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
142 \maintain_unincluded_children no
144 \language_package default
147 \font_roman "lmodern" "default"
148 \font_sans "lmss" "default"
149 \font_typewriter "lmtt" "default"
150 \font_math "auto" "auto"
151 \font_default_family default
152 \use_non_tex_fonts false
154 \font_roman_osf false
156 \font_typewriter_osf false
157 \font_sf_scale 100 100
158 \font_tt_scale 100 100
160 \use_dash_ligatures false
162 \default_output_format pdf2
164 \bibtex_command default
165 \index_command makeindex
166 \float_placement class
167 \float_alignment class
171 \pdf_title "LyX's Math Manual"
172 \pdf_author "LyX Team, Uwe Stöhr"
173 \pdf_subject "LyX-documentation about math"
174 \pdf_keywords "LyX, Mathed"
176 \pdf_bookmarksnumbered true
177 \pdf_bookmarksopen true
178 \pdf_bookmarksopenlevel 1
179 \pdf_breaklinks false
183 \pdf_pdfusetitle false
184 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
187 \use_package amsmath 2
188 \use_package amssymb 2
189 \use_package cancel 1
191 \use_package mathdots 1
192 \use_package mathtools 2
193 \use_package mhchem 1
194 \use_package stackrel 1
195 \use_package stmaryrd 1
196 \use_package undertilde 0
198 \cite_engine_type default
202 \paperorientation portrait
208 \notefontcolor #0000ff
215 \paragraph_separation skip
218 \math_numbering_side default
219 \quotes_style english
223 \paperpagestyle plain
228 \tracking_changes true
229 \output_changes false
231 \postpone_fragile_content false
234 \html_be_strict false
235 \docbook_table_output 0
236 \docbook_mathml_prefix 1
237 \author -584632292 "Richard Kimberly Heck"
238 \author -563046850 "Jean-Marc LASGOUTTES"
239 \author -495245474 "Jean-Marc Lasgouttes"
242 \author 47243155 "Jean-Marc"
243 \author 232239728 "Owner"
250 's Detailed Math Manual
254 by the \SpecialChar LyX
259 \begin_layout Plain Layout
261 If you have comments or error corrections,
262 please send them to the \SpecialChar LyX
263 Documentation mailing list:
267 \begin_inset CommandInset href
269 name "lyx-docs@lists.lyx.org"
270 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
282 \begin_inset Note Note
285 \begin_layout Plain Layout
293 \begin_inset Newline newline
297 \begin_inset Newline newline
303 \change_inserted 47243155 1563226038
305 \change_deleted 47243155 1563226038
311 \begin_layout Standard
312 \begin_inset CommandInset toc
313 LatexCommand tableofcontents
320 \begin_layout Standard
321 \begin_inset Note Note
324 \begin_layout Plain Layout
325 To export this document to PDF,
326 PS or DVI the \SpecialChar LaTeX
342 If they are not installed the document can be exported anyway but the sections where the packages are required will not appear in the output.
348 if it is not installed,
349 this file cannot be exported.
352 \begin_layout Plain Layout
353 The latest PDF-version of this document can be found here:
354 \begin_inset Newline newline
359 https://wiki.lyx.org/LyX/Manuals#Math
367 \begin_layout Standard
368 \begin_inset Newpage newpage
374 \begin_layout Section
378 \begin_layout Standard
379 This document details \SpecialChar LyX
380 's math features and the \SpecialChar LaTeX
381 -commands used for mathematical characters and constructs.
382 It is oriented toward the use of commands.
383 The user should read the
391 section of the User's Guide before proceeding.
394 \begin_layout Standard
395 Most of the characters and many constructs explained in this manual are also accessible via the menu
399 \SpecialChar menuseparator
415 But everybody who has to write lots of formulas will notice that it is much faster to use commands instead of the math toolbar.
416 Therefore this manual is focused on commands but also mentions the corresponding toolbar buttons when available.
419 \begin_layout Standard
420 Unless specially mentioned,
421 math commands are only available within formulas.
422 To be able to use all of the commands explained in this document,
427 must be checked in the document settings (menu
429 Document\SpecialChar menuseparator
430 Settings\SpecialChar menuseparator
441 \begin_layout Plain Layout
444 Use AMS math package automatically
450 \begin_layout Plain Layout
459 -math when math constructs are found that are supported by \SpecialChar LyX
468 \begin_layout Standard
469 This document doesn't list all
473 \begin_layout Plain Layout
486 \begin_layout Plain Layout
487 A list containing all
491 \begin_layout Plain Layout
500 -math commands is in the file
503 \begin_inset CommandInset href
506 target "https://www.ctan.org/tex-archive/macros/amstex/doc/amsguide.pdf"
514 which is part of every \SpecialChar LaTeX
515 standard installation.
520 for lucidity reasons.
523 \begin_layout Section
527 \begin_layout Standard
528 To create an inline formula
529 \begin_inset Index idx
534 \begin_layout Plain Layout
536 \begin_inset IndexMacro subentry
539 \begin_layout Plain Layout
550 that is embedded in a text line,
551 use one of the shortcuts
557 or the toolbar button
564 \begin_inset Newline newline
567 To create a display style formula
568 \begin_inset Index idx
573 \begin_layout Plain Layout
575 \begin_inset IndexMacro subentry
578 \begin_layout Plain Layout
589 which will appear bigger,
590 has a different format,
591 and will be in a separate paragraph,
592 use one of these shortcuts:
602 \begin_layout Standard
603 To change a display style formula to an inline formula,
604 place the cursor inside the formula and use
605 \change_deleted 5863208 1612729312
609 \change_deleted 5863208 1612729314
613 \change_deleted 5863208 1612729303
621 \change_inserted 5863208 1612729281
625 arg "math-mutate simple"
632 Edit\SpecialChar menuseparator
633 Math\SpecialChar menuseparator
638 \change_inserted 5863208 1612729555
639 Similarly you can use the shortcut
642 arg "math-mutate equation"
645 to change from an inline to a display style formula.
647 \change_deleted 5863208 1612729557
648 The same method is used to change an inline formula to a display style formula.
653 \begin_layout Standard
654 To display parts of an inline formula in the size of a display style formula,
662 \begin_inset Index idx
667 \begin_layout Plain Layout
669 \begin_inset IndexMacro subentry
672 \begin_layout Plain Layout
679 \begin_inset IndexMacro subentry
682 \begin_layout Plain Layout
696 A new blue box will appear in which the desired formula part is inserted.
699 \begin_layout Standard
700 Only inline formulas are allowed inside tables.
703 \begin_layout Standard
705 \change_deleted 232239728 1610897673
710 can be turned on in the menu
712 View\SpecialChar menuseparator
716 When you click there on
717 \begin_inset Quotes eld
721 \begin_inset Quotes erd
724 the toolbar will be shown permanently at the bottom;
725 this state is visualized in the
729 menu with a checkmark.
730 When you click in this state again on
731 \begin_inset Quotes eld
735 \begin_inset Quotes erd
747 is only shown when the cursor is within a formula;
748 this state is visualized by the renaming of the menu entry from
749 \begin_inset Quotes eld
753 \begin_inset Quotes erd
757 \begin_inset Quotes eld
765 \begin_inset Quotes erd
769 \change_inserted 232239728 1610897478
773 \begin_layout Standard
775 \change_inserted 232239728 1610918987
780 visibility is controlled in the menu
782 View\SpecialChar menuseparator
783 Toolbars\SpecialChar menuseparator
787 Three options will be presented,
791 Selecting On will cause the toolbar to be shown permanently at the bottom of the screen.
792 Selecting Off will disable the toolbar.
793 Selecting Automatic will cause the toolbar to automatically appear when the cursor is located within a formula.
794 The active state of the toolbar is indicated by a checkmark next to the current menu selection.
795 \begin_inset Note Note
798 \begin_layout Plain Layout
800 \change_inserted 232239728 1610897730
801 The menu functionality appears to have changed,
802 I rewrote the paragraph for the current functionality
814 \begin_layout Standard
817 \begin_inset Index idx
822 \begin_layout Plain Layout
823 \begin_inset IndexMacro sortkey
826 \begin_layout Plain Layout
838 is invoked by pressing the toolbar button
846 Insert\SpecialChar menuseparator
858 \begin_layout Standard
859 To change the \SpecialChar LaTeX
861 \begin_inset Index idx
866 \begin_layout Plain Layout
867 \begin_inset IndexMacro sortkey
870 \begin_layout Plain Layout
885 Document\SpecialChar menuseparator
886 Settings\SpecialChar menuseparator
896 \begin_layout Standard
898 case differentiations and multiline formulas,
901 Edit\SpecialChar menuseparator
906 Edit\SpecialChar menuseparator
908 \begin_inset space \thinspace{}
912 \begin_inset space \thinspace{}
923 When lines and columns are swapped via the menu,
924 the column or line where the cursor is in is exchanged with the column to the right or the line below,
926 If the cursor is in the last column or row,
927 the exchange is done with the column to the left or the line above.
930 \begin_layout Standard
931 To write text in formulas
935 \begin_layout Plain Layout
936 For multiline formulas the command
944 \begin_inset CommandInset ref
946 reference "subsec:Text-in-multiline"
961 \begin_inset Index idx
966 \begin_layout Plain Layout
968 \begin_inset IndexMacro subentry
971 \begin_layout Plain Layout
983 \begin_inset Index idx
988 \begin_layout Plain Layout
995 This mode is invoked with the shortcut
1001 or by the insertion of the command
1008 \begin_inset Index idx
1013 \begin_layout Plain Layout
1015 \begin_inset IndexMacro subentry
1018 \begin_layout Plain Layout
1025 \begin_inset IndexMacro subentry
1028 \begin_layout Plain Layout
1042 The text appears black in \SpecialChar LyX
1043 and can therefore be distinguished from the other formula parts which appear blue.
1045 mathematical text is set upright contrary to other formula parts.
1048 \begin_layout Subsection*
1052 \begin_layout Standard
1053 Most \SpecialChar LaTeX
1054 -commands for math constructs have the following syntax:
1057 \begin_layout Standard
1062 commandname[optional
1073 \begin_layout Standard
1074 A command always starts with a backslash
1075 \begin_inset Quotes gld
1085 \begin_inset Quotes grd
1098 also omit the associated brackets.
1099 The braces around the
1107 are referred to in this document as \SpecialChar TeX
1109 \begin_inset Index idx
1114 \begin_layout Plain Layout
1115 \begin_inset IndexMacro sortkey
1118 \begin_layout Plain Layout
1131 If you append a left brace to a command name inside a formula,
1133 automatically creates a right \SpecialChar TeX
1135 In all other cases standalone \SpecialChar TeX
1136 braces are created in formulas with the command
1143 Normal braces are created by typing
1149 braces appear red in \SpecialChar LyX
1151 normal braces appear blue.
1153 mode a command is not needed to get \SpecialChar TeX
1156 braces don't appear in the output while normal braces do.
1159 \begin_layout Standard
1160 When commands without arguments,
1161 like commands for symbols,
1162 are entered in \SpecialChar TeX
1164 a space character must
1168 be behind the command to end it.
1169 This space doesn't appear in the output.
1170 When the space should appear in the output,
1171 the space must be followed by a
1172 \change_deleted 177693 1654668848
1174 \change_inserted 177693 1654668851
1177 space in normal text.
1180 \begin_layout Standard
1182 \change_deleted 177693 1654668857
1184 \change_inserted 177693 1654668860
1187 space is inserted with
1188 \change_inserted 232239728 1610908934
1190 \change_deleted 5863208 1612729787
1192 \change_inserted 5863208 1612729774
1196 arg "command-alternatives math-space ; space-insert protected"
1200 \change_deleted 232239728 1610908788
1204 arg "command-alternatives space-insert protected; math-space"
1208 \change_inserted 5863208 1612729766
1209 or with the menu selection
1212 \change_inserted 232239728 1610908897
1213 Insert\SpecialChar menuseparator
1214 Formatting\SpecialChar menuseparator
1216 \change_deleted 177693 1654668863
1218 \change_inserted 177693 1654668975
1220 \change_inserted 232239728 1610908897
1224 \change_inserted 5863208 1612729638
1228 \change_deleted 5863208 1612729640
1236 \begin_layout Subsection*
1237 \begin_inset Newpage newpage
1241 \change_deleted 5863208 1612098922
1245 \change_inserted 5863208 1612100879
1246 of Syntax Used in this Manual
1251 \begin_layout Itemize
1253 \begin_inset space \textvisiblespace{}
1256 denotes a space character to be input
1257 \change_inserted 5863208 1612098935
1263 \begin_layout Itemize
1265 \begin_inset Formula $\to$
1268 denotes the usage of the corresponding arrow key on the keyboard.
1273 key can often be used instead of
1274 \begin_inset Formula $\to$
1278 \begin_inset Formula $\downarrow$
1287 \begin_inset Formula $\leftarrow$
1291 \begin_inset Formula $\uparrow$
1297 \begin_layout Subsection*
1301 \begin_layout Standard
1303 \begin_inset Float table
1310 \begin_layout Plain Layout
1312 \begin_inset Caption Standard
1314 \begin_layout Plain Layout
1315 \begin_inset CommandInset label
1317 name "tab:Available-units"
1329 \begin_layout Plain Layout
1331 \begin_inset Tabular
1332 <lyxtabular version="3" rows="13" columns="2">
1333 <features booktabs="true" tabularvalignment="middle">
1334 <column alignment="center" valignment="top">
1335 <column alignment="center" valignment="top" width="0pt">
1337 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1340 \begin_layout Plain Layout
1346 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1349 \begin_layout Plain Layout
1357 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1360 \begin_layout Plain Layout
1366 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1369 \begin_layout Plain Layout
1377 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1380 \begin_layout Plain Layout
1386 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1389 \begin_layout Plain Layout
1397 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1400 \begin_layout Plain Layout
1406 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1409 \begin_layout Plain Layout
1411 \begin_inset space \thinspace{}
1415 \change_deleted 232239728 1610909338
1417 \change_inserted 232239728 1610909338
1421 \begin_inset space \thinspace{}
1431 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1434 \begin_layout Plain Layout
1440 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1443 \begin_layout Plain Layout
1445 \begin_inset space \thinspace{}
1449 \begin_inset space \thinspace{}
1459 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1462 \begin_layout Plain Layout
1468 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1471 \begin_layout Plain Layout
1473 \begin_inset space \thinspace{}
1477 \begin_inset space \thinspace{}
1487 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1490 \begin_layout Plain Layout
1496 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1499 \begin_layout Plain Layout
1501 \begin_inset space \thinspace{}
1505 \begin_inset space \thinspace{}
1515 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1518 \begin_layout Plain Layout
1524 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1527 \begin_layout Plain Layout
1529 \begin_inset space \thinspace{}
1533 \begin_inset space \thinspace{}
1543 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1546 \begin_layout Plain Layout
1552 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1555 \begin_layout Plain Layout
1557 \begin_inset space \thinspace{}
1561 \begin_inset Formula $\approx$
1565 \begin_inset space \thinspace{}
1575 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1578 \begin_layout Plain Layout
1584 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1587 \begin_layout Plain Layout
1589 \begin_inset space \thinspace{}
1593 \begin_inset space \thinspace{}
1603 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1606 \begin_layout Plain Layout
1612 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1615 \begin_layout Plain Layout
1619 \begin_inset Quotes eld
1625 \begin_inset Quotes erd
1635 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1638 \begin_layout Plain Layout
1644 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1647 \begin_layout Plain Layout
1649 \begin_inset Quotes eld
1657 \begin_inset Quotes erd
1667 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1670 \begin_layout Plain Layout
1676 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1679 \begin_layout Plain Layout
1681 \begin_inset space \thinspace{}
1685 \begin_inset Formula $\nicefrac{1}{18}$
1689 \begin_inset space \thinspace{}
1710 \begin_layout Section
1714 \begin_layout Subsection
1716 \begin_inset Index idx
1721 \begin_layout Plain Layout
1728 \begin_inset Index idx
1733 \begin_layout Plain Layout
1740 \begin_inset Index idx
1745 \begin_layout Plain Layout
1747 \begin_inset IndexMacro see
1750 \begin_layout Plain Layout
1762 \begin_inset Index idx
1767 \begin_layout Plain Layout
1769 \begin_inset IndexMacro see
1772 \begin_layout Plain Layout
1786 \begin_layout Standard
1787 Indices are created with an underscore
1788 \begin_inset Quotes eld
1792 \begin_inset Quotes erd
1795 or via the math toolbar button
1798 arg "math-subscript"
1802 exponents with a caret
1803 \begin_inset Quotes eld
1807 \begin_inset Quotes erd
1810 or via the math toolbar button
1813 arg "math-superscript"
1819 \begin_layout Standard
1821 \begin_inset Tabular
1822 <lyxtabular version="3" rows="4" columns="2">
1823 <features booktabs="true" tabularvalignment="middle">
1824 <column alignment="center" valignment="top" width="0pt">
1825 <column alignment="center" valignment="top" width="0pt">
1827 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1830 \begin_layout Plain Layout
1836 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1839 \begin_layout Plain Layout
1847 <cell alignment="center" valignment="top" usebox="none">
1850 \begin_layout Plain Layout
1856 <cell alignment="center" valignment="top" usebox="none">
1859 \begin_layout Plain Layout
1860 \begin_inset Formula $B_{V}$
1869 <row topspace="1.5mm">
1870 <cell alignment="center" valignment="top" usebox="none">
1873 \begin_layout Plain Layout
1879 <cell alignment="center" valignment="top" usebox="none">
1882 \begin_layout Plain Layout
1883 \begin_inset Formula $B^{V}$
1892 <row topspace="1.5mm">
1893 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1896 \begin_layout Plain Layout
1898 \begin_inset space \textvisiblespace{}
1906 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1909 \begin_layout Plain Layout
1910 \begin_inset Formula $B^{A}$
1926 \begin_layout Standard
1927 As the caret is in some languages an accent,
1928 vowels will be accentuated in this case and not set as exponents
1932 \begin_layout Plain Layout
1933 Depending on the keyboard settings used this can also happen for characters other than vowels.
1939 To get exponents in this case,
1944 after the caret as in the last example.
1947 \begin_layout Subsection
1949 \begin_inset CommandInset label
1951 name "subsec:Fractions"
1956 \begin_inset Index idx
1961 \begin_layout Plain Layout
1970 \begin_layout Standard
1971 Fractions are generated with the command
1978 \begin_inset Index idx
1983 \begin_layout Plain Layout
1985 \begin_inset IndexMacro subentry
1988 \begin_layout Plain Layout
1995 \begin_inset IndexMacro subentry
1998 \begin_layout Plain Layout
2011 or via the math toolbar button
2014 arg "math-insert \\frac"
2018 The font size is adjusted automatically,
2019 depending on whether the fraction is in an inline or display style formula.
2020 With the math toolbar button
2023 arg "math-insert \\frac-square"
2026 you can select different fraction types.
2029 \begin_layout Standard
2037 \begin_inset Index idx
2042 \begin_layout Plain Layout
2044 \begin_inset IndexMacro subentry
2047 \begin_layout Plain Layout
2054 \begin_inset IndexMacro subentry
2057 \begin_layout Plain Layout
2070 a fraction can be created that always has the size of a display style formula.
2078 \begin_inset Index idx
2083 \begin_layout Plain Layout
2085 \begin_inset IndexMacro subentry
2088 \begin_layout Plain Layout
2095 \begin_inset IndexMacro subentry
2098 \begin_layout Plain Layout
2111 the fraction appears always with the size of an inline formula.
2115 \begin_layout Standard
2116 A line with the fraction
2117 \begin_inset Formula $\frac{1}{2}$
2120 that was created with the command
2129 \begin_layout Standard
2130 A line with the fraction
2131 \begin_inset Formula $\dfrac{1}{2}$
2134 that was created with the command
2143 \begin_layout Standard
2145 \begin_inset Tabular
2146 <lyxtabular version="3" rows="4" columns="2">
2147 <features booktabs="true" tabularvalignment="middle">
2148 <column alignment="center" valignment="top" width="0pt">
2149 <column alignment="center" valignment="top" width="0pt">
2151 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2154 \begin_layout Plain Layout
2160 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2163 \begin_layout Plain Layout
2170 <row topspace="1.5mm">
2171 <cell alignment="center" valignment="top" usebox="none">
2174 \begin_layout Plain Layout
2178 \begin_inset space \textvisiblespace{}
2182 \begin_inset Formula $\downarrow$
2190 <cell alignment="center" valignment="top" usebox="none">
2193 \begin_layout Plain Layout
2194 \begin_inset Formula $\frac{A}{B}$
2203 <row topspace="2mm">
2204 <cell alignment="center" valignment="top" usebox="none">
2207 \begin_layout Plain Layout
2211 \begin_inset space \textvisiblespace{}
2215 \begin_inset Formula $\downarrow$
2223 <cell alignment="center" valignment="top" usebox="none">
2226 \begin_layout Plain Layout
2227 \begin_inset Formula $\dfrac{A}{B}$
2236 <row topspace="2mm" bottomspace="1mm">
2237 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2240 \begin_layout Plain Layout
2244 \begin_inset space \textvisiblespace{}
2250 \begin_inset space \textvisiblespace{}
2254 \begin_inset Formula $\downarrow$
2258 \begin_inset Formula $\downarrow\downarrow$
2266 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2269 \begin_layout Plain Layout
2270 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
2286 \begin_layout Standard
2287 \begin_inset VSpace bigskip
2291 \begin_inset Newpage newpage
2294 For nested fractions the command
2301 \begin_inset Index idx
2306 \begin_layout Plain Layout
2308 \begin_inset IndexMacro subentry
2311 \begin_layout Plain Layout
2318 \begin_inset IndexMacro subentry
2321 \begin_layout Plain Layout
2336 \begin_inset VSpace -3mm
2342 \begin_layout Standard
2343 \begin_inset Formula
2345 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2346 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2354 \begin_layout Standard
2355 The command for the example above is:
2358 \begin_layout Standard
2364 \begin_inset space \textvisiblespace{}
2368 \begin_inset Formula $\downarrow$
2374 \begin_inset space \textvisiblespace{}
2380 \begin_inset space \textvisiblespace{}
2384 \begin_inset Formula $\downarrow$
2388 \begin_inset Formula $\downarrow$
2394 \begin_layout Standard
2395 \begin_inset VSpace medskip
2401 \begin_layout Standard
2408 always sets the fraction size to that of a displayed formula,
2409 even when it is part of another fraction.
2412 \begin_layout Standard
2413 It is possible to specify the alignment of the numerator.
2420 is used to left align it,
2434 centers the numerator.
2435 These fractions demonstrate the different alignments:
2438 \begin_layout Standard
2441 \begin_inset Formula
2443 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2451 \begin_layout Standard
2452 \begin_inset Note Greyedout
2455 \begin_layout Plain Layout
2473 are not real \SpecialChar LaTeX
2474 commands but represent the command
2478 cfrac[alignment]{numerator}{denominator}
2481 Therefore you cannot use them in \SpecialChar TeX
2490 \begin_layout Standard
2491 \begin_inset VSpace medskip
2494 It is often advantageous to combine
2507 \begin_inset Formula
2509 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2517 \begin_layout Standard
2518 For inline fractions with a sloped fraction stroke you can use the command
2525 \begin_inset Index idx
2530 \begin_layout Plain Layout
2532 \begin_inset IndexMacro subentry
2535 \begin_layout Plain Layout
2542 \begin_inset IndexMacro subentry
2545 \begin_layout Plain Layout
2560 \begin_inset Formula $\nicefrac{5}{31}$
2570 \begin_inset Index idx
2575 \begin_layout Plain Layout
2577 \begin_inset IndexMacro subentry
2580 \begin_layout Plain Layout
2587 \begin_inset IndexMacro subentry
2590 \begin_layout Plain Layout
2605 \begin_inset Formula $\unitfrac{5}{31}$
2608 There is also the command
2614 which allows you to write a fraction in combination with a number:
2616 \begin_inset Formula $\unitfrac[2]{1}{3}$
2622 \begin_layout Standard
2623 \begin_inset Note Greyedout
2626 \begin_layout Plain Layout
2638 is not a real \SpecialChar LaTeX
2639 command but the command
2640 \begin_inset Newline newline
2647 unitfrac[number]{numerator}{denominator}
2650 Therefore you cannot use it in \SpecialChar TeX
2659 \begin_layout Standard
2660 How to define your own fractions where the fraction stroke can be changed is explained in
2661 \begin_inset CommandInset ref
2663 reference "subsec:Self-defined-Fractions"
2671 \begin_layout Standard
2672 Multiline fractions are explained in
2673 \begin_inset CommandInset ref
2675 reference "subsec:Multiline-Fractions"
2683 \begin_layout Subsection
2685 \begin_inset Index idx
2690 \begin_layout Plain Layout
2699 \begin_layout Standard
2700 Square roots are created with
2707 \begin_inset Index idx
2712 \begin_layout Plain Layout
2714 \begin_inset IndexMacro subentry
2717 \begin_layout Plain Layout
2724 \begin_inset IndexMacro subentry
2727 \begin_layout Plain Layout
2740 or the math toolbar button
2743 arg "math-insert \\sqrt"
2747 all other roots with the command
2754 \begin_inset Index idx
2759 \begin_layout Plain Layout
2761 \begin_inset IndexMacro subentry
2764 \begin_layout Plain Layout
2771 \begin_inset IndexMacro subentry
2774 \begin_layout Plain Layout
2787 or with the math toolbar button
2790 arg "math-insert \\root"
2796 \begin_layout Standard
2798 \begin_inset Tabular
2799 <lyxtabular version="3" rows="3" columns="2">
2800 <features booktabs="true" tabularvalignment="middle">
2801 <column alignment="center" valignment="top" width="0pt">
2802 <column alignment="center" valignment="top" width="0pt">
2804 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2807 \begin_layout Plain Layout
2813 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2816 \begin_layout Plain Layout
2823 <row topspace="1mm">
2824 <cell alignment="center" valignment="top" usebox="none">
2827 \begin_layout Plain Layout
2831 \begin_inset space \textvisiblespace{}
2839 <cell alignment="center" valignment="top" usebox="none">
2842 \begin_layout Plain Layout
2843 \begin_inset Formula $\sqrt{A-B}$
2852 <row topspace="1mm">
2853 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2856 \begin_layout Plain Layout
2860 \begin_inset space \textvisiblespace{}
2864 \begin_inset Formula $\downarrow$
2872 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2875 \begin_layout Plain Layout
2876 \begin_inset Formula $\sqrt[3]{A-B}$
2892 \begin_layout Standard
2893 A square root can also be created with
2899 when the root index field is left empty.
2902 \begin_layout Standard
2903 With certain indices the distance to the root is too small,
2904 like in this formula:
2906 \begin_inset Formula $\sqrt[\beta]{B}$
2910 \begin_inset Newline newline
2914 \begin_inset Formula $\beta$
2926 \begin_inset Index idx
2931 \begin_layout Plain Layout
2933 \begin_inset IndexMacro subentry
2936 \begin_layout Plain Layout
2943 \begin_inset IndexMacro subentry
2946 \begin_layout Plain Layout
2966 \begin_inset Index idx
2971 \begin_layout Plain Layout
2973 \begin_inset IndexMacro subentry
2976 \begin_layout Plain Layout
2983 \begin_inset IndexMacro subentry
2986 \begin_layout Plain Layout
2999 are used with the following scheme:
3002 \begin_layout Standard
3016 \begin_layout Standard
3017 Distance is the number of Big Points (unit bp;
3019 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
3023 that the index should be moved to the left or up,
3025 The commands are written to the index.
3026 This way the command
3027 \begin_inset Newline newline
3037 \begin_inset Formula $\to$
3043 \begin_inset Formula $\to$
3049 \begin_inset space \textvisiblespace{}
3053 \begin_inset Formula $\to$
3057 \begin_inset Newline newline
3062 produces a correct typeset formula:
3064 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
3070 \begin_layout Subsection
3071 Binomial Coefficients
3072 \begin_inset Index idx
3077 \begin_layout Plain Layout
3078 Binomial coefficients
3086 \begin_layout Standard
3087 Binomial coefficients are inserted with the command
3094 \begin_inset Index idx
3099 \begin_layout Plain Layout
3101 \begin_inset IndexMacro subentry
3104 \begin_layout Plain Layout
3111 \begin_inset IndexMacro subentry
3114 \begin_layout Plain Layout
3127 or with the submenu of the math toolbar button
3130 arg "math-insert \\frac-square"
3146 there are the commands
3153 \begin_inset Index idx
3158 \begin_layout Plain Layout
3160 \begin_inset IndexMacro subentry
3163 \begin_layout Plain Layout
3170 \begin_inset IndexMacro subentry
3173 \begin_layout Plain Layout
3193 \begin_inset Index idx
3198 \begin_layout Plain Layout
3200 \begin_inset IndexMacro subentry
3203 \begin_layout Plain Layout
3210 \begin_inset IndexMacro subentry
3213 \begin_layout Plain Layout
3227 For other brackets around binomial coefficients there are the commands
3234 \begin_inset Index idx
3239 \begin_layout Plain Layout
3241 \begin_inset IndexMacro subentry
3244 \begin_layout Plain Layout
3251 \begin_inset IndexMacro subentry
3254 \begin_layout Plain Layout
3274 \begin_inset Index idx
3279 \begin_layout Plain Layout
3281 \begin_inset IndexMacro subentry
3284 \begin_layout Plain Layout
3291 \begin_inset IndexMacro subentry
3294 \begin_layout Plain Layout
3310 \begin_layout Standard
3312 \begin_inset Tabular
3313 <lyxtabular version="3" rows="6" columns="2">
3314 <features booktabs="true" tabularvalignment="middle">
3315 <column alignment="center" valignment="top" width="0pt">
3316 <column alignment="center" valignment="top" width="0pt">
3318 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3321 \begin_layout Plain Layout
3327 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3330 \begin_layout Plain Layout
3337 <row topspace="1mm">
3338 <cell alignment="center" valignment="top" usebox="none">
3341 \begin_layout Plain Layout
3345 \begin_inset space \textvisiblespace{}
3349 \begin_inset Formula $\downarrow$
3357 <cell alignment="center" valignment="top" usebox="none">
3360 \begin_layout Plain Layout
3361 \begin_inset Formula $\binom{A}{B}$
3370 <row topspace="2mm">
3371 <cell alignment="center" valignment="top" usebox="none">
3374 \begin_layout Plain Layout
3378 \begin_inset space \textvisiblespace{}
3382 \begin_inset Formula $\downarrow$
3390 <cell alignment="center" valignment="top" usebox="none">
3393 \begin_layout Plain Layout
3394 \begin_inset Formula $\dbinom{A}{B}$
3403 <row topspace="2mm" bottomspace="0.5mm">
3404 <cell alignment="center" valignment="top" usebox="none">
3407 \begin_layout Plain Layout
3411 \begin_inset space \textvisiblespace{}
3415 \begin_inset Formula $\downarrow$
3423 <cell alignment="center" valignment="top" usebox="none">
3426 \begin_layout Plain Layout
3427 \begin_inset Formula $\tbinom{A}{B}$
3436 <row topspace="1mm">
3437 <cell alignment="center" valignment="top" topline="true" usebox="none">
3440 \begin_layout Plain Layout
3444 \begin_inset space \textvisiblespace{}
3448 \begin_inset Formula $\downarrow$
3456 <cell alignment="center" valignment="top" topline="true" usebox="none">
3459 \begin_layout Plain Layout
3460 \begin_inset Formula ${A \brack B}$
3469 <row topspace="2mm" bottomspace="0.5mm">
3470 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3473 \begin_layout Plain Layout
3477 \begin_inset space \textvisiblespace{}
3481 \begin_inset Formula $\downarrow$
3489 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3492 \begin_layout Plain Layout
3493 \begin_inset Formula ${A \brace B}$
3509 \begin_layout Subsection
3510 Case Differentiations
3511 \begin_inset Index idx
3516 \begin_layout Plain Layout
3517 Case differentiations
3525 \begin_layout Standard
3527 \begin_inset Tabular
3528 <lyxtabular version="3" rows="3" columns="2">
3529 <features booktabs="true" tabularvalignment="middle">
3530 <column alignment="center" valignment="top" width="0pt">
3531 <column alignment="center" valignment="top" width="0pt">
3533 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3536 \begin_layout Plain Layout
3542 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3545 \begin_layout Plain Layout
3553 <cell alignment="center" valignment="top" usebox="none">
3556 \begin_layout Plain Layout
3560 \begin_inset space \textvisiblespace{}
3564 \begin_inset Formula $\to$
3568 \begin_inset Index idx
3573 \begin_layout Plain Layout
3575 \begin_inset IndexMacro subentry
3578 \begin_layout Plain Layout
3585 \begin_inset IndexMacro subentry
3588 \begin_layout Plain Layout
3606 <cell alignment="center" valignment="top" usebox="none">
3609 \begin_layout Plain Layout
3610 \begin_inset Formula $\begin{cases}
3620 <row topspace="1.5mm">
3621 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3624 \begin_layout Plain Layout
3628 \begin_inset space \textvisiblespace{}
3634 arg "newline-insert newline"
3642 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3645 \begin_layout Plain Layout
3646 \begin_inset Formula $\begin{cases}
3647 A & \textrm{for }x>0\\
3648 B & \textrm{for }x=0
3665 \begin_layout Standard
3672 or pressing the math toolbar button
3675 arg "math-insert \\cases"
3678 you can create new lines with the shortcut
3681 arg "newline-insert newline"
3684 or the table toolbar button
3687 arg "tabular-feature append-row"
3693 \begin_layout Standard
3700 is also available via the menu
3702 Insert\SpecialChar menuseparator
3703 Math\SpecialChar menuseparator
3709 \begin_layout Subsection
3711 \begin_inset Index idx
3716 \begin_layout Plain Layout
3725 \begin_layout Standard
3733 \begin_inset Index idx
3738 \begin_layout Plain Layout
3740 \begin_inset IndexMacro subentry
3743 \begin_layout Plain Layout
3750 \begin_inset IndexMacro subentry
3753 \begin_layout Plain Layout
3766 every character can be displayed canceled.
