to a formula, in our
33765 Our macro looks in \SpecialChar LyX
33767 \begin_inset Newline newline
33771 \begin_inset space \hspace*{\fill}
33775 \begin_inset Graphics
33776 filename clipart/macrouse.png
33782 \begin_inset space \hspace*{\fill}
33786 \begin_inset Newline newline
33789 Here is our macro example with the arguments
33790 \begin_inset Formula $x$
33794 \begin_inset Formula $\ln(x)$
33798 \begin_inset Formula $B$
33804 \begin_layout Standard
33805 \begin_inset Formula
33815 \begin_layout Standard
33819 Tools\SpecialChar menuseparator
33820 Preferences\SpecialChar menuseparator
33821 Editing\SpecialChar menuseparator
33824 different styles to edit macros.
33825 To find the style that suits you best, choose a style and set the cursor
33826 in a macro formula to see the difference.
33829 \begin_layout Standard
33830 A math macro is transformed internally to a
33836 command when exporting the document.
33843 command is not placed in the \SpecialChar LaTeX
33844 -preamble, therefore macros can only be used
33845 in formulas that are in the document below the macro definition box.
33848 \begin_layout Standard
33849 Math macros can also be directly created from a
33856 When writing for example the command
33859 \begin_inset Newline newline
33868 xleftarrow[#2]{#1}}
33869 \begin_inset Newline newline
33874 in \SpecialChar LyX
33875 as normal text, highlighting it completely and using the shortcut
33879 , the command will be transformed to a math macro.
33880 Using this method you need to be careful that the
33886 command is typed correctly, otherwise you get a faulty macro leading to
33891 \begin_layout Standard
33892 Math macros currently have the problem that further formulas in macro definition
33893 s are handled wrong.
33894 Therefore the example
33901 \begin_inset CommandInset ref
33903 reference "subsec:The-Command-newcommand"
33907 cannot be created as macro.
33910 \begin_layout Standard
33911 When the cursor is in a macro definition box, you will see the macro toolbar
33912 in \SpecialChar LyX
33916 \begin_layout Standard
33917 \begin_inset VSpace defskip
33923 \begin_layout Standard
33924 \begin_inset Graphics
33925 filename clipart/MacroToolbar.png
33930 \begin_inset Index idx
33933 \begin_layout Plain Layout
33942 \begin_layout Standard
33943 \begin_inset VSpace defskip
33949 \begin_layout Standard
33950 The macro toolbar contains from left to right the following buttons:
33953 \begin_layout Standard
33954 \begin_inset VSpace defskip
33960 \begin_layout Standard
33961 \begin_inset Tabular
33962 <lyxtabular version="3" rows="9" columns="2">
33963 <features islongtable="true" longtabularalignment="center">
33964 <column alignment="left" valignment="top">
33965 <column alignment="left" valignment="top" width="85col%">
33966 <row interlinespace="2.5mm">
33967 <cell alignment="center" valignment="top" usebox="none">
33970 \begin_layout Plain Layout
33973 arg "math-macro-remove-param"
33981 <cell alignment="center" valignment="top" usebox="none">
33984 \begin_layout Plain Layout
33987 Edit\SpecialChar menuseparator
33988 Math\SpecialChar menuseparator
33990 \begin_inset space ~
33993 Definition\SpecialChar menuseparator
33994 Remove Last Argument
34000 <row interlinespace="2.5mm">
34001 <cell alignment="center" valignment="top" usebox="none">
34004 \begin_layout Plain Layout
34007 arg "math-macro-add-param"
34015 <cell alignment="center" valignment="top" usebox="none">
34018 \begin_layout Plain Layout
34021 Edit\SpecialChar menuseparator
34022 Math\SpecialChar menuseparator
34024 \begin_inset space ~
34027 Definition\SpecialChar menuseparator
34034 <row interlinespace="2.5mm">
34035 <cell alignment="center" valignment="top" usebox="none">
34038 \begin_layout Plain Layout
34041 arg "math-macro-make-optional"
34049 <cell alignment="center" valignment="top" usebox="none">
34052 \begin_layout Plain Layout
34055 Edit\SpecialChar menuseparator
34056 Math\SpecialChar menuseparator
34058 \begin_inset space ~
34061 Definition\SpecialChar menuseparator
34062 Transform First Non-Optional to
34063 \begin_inset Newline newline
34067 \begin_inset Phantom HPhantom
34070 \begin_layout Plain Layout
34073 Edit\SpecialChar menuseparator
34074 Math\SpecialChar menuseparator
34076 \begin_inset space ~
34079 Definition\SpecialChar menuseparator
34091 <row interlinespace="2.5mm">
34092 <cell alignment="center" valignment="top" usebox="none">
34095 \begin_layout Plain Layout
34098 arg "math-macro-make-nonoptional"
34106 <cell alignment="center" valignment="top" usebox="none">
34109 \begin_layout Plain Layout
34112 Edit\SpecialChar menuseparator
34113 Math\SpecialChar menuseparator
34115 \begin_inset space ~
34118 Definition\SpecialChar menuseparator
34119 Transform Last Optional to
34120 \begin_inset Newline newline
34124 \begin_inset Phantom HPhantom
34127 \begin_layout Plain Layout
34130 Edit\SpecialChar menuseparator
34131 Math\SpecialChar menuseparator
34133 \begin_inset space ~
34136 Definition\SpecialChar menuseparator
34142 Non-Optional Argument
34148 <row interlinespace="2.5mm">
34149 <cell alignment="center" valignment="top" usebox="none">
34152 \begin_layout Plain Layout
34155 arg "math-macro-remove-optional-param"
34163 <cell alignment="center" valignment="top" usebox="none">
34166 \begin_layout Plain Layout
34169 Edit\SpecialChar menuseparator
34170 Math\SpecialChar menuseparator
34172 \begin_inset space ~
34175 Definition\SpecialChar menuseparator
34176 Remove Optional Argument
34182 <row interlinespace="2.5mm">
34183 <cell alignment="center" valignment="top" usebox="none">
34186 \begin_layout Plain Layout
34189 arg "math-macro-add-optional-param"
34197 <cell alignment="center" valignment="top" usebox="none">
34200 \begin_layout Plain Layout
34203 Edit\SpecialChar menuseparator
34204 Math\SpecialChar menuseparator
34206 \begin_inset space ~
34209 Definition\SpecialChar menuseparator
34210 Insert Optional Argument
34216 <row interlinespace="2.5mm">
34217 <cell alignment="center" valignment="top" usebox="none">
34220 \begin_layout Plain Layout
34223 arg "math-macro-remove-greedy-param"
34231 <cell alignment="center" valignment="top" usebox="none">
34234 \begin_layout Plain Layout
34237 Edit\SpecialChar menuseparator
34238 Math\SpecialChar menuseparator
34240 \begin_inset space ~
34243 Definition\SpecialChar menuseparator
34244 Remove Last Argument
34245 \begin_inset Newline newline
34249 \begin_inset Phantom HPhantom
34252 \begin_layout Plain Layout
34255 Edit\SpecialChar menuseparator
34256 Math\SpecialChar menuseparator
34258 \begin_inset space ~
34261 Definition\SpecialChar menuseparator
34267 Spitting Out To The Right
34273 <row interlinespace="2.5mm">
34274 <cell alignment="center" valignment="top" usebox="none">
34277 \begin_layout Plain Layout
34280 arg "math-macro-append-greedy-param"
34288 <cell alignment="center" valignment="top" usebox="none">
34291 \begin_layout Plain Layout
34294 Edit\SpecialChar menuseparator
34295 Math\SpecialChar menuseparator
34297 \begin_inset space ~
34300 Definition\SpecialChar menuseparator
34302 \begin_inset Newline newline
34306 \begin_inset Phantom HPhantom
34309 \begin_layout Plain Layout
34312 Edit\SpecialChar menuseparator
34313 Math\SpecialChar menuseparator
34315 \begin_inset space ~
34318 Definition\SpecialChar menuseparator
34324 Eating From The Right
34330 <row interlinespace="2.5mm">
34331 <cell alignment="center" valignment="top" usebox="none">
34334 \begin_layout Plain Layout
34337 arg "math-macro-add-greedy-optional-param"
34345 <cell alignment="center" valignment="top" usebox="none">
34348 \begin_layout Plain Layout
34351 Edit\SpecialChar menuseparator
34352 Math\SpecialChar menuseparator
34354 \begin_inset space ~
34357 Definition\SpecialChar menuseparator
34358 Append Optional Argument
34359 \begin_inset Newline newline
34363 \begin_inset Phantom HPhantom
34366 \begin_layout Plain Layout
34369 Edit\SpecialChar menuseparator
34370 Math\SpecialChar menuseparator
34372 \begin_inset space ~
34375 Definition\SpecialChar menuseparator
34381 Eating From The Right
34394 \begin_layout Section
34395 Computer Algebra Systems
34398 \begin_layout Standard
34400 offers the exchange between mathematical expressions written in \SpecialChar LyX
34402 editor and external applications or user defined scripts.
34403 Currently supported applications are
34420 Note that the set of supported mathematical constructs is limited only
34421 to very simple cases.
34424 \begin_layout Subsection
34428 \begin_layout Standard
34429 Write some expression in a formula, go to the
34431 Edit\SpecialChar menuseparator
34432 Math\SpecialChar menuseparator
34433 Use Computer Algebra System
34435 menu and choose the application you have installed on the computer.
34436 After that the result of computation should show on the right side of the
34437 expression together with the
34438 \begin_inset Quotes eld
34442 \begin_inset Quotes erd
34448 \begin_layout Standard
34449 Here are few simple examples (with results from
34453 ) to show what kind of computations can be performed:
34456 \begin_layout Itemize
34457 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34463 \begin_layout Itemize
34464 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34470 \begin_layout Itemize
34471 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34477 \begin_layout Itemize
34478 \begin_inset Formula $\int\left(\frac{1}{1+x^{3}}\right)dx=-\frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\,x-1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log\left(x+1\right)}{3}$
34482 \begin_inset Newline newline
34486 \begin_inset Note Greyedout
34489 \begin_layout Plain Layout
34494 One needs to use proper delimiter insets
34495 \begin_inset Formula $\left(\right)$
34498 instead of simple '(' ')' characters.
34506 \begin_layout Itemize
34507 \begin_inset Formula $\det\left[\begin{array}{ccc}
34511 \end{array}\right]=-56$
34517 \begin_layout Itemize
34518 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34524 \begin_layout Itemize
34525 \begin_inset Formula $powerseries\left(-\log\left(5-x\right),x,1\right)=\sum_{{\mathit{i}_{2}}=0}^{\infty}{\frac{4^{-{\mathit{i}_{2}}-1}\,\left(x-1\right)^{{\mathit{i}_{2}}+1}}{{\mathit{i}_{2}}+1}}-\log4$
34531 \begin_layout Itemize
34532 \begin_inset Formula $solve\left(x_{1}+y_{1}^{3}=y_{1}+x_{1}^{2},x_{1}\right)=\left[x_{1}=-\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}-1}{2},x_{1}=\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}+1}{2}\right]$
34538 \begin_layout Subsection
34542 \begin_layout Standard
34543 Currently there is no keyboard shortcut for calling the algebra applications.
34544 One can easily bind a shortcut to the
34558 \begin_inset space \thinspace{}
34562 \begin_inset space \space{}
34569 key inside the math editor.
34574 one would use this shortcut definition command:
34577 \begin_layout Standard
34580 command-alternatives paragraph-break;math-extern maxima
34583 \begin_layout Section
34585 \begin_inset Index idx
34588 \begin_layout Plain Layout
34597 \begin_layout Subsection
34599 \begin_inset Index idx
34602 \begin_layout Plain Layout
34611 \begin_layout Standard
34612 Negative numbers often look ugly in formulas because the minus sign before
34613 the number is set with the same length as the minus operator sign.