3767 The characters are quasi accentuated by a slash.
3770 \begin_layout Standard
3772 \begin_inset Tabular
3773 <lyxtabular version="3" rows="4" columns="2">
3774 <features booktabs="true" tabularvalignment="middle">
3775 <column alignment="center" valignment="top" width="0pt">
3776 <column alignment="center" valignment="top" width="0pt">
3778 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3781 \begin_layout Plain Layout
3787 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3790 \begin_layout Plain Layout
3798 <cell alignment="center" valignment="top" usebox="none">
3801 \begin_layout Plain Layout
3809 <cell alignment="center" valignment="top" usebox="none">
3812 \begin_layout Plain Layout
3813 \begin_inset Formula $\not=$
3823 <cell alignment="center" valignment="top" usebox="none">
3826 \begin_layout Plain Layout
3836 <cell alignment="center" valignment="top" usebox="none">
3839 \begin_layout Plain Layout
3840 \begin_inset Formula $\not\le$
3850 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3853 \begin_layout Plain Layout
3863 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3866 \begin_layout Plain Layout
3867 \begin_inset Formula $\not\parallel$
3883 \begin_layout Standard
3884 The last example shows that not all negations look good.
3885 Therefore there are special commands for some negations (see
3886 \begin_inset CommandInset ref
3888 reference "subsec:Mathematical-Symbols"
3894 \begin_inset CommandInset ref
3896 reference "sec:Relations"
3904 \begin_layout Subsection
3906 \begin_inset CommandInset label
3908 name "subsec:Placeholders"
3913 \begin_inset Index idx
3918 \begin_layout Plain Layout
3925 \begin_inset Index idx
3930 \begin_layout Plain Layout
3932 \begin_inset IndexMacro subentry
3935 \begin_layout Plain Layout
3947 \begin_inset Index idx
3952 \begin_layout Plain Layout
3954 \begin_inset IndexMacro see
3957 \begin_layout Plain Layout
3971 \begin_layout Standard
3973 \begin_inset space \thinspace{}
3977 \begin_inset space \space{}
3984 \begin_layout Plain Layout
3985 Typesetting isotopes and chemical symbols is described in
3986 \begin_inset CommandInset ref
3988 reference "subsec:Chemical-Symbols-and"
3998 the following problem occurs:
4001 \begin_layout Standard
4003 \begin_inset Tabular
4004 <lyxtabular version="3" rows="2" columns="2">
4005 <features booktabs="true" tabularvalignment="middle">
4006 <column alignment="center" valignment="top" width="0pt">
4007 <column alignment="center" valignment="top" width="0pt">
4009 <cell alignment="center" valignment="top" usebox="none">
4012 \begin_layout Plain Layout
4013 Indices created with sub- and superscripts:
4018 <cell alignment="center" valignment="top" usebox="none">
4021 \begin_layout Plain Layout
4022 \begin_inset Formula $_{9}^{19}\mathrm{F}$
4031 <row topspace="1.5mm">
4032 <cell alignment="center" valignment="top" usebox="none">
4035 \begin_layout Plain Layout
4041 <cell alignment="center" valignment="top" usebox="none">
4044 \begin_layout Plain Layout
4045 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
4061 \begin_layout Standard
4062 The shorter index is placed by default below or above the first character of the longer index.
4063 This is corrected using the command
4070 \begin_inset Index idx
4075 \begin_layout Plain Layout
4077 \begin_inset IndexMacro subentry
4080 \begin_layout Plain Layout
4087 \begin_inset IndexMacro subentry
4090 \begin_layout Plain Layout
4103 or the math toolbar button
4104 \begin_inset space \thinspace{}
4111 \begin_layout Plain Layout
4112 Found in the submenu of the toolbar button
4115 arg "math-insert \\space"
4129 to create one or more phantom characters.
4130 When inserting phantom characters a small blue box appears that is superposed with two red arrows.
4131 The arrows indicate the width and height of the box to be created as a placeholder.
4132 Phantom characters are placeholders with the same character size.
4135 \begin_layout Standard
4137 \begin_inset Tabular
4138 <lyxtabular version="3" rows="4" columns="2">
4139 <features booktabs="true" tabularvalignment="middle">
4140 <column alignment="center" valignment="top" width="0pt">
4141 <column alignment="center" valignment="top" width="0pt">
4143 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4146 \begin_layout Plain Layout
4152 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4155 \begin_layout Plain Layout
4162 <row topspace="1.5mm">
4163 <cell alignment="center" valignment="top" usebox="none">
4166 \begin_layout Plain Layout
4168 \begin_inset space \textvisiblespace{}
4174 \begin_inset space \textvisiblespace{}
4178 \begin_inset Formula $\to$
4182 \begin_inset space \textvisiblespace{}
4186 \change_inserted 5863208 1612176450
4190 \begin_inset space \textvisiblespace{}
4200 <cell alignment="center" valignment="top" usebox="none">
4203 \begin_layout Plain Layout
4204 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
4213 <row topspace="1.5mm" bottomspace="0.5mm">
4214 <cell alignment="center" valignment="top" usebox="none">
4217 \begin_layout Plain Layout
4219 \begin_inset space \textvisiblespace{}
4225 \begin_inset space \textvisiblespace{}
4229 \begin_inset Formula $\to$
4233 \begin_inset space \textvisiblespace{}
4237 \change_inserted 5863208 1612707447
4241 \begin_inset space \textvisiblespace{}
4251 <cell alignment="center" valignment="top" usebox="none">
4254 \begin_layout Plain Layout
4255 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
4264 <row topspace="1.5mm" bottomspace="0.5mm">
4265 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4268 \begin_layout Plain Layout
4272 \change_inserted 5863208 1612707546
4274 \begin_inset space \textvisiblespace{}
4280 \change_deleted 5863208 1612707563
4282 \begin_inset space \textvisiblespace{}
4290 \begin_inset space \textvisiblespace{}
4294 \begin_inset Formula $\to$
4298 \begin_inset space \textvisiblespace{}
4306 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4309 \begin_layout Plain Layout
4310 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
4326 \begin_layout Standard
4327 Furthermore there are the commands
4334 \begin_inset Index idx
4339 \begin_layout Plain Layout
4341 \begin_inset IndexMacro subentry
4344 \begin_layout Plain Layout
4351 \begin_inset IndexMacro subentry
4354 \begin_layout Plain Layout
4380 \begin_inset Index idx
4385 \begin_layout Plain Layout
4387 \begin_inset IndexMacro subentry
4390 \begin_layout Plain Layout
4397 \begin_inset IndexMacro subentry
4400 \begin_layout Plain Layout
4426 creates only space for the maximal height of the characters in the box but not for its width.
4433 creates only space for the width of the box content.
4434 Therefore the boxes of both commands have only one red arrow.
4437 \begin_layout Standard
4438 For example the command
4443 \begin_inset space \textvisiblespace{}
4450 creates space for the height of the integral sign,
4454 \begin_layout Plain Layout
4461 creates an integral sign,
4463 \begin_inset CommandInset ref
4465 reference "subsec:Big-Operators"
4475 because this is the larger character.
4476 An example application is in
4477 \begin_inset CommandInset ref
4479 reference "subsec:Multiline-Brackets"
4487 \begin_layout Standard
4488 Placeholders can also be used for text when they are inserted via the menu
4490 Insert\SpecialChar menuseparator
4491 Formatting\SpecialChar menuseparator
4497 \begin_layout Standard
4499 \begin_inset Newline newline
4503 \begin_inset Phantom Phantom
4506 \begin_layout Plain Layout
4515 \begin_layout Subsection
4517 \begin_inset Index idx
4522 \begin_layout Plain Layout
4529 \begin_inset Index idx
4534 \begin_layout Plain Layout
4536 \begin_inset IndexMacro subentry
4539 \begin_layout Plain Layout
4553 \begin_layout Standard
4555 \begin_inset Tabular
4556 <lyxtabular version="3" rows="4" columns="2">
4557 <features booktabs="true" tabularvalignment="middle">
4558 <column alignment="center" valignment="top" width="0pt">
4559 <column alignment="center" valignment="top" width="0pt">
4561 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4564 \begin_layout Plain Layout
4570 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4573 \begin_layout Plain Layout
4580 <row topspace="2mm">
4581 <cell alignment="center" valignment="top" usebox="none">
4584 \begin_layout Plain Layout
4588 \begin_inset space \textvisiblespace{}
4592 \begin_inset Index idx
4597 \begin_layout Plain Layout
4599 \begin_inset IndexMacro subentry
4602 \begin_layout Plain Layout
4609 \begin_inset IndexMacro subentry
4612 \begin_layout Plain Layout
4630 <cell alignment="center" valignment="top" usebox="none">
4633 \begin_layout Plain Layout
4634 \begin_inset Formula $\overline{A+B}$
4643 <row bottomspace="1mm">
4644 <cell alignment="center" valignment="top" usebox="none">
4647 \begin_layout Plain Layout
4651 \begin_inset space \textvisiblespace{}
4655 \begin_inset Index idx
4660 \begin_layout Plain Layout
4662 \begin_inset IndexMacro subentry
4665 \begin_layout Plain Layout
4672 \begin_inset IndexMacro subentry
4675 \begin_layout Plain Layout
4693 <cell alignment="center" valignment="top" usebox="none">
4696 \begin_layout Plain Layout
4697 \begin_inset Formula $\underline{A+B}$
4706 <row topspace="2mm" bottomspace="1mm">
4707 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4710 \begin_layout Plain Layout
4714 \begin_inset space \textvisiblespace{}
4720 \begin_inset space \textvisiblespace{}
4728 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4731 \begin_layout Plain Layout
4732 \begin_inset Formula $\overline{\underline{A+B}}$
4748 \begin_layout Standard
4749 In the last example it doesn't matter if
4764 \begin_layout Standard
4765 To double underline use
4772 \change_deleted 5863208 1612707977
4774 \change_inserted 5863208 1612707993
4775 (or as many times you want).
4780 \begin_layout Standard
4782 \change_deleted 232239728 1610990247
4783 It is possible to place up to 6 lines above or below characters.
4784 \change_deleted 5863208 1612729848
4786 \begin_inset Note Note
4789 \begin_layout Plain Layout
4791 \change_inserted 232239728 1610990434
4792 I put 30 over and under lines in my test so I don't know what the actual maximum is,
4793 but it's greater than 6.
4803 \begin_layout Standard
4804 \begin_inset VSpace bigskip
4807 Custom lines can be created using the command
4814 \begin_inset Index idx
4819 \begin_layout Plain Layout
4821 \begin_inset IndexMacro subentry
4824 \begin_layout Plain Layout
4831 \begin_inset IndexMacro subentry
4834 \begin_layout Plain Layout
4847 which has the following scheme:
4850 \begin_layout Standard
4855 rule[vertical offset]{length}{thickness}
4858 \begin_layout Standard
4859 The optional vertical offset shifts the line upwards (or downwards,
4860 when the value is negative).
4862 \begin_inset CommandInset ref
4864 reference "tab:Available-units"
4869 can be used for the values.
4870 Here are two example lines created with the commands
4871 \begin_inset Newline newline
4878 rule[-2ex]{3cm}{2pt}
4889 \begin_layout Standard
4891 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4897 \begin_layout Standard
4904 can also be used for text when a line is inserted via the menu
4906 Insert\SpecialChar menuseparator
4907 Formatting\SpecialChar menuseparator
4909 \begin_inset space ~
4917 \begin_layout Standard
4919 \begin_inset CommandInset line
4930 \begin_layout Subsection
4932 \begin_inset CommandInset label
4934 name "subsec:Ellipses"
4939 \begin_inset Index idx
4944 \begin_layout Plain Layout
4953 \begin_layout Standard
4954 There are different types of ellipses available.
4958 \begin_layout Plain Layout
4959 In the math toolbar in the submenu of the button
4962 arg "math-insert \\ldots"
4971 dots at the baseline are used (
4978 \begin_inset Index idx
4983 \begin_layout Plain Layout
4985 \begin_inset IndexMacro subentry
4988 \begin_layout Plain Layout
4995 \begin_inset IndexMacro subentry
4998 \begin_layout Plain Layout
5012 while for operations,
5013 dots are needed that are on the same height as the operators (
5020 \begin_inset Index idx
5025 \begin_layout Plain Layout
5027 \begin_inset IndexMacro subentry
5030 \begin_layout Plain Layout
5037 \begin_inset IndexMacro subentry
5040 \begin_layout Plain Layout
5054 When using the command
5061 \begin_inset Index idx
5066 \begin_layout Plain Layout
5068 \begin_inset IndexMacro subentry
5071 \begin_layout Plain Layout
5078 \begin_inset IndexMacro subentry
5081 \begin_layout Plain Layout
5096 decides on the basis of the next character what type is used.
5099 \begin_layout Standard
5101 \begin_inset Tabular
5102 <lyxtabular version="3" rows="9" columns="2">
5103 <features booktabs="true" tabularvalignment="middle">
5104 <column alignment="center" valignment="top" width="0pt">
5105 <column alignment="center" valignment="top" width="0pt">
5107 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5110 \begin_layout Plain Layout
5116 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5119 \begin_layout Plain Layout
5127 <cell alignment="center" valignment="top" usebox="none">
5130 \begin_layout Plain Layout
5132 \begin_inset space \textvisiblespace{}
5138 \begin_inset space \textvisiblespace{}
5146 <cell alignment="center" valignment="top" usebox="none">
5149 \begin_layout Plain Layout
5150 \begin_inset Formula $A_{1},\dots,A_{n}$
5160 <cell alignment="center" valignment="top" usebox="none">
5163 \begin_layout Plain Layout
5165 \begin_inset space \textvisiblespace{}
5171 \begin_inset space \textvisiblespace{}
5179 <cell alignment="center" valignment="top" usebox="none">
5182 \begin_layout Plain Layout
5183 \begin_inset Formula $A_{1}+\dots+A_{n}$
5193 <cell alignment="center" valignment="top" usebox="none">
5196 \begin_layout Plain Layout
5198 \begin_inset space \textvisiblespace{}
5204 \begin_inset space \textvisiblespace{}
5212 <cell alignment="center" valignment="top" usebox="none">
5215 \begin_layout Plain Layout
5216 \begin_inset Formula $A_{1},\ldots,A_{n}$
5226 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5229 \begin_layout Plain Layout
5231 \begin_inset space \textvisiblespace{}
5237 \begin_inset space \textvisiblespace{}
5245 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5248 \begin_layout Plain Layout
5249 \begin_inset Formula $A_{1}+\cdots+A_{n}$
5259 <cell alignment="center" valignment="top" usebox="none">
5262 \begin_layout Plain Layout
5270 <cell alignment="center" valignment="top" usebox="none">
5273 \begin_layout Plain Layout
5274 \begin_inset Formula $\vdots$
5284 <cell alignment="center" valignment="top" usebox="none">
5287 \begin_layout Plain Layout
5295 <cell alignment="center" valignment="top" usebox="none">
5298 \begin_layout Plain Layout
5299 \begin_inset Formula $\ddots$
5309 <cell alignment="center" valignment="top" usebox="none">
5312 \begin_layout Plain Layout
5320 <cell alignment="center" valignment="top" usebox="none">
5323 \begin_layout Plain Layout
5324 \begin_inset Formula $\iddots$
5334 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5337 \begin_layout Plain Layout
5339 \begin_inset space \thinspace{}
5342 matrix with the different dots
5347 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5350 \begin_layout Plain Layout
5351 \begin_inset Formula $\begin{array}{ccc}
5352 A_{11} & \cdots & A_{1m}\\
5353 \vdots & \ddots & \vdots\\
5354 A_{n1} & \cdots & A_{nm}
5371 \begin_layout Standard
5372 The ellipses available in menu
5374 Insert\SpecialChar menuseparator
5376 \begin_inset space ~
5390 \begin_layout Standard
5391 \begin_inset VSpace medskip
5403 Use mathdots package (automatically)
5405 must be set in the document settings under
5408 \begin_inset space ~
5414 \begin_inset Newline newline
5419 Use mathdots package
5421 will improve the appearance of all dots in the documents if their font style or size is not the default.
5424 \begin_layout Standard
5425 \begin_inset VSpace medskip
5428 Specially for matrices there are ellipses that span over several columns.
5429 They are created with the command
5436 \begin_inset Index idx
5441 \begin_layout Plain Layout
5443 \begin_inset IndexMacro subentry
5446 \begin_layout Plain Layout
5453 \begin_inset IndexMacro subentry
5456 \begin_layout Plain Layout
5469 and have the following scheme
5470 \change_inserted 5863208 1612709418
5482 \begin_inset space ~
5492 \begin_layout Standard
5497 hdotsfor[distance]{number of columns}
5500 \begin_layout Standard
5501 The number of columns specifies how many columns should be spanned.
5502 Distance is a factor for the distance between the dots.
5505 \begin_layout Standard
5506 In the following matrix the command
5512 was inserted in the first box of the second line to get an ellipsis with a dot distance twice as long as with the command
5519 \begin_inset Formula
5521 \left(\begin{array}{cccc}
5530 Note that the matrix fields that should be spanned must be empty,
5531 otherwise you get \SpecialChar LaTeX
5535 \begin_layout Standard
5536 \begin_inset VSpace bigskip
5539 Furthermore you can fill with the command
5546 \begin_inset Index idx
5551 \begin_layout Plain Layout
5553 \begin_inset IndexMacro subentry
5556 \begin_layout Plain Layout
5563 \begin_inset IndexMacro subentry
5566 \begin_layout Plain Layout
5579 the rest of a line with dots.
5580 The effect of these commands is the same as with
5588 \begin_inset CommandInset ref
5590 reference "subsec:Variable-Space"
5598 \begin_layout Standard
5599 For example the command
5604 \begin_inset space \textvisiblespace{}
5612 \begin_layout Standard
5613 \begin_inset Formula $A\dotfill B$
5619 \begin_layout Standard
5626 there is for a line the command
5633 \begin_inset Index idx
5638 \begin_layout Plain Layout
5640 \begin_inset IndexMacro subentry
5643 \begin_layout Plain Layout
5650 \begin_inset IndexMacro subentry
5653 \begin_layout Plain Layout
5669 \begin_layout Standard
5670 \begin_inset Formula $A\hrulefill B$
5676 \begin_layout Standard
5677 To use the commands for text,
5678 they have to be inserted in \SpecialChar TeX
5682 \begin_layout Section
5684 \begin_inset CommandInset label
5691 \begin_inset Index idx
5696 \begin_layout Plain Layout
5705 \begin_layout Standard
5706 Matrices can be inserted via the math toolbar button
5709 arg "dialog-show mathmatrix"
5714 Insert\SpecialChar menuseparator
5715 Math\SpecialChar menuseparator
5719 In the matrix dialog you can specify the number of columns and rows,
5720 the alignment and the decoration.
5721 The vertical alignment is only of importance for matrices in inline formulas:
5724 \begin_layout Standard
5725 The first matrix is top
5726 \begin_inset Formula $\begin{array}[t]{cccc}
5735 \begin_inset Formula $\begin{array}{cccc}
5742 and the third bottom
5743 \begin_inset Formula $\begin{array}[b]{cccc}
5753 \begin_layout Standard
5754 The horizontal alignment specifies how the column entries should be aligned.
5755 It is set by entering a letter for every column.
5760 denotes left aligned,
5770 To create for example a 4
5775 \begin_inset space ~
5778 matrix where the first column is left aligned,
5779 the second and third are centered and the last one is right aligned,
5780 one enters for the horizontal alignment
5785 Normally in a matrix all columns are centered,
5786 therefore the default for every column is a
5793 \begin_layout Standard
5794 Horizontal alignment:
5797 \begin_layout Standard
5804 \begin_inset Formula $\begin{array}{lll}
5818 \begin_inset Formula $\begin{array}{ccc}
5832 \begin_inset Formula $\begin{array}{rrr}
5842 \begin_layout Standard
5843 To subsequently add or delete rows and columns,
5844 the math toolbar buttons
5847 arg "tabular-feature append-row"
5854 arg "tabular-feature delete-row"
5859 \begin_inset space \thinspace{}
5865 Edit\SpecialChar menuseparator
5869 New rows can also be created with
5872 arg "newline-insert newline"
5878 \begin_layout Standard
5879 \begin_inset VSpace bigskip
5883 \change_deleted 47243155 1563226130
5885 \change_deleted -563046850 1563190969
5889 \change_inserted -563046850 1563190971
5895 \change_deleted -563046850 1563192602
5897 \change_inserted -563046850 1563192607
5900 parentheses in the selected style around the matrix
5901 \change_inserted -563046850 1563192780
5907 suitable for an inline matrix like this one
5908 \begin_inset Formula $\bigl(\begin{smallmatrix}0 & \textrm{-}\mathrm{i}\\
5910 \end{smallmatrix}\bigr)$
5917 \change_inserted -563046850 1563192943
5918 Here the parentheses have been added manually using commands
5931 \begin_layout Standard
5933 \change_deleted -563046850 1563192735
5938 \change_deleted -563046850 1563192971
5941 be created with the commands
5948 \begin_inset Index idx
5953 \begin_layout Plain Layout
5955 \begin_inset IndexMacro subentry
5958 \begin_layout Plain Layout
5965 \begin_inset IndexMacro subentry
5968 \begin_layout Plain Layout
5988 \begin_inset Index idx
5993 \begin_layout Plain Layout
5995 \begin_inset IndexMacro subentry
5998 \begin_layout Plain Layout
6005 \begin_inset IndexMacro subentry
6008 \begin_layout Plain Layout
6024 \begin_inset space ~
6031 \begin_inset CommandInset ref
6033 reference "subsec:Automatic-Bracket-Size"
6039 or by using the following commands:
6040 \begin_inset VSpace medskip
6046 \begin_layout Standard
6047 \begin_inset space \hfill{}
6051 \begin_inset Tabular
6052 <lyxtabular version="3" rows="4" columns="2">
6053 <features booktabs="true" tabularvalignment="middle">
6054 <column alignment="center" valignment="top" width="0pt">
6055 <column alignment="center" valignment="top">
6057 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6060 \begin_layout Plain Layout
6066 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6069 \begin_layout Plain Layout
6076 <row topspace="1.5mm">
6077 <cell alignment="center" valignment="top" usebox="none">
6080 \begin_layout Plain Layout
6084 \begin_inset space \textvisiblespace{}
6092 \begin_inset space \thinspace{}
6100 <cell alignment="center" valignment="top" usebox="none">
6103 \begin_layout Plain Layout
6104 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
6105 0 & \textrm{-}\mathrm{i}\\
6107 \end{array}\end{bmatrix}$
6116 <row topspace="1.5mm" bottomspace="0.5mm">
6117 <cell alignment="center" valignment="top" usebox="none">
6120 \begin_layout Plain Layout
6124 \begin_inset space \textvisiblespace{}
6132 \begin_inset space \thinspace{}
6140 <cell alignment="center" valignment="top" usebox="none">
6143 \begin_layout Plain Layout
6144 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
6145 0 & \textrm{-}\mathrm{i}\\
6147 \end{array}\end{Bmatrix}$
6157 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6160 \begin_layout Plain Layout
6164 \begin_inset space \textvisiblespace{}
6172 \begin_inset space \thinspace{}
6180 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6183 \begin_layout Plain Layout
6184 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
6185 0 & \textrm{-}\mathrm{i}\\
6187 \end{array}\end{pmatrix}$
6201 \begin_inset space \hfill{}
6205 \begin_inset Tabular
6206 <lyxtabular version="3" rows="4" columns="2">
6207 <features booktabs="true" tabularvalignment="middle">
6208 <column alignment="center" valignment="top" width="0pt">
6209 <column alignment="center" valignment="top">
6211 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6214 \begin_layout Plain Layout
6220 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6223 \begin_layout Plain Layout
6230 <row topspace="1.5mm">
6231 <cell alignment="center" valignment="top" usebox="none">
6234 \begin_layout Plain Layout
6238 \begin_inset space \textvisiblespace{}
6246 \begin_inset space \thinspace{}
6254 <cell alignment="center" valignment="top" usebox="none">
6257 \begin_layout Plain Layout
6258 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
6259 0 & \textrm{-}\mathrm{i}\\
6261 \end{array}\end{vmatrix}$
6270 <row topspace="1.5mm" bottomspace="0.5mm">
6271 <cell alignment="center" valignment="top" usebox="none">
6274 \begin_layout Plain Layout
6278 \begin_inset space \textvisiblespace{}
6286 \begin_inset space \thinspace{}
6294 <cell alignment="center" valignment="top" usebox="none">
6297 \begin_layout Plain Layout
6298 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
6299 0 & \textrm{-}\mathrm{i}\\
6301 \end{array}\end{Vmatrix}$
6311 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6314 \begin_layout Plain Layout
6318 \begin_inset space \textvisiblespace{}
6326 \begin_inset space \thinspace{}
6334 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6337 \begin_layout Plain Layout
6338 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
6339 0 & \textrm{-}\mathrm{i}\\
6341 \end{array}\end{matrix}$
6355 \begin_inset space \hfill{}
6361 \begin_layout Standard
6362 \begin_inset VSpace medskip
6366 \begin_inset space \thinspace{}
6370 \begin_inset space \space{}
6380 a blue box appears between two vertical lines where the matrix is inserted.
6381 \begin_inset Newline newline
6384 Note that decorated matrices ignore the vertical alignment.
6387 \begin_layout Standard
6388 \begin_inset VSpace bigskip
6391 As all multiline formulas are matrices,
6399 \begin_inset Index idx
6404 \begin_layout Plain Layout
6406 \begin_inset IndexMacro subentry
6409 \begin_layout Plain Layout
6416 \begin_inset IndexMacro subentry
6419 \begin_layout Plain Layout
6432 that is described in
6433 \begin_inset CommandInset ref
6435 reference "subsec:Column-Separation"
6440 can also be used to change the column separation of matrices.
6443 \begin_layout Standard
6444 To change the row separation,
6452 \begin_inset Index idx
6457 \begin_layout Plain Layout
6459 \begin_inset IndexMacro subentry
6462 \begin_layout Plain Layout
6469 \begin_inset IndexMacro subentry
6472 \begin_layout Plain Layout
6488 \begin_layout Standard
6495 arraystretch}{stretch factor}
6496 \begin_inset Index idx
6501 \begin_layout Plain Layout
6503 \begin_inset IndexMacro subentry
6506 \begin_layout Plain Layout
6513 \begin_inset IndexMacro subentry
6516 \begin_layout Plain Layout
6532 \begin_layout Standard
6539 assigns the stretch factor to the predefined command
6546 For example to double the row separation,
6547 use a stretch factor of 2.
6548 This is then used for all following matrices.
6549 To restore the original separation,
6550 assign a stretch factor of 1 to
6559 \begin_layout Standard
6561 \change_inserted 47243155 1563226178
6562 Small inline matrices can also be obtained using
6563 \change_deleted 47243155 1563226182
6564 To set matrices into a text line,
6574 \begin_inset Index idx
6579 \begin_layout Plain Layout
6581 \begin_inset IndexMacro subentry
6584 \begin_layout Plain Layout
6591 \begin_inset IndexMacro subentry
6594 \begin_layout Plain Layout
6608 \change_deleted 47243155 1563226186
6612 When it is inserted in a line a blue box with two dashed lines appears.
6613 Adjust the matrix rows and columns as desired.
6616 \begin_layout Standard
6618 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
6620 \end{smallmatrix}\right)$
6624 \change_inserted 47243155 1563226243
6625 with automatic delimiters around it
6630 \begin_layout Section
6631 Brackets and Delimiters
6632 \begin_inset Index idx
6637 \begin_layout Plain Layout
6644 \begin_inset Index idx
6649 \begin_layout Plain Layout
6658 \begin_layout Subsection
6659 Vertical Brackets and Delimiters
6660 \begin_inset Index idx
6665 \begin_layout Plain Layout
6667 \begin_inset IndexMacro subentry
6670 \begin_layout Plain Layout
6684 \begin_layout Standard
6685 \begin_inset space \hfill{}
6689 \begin_inset Tabular
6690 <lyxtabular version="3" rows="9" columns="2">
6691 <features booktabs="true" tabularvalignment="middle">
6692 <column alignment="center" valignment="top" width="0pt">
6693 <column alignment="center" valignment="top" width="0pt">
6695 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6698 \begin_layout Plain Layout
6704 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6707 \begin_layout Plain Layout
6715 <cell alignment="center" valignment="top" usebox="none">
6718 \begin_layout Plain Layout
6724 <cell alignment="center" valignment="top" usebox="none">
6727 \begin_layout Plain Layout
6728 \begin_inset Formula $($
6738 <cell alignment="center" valignment="top" usebox="none">
6741 \begin_layout Plain Layout
6747 <cell alignment="center" valignment="top" usebox="none">
6750 \begin_layout Plain Layout
6751 \begin_inset Formula $\{$
6761 <cell alignment="center" valignment="top" usebox="none">
6764 \begin_layout Plain Layout
6770 <cell alignment="center" valignment="top" usebox="none">
6773 \begin_layout Plain Layout
6774 \begin_inset Formula $[$
6784 <cell alignment="center" valignment="top" usebox="none">
6787 \begin_layout Plain Layout
6795 <cell alignment="center" valignment="top" usebox="none">
6798 \begin_layout Plain Layout
6799 \begin_inset Formula $\langle$
6809 <cell alignment="center" valignment="top" usebox="none">
6812 \begin_layout Plain Layout
6820 <cell alignment="center" valignment="top" usebox="none">
6823 \begin_layout Plain Layout
6824 \begin_inset Formula $\lceil$
6834 <cell alignment="center" valignment="top" usebox="none">
6837 \begin_layout Plain Layout
6845 <cell alignment="center" valignment="top" usebox="none">
6848 \begin_layout Plain Layout
6849 \begin_inset Formula $\lfloor$
6859 <cell alignment="center" valignment="top" usebox="none">
6862 \begin_layout Plain Layout
6868 <cell alignment="center" valignment="top" usebox="none">
6871 \begin_layout Plain Layout
6872 \begin_inset Formula $/$
6882 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6885 \begin_layout Plain Layout
6891 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6894 \begin_layout Plain Layout
6895 \begin_inset Formula $|$
6909 \begin_inset space \hfill{}
6913 \begin_inset Tabular
6914 <lyxtabular version="3" rows="9" columns="2">
6915 <features booktabs="true" tabularvalignment="middle">
6916 <column alignment="center" valignment="top" width="0pt">
6917 <column alignment="center" valignment="top" width="0pt">
6919 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6922 \begin_layout Plain Layout
6928 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6931 \begin_layout Plain Layout
6939 <cell alignment="center" valignment="top" usebox="none">
6942 \begin_layout Plain Layout
6948 <cell alignment="center" valignment="top" usebox="none">
6951 \begin_layout Plain Layout
6952 \begin_inset Formula $)$
6962 <cell alignment="center" valignment="top" usebox="none">
6965 \begin_layout Plain Layout
6971 <cell alignment="center" valignment="top" usebox="none">
6974 \begin_layout Plain Layout
6975 \begin_inset Formula $\}$
6985 <cell alignment="center" valignment="top" usebox="none">
6988 \begin_layout Plain Layout
6994 <cell alignment="center" valignment="top" usebox="none">
6997 \begin_layout Plain Layout
6998 \begin_inset Formula $]$
7008 <cell alignment="center" valignment="top" usebox="none">
7011 \begin_layout Plain Layout
7019 <cell alignment="center" valignment="top" usebox="none">
7022 \begin_layout Plain Layout
7023 \begin_inset Formula $\rangle$
7033 <cell alignment="center" valignment="top" usebox="none">
7036 \begin_layout Plain Layout
7044 <cell alignment="center" valignment="top" usebox="none">
7047 \begin_layout Plain Layout
7048 \begin_inset Formula $\rceil$
7058 <cell alignment="center" valignment="top" usebox="none">
7061 \begin_layout Plain Layout
7069 <cell alignment="center" valignment="top" usebox="none">
7072 \begin_layout Plain Layout
7073 \begin_inset Formula $\rfloor$
7083 <cell alignment="center" valignment="top" usebox="none">
7086 \begin_layout Plain Layout
7096 <cell alignment="center" valignment="top" usebox="none">
7099 \begin_layout Plain Layout
7100 \begin_inset Formula $\backslash$
7110 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7113 \begin_layout Plain Layout
7121 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7124 \begin_layout Plain Layout
7125 \begin_inset Formula $\|$
7139 \begin_inset space \hfill{}
7145 \begin_layout Standard
7148 \begin_inset Note Greyedout
7151 \begin_layout Plain Layout
7165 \begin_inset Index idx
7170 \begin_layout Plain Layout
7172 \begin_inset IndexMacro subentry
7175 \begin_layout Plain Layout
7182 \begin_inset IndexMacro subentry
7185 \begin_layout Plain Layout
7198 must be used for the backslash,
7207 produces a line break there.
7215 \begin_layout Standard
7216 For all characters listed above the size can be adjusted with the commands described in the following two subsections.
7217 When using these commands,
7218 the characters < and > can directly be used instead of the commands
7233 \begin_layout Subsubsection
7235 \begin_inset CommandInset label
7237 name "subsec:Manual-Bracket-Size"
7242 \begin_inset Index idx
7247 \begin_layout Plain Layout
7249 \begin_inset IndexMacro subentry
7252 \begin_layout Plain Layout
7266 \begin_layout Standard
7267 The bracket size can be specified manually by the \SpecialChar LaTeX
7275 \begin_inset Index idx
7280 \begin_layout Plain Layout
7282 \begin_inset IndexMacro subentry
7285 \begin_layout Plain Layout
7292 \begin_inset IndexMacro subentry
7295 \begin_layout Plain Layout
7335 denotes the smallest and
7341 the largest bracket size.