34614 When writing the negative number in normal text, the minus sign appears
34618 \begin_layout Standard
34619 Thus, the problem disappears when converting the minus sign to mathematical
34623 \begin_layout Standard
34624 An example to visualize the problem:
34627 \begin_layout Standard
34629 \begin_inset Tabular
34630 <lyxtabular version="3" rows="3" columns="2">
34631 <features booktabs="true" tabularvalignment="middle">
34632 <column alignment="right" valignment="top" width="0pt">
34633 <column alignment="left" valignment="top">
34635 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34638 \begin_layout Plain Layout
34644 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34647 \begin_layout Plain Layout
34655 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34658 \begin_layout Plain Layout
34664 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34667 \begin_layout Plain Layout
34668 \begin_inset Formula $x=-2$
34678 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34681 \begin_layout Plain Layout
34687 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34690 \begin_layout Plain Layout
34691 \begin_inset Formula $x=\textrm{-}2$
34707 \begin_layout Subsection
34708 Comma as decimal Separator
34709 \begin_inset Index idx
34712 \begin_layout Plain Layout
34721 \begin_layout Standard
34722 In \SpecialChar LaTeX
34723 a comma inside a formula is used, according to the English convention,
34724 as number group separator.
34725 So there will be space added behind all commas in formulas.
34728 \begin_layout Standard
34729 To avoid this, the comma is highlighted and changed to mathematical text
34739 \begin_layout Standard
34740 To use all formula commas in the document as decimal separator, the file
34749 \begin_layout Plain Layout
34754 is part of the \SpecialChar LaTeX
34760 \begin_inset Index idx
34763 \begin_layout Plain Layout
34768 \begin_layout Plain Layout
34788 \begin_inset Index idx
34791 \begin_layout Plain Layout
34797 is loaded with the \SpecialChar LaTeX
34801 \begin_layout Standard
34809 \begin_layout Subsection
34811 \begin_inset CommandInset label
34813 name "subsec:Physical-Vectors"
34818 \begin_inset Index idx
34821 \begin_layout Plain Layout
34830 \begin_layout Standard
34831 Predefined vectors are offered by the \SpecialChar LaTeX
34837 \begin_inset Index idx
34840 \begin_layout Plain Layout
34846 that is loaded with the \SpecialChar LaTeX
34850 \begin_layout Standard
34858 \begin_layout Standard
34862 \begin_layout Plain Layout
34872 \begin_inset Note Note
34875 \begin_layout Plain Layout
34876 The following table will only be displayed when the \SpecialChar LaTeX
34889 \begin_layout Standard
34890 The following commands are defined:
34893 \begin_layout Standard
34895 \begin_inset Tabular
34896 <lyxtabular version="3" rows="4" columns="2">
34897 <features booktabs="true" tabularvalignment="middle">
34898 <column alignment="center" valignment="top" width="0pt">
34899 <column alignment="center" valignment="top">
34901 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34904 \begin_layout Plain Layout
34910 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34913 \begin_layout Plain Layout
34921 <cell alignment="center" valignment="top" usebox="none">
34924 \begin_layout Plain Layout
34934 <cell alignment="center" valignment="top" usebox="none">
34937 \begin_layout Plain Layout
34938 \begin_inset Formula $\Bra{\psi}$
34948 <cell alignment="center" valignment="top" usebox="none">
34951 \begin_layout Plain Layout
34961 <cell alignment="center" valignment="top" usebox="none">
34964 \begin_layout Plain Layout
34965 \begin_inset Formula $\Ket{\psi}$
34975 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34978 \begin_layout Plain Layout
34990 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34993 \begin_layout Plain Layout
34994 \begin_inset Formula $\Braket{\psi|\phi}$
35010 \begin_layout Standard
35017 assures that all vertical bars are set in the size of the surrounding brackets:
35018 \begin_inset Formula
35020 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
35029 \begin_layout Plain Layout
35039 \begin_inset Note Note
35042 \begin_layout Plain Layout
35043 The following will be displayed when the \SpecialChar LaTeX
35056 \begin_layout Standard
35057 You need to install the \SpecialChar LaTeX
35062 to see the rest of this subsection in the output.
35065 \begin_layout Standard
35069 \begin_layout Plain Layout
35081 \begin_layout Standard
35088 can also be achieved using the command
35094 , that is described in
35095 \begin_inset CommandInset ref
35097 reference "subsec:Automatic-Bracket-Size"
35104 \begin_layout Subsection
35105 Self-defined Fractions
35106 \begin_inset CommandInset label
35108 name "subsec:Self-defined-Fractions"
35113 \begin_inset Index idx
35116 \begin_layout Plain Layout
35117 Fractions ! self-defined
35125 \begin_layout Standard
35126 To define custom commands for fractions, the command
35133 \begin_inset Index idx
35136 \begin_layout Plain Layout
35143 \begin_layout Plain Layout
35157 is used in the following scheme:
35160 \begin_layout Standard
35173 bracket}{fraction bar thickness}{style}
35174 \begin_inset Newline newline
35178 \begin_inset Phantom HPhantom
35181 \begin_layout Plain Layout
35191 {numerator}{denominator}
35194 \begin_layout Standard
35195 The style is a number in the range of 0
35196 \begin_inset space \thinspace{}
35200 \begin_inset space \thinspace{}
35206 \begin_layout Standard
35208 \begin_inset Tabular
35209 <lyxtabular version="3" rows="5" columns="2">
35210 <features booktabs="true" tabularvalignment="middle">
35211 <column alignment="center" valignment="top" width="0pt">
35212 <column alignment="center" valignment="top">
35214 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35217 \begin_layout Plain Layout
35223 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35226 \begin_layout Plain Layout
35234 <cell alignment="center" valignment="top" usebox="none">
35237 \begin_layout Plain Layout
35243 <cell alignment="center" valignment="top" usebox="none">
35246 \begin_layout Plain Layout
35247 display style formula
35254 <cell alignment="center" valignment="top" usebox="none">
35257 \begin_layout Plain Layout
35263 <cell alignment="center" valignment="top" usebox="none">
35266 \begin_layout Plain Layout
35274 <cell alignment="center" valignment="top" usebox="none">
35277 \begin_layout Plain Layout
35283 <cell alignment="center" valignment="top" usebox="none">
35286 \begin_layout Plain Layout
35294 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35297 \begin_layout Plain Layout
35303 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35306 \begin_layout Plain Layout
35320 \begin_layout Standard
35321 When no style is given, the size is adjusted to the surrounding environment
35322 like for the command
35331 \begin_layout Standard
35332 When no fraction bar thickness is given, the predefined value of 0.4
35333 \begin_inset space \thinspace{}
35339 \begin_layout Standard
35340 \begin_inset VSpace medskip
35343 For example, the commands
35356 \begin_inset CommandInset ref
35358 reference "subsec:Fractions"
35362 are defined with the commands
35365 \begin_layout Standard
35374 genfrac{}{}{}{0}{#1}{#2}}
35377 \begin_layout Standard
35381 \begin_layout Standard
35390 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35393 \begin_layout Standard
35394 \begin_inset VSpace medskip
35397 To define a fraction where the fraction bar thickness can be given as optional
35398 argument, the following line is inserted to the \SpecialChar LaTeX
35402 \begin_layout Standard
35411 genfrac{}{}{#1}{}{#2}{#3}}
35414 \begin_layout Standard
35416 \begin_inset Formula
35418 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35419 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35424 As one can see, the distance of the numerator and the denominator to the
35425 fraction bar is round about three times the bar thickness.
35428 \begin_layout Subsection
35430 \begin_inset Index idx
35433 \begin_layout Plain Layout
35442 \begin_layout Standard
35443 There are four ways to cancel formulas or parts of formulas:
35446 \begin_layout Standard
35450 \begin_layout Plain Layout
35460 \begin_inset Note Note
35463 \begin_layout Plain Layout
35464 The following table will only be displayed when the \SpecialChar LaTeX
35477 \begin_layout Standard
35479 \begin_inset Tabular
35480 <lyxtabular version="3" rows="5" columns="2">
35481 <features booktabs="true" tabularvalignment="middle">
35482 <column alignment="center" valignment="top" width="0pt">
35483 <column alignment="center" valignment="top">
35485 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35488 \begin_layout Plain Layout
35494 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35497 \begin_layout Plain Layout
35505 <cell alignment="center" valignment="top" usebox="none">
35508 \begin_layout Plain Layout
35512 \begin_inset space \textvisiblespace{}
35518 \begin_inset space \textvisiblespace{}
35526 <cell alignment="center" valignment="top" usebox="none">
35529 \begin_layout Plain Layout
35530 \begin_inset Formula $\cancel{\int A=B}$
35539 <row topspace="1.5mm">
35540 <cell alignment="center" valignment="top" usebox="none">
35543 \begin_layout Plain Layout
35547 \begin_inset space \textvisiblespace{}
35553 \begin_inset space \textvisiblespace{}
35561 <cell alignment="center" valignment="top" usebox="none">
35564 \begin_layout Plain Layout
35565 \begin_inset Formula $\bcancel{\int A=B}$
35574 <row topspace="1.5mm">
35575 <cell alignment="center" valignment="top" usebox="none">
35578 \begin_layout Plain Layout
35582 \begin_inset space \textvisiblespace{}
35588 \begin_inset space \textvisiblespace{}
35596 <cell alignment="center" valignment="top" usebox="none">
35599 \begin_layout Plain Layout
35600 \begin_inset Formula $\xcancel{\int A=B}$
35610 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35613 \begin_layout Plain Layout
35617 \begin_inset space \textvisiblespace{}
35623 \begin_inset space \textvisiblespace{}
35627 \begin_inset Formula $\to$
35635 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35638 \begin_layout Plain Layout
35639 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35655 \begin_layout Standard
35662 is especially suitable to visualize the reduction of fractions within formulas:
35663 \begin_inset Formula
35665 \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}}}
35673 \begin_layout Standard
35674 To change the size of
35681 \begin_inset Quotes eld
35685 \begin_inset Quotes erd
35688 value one can add the \SpecialChar LaTeX
35692 \begin_layout Standard
35697 PassOptionsToPackage{option}{cancel}
35700 \begin_layout Standard
35709 which leads to the same size as for the canceled value, or
35713 which makes is it a bit smaller than normal.
35716 \begin_layout Standard
35717 To color the cancellation bar one adds this command as \SpecialChar TeX
35721 \begin_layout Standard
35733 \begin_layout Standard
35738 can be replaced by a color of your choice.
35741 \begin_layout Standard
35745 \begin_layout Plain Layout
35761 \begin_layout Standard
35762 \begin_inset Formula
35764 \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}}}
35772 \begin_layout Standard
35776 \begin_layout Plain Layout
35790 \begin_inset Note Note
35793 \begin_layout Plain Layout
35802 \begin_layout Standard
35803 For further customizations, see the documentation of the package
35808 \begin_inset CommandInset citation
35816 \begin_inset Index idx
35819 \begin_layout Plain Layout
35828 \begin_layout Standard
35832 \begin_layout Plain Layout
35842 \begin_inset Note Note
35845 \begin_layout Plain Layout
35846 The following will be displayed when the \SpecialChar LaTeX
35859 \begin_layout Standard
35860 You need to install the \SpecialChar LaTeX
35865 to see the rest of this subsection in the output.