7344 \begin_layout Standard
7345 These commands are used to emphasize levels of brackets:
7348 \begin_layout Standard
7350 \begin_inset Tabular
7351 <lyxtabular version="3" rows="2" columns="2">
7352 <features booktabs="true" tabularvalignment="middle">
7353 <column alignment="center" valignment="top" width="0pt">
7354 <column alignment="center" valignment="top" width="0pt">
7356 <cell alignment="center" valignment="top" usebox="none">
7359 \begin_layout Plain Layout
7360 All brackets in the same size:
7365 <cell alignment="center" valignment="top" usebox="none">
7368 \begin_layout Plain Layout
7369 \begin_inset Formula $((A+B)(A-B))^{C}$
7378 <row topspace="2mm">
7379 <cell alignment="center" valignment="top" usebox="none">
7382 \begin_layout Plain Layout
7388 <cell alignment="center" valignment="top" usebox="none">
7391 \begin_layout Plain Layout
7392 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
7408 \begin_layout Standard
7409 For the second formula the command
7416 \begin_inset space \textvisiblespace{}
7424 \begin_layout Standard
7425 Here is an example containing all bracket sizes:
7428 \begin_layout Standard
7445 \begin_inset space \textvisiblespace{}
7453 \begin_inset space \textvisiblespace{}
7457 \begin_inset space \textvisiblespace{}
7467 \begin_layout Standard
7469 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
7475 \begin_layout Standard
7482 -commands there is a variant,
7490 \begin_inset Index idx
7495 \begin_layout Plain Layout
7497 \begin_inset IndexMacro subentry
7500 \begin_layout Plain Layout
7507 \begin_inset IndexMacro subentry
7510 \begin_layout Plain Layout
7524 that adds a bit more space between the bracket and its content.
7538 \begin_inset Index idx
7543 \begin_layout Plain Layout
7545 \begin_inset IndexMacro subentry
7548 \begin_layout Plain Layout
7555 \begin_inset IndexMacro subentry
7558 \begin_layout Plain Layout
7574 don't add additional space.
7579 at the end of the command
7585 is for a left bracket;
7586 for a right bracket this is replaced by an
7591 A left or right bracket can each be an opening or closing bracket.
7594 \begin_layout Standard
7595 The following table contains comparisons of the variants:
7598 \begin_layout Standard
7600 \begin_inset Tabular
7601 <lyxtabular version="3" rows="5" columns="2">
7602 <features booktabs="true" tabularvalignment="middle">
7603 <column alignment="center" valignment="top" width="0pt">
7604 <column alignment="center" valignment="middle">
7606 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7609 \begin_layout Plain Layout
7615 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7618 \begin_layout Plain Layout
7625 <row topspace="2mm">
7626 <cell alignment="center" valignment="top" usebox="none">
7629 \begin_layout Plain Layout
7639 \begin_inset space \textvisiblespace{}
7649 <cell alignment="center" valignment="top" usebox="none">
7652 \begin_layout Plain Layout
7653 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
7662 <row topspace="2mm">
7663 <cell alignment="center" valignment="top" usebox="none">
7666 \begin_layout Plain Layout
7676 \begin_inset space \textvisiblespace{}
7686 <cell alignment="center" valignment="top" usebox="none">
7689 \begin_layout Plain Layout
7690 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
7699 <row topspace="2mm" bottomspace="0.5mm">
7700 <cell alignment="center" valignment="top" usebox="none">
7703 \begin_layout Plain Layout
7713 \begin_inset space \textvisiblespace{}
7723 <cell alignment="center" valignment="top" usebox="none">
7726 \begin_layout Plain Layout
7727 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
7736 <row topspace="1.5mm" bottomspace="0.5mm">
7737 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7740 \begin_layout Plain Layout
7752 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7755 \begin_layout Plain Layout
7756 \begin_inset Formula $\bigl)\ln(3x)\bigr($
7772 \begin_layout Subsubsection
7773 Automatic Bracket Size
7774 \begin_inset CommandInset label
7776 name "subsec:Automatic-Bracket-Size"
7781 \begin_inset Index idx
7786 \begin_layout Plain Layout
7788 \begin_inset IndexMacro subentry
7791 \begin_layout Plain Layout
7805 \begin_layout Standard
7806 Variably sized brackets can be inserted with the commands
7813 \begin_inset Index idx
7818 \begin_layout Plain Layout
7820 \begin_inset IndexMacro subentry
7823 \begin_layout Plain Layout
7830 \begin_inset IndexMacro subentry
7833 \begin_layout Plain Layout
7853 \begin_inset Index idx
7858 \begin_layout Plain Layout
7860 \begin_inset IndexMacro subentry
7863 \begin_layout Plain Layout
7870 \begin_inset IndexMacro subentry
7873 \begin_layout Plain Layout
7886 or via the math toolbar button
7889 arg "dialog-show mathdelimiter"
7893 The desired bracket must be inserted directly behind the
7906 The bracket size will then automatically be calculated for the output.
7909 \begin_layout Standard
7919 \begin_inset space \textvisiblespace{}
7923 \begin_inset Formula $\downarrow$
7927 \begin_inset space \textvisiblespace{}
7933 \begin_inset Formula
7943 \begin_layout Standard
7955 \begin_inset space \textvisiblespace{}
7959 \begin_inset Formula $\downarrow$
7963 \begin_inset space \textvisiblespace{}
7971 \begin_inset Formula
7973 \ln\left(\frac{A}{C}\right)
7981 \begin_layout Standard
7997 \begin_inset space ~
8003 This has the advantage that you can see in \SpecialChar LyX
8004 immediately the real bracket size and that the matching right bracket will be created too.
8005 \begin_inset Newline newline
8008 The command for the last example would then be:
8020 \begin_inset space \textvisiblespace{}
8024 \begin_inset Formula $\downarrow$
8030 \begin_layout Standard
8031 To omit a left or right bracket,
8032 a dot is inserted for the omitted bracket.
8033 For example the command
8040 \begin_inset space \textvisiblespace{}
8044 \begin_inset Formula $\downarrow$
8048 \begin_inset space \textvisiblespace{}
8058 \begin_inset Formula
8060 \left.\frac{A}{B}\right\}
8079 will be converted by \SpecialChar LyX
8080 to brackets with the correct size when the document is reloaded and an omitted bracket will appear as dashed line.
8083 \begin_layout Standard
8084 \begin_inset VSpace bigskip
8087 Because all popular \SpecialChar LaTeX
8088 distributions use e\SpecialChar TeX
8090 an extension to \SpecialChar LaTeX
8099 \begin_inset Index idx
8104 \begin_layout Plain Layout
8106 \begin_inset IndexMacro subentry
8109 \begin_layout Plain Layout
8116 \begin_inset IndexMacro subentry
8119 \begin_layout Plain Layout
8132 is available for all brackets and limits.
8133 With this command the height of the following character is adapted to the one of the surrounding brackets,
8134 for example in the case of physical vectors:
8135 \begin_inset Formula
8137 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
8142 For physical vectors there is a special \SpecialChar LaTeX
8145 \begin_inset CommandInset ref
8147 reference "subsec:Physical-Vectors"
8155 \begin_layout Subsection
8157 \begin_inset Index idx
8162 \begin_layout Plain Layout
8164 \begin_inset IndexMacro subentry
8167 \begin_layout Plain Layout
8181 \begin_layout Standard
8183 \begin_inset Tabular
8184 <lyxtabular version="3" rows="4" columns="2">
8185 <features booktabs="true" tabularvalignment="middle">
8186 <column alignment="center" valignment="top" width="0pt">
8187 <column alignment="center" valignment="top" width="0pt">
8189 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8192 \begin_layout Plain Layout
8198 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8201 \begin_layout Plain Layout
8209 <cell alignment="center" valignment="top" usebox="none">
8212 \begin_layout Plain Layout
8216 \begin_inset space \textvisiblespace{}
8220 \begin_inset space \textvisiblespace{}
8224 \begin_inset Index idx
8229 \begin_layout Plain Layout
8231 \begin_inset IndexMacro subentry
8234 \begin_layout Plain Layout
8241 \begin_inset IndexMacro subentry
8244 \begin_layout Plain Layout
8262 <cell alignment="center" valignment="top" usebox="none">
8265 \begin_layout Plain Layout
8266 \begin_inset Formula $\overbrace{A+B}^{3}$
8275 <row topspace="2mm">
8276 <cell alignment="center" valignment="top" usebox="none">
8279 \begin_layout Plain Layout
8283 \begin_inset space \textvisiblespace{}
8287 \begin_inset space \textvisiblespace{}
8291 \begin_inset Index idx
8296 \begin_layout Plain Layout
8298 \begin_inset IndexMacro subentry
8301 \begin_layout Plain Layout
8308 \begin_inset IndexMacro subentry
8311 \begin_layout Plain Layout
8329 <cell alignment="center" valignment="top" usebox="none">
8332 \begin_layout Plain Layout
8333 \begin_inset Formula $\underbrace{A+B}_{5}$
8343 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8346 \begin_layout Plain Layout
8350 \begin_inset space \textvisiblespace{}
8356 \begin_inset space \textvisiblespace{}
8360 \begin_inset space \textvisiblespace{}
8364 \begin_inset space \textvisiblespace{}
8368 \begin_inset space \textvisiblespace{}
8372 \begin_inset space \textvisiblespace{}
8376 \begin_inset space \textvisiblespace{}
8384 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8387 \begin_layout Plain Layout
8388 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
8404 \begin_layout Standard
8405 In the last example it doesn't matter if
8420 \begin_layout Standard
8421 \begin_inset VSpace medskip
8427 \begin_layout Standard
8428 If in document settings under
8431 \begin_inset space ~
8436 the option for the package
8441 \begin_inset Index idx
8446 \begin_layout Plain Layout
8448 \begin_inset IndexMacro subentry
8451 \begin_layout Plain Layout
8465 \begin_inset space ~
8471 you will also have access to square brackets:
8474 \begin_layout Standard
8476 \begin_inset Tabular
8477 <lyxtabular version="3" rows="4" columns="2">
8478 <features booktabs="true" tabularvalignment="middle">
8479 <column alignment="center" valignment="top" width="0pt">
8480 <column alignment="center" valignment="top" width="0pt">
8482 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8485 \begin_layout Plain Layout
8491 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8494 \begin_layout Plain Layout
8502 <cell alignment="center" valignment="top" usebox="none">
8505 \begin_layout Plain Layout
8533 \begin_inset space \textvisiblespace{}
8537 \begin_inset Index idx
8542 \begin_layout Plain Layout
8544 \begin_inset IndexMacro subentry
8547 \begin_layout Plain Layout
8554 \begin_inset IndexMacro subentry
8557 \begin_layout Plain Layout
8575 <cell alignment="center" valignment="top" usebox="none">
8578 \begin_layout Plain Layout
8579 \begin_inset Formula $\overbracket{A+B}^{3}$
8588 <row topspace="2mm">
8589 <cell alignment="center" valignment="top" usebox="none">
8592 \begin_layout Plain Layout
8620 \begin_inset space \textvisiblespace{}
8624 \begin_inset Index idx
8629 \begin_layout Plain Layout
8631 \begin_inset IndexMacro subentry
8634 \begin_layout Plain Layout
8641 \begin_inset IndexMacro subentry
8644 \begin_layout Plain Layout
8674 <cell alignment="center" valignment="top" usebox="none">
8677 \begin_layout Plain Layout
8678 \begin_inset Formula $\underbracket{A+B}_{5}$
8688 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8691 \begin_layout Plain Layout
8697 \begin_inset space \textvisiblespace{}
8701 \begin_inset space \textvisiblespace{}
8705 \begin_inset space \textvisiblespace{}
8709 \begin_inset space \textvisiblespace{}
8713 \change_deleted 5863208 1612711596
8715 \begin_inset space \textvisiblespace{}
8725 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8728 \begin_layout Plain Layout
8729 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
8745 \begin_layout Standard
8758 you can change the thickness of the bracket's stroke by specifying the desired thickness in square brackets behind the command:
8761 \begin_layout Standard
8763 \begin_inset Tabular
8764 <lyxtabular version="3" rows="3" columns="2">
8765 <features booktabs="true" tabularvalignment="middle">
8766 <column alignment="center" valignment="top" width="0pt">
8767 <column alignment="center" valignment="top" width="0pt">
8769 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8772 \begin_layout Plain Layout
8778 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8781 \begin_layout Plain Layout
8789 <cell alignment="center" valignment="top" usebox="none">
8792 \begin_layout Plain Layout
8822 \begin_inset space \textvisiblespace{}
8830 <cell alignment="center" valignment="top" usebox="none">
8833 \begin_layout Plain Layout
8834 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
8843 <row topspace="2mm">
8844 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8847 \begin_layout Plain Layout
8877 \begin_inset space \textvisiblespace{}
8885 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8888 \begin_layout Plain Layout
8889 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
8905 \begin_layout Standard
8906 \begin_inset VSpace bigskip
8909 When brackets overlap each other,
8910 multiline formulas as described in
8911 \begin_inset CommandInset ref
8913 reference "sec:Multiline-Formulas"
8919 \begin_inset Formula
8921 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
8922 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
8928 the formula is inserted together with the first brace.
8929 It is important that the space command
8933 \begin_layout Plain Layout
8934 Space commands are explained in
8935 \begin_inset CommandInset ref
8937 reference "subsec:Predefined-Space"
8954 is inserted before the first
8955 \begin_inset Formula $d$
8958 because the brace that ends behind the
8959 \begin_inset Formula $q$
8962 prevents the following
8963 \begin_inset Quotes eld
8967 \begin_inset Quotes erd
8970 from being surrounded by spaces.
8974 \begin_layout Plain Layout
8975 Because a bracket is not handled as a character,
8977 \begin_inset CommandInset ref
8979 reference "subsec:Binary-Operators"
8989 The second brace is inserted in the second row.
8990 As it should begin before the
8991 \begin_inset Formula $b$
9007 \begin_layout Plain Layout
9015 \begin_inset CommandInset ref
9017 reference "subsec:Placeholders"
9027 This space is needed because the
9028 \begin_inset Quotes eld
9032 \begin_inset Quotes erd
9035 is surrounded by spaces in the formula.
9036 The brace is placed under the command
9045 \begin_layout Standard
9046 It gets more complicated when brackets overlap each other above and under the formula as in the following example:
9050 \begin_layout Plain Layout
9062 \begin_inset Formula
9064 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
9065 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
9074 \begin_layout Plain Layout
9085 The first formula row is the same as the second row of the previous example,
9086 with the difference that the brace is above.
9087 The second row contains the formula together with the second brace.
9088 To avoid the space between the upper brace in the first row and the formula,
9089 the row spacing needs to be reduced.
9090 This is not easily done due to a bug in \SpecialChar LyX
9095 \begin_layout Plain Layout
9096 \begin_inset CommandInset href
9098 name "LyX-bug #1505"
9099 target "https://www.lyx.org/trac/ticket/1505"
9109 As a solution for the problem,
9110 the global formula row separation
9117 \begin_inset Index idx
9122 \begin_layout Plain Layout
9124 \begin_inset IndexMacro subentry
9127 \begin_layout Plain Layout
9134 \begin_inset IndexMacro subentry
9137 \begin_layout Plain Layout
9150 must be changed to -6
9151 \begin_inset space \thinspace{}
9154 pt before the formula with the command
9170 is set back after the formula to the standard value of 3
9171 \begin_inset space \thinspace{}
9174 pt using the same command.
9175 More about the row separation in formulas is explained in
9176 \begin_inset CommandInset ref
9178 reference "subsec:Line-Separation"
9186 \begin_layout Section
9188 \begin_inset Index idx
9193 \begin_layout Plain Layout
9202 \begin_layout Standard
9203 Arrows can be inserted via the math toolbar button
9206 arg "math-insert \\leftarrow"
9209 or the commands listed in the following subsections.
9212 \begin_layout Subsection
9214 \begin_inset Index idx
9219 \begin_layout Plain Layout
9221 \begin_inset IndexMacro subentry
9224 \begin_layout Plain Layout
9238 \begin_layout Standard
9239 \begin_inset space \hfill{}
9243 \begin_inset Tabular
9244 <lyxtabular version="3" rows="8" columns="2">
9245 <features booktabs="true" tabularvalignment="middle">
9246 <column alignment="center" valignment="top" width="0pt">
9247 <column alignment="center" valignment="top" width="0pt">
9249 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9252 \begin_layout Plain Layout
9258 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9261 \begin_layout Plain Layout
9269 <cell alignment="center" valignment="top" usebox="none">
9272 \begin_layout Plain Layout
9280 <cell alignment="center" valignment="top" usebox="none">
9283 \begin_layout Plain Layout
9284 \begin_inset Formula $\gets$
9294 <cell alignment="center" valignment="top" usebox="none">
9297 \begin_layout Plain Layout
9305 <cell alignment="center" valignment="top" usebox="none">
9308 \begin_layout Plain Layout
9309 \begin_inset Formula $\Leftarrow$
9319 <cell alignment="center" valignment="top" usebox="none">
9322 \begin_layout Plain Layout
9330 <cell alignment="center" valignment="top" usebox="none">
9333 \begin_layout Plain Layout
9334 \begin_inset Formula $\longleftarrow$
9344 <cell alignment="center" valignment="top" usebox="none">
9347 \begin_layout Plain Layout
9355 <cell alignment="center" valignment="top" usebox="none">
9358 \begin_layout Plain Layout
9359 \begin_inset Formula $\Longleftarrow$
9369 <cell alignment="center" valignment="top" usebox="none">
9372 \begin_layout Plain Layout
9380 <cell alignment="center" valignment="top" usebox="none">
9383 \begin_layout Plain Layout
9384 \begin_inset Formula $\leftharpoonup$
9394 <cell alignment="center" valignment="top" usebox="none">
9397 \begin_layout Plain Layout
9405 <cell alignment="center" valignment="top" usebox="none">
9408 \begin_layout Plain Layout
9409 \begin_inset Formula $\leftharpoondown$
9419 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9422 \begin_layout Plain Layout
9430 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9433 \begin_layout Plain Layout
9434 \begin_inset Formula $\hookleftarrow$
9448 \begin_inset space \hfill{}
9452 \begin_inset Tabular
9453 <lyxtabular version="3" rows="8" columns="2">
9454 <features booktabs="true" tabularvalignment="middle">
9455 <column alignment="center" valignment="top" width="0pt">
9456 <column alignment="center" valignment="top" width="0pt">
9458 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9461 \begin_layout Plain Layout
9467 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9470 \begin_layout Plain Layout
9478 <cell alignment="center" valignment="top" usebox="none">
9481 \begin_layout Plain Layout
9489 <cell alignment="center" valignment="top" usebox="none">
9492 \begin_layout Plain Layout
9493 \begin_inset Formula $\to$
9503 <cell alignment="center" valignment="top" usebox="none">
9506 \begin_layout Plain Layout
9514 <cell alignment="center" valignment="top" usebox="none">
9517 \begin_layout Plain Layout
9518 \begin_inset Formula $\Rightarrow$
9528 <cell alignment="center" valignment="top" usebox="none">
9531 \begin_layout Plain Layout
9539 <cell alignment="center" valignment="top" usebox="none">
9542 \begin_layout Plain Layout
9543 \begin_inset Formula $\longrightarrow$
9553 <cell alignment="center" valignment="top" usebox="none">
9556 \begin_layout Plain Layout
9564 <cell alignment="center" valignment="top" usebox="none">
9567 \begin_layout Plain Layout
9568 \begin_inset Formula $\Longrightarrow$
9578 <cell alignment="center" valignment="top" usebox="none">
9581 \begin_layout Plain Layout
9589 <cell alignment="center" valignment="top" usebox="none">
9592 \begin_layout Plain Layout
9593 \begin_inset Formula $\rightharpoonup$
9603 <cell alignment="center" valignment="top" usebox="none">
9606 \begin_layout Plain Layout
9614 <cell alignment="center" valignment="top" usebox="none">
9617 \begin_layout Plain Layout
9618 \begin_inset Formula $\rightharpoondown$
9628 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9631 \begin_layout Plain Layout
9639 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9642 \begin_layout Plain Layout
9643 \begin_inset Formula $\hookrightarrow$
9657 \begin_inset space \hfill{}
9663 \begin_layout Standard
9664 \begin_inset space \hfill{}
9668 \begin_inset Tabular
9669 <lyxtabular version="3" rows="6" columns="2">
9670 <features booktabs="true" tabularvalignment="middle">
9671 <column alignment="center" valignment="top" width="0pt">
9672 <column alignment="center" valignment="top" width="0pt">
9674 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9677 \begin_layout Plain Layout
9683 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9686 \begin_layout Plain Layout
9694 <cell alignment="center" valignment="top" usebox="none">
9697 \begin_layout Plain Layout
9705 <cell alignment="center" valignment="top" usebox="none">
9708 \begin_layout Plain Layout
9709 \begin_inset Formula $\leftrightarrow$
9719 <cell alignment="center" valignment="top" usebox="none">
9722 \begin_layout Plain Layout
9730 <cell alignment="center" valignment="top" usebox="none">
9733 \begin_layout Plain Layout
9734 \begin_inset Formula $\Leftrightarrow$
9744 <cell alignment="center" valignment="top" usebox="none">
9747 \begin_layout Plain Layout
9755 <cell alignment="center" valignment="top" usebox="none">
9758 \begin_layout Plain Layout
9759 \begin_inset Formula $\longleftrightarrow$
9769 <cell alignment="center" valignment="top" usebox="none">
9772 \begin_layout Plain Layout
9780 <cell alignment="center" valignment="top" usebox="none">
9783 \begin_layout Plain Layout
9784 \begin_inset Formula $\Longleftrightarrow$
9794 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9797 \begin_layout Plain Layout
9805 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9808 \begin_layout Plain Layout
9809 \begin_inset Formula $\rightleftharpoons$
9823 \begin_inset space \hspace{}
9828 \begin_inset space \hfill{}
9832 \begin_inset Tabular
9833 <lyxtabular version="3" rows="5" columns="2">
9834 <features booktabs="true" tabularvalignment="middle">
9835 <column alignment="center" valignment="top" width="0pt">
9836 <column alignment="center" valignment="top" width="0pt">
9838 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9841 \begin_layout Plain Layout
9847 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9850 \begin_layout Plain Layout
9858 <cell alignment="center" valignment="top" usebox="none">
9861 \begin_layout Plain Layout
9869 <cell alignment="center" valignment="top" usebox="none">
9872 \begin_layout Plain Layout
9873 \begin_inset Formula $\mapsto$
9883 <cell alignment="center" valignment="top" usebox="none">
9886 \begin_layout Plain Layout
9894 <cell alignment="center" valignment="top" usebox="none">
9897 \begin_layout Plain Layout
9898 \begin_inset Formula $\longmapsto$
9908 <cell alignment="center" valignment="top" usebox="none">
9911 \begin_layout Plain Layout
9919 <cell alignment="center" valignment="top" usebox="none">
9922 \begin_layout Plain Layout
9923 \begin_inset Formula $\leadsto$
9933 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9936 \begin_layout Plain Layout
9944 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9947 \begin_layout Plain Layout
9948 \begin_inset Formula $\dasharrow$
9962 \begin_inset space \hfill{}
9968 \begin_layout Standard
9969 \begin_inset VSpace medskip
9972 Arrows used as accents such as vector arrows are listed in
9973 \begin_inset CommandInset ref
9975 reference "sec:Accents"
9983 \begin_layout Standard
9984 \begin_inset VSpace bigskip
9988 \begin_inset Index idx
9993 \begin_layout Plain Layout
9995 \begin_inset IndexMacro subentry
9998 \begin_layout Plain Layout
10009 are also available using the commands
10016 \begin_inset Index idx
10021 \begin_layout Plain Layout
10023 \begin_inset IndexMacro subentry
10026 \begin_layout Plain Layout
10033 \begin_inset IndexMacro subentry
10036 \begin_layout Plain Layout
10056 \begin_inset Index idx
10061 \begin_layout Plain Layout
10063 \begin_inset IndexMacro subentry
10066 \begin_layout Plain Layout
10073 \begin_inset IndexMacro subentry
10076 \begin_layout Plain Layout
10090 When inserting one of these commands in a formula,
10091 an arrow with two blue boxes appears indicating where the labels can be inserted.
10092 The length of the arrow adapts to the label width.
10095 \begin_layout Standard
10097 \begin_inset Tabular
10098 <lyxtabular version="3" rows="3" columns="2">
10099 <features booktabs="true" tabularvalignment="middle">
10100 <column alignment="center" valignment="top" width="0pt">
10101 <column alignment="center" valignment="top" width="0pt">
10103 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10106 \begin_layout Plain Layout
10112 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10115 \begin_layout Plain Layout
10123 <cell alignment="center" valignment="top" usebox="none">
10126 \begin_layout Plain Layout
10130 \begin_inset space \textvisiblespace{}
10134 \begin_inset Formula $\downarrow$
10138 \begin_inset Formula $\to$
10146 <cell alignment="center" valignment="top" usebox="none">
10149 \begin_layout Plain Layout
10150 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
10159 <row topspace="2mm">
10160 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10163 \begin_layout Plain Layout
10167 \begin_inset space \textvisiblespace{}
10171 \begin_inset Formula $\downarrow$
10175 \begin_inset Formula $\to$
10183 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10186 \begin_layout Plain Layout
10187 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
10203 \begin_layout Standard
10204 \begin_inset VSpace medskip
10210 \begin_layout Standard
10211 If in the document settings under
10214 \begin_inset space ~
10224 \begin_inset Index idx
10229 \begin_layout Plain Layout
10231 \begin_inset IndexMacro subentry
10234 \begin_layout Plain Layout
10248 \begin_inset space ~
10254 you will have access to the following labeled arrows:
10257 \begin_layout Standard
10258 \begin_inset Newpage newpage
10264 \begin_layout Standard
10266 \begin_inset space \hspace*{\fill}
10270 \begin_inset Tabular
10271 <lyxtabular version="3" rows="7" columns="2">
10272 <features booktabs="true" tabularvalignment="middle">
10273 <column alignment="center" valignment="top" width="0pt">
10274 <column alignment="center" valignment="top" width="0pt">
10276 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10279 \begin_layout Plain Layout
10285 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10288 \begin_layout Plain Layout
10296 <cell alignment="center" valignment="top" usebox="none">
10299 \begin_layout Plain Layout
10319 <cell alignment="center" valignment="top" usebox="none">
10322 \begin_layout Plain Layout
10323 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
10332 <row topspace="2mm">
10333 <cell alignment="center" valignment="top" usebox="none">
10336 \begin_layout Plain Layout
10356 <cell alignment="center" valignment="top" usebox="none">
10359 \begin_layout Plain Layout
10360 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
10369 <row topspace="2mm">
10370 <cell alignment="center" valignment="top" usebox="none">
10373 \begin_layout Plain Layout
10393 <cell alignment="center" valignment="top" usebox="none">
10396 \begin_layout Plain Layout
10397 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
10406 <row topspace="2mm">
10407 <cell alignment="center" valignment="top" usebox="none">
10410 \begin_layout Plain Layout
10430 <cell alignment="center" valignment="top" usebox="none">
10433 \begin_layout Plain Layout
10434 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
10443 <row topspace="2mm">
10444 <cell alignment="center" valignment="top" usebox="none">
10447 \begin_layout Plain Layout
10467 <cell alignment="center" valignment="top" usebox="none">
10470 \begin_layout Plain Layout
10471 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
10480 <row topspace="2mm">
10481 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10484 \begin_layout Plain Layout
10504 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10507 \begin_layout Plain Layout
10508 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
10522 \begin_inset space \hspace*{\fill}
10526 \begin_inset Tabular
10527 <lyxtabular version="3" rows="7" columns="2">
10528 <features booktabs="true" tabularvalignment="middle">
10529 <column alignment="center" valignment="top" width="0pt">
10530 <column alignment="center" valignment="top" width="0pt">
10532 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10535 \begin_layout Plain Layout
10541 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10544 \begin_layout Plain Layout
10552 <cell alignment="center" valignment="top" usebox="none">
10555 \begin_layout Plain Layout
10575 <cell alignment="center" valignment="top" usebox="none">
10578 \begin_layout Plain Layout
10579 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
10588 <row topspace="2mm">
10589 <cell alignment="center" valignment="top" usebox="none">
10592 \begin_layout Plain Layout
10612 <cell alignment="center" valignment="top" usebox="none">
10615 \begin_layout Plain Layout
10616 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
10625 <row topspace="2mm">
10626 <cell alignment="center" valignment="top" usebox="none">
10629 \begin_layout Plain Layout
10649 <cell alignment="center" valignment="top" usebox="none">
10652 \begin_layout Plain Layout
10653 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
10662 <row topspace="2mm">
10663 <cell alignment="center" valignment="top" usebox="none">
10666 \begin_layout Plain Layout
10686 <cell alignment="center" valignment="top" usebox="none">
10689 \begin_layout Plain Layout
10690 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
10699 <row topspace="2mm">
10700 <cell alignment="center" valignment="top" usebox="none">
10703 \begin_layout Plain Layout
10723 <cell alignment="center" valignment="top" usebox="none">
10726 \begin_layout Plain Layout
10727 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
10736 <row topspace="2mm">
10737 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10740 \begin_layout Plain Layout
10760 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10763 \begin_layout Plain Layout
10764 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
10778 \begin_inset space \hspace*{\fill}
10784 \begin_layout Standard
10785 The command scheme for all of these arrows is:
10788 \begin_layout Standard
10790 \begin_inset Tabular
10791 <lyxtabular version="3" rows="2" columns="2">
10792 <features booktabs="true" tabularvalignment="middle">
10793 <column alignment="center" valignment="top" width="0pt">
10794 <column alignment="center" valignment="top" width="0pt">
10796 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10799 \begin_layout Plain Layout
10805 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10808 \begin_layout Plain Layout
10815 <row bottomspace="0.5mm">
10816 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10819 \begin_layout Plain Layout
10822 xleftrightarrow[x=a]
10825 \begin_inset Formula $\to$
10833 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10836 \begin_layout Plain Layout
10837 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
10853 \begin_layout Subsection
10854 Vertical and Diagonal Arrows
10855 \begin_inset Index idx
10860 \begin_layout Plain Layout
10862 \begin_inset IndexMacro subentry
10865 \begin_layout Plain Layout
10877 \begin_inset Index idx
10882 \begin_layout Plain Layout
10884 \begin_inset IndexMacro subentry
10887 \begin_layout Plain Layout
10901 \begin_layout Standard
10902 \begin_inset space \hfill{}
10906 \begin_inset Tabular
10907 <lyxtabular version="3" rows="7" columns="2">
10908 <features booktabs="true" tabularvalignment="middle">
10909 <column alignment="center" valignment="top" width="0pt">
10910 <column alignment="center" valignment="top" width="0pt">
10912 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10915 \begin_layout Plain Layout
10921 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10924 \begin_layout Plain Layout
10932 <cell alignment="center" valignment="top" usebox="none">
10935 \begin_layout Plain Layout
10943 <cell alignment="center" valignment="top" usebox="none">
10946 \begin_layout Plain Layout
10947 \begin_inset Formula $\uparrow$
10957 <cell alignment="center" valignment="top" usebox="none">
10960 \begin_layout Plain Layout
10968 <cell alignment="center" valignment="top" usebox="none">
10971 \begin_layout Plain Layout
10972 \begin_inset Formula $\Uparrow$
10982 <cell alignment="center" valignment="top" usebox="none">
10985 \begin_layout Plain Layout
10993 <cell alignment="center" valignment="top" usebox="none">
10996 \begin_layout Plain Layout
10997 \begin_inset Formula $\updownarrow$
11007 <cell alignment="center" valignment="top" usebox="none">
11010 \begin_layout Plain Layout
11018 <cell alignment="center" valignment="top" usebox="none">
11021 \begin_layout Plain Layout
11022 \begin_inset Formula $\Updownarrow$
11032 <cell alignment="center" valignment="top" usebox="none">
11035 \begin_layout Plain Layout
11043 <cell alignment="center" valignment="top" usebox="none">
11046 \begin_layout Plain Layout
11047 \begin_inset Formula $\Downarrow$
11057 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11060 \begin_layout Plain Layout
11068 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11071 \begin_layout Plain Layout
11072 \begin_inset Formula $\downarrow$
11086 \begin_inset space \hfill{}
11090 \begin_inset Tabular
11091 <lyxtabular version="3" rows="5" columns="2">
11092 <features booktabs="true" tabularvalignment="middle">
11093 <column alignment="center" valignment="top" width="0pt">
11094 <column alignment="center" valignment="top" width="0pt">
11096 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11099 \begin_layout Plain Layout
11105 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11108 \begin_layout Plain Layout
11116 <cell alignment="center" valignment="top" usebox="none">
11119 \begin_layout Plain Layout
11127 <cell alignment="center" valignment="top" usebox="none">
11130 \begin_layout Plain Layout
11131 \begin_inset Formula $\nearrow$
11141 <cell alignment="center" valignment="top" usebox="none">
11144 \begin_layout Plain Layout
11152 <cell alignment="center" valignment="top" usebox="none">
11155 \begin_layout Plain Layout
11156 \begin_inset Formula $\searrow$
11166 <cell alignment="center" valignment="top" usebox="none">
11169 \begin_layout Plain Layout
11177 <cell alignment="center" valignment="top" usebox="none">
11180 \begin_layout Plain Layout
11181 \begin_inset Formula $\swarrow$
11191 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11194 \begin_layout Plain Layout
11202 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11205 \begin_layout Plain Layout
11206 \begin_inset Formula $\nwarrow$
11220 \begin_inset space \hfill{}
11226 \begin_layout Standard
11227 \begin_inset VSpace medskip
11230 Vertical arrows can also be used as delimiters together with the commands described in
11231 \begin_inset CommandInset ref
11233 reference "subsec:Manual-Bracket-Size"
11239 \begin_inset CommandInset ref
11241 reference "subsec:Automatic-Bracket-Size"
11249 \begin_layout Section
11251 \begin_inset CommandInset label
11258 \begin_inset Index idx
11263 \begin_layout Plain Layout
11272 \begin_layout Standard
11273 Accents can be inserted via the math toolbar button
11276 arg "math-insert \\hat"
11279 or the commands listed in the following subsections.
11282 \begin_layout Subsection
11283 Accents for One Character
11287 \begin_layout Plain Layout
11300 \begin_layout Plain Layout
11301 For accents in text see
11302 \begin_inset CommandInset ref
11304 reference "subsec:Accents-in-Text"
11318 \begin_layout Plain Layout
11326 \begin_inset Note Note
11329 \begin_layout Plain Layout
11336 is used to avoid that the footnote appears in the PDF-bookmark.
11339 \begin_layout Plain Layout
11347 \begin_inset CommandInset ref
11349 reference "subsec:Formulas-in-Section"
11360 \begin_inset CommandInset label
11362 name "subsec:Accents-for-one"
11367 \begin_inset Index idx
11372 \begin_layout Plain Layout
11374 \begin_inset IndexMacro subentry
11377 \begin_layout Plain Layout
11391 \begin_layout Standard
11392 \begin_inset space \hfill{}
11396 \begin_inset Tabular
11397 <lyxtabular version="3" rows="8" columns="2">
11398 <features booktabs="true" tabularvalignment="middle">
11399 <column alignment="center" valignment="top" width="0pt">
11400 <column alignment="center" valignment="top" width="0pt">
11402 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11405 \begin_layout Plain Layout
11411 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11414 \begin_layout Plain Layout
11421 <row topspace="1.5mm">
11422 <cell alignment="center" valignment="top" usebox="none">
11425 \begin_layout Plain Layout
11429 \begin_inset space \textvisiblespace{}
11437 <cell alignment="center" valignment="top" usebox="none">
11440 \begin_layout Plain Layout
11441 \begin_inset Formula $\dot{A}$
11450 <row topspace="1.5mm">
11451 <cell alignment="center" valignment="top" usebox="none">
11454 \begin_layout Plain Layout
11458 \begin_inset space \textvisiblespace{}
11466 <cell alignment="center" valignment="top" usebox="none">
11469 \begin_layout Plain Layout
11470 \begin_inset Formula $\ddot{A}$
11479 <row topspace="1.5mm">
11480 <cell alignment="center" valignment="top" usebox="none">
11483 \begin_layout Plain Layout
11487 \begin_inset space \textvisiblespace{}
11495 <cell alignment="center" valignment="top" usebox="none">
11498 \begin_layout Plain Layout
11499 \begin_inset Formula $\dddot{A}$
11508 <row topspace="1.5mm">
11509 <cell alignment="center" valignment="top" usebox="none">
11512 \begin_layout Plain Layout
11516 \begin_inset space \textvisiblespace{}
11524 <cell alignment="center" valignment="top" usebox="none">
11527 \begin_layout Plain Layout
11528 \begin_inset Formula $\ddddot{A}$
11537 <row topspace="1.5mm">
11538 <cell alignment="center" valignment="top" usebox="none">
11541 \begin_layout Plain Layout
11545 \begin_inset space \textvisiblespace{}
11549 \begin_inset Index idx
11554 \begin_layout Plain Layout
11565 <cell alignment="center" valignment="top" usebox="none">
11568 \begin_layout Plain Layout
11569 \begin_inset Formula $\vec{A}$
11578 <row topspace="1.5mm">
11579 <cell alignment="center" valignment="top" usebox="none">
11582 \begin_layout Plain Layout
11586 \begin_inset space \textvisiblespace{}
11594 <cell alignment="center" valignment="top" usebox="none">
11597 \begin_layout Plain Layout
11598 \begin_inset Formula $\bar{A}$
11607 <row topspace="1.5mm">
11608 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11611 \begin_layout Plain Layout
11615 \begin_inset space \textvisiblespace{}
11623 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11626 \begin_layout Plain Layout
11627 \begin_inset Formula $\mathring{A}$
11641 \begin_inset space \hfill{}
11645 \begin_inset Tabular
11646 <lyxtabular version="3" rows="7" columns="2">
11647 <features booktabs="true" tabularvalignment="middle">
11648 <column alignment="center" valignment="top" width="0pt">
11649 <column alignment="center" valignment="top" width="0pt">
11651 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11654 \begin_layout Plain Layout
11660 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11663 \begin_layout Plain Layout
11670 <row topspace="1.5mm">
11671 <cell alignment="center" valignment="top" usebox="none">
11674 \begin_layout Plain Layout
11678 \begin_inset space \textvisiblespace{}
11686 <cell alignment="center" valignment="top" usebox="none">
11689 \begin_layout Plain Layout
11690 \begin_inset Formula $\tilde{A}$
11699 <row topspace="1.5mm">
11700 <cell alignment="center" valignment="top" usebox="none">
11703 \begin_layout Plain Layout
11707 \begin_inset space \textvisiblespace{}
11715 <cell alignment="center" valignment="top" usebox="none">
11718 \begin_layout Plain Layout
11719 \begin_inset Formula $\hat{A}$
11728 <row topspace="1.5mm">
11729 <cell alignment="center" valignment="top" usebox="none">
11732 \begin_layout Plain Layout
11736 \begin_inset space \textvisiblespace{}
11744 <cell alignment="center" valignment="top" usebox="none">
11747 \begin_layout Plain Layout
11748 \begin_inset Formula $\check{A}$
11757 <row topspace="1.5mm">
11758 <cell alignment="center" valignment="top" usebox="none">
11761 \begin_layout Plain Layout
11765 \begin_inset space \textvisiblespace{}
11773 <cell alignment="center" valignment="top" usebox="none">
11776 \begin_layout Plain Layout
11777 \begin_inset Formula $\acute{A}$
11786 <row topspace="1.5mm">
11787 <cell alignment="center" valignment="top" usebox="none">
11790 \begin_layout Plain Layout
11794 \begin_inset space \textvisiblespace{}
11802 <cell alignment="center" valignment="top" usebox="none">
11805 \begin_layout Plain Layout
11806 \begin_inset Formula $\grave{A}$
11815 <row topspace="1.5mm">
11816 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11819 \begin_layout Plain Layout
11823 \begin_inset space \textvisiblespace{}
11831 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11834 \begin_layout Plain Layout
11835 \begin_inset Formula $\breve{A}$
11849 \begin_inset space \hfill{}
11855 \begin_layout Standard
11856 \begin_inset VSpace bigskip
11862 \begin_layout Standard
11863 You can directly insert accents such as é in formulas.
11865 will transform them to the corresponding accent command.
11867 \begin_inset Index idx
11872 \begin_layout Plain Layout
11878 however it is better to insert a quotation mark before the vowel.
11879 These two characters are then treated by \SpecialChar LaTeX
11884 character when the formula part with the umlaut is marked as German.
11893 \begin_inset Quotes eld
11897 \begin_inset Quotes erd
11900 umlauts are created as demonstrated in the following example:
11903 \begin_layout Standard
11904 \begin_inset VSpace -2mm
11910 \begin_layout Standard
11912 \begin_inset Tabular
11913 <lyxtabular version="3" rows="3" columns="2">
11914 <features booktabs="true" tabularvalignment="middle">
11915 <column alignment="center" valignment="top" width="0pt">
11916 <column alignment="center" valignment="top">
11918 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11921 \begin_layout Plain Layout
11927 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11930 \begin_layout Plain Layout
11938 <cell alignment="center" valignment="top" usebox="none">
11941 \begin_layout Plain Layout
11942 \begin_inset Quotes grd
11950 <cell alignment="center" valignment="top" usebox="none">
11953 \begin_layout Plain Layout
11954 \begin_inset space \hspace{}
11961 \begin_inset Formula $"i$
11970 <row topspace="1.5mm">
11971 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11974 \begin_layout Plain Layout
11978 \begin_inset space \textvisiblespace{}
11986 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11989 \begin_layout Plain Layout
11990 \begin_inset Formula $\ddot{i}$
12006 \begin_layout Standard
12013 is that umlauts can be directly converted to mathematical text because the accent commands above are
12019 in mathematical text
12022 To convert an accented character to mathematical text,
12023 only the character under the accent may be converted.
12024 This applies for all conversions,
12026 \begin_inset space \thinspace{}
12030 \begin_inset space \space{}
12036 \begin_layout Standard
12037 \begin_inset VSpace bigskip
12043 \begin_layout Standard
12045 also supports a tilde under the character if the \SpecialChar LaTeX
12051 \begin_inset Index idx
12056 \begin_layout Plain Layout
12058 \begin_inset IndexMacro subentry
12061 \begin_layout Plain Layout
12072 is installed on your system:
12075 \begin_layout Standard
12079 \begin_layout Plain Layout
12089 \begin_inset Note Note
12092 \begin_layout Plain Layout
12093 The following table will only be displayed when the \SpecialChar LaTeX
12106 \begin_layout Standard
12109 \begin_inset Tabular
12110 <lyxtabular version="3" rows="2" columns="2">
12111 <features booktabs="true" tabularvalignment="middle">
12112 <column alignment="center" valignment="top" width="0pt">
12113 <column alignment="center" valignment="top" width="0pt">
12115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12118 \begin_layout Plain Layout
12124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12127 \begin_layout Plain Layout
12135 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
12138 \begin_layout Plain Layout
12142 \begin_inset space \textvisiblespace{}
12150 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12153 \begin_layout Plain Layout
12154 \begin_inset Formula $\utilde{A}$
12170 \begin_layout Standard
12174 \begin_layout Plain Layout
12184 \begin_inset Note Note
12187 \begin_layout Plain Layout
12188 The following will be displayed when the \SpecialChar LaTeX
12201 \begin_layout Standard
12202 You need to install the \SpecialChar LaTeX
12207 to see the rest of this subsection in the output.
12210 \begin_layout Standard
12214 \begin_layout Plain Layout
12226 \begin_layout Subsection
12227 Accents for Several Characters
12228 \begin_inset Index idx
12233 \begin_layout Plain Layout
12235 \begin_inset IndexMacro subentry
12238 \begin_layout Plain Layout
12239 for several characters
12252 \begin_layout Standard
12253 \begin_inset space \hfill{}
12257 \begin_inset Tabular
12258 <lyxtabular version="3" rows="5" columns="2">
12259 <features booktabs="true" tabularvalignment="middle">
12260 <column alignment="center" valignment="top" width="0pt">
12261 <column alignment="center" valignment="top" width="0pt">
12263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12266 \begin_layout Plain Layout
12272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12275 \begin_layout Plain Layout
12282 <row topspace="1.5mm">
12283 <cell alignment="center" valignment="top" usebox="none">
12286 \begin_layout Plain Layout
12290 \begin_inset space \textvisiblespace{}
12298 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12301 \begin_layout Plain Layout
12302 \begin_inset Formula $\overleftarrow{A=B}$
12311 <row topspace="1.5mm">
12312 <cell alignment="center" valignment="top" usebox="none">
12315 \begin_layout Plain Layout
12319 \begin_inset space \textvisiblespace{}
12327 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12330 \begin_layout Plain Layout
12331 \begin_inset Formula $\underleftarrow{A=B}$
12340 <row topspace="1.5mm">
12341 <cell alignment="center" valignment="top" usebox="none">
12344 \begin_layout Plain Layout
12348 \begin_inset space \textvisiblespace{}
12356 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12359 \begin_layout Plain Layout
12360 \begin_inset Formula $\overleftrightarrow{A=B}$
12369 <row topspace="1.5mm" bottomspace="1mm">
12370 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12373 \begin_layout Plain Layout
12376 underleftrightarrow
12377 \begin_inset space \textvisiblespace{}
12385 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12388 \begin_layout Plain Layout
12389 \begin_inset Formula $\underleftrightarrow{A=B}$
12403 \begin_inset space \hfill{}
12407 \begin_inset Tabular
12408 <lyxtabular version="3" rows="5" columns="2">
12409 <features booktabs="true" tabularvalignment="middle">
12410 <column alignment="center" valignment="top" width="0pt">
12411 <column alignment="center" valignment="top" width="0pt">
12413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12416 \begin_layout Plain Layout
12422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12425 \begin_layout Plain Layout
12432 <row topspace="1.5mm">
12433 <cell alignment="center" valignment="top" usebox="none">
12436 \begin_layout Plain Layout
12440 \begin_inset space \textvisiblespace{}
12448 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12451 \begin_layout Plain Layout
12452 \begin_inset Formula $\overrightarrow{A=B}$
12461 <row topspace="1.5mm">
12462 <cell alignment="center" valignment="top" usebox="none">
12465 \begin_layout Plain Layout
12469 \begin_inset space \textvisiblespace{}
12477 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12480 \begin_layout Plain Layout
12481 \begin_inset Formula $\underrightarrow{A=B}$
12490 <row topspace="1.5mm">
12491 <cell alignment="center" valignment="top" usebox="none">
12494 \begin_layout Plain Layout
12498 \begin_inset space \textvisiblespace{}
12506 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12509 \begin_layout Plain Layout
12510 \begin_inset Formula $\widetilde{A=B}$
12519 <row topspace="1.5mm" bottomspace="1mm">
12520 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12523 \begin_layout Plain Layout
12527 \begin_inset space \textvisiblespace{}
12535 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12538 \begin_layout Plain Layout
12539 \begin_inset Formula $\widehat{A=B}$
12553 \begin_inset space \hfill{}
12559 \begin_layout Standard
12560 \begin_inset VSpace medskip
12563 Using these commands you can accent as many characters as you like.
12576 will only be set in the output with a length of three characters,
12577 as shown in the following example:
12578 \begin_inset Formula
12580 \widetilde{A+B=C-D}
12588 \begin_layout Standard
12589 It is also possible to accent several characters using the commands
12596 \begin_inset Index idx
12601 \begin_layout Plain Layout
12603 \begin_inset IndexMacro subentry
12606 \begin_layout Plain Layout
12613 \begin_inset IndexMacro subentry
12616 \begin_layout Plain Layout
12636 \begin_inset Index idx
12641 \begin_layout Plain Layout
12643 \begin_inset IndexMacro subentry
12646 \begin_layout Plain Layout
12653 \begin_inset IndexMacro subentry
12656 \begin_layout Plain Layout
12669 described in the previous subsection.
12675 \begin_inset space \textvisiblespace{}
12679 \begin_inset Formula $\downarrow$
12685 \begin_inset Formula
12687 \underset{***}{A=B}
12695 \begin_layout Section
12697 \begin_inset CommandInset label
12699 name "subsec:Space"
12704 \begin_inset Index idx
12709 \begin_layout Plain Layout
12711 \begin_inset IndexMacro subentry
12714 \begin_layout Plain Layout
12728 \begin_layout Subsection
12730 \begin_inset CommandInset label
12732 name "subsec:Predefined-Space"
12737 \begin_inset Index idx
12742 \begin_layout Plain Layout
12744 \begin_inset IndexMacro subentry
12747 \begin_layout Plain Layout
12754 \begin_inset IndexMacro subentry
12757 \begin_layout Plain Layout
12771 \begin_layout Standard
12772 Sometimes it is necessary to insert horizontal space into a formula.
12773 This is done by inserting a
12774 \change_deleted 177693 1654668870
12776 \change_inserted 177693 1654668872
12780 \change_inserted 5863208 1612729962
12784 arg "command-alternatives math-space ; space-insert protected"
12788 \change_deleted 5863208 1612729965
12792 arg "command-alternatives space-insert protected ; math-space"
12796 \begin_inset Note Note
12799 \begin_layout Plain Layout
12801 \change_inserted 232239728 1611160593
12802 What is intended here?
12813 \begin_inset Quotes eld
12819 \begin_inset space \textvisiblespace{}
12825 \begin_inset Quotes erd
12828 appears and by pressing
12832 several times one can select one of eight different space sizes.
12833 The spaces can also be inserted using the math toolbar button
12836 arg "math-insert \\space"
12839 or special commands.
12840 The size can be adjusted at any time by positioning the cursor on the
12843 arg "math-insert \\space"
12850 until the desired size is achieved.
12853 \begin_layout Standard
12856 \begin_inset Tabular
12857 <lyxtabular version="3" rows="6" columns="3">
12858 <features booktabs="true" tabularvalignment="middle">
12859 <column alignment="center" valignment="top">
12860 <column alignment="center" valignment="top" width="15col%">
12861 <column alignment="center" valignment="top">
12863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12866 \begin_layout Plain Layout
12872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12875 \begin_layout Plain Layout
12885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12888 \begin_layout Plain Layout
12896 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12899 \begin_layout Plain Layout
12907 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12910 \begin_layout Plain Layout
12916 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12919 \begin_layout Plain Layout
12920 \begin_inset Formula $A\,B$
12930 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12933 \begin_layout Plain Layout
12941 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12944 \begin_layout Plain Layout
12950 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12953 \begin_layout Plain Layout
12954 \begin_inset Formula $A\:B$
12964 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12967 \begin_layout Plain Layout
12975 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12978 \begin_layout Plain Layout
12984 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12987 \begin_layout Plain Layout
12988 \begin_inset Formula $A\;B$
12998 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13001 \begin_layout Plain Layout
13009 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13012 \begin_layout Plain Layout
13018 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13021 \begin_layout Plain Layout
13022 \begin_inset Formula $A\quad B$
13032 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13035 \begin_layout Plain Layout
13043 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13046 \begin_layout Plain Layout
13052 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13055 \begin_layout Plain Layout
13056 \begin_inset Formula $A\qquad B$
13070 \begin_inset space \hfill{}
13074 \begin_inset Tabular
13075 <lyxtabular version="3" rows="6" columns="3">
13076 <features booktabs="true" tabularvalignment="middle">
13077 <column alignment="center" valignment="top">
13078 <column alignment="center" valignment="top" width="15col%">
13079 <column alignment="center" valignment="top">
13081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13084 \begin_layout Plain Layout
13090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13093 \begin_layout Plain Layout
13103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13106 \begin_layout Plain Layout
13114 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13117 \begin_layout Plain Layout
13125 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13128 \begin_layout Plain Layout
13134 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13137 \begin_layout Plain Layout
13138 \begin_inset Formula $A\hfill B$
13148 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13151 \begin_layout Plain Layout
13159 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13162 \begin_layout Plain Layout
13168 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13171 \begin_layout Plain Layout
13172 \begin_inset Formula $A\hspace*{1em}B$
13182 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13185 \begin_layout Plain Layout
13193 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13196 \begin_layout Plain Layout
13202 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13205 \begin_layout Plain Layout
13206 \begin_inset Formula $A\hspace{1em}B$
13216 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13219 \begin_layout Plain Layout
13223 \begin_inset space \textvisiblespace{}
13231 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13234 \begin_layout Plain Layout
13240 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13243 \begin_layout Plain Layout
13244 \begin_inset Formula $A\ B$
13254 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13257 \begin_layout Plain Layout
13265 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13268 \begin_layout Plain Layout
13274 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13277 \begin_layout Plain Layout
13278 \begin_inset Formula $A\!B$
13294 \begin_layout Standard
13296 \begin_inset space ~
13300 \begin_inset space \thinspace{}
13304 \begin_inset space \thinspace{}
13307 7 are variable spaces which are explained in
13308 \begin_inset CommandInset ref
13310 reference "subsec:Variable-Space"
13317 \begin_inset space ~
13320 9 appears to produce no space.
13321 It is displayed red in \SpecialChar LyX
13322 contrary to the other sizes,
13323 because it is a negative space.
13324 There are two more negative spaces:
13327 \begin_layout Standard
13329 \begin_inset Tabular
13330 <lyxtabular version="3" rows="3" columns="3">
13331 <features booktabs="true" tabularvalignment="middle">
13332 <column alignment="center" valignment="middle" width="6.8cm">
13333 <column alignment="center" valignment="top" width="0pt">
13334 <column alignment="center" valignment="top" width="0pt">
13336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13339 \begin_layout Plain Layout
13345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13348 \begin_layout Plain Layout
13356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13359 \begin_layout Plain Layout
13369 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13372 \begin_layout Plain Layout
13377 keystrokes after inserting the
13378 \change_deleted 177693 1654668881
13380 \change_inserted 177693 1654668883
13388 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13391 \begin_layout Plain Layout
13397 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13400 \begin_layout Plain Layout
13408 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13411 \begin_layout Plain Layout
13417 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13420 \begin_layout Plain Layout
13421 \begin_inset Formula $A\negmedspace B$
13429 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13432 \begin_layout Plain Layout
13433 \begin_inset Formula $A\negthickspace B$
13449 \begin_layout Standard
13450 Negative spaces can lead to characters overlapping each other.
13451 Thus they can be used to enforce ligatures,
13452 which are useful for things such as summation operators:
13455 \begin_layout Standard
13457 \begin_inset Tabular
13458 <lyxtabular version="3" rows="3" columns="2">
13459 <features booktabs="true" tabularvalignment="middle">
13460 <column alignment="center" valignment="top" width="0pt">
13461 <column alignment="center" valignment="top">
13463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13466 \begin_layout Plain Layout
13472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13475 \begin_layout Plain Layout
13483 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13486 \begin_layout Plain Layout
13492 \begin_inset space \textvisiblespace{}
13500 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13503 \begin_layout Plain Layout
13504 \begin_inset Formula $\sum\sum f_{kl}$
13514 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13517 \begin_layout Plain Layout
13525 \begin_inset space \textvisiblespace{}
13533 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13536 \begin_layout Plain Layout
13537 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
13553 \begin_layout Standard
13555 \begin_inset VSpace medskip
13561 \begin_layout Standard
13563 Relational operators,
13564 for example equal or less than signs,
13565 are always surrounded by space.
13567 the operator is placed into a \SpecialChar TeX
13569 The following example demonstrates this:
13572 \begin_layout Standard
13574 \begin_inset Tabular
13575 <lyxtabular version="3" rows="2" columns="2">
13576 <features tabularvalignment="middle">
13577 <column alignment="center" valignment="top" width="0pt">
13578 <column alignment="center" valignment="top" width="0pt">
13580 <cell alignment="center" valignment="top" usebox="none">
13583 \begin_layout Plain Layout
13589 <cell alignment="center" valignment="top" usebox="none">
13592 \begin_layout Plain Layout
13593 \begin_inset Formula $A=B$
13603 <cell alignment="center" valignment="top" usebox="none">
13606 \begin_layout Plain Layout
13607 Equation without space
13612 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
13615 \begin_layout Plain Layout
13616 \begin_inset Formula $A{=}B$
13632 \begin_layout Standard
13634 The command for the last formula is:
13640 \begin_inset Formula $\to$
13646 \begin_layout Standard
13647 \begin_inset VSpace bigskip
13653 \begin_layout Standard
13654 Another example of controlled spaces is physical units.
13655 The space between a value and its unit is smaller than a normal space,
13656 typically a thin space is used.
13658 the smaller space is inserted via the menu
13660 Insert\SpecialChar menuseparator
13661 Formatting\SpecialChar menuseparator
13663 \begin_inset space ~
13671 arg "space-insert thin"
13677 \begin_layout Standard
13678 An example to visualize the difference:
13681 \begin_layout Standard
13682 \begin_inset Tabular
13683 <lyxtabular version="3" rows="2" columns="2">
13684 <features tabularvalignment="middle">
13685 <column alignment="left" valignment="top">
13686 <column alignment="left" valignment="top">
13688 <cell alignment="center" valignment="top" usebox="none">
13691 \begin_layout Plain Layout
13693 \begin_inset Formula $\cdot$
13701 <cell alignment="center" valignment="top" usebox="none">
13704 \begin_layout Plain Layout
13705 Space between value and unit
13712 <cell alignment="center" valignment="top" usebox="none">
13715 \begin_layout Plain Layout
13717 \begin_inset space \thinspace{}
13721 \begin_inset Formula $\cdot$
13729 <cell alignment="center" valignment="top" usebox="none">
13732 \begin_layout Plain Layout
13733 Thin space between value and unit
13746 \begin_layout Subsection
13751 \begin_layout Plain Layout
13764 \begin_layout Plain Layout
13765 For vertical space in formulas see
13766 \begin_inset CommandInset ref
13768 reference "subsec:Line-Separation"
13782 \begin_layout Plain Layout
13790 \begin_inset Note Note
13793 \begin_layout Plain Layout
13796 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
13799 \begin_layout Plain Layout
13802 texorpdfstring is in section
13803 \begin_inset CommandInset ref
13805 reference "subsec:Formulas-in-Section"
13816 \begin_inset CommandInset label
13818 name "subsec:Variable-Space"
13823 \begin_inset Index idx
13828 \begin_layout Plain Layout
13830 \begin_inset IndexMacro subentry
13833 \begin_layout Plain Layout
13840 \begin_inset IndexMacro subentry
13843 \begin_layout Plain Layout
13857 \begin_layout Standard
13858 Space with a defined length can be inserted with the command
13865 \begin_inset Index idx
13870 \begin_layout Plain Layout
13872 \begin_inset IndexMacro subentry
13875 \begin_layout Plain Layout
13882 \begin_inset IndexMacro subentry
13885 \begin_layout Plain Layout
13900 \begin_inset Quotes eld
13906 \begin_inset space \textvisiblespace{}
13912 \begin_inset Quotes erd
13916 the length of which can be specified by left-clicking on the
13917 \begin_inset Quotes eld
13923 \begin_inset space \textvisiblespace{}
13929 \begin_inset Quotes erd
13933 The length may also be negative.
13934 If the space is the first character in a line,
13935 it will ordinarily be omitted.
13936 To force its output use the command
13948 or left-click on the
13949 \begin_inset Quotes eld
13955 \begin_inset space \textvisiblespace{}
13961 \begin_inset Quotes erd
13964 and check the option
13969 \begin_inset Newline newline
13972 To insert as much space as is available,
13980 \begin_inset Index idx
13985 \begin_layout Plain Layout
13987 \begin_inset IndexMacro subentry
13990 \begin_layout Plain Layout
13997 \begin_inset IndexMacro subentry
14000 \begin_layout Plain Layout
14016 \begin_layout Standard
14018 \begin_inset Tabular
14019 <lyxtabular version="3" rows="4" columns="2">
14020 <features booktabs="true" tabularvalignment="middle">
14021 <column alignment="center" valignment="top" width="0pt">
14022 <column alignment="center" valignment="top">
14024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14027 \begin_layout Plain Layout
14035 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14038 \begin_layout Plain Layout
14046 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14049 \begin_layout Plain Layout
14053 \begin_inset space \textvisiblespace{}
14059 \begin_inset space \thinspace{}
14067 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14070 \begin_layout Plain Layout
14071 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
14081 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14084 \begin_layout Plain Layout
14088 \begin_inset space \textvisiblespace{}
14094 \begin_inset space \thinspace{}
14102 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14105 \begin_layout Plain Layout
14106 \begin_inset Formula $A\hspace{-1mm}A\not=A$
14116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14119 \begin_layout Plain Layout
14123 \begin_inset space \textvisiblespace{}
14131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14134 \begin_layout Plain Layout
14135 \begin_inset Formula $A=A\hfill B=B$
14151 \begin_layout Standard
14152 In the last example the available space is given by the longest column entry of the table.
14153 In an inline formula the space depends on the length of the line in which
14161 when the line uses the full width,
14162 no space will be created.
14169 only has an effect on displayed formulas when the formula style
14174 (Formula styles are explained in
14175 \begin_inset CommandInset ref
14177 reference "sec:Formula-Styles"
14185 \begin_layout Standard
14193 there are also commands,
14207 that fill the space with a pattern.
14209 \begin_inset CommandInset ref
14211 reference "subsec:Ellipses"
14219 \begin_layout Standard
14221 variable space can be inserted via the menu
14223 Insert\SpecialChar menuseparator
14224 Formatting\SpecialChar menuseparator
14226 \begin_inset space ~
14234 \begin_layout Standard
14235 This is a line with
14236 \begin_inset space \hspace{}
14241 \begin_inset space \thinspace{}
14247 \begin_layout Standard
14248 This is a line with
14249 \begin_inset space \hfill{}
14255 \begin_layout Subsection
14256 Space Besides Inline Formulas
14257 \begin_inset Index idx
14262 \begin_layout Plain Layout
14264 \begin_inset IndexMacro subentry
14267 \begin_layout Plain Layout
14268 besides inline formulas
14281 \begin_layout Standard
14282 The space that surrounds inline formulas can be adjusted with the length
14289 \begin_inset Index idx
14294 \begin_layout Plain Layout
14296 \begin_inset IndexMacro subentry
14299 \begin_layout Plain Layout
14306 \begin_inset IndexMacro subentry
14309 \begin_layout Plain Layout
14323 The value of a length is set with the command
14330 \begin_inset Index idx
14335 \begin_layout Plain Layout
14337 \begin_inset IndexMacro subentry
14340 \begin_layout Plain Layout
14347 \begin_inset IndexMacro subentry
14350 \begin_layout Plain Layout
14363 which has the following scheme:
14366 \begin_layout Standard
14371 setlength{length name}{value}
14374 \begin_layout Standard
14382 \begin_inset space \thinspace{}
14389 \begin_layout Standard
14399 \begin_layout Standard
14400 is inserted in \SpecialChar TeX
14403 \begin_inset space \thinspace{}
14406 mm space will now be set around all inline formulas:
14410 \begin_layout Plain Layout
14424 \begin_layout Standard
14425 This is a line with an inline formula
14426 \begin_inset Formula $A=B$
14430 \begin_inset space \thinspace{}
14433 mm surrounding space.
14437 \begin_layout Plain Layout
14451 \begin_layout Standard
14452 To return to the predefined value,
14459 is set to the value 0
14460 \begin_inset space \thinspace{}
14466 \begin_layout Section
14468 \begin_inset Index idx
14473 \begin_layout Plain Layout
14480 \begin_inset Index idx
14485 \begin_layout Plain Layout
14487 \begin_inset IndexMacro see
14490 \begin_layout Plain Layout
14504 \begin_layout Standard
14505 Boxes for text are described in chapter
14512 \begin_inset space ~
14520 \begin_layout Subsection
14522 \begin_inset CommandInset label
14524 name "subsec:Boxes-with-Frame"
14529 \begin_inset Index idx
14534 \begin_layout Plain Layout
14536 \begin_inset IndexMacro subentry
14539 \begin_layout Plain Layout
14553 \begin_layout Standard
14554 It is possible to frame a formula or part of one with the commands
14561 \begin_inset Index idx
14566 \begin_layout Plain Layout
14568 \begin_inset IndexMacro subentry
14571 \begin_layout Plain Layout
14578 \begin_inset IndexMacro subentry
14581 \begin_layout Plain Layout
14601 \begin_inset Index idx
14606 \begin_layout Plain Layout
14608 \begin_inset IndexMacro subentry
14611 \begin_layout Plain Layout
14618 \begin_inset IndexMacro subentry
14621 \begin_layout Plain Layout
14637 \begin_layout Standard
14638 When one of these commands is inserted in a formula,
14639 a blue box appears within a frame to enter formula parts.
14646 an additional formula has to be created by
14651 because the box content will otherwise be treated as mathematical text.
14659 a new formula is automatically created inside the frame.
14662 \begin_layout Standard
14669 is not suitable to frame displayed formulas because the formula will always be set in the size of the documents text.
14676 is not suitable to frame inline formulas because the formula will always be set in the size of a displayed formula.
14679 \begin_layout Standard
14693 \begin_inset Index idx
14698 \begin_layout Plain Layout
14700 \begin_inset IndexMacro subentry
14703 \begin_layout Plain Layout
14710 \begin_inset IndexMacro subentry
14713 \begin_layout Plain Layout
14726 with which the frame width and the alignment can be specified.
14733 is used in the following scheme:
14736 \begin_layout Standard
14741 framebox[frame width][position]{box content}
14744 \begin_layout Standard
14745 The position can either be
14762 right aligns the formula in the box.
14763 If no position is given the formula will be centered.
14764 \begin_inset Newline newline
14767 If width is not given then position can not be given.
14768 In this case the frame width is adjusted to the box content like for
14777 \begin_layout Standard
14785 a box appears containing three blue boxes.
14786 The first two boxes are surrounded by brackets and denote the two optional arguments.
14787 The third box is for formula parts like for
14796 \begin_layout Standard
14798 \begin_inset Tabular
14799 <lyxtabular version="3" rows="5" columns="2">
14800 <features booktabs="true" tabularvalignment="middle">
14801 <column alignment="center" valignment="top" width="0pt">
14802 <column alignment="center" valignment="top">
14804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14807 \begin_layout Plain Layout
14813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14816 \begin_layout Plain Layout
14823 <row topspace="1.5mm">
14824 <cell alignment="center" valignment="top" usebox="none">
14827 \begin_layout Plain Layout
14831 \begin_inset space \textvisiblespace{}
14841 \begin_inset space \textvisiblespace{}
14849 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14852 \begin_layout Plain Layout
14853 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
14862 <row topspace="1.5mm">
14863 <cell alignment="center" valignment="top" usebox="none">
14866 \begin_layout Plain Layout
14870 \begin_inset space \textvisiblespace{}
14876 \begin_inset space \textvisiblespace{}
14884 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14887 \begin_layout Plain Layout
14888 \begin_inset Formula $\boxed{\int A=B}$
14897 <row topspace="1.5mm">
14898 <cell alignment="center" valignment="top" usebox="none">
14901 \begin_layout Plain Layout
14905 \begin_inset space \textvisiblespace{}
14913 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14916 \begin_layout Plain Layout
14917 \begin_inset Formula $A+\fbox{B}$
14926 <row topspace="1.5mm" bottomspace="1mm">
14927 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
14930 \begin_layout Plain Layout
14934 \begin_inset space \textvisiblespace{}
14938 \begin_inset Formula $\to$
14942 \begin_inset Formula $\to$
14952 \begin_inset space \textvisiblespace{}
14956 \begin_inset Formula $\downarrow$
14964 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
14967 \begin_layout Plain Layout
14968 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
14984 \begin_layout Standard
14985 To adjust the frame thickness the following commands are inserted in \SpecialChar TeX
14986 mode before the formula:
14989 \begin_layout Standard
14999 \begin_inset Quotes eld
15003 \begin_inset Quotes erd
15017 \begin_inset Quotes eld
15021 \begin_inset Quotes erd
15027 \begin_layout Standard
15028 \begin_inset Quotes eld
15032 \begin_inset Quotes erd
15035 specifies the minimum distance between the frame and the first character in the box.
15036 An example of this is given in the following framed formula:
15040 \begin_layout Plain Layout
15052 \begin_inset Formula
15059 Before this formula the commands
15062 \begin_layout Standard
15084 \begin_layout Standard
15085 were inserted in \SpecialChar TeX
15087 These values are then used for all following boxes.
15090 \begin_layout Standard
15091 To return to the standard frame size,
15095 \begin_layout Standard
15120 \begin_layout Plain Layout
15134 \begin_layout Standard
15135 is inserted in \SpecialChar TeX
15136 mode before the next formula.