35868 \begin_layout Standard
35872 \begin_layout Plain Layout
35884 \begin_layout Subsection
35885 Formulas in Section Headings
35886 \begin_inset CommandInset label
35888 name "subsec:Formulas-in-Section"
35893 \begin_inset Index idx
35896 \begin_layout Plain Layout
35897 Formula ! in section headings
35905 \begin_layout Standard
35906 When formulas are used in section headings, the following has to be taken
35910 \begin_layout Standard
35911 \begin_inset Note Greyedout
35914 \begin_layout Plain Layout
35920 \begin_inset Index idx
35923 \begin_layout Plain Layout
35924 Packages ! hyperref
35929 support is enabled in the document settings dialog under
35932 \begin_inset space ~
35937 , PDF-bookmarks are created for every section heading in the table of contents.
35938 If a section heading contains formulas, they are incorrectly displayed
35939 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35948 \begin_layout Standard
35949 Both problems can be solved by inserting at the end of the section heading
35950 a short title with the menu
35952 Insert\SpecialChar menuseparator
35954 \begin_inset space ~
35960 Short titles are used as alternative for multiline section headings to
35961 keep the table of contents clearly arranged.
35962 Only the short title appears in the table of contents and therefore also
35963 in the PDF-bookmark.
35966 \begin_layout Standard
35967 When formulas should be used in the table of contents but
35971 is used, one can use the following command in \SpecialChar TeX
35975 \begin_layout Standard
35980 texorpdfstring{part}{alternative}
35981 \begin_inset Index idx
35984 \begin_layout Plain Layout
35995 \begin_layout Standard
35996 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35997 This can be characters, formulas, footnotes, but also cross-references.
35998 The alternative is used instead of the part for the bookmark.
36001 \begin_layout Standard
36002 Here are two example headings:
36003 \begin_inset VSpace -3mm
36010 \begin_layout Plain Layout
36022 \begin_layout Subsubsection
36023 Heading without formula in table of contents
36024 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36028 \begin_inset Argument 1
36031 \begin_layout Plain Layout
36032 Heading without formula in table of contents
36040 \begin_layout Subsubsection
36041 Heading with formula in table of contents
36045 \begin_layout Plain Layout
36055 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36062 \begin_layout Plain Layout
36072 \begin_layout Standard
36076 \begin_layout Plain Layout
36085 In the first heading a short title was used, in the second one
36094 \begin_layout Standard
36095 To get the same formatting as for the other headings, the complete heading
36104 \begin_layout Plain Layout
36106 \begin_inset CommandInset ref
36108 reference "subsec:Bold-Formulas"
36120 \begin_layout Subsection
36121 Formulas in multi-column Text
36122 \begin_inset Index idx
36125 \begin_layout Plain Layout
36126 Formula ! in multi-column text
36134 \begin_layout Standard
36135 Formulas in multi-column text are often too wide to fit into a column and
36136 thus need to be set over the whole page width.
36137 This is done by using the \SpecialChar LaTeX
36146 \begin_layout Plain Layout
36151 is part of every \SpecialChar LaTeX
36152 standard installation.
36158 \begin_inset Index idx
36161 \begin_layout Plain Layout
36162 Packages ! multicol
36167 , that is loaded with the \SpecialChar LaTeX
36171 \begin_layout Standard
36176 usepackage{multicol}
36179 \begin_layout Standard
36180 \begin_inset Note Greyedout
36183 \begin_layout Plain Layout
36184 Note that in this case the setting
36187 \begin_inset space ~
36194 Document\SpecialChar menuseparator
36200 \begin_inset space ~
36220 \begin_layout Standard
36221 Before the multi-column text the command
36224 \begin_layout Standard
36229 begin{multicols}{column number}
36232 \begin_layout Standard
36233 is written in \SpecialChar TeX
36235 The column number is a number in the range of 2
36236 \begin_inset space \thinspace{}
36240 \begin_inset space \thinspace{}
36244 Before the formula the multi-column text is ended by inserting the command
36247 \begin_layout Standard
36255 \begin_layout Standard
36256 in \SpecialChar TeX
36260 \begin_layout Standard
36261 Due to the command some space is automatically added before the formula.
36262 To correct this, -6
36263 \begin_inset space \thinspace{}
36266 mm vertical space is inserted before the formula.
36267 When the formula style
36273 \begin_layout Plain Layout
36274 For formula styles see
36275 \begin_inset CommandInset ref
36277 reference "sec:Formula-Styles"
36289 \begin_inset space \thinspace{}
36292 mm space is inserted instead.
36295 \begin_layout Standard
36296 As example a multi-column text with a displayed formula:
36299 \begin_layout Standard
36305 \begin_layout Plain Layout
36309 begin{multicols}{2}
36314 Das Spektrum wird fouriertransformiert.
36315 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36316 , Lösungsmittel) zu trennen.
36317 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36318 nun das Aussehen des Ausgangssignals.
36319 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36320 über alle Phasen integrieren muss.
36322 \begin_inset Formula $S$
36325 unser normiertes Ausgangssignal und
36326 \begin_inset Formula $P$
36329 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36333 \begin_layout Plain Layout
36343 \begin_inset VSpace -6mm
36347 \begin_inset Formula
36349 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36358 \begin_layout Plain Layout
36362 begin{multicols}{2}
36368 \begin_inset Formula $S_{0}$
36371 das Signal ohne Gradient ist und die Normierungsbedingung
36372 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36376 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36378 \begin_inset Formula $\nicefrac{\pi}{2}$
36382 \begin_inset space \thinspace{}
36385 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36386 das Signal zusätzlich abschwächt.