15139 \begin_layout Subsection
15140 Boxes Without Frame
15141 \begin_inset CommandInset label
15143 name "subsec:Boxes-without-Frame"
15148 \begin_inset Index idx
15153 \begin_layout Plain Layout
15155 \begin_inset IndexMacro subentry
15158 \begin_layout Plain Layout
15172 \begin_layout Standard
15173 For boxes without a frame the following box commands:
15181 \begin_inset Index idx
15186 \begin_layout Plain Layout
15188 \begin_inset IndexMacro subentry
15191 \begin_layout Plain Layout
15198 \begin_inset IndexMacro subentry
15201 \begin_layout Plain Layout
15222 \begin_inset Index idx
15227 \begin_layout Plain Layout
15229 \begin_inset IndexMacro subentry
15232 \begin_layout Plain Layout
15239 \begin_inset IndexMacro subentry
15242 \begin_layout Plain Layout
15262 \begin_inset Index idx
15267 \begin_layout Plain Layout
15269 \begin_inset IndexMacro subentry
15272 \begin_layout Plain Layout
15279 \begin_inset IndexMacro subentry
15282 \begin_layout Plain Layout
15298 \begin_layout Standard
15305 a box can be super- or subscripted.
15306 But in contrary to normal super- and subscripting,
15307 the characters in the box keep their font size.
15314 is used in the following scheme:
15317 \begin_layout Standard
15322 raisebox{height}{box content}
15325 \begin_layout Standard
15326 When the box contains a formula,
15327 an extra formula is needed like for
15336 \begin_layout Standard
15339 \begin_inset Note Greyedout
15342 \begin_layout Plain Layout
15354 this extra formula is created by pressing
15358 twice instead of once because \SpecialChar LyX
15359 doesn't yet support
15373 \begin_layout Standard
15375 \begin_inset Tabular
15376 <lyxtabular version="3" rows="4" columns="2">
15377 <features booktabs="true" tabularvalignment="middle">
15378 <column alignment="center" valignment="top" width="0pt">
15379 <column alignment="center" valignment="top">
15381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15384 \begin_layout Plain Layout
15390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15393 \begin_layout Plain Layout
15401 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15404 \begin_layout Plain Layout
15408 \begin_inset Formula $\to$
15414 \begin_inset Formula $\to$
15422 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15425 \begin_layout Plain Layout
15426 \begin_inset Formula $H\raisebox{2mm}{al}lo$
15436 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15439 \begin_layout Plain Layout
15443 \begin_inset Formula $\to$
15449 \begin_inset Formula $\to$
15457 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15460 \begin_layout Plain Layout
15461 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
15471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15474 \begin_layout Plain Layout
15478 \begin_inset Formula $\to$
15494 \begin_inset space \textvisiblespace{}
15502 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15505 \begin_layout Plain Layout
15506 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
15522 \begin_layout Standard
15548 except that there is no frame.
15551 \begin_layout Subsection
15553 \begin_inset CommandInset label
15555 name "subsec:Colored-Boxes"
15560 \begin_inset Index idx
15565 \begin_layout Plain Layout
15567 \begin_inset IndexMacro subentry
15570 \begin_layout Plain Layout
15584 \begin_layout Standard
15585 To be able to use all commands explained in this section,
15586 the \SpecialChar LaTeX
15595 \begin_layout Plain Layout
15596 The \SpecialChar LaTeX
15601 is part of every \SpecialChar LaTeX
15602 standard installation.
15608 \begin_inset Index idx
15613 \begin_layout Plain Layout
15615 \begin_inset IndexMacro subentry
15618 \begin_layout Plain Layout
15629 must be loaded in the \SpecialChar LaTeX
15630 -preamble with the line
15634 \begin_layout Plain Layout
15635 When text is colored somewhere in the document with a predefined color,
15637 loads the \SpecialChar LaTeX
15643 Thus it is possible that the package is loaded twice,
15644 but this does not cause problems.
15650 \begin_inset Note Note
15653 \begin_layout Plain Layout
15654 To avoid that the package is loaded twice,
15655 a macro was inserted to the \SpecialChar LaTeX
15664 \begin_layout Standard
15672 \begin_layout Standard
15673 \begin_inset VSpace medskip
15676 To create color boxes,
15684 \begin_inset Index idx
15689 \begin_layout Plain Layout
15691 \begin_inset IndexMacro subentry
15694 \begin_layout Plain Layout
15701 \begin_inset IndexMacro subentry
15704 \begin_layout Plain Layout
15717 is used in the following scheme:
15720 \begin_layout Standard
15725 colorbox{color}{box content}
15728 \begin_layout Standard
15729 The box content can also be a box and a
15735 can also be part of another box (see the 2nd and 3rd example).
15736 When the box should contain a formula,
15737 an extra formula has to be created,
15738 the same way as for
15748 \begin_layout Plain Layout
15749 This also applies for the command
15763 \begin_layout Standard
15764 One of the following predefined colors can be chosen:
15767 \begin_layout Standard
15805 \begin_inset VSpace smallskip
15811 \begin_layout Standard
15813 \begin_inset Tabular
15814 <lyxtabular version="3" rows="4" columns="2">
15815 <features booktabs="true" tabularvalignment="middle">
15816 <column alignment="center" valignment="top" width="0pt">
15817 <column alignment="center" valignment="top">
15819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15822 \begin_layout Plain Layout
15828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15831 \begin_layout Plain Layout
15839 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15842 \begin_layout Plain Layout
15846 \begin_inset Formula $\to$
15856 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15859 \begin_layout Plain Layout
15860 \begin_inset Formula $\colorbox{yellow}{A=B}$
15869 <row topspace="1.5mm">
15870 <cell alignment="center" valignment="top" usebox="none">
15873 \begin_layout Plain Layout
15877 \begin_inset Formula $\to$
15885 \begin_inset space \textvisiblespace{}
15889 \change_inserted 232239728 1611182042
15891 \begin_inset Formula $\gets\gets$
15901 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15904 \begin_layout Plain Layout
15905 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
15914 <row topspace="1.5mm" bottomspace="1mm">
15915 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15918 \begin_layout Plain Layout
15922 \begin_inset space \textvisiblespace{}
15926 \change_inserted 232239728 1611182036
15928 \begin_inset Formula $\gets\gets$
15936 \begin_inset Formula $\to$
15952 \begin_inset space \textvisiblespace{}
15960 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15963 \begin_layout Plain Layout
15964 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
15978 \begin_inset VSpace smallskip
15984 \begin_layout Standard
15991 only colors the box background,
15992 not the characters in the box.
15993 To color all characters,
15994 the whole formula is highlighted and the desired color is chosen in the
15997 \begin_inset space ~
16003 The dialog can be called with the toolbar button
16006 arg "dialog-show character"
16011 Edit\SpecialChar menuseparator
16013 \begin_inset space ~
16016 Properties\SpecialChar menuseparator
16020 The formula number will have the same color as the formula.
16021 If a different color for the formula number is desired,
16022 the color must be changed within the formula.
16025 \begin_layout Standard
16029 \begin_layout Standard
16032 \begin_inset Formula
16034 \int A=B\label{eq:red}
16042 \begin_inset Formula
16044 \textcolor{red}{\int A=B}\label{eq:redgreen}
16052 \begin_layout Standard
16054 \begin_inset CommandInset ref
16061 is completely colored red.
16062 \begin_inset Newline newline
16066 \begin_inset CommandInset ref
16068 reference "eq:redgreen"
16073 was first completely colored green to set the color for the formula number.
16074 Subsequently the formula characters were colored red.
16077 \begin_layout Standard
16078 \begin_inset VSpace bigskip
16081 To color the frame different than the rest of the box,
16089 \begin_inset Index idx
16094 \begin_layout Plain Layout
16096 \begin_inset IndexMacro subentry
16099 \begin_layout Plain Layout
16106 \begin_inset IndexMacro subentry
16109 \begin_layout Plain Layout
16122 is used in the following scheme:
16125 \begin_layout Standard
16130 fcolorbox{frame color}{color}{box content}
16133 \begin_layout Standard
16140 is an extension of the command
16147 The frame width is set,
16172 \begin_layout Plain Layout
16184 \begin_inset Formula
16186 \fcolorbox{cyan}{magenta}{A=B}
16195 \begin_layout Plain Layout
16209 \begin_layout Standard
16210 This formula was created with the command
16211 \begin_inset Newline newline
16219 \begin_inset Formula $\to$
16225 \begin_inset Formula $\to$
16235 \begin_layout Standard
16236 \begin_inset VSpace bigskip
16239 To use colors other than predefined ones,
16240 they must be defined first.
16243 \begin_layout Standard
16244 One can for example define the color
16245 \begin_inset Quotes eld
16253 \begin_inset Quotes erd
16256 with the \SpecialChar LaTeX
16260 \begin_layout Standard
16265 definecolor{darkgreen}{cmyk}{0.5,
16283 \begin_inset Index idx
16288 \begin_layout Plain Layout
16290 \begin_inset IndexMacro subentry
16293 \begin_layout Plain Layout
16300 \begin_inset IndexMacro subentry
16303 \begin_layout Plain Layout
16319 \begin_layout Standard
16324 is the color space denoting the colors
16343 The four comma separated numbers are the portion factors for the corresponding colors of the color space.
16344 The factors can be in the range of 0
16345 \begin_inset space \thinspace{}
16349 \begin_inset space \thinspace{}
16362 can also be used for definitions.
16381 so there are three portion factors for the corresponding colors.
16382 Furthermore there is the color space
16386 with one portion factor for the gray value.
16389 \begin_layout Standard
16390 As an example here is a framed box with the newly defined color
16394 where the characters have been colored
16399 \begin_inset Formula
16401 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
16409 \begin_layout Standard
16410 Self-defined colors can also be used for text with the help of the command
16417 \begin_inset Index idx
16422 \begin_layout Plain Layout
16424 \begin_inset IndexMacro subentry
16427 \begin_layout Plain Layout
16441 \begin_layout Standard
16445 \begin_layout Plain Layout
16449 textcolor{darkgreen}{
16455 \begin_inset Quotes eld
16459 \begin_inset Quotes erd
16466 \begin_layout Plain Layout
16476 \begin_layout Standard
16484 \begin_inset Index idx
16489 \begin_layout Plain Layout
16491 \begin_inset IndexMacro subentry
16494 \begin_layout Plain Layout
16501 \begin_inset IndexMacro subentry
16504 \begin_layout Plain Layout
16517 is used in the scheme
16521 textcolor{color}{characters to color}
16526 \begin_layout Subsection
16528 \begin_inset CommandInset label
16530 name "subsec:Paragraph-Boxes"
16535 \begin_inset Index idx
16540 \begin_layout Plain Layout
16542 \begin_inset IndexMacro subentry
16545 \begin_layout Plain Layout
16559 \begin_layout Standard
16560 A box that can contain several lines and paragraphs,
16561 a so-called paragraph box (parbox),
16562 can be created with the menu
16564 Insert\SpecialChar menuseparator
16567 or the toolbar button
16576 \begin_layout Standard
16577 The following example shows a framed parbox in a line:
16580 \begin_layout Standard
16581 \begin_inset VSpace medskip
16585 \begin_inset Box Boxed
16595 height_special "totalheight"
16600 backgroundcolor "none"
16603 \begin_layout Plain Layout
16604 This is a paragraph box.
16606 \begin_inset space \thinspace{}
16609 cm long and can also contain formulas:
16611 \begin_inset Formula $\int A\,\mathrm{d}s=C$
16622 \begin_layout Standard
16623 \begin_inset VSpace medskip
16629 \begin_layout Standard
16630 Such a box is created by right-clicking on the gray box inset.
16631 A dialog pops up showing the box properties.
16651 \begin_inset space \thinspace{}
16657 Vertical Box Alignment
16663 \begin_layout Standard
16664 \begin_inset VSpace medskip
16667 In \SpecialChar LaTeX
16668 a parbox is created with the command
16675 \begin_inset Index idx
16680 \begin_layout Plain Layout
16682 \begin_inset IndexMacro subentry
16685 \begin_layout Plain Layout
16692 \begin_inset IndexMacro subentry
16695 \begin_layout Plain Layout
16708 which has the following scheme:
16711 \begin_layout Standard
16716 parbox[position]{width}{box content}
16719 \begin_layout Standard
16734 \begin_inset Quotes eld
16738 \begin_inset Quotes erd
16741 means that the box is aligned within the surrounding text with its last line.
16747 \begin_inset Quotes eld
16751 \begin_inset Quotes erd
16754 this is done with the first line.
16755 When no position is given,
16756 the box will be vertically centered,
16764 \begin_inset space ~
16769 manual for examples.
16772 \begin_layout Standard
16773 \begin_inset VSpace bigskip
16776 To frame formulas completely,
16777 including the formula number,
16778 the formula must be set into a parbox.
16794 is inserted in \SpecialChar TeX
16795 mode before the formula.
16803 \begin_inset Index idx
16808 \begin_layout Plain Layout
16810 \begin_inset IndexMacro subentry
16813 \begin_layout Plain Layout
16820 \begin_inset IndexMacro subentry
16823 \begin_layout Plain Layout
16836 is the line width set for the document.
16837 Because the frame is outside the parbox,
16838 two times the frame separation and the frame thickness must be subtracted from the line width.
16839 To be able to multiply and subtract in arguments,
16840 the \SpecialChar LaTeX
16849 \begin_layout Plain Layout
16854 is part of every \SpecialChar LaTeX
16855 standard installation.
16861 \begin_inset Index idx
16866 \begin_layout Plain Layout
16868 \begin_inset IndexMacro subentry
16871 \begin_layout Plain Layout
16882 must be loaded in the \SpecialChar LaTeX
16883 -preamble with the line
16886 \begin_layout Standard
16894 \begin_layout Standard
16895 Behind the formula both boxes are closed by entering
16899 in \SpecialChar TeX
16901 Here is an example:
16905 \begin_layout Plain Layout
16919 \begin_layout Standard
16923 \begin_layout Plain Layout
16941 \begin_inset Formula
16943 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
16952 \begin_layout Plain Layout
16963 \begin_layout Plain Layout
16977 \begin_layout Standard
16978 \begin_inset VSpace medskip
16981 As a parbox is used as the argument of
16988 there is in this case no difference between
17003 \begin_layout Standard
17004 \begin_inset VSpace bigskip
17007 Paragraph boxes are very useful to comment formulas directly.
17015 is used in combination with the command
17029 \begin_inset CommandInset ref
17031 reference "subsec:User-defined-Numbering"
17039 \begin_layout Standard
17040 An example of a formula commented with
17049 \begin_layout Standard
17053 \begin_layout Plain Layout
17066 This is a description.
17067 It is distinctly separated from the formula and multiline.
17071 \begin_layout Plain Layout
17083 \begin_layout Standard
17084 Such a formula must be inserted completely in \SpecialChar TeX
17085 mode because \SpecialChar LyX
17086 does not yet support the command
17093 The formula is created with the following command sequence:
17096 \begin_layout Standard
17109 is inserted in \SpecialChar TeX
17114 \begin_layout Plain Layout
17115 When the formula style
17128 can also be replaced by
17135 (formula styles see
17136 \begin_inset CommandInset ref
17138 reference "sec:Formula-Styles"
17148 Then the description follows as normal text and finally
17154 is inserted in \SpecialChar TeX
17168 create a displayed formula.
17171 \begin_layout Standard
17178 can be seen in this example that was
17179 \begin_inset Quotes eld
17183 \begin_inset Quotes erd
17186 using the mathematical textmode:
17187 \begin_inset Formula
17189 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
17197 \begin_layout Section
17199 \begin_inset Index idx
17204 \begin_layout Plain Layout
17213 \begin_layout Subsection
17215 \begin_inset CommandInset label
17217 name "subsec:Big-Operators"
17222 \begin_inset Index idx
17227 \begin_layout Plain Layout
17229 \begin_inset IndexMacro subentry
17232 \begin_layout Plain Layout
17244 \begin_inset Index idx
17249 \begin_layout Plain Layout
17256 \begin_inset Index idx
17261 \begin_layout Plain Layout
17270 \begin_layout Standard
17271 To be able to use all of the integral operators listed here,
17280 must be set in the document settings under
17283 \begin_inset space ~
17291 \begin_layout Standard
17292 \begin_inset space \hfill{}
17296 \begin_inset Tabular
17297 <lyxtabular version="3" rows="11" columns="2">
17298 <features booktabs="true" tabularvalignment="middle">
17299 <column alignment="center" valignment="top" width="0pt">
17300 <column alignment="center" valignment="top" width="0pt">
17302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17305 \begin_layout Plain Layout
17311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17314 \begin_layout Plain Layout
17322 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17325 \begin_layout Plain Layout
17329 \begin_inset Index idx
17334 \begin_layout Plain Layout
17336 \begin_inset IndexMacro subentry
17339 \begin_layout Plain Layout
17346 \begin_inset IndexMacro subentry
17349 \begin_layout Plain Layout
17367 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17370 \begin_layout Plain Layout
17371 \begin_inset Formula $\int$
17381 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17384 \begin_layout Plain Layout
17392 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17395 \begin_layout Plain Layout
17396 \begin_inset Formula $\oint$
17406 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17409 \begin_layout Plain Layout
17417 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17420 \begin_layout Plain Layout
17421 \begin_inset Formula $\ointctrclockwise$
17431 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17434 \begin_layout Plain Layout
17442 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17445 \begin_layout Plain Layout
17446 \begin_inset Formula $\ointclockwise$
17456 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17459 \begin_layout Plain Layout
17467 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17470 \begin_layout Plain Layout
17471 \begin_inset Formula $\sqint$
17481 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17484 \begin_layout Plain Layout
17492 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17495 \begin_layout Plain Layout
17497 \begin_inset Formula $\fint$
17507 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17510 \begin_layout Plain Layout
17518 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17521 \begin_layout Plain Layout
17523 \begin_inset Formula $\landupint$
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
17549 \begin_inset Formula $\landdownint$
17559 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17562 \begin_layout Plain Layout
17570 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17573 \begin_layout Plain Layout
17574 \begin_inset Formula $\bigcap$
17584 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17587 \begin_layout Plain Layout
17595 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17598 \begin_layout Plain Layout
17599 \begin_inset Formula $\bigcup$
17613 \begin_inset space \hfill{}
17617 \begin_inset Tabular
17618 <lyxtabular version="3" rows="11" columns="2">
17619 <features booktabs="true" tabularvalignment="middle">
17620 <column alignment="center" valignment="top" width="0pt">
17621 <column alignment="center" valignment="top" width="0pt">
17623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17626 \begin_layout Plain Layout
17632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17635 \begin_layout Plain Layout
17643 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17646 \begin_layout Plain Layout
17650 \begin_inset Index idx
17655 \begin_layout Plain Layout
17657 \begin_inset IndexMacro subentry
17660 \begin_layout Plain Layout
17667 \begin_inset IndexMacro subentry
17670 \begin_layout Plain Layout
17688 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17691 \begin_layout Plain Layout
17692 \begin_inset Formula $\sum$
17702 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17705 \begin_layout Plain Layout
17709 \begin_inset Index idx
17714 \begin_layout Plain Layout
17716 \begin_inset IndexMacro subentry
17719 \begin_layout Plain Layout
17726 \begin_inset IndexMacro subentry
17729 \begin_layout Plain Layout
17747 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17750 \begin_layout Plain Layout
17751 \begin_inset Formula $\prod$
17761 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17764 \begin_layout Plain Layout
17772 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17775 \begin_layout Plain Layout
17776 \begin_inset Formula $\coprod$
17786 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17789 \begin_layout Plain Layout
17797 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17800 \begin_layout Plain Layout
17801 \begin_inset Formula $\bigodot$
17811 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17814 \begin_layout Plain Layout
17822 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17825 \begin_layout Plain Layout
17826 \begin_inset Formula $\bigotimes$
17836 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17839 \begin_layout Plain Layout
17847 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17850 \begin_layout Plain Layout
17851 \begin_inset Formula $\bigoplus$
17861 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17864 \begin_layout Plain Layout
17872 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17875 \begin_layout Plain Layout
17876 \begin_inset Formula $\bigwedge$
17886 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17889 \begin_layout Plain Layout
17897 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17900 \begin_layout Plain Layout
17901 \begin_inset Formula $\bigvee$
17911 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17914 \begin_layout Plain Layout
17922 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17925 \begin_layout Plain Layout
17926 \begin_inset Formula $\bigsqcup$
17936 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17939 \begin_layout Plain Layout
17947 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17950 \begin_layout Plain Layout
17951 \begin_inset Formula $\biguplus$
17965 \begin_inset space \hfill{}
17971 \begin_layout Standard
17972 All big operators can also be inserted via the math toolbar button
17975 arg "math-insert \\intop"
17981 \begin_layout Standard
17982 The operators are called big because they are bigger than the sometimes equal looking binary operators.
17983 All big operators can have limits as described in the next subsection.
17986 \begin_layout Standard
17987 For all integral operators there is a second version available,
18007 These operators differ in the style the operator limits are displayed,
18009 \begin_inset CommandInset ref
18011 reference "subsec:Operator-Limits"
18019 \begin_layout Subsubsection*
18020 Advice for Integrals
18023 \begin_layout Standard
18028 in an integral is an operator that has to be set upright.
18029 This is done by highlighting the
18033 and using the keyboard shortcut
18043 \begin_layout Plain Layout
18049 \begin_inset CommandInset ref
18051 reference "subsec:Font-Styles"
18062 Also the smallest space is inserted before the
18067 as this is usual for operators.
18071 \begin_layout Standard
18074 \begin_inset Formula $\int A(x)dx$
18078 \begin_inset Newline newline
18082 \begin_inset Phantom HPhantom
18085 \begin_layout Plain Layout
18093 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
18099 \begin_layout Standard
18100 The following commands exist for multiple integrals:
18101 \begin_inset VSpace medskip
18107 \begin_layout Standard
18108 \begin_inset space \hfill{}
18112 \begin_inset Tabular
18113 <lyxtabular version="3" rows="4" columns="2">
18114 <features booktabs="true" tabularvalignment="middle">
18115 <column alignment="center" valignment="top" width="0pt">
18116 <column alignment="center" valignment="top" width="0pt">
18118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18121 \begin_layout Plain Layout
18127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18130 \begin_layout Plain Layout
18137 <row bottomspace="1mm">
18138 <cell alignment="center" valignment="top" usebox="none">
18141 \begin_layout Plain Layout
18149 <cell alignment="center" valignment="top" usebox="none">
18152 \begin_layout Plain Layout
18153 \begin_inset Formula $\iint$
18162 <row bottomspace="1mm">
18163 <cell alignment="center" valignment="top" usebox="none">
18166 \begin_layout Plain Layout
18174 <cell alignment="center" valignment="top" usebox="none">
18177 \begin_layout Plain Layout
18178 \begin_inset Formula $\oiint$
18187 <row bottomspace="1mm">
18188 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18191 \begin_layout Plain Layout
18199 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18202 \begin_layout Plain Layout
18203 \begin_inset Formula $\sqiint$
18217 \begin_inset space \hfill{}
18221 \begin_inset Tabular
18222 <lyxtabular version="3" rows="4" columns="2">
18223 <features booktabs="true" tabularvalignment="middle">
18224 <column alignment="center" valignment="top" width="0pt">
18225 <column alignment="center" valignment="top" width="0pt">
18227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18230 \begin_layout Plain Layout
18236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18239 \begin_layout Plain Layout
18246 <row bottomspace="1mm">
18247 <cell alignment="center" valignment="top" usebox="none">
18250 \begin_layout Plain Layout
18258 <cell alignment="center" valignment="top" usebox="none">
18261 \begin_layout Plain Layout
18262 \begin_inset Formula $\iiint$
18271 <row bottomspace="1mm">
18272 <cell alignment="center" valignment="top" usebox="none">
18275 \begin_layout Plain Layout
18283 <cell alignment="center" valignment="top" usebox="none">
18286 \begin_layout Plain Layout
18287 \begin_inset Formula $\iiiint$
18296 <row bottomspace="1mm">
18297 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18300 \begin_layout Plain Layout
18308 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18311 \begin_layout Plain Layout
18312 \begin_inset Formula $\dotsint$
18326 \begin_inset space \hfill{}
18332 \begin_layout Subsection
18334 \begin_inset CommandInset label
18336 name "subsec:Operator-Limits"
18341 \begin_inset Index idx
18346 \begin_layout Plain Layout
18348 \begin_inset IndexMacro subentry
18351 \begin_layout Plain Layout
18365 \begin_layout Standard
18366 Limits are created by super- and subscripts:
18369 \begin_layout Standard
18371 \begin_inset Tabular
18372 <lyxtabular version="3" rows="2" columns="2">
18373 <features booktabs="true" tabularvalignment="middle">
18374 <column alignment="center" valignment="top" width="0pt">
18375 <column alignment="center" valignment="top" width="0pt">
18377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18380 \begin_layout Plain Layout
18386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18389 \begin_layout Plain Layout
18397 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18400 \begin_layout Plain Layout
18406 \begin_inset space \textvisiblespace{}
18410 \begin_inset Formula $\to$
18414 \begin_inset Formula $\to$
18422 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18425 \begin_layout Plain Layout
18426 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
18442 \begin_layout Standard
18443 Limits of inline formulas are set on the right side of the operator.
18444 Limits in displayed formulas are set above or below the operator,
18445 except for integral limits.
18448 \begin_layout Standard
18449 To force the limits to be set beside the operator,
18450 the cursor is placed directly behind the operator and the limits type is changed with the menu
18452 Edit\SpecialChar menuseparator
18453 Math\SpecialChar menuseparator
18472 \begin_layout Standard
18473 The default displayed formulas limits type is this:
18474 \begin_inset Formula
18476 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
18481 This is how it looks when the limits type is changed to
18488 \begin_inset Formula
18490 \sum\nolimits_{x=0}^{\infty}\frac{1}{x^{2}}
18496 except those ending with
18514 the limits by default are set beside the operator.
18515 But for multiple integrals the limits are often set below the operator.
18516 In the following example the limits type was set to
18520 and so set below the integrals:
18521 \begin_inset Formula
18523 \iiint\limits_{V}X\,\mathrm{d}V=U\label{eq:VolInt}
18529 \change_deleted 5863208 1612725771
18531 \begin_inset Note Note
18534 \begin_layout Plain Layout
18536 \change_inserted 232239728 1611193306
18537 This integral did not have its limits set to Display in the original document
18549 \begin_layout Standard
18550 \begin_inset VSpace medskip
18553 To specify conditions for limits,
18561 \begin_inset Index idx
18566 \begin_layout Plain Layout
18568 \begin_inset IndexMacro subentry
18571 \begin_layout Plain Layout
18578 \begin_inset IndexMacro subentry
18581 \begin_layout Plain Layout
18601 \begin_inset Index idx
18606 \begin_layout Plain Layout
18608 \begin_inset IndexMacro subentry
18611 \begin_layout Plain Layout
18618 \begin_inset IndexMacro subentry
18621 \begin_layout Plain Layout
18635 To create this expression
18636 \begin_inset Formula
18638 \sum_{\begin{subarray}{c}
18640 \\k\,\in\,\mathbb{N}
18641 \end{subarray}}^{n}k^{-2}\label{eq:substack}
18649 \begin_layout Standard
18650 the following must be done:
18651 \begin_inset Newline newline
18663 \begin_inset space \textvisiblespace{}
18669 The cursor is now in a blue box under the summation operator.
18675 \begin_inset space \textvisiblespace{}
18681 The blue box is now within a purple box and now multiple limit lines can be written.
18682 A new line is created by inserting a line break (
18685 arg "newline-insert newline"
18690 \begin_inset Newline newline
18695 0<k<1000 Ctrl+Return
18696 \begin_inset Newline newline
18702 a new box appears below for the new limit line.
18705 \begin_layout Standard
18706 The alignment of the lines can be changed to left aligned with the
18716 Edit\SpecialChar menuseparator
18720 To get right alignment,
18726 \begin_inset space \textvisiblespace{}
18731 is inserted at the beginning of the line.
18734 \begin_layout Standard
18747 with the difference that the lines are always centered.
18750 \begin_layout Standard
18751 \begin_inset VSpace bigskip
18755 \begin_inset CommandInset ref
18757 reference "eq:substack"
18762 there can be too much space beside an operator.
18763 This occurs because the characters following the operator are set beside the limits.
18764 To avoid this the command
18771 \begin_inset Index idx
18776 \begin_layout Plain Layout
18778 \begin_inset IndexMacro subentry
18781 \begin_layout Plain Layout
18788 \begin_inset IndexMacro subentry
18791 \begin_layout Plain Layout
18811 \begin_inset Index idx
18816 \begin_layout Plain Layout
18818 \begin_inset IndexMacro subentry
18821 \begin_layout Plain Layout
18832 in the document settings under
18835 \begin_inset space ~
18843 \begin_inset space ~
18855 sets the space besides the operator to 0
18856 \begin_inset space \thinspace{}
18860 \begin_inset Newline newline
18864 \begin_inset CommandInset ref
18866 reference "eq:substack"
18872 one uses the command
18875 \begin_layout Standard
18883 \begin_layout Standard
18884 and inserts the operator with its limits into the braces.
18885 Behind the brace one continues the formula:
18886 \begin_inset Formula
18888 \smashoperator{\sum_{\begin{subarray}{c}
18890 \\k\,\in\,\mathbb{N}
18891 \end{subarray}}^{n}}k^{-2}
18899 \begin_layout Standard
18900 It is possible to set the space of only one side of the operator to 0
18901 \begin_inset space \thinspace{}
18905 To do this write either
18924 stands for the left and
18928 for the right side of the operator.
18929 Here is an example of the possible
18938 \begin_layout Standard
18939 \begin_inset Formula
18941 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}
18949 \begin_layout Standard
18950 \begin_inset VSpace bigskip
18956 \begin_layout Standard
18957 When several consecutive operators have limits the typesetting of the limits looks often imperfect in the output,
18959 \begin_inset Formula
18961 \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}
18966 To improve the typesetting,
18967 in the document settings under
18970 \begin_inset space ~
18980 \begin_inset Index idx
18985 \begin_layout Plain Layout
18987 \begin_inset IndexMacro subentry
18990 \begin_layout Plain Layout
19005 \begin_inset space ~
19011 Then insert the command
19018 \begin_inset Index idx
19023 \begin_layout Plain Layout
19025 \begin_inset IndexMacro subentry
19028 \begin_layout Plain Layout
19035 \begin_inset IndexMacro subentry
19038 \begin_layout Plain Layout
19051 directly before the first operator.
19052 The example will then look like this:
19053 \begin_inset Formula
19055 \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}
19063 \begin_layout Standard
19064 \begin_inset VSpace bigskip
19067 How to use one limit for several operators is described in
19068 \begin_inset CommandInset ref
19070 reference "subsec:Self-defined-Operators"
19078 \begin_layout Subsection
19079 Decoration for Operators
19080 \begin_inset Index idx
19085 \begin_layout Plain Layout
19087 \begin_inset IndexMacro subentry
19090 \begin_layout Plain Layout
19104 \begin_layout Standard
19112 \begin_inset Index idx
19117 \begin_layout Plain Layout
19119 \begin_inset IndexMacro subentry
19122 \begin_layout Plain Layout
19129 \begin_inset IndexMacro subentry
19132 \begin_layout Plain Layout
19152 \begin_inset Index idx
19157 \begin_layout Plain Layout
19159 \begin_inset IndexMacro subentry
19162 \begin_layout Plain Layout
19169 \begin_inset IndexMacro subentry
19172 \begin_layout Plain Layout
19185 characters can be placed above or below an operator respectively.
19193 \begin_inset Index idx
19198 \begin_layout Plain Layout
19200 \begin_inset IndexMacro subentry
19203 \begin_layout Plain Layout
19210 \begin_inset IndexMacro subentry
19213 \begin_layout Plain Layout
19226 characters can be set before and behind a big operator.
19229 \begin_layout Standard
19231 \begin_inset space ~
19243 \begin_layout Itemize
19250 is used to set characters at the corners of the operator
19253 \begin_layout Itemize
19260 is used to set characters before and/or behind the operator (this variant represents \SpecialChar LaTeX
19270 \begin_layout Itemize
19277 is used to set characters at the left corners and/or behind the operator
19280 \begin_layout Itemize
19287 is used to set characters at the right corners and/or before the operator
19290 \begin_layout Standard
19291 For example the command
19296 \begin_inset space \textvisiblespace{}
19302 \begin_inset space \textvisiblespace{}
19306 \begin_inset Formula $\to$
19310 \begin_inset Formula $\to$
19314 \begin_inset space \textvisiblespace{}
19324 \begin_inset Formula
19326 \sideset{}{'}\sum_{k=1}^{n}
19334 \begin_layout Standard
19335 \begin_inset Note Greyedout
19338 \begin_layout Plain Layout
19346 can only be used to decorate big operators,
19347 binary operators are not allowed.
19355 \begin_layout Standard
19368 can also be used to decorate symbols and characters.
19375 \begin_inset space \textvisiblespace{}
19381 \begin_inset space \textvisiblespace{}
19387 \begin_inset Formula $\uparrow$
19395 \begin_inset Formula
19397 \overset{a}{\maltese}
19405 \begin_layout Subsection
19407 \begin_inset CommandInset label
19409 name "subsec:Binary-Operators"
19414 \begin_inset Index idx
19419 \begin_layout Plain Layout
19421 \begin_inset IndexMacro subentry
19424 \begin_layout Plain Layout
19438 \begin_layout Standard
19439 Binary operators are surrounded by space when there is a character before and after them.
19440 \begin_inset VSpace medskip
19446 \begin_layout Standard
19447 \begin_inset Tabular
19448 <lyxtabular version="3" rows="13" columns="2">
19449 <features booktabs="true" tabularvalignment="middle">
19450 <column alignment="center" valignment="top" width="0pt">
19451 <column alignment="center" valignment="top" width="0pt">
19453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19456 \begin_layout Plain Layout
19458 \begin_inset Note Note
19461 \begin_layout Plain Layout
19468 is only used as spacer.