36387 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36389 \begin_inset Formula $T_{2}$
36395 \begin_layout Standard
36401 \begin_layout Plain Layout
36413 \begin_layout Subsection
36414 Formulas with Description of Variables
36415 \begin_inset Index idx
36418 \begin_layout Plain Layout
36419 Formula ! with description of variables
36427 \begin_layout Standard
36428 To describe variables within a formula, like in formula
36429 \begin_inset CommandInset ref
36431 reference "eq:within"
36440 \begin_inset Formula $n$
36444 \begin_inset space ~
36447 matrix is used with left aligned columns for the
36448 \begin_inset Formula $n$
36455 \begin_layout Plain Layout
36457 \begin_inset CommandInset ref
36459 reference "sec:Matrices"
36468 To set the description in a smaller size, before the matrix e.
36469 \begin_inset space \thinspace{}
36473 \begin_inset space \space{}
36486 \begin_layout Plain Layout
36488 \begin_inset CommandInset ref
36490 reference "subsec:Font-Sizes"
36502 \begin_layout Standard
36503 When the formula style
36509 \begin_layout Plain Layout
36510 For formula styles see
36511 \begin_inset CommandInset ref
36513 reference "sec:Formula-Styles"
36534 \begin_layout Plain Layout
36541 only works in formulas with the style
36546 \begin_inset CommandInset ref
36548 reference "subsec:Variable-Space"
36557 is inserted before and after the matrix to have the same separation of
36558 the matrix from the equation and the side margin.
36561 \begin_layout Standard
36562 When the formula style
36566 is used, the method described in
36567 \begin_inset CommandInset ref
36569 reference "subsec:Flalign-Environment"
36573 is used to indent formulas.
36575 \begin_inset CommandInset ref
36577 reference "eq:within"
36581 consists of five columns where in the first two columns contain the equation,
36582 the third the matrix and the last one an empty \SpecialChar TeX
36584 \begin_inset Formula
36586 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36587 \rho & \textrm{density}\\
36588 V & \textrm{volume}\\
36589 g & \textrm{gravitational acceleration}
36590 \end{array} & & {}\label{eq:within}
36598 \begin_layout Subsection
36599 Upright small Greek Letters
36600 \begin_inset CommandInset label
36602 name "subsec:Upright-small-Greek"
36607 \begin_inset Index idx
36610 \begin_layout Plain Layout
36611 Greek letters ! upright
36619 \begin_layout Standard
36620 Most of the math fonts only provide italic small Greek letters.
36621 But for symbols of elementary particles like pions and neutrinos, upright
36622 Greek letters are needed.
36631 \begin_layout Plain Layout
36636 is part of the \SpecialChar LaTeX
36642 \begin_inset Index idx
36645 \begin_layout Plain Layout
36650 \begin_layout Plain Layout
36670 \begin_inset Index idx
36673 \begin_layout Plain Layout
36679 that is loaded with the \SpecialChar LaTeX
36683 \begin_layout Standard
36688 usepackage{upgreek}
36691 \begin_layout Standard
36697 \begin_layout Plain Layout
36707 \begin_inset Note Note
36710 \begin_layout Plain Layout
36711 The following table will only be displayed when the \SpecialChar LaTeX
36721 They are created when the command for a small Greek letter is started with
36727 For example the command
36734 \begin_inset Formula $\uptau$
36740 \begin_layout Standard
36741 With these commands reactions of elementary particles can be typeset:
36742 \begin_inset Formula
36744 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36752 \begin_layout Standard
36753 The upright letters are more bold and wider than the italic ones.
36754 They should therefore not be used for units like
36755 \begin_inset Quotes eld
36759 \begin_inset Quotes erd
36765 \begin_layout Standard
36769 \begin_layout Plain Layout
36779 \begin_inset Note Note
36782 \begin_layout Plain Layout
36783 The following will be displayed when the \SpecialChar LaTeX
36796 \begin_layout Standard
36797 You need to install the \SpecialChar LaTeX
36802 to see the rest of this subsection in the output.
36805 \begin_layout Standard
36809 \begin_layout Plain Layout
36821 \begin_layout Subsection
36822 Text Characters in Formulas
36823 \begin_inset Index idx
36826 \begin_layout Plain Layout
36835 \begin_layout Standard
36836 In some cases you might want to insert text characters directly into formulas.
36837 For example the centered dot · is often used in formulas like
36838 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36842 One would have to insert the command
36852 \begin_layout Plain Layout
36854 \begin_inset CommandInset ref
36856 reference "subsec:Binary-Operators"
36865 all the time, because this character is defined in all encodings as a text
36867 But the encoding can be changed by this \SpecialChar LaTeX
36871 \begin_layout Standard
36876 Declare Inputtext{183}{
36886 f\SpecialChar ligaturebreak
36890 \begin_layout Standard
36891 The character encoding (menu
36893 Document\SpecialChar menuseparator
36894 Settings\SpecialChar menuseparator
36897 ) specifies what character appears when a keyboard key is pressed.
36898 When the key for the character '·' is pressed, internally the command
36905 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36907 With the changed encoding the correct command is chosen automatically,
36908 depending on if the character was inserted into a formula or not.
36911 \begin_layout Standard
36912 The encoding of several characters is saved in definition files.
36913 For example the encoding
36917 is defined in the file
36921 which is in the installation folder of \SpecialChar LaTeX
36923 Encodings should only be changed via the \SpecialChar LaTeX
36924 -preamble and not in the definition
36926 Otherwise documents could not be edited by other \SpecialChar LyX
36927 users working on other
36931 \begin_layout Standard
36932 \begin_inset VSpace medskip
36935 Besides the centered dot, in this document the degree sign ° is defined
36936 with the following \SpecialChar LaTeX
36937 -preamble line so that it can be directly inserted into
36941 \begin_layout Standard
36946 DeclareInputtext{176}{
36956 f\SpecialChar ligaturebreak
36960 \begin_layout Subsection
36962 -comments in formulas
36963 \begin_inset Index idx
36966 \begin_layout Plain Layout
36976 \begin_layout Standard
36977 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36979 code of your file with the menu