19478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19481 \begin_layout Plain Layout
19489 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19492 \begin_layout Plain Layout
19498 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19501 \begin_layout Plain Layout
19502 \begin_inset Formula $+$
19512 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19515 \begin_layout Plain Layout
19521 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19524 \begin_layout Plain Layout
19525 \begin_inset Formula $-$
19535 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19538 \begin_layout Plain Layout
19546 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19549 \begin_layout Plain Layout
19550 \begin_inset Formula $\pm$
19560 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19563 \begin_layout Plain Layout
19571 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19574 \begin_layout Plain Layout
19575 \begin_inset Formula $\mp$
19585 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19588 \begin_layout Plain Layout
19596 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19599 \begin_layout Plain Layout
19600 \begin_inset Formula $\cdot$
19610 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19613 \begin_layout Plain Layout
19621 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19624 \begin_layout Plain Layout
19625 \begin_inset Formula $\times$
19635 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19638 \begin_layout Plain Layout
19646 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19649 \begin_layout Plain Layout
19650 \begin_inset Formula $\div$
19660 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19663 \begin_layout Plain Layout
19667 \begin_layout Plain Layout
19680 \begin_layout Plain Layout
19692 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19695 \begin_layout Plain Layout
19696 \begin_inset Formula $*$
19706 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19709 \begin_layout Plain Layout
19717 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19720 \begin_layout Plain Layout
19721 \begin_inset Formula $\star$
19731 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19734 \begin_layout Plain Layout
19742 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19745 \begin_layout Plain Layout
19746 \begin_inset Formula $\circ$
19756 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19759 \begin_layout Plain Layout
19767 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19770 \begin_layout Plain Layout
19771 \begin_inset Formula $\diamond$
19781 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19784 \begin_layout Plain Layout
19792 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19795 \begin_layout Plain Layout
19796 \begin_inset Formula $\bullet$
19810 \begin_inset space \hfill{}
19814 \begin_inset Tabular
19815 <lyxtabular version="3" rows="13" columns="2">
19816 <features booktabs="true" tabularvalignment="middle">
19817 <column alignment="center" valignment="top" width="0pt">
19818 <column alignment="center" valignment="top" width="0pt">
19820 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19823 \begin_layout Plain Layout
19829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19832 \begin_layout Plain Layout
19840 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19843 \begin_layout Plain Layout
19851 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19854 \begin_layout Plain Layout
19855 \begin_inset Formula $\nabla$
19865 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19868 \begin_layout Plain Layout
19876 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19879 \begin_layout Plain Layout
19880 \begin_inset Formula $\bigtriangledown$
19890 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19893 \begin_layout Plain Layout
19901 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19904 \begin_layout Plain Layout
19905 \begin_inset Formula $\bigtriangleup$
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 $\Box$
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 $\cap$
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 $\cup$
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 $\dagger$
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 $\ddagger$
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 $\wr$
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 $\bigcirc$
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 $\wedge$
20115 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20118 \begin_layout Plain Layout
20126 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20129 \begin_layout Plain Layout
20130 \begin_inset Formula $\vee$
20144 \begin_inset space \hfill{}
20148 \begin_inset Tabular
20149 <lyxtabular version="3" rows="13" columns="2">
20150 <features booktabs="true" tabularvalignment="middle">
20151 <column alignment="center" valignment="top" width="0pt">
20152 <column alignment="center" valignment="top" width="0pt">
20154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20157 \begin_layout Plain Layout
20163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20166 \begin_layout Plain Layout
20174 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20177 \begin_layout Plain Layout
20185 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20188 \begin_layout Plain Layout
20189 \begin_inset Formula $\oplus$
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 $\ominus$
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 $\otimes$
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 $\oslash$
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 $\odot$
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 $\amalg$
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 $\uplus$
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 $\setminus$
20374 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20377 \begin_layout Plain Layout
20385 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20388 \begin_layout Plain Layout
20389 \begin_inset Formula $\sqcap$
20399 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20402 \begin_layout Plain Layout
20410 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20413 \begin_layout Plain Layout
20414 \begin_inset Formula $\sqcup$
20424 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20427 \begin_layout Plain Layout
20435 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20438 \begin_layout Plain Layout
20439 \begin_inset Formula $\triangleleft$
20449 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20452 \begin_layout Plain Layout
20460 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20463 \begin_layout Plain Layout
20464 \begin_inset Formula $\triangleright$
20480 \begin_layout Standard
20481 All binary operators can also be inserted via the math toolbar button
20484 arg "math-insert \\pm"
20490 \begin_layout Standard
20491 To typeset the Laplace operator,
20509 \begin_inset Formula $\nabla^{2}$
20512 ) can also be used instead of
20521 \begin_layout Standard
20528 Insert\SpecialChar menuseparator
20540 \begin_layout Subsection
20541 Self-defined Operators
20542 \begin_inset CommandInset label
20544 name "subsec:Self-defined-Operators"
20549 \begin_inset Index idx
20554 \begin_layout Plain Layout
20556 \begin_inset IndexMacro subentry
20559 \begin_layout Plain Layout
20573 \begin_layout Standard
20574 With the help of the command
20578 DeclareMathOperator
20581 \begin_inset Index idx
20586 \begin_layout Plain Layout
20588 \begin_inset IndexMacro subentry
20591 \begin_layout Plain Layout
20598 \begin_inset IndexMacro subentry
20601 \begin_layout Plain Layout
20602 \begin_inset IndexMacro sortkey
20605 \begin_layout Plain Layout
20615 DeclareMathOperator
20626 custom operators can be defined in the \SpecialChar LaTeX
20628 Its command scheme is:
20631 \begin_layout Standard
20636 DeclareMathOperator{new command}{display}
20639 \begin_layout Standard
20640 Display can be characters or symbols that define how the operator looks in the output.
20641 To define a big operator a * is set behind the command.
20642 All self-defined big operators can have limits as described in
20643 \begin_inset CommandInset ref
20645 reference "subsec:Operator-Limits"
20653 \begin_layout Standard
20654 For example the \SpecialChar LaTeX
20658 \begin_layout Standard
20663 DeclareMathOperator*{
20670 \begin_layout Standard
20671 defines the command
20678 that inserts a big operator consisting of the black lozenge symbol from
20679 \begin_inset CommandInset ref
20681 reference "subsec:Miscellaneous-Symbols"
20687 \begin_inset Formula
20689 \Lozenge_{n=1}^{\infty}
20694 The command for this formula is:
20706 \begin_inset Formula $\to$
20712 \begin_layout Standard
20713 \begin_inset VSpace bigskip
20716 When self-defined operators are not used several times in the document,
20717 they can also be defined with the commands
20724 \begin_inset Index idx
20729 \begin_layout Plain Layout
20731 \begin_inset IndexMacro subentry
20734 \begin_layout Plain Layout
20741 \begin_inset IndexMacro subentry
20744 \begin_layout Plain Layout
20764 \begin_inset Index idx
20769 \begin_layout Plain Layout
20771 \begin_inset IndexMacro subentry
20774 \begin_layout Plain Layout
20781 \begin_inset IndexMacro subentry
20784 \begin_layout Plain Layout
20798 which have the following scheme:
20801 \begin_layout Standard
20815 \begin_layout Standard
20822 defines big operators,
20832 \begin_layout Standard
20839 can be used to use one limit for several operators:
20842 \begin_layout Standard
20843 \begin_inset Formula
20845 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
20853 \begin_layout Standard
20854 The command for the formula above is:
20855 \begin_inset Newline newline
20871 \begin_inset space \textvisiblespace{}
20877 \begin_inset Formula $\to$
20883 \begin_inset space \textvisiblespace{}
20891 \begin_layout Section
20893 \begin_inset Index idx
20898 \begin_layout Plain Layout
20907 \begin_layout Subsection
20909 \begin_inset CommandInset label
20911 name "subsec:Font-Styles"
20916 \begin_inset Index idx
20921 \begin_layout Plain Layout
20923 \begin_inset IndexMacro subentry
20926 \begin_layout Plain Layout
20940 \begin_layout Standard
20941 Latin letters in formulas can be set in one of the following font styles:
20944 \begin_layout Standard
20946 \begin_inset Tabular
20947 <lyxtabular version="3" rows="6" columns="3">
20948 <features booktabs="true" tabularvalignment="middle">
20949 <column alignment="center" valignment="top" width="0pt">
20950 <column alignment="center" valignment="top">
20951 <column alignment="center" valignment="top">
20953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20956 \begin_layout Plain Layout
20962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20965 \begin_layout Plain Layout
20971 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
20974 \begin_layout Plain Layout
20982 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20985 \begin_layout Plain Layout
20991 \begin_inset space \textvisiblespace{}
21001 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21004 \begin_layout Plain Layout
21005 \begin_inset Formula $\mathbb{ABC}$
21013 <cell alignment="center" valignment="top" usebox="none">
21016 \begin_layout Plain Layout
21024 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21027 \begin_layout Plain Layout
21033 \begin_inset space \textvisiblespace{}
21043 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21046 \begin_layout Plain Layout
21047 \begin_inset Formula $\mathbf{AbC}$
21055 <cell alignment="center" valignment="top" usebox="none">
21058 \begin_layout Plain Layout
21071 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21074 \begin_layout Plain Layout
21080 \begin_inset space \textvisiblespace{}
21090 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21093 \begin_layout Plain Layout
21094 \begin_inset Formula $\boldsymbol{AbC}$
21102 <cell alignment="center" valignment="top" usebox="none">
21105 \begin_layout Plain Layout
21108 arg "font-boldsymbol"
21118 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21121 \begin_layout Plain Layout
21127 \begin_inset space \textvisiblespace{}
21137 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21140 \begin_layout Plain Layout
21141 \begin_inset Formula $\mathcal{ABC}$
21149 <cell alignment="center" valignment="top" usebox="none">
21152 \begin_layout Plain Layout
21160 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21163 \begin_layout Plain Layout
21169 \begin_inset space \textvisiblespace{}
21179 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21182 \begin_layout Plain Layout
21183 \begin_inset Formula $\mathfrak{AbC}$
21191 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
21194 \begin_layout Plain Layout
21208 \begin_layout Standard
21210 \begin_inset Tabular
21211 <lyxtabular version="3" rows="6" columns="3">
21212 <features booktabs="true" tabularvalignment="middle">
21213 <column alignment="center" valignment="top" width="0pt">
21214 <column alignment="center" valignment="top">
21215 <column alignment="center" valignment="top">
21217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21220 \begin_layout Plain Layout
21226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21229 \begin_layout Plain Layout
21235 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
21238 \begin_layout Plain Layout
21246 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21249 \begin_layout Plain Layout
21255 \begin_inset space \textvisiblespace{}
21265 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21268 \begin_layout Plain Layout
21269 \begin_inset Formula $\mathit{AbC}$
21277 <cell alignment="center" valignment="top" usebox="none">
21280 \begin_layout Plain Layout
21288 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21291 \begin_layout Plain Layout
21297 \begin_inset space \textvisiblespace{}
21307 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21310 \begin_layout Plain Layout
21311 \begin_inset Formula $\mathrm{AbC}$
21319 <cell alignment="center" valignment="top" usebox="none">
21322 \begin_layout Plain Layout
21335 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21338 \begin_layout Plain Layout
21344 \begin_inset space \textvisiblespace{}
21354 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21357 \begin_layout Plain Layout
21358 \begin_inset Formula $\mathsf{AbC}$
21366 <cell alignment="center" valignment="top" usebox="none">
21369 \begin_layout Plain Layout
21382 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21385 \begin_layout Plain Layout
21391 \begin_inset space \textvisiblespace{}
21401 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21404 \begin_layout Plain Layout
21405 \begin_inset Formula $\mathtt{AbC}$
21413 <cell alignment="center" valignment="top" usebox="none">
21416 \begin_layout Plain Layout
21419 arg "font-typewriter"
21429 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21432 \begin_layout Plain Layout
21438 \begin_inset space \textvisiblespace{}
21448 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21451 \begin_layout Plain Layout
21452 \begin_inset Formula $\mathscr{ABC}$
21460 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
21463 \begin_layout Plain Layout
21477 \begin_layout Standard
21478 \begin_inset Note Greyedout
21481 \begin_layout Plain Layout
21506 can only be used for big letters.
21514 \begin_layout Standard
21524 \begin_layout Standard
21525 The style commands also work for letters in mathematical constructs:
21526 \begin_inset Formula
21528 \mathfrak{A=\frac{b}{C}}
21536 \begin_layout Standard
21537 Characters in mathematical text don't appear in a math font style but in the text font style
21544 Note that their style can't be set correctly via the text style dialog.
21545 This is a known bug in \SpecialChar LyX
21550 \begin_layout Plain Layout
21551 \begin_inset CommandInset href
21553 name "LyX-bug #4629"
21554 target "https://www.lyx.org/trac/ticket/4629"
21567 \begin_layout Standard
21568 Instead of the style commands,
21571 Edit\SpecialChar menuseparator
21572 Math\SpecialChar menuseparator
21576 or the toolbar button,
21580 arg "math-insert \\font"
21586 \begin_layout Subsection
21588 \begin_inset CommandInset label
21590 name "subsec:Bold-Formulas"
21595 \begin_inset Index idx
21600 \begin_layout Plain Layout
21602 \begin_inset IndexMacro subentry
21605 \begin_layout Plain Layout
21619 \begin_layout Standard
21620 To make a complete formula bold,
21627 from the previous subsection cannot be used because it doesn't work for small Greek letters.
21628 Additionally it always prints Latin letters upright,
21629 as in the following equation:
21632 \begin_layout Standard
21633 \begin_inset Formula
21635 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
21643 \begin_layout Standard
21644 To display the formula correctly,
21652 \begin_inset Formula
21654 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
21659 It is also possible to set the formula in a
21661 boldmath environment
21664 This environment is created by inserting the command
21671 \begin_inset Index idx
21676 \begin_layout Plain Layout
21678 \begin_inset IndexMacro subentry
21681 \begin_layout Plain Layout
21688 \begin_inset IndexMacro subentry
21691 \begin_layout Plain Layout
21704 in \SpecialChar TeX
21706 To end the environment,
21714 \begin_inset Index idx
21719 \begin_layout Plain Layout
21721 \begin_inset IndexMacro subentry
21724 \begin_layout Plain Layout
21731 \begin_inset IndexMacro subentry
21734 \begin_layout Plain Layout
21747 is inserted in \SpecialChar TeX
21752 \begin_layout Plain Layout
21762 \begin_inset Formula
21764 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
21773 \begin_layout Plain Layout
21785 \begin_layout Subsection
21787 \begin_inset Index idx
21792 \begin_layout Plain Layout
21794 \begin_inset IndexMacro subentry
21797 \begin_layout Plain Layout
21811 \begin_layout Standard
21812 Formulas can be colored like normal text:
21813 Highlight a formula or a formula part and use the
21818 Here is a formula in magenta:
21819 \begin_inset Formula
21821 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
21829 \begin_layout Standard
21830 You can also define your own colors as described in
21831 \begin_inset CommandInset ref
21833 reference "subsec:Colored-Boxes"
21839 They can be used with the \SpecialChar TeX
21847 \begin_inset Index idx
21852 \begin_layout Plain Layout
21854 \begin_inset IndexMacro subentry
21857 \begin_layout Plain Layout
21864 \begin_inset IndexMacro subentry
21867 \begin_layout Plain Layout
21883 \begin_layout Standard
21888 textcolor{color}{characters or formula}
21891 \begin_layout Standard
21892 The following example was colored completely dark green and partly red:
21895 \begin_layout Standard
21899 \begin_layout Plain Layout
21903 textcolor{darkgreen}{
21909 \begin_inset Formula
21911 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
21920 \begin_layout Plain Layout
21930 \begin_layout Standard
21931 Due to a bug in \SpecialChar LyX
21932 only complete formulas can be colored with self-defined colors.
21936 \begin_layout Plain Layout
21937 \begin_inset CommandInset href
21939 name "LyX-bug #5269"
21940 target "https://www.lyx.org/trac/ticket/5269"
21953 \begin_layout Subsection
21955 \begin_inset CommandInset label
21957 name "subsec:Font-Sizes"
21962 \begin_inset Index idx
21967 \begin_layout Plain Layout
21969 \begin_inset IndexMacro subentry
21972 \begin_layout Plain Layout
21986 \begin_layout Standard
21987 As with characters in text,
21988 the following size commands are available for formula characters:
21991 \begin_layout Standard
22041 \begin_inset Newline newline
22064 \begin_layout Standard
22065 The font size produced by the commands depends on the document's original font size,
22066 which corresponds to the command
22073 The other commands produce character sizes smaller or larger than
22080 There are however limits to how small or large the font size can be changed.
22081 If for example the document font size is 12
22082 \begin_inset space \thinspace{}
22092 switches to the same size as
22101 \begin_layout Standard
22102 A size command is inserted in \SpecialChar TeX
22103 mode before a formula and sets the size for all of the following formulas and text characters.
22104 To switch back to the initial size,
22111 is inserted behind the formula,
22112 again in \SpecialChar TeX
22116 \begin_layout Standard
22117 Size can also be changed within a formula using the following size commands or the toolbar button
22120 arg "math-insert \\style"
22126 \begin_layout Standard
22129 \begin_inset Tabular
22130 <lyxtabular version="3" rows="5" columns="2">
22131 <features booktabs="true" tabularvalignment="middle">
22132 <column alignment="center" valignment="top" width="0pt">
22133 <column alignment="center" valignment="top">
22135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22138 \begin_layout Plain Layout
22144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22147 \begin_layout Plain Layout
22155 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22158 \begin_layout Plain Layout
22162 \begin_inset Index idx
22167 \begin_layout Plain Layout
22169 \begin_inset IndexMacro subentry
22172 \begin_layout Plain Layout
22179 \begin_inset IndexMacro subentry
22182 \begin_layout Plain Layout
22200 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22203 \begin_layout Plain Layout
22204 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
22213 <row topspace="1mm">
22214 <cell alignment="center" valignment="top" usebox="none">
22217 \begin_layout Plain Layout
22225 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22228 \begin_layout Plain Layout
22229 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
22239 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22242 \begin_layout Plain Layout
22250 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22253 \begin_layout Plain Layout
22254 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
22264 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22267 \begin_layout Plain Layout
22275 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22278 \begin_layout Plain Layout
22279 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
22295 \begin_layout Standard
22296 After entering these commands,
22297 a blue box appears in which the formula parts are inserted.
22300 \begin_layout Standard
22301 There is another method for changing the font size,
22302 although it only works for symbols or letters in mathematical text.
22304 one of the above text size commands is inserted into mathematical text.
22305 All characters until the end of the mathematical text or until another size command will have the selected size.
22307 \begin_inset VSpace -2mm
22313 \begin_layout Standard
22317 \begin_layout Plain Layout
22327 \begin_inset Formula
22329 A=\frac{B}{c}\cdot\maltese
22335 \begin_inset Formula
22337 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
22346 \begin_layout Plain Layout
22356 \begin_inset VSpace medskip
22359 Before the first formula the command
22366 The command for the second formula is:
22367 \begin_inset Newline newline
22375 \begin_inset space \textvisiblespace{}
22381 \begin_inset space \textvisiblespace{}
22387 \begin_inset space \textvisiblespace{}
22393 \begin_inset space \textvisiblespace{}
22397 \begin_inset Formula $\to$
22401 \begin_inset Formula $\to$
22405 \begin_inset Newline newline
22409 \begin_inset space \hspace*{}
22420 \begin_inset space \textvisiblespace{}
22426 \begin_inset space \textvisiblespace{}
22432 \begin_inset space \textvisiblespace{}
22438 \begin_layout Standard
22439 If a symbol cannot be displayed in different sizes,
22440 it will always be displayed in the default size.
22443 \begin_layout Section
22445 \begin_inset Index idx
22450 \begin_layout Plain Layout
22459 \begin_layout Standard
22460 Greek letters can be inserted via the toolbar button
22463 arg "math-insert \\alpha"
22466 as well as by command.
22467 All international typesetting norms purport that Greek letters in math have to be typeset italic/slanted.
22469 like French or Russian,
22470 they are nevertheless sometimes typeset upright.
22473 \begin_layout Subsection
22475 \begin_inset Index idx
22480 \begin_layout Plain Layout
22482 \begin_inset IndexMacro subentry
22485 \begin_layout Plain Layout
22499 \begin_layout Standard
22500 \begin_inset space \hfill{}
22504 \begin_inset Tabular
22505 <lyxtabular version="3" rows="11" columns="2">
22506 <features booktabs="true" tabularvalignment="middle">
22507 <column alignment="center" valignment="top" width="0pt">
22508 <column alignment="center" valignment="top" width="0pt">
22510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22513 \begin_layout Plain Layout
22519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22522 \begin_layout Plain Layout
22530 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22533 \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 $\alpha$
22555 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22558 \begin_layout Plain Layout
22566 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22569 \begin_layout Plain Layout
22570 \begin_inset Formula $\beta$
22580 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22583 \begin_layout Plain Layout
22591 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22594 \begin_layout Plain Layout
22595 \begin_inset Formula $\gamma$
22605 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22608 \begin_layout Plain Layout
22616 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22619 \begin_layout Plain Layout
22620 \begin_inset Formula $\delta$
22630 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22633 \begin_layout Plain Layout
22641 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22644 \begin_layout Plain Layout
22645 \begin_inset Formula $\epsilon$
22655 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22658 \begin_layout Plain Layout
22666 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22669 \begin_layout Plain Layout
22670 \begin_inset Formula $\varepsilon$
22680 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22683 \begin_layout Plain Layout
22691 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22694 \begin_layout Plain Layout
22695 \begin_inset Formula $\zeta$
22705 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22708 \begin_layout Plain Layout
22716 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22719 \begin_layout Plain Layout
22720 \begin_inset Formula $\eta$
22730 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22733 \begin_layout Plain Layout
22741 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22744 \begin_layout Plain Layout
22745 \begin_inset Formula $\theta$
22755 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22758 \begin_layout Plain Layout
22766 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22769 \begin_layout Plain Layout
22770 \begin_inset Formula $\vartheta$
22784 \begin_inset space \hfill{}
22788 \begin_inset Tabular
22789 <lyxtabular version="3" rows="12" columns="2">
22790 <features booktabs="true" tabularvalignment="middle">
22791 <column alignment="center" valignment="top" width="0pt">
22792 <column alignment="center" valignment="top" width="0pt">
22794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22797 \begin_layout Plain Layout
22803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22806 \begin_layout Plain Layout
22814 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22817 \begin_layout Plain Layout
22825 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22828 \begin_layout Plain Layout
22829 \begin_inset Formula $\iota$
22839 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22842 \begin_layout Plain Layout
22850 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22853 \begin_layout Plain Layout
22854 \begin_inset Formula $\kappa$
22864 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22867 \begin_layout Plain Layout
22875 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22878 \begin_layout Plain Layout
22879 \begin_inset Formula $\varkappa$
22889 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22892 \begin_layout Plain Layout
22900 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22903 \begin_layout Plain Layout
22904 \begin_inset Formula $\lambda$
22914 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22917 \begin_layout Plain Layout
22925 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22928 \begin_layout Plain Layout
22929 \begin_inset Formula $\mu$
22939 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22942 \begin_layout Plain Layout
22950 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22953 \begin_layout Plain Layout
22954 \begin_inset Formula $\nu$
22964 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22967 \begin_layout Plain Layout
22975 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22978 \begin_layout Plain Layout
22979 \begin_inset Formula $\xi$
22989 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22992 \begin_layout Plain Layout
22998 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23001 \begin_layout Plain Layout
23002 \begin_inset Formula $o$
23012 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23015 \begin_layout Plain Layout
23023 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23026 \begin_layout Plain Layout
23027 \begin_inset Formula $\pi$
23037 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23040 \begin_layout Plain Layout
23048 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23051 \begin_layout Plain Layout
23052 \begin_inset Formula $\varpi$
23062 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23065 \begin_layout Plain Layout
23073 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23076 \begin_layout Plain Layout
23077 \begin_inset Formula $\rho$
23091 \begin_inset space \hfill{}
23095 \begin_inset Tabular
23096 <lyxtabular version="3" rows="11" columns="2">
23097 <features booktabs="true" tabularvalignment="middle">
23098 <column alignment="center" valignment="top" width="0pt">
23099 <column alignment="center" valignment="top" width="0pt">
23101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23104 \begin_layout Plain Layout
23110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23113 \begin_layout Plain Layout
23121 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23124 \begin_layout Plain Layout
23132 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23135 \begin_layout Plain Layout
23136 \begin_inset Formula $\varrho$
23146 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23149 \begin_layout Plain Layout
23157 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23160 \begin_layout Plain Layout
23161 \begin_inset Formula $\sigma$
23171 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23174 \begin_layout Plain Layout
23182 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23185 \begin_layout Plain Layout
23186 \begin_inset Formula $\varsigma$
23196 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23199 \begin_layout Plain Layout
23207 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23210 \begin_layout Plain Layout
23211 \begin_inset Formula $\tau$
23221 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23224 \begin_layout Plain Layout
23232 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23235 \begin_layout Plain Layout
23236 \begin_inset Formula $\upsilon$
23246 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23249 \begin_layout Plain Layout
23257 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23260 \begin_layout Plain Layout
23261 \begin_inset Formula $\phi$
23271 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23274 \begin_layout Plain Layout
23282 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23285 \begin_layout Plain Layout
23286 \begin_inset Formula $\varphi$
23296 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23299 \begin_layout Plain Layout
23307 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23310 \begin_layout Plain Layout
23311 \begin_inset Formula $\chi$
23321 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23324 \begin_layout Plain Layout
23332 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23335 \begin_layout Plain Layout
23336 \begin_inset Formula $\psi$
23346 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23349 \begin_layout Plain Layout
23357 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23360 \begin_layout Plain Layout
23361 \begin_inset Formula $\omega$
23375 \begin_inset space \hfill{}
23381 \begin_layout Standard
23382 \begin_inset VSpace medskip
23388 \begin_layout Standard
23389 Creating upright Greek letters is explained in
23390 \begin_inset CommandInset ref
23392 reference "subsec:Upright-small-Greek"
23400 \begin_layout Subsection
23402 \begin_inset Index idx
23407 \begin_layout Plain Layout
23409 \begin_inset IndexMacro subentry
23412 \begin_layout Plain Layout
23426 \begin_layout Standard
23427 \begin_inset space \hfill{}
23431 \begin_inset Tabular
23432 <lyxtabular version="3" rows="7" columns="2">
23433 <features booktabs="true" tabularvalignment="middle">
23434 <column alignment="center" valignment="top" width="0pt">
23435 <column alignment="center" valignment="top" width="0pt">
23437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23440 \begin_layout Plain Layout
23446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23449 \begin_layout Plain Layout
23457 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23460 \begin_layout Plain Layout
23468 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23471 \begin_layout Plain Layout
23472 \begin_inset Formula $\Gamma$
23482 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23485 \begin_layout Plain Layout
23493 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23496 \begin_layout Plain Layout
23497 \begin_inset Formula $\Delta$
23507 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23510 \begin_layout Plain Layout
23518 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23521 \begin_layout Plain Layout
23522 \begin_inset Formula $\Theta$
23532 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23535 \begin_layout Plain Layout
23543 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23546 \begin_layout Plain Layout
23547 \begin_inset Formula $\Lambda$
23557 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23560 \begin_layout Plain Layout
23568 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23571 \begin_layout Plain Layout
23572 \begin_inset Formula $\Xi$
23582 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23585 \begin_layout Plain Layout
23593 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23596 \begin_layout Plain Layout
23597 \begin_inset Formula $\Pi$
23611 \begin_inset space \hfill{}
23615 \begin_inset Tabular
23616 <lyxtabular version="3" rows="6" columns="2">
23617 <features booktabs="true" tabularvalignment="middle">
23618 <column alignment="center" valignment="top" width="0pt">
23619 <column alignment="center" valignment="top" width="0pt">
23621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23624 \begin_layout Plain Layout
23630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23633 \begin_layout Plain Layout
23641 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23644 \begin_layout Plain Layout
23652 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23655 \begin_layout Plain Layout
23656 \begin_inset Formula $\Sigma$
23666 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23669 \begin_layout Plain Layout
23677 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23680 \begin_layout Plain Layout
23681 \begin_inset Formula $\Upsilon$
23691 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23694 \begin_layout Plain Layout
23702 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23705 \begin_layout Plain Layout
23706 \begin_inset Formula $\Phi$
23716 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23719 \begin_layout Plain Layout
23727 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23730 \begin_layout Plain Layout
23731 \begin_inset Formula $\Psi$
23741 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23744 \begin_layout Plain Layout
23752 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23755 \begin_layout Plain Layout
23756 \begin_inset Formula $\Omega$
23770 \begin_inset space \hfill{}
23776 \begin_layout Standard
23777 \begin_inset VSpace medskip
23780 The big Greek letters appearing upright is caused by a design bug in \SpecialChar TeX
23782 To create correct italic big letters,
23783 begin every command with
23788 For example the command
23795 \begin_inset Formula $\varGamma$
23799 Another way is to load the package
23807 \begin_layout Plain Layout
23812 is part of the \SpecialChar LaTeX
23818 \begin_inset Index idx
23823 \begin_layout Plain Layout
23825 \begin_inset IndexMacro subentry
23828 \begin_layout Plain Layout
23845 \begin_inset Index idx
23850 \begin_layout Plain Layout
23852 \begin_inset IndexMacro subentry
23855 \begin_layout Plain Layout
23866 with the \SpecialChar LaTeX
23870 \begin_layout Standard
23875 usepackage{fixmath}
23878 \begin_layout Standard
23879 Then all big Greek letters in a document will automatically be typeset italic.
23882 \begin_layout Subsection
23884 \begin_inset Index idx
23889 \begin_layout Plain Layout
23891 \begin_inset IndexMacro subentry
23894 \begin_layout Plain Layout
23908 \begin_layout Standard
23909 Greek letters cannot be set with different font styles like Latin letters.
23910 They can only be made bold with the command
23917 \begin_inset Index idx
23922 \begin_layout Plain Layout
23924 \begin_inset IndexMacro subentry
23927 \begin_layout Plain Layout
23934 \begin_inset IndexMacro subentry
23937 \begin_layout Plain Layout
23953 \begin_layout Standard
23955 \begin_inset Tabular
23956 <lyxtabular version="3" rows="3" columns="2">
23957 <features booktabs="true" tabularvalignment="middle">
23958 <column alignment="center" valignment="top" width="0pt">
23959 <column alignment="center" valignment="top">
23961 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23964 \begin_layout Plain Layout
23970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23973 \begin_layout Plain Layout
23981 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23984 \begin_layout Plain Layout
23996 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23999 \begin_layout Plain Layout
24000 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
24010 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24013 \begin_layout Plain Layout
24025 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24028 \begin_layout Plain Layout
24029 \begin_inset Formula $\theta\boldsymbol{\theta}$
24045 \begin_layout Section
24050 \begin_layout Plain Layout
24063 \begin_layout Plain Layout
24064 A list with all symbols of most of the \SpecialChar LaTeX
24065 -packages can be found in
24066 \begin_inset CommandInset citation
24082 \begin_layout Plain Layout
24090 \begin_inset Note Note
24093 \begin_layout Plain Layout
24096 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
24099 \begin_layout Plain Layout
24102 texorpdfstring is in section
24103 \begin_inset CommandInset ref
24105 reference "subsec:Formulas-in-Section"
24116 \begin_inset Index idx
24121 \begin_layout Plain Layout
24130 \begin_layout Standard
24131 Many of the symbols listed in this section can also be inserted via the toolbar buttons
24134 arg "math-insert \\nabla"
24140 arg "math-insert \\digamma"
24146 \begin_layout Subsection
24147 Mathematical Symbols
24148 \begin_inset CommandInset label
24150 name "subsec:Mathematical-Symbols"
24155 \begin_inset Index idx
24160 \begin_layout Plain Layout
24162 \begin_inset IndexMacro subentry
24165 \begin_layout Plain Layout
24179 \begin_layout Standard
24180 \begin_inset Tabular
24181 <lyxtabular version="3" rows="10" columns="2">
24182 <features booktabs="true" tabularvalignment="middle">
24183 <column alignment="center" valignment="top" width="0pt">
24184 <column alignment="center" valignment="top" width="0pt">
24186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24189 \begin_layout Plain Layout
24195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24198 \begin_layout Plain Layout
24206 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24209 \begin_layout Plain Layout
24217 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24220 \begin_layout Plain Layout
24221 \begin_inset Formula $\neg$
24231 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24234 \begin_layout Plain Layout
24242 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24245 \begin_layout Plain Layout
24246 \begin_inset Formula $\Im$
24256 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24259 \begin_layout Plain Layout
24267 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24270 \begin_layout Plain Layout
24271 \begin_inset Formula $\Re$
24281 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24284 \begin_layout Plain Layout
24292 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24295 \begin_layout Plain Layout
24296 \begin_inset Formula $\aleph$
24306 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24309 \begin_layout Plain Layout
24317 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24320 \begin_layout Plain Layout
24321 \begin_inset Formula $\partial$
24331 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24334 \begin_layout Plain Layout
24342 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24345 \begin_layout Plain Layout
24346 \begin_inset Formula $\infty$
24356 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24359 \begin_layout Plain Layout
24367 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24370 \begin_layout Plain Layout
24371 \begin_inset Formula $\wp$
24381 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24384 \begin_layout Plain Layout
24392 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24395 \begin_layout Plain Layout
24396 \begin_inset Formula $\imath$
24406 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24409 \begin_layout Plain Layout
24417 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24420 \begin_layout Plain Layout
24421 \begin_inset Formula $\jmath$
24435 \begin_inset space \hfill{}
24439 \begin_inset Tabular
24440 <lyxtabular version="3" rows="10" columns="2">
24441 <features booktabs="true" tabularvalignment="middle">
24442 <column alignment="center" valignment="top" width="0pt">
24443 <column alignment="center" valignment="top" width="0pt">
24445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24448 \begin_layout Plain Layout
24454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24457 \begin_layout Plain Layout
24459 \begin_inset Note Note
24462 \begin_layout Plain Layout
24469 is only used as spacer.
24481 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24484 \begin_layout Plain Layout
24492 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24495 \begin_layout Plain Layout
24496 \begin_inset Formula $\forall$
24506 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24509 \begin_layout Plain Layout
24517 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24520 \begin_layout Plain Layout
24521 \begin_inset Formula $\exists$
24531 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24534 \begin_layout Plain Layout
24542 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24545 \begin_layout Plain Layout
24546 \begin_inset Formula $\nexists$
24556 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24559 \begin_layout Plain Layout
24567 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24570 \begin_layout Plain Layout
24571 \begin_inset Formula $\emptyset$
24581 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24584 \begin_layout Plain Layout
24592 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24595 \begin_layout Plain Layout
24596 \begin_inset Formula $\varnothing$
24606 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24609 \begin_layout Plain Layout
24617 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24620 \begin_layout Plain Layout
24621 \begin_inset Formula $\dag$
24631 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24634 \begin_layout Plain Layout
24642 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24645 \begin_layout Plain Layout
24646 \begin_inset Formula $\ddag$
24656 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24659 \begin_layout Plain Layout
24667 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24670 \begin_layout Plain Layout
24674 \begin_layout Plain Layout
24684 \begin_inset Formula $\complement$
24691 \begin_layout Plain Layout
24705 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24708 \begin_layout Plain Layout
24716 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24719 \begin_layout Plain Layout
24720 \begin_inset Formula $\Bbbk$
24734 \begin_inset space \hfill{}
24738 \begin_inset Tabular
24739 <lyxtabular version="3" rows="10" columns="2">
24740 <features booktabs="true" tabularvalignment="middle">
24741 <column alignment="center" valignment="top" width="0pt">
24742 <column alignment="center" valignment="top" width="0pt">
24744 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24747 \begin_layout Plain Layout
24753 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24756 \begin_layout Plain Layout
24764 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24767 \begin_layout Plain Layout
24775 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24778 \begin_layout Plain Layout
24779 \begin_inset Formula $\prime$
24789 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24792 \begin_layout Plain Layout
24800 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24803 \begin_layout Plain Layout
24804 \begin_inset Formula $\backprime$
24814 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24817 \begin_layout Plain Layout
24825 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24828 \begin_layout Plain Layout
24829 \begin_inset Formula $\mho$
24839 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24842 \begin_layout Plain Layout
24850 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24853 \begin_layout Plain Layout
24854 \begin_inset Formula $\triangle$
24864 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24867 \begin_layout Plain Layout
24875 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24878 \begin_layout Plain Layout
24879 \begin_inset Formula $\angle$
24889 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24892 \begin_layout Plain Layout
24900 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24903 \begin_layout Plain Layout
24904 \begin_inset Formula $\measuredangle$
24914 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24917 \begin_layout Plain Layout
24925 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24928 \begin_layout Plain Layout
24929 \begin_inset Formula $\sphericalangle$
24939 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24942 \begin_layout Plain Layout
24950 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24953 \begin_layout Plain Layout
24954 \begin_inset Formula $\top$
24964 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24967 \begin_layout Plain Layout
24975 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24978 \begin_layout Plain Layout
24979 \begin_inset Formula $\bot$
24995 \begin_layout Subsection
24996 Miscellaneous Symbols
24997 \begin_inset CommandInset label
24999 name "subsec:Miscellaneous-Symbols"
25004 \begin_inset Index idx
25009 \begin_layout Plain Layout
25011 \begin_inset IndexMacro subentry
25014 \begin_layout Plain Layout
25028 \begin_layout Standard
25031 \begin_inset Tabular
25032 <lyxtabular version="3" rows="10" columns="2">
25033 <features booktabs="true" tabularvalignment="middle">
25034 <column alignment="center" valignment="top" width="0pt">
25035 <column alignment="center" valignment="top" width="0pt">
25037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25040 \begin_layout Plain Layout
25046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25049 \begin_layout Plain Layout
25057 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25060 \begin_layout Plain Layout
25068 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25071 \begin_layout Plain Layout
25072 \begin_inset Formula $\flat$
25082 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25085 \begin_layout Plain Layout
25093 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25096 \begin_layout Plain Layout
25097 \begin_inset Formula $\natural$
25107 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25110 \begin_layout Plain Layout
25118 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25121 \begin_layout Plain Layout
25122 \begin_inset Formula $\sharp$
25132 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25135 \begin_layout Plain Layout
25143 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25146 \begin_layout Plain Layout
25147 \begin_inset Formula $\surd$
25157 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25160 \begin_layout Plain Layout
25168 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25171 \begin_layout Plain Layout
25172 \begin_inset Formula $\checkmark$
25182 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25185 \begin_layout Plain Layout
25193 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25196 \begin_layout Plain Layout
25197 \begin_inset Formula $\yen$
25207 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25210 \begin_layout Plain Layout
25218 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25221 \begin_layout Plain Layout
25222 \begin_inset Formula $\pounds$
25232 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25235 \begin_layout Plain Layout
25241 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25244 \begin_layout Plain Layout
25245 \begin_inset Formula $\$$
25255 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25258 \begin_layout Plain Layout
25264 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25267 \begin_layout Plain Layout
25268 \begin_inset Formula $§$
25282 \begin_inset space \hfill{}
25286 \begin_inset Tabular
25287 <lyxtabular version="3" rows="10" columns="2">
25288 <features booktabs="true" tabularvalignment="middle">
25289 <column alignment="center" valignment="top" width="0pt">
25290 <column alignment="center" valignment="top">
25292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25295 \begin_layout Plain Layout
25301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25304 \begin_layout Plain Layout
25312 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25315 \begin_layout Plain Layout
25323 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25326 \begin_layout Plain Layout
25327 \begin_inset Formula $\hbar$
25337 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25340 \begin_layout Plain Layout
25348 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25351 \begin_layout Plain Layout
25352 \begin_inset Formula $\hslash$
25362 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25365 \begin_layout Plain Layout
25373 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25376 \begin_layout Plain Layout
25377 \begin_inset Formula $\clubsuit$
25387 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25390 \begin_layout Plain Layout
25398 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25401 \begin_layout Plain Layout
25402 \begin_inset Formula $\spadesuit$
25412 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25415 \begin_layout Plain Layout
25423 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25426 \begin_layout Plain Layout
25427 \begin_inset Formula $\bigstar$
25437 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25440 \begin_layout Plain Layout
25448 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25451 \begin_layout Plain Layout
25452 \begin_inset Formula $\blacklozenge$
25462 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25465 \begin_layout Plain Layout
25473 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25476 \begin_layout Plain Layout
25477 \begin_inset Formula $\blacktriangle$
25487 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25490 \begin_layout Plain Layout
25498 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25501 \begin_layout Plain Layout
25502 \begin_inset Formula $\blacktriangledown$
25512 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25515 \begin_layout Plain Layout
25523 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25526 \begin_layout Plain Layout
25527 \begin_inset Formula $\bullet$
25541 \begin_inset space \hfill{}
25545 \begin_inset Tabular
25546 <lyxtabular version="3" rows="10" columns="2">
25547 <features booktabs="true" tabularvalignment="middle">
25548 <column alignment="center" valignment="top" width="0pt">
25549 <column alignment="center" valignment="top" width="0pt">
25551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25554 \begin_layout Plain Layout
25560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25563 \begin_layout Plain Layout
25571 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25574 \begin_layout Plain Layout
25582 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25585 \begin_layout Plain Layout
25586 \begin_inset Formula $\diamondsuit$
25596 <cell alignment="center" valignment="top" rightline="true" usebox="none">
25599 \begin_layout Plain Layout
25607 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25610 \begin_layout Plain Layout
25611 \begin_inset Formula $\Diamond$
25621 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25624 \begin_layout Plain Layout
25632 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25635 \begin_layout Plain Layout
25636 \begin_inset Formula $\heartsuit$
25646 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25649 \begin_layout Plain Layout
25657 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25660 \begin_layout Plain Layout
25661 \begin_inset Formula $\P$
25671 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25674 \begin_layout Plain Layout
25682 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25685 \begin_layout Plain Layout
25686 \begin_inset Formula $\copyright$
25696 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25699 \begin_layout Plain Layout
25707 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25710 \begin_layout Plain Layout
25711 \begin_inset Formula $\circledR$
25721 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25724 \begin_layout Plain Layout
25732 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25735 \begin_layout Plain Layout
25736 \begin_inset Formula $\maltese$
25746 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25749 \begin_layout Plain Layout
25757 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25760 \begin_layout Plain Layout
25761 \begin_inset Formula $\diagup$
25771 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25774 \begin_layout Plain Layout
25782 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25785 \begin_layout Plain Layout
25786 \begin_inset Formula $\diagdown$
25802 \begin_layout Standard
25803 \begin_inset VSpace medskip
25809 \begin_layout Standard
25810 Some symbols can be displayed in different sizes,
25812 \begin_inset CommandInset ref
25814 reference "subsec:Font-Sizes"
25822 \begin_layout Subsection
25824 \begin_inset Index idx
25829 \begin_layout Plain Layout
25831 \begin_inset IndexMacro subentry
25834 \begin_layout Plain Layout
25846 \begin_inset Index idx
25851 \begin_layout Plain Layout
25852 \begin_inset IndexMacro sortkey
25855 \begin_layout Plain Layout
25867 \begin_layout Plain Layout
25884 \begin_layout Standard
25885 To use the Euro symbol in formulas,
25886 the \SpecialChar LaTeX
25892 \begin_inset Index idx
25897 \begin_layout Plain Layout
25899 \begin_inset IndexMacro subentry
25902 \begin_layout Plain Layout
25913 must be installed and loaded with the \SpecialChar LaTeX
25917 \begin_layout Standard
25922 usepackage[gennarrow]{eurosym}
25925 \begin_layout Standard
25926 The Euro symbol can now be inserted with the command
25933 \begin_inset Index idx
25938 \begin_layout Plain Layout
25940 \begin_inset IndexMacro subentry
25943 \begin_layout Plain Layout
25950 \begin_inset IndexMacro subentry
25953 \begin_layout Plain Layout
25969 \begin_layout Standard
25970 The Euro symbol can directly be inserted with the € key in mathematical text,
25987 can also be inserted in \SpecialChar TeX
25989 The official currency symbol can then be inserted with the command
25996 \begin_inset Index idx
26001 \begin_layout Plain Layout
26003 \begin_inset IndexMacro subentry
26006 \begin_layout Plain Layout
26013 \begin_inset IndexMacro subentry
26016 \begin_layout Plain Layout
26030 which is also only available in \SpecialChar TeX
26034 \begin_layout Standard
26038 \begin_layout Plain Layout
26048 \begin_inset Note Note
26051 \begin_layout Plain Layout
26052 The following table will only be displayed when the \SpecialChar LaTeX
26065 \begin_layout Standard
26066 An overview about the different Euro symbols:
26069 \begin_layout Standard
26071 \begin_inset Tabular
26072 <lyxtabular version="3" rows="4" columns="3">
26073 <features booktabs="true" tabularvalignment="middle">
26074 <column alignment="center" valignment="top" width="0pt">
26075 <column alignment="center" valignment="top" width="0pt">
26076 <column alignment="center" valignment="top" width="0pt">
26078 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
26081 \begin_layout Plain Layout
26085 \begin_layout Plain Layout
26089 cmidrule[0.08em]{2-3}
26099 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26102 \begin_layout Plain Layout
26108 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26111 \begin_layout Plain Layout
26119 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26122 \begin_layout Plain Layout
26128 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26131 \begin_layout Plain Layout
26139 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26142 \begin_layout Plain Layout
26143 \begin_inset Formula $\euro$
26153 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26156 \begin_layout Plain Layout
26162 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26165 \begin_layout Plain Layout
26171 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26174 \begin_layout Plain Layout
26175 \begin_inset Formula $\mbox{€}$
26185 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26188 \begin_layout Plain Layout
26195 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26198 \begin_layout Plain Layout
26206 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26209 \begin_layout Plain Layout
26213 \begin_layout Plain Layout
26233 \begin_inset Note Note
26236 \begin_layout Plain Layout
26243 is used here only for table borders.
26253 manual for details.
26261 \begin_layout Standard
26265 \begin_layout Plain Layout
26275 \begin_inset Note Note
26278 \begin_layout Plain Layout
26279 The following will be displayed when the \SpecialChar LaTeX
26292 \begin_layout Standard
26293 You need to install the \SpecialChar LaTeX
26298 to see the rest of this subsection in the output.
26301 \begin_layout Standard
26305 \begin_layout Plain Layout
26317 \begin_layout Section
26319 \begin_inset CommandInset label
26321 name "sec:Relations"
26326 \begin_inset Index idx
26331 \begin_layout Plain Layout
26338 \begin_inset Index idx
26343 \begin_layout Plain Layout
26345 \begin_inset IndexMacro see
26348 \begin_layout Plain Layout
26362 \begin_layout Standard
26363 All of the following relations can also be inserted via the toolbar button
26366 arg "math-insert \\leq"
26372 \begin_layout Standard
26373 \begin_inset Tabular
26374 <lyxtabular version="3" rows="17" columns="2">
26375 <features booktabs="true" tabularvalignment="middle">
26376 <column alignment="center" valignment="top" width="0pt">
26377 <column alignment="center" valignment="top" width="0pt">
26379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26382 \begin_layout Plain Layout
26388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26391 \begin_layout Plain Layout
26399 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26402 \begin_layout Plain Layout
26408 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26411 \begin_layout Plain Layout
26412 \begin_inset Formula $<$
26422 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26425 \begin_layout Plain Layout
26433 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26436 \begin_layout Plain Layout
26437 \begin_inset Formula $\le$
26447 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26450 \begin_layout Plain Layout
26458 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26461 \begin_layout Plain Layout
26462 \begin_inset Formula $\ll$
26472 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26475 \begin_layout Plain Layout
26483 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26486 \begin_layout Plain Layout
26487 \begin_inset Formula $\prec$
26497 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26500 \begin_layout Plain Layout
26508 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26511 \begin_layout Plain Layout
26512 \begin_inset Formula $\preceq$
26522 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26525 \begin_layout Plain Layout
26533 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26536 \begin_layout Plain Layout
26537 \begin_inset Formula $\subset$
26547 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26550 \begin_layout Plain Layout
26558 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26561 \begin_layout Plain Layout
26562 \begin_inset Formula $\subseteq$
26572 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26575 \begin_layout Plain Layout
26583 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26586 \begin_layout Plain Layout
26587 \begin_inset Formula $\sqsubseteq$
26597 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26600 \begin_layout Plain Layout
26608 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26611 \begin_layout Plain Layout
26612 \begin_inset Formula $\in$
26622 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26625 \begin_layout Plain Layout
26633 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26636 \begin_layout Plain Layout
26637 \begin_inset Formula $\vdash$
26647 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26650 \begin_layout Plain Layout
26658 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26661 \begin_layout Plain Layout
26662 \begin_inset Formula $\smile$
26672 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26675 \begin_layout Plain Layout
26683 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26686 \begin_layout Plain Layout
26687 \begin_inset Formula $\lhd$
26697 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26700 \begin_layout Plain Layout
26708 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26711 \begin_layout Plain Layout
26712 \begin_inset Formula $\unlhd$
26722 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26725 \begin_layout Plain Layout
26733 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26736 \begin_layout Plain Layout
26737 \begin_inset Formula $\gtrless$
26747 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26750 \begin_layout Plain Layout
26758 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26761 \begin_layout Plain Layout
26762 \begin_inset Formula $\mid$
26772 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26775 \begin_layout Plain Layout
26783 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26786 \begin_layout Plain Layout
26787 \begin_inset Formula $\nmid$
26801 \begin_inset space \hfill{}
26805 \begin_inset Tabular
26806 <lyxtabular version="3" rows="17" columns="2">
26807 <features booktabs="true" tabularvalignment="middle">
26808 <column alignment="center" valignment="top" width="0pt">
26809 <column alignment="center" valignment="top" width="0pt">
26811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26814 \begin_layout Plain Layout
26820 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26823 \begin_layout Plain Layout
26831 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26834 \begin_layout Plain Layout
26840 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26843 \begin_layout Plain Layout
26844 \begin_inset Formula $=$
26854 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26857 \begin_layout Plain Layout
26865 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26868 \begin_layout Plain Layout
26869 \begin_inset Formula $\not=$
26879 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26882 \begin_layout Plain Layout
26890 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26893 \begin_layout Plain Layout
26894 \begin_inset Formula $\equiv$
26904 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26907 \begin_layout Plain Layout
26915 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26918 \begin_layout Plain Layout
26919 \begin_inset Formula $\sim$
26929 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26932 \begin_layout Plain Layout
26940 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26943 \begin_layout Plain Layout
26944 \begin_inset Formula $\simeq$
26954 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26957 \begin_layout Plain Layout
26965 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26968 \begin_layout Plain Layout
26969 \begin_inset Formula $\approx$
26979 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26982 \begin_layout Plain Layout
26990 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26993 \begin_layout Plain Layout
26994 \begin_inset Formula $\cong$
27004 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27007 \begin_layout Plain Layout
27015 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27018 \begin_layout Plain Layout
27019 \begin_inset Formula $\bowtie$
27029 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27032 \begin_layout Plain Layout
27040 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27043 \begin_layout Plain Layout
27044 \begin_inset Formula $\notin$
27054 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27057 \begin_layout Plain Layout
27065 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27068 \begin_layout Plain Layout
27069 \begin_inset Formula $\perp$
27079 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27082 \begin_layout Plain Layout
27090 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27093 \begin_layout Plain Layout
27094 \begin_inset Formula $\propto$
27104 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27107 \begin_layout Plain Layout
27115 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27118 \begin_layout Plain Layout
27119 \begin_inset Formula $\asymp$
27129 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27132 \begin_layout Plain Layout
27140 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27143 \begin_layout Plain Layout
27144 \begin_inset Formula $\doteq$
27154 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27157 \begin_layout Plain Layout
27165 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27168 \begin_layout Plain Layout
27169 \begin_inset Formula $\circeq$
27179 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27182 \begin_layout Plain Layout
27190 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27193 \begin_layout Plain Layout
27194 \begin_inset Formula $\models$
27204 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27207 \begin_layout Plain Layout
27215 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27218 \begin_layout Plain Layout
27219 \begin_inset Formula $\widehat{=}$
27233 \begin_inset space \hfill{}
27237 \begin_inset Tabular
27238 <lyxtabular version="3" rows="17" columns="2">
27239 <features booktabs="true" tabularvalignment="middle">
27240 <column alignment="center" valignment="top" width="0pt">
27241 <column alignment="center" valignment="top" width="0pt">
27243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27246 \begin_layout Plain Layout
27252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27255 \begin_layout Plain Layout
27263 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27266 \begin_layout Plain Layout
27272 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27275 \begin_layout Plain Layout
27276 \begin_inset Formula $>$
27286 <cell alignment="center" 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
27301 \begin_inset Formula $\ge$
27311 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27314 \begin_layout Plain Layout
27322 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27325 \begin_layout Plain Layout
27326 \begin_inset Formula $\gg$
27336 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27339 \begin_layout Plain Layout
27347 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27350 \begin_layout Plain Layout
27351 \begin_inset Formula $\succ$
27361 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27364 \begin_layout Plain Layout
27372 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27375 \begin_layout Plain Layout
27376 \begin_inset Formula $\succeq$
27386 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27389 \begin_layout Plain Layout
27397 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27400 \begin_layout Plain Layout
27401 \begin_inset Formula $\supset$
27411 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27414 \begin_layout Plain Layout
27422 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27425 \begin_layout Plain Layout
27426 \begin_inset Formula $\supseteq$
27436 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27439 \begin_layout Plain Layout
27447 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27450 \begin_layout Plain Layout
27451 \begin_inset Formula $\sqsupseteq$
27461 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27464 \begin_layout Plain Layout
27472 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27475 \begin_layout Plain Layout
27476 \begin_inset Formula $\ni$
27486 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27489 \begin_layout Plain Layout
27497 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27500 \begin_layout Plain Layout
27501 \begin_inset Formula $\dashv$
27511 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27514 \begin_layout Plain Layout
27522 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27525 \begin_layout Plain Layout
27526 \begin_inset Formula $\frown$
27536 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27539 \begin_layout Plain Layout
27547 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27550 \begin_layout Plain Layout
27551 \begin_inset Formula $\rhd$
27561 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27564 \begin_layout Plain Layout
27572 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27575 \begin_layout Plain Layout
27576 \begin_inset Formula $\unrhd$
27586 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27589 \begin_layout Plain Layout
27597 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27600 \begin_layout Plain Layout
27601 \begin_inset Formula $\lessgtr$
27611 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27614 \begin_layout Plain Layout
27622 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27625 \begin_layout Plain Layout
27626 \begin_inset Formula $\parallel$
27636 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27639 \begin_layout Plain Layout
27647 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27650 \begin_layout Plain Layout
27651 \begin_inset Formula $\nparallel$
27667 \begin_layout Standard
27668 \begin_inset VSpace medskip
27683 are bigger than the equal looking operators
27699 \begin_layout Standard
27701 supports also many special relations.
27702 Use the toolbar button
27705 arg "math-insert \\leqq"
27708 to see a list of these relations.
27711 \begin_layout Standard
27712 Contrary to symbols,
27713 relations are always surrounded by space.
27716 \begin_layout Standard
27717 Relations with labels can be created with the command
27724 \begin_inset Index idx
27729 \begin_layout Plain Layout
27731 \begin_inset IndexMacro subentry
27734 \begin_layout Plain Layout
27741 \begin_inset IndexMacro subentry
27744 \begin_layout Plain Layout
27760 \begin_layout Standard
27762 \begin_inset Tabular
27763 <lyxtabular version="3" rows="2" columns="2">
27764 <features booktabs="true" tabularvalignment="middle">
27765 <column alignment="center" valignment="top" width="0pt">
27766 <column alignment="center" valignment="top">
27768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27771 \begin_layout Plain Layout
27777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27780 \begin_layout Plain Layout
27787 <row topspace="1.5mm">
27788 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27791 \begin_layout Plain Layout
27795 \begin_inset space \textvisiblespace{}
27803 \begin_inset space \textvisiblespace{}
27807 \begin_inset Formula $\downarrow$
27813 \begin_inset space \textvisiblespace{}
27817 \begin_inset space \textvisiblespace{}
27825 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27828 \begin_layout Plain Layout
27829 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
27845 \begin_layout Section
27849 \begin_layout Subsection
27850 Predefined Functions
27851 \begin_inset CommandInset label
27853 name "subsec:Predefined-Functions"
27858 \begin_inset Index idx
27863 \begin_layout Plain Layout
27865 \begin_inset IndexMacro subentry
27868 \begin_layout Plain Layout
27882 \begin_layout Standard
27888 in mathematical expressions,
27889 but not function names,
27891 \begin_inset Formula $sin$
27894 could be misunderstood as
27895 \begin_inset Formula $s\cdot i\cdot n$
27899 Also predefined functions are separated a bit from the character in front of them.
27900 They are inserted as commands starting with a backslash before their name.
27903 \begin_layout Standard
27905 \begin_inset Tabular
27906 <lyxtabular version="3" rows="2" columns="2">
27907 <features booktabs="true" tabularvalignment="middle">
27908 <column alignment="center" valignment="top" width="0pt">
27909 <column alignment="center" valignment="top" width="0pt">
27911 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
27914 \begin_layout Plain Layout
27920 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
27923 \begin_layout Plain Layout
27931 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27934 \begin_layout Plain Layout
27940 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
27943 \begin_layout Plain Layout
27944 \begin_inset Formula $Asin(x)+B$
27958 \begin_inset space \quad{}
27962 \begin_inset Tabular
27963 <lyxtabular version="3" rows="2" columns="2">
27964 <features booktabs="true" tabularvalignment="middle">
27965 <column alignment="center" valignment="top" width="0pt">
27966 <column alignment="center" valignment="top" width="0pt">
27968 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
27971 \begin_layout Plain Layout
27977 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
27980 \begin_layout Plain Layout
27988 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27991 \begin_layout Plain Layout
27999 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
28002 \begin_layout Plain Layout
28003 \begin_inset Formula $A\sin(x)+B$
28019 \begin_layout Standard
28020 The following functions are predefined:
28023 \begin_layout Standard
28024 \begin_inset VSpace -2mm
28030 \begin_layout Standard
28032 \begin_inset Tabular
28033 <lyxtabular version="3" rows="9" columns="4">
28034 <features booktabs="true" tabularvalignment="middle">
28035 <column alignment="center" valignment="top" width="0pt">
28036 <column alignment="center" valignment="top" width="0pt">
28037 <column alignment="center" valignment="top" width="0pt">
28038 <column alignment="center" valignment="top" width="0pt">
28040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28043 \begin_layout Plain Layout
28049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28052 \begin_layout Plain Layout
28058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28061 \begin_layout Plain Layout
28067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
28070 \begin_layout Plain Layout
28078 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28081 \begin_layout Plain Layout
28089 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28092 \begin_layout Plain Layout
28100 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28103 \begin_layout Plain Layout
28111 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28114 \begin_layout Plain Layout
28124 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28127 \begin_layout Plain Layout
28135 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28138 \begin_layout Plain Layout
28146 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28149 \begin_layout Plain Layout
28157 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28160 \begin_layout Plain Layout
28170 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28173 \begin_layout Plain Layout
28181 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28184 \begin_layout Plain Layout
28192 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28195 \begin_layout Plain Layout
28203 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28206 \begin_layout Plain Layout
28216 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28219 \begin_layout Plain Layout
28227 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28230 \begin_layout Plain Layout
28238 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28241 \begin_layout Plain Layout
28249 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28252 \begin_layout Plain Layout
28262 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28265 \begin_layout Plain Layout
28273 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28276 \begin_layout Plain Layout
28284 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28287 \begin_layout Plain Layout
28295 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28298 \begin_layout Plain Layout
28308 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28311 \begin_layout Plain Layout
28319 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28322 \begin_layout Plain Layout
28330 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28333 \begin_layout Plain Layout
28341 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28344 \begin_layout Plain Layout
28354 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28357 \begin_layout Plain Layout
28365 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28368 \begin_layout Plain Layout
28376 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28379 \begin_layout Plain Layout
28387 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28390 \begin_layout Plain Layout
28400 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
28403 \begin_layout Plain Layout
28411 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
28414 \begin_layout Plain Layout
28422 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
28425 \begin_layout Plain Layout
28433 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
28436 \begin_layout Plain Layout
28452 \begin_layout Standard
28453 They can also be inserted with the math toolbar button
28456 arg "math-insert \\functions"
28462 \begin_layout Subsection
28463 Self-defined Functions
28464 \begin_inset Index idx
28469 \begin_layout Plain Layout
28471 \begin_inset IndexMacro subentry
28474 \begin_layout Plain Layout
28488 \begin_layout Standard
28489 To use a function that is not predefined,
28490 for instance the sign function sgn(x),
28491 there are two possibilities:
28494 \begin_layout Itemize
28495 Define the function by inserting the following line in the \SpecialChar LaTeX
28500 \begin_layout Plain Layout
28505 DeclareMathOperator
28508 \begin_inset CommandInset ref
28510 reference "subsec:Self-defined-Operators"
28521 \begin_inset Newline newline
28525 \begin_inset VSpace -3mm
28529 \begin_inset Newline newline
28536 DeclareMathOperator{
28541 \begin_inset Index idx
28546 \begin_layout Plain Layout
28548 \begin_inset IndexMacro subentry
28551 \begin_layout Plain Layout
28558 \begin_inset IndexMacro subentry
28561 \begin_layout Plain Layout
28562 \begin_inset IndexMacro sortkey
28565 \begin_layout Plain Layout
28575 DeclareMathOperator
28586 \begin_inset Newline newline
28590 \begin_inset VSpace -2mm
28594 \begin_inset Newline newline
28597 Now the newly defined function can be called with the command
28606 \begin_layout Itemize
28607 Write the formula as usual,
28608 mark the formula name,
28609 in our example the letters
28614 and change it to mathematical text.
28616 insert a space between the prefactor and function.
28619 \begin_layout Standard
28620 The result is the same with both methods as with a predefined function
28624 \begin_layout Plain Layout
28625 In \SpecialChar LyX
28626 self-defined functions are displayed red,
28627 predefined ones black.
28635 \begin_layout Standard
28637 \begin_inset Tabular
28638 <lyxtabular version="3" rows="3" columns="2">
28639 <features booktabs="true" tabularvalignment="middle">
28640 <column alignment="center" valignment="top" width="0pt">
28641 <column alignment="center" valignment="top" width="0pt">
28643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28646 \begin_layout Plain Layout
28652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
28655 \begin_layout Plain Layout
28663 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28666 \begin_layout Plain Layout
28674 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28677 \begin_layout Plain Layout
28678 \begin_inset Formula $A\sgn(x)+B$
28688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28691 \begin_layout Plain Layout
28695 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
28703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
28706 \begin_layout Plain Layout
28707 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
28723 \begin_layout Standard
28724 The first method is more suitable when the self-defined function will be used several times.
28727 \begin_layout Subsection
28729 \begin_inset Index idx
28734 \begin_layout Plain Layout
28743 \begin_layout Standard
28745 in addition to the commands
28752 \begin_inset Index idx
28757 \begin_layout Plain Layout
28759 \begin_inset IndexMacro subentry
28762 \begin_layout Plain Layout
28769 \begin_inset IndexMacro subentry
28772 \begin_layout Plain Layout
28798 the following functions are defined:
28801 \begin_layout Standard
28803 \begin_inset Tabular
28804 <lyxtabular version="3" rows="5" columns="2">
28805 <features booktabs="true" tabularvalignment="middle">
28806 <column alignment="center" valignment="top" width="0pt">
28807 <column alignment="center" valignment="top" width="0pt">
28809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28812 \begin_layout Plain Layout
28818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
28821 \begin_layout Plain Layout
28829 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28832 \begin_layout Plain Layout
28840 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28843 \begin_layout Plain Layout
28844 \begin_inset Formula $\varliminf$
28853 <row topspace="1.5mm">
28854 <cell alignment="center" valignment="top" usebox="none">
28857 \begin_layout Plain Layout
28865 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28868 \begin_layout Plain Layout
28869 \begin_inset Formula $\varlimsup$
28878 <row topspace="1.5mm">
28879 <cell alignment="center" valignment="top" usebox="none">
28882 \begin_layout Plain Layout
28890 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28893 \begin_layout Plain Layout
28894 \begin_inset Formula $\varprojlim$
28903 <row topspace="1.5mm" bottomspace="1mm">
28904 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
28907 \begin_layout Plain Layout
28915 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
28918 \begin_layout Plain Layout
28919 \begin_inset Formula $\varinjlim$
28935 \begin_layout Standard
28936 \begin_inset VSpace medskip
28939 The limit is created by inserting a subscript.
28940 It is set right beside the function in an inline formula:
28943 \begin_layout Standard
28945 \begin_inset Tabular
28946 <lyxtabular version="3" rows="2" columns="2">
28947 <features booktabs="true" tabularvalignment="middle">
28948 <column alignment="center" valignment="top" width="0pt">
28949 <column alignment="center" valignment="top" width="0pt">
28951 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
28954 \begin_layout Plain Layout
28960 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
28963 \begin_layout Plain Layout
28971 <cell alignment="center" valignment="top" usebox="none">
28974 \begin_layout Plain Layout
28980 \begin_inset space \textvisiblespace{}
28984 \begin_inset space \textvisiblespace{}
28992 <cell alignment="center" valignment="top" usebox="none">
28995 \begin_layout Plain Layout
28996 \begin_inset Formula $\lim_{x\to A}x=B$
29012 \begin_layout Standard
29013 In a displayed formula the limit is set below the formula,
29015 \begin_inset Formula
29025 \begin_layout Standard
29026 \begin_inset VSpace medskip
29032 \begin_layout Standard
29033 How to adjust the typesetting of the limits see
29034 \begin_inset CommandInset ref
29036 reference "subsec:Operator-Limits"
29044 \begin_layout Subsection
29046 \begin_inset Index idx
29051 \begin_layout Plain Layout
29053 \begin_inset IndexMacro subentry
29056 \begin_layout Plain Layout
29070 \begin_layout Standard
29071 The modulo-function is special,
29072 because it exists in four variants.