36981 Insert\SpecialChar menuseparator
36982 Note\SpecialChar menuseparator
36986 This is not possible in a formula but you can insert \SpecialChar LaTeX
36991 \begin_layout Standard
36999 \begin_layout Standard
37000 This creates a box in which you can write your comment.
37001 Due to a bug in \SpecialChar LyX
37006 \begin_layout Plain Layout
37007 \begin_inset CommandInset href
37009 name "LyX-bug #9002"
37010 target "https://www.lyx.org/trac/ticket/9002"
37020 you cannot write normal text inside the comment, even when you use mathematical
37021 text, you will see its \SpecialChar LaTeX
37022 -commands in the \SpecialChar LaTeX
37024 \begin_inset Newline newline
37027 This a formula with a \SpecialChar LaTeX
37029 \begin_inset Formula
37031 A=B%\text{This is the comment}
37039 \begin_layout Standard
37040 \begin_inset Newpage newpage
37046 \begin_layout Section
37049 \begin_inset Index idx
37052 \begin_layout Plain Layout
37061 \begin_layout Standard
37062 This section is a summary of the most important typographic rules, listed
37067 \begin_layout Plain Layout
37068 This collection was partly taken from the German semi-official dictionary
37070 \begin_inset Quotes eld
37074 \begin_inset Quotes erd
37078 \begin_inset CommandInset citation
37085 that lists some of the ISO rules.
37086 More rules are listed in
37087 \begin_inset CommandInset citation
37102 \begin_layout Itemize
37111 \begin_layout Plain Layout
37112 Done with font styles, see
37113 \begin_inset CommandInset ref
37115 reference "subsec:Font-Styles"
37124 , no matter if they appear in italic text: 30
37125 \begin_inset space \thinspace{}
37129 \begin_inset Newline newline
37132 Between the value and the unit is the smallest space, see
37133 \begin_inset CommandInset ref
37135 reference "subsec:Predefined-Space"
37140 \begin_inset Newline newline
37143 This convention is automatically fulfilled when the command
37150 When it is entered in a formula, two boxes appear.
37151 In the first one the value is inserted, in the second one the unit, and
37152 the result is as above:
37153 \begin_inset Formula $\unit[30]{km/h}$
37157 \begin_inset space \thinspace{}
37167 is not a real \SpecialChar LaTeX
37168 command but the command
37174 , therefore you cannot use it in \SpecialChar TeX
37178 \begin_layout Itemize
37179 Percent and perthousand signs are set like physical units:
37180 \begin_inset Newline newline
37184 \begin_inset space \thinspace{}
37190 \begin_layout Itemize
37191 The degree sign follows the value directly: 15°, except when it is used
37193 \begin_inset space \thinspace{}
37199 \begin_layout Itemize
37200 In numbers with more than four digits the smallest space is inserted before
37201 every third digit to group them:
37211 \begin_inset space \thinspace{}
37215 \begin_inset space \thinspace{}
37221 \begin_layout Itemize
37222 For dimensions like 120×90×40
37223 \begin_inset space \thinspace{}
37226 cm the multiplication sign
37227 \begin_inset Quotes eld
37231 \begin_inset Quotes erd
37235 It is available either via the command
37243 Insert\SpecialChar menuseparator
37244 Special Character\SpecialChar menuseparator
37250 \begin_layout Itemize
37251 Functions with names consisting of several letters are set upright to avoid
37253 \begin_inset CommandInset ref
37255 reference "subsec:Predefined-Functions"
37262 \begin_layout Itemize
37263 Indices consisting of several letters, are set upright:
37264 \begin_inset Formula $E_{\mathrm{kin}}$
37268 \begin_inset Newline newline
37271 Components of matrices are set italic:
37272 \begin_inset Formula $\hat{H}_{kl}$
37278 \begin_layout Itemize
37279 The differentiation/integration operator 'd', the Euler's number 'e' and
37280 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37284 \begin_layout Itemize