29074 \change_deleted -495245474 1689684546
29076 \change_inserted -495245474 1689684548
29080 \change_deleted -495245474 1689684526
29082 \begin_inset Formula
29084 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
29085 \mathrm{a\backslash mod\textrm{␣}b\textrm{␣}} & & a\mod b\\
29086 \mathrm{a\backslash pmod\textrm{␣}b\textrm{␣}} & & a\pmod b\\
29087 \mathrm{a\backslash bmod\textrm{␣}b\textrm{␣}} & & a\bmod b\\
29088 \mathrm{a\backslash pod\textrm{␣}b\textrm{␣}} & & a\pod b
29094 \change_inserted -495245474 1689684215
29098 \begin_layout Standard
29102 \change_inserted -495245474 1689684215
29103 \begin_inset Tabular
29104 <lyxtabular version="3" rows="5" columns="2">
29105 <features booktabs="true" tabularvalignment="middle">
29106 <column alignment="left" valignment="top" width="0pt">
29107 <column alignment="block" valignment="top">
29109 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
29112 \begin_layout Plain Layout
29114 \change_inserted -495245474 1689684215
29120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
29123 \begin_layout Plain Layout
29125 \change_inserted -495245474 1689684215
29133 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29136 \begin_layout Plain Layout
29138 \change_inserted -495245474 1689684286
29142 \begin_inset space \textvisiblespace{}
29152 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29155 \begin_layout Plain Layout
29157 \change_inserted -495245474 1689684457
29158 \begin_inset Formula $a\mod b$
29168 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29171 \begin_layout Plain Layout
29173 \change_inserted -495245474 1689684416
29177 \begin_inset space \textvisiblespace{}
29181 \begin_inset space \textvisiblespace{}
29189 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29192 \begin_layout Plain Layout
29194 \change_inserted -495245474 1689684474
29195 \begin_inset Formula $a\pmod b$
29204 <row change="inserted -495245474 1689684088">
29205 <cell alignment="center" valignment="top" usebox="none">
29208 \begin_layout Plain Layout
29210 \change_inserted -495245474 1689684419
29214 \begin_inset space \textvisiblespace{}
29218 \begin_inset space \textvisiblespace{}
29226 <cell alignment="center" valignment="top" usebox="none">
29229 \begin_layout Plain Layout
29231 \change_inserted -495245474 1689684488
29232 \begin_inset Formula $a\bmod b$
29241 <row change="inserted -495245474 1689684088">
29242 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
29245 \begin_layout Plain Layout
29247 \change_inserted -495245474 1689684421
29251 \begin_inset space \textvisiblespace{}
29255 \begin_inset space \textvisiblespace{}
29263 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
29266 \begin_layout Plain Layout
29268 \change_inserted -495245474 1689684502
29269 \begin_inset Formula $a\pod b$
29287 \begin_layout Standard
29289 \change_deleted -495245474 1689684554
29291 \change_inserted -495245474 1689684556
29295 \change_inserted -495245474 1689684559
29300 \change_deleted -495245474 1689684562
29302 \change_inserted -495245474 1689684563
29305 space is set before the function names for all variants
29306 \change_inserted -495245474 1689684688
29314 This later version is also the only one that does not take the
29318 as argument but acts as a binary operator
29322 \change_deleted -495245474 1689684609
29323 By default the modulo-functions take only the first character following the command into account.
29324 To use more than one character,
29325 put them in \SpecialChar TeX
29327 \begin_inset Formula
29329 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
29330 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
29331 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
29341 \begin_layout Section
29343 \begin_inset Index idx
29348 \begin_layout Plain Layout
29357 \begin_layout Standard
29358 The characters ^ and _ would normally create a superscript and subscript,
29360 To get these characters you have to insert them with a leading
29365 \begin_layout Standard
29368 \begin_inset Tabular
29369 <lyxtabular version="3" rows="3" columns="2">
29370 <features booktabs="true" tabularvalignment="middle">
29371 <column alignment="left" valignment="top" width="0pt">
29372 <column alignment="block" valignment="top">
29374 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
29377 \begin_layout Plain Layout
29383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
29386 \begin_layout Plain Layout
29394 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29397 \begin_layout Plain Layout
29401 \begin_inset space \textvisiblespace{}
29409 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29412 \begin_layout Plain Layout
29413 \begin_inset Formula $\mathcircumflex$
29423 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
29426 \begin_layout Plain Layout
29434 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
29437 \begin_layout Plain Layout
29438 \begin_inset Formula $\_$
29454 \begin_layout Subsection
29455 Special Characters in Mathematical Text
29458 \begin_layout Standard
29459 The following commands can only be used in mathematical text or in \SpecialChar TeX
29463 \begin_layout Standard
29464 \begin_inset space \hfill{}
29468 \begin_inset Tabular
29469 <lyxtabular version="3" rows="8" columns="2">
29470 <features booktabs="true" tabularvalignment="middle">
29471 <column alignment="left" valignment="top" width="0pt">
29472 <column alignment="block" valignment="top">
29474 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
29477 \begin_layout Plain Layout
29483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
29486 \begin_layout Plain Layout
29494 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29497 \begin_layout Plain Layout
29505 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29508 \begin_layout Plain Layout
29509 \begin_inset Formula $\textrm{œ}$
29519 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29522 \begin_layout Plain Layout
29530 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29533 \begin_layout Plain Layout
29534 \begin_inset Formula $\textrm{Œ}$
29544 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29547 \begin_layout Plain Layout
29555 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29558 \begin_layout Plain Layout
29559 \begin_inset Formula $\textrm{æ}$
29569 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29572 \begin_layout Plain Layout
29580 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29583 \begin_layout Plain Layout
29584 \begin_inset Formula $\textrm{Æ}$
29594 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29597 \begin_layout Plain Layout
29605 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29608 \begin_layout Plain Layout
29609 \begin_inset Formula $\textrm{å}$
29619 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29622 \begin_layout Plain Layout
29630 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29633 \begin_layout Plain Layout
29634 \begin_inset Formula $\textrm{Å}$
29644 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
29647 \begin_layout Plain Layout
29655 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
29658 \begin_layout Plain Layout
29659 \begin_inset Formula $\textrm{ı}$
29673 \begin_inset space \hfill{}
29677 \begin_inset Tabular
29678 <lyxtabular version="3" rows="8" columns="2">
29679 <features booktabs="true" tabularvalignment="middle">
29680 <column alignment="left" valignment="top" width="0pt">
29681 <column alignment="center" valignment="top">
29683 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
29686 \begin_layout Plain Layout
29688 \begin_inset Note Note
29691 \begin_layout Plain Layout
29693 \begin_inset space \thinspace{}
29696 mm is used for separation,
29697 because otherwise the output will be ¡ and ¿ respectively.
29707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
29710 \begin_layout Plain Layout
29718 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29721 \begin_layout Plain Layout
29729 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29732 \begin_layout Plain Layout
29733 \begin_inset Formula $\textrm{ø}$
29743 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29746 \begin_layout Plain Layout
29754 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29757 \begin_layout Plain Layout
29758 \begin_inset Formula $\textrm{Ø}$
29768 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29771 \begin_layout Plain Layout
29779 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29782 \begin_layout Plain Layout
29783 \begin_inset Formula $\textrm{ł}$
29793 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29796 \begin_layout Plain Layout
29804 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29807 \begin_layout Plain Layout
29808 \begin_inset Formula $\textrm{Ł}$
29818 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29821 \begin_layout Plain Layout
29823 \begin_inset space \hspace{}
29828 \begin_inset space \textvisiblespace{}
29836 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29839 \begin_layout Plain Layout
29840 \begin_inset Formula $\textrm{!`}$
29850 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29853 \begin_layout Plain Layout
29855 \begin_inset space \hspace{}
29860 \begin_inset space \textvisiblespace{}
29868 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29871 \begin_layout Plain Layout
29872 \begin_inset Formula $\textrm{?`}$
29882 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
29885 \begin_layout Plain Layout
29893 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
29896 \begin_layout Plain Layout
29897 \begin_inset Formula $\textrm{ȷ}$
29911 \begin_inset space \hfill{}
29917 \begin_layout Standard
29919 \begin_inset Formula $\textrm{Å}$
29923 \begin_inset Formula $\textrm{Ø}$
29926 can also be inserted via the math toolbar button
29929 arg "math-insert \\digamma"
29935 \begin_layout Standard
29939 \begin_inset space \hspace{}
29948 \begin_inset space \hspace{}
29954 are exceptions because they can be inserted in \SpecialChar LyX
29958 \begin_layout Subsection
29960 \begin_inset CommandInset label
29962 name "subsec:Accents-in-Text"
29967 \begin_inset Index idx
29972 \begin_layout Plain Layout
29974 \begin_inset IndexMacro subentry
29977 \begin_layout Plain Layout
29991 \begin_layout Standard
29992 Any letter can be accented with the following commands.
29993 The commands must be inserted in \SpecialChar TeX
29997 \begin_layout Standard
29998 \begin_inset space \hfill{}
30002 \begin_inset Tabular
30003 <lyxtabular version="3" rows="8" columns="2">
30004 <features booktabs="true" tabularvalignment="middle">
30005 <column alignment="left" valignment="top" width="0pt">
30006 <column alignment="block" valignment="top">
30008 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30011 \begin_layout Plain Layout
30017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30020 \begin_layout Plain Layout
30028 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30031 \begin_layout Plain Layout
30035 \begin_inset Quotes grd
30043 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30046 \begin_layout Plain Layout
30050 \begin_layout Plain Layout
30066 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30069 \begin_layout Plain Layout
30077 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30080 \begin_layout Plain Layout
30084 \begin_layout Plain Layout
30100 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30103 \begin_layout Plain Layout
30107 \begin_inset space \textvisiblespace{}
30115 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30118 \begin_layout Plain Layout
30122 \begin_layout Plain Layout
30138 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30141 \begin_layout Plain Layout
30149 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30152 \begin_layout Plain Layout
30156 \begin_layout Plain Layout
30172 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30175 \begin_layout Plain Layout
30179 \begin_inset space \textvisiblespace{}
30187 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30190 \begin_layout Plain Layout
30194 \begin_layout Plain Layout
30210 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30213 \begin_layout Plain Layout
30217 \begin_inset space \textvisiblespace{}
30225 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30228 \begin_layout Plain Layout
30232 \begin_layout Plain Layout
30248 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
30251 \begin_layout Plain Layout
30255 \begin_inset space \textvisiblespace{}
30263 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
30266 \begin_layout Plain Layout
30270 \begin_layout Plain Layout
30290 \begin_inset space \hfill{}
30294 \begin_inset Tabular
30295 <lyxtabular version="3" rows="8" columns="2">
30296 <features booktabs="true" tabularvalignment="middle">
30297 <column alignment="left" valignment="top" width="0pt">
30298 <column alignment="center" valignment="top">
30300 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30303 \begin_layout Plain Layout
30309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30312 \begin_layout Plain Layout
30320 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30323 \begin_layout Plain Layout
30327 \begin_inset space \textvisiblespace{}
30335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30338 \begin_layout Plain Layout
30342 \begin_layout Plain Layout
30358 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30361 \begin_layout Plain Layout
30369 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30372 \begin_layout Plain Layout
30376 \begin_layout Plain Layout
30392 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30395 \begin_layout Plain Layout
30399 \begin_inset Index idx
30404 \begin_layout Plain Layout
30415 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30418 \begin_layout Plain Layout
30422 \begin_layout Plain Layout
30438 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30441 \begin_layout Plain Layout
30449 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30452 \begin_layout Plain Layout
30456 \begin_layout Plain Layout
30472 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30475 \begin_layout Plain Layout
30479 \begin_inset space \textvisiblespace{}
30487 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30490 \begin_layout Plain Layout
30494 \begin_layout Plain Layout
30510 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30513 \begin_layout Plain Layout
30517 \begin_inset space \textvisiblespace{}
30525 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30528 \begin_layout Plain Layout
30532 \begin_layout Plain Layout
30548 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30551 \begin_layout Plain Layout
30555 \begin_inset space \textvisiblespace{}
30563 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30566 \begin_layout Plain Layout
30570 \begin_layout Plain Layout
30590 \begin_inset space \hfill{}
30596 \begin_layout Standard
30597 \begin_inset VSpace medskip
30606 also two different characters can be accented.
30612 \begin_inset space \textvisiblespace{}
30622 \begin_layout Plain Layout
30634 \begin_layout Standard
30648 can in combination with vowels be directly inserted with the keyboard without using \SpecialChar TeX
30650 The same applies for the tilde
30654 \begin_layout Plain Layout
30655 This only applies for keyboards where the tilde is defined as accent.
30664 in combination with
30681 \begin_layout Standard
30730 and accents that are inserted directly with the keyboard are also available in mathematical text.
30731 For the other accents there are special math commands used in formulas,
30733 \begin_inset CommandInset ref
30735 reference "subsec:Accents-for-one"
30743 \begin_layout Standard
30744 \begin_inset VSpace bigskip
30754 \begin_inset Index idx
30759 \begin_layout Plain Layout
30761 \begin_inset IndexMacro subentry
30764 \begin_layout Plain Layout
30771 \begin_inset IndexMacro subentry
30774 \begin_layout Plain Layout
30787 any number or letter can be set into a circle,
30788 quasi accented with a circle,
30789 similar to the copyright symbol.
30792 \begin_layout Standard
30794 \begin_inset Tabular
30795 <lyxtabular version="3" rows="3" columns="2">
30796 <features booktabs="true" tabularvalignment="middle">
30797 <column alignment="center" valignment="top" width="0pt">
30798 <column alignment="center" valignment="top">
30800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30803 \begin_layout Plain Layout
30809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30812 \begin_layout Plain Layout
30820 <cell alignment="center" valignment="top" leftline="true" usebox="none">
30823 \begin_layout Plain Layout
30831 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30834 \begin_layout Plain Layout
30838 \begin_layout Plain Layout
30853 <row topspace="1mm">
30854 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
30857 \begin_layout Plain Layout
30868 raisebox{-1.5pt}{W}}
30873 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
30876 \begin_layout Plain Layout
30880 \begin_layout Plain Layout
30910 \begin_layout Standard
30911 One has to take care that the character fits into the circle.
30922 \begin_layout Plain Layout
30924 \begin_inset CommandInset ref
30926 reference "subsec:Font-Sizes"
30936 specifies the size of the circle.
30947 \begin_layout Plain Layout
30949 \begin_inset CommandInset ref
30951 reference "subsec:Boxes-without-Frame"
30961 the character can be centered.
30964 \begin_layout Subsection
30966 \begin_inset Index idx
30971 \begin_layout Plain Layout
30980 \begin_layout Standard
30981 Old-style figures (also known as old-style numerals) are created with the command
30988 \begin_inset Index idx
30993 \begin_layout Plain Layout
30995 \begin_inset IndexMacro subentry
30998 \begin_layout Plain Layout
31005 \begin_inset IndexMacro subentry
31008 \begin_layout Plain Layout
31022 The command can be used in formulas and in \SpecialChar TeX
31024 The command scheme is:
31027 \begin_layout Standard
31032 oldstylenums{number}
31035 \begin_layout Standard
31040 oldstylenums{0123456789}
31044 \begin_inset Formula $\oldstylenums{0123456789}$
31050 \begin_layout Section
31052 \begin_inset CommandInset label
31054 name "sec:Formula-Styles"
31059 \begin_inset Index idx
31064 \begin_layout Plain Layout
31066 \begin_inset IndexMacro subentry
31069 \begin_layout Plain Layout
31083 \begin_layout Itemize
31084 There are two different alignment styles:
31088 \begin_layout Description
31089 Centered is the predefined standard.
31092 \begin_layout Description
31093 Indented can be set using the menu
31095 Document\SpecialChar menuseparator
31101 \begin_inset space ~
31107 \begin_layout Standard
31113 the indentation can be adjusted.
31114 The default value depends on the document class.
31118 \begin_layout Itemize
31119 Two different numbering styles are available in the menu
31121 Document\SpecialChar menuseparator
31127 \begin_inset space ~
31136 \begin_layout Description
31137 Right is in most cases the default.
31140 \begin_layout Description
31145 \begin_layout Standard
31146 The chosen styles are used for all displayed formulas of the document.
31148 centered and indented formulas should be created in a document,
31154 The indented formulas are then set in a flalign environment,
31156 \begin_inset CommandInset ref
31158 reference "subsec:Flalign-Environment"
31166 \begin_layout Section
31168 \begin_inset CommandInset label
31170 name "sec:Multiline-Formulas"
31175 \begin_inset Index idx
31180 \begin_layout Plain Layout
31182 \begin_inset IndexMacro subentry
31185 \begin_layout Plain Layout
31199 \begin_layout Subsection
31203 \begin_layout Standard
31204 In \SpecialChar LyX
31206 multiline formulas are created by pressing
31209 arg "newline-insert newline"
31213 This creates either an
31217 that is described in
31218 \begin_inset CommandInset ref
31220 reference "subsec:Standard-align-Environment"
31226 when automatically loading of the package
31230 is disabled in the document settings,
31233 eqnarray environment
31235 that is described in
31236 \begin_inset CommandInset ref
31238 reference "subsec:Eqnarray-Environment"
31244 The align environment is recommended as it provides a typographically correct output in all cases.
31247 \begin_layout Standard
31248 There are other multiline formula environments that can be created via the menu
31250 Insert\SpecialChar menuseparator
31254 These environments are described in the following sections.
31257 \begin_layout Standard
31258 In all multiline formula environments a new line is created by pressing
31261 arg "newline-insert newline"
31265 To add or delete lines,
31266 use the math toolbar buttons
31269 arg "tabular-feature append-row"
31275 arg "tabular-feature delete-row"
31281 Edit\SpecialChar menuseparator
31287 \begin_layout Subsubsection
31289 \begin_inset CommandInset label
31291 name "subsec:Line-Separation"
31296 \begin_inset Index idx
31301 \begin_layout Plain Layout
31303 \begin_inset IndexMacro subentry
31306 \begin_layout Plain Layout
31313 \begin_inset IndexMacro subentry
31316 \begin_layout Plain Layout
31330 \begin_layout Standard
31331 Sometimes there is not enough space in multiline formulas between the lines:
31332 \begin_inset Formula
31334 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}\\
31335 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
31343 \begin_layout Standard
31344 In \SpecialChar LaTeX
31345 additional line space is specified as an optional argument of the new line command.
31346 This is not yet possible in \SpecialChar LyX
31351 \begin_layout Plain Layout
31353 \begin_inset CommandInset href
31355 name "LyX-bug #1505"
31356 target "https://www.lyx.org/trac/ticket/1505"
31367 therefore the whole formula must be inserted in \SpecialChar TeX
31369 To add in our example space,
31378 is inserted at the end of the first line.
31384 \begin_layout Plain Layout
31391 \begin_layout Plain Layout
31393 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = &
31395 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
31402 \begin_layout Plain Layout
31406 left(B^{2}+x_{0}^{2}
31414 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
31419 \begin_layout Plain Layout
31431 \begin_layout Standard
31432 \begin_inset VSpace bigskip
31435 To set the line separation for all lines in a formula,
31443 \begin_inset Index idx
31448 \begin_layout Plain Layout
31450 \begin_inset IndexMacro subentry
31453 \begin_layout Plain Layout
31460 \begin_inset IndexMacro subentry
31463 \begin_layout Plain Layout
31479 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
31490 \begin_inset space \thinspace{}
31495 \begin_inset space \thinspace{}
31498 mm of additional line separation as in the previous example,
31502 \begin_layout Standard
31512 \begin_layout Standard
31513 is inserted in \SpecialChar TeX
31514 mode before the formula.
31515 This requires that the \SpecialChar LaTeX
31524 \begin_layout Plain Layout
31529 is part of every \SpecialChar LaTeX
31530 standard installation.
31536 \begin_inset Index idx
31541 \begin_layout Plain Layout
31543 \begin_inset IndexMacro subentry
31546 \begin_layout Plain Layout
31557 was loaded in \SpecialChar LaTeX
31558 -preamble with the line
31561 \begin_layout Standard
31569 \begin_layout Standard
31575 \begin_layout Plain Layout
31587 \begin_inset Formula
31589 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}\\
31590 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
31598 \begin_layout Standard
31602 \begin_layout Plain Layout
31619 to its original value,
31626 is set to the value 3
31627 \begin_inset space \thinspace{}
31633 \begin_layout Subsubsection
31635 \begin_inset CommandInset label
31637 name "subsec:Column-Separation"
31642 \begin_inset Index idx
31647 \begin_layout Plain Layout
31649 \begin_inset IndexMacro subentry
31652 \begin_layout Plain Layout
31659 \begin_inset IndexMacro subentry
31662 \begin_layout Plain Layout
31676 \begin_layout Standard
31677 Multiline formulas form a matrix.
31678 A formula in the eqnarray environment for example is a matrix with three columns.
31679 By changing the column separation in this environment,
31680 the space beside the relation sign can be changed.
31683 \begin_layout Standard
31684 The column separation is specified with the length
31691 \begin_inset Index idx
31696 \begin_layout Plain Layout
31698 \begin_inset IndexMacro subentry
31701 \begin_layout Plain Layout
31708 \begin_inset IndexMacro subentry
31711 \begin_layout Plain Layout
31724 according to the formula:
31725 column separation = 2
31726 \begin_inset space \thinspace{}
31734 \change_deleted 5863208 1612730022
31738 \begin_inset Note Note
31741 \begin_layout Plain Layout
31743 \change_inserted 232239728 1611406079
31744 How does units play into this?
31745 (cm/in/pt) Is the 2 unitless and the result takes on the units of the input value?
31755 \begin_inset Newline newline
31762 \begin_layout Standard
31772 \begin_layout Standard
31773 inserted in \SpecialChar TeX
31775 sets all following formula column separations to 2
31776 \begin_inset space \thinspace{}
31780 To return to the predefined distance,
31788 \begin_inset space \thinspace{}
31794 \begin_layout Standard
31796 \begin_inset space \thinspace{}
31799 cm column separation:
31803 \begin_layout Plain Layout
31815 \begin_inset Formula
31823 A formula with the predefined column separation for matrices of 10
31824 \begin_inset space \thinspace{}
31831 \begin_layout Plain Layout
31843 \begin_inset Formula
31854 \begin_layout Standard
31855 \begin_inset Newpage newpage
31861 \begin_layout Subsubsection
31863 \begin_inset Index idx
31868 \begin_layout Plain Layout
31870 \begin_inset IndexMacro subentry
31873 \begin_layout Plain Layout
31887 \begin_layout Standard
31888 Long formulas can be typeset using these methods:
31891 \begin_layout Itemize
31892 If one side of an equation is much shorter than the line width,
31893 this is chosen for the left side and the right side is typeset over two lines:
31894 \begin_inset Formula
31896 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 \\
31897 & & -\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}
31902 The minus sign at the beginning of the second line does normally not appear as an operator because it is the first character of the line.
31903 Thus it would not be surrounded by space and could not be distinguished from the fraction bar.
31906 \begin_inset space \thinspace{}
31909 pt space was inserted behind the minus sign with the command
31919 \begin_layout Plain Layout
31927 \begin_inset CommandInset ref
31929 reference "subsec:Variable-Space"
31940 \begin_inset Index idx
31945 \begin_layout Plain Layout
31947 \begin_inset IndexMacro subentry
31950 \begin_layout Plain Layout
31957 \begin_inset IndexMacro subentry
31960 \begin_layout Plain Layout
31976 \begin_layout Itemize
31977 When both sides of the equation are long,
31985 \begin_inset Index idx
31990 \begin_layout Plain Layout
31992 \begin_inset IndexMacro subentry
31995 \begin_layout Plain Layout
32002 \begin_inset IndexMacro subentry
32005 \begin_layout Plain Layout
32019 It is inserted in the first column of the first line and causes all further insertions to overwrite the following columns:
32020 \begin_inset Formula
32022 \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 \\
32023 & & -\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 \\
32024 & & =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}
32029 After the insertion of
32036 the cursor is in a purple box that is shifted a bit to the left from the blue one.
32037 The formula is inserted there.
32038 \begin_inset Newline newline
32041 The content of additional lines is inserted in the second or another formula column.
32042 The greater the insertion column number ,
32043 the larger the indentation.
32044 \begin_inset VSpace medskip
32048 \begin_inset Newline newline
32052 \begin_inset Note Greyedout
32055 \begin_layout Plain Layout
32056 Note the following when using
32065 \begin_layout Itemize
32066 The formula doesn't use the full page width.
32068 \begin_inset space \thinspace{}
32072 \begin_inset space \space{}
32076 \begin_inset Formula $-B^{2}$
32079 is added to the first line in the above example,
32080 it would have been outside the page margin.
32081 To better use the width,
32082 negative space can be inserted at the beginning of the first line.
32085 \begin_layout Itemize
32086 Due to a bug in \SpecialChar LyX
32087 the cursor cannot be set with the mouse in the first line.
32091 \begin_layout Plain Layout
32092 \begin_inset CommandInset href
32094 name "LyX-bug #1429"
32095 target "https://www.lyx.org/trac/ticket/1429"
32105 One can only set the cursor at the beginning of the line and move it with the arrow keys.
32113 \begin_layout Itemize
32114 Other methods to set long formulas are offered by the environments described in
32115 \begin_inset CommandInset ref
32117 reference "subsec:Multline-Environment"
32123 \begin_inset CommandInset ref
32125 reference "subsec:Multiline-Formula-Parts"
32133 \begin_layout Subsubsection
32134 Multiline Fractions
32135 \begin_inset CommandInset label
32137 name "subsec:Multiline-Fractions"
32142 \begin_inset Index idx
32147 \begin_layout Plain Layout
32149 \begin_inset IndexMacro subentry
32152 \begin_layout Plain Layout
32166 \begin_layout Standard
32167 There are cases where the denominator and/or the numerator of a fraction is so long that the fraction does not fit on one line.
32168 It is then necessary to add a line break within the fraction.
32169 This can be done using the command
32176 \begin_inset Index idx
32181 \begin_layout Plain Layout
32183 \begin_inset IndexMacro subentry
32186 \begin_layout Plain Layout
32193 \begin_inset IndexMacro subentry
32196 \begin_layout Plain Layout
32211 go to the document settings under
32214 \begin_inset space ~
32224 \begin_inset Index idx
32229 \begin_layout Plain Layout
32231 \begin_inset IndexMacro subentry
32234 \begin_layout Plain Layout
32245 and set its option to
32248 \begin_inset space ~
32263 \begin_layout Standard
32268 splitfrac{first line}{second line}
32271 \begin_layout Standard
32272 and is used for either the denominator or numerator:
32275 \begin_layout Standard
32276 \begin_inset Formula
32278 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}
32283 The command for the first numerator above is:
32286 \begin_layout Standard
32291 splitfrac{xy+xy+xy+xy+xy
32292 \begin_inset space \textvisiblespace{}
32300 \begin_layout Subsubsection
32302 \begin_inset CommandInset label
32304 name "subsec:Multiline-Brackets"
32309 \begin_inset Index idx
32314 \begin_layout Plain Layout
32316 \begin_inset IndexMacro subentry
32319 \begin_layout Plain Layout
32320 for multiline expressions
32333 \begin_layout Standard
32334 For brackets spanning multiple lines the following problem occurs:
32335 \begin_inset Formula
32337 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
32338 & & \left.\cdots+B-D\right]
32346 \begin_layout Standard
32347 The closing bracket is smaller than the opening bracket because brackets with variable size may not span multiple lines.
32350 \begin_layout Standard
32351 To set the bracket size for the second line correctly,
32352 the first line is ended with
32359 \begin_inset Index idx
32364 \begin_layout Plain Layout
32366 \begin_inset IndexMacro subentry
32369 \begin_layout Plain Layout
32376 \begin_inset IndexMacro subentry
32379 \begin_layout Plain Layout
32392 and the second line with
32400 \begin_layout Plain Layout
32414 \begin_inset CommandInset ref
32416 reference "subsec:Automatic-Bracket-Size"
32429 \begin_inset Index idx
32434 \begin_layout Plain Layout
32436 \begin_inset IndexMacro subentry
32439 \begin_layout Plain Layout
32446 \begin_inset IndexMacro subentry
32449 \begin_layout Plain Layout
32477 \begin_inset space \textvisiblespace{}
32487 \begin_inset space \textvisiblespace{}
32497 \begin_inset space \textvisiblespace{}
32503 \begin_inset Formula $\downarrow$
32509 \begin_inset Index idx
32514 \begin_layout Plain Layout
32516 \begin_inset IndexMacro subentry
32519 \begin_layout Plain Layout
32526 \begin_inset IndexMacro subentry
32529 \begin_layout Plain Layout
32543 because the multiplication operator with its limits is the largest symbol in the first line and this should be the size for the bracket in the second line.
32546 \begin_layout Standard
32547 The result is this:
32548 \begin_inset Formula
32550 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
32551 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
32559 \begin_layout Subsection
32563 \begin_layout Standard
32564 Align environments can be used for every kind of multiline formulas.
32565 They are especially useful to set several formulas side by side.
32568 \begin_layout Standard
32569 Align environments consist of columns.
32570 The odd columns are right aligned,
32571 the even ones left aligned.
32572 Every line in an Align environment can be numbered.
32575 \begin_layout Standard
32576 Align environments are created via the menu
32578 Insert\SpecialChar menuseparator
32584 Edit\SpecialChar menuseparator
32585 Math\SpecialChar menuseparator
32586 Change Formula Type
32588 pre-existing formulas can be converted to Align environments.
32591 \begin_layout Standard
32592 To add or delete columns,
32593 use the math toolbar buttons
32596 arg "tabular-feature append-column"
32602 arg "tabular-feature delete-column"
32608 Edit\SpecialChar menuseparator
32614 \begin_layout Subsubsection
32615 Standard Align Environment
32616 \begin_inset CommandInset label
32618 name "subsec:Standard-align-Environment"
32623 \begin_inset Index idx
32628 \begin_layout Plain Layout
32630 \begin_inset IndexMacro subentry
32633 \begin_layout Plain Layout
32640 \begin_inset IndexMacro subentry
32643 \begin_layout Plain Layout
32657 \begin_layout Standard
32658 This align environment is created by pressing
32661 arg "newline-insert newline"
32664 in a formula or by the menu
32666 Insert\SpecialChar menuseparator
32667 Math\SpecialChar menuseparator
32668 AMS align Environment
32673 \begin_layout Standard
32674 An example for two formulas set side by side,
32675 that are created with a four column align environment:
32676 \begin_inset Formula
32678 A & =\sin(B) & C & =D\\
32679 C & \ne A & B & \ne D
32685 the formulas in this environment are placed so as if there would be a
32693 \begin_layout Plain Layout
32701 \begin_inset CommandInset ref
32703 reference "subsec:Variable-Space"
32715 before the first and after every even column.
32716 When the formula style
32722 \begin_layout Plain Layout
32723 For formula styles see
32724 \begin_inset CommandInset ref
32726 reference "sec:Formula-Styles"
32739 the formula is set without the
32745 before the first column.
32748 \begin_layout Subsubsection
32749 Alignat Environment
32750 \begin_inset Index idx
32755 \begin_layout Plain Layout
32757 \begin_inset IndexMacro subentry
32760 \begin_layout Plain Layout
32767 \begin_inset IndexMacro subentry
32770 \begin_layout Plain Layout
32771 alignat environment
32784 \begin_layout Standard
32785 The alignat environment has no predefined column separation.
32786 It can be inserted manually with the spaces that are described in
32787 \begin_inset CommandInset ref
32789 reference "subsec:Space"
32797 \begin_layout Standard
32798 The above example is shown in the alignat environment where 1
32799 \begin_inset space \thinspace{}
32802 cm space was inserted at the beginning of the second formula:
32803 \begin_inset Formula
32804 \begin{alignat*}{2}
32805 A & =\sin(B) & \hspace{1cm}C & =D\\
32806 C & \ne A & B & \ne D
32811 Because the column separation can be set separately for every column,
32812 this environment is especially suitable to set three or more formulas side by side.
32815 \begin_layout Subsubsection
32816 Flalign Environment
32817 \begin_inset CommandInset label
32819 name "subsec:Flalign-Environment"
32824 \begin_inset Index idx
32829 \begin_layout Plain Layout
32831 \begin_inset IndexMacro subentry
32834 \begin_layout Plain Layout
32841 \begin_inset IndexMacro subentry
32844 \begin_layout Plain Layout
32845 flalign environment
32858 \begin_layout Standard
32859 In this environment the first column is always set to the left as much as possible and the last one to the right.
32861 \begin_inset Formula
32863 A & =1 & B & =2 & C & =3\\
32864 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
32872 \begin_layout Standard
32873 By creating a flalign environment with an odd number of columns where an empty \SpecialChar TeX
32874 brace is inserted in the last column,
32875 several formulas in a document can be set to the left,
32876 although the formula style
32881 As example the indented formula
32882 \begin_inset CommandInset ref
32884 reference "eq:VolInt"
32890 \begin_inset Formula
32892 \hspace{30pt}\iiint_{V}X\,\mathrm{d}V & =U & {}
32897 The first two columns contain the formula.
32898 To indent it as with the formula style
32904 \begin_inset space \thinspace{}
32907 pt space was inserted at the beginning of the first column.
32910 \begin_layout Subsection
32911 Eqnarray Environment
32912 \begin_inset CommandInset label
32914 name "subsec:Eqnarray-Environment"
32919 \begin_inset Index idx
32924 \begin_layout Plain Layout
32926 \begin_inset IndexMacro subentry
32929 \begin_layout Plain Layout
32936 \begin_inset IndexMacro subentry
32939 \begin_layout Plain Layout
32940 eqnarray environment
32953 \begin_layout Standard
32954 When this environment is created,
32955 three blue boxes appear.
32956 The content of the first box is right aligned,
32957 the content of the last box left aligned.
32958 The content of the middle box appears centered and a bit smaller because it is intended for relational characters only.
32959 \begin_inset Formula
32961 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
32971 \begin_layout Subsection
32973 \begin_inset Index idx
32978 \begin_layout Plain Layout
32980 \begin_inset IndexMacro subentry
32983 \begin_layout Plain Layout
32990 \begin_inset IndexMacro subentry
32993 \begin_layout Plain Layout
33007 \begin_layout Standard
33008 This environment consists of one centered column.
33009 Every line can be numbered.
33010 \begin_inset Formula
33021 \begin_layout Subsection
33022 Multline Environment
33023 \begin_inset CommandInset label
33025 name "subsec:Multline-Environment"
33030 \begin_inset Index idx
33035 \begin_layout Plain Layout
33037 \begin_inset IndexMacro subentry
33040 \begin_layout Plain Layout
33047 \begin_inset IndexMacro subentry
33050 \begin_layout Plain Layout
33051 multline environment
33064 \begin_layout Standard
33065 The multline environment consists,
33066 like the gather environment,
33068 But the first line is left aligned,
33069 the last one right aligned.
33070 All other lines are centered.
33071 Therefore this environment is suitable for long formulas.
33072 Using example formula
33073 \begin_inset CommandInset ref
33075 reference "eq:lefteqn"
33080 in the multline environment:
33081 \begin_inset Formula
33083 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}\\
33084 -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}\\
33085 =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}}
33093 \begin_layout Standard
33095 only the last line of a multline environment appears numbered when the document numbering is on the right .
33096 If the document numbering is on the left then only the first line will appear numbered.
33100 \begin_layout Plain Layout
33101 For numbering styles see
33102 \begin_inset CommandInset ref
33104 reference "sec:Formula-Styles"
33117 \begin_layout Standard
33125 \begin_inset Index idx
33130 \begin_layout Plain Layout
33132 \begin_inset IndexMacro subentry
33135 \begin_layout Plain Layout
33142 \begin_inset IndexMacro subentry
33145 \begin_layout Plain Layout
33165 \begin_inset Index idx
33170 \begin_layout Plain Layout
33172 \begin_inset IndexMacro subentry
33175 \begin_layout Plain Layout
33182 \begin_inset IndexMacro subentry
33185 \begin_layout Plain Layout
33198 a centered line can be right or left aligned,
33200 The commands are used as follows:
33203 \begin_layout Standard
33208 shoveright{line content}
33214 shoveleft{line content}
33217 \begin_layout Standard
33218 \begin_inset VSpace medskip
33228 \begin_inset Index idx
33233 \begin_layout Plain Layout
33235 \begin_inset IndexMacro subentry
33238 \begin_layout Plain Layout
33245 \begin_inset IndexMacro subentry
33248 \begin_layout Plain Layout
33261 specifies the distance of the first line from the left page margin.
33262 Predefined