37285 The character that denotes a
37289 transformation is inserted either by the command
37294 \begin_inset space \textvisiblespace{}
37301 Insert\SpecialChar menuseparator
37302 Special Character\SpecialChar menuseparator
37303 Symbols\SpecialChar menuseparator
37305 \begin_inset space ~
37311 \begin_inset Formula $\mathscr{F}$
37317 \begin_layout Standard
37318 \begin_inset Newpage newpage
37324 \begin_layout Section
37326 \begin_inset Index idx
37329 \begin_layout Plain Layout
37338 \begin_layout Standard
37339 Some characters and symbols can be created with several commands.
37340 Here is a list of the synonym commands:
37343 \begin_layout Standard
37344 \begin_inset VSpace bigskip
37348 \begin_inset space \hfill{}
37352 \begin_inset Tabular
37353 <lyxtabular version="3" rows="12" columns="2">
37354 <features booktabs="true" tabularvalignment="middle">
37355 <column alignment="center" valignment="top" width="0pt">
37356 <column alignment="center" valignment="top" width="0pt">
37358 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37361 \begin_layout Plain Layout
37367 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37370 \begin_layout Plain Layout
37378 <cell alignment="center" valignment="top" usebox="none">
37381 \begin_layout Plain Layout
37389 <cell alignment="center" valignment="top" usebox="none">
37392 \begin_layout Plain Layout
37400 <cell alignment="center" valignment="top" usebox="none">
37403 \begin_layout Plain Layout
37411 <cell alignment="center" valignment="top" usebox="none">
37414 \begin_layout Plain Layout
37424 <cell alignment="center" valignment="top" usebox="none">
37427 \begin_layout Plain Layout
37435 <cell alignment="center" valignment="top" usebox="none">
37438 \begin_layout Plain Layout
37448 <cell alignment="center" valignment="top" usebox="none">
37451 \begin_layout Plain Layout
37459 <cell alignment="center" valignment="top" usebox="none">
37462 \begin_layout Plain Layout
37470 <cell alignment="center" valignment="top" usebox="none">
37473 \begin_layout Plain Layout
37481 <cell alignment="center" valignment="top" usebox="none">
37484 \begin_layout Plain Layout
37492 <cell alignment="center" valignment="top" usebox="none">
37495 \begin_layout Plain Layout
37503 <cell alignment="center" valignment="top" usebox="none">
37506 \begin_layout Plain Layout
37516 <cell alignment="center" valignment="top" usebox="none">
37519 \begin_layout Plain Layout
37527 <cell alignment="center" valignment="top" usebox="none">
37530 \begin_layout Plain Layout
37540 <cell alignment="center" valignment="top" usebox="none">
37543 \begin_layout Plain Layout
37551 <cell alignment="center" valignment="top" usebox="none">
37554 \begin_layout Plain Layout
37564 <cell alignment="center" valignment="top" usebox="none">
37567 \begin_layout Plain Layout
37575 <cell alignment="center" valignment="top" usebox="none">
37578 \begin_layout Plain Layout
37588 <cell alignment="center" valignment="top" usebox="none">
37591 \begin_layout Plain Layout
37599 <cell alignment="center" valignment="top" usebox="none">
37602 \begin_layout Plain Layout
37610 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37613 \begin_layout Plain Layout
37621 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37624 \begin_layout Plain Layout
37636 \begin_inset space \hfill{}
37640 \begin_inset Tabular
37641 <lyxtabular version="3" rows="12" columns="2">
37642 <features booktabs="true" tabularvalignment="middle">
37643 <column alignment="center" valignment="top" width="0pt">
37644 <column alignment="center" valignment="top" width="0pt">
37646 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37649 \begin_layout Plain Layout
37655 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37658 \begin_layout Plain Layout
37666 <cell alignment="center" valignment="top" usebox="none">
37669 \begin_layout Plain Layout
37677 <cell alignment="center" valignment="top" usebox="none">
37680 \begin_layout Plain Layout
37692 <cell alignment="center" valignment="top" usebox="none">
37695 \begin_layout Plain Layout
37703 <cell alignment="center" valignment="top" usebox="none">
37706 \begin_layout Plain Layout
37716 <cell alignment="center" valignment="top" usebox="none">
37719 \begin_layout Plain Layout
37727 <cell alignment="center" valignment="top" usebox="none">
37730 \begin_layout Plain Layout
37740 <cell alignment="center" valignment="top" usebox="none">
37743 \begin_layout Plain Layout
37751 <cell alignment="center" valignment="top" usebox="none">
37754 \begin_layout Plain Layout
37762 <cell alignment="center" valignment="top" usebox="none">
37765 \begin_layout Plain Layout
37773 <cell alignment="center" valignment="top" usebox="none">
37776 \begin_layout Plain Layout
37784 <cell alignment="center" valignment="top" usebox="none">
37787 \begin_layout Plain Layout
37795 <cell alignment="center" valignment="top" usebox="none">
37798 \begin_layout Plain Layout
37808 <cell alignment="center" valignment="top" usebox="none">
37811 \begin_layout Plain Layout
37819 <cell alignment="center" valignment="top" usebox="none">
37822 \begin_layout Plain Layout
37832 <cell alignment="center" valignment="top" usebox="none">
37835 \begin_layout Plain Layout
37843 <cell alignment="center" valignment="top" usebox="none">
37846 \begin_layout Plain Layout
37856 <cell alignment="center" valignment="top" usebox="none">
37859 \begin_layout Plain Layout
37867 <cell alignment="center" valignment="top" usebox="none">
37870 \begin_layout Plain Layout
37880 <cell alignment="center" valignment="top" usebox="none">
37883 \begin_layout Plain Layout
37891 <cell alignment="center" valignment="top" usebox="none">
37894 \begin_layout Plain Layout
37904 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37907 \begin_layout Plain Layout
37915 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37918 \begin_layout Plain Layout
37932 \begin_inset space \hfill{}
37936 \begin_inset CommandInset href
37939 target "https://ctan.org/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37947 \begin_layout Standard
37948 \begin_inset Newpage newpage
37954 \begin_layout Bibliography
37955 \begin_inset CommandInset bibitem
37956 LatexCommand bibitem
37970 The \SpecialChar LaTeX
37974 Addison Wesley, 2004
37977 \begin_layout Bibliography
37978 \begin_inset CommandInset bibitem
37979 LatexCommand bibitem
37986 \change_inserted 5863208 1612728717
37988 \begin_inset CommandInset href
37991 target "http://mirrors.ctan.org/obsolete/info/math/voss/mathmode/Mathmode.pdf"
37997 \change_deleted 5863208 1612728717
37999 \begin_inset CommandInset href
38002 target "https://www.tug.org/~hvoss/PDF/mathmode.pdf"
38009 of \SpecialChar LaTeX
38011 \change_deleted 5863208 1612728849
38013 \begin_inset Note Note
38016 \begin_layout Plain Layout
38018 \change_inserted 232239728 1611367909
38031 \begin_layout Bibliography
38032 \begin_inset CommandInset bibitem
38033 LatexCommand bibitem
38040 \change_inserted 5863208 1612728836
38042 \begin_inset CommandInset href
38045 target "http://tug.ctan.org/info/amslatex/english/amsldoc.pdf"
38051 \change_deleted 5863208 1612728836
38053 \begin_inset CommandInset href
38056 target "https://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/amsldoc.pdf"
38067 \begin_layout Plain Layout
38076 -\SpecialChar LaTeX
38078 \change_deleted 5863208 1612728851
38080 \begin_inset Note Note
38083 \begin_layout Plain Layout
38085 \change_inserted 232239728 1611367919
38098 \begin_layout Bibliography
38099 \begin_inset CommandInset bibitem
38100 LatexCommand bibitem
38107 \change_inserted 5863208 1612728963
38109 \begin_inset CommandInset href
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38130 of all symbols available with \SpecialChar LaTeX
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38278 Auflage, Dudenverlag, 2000
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38298 for reviewing manuscripts
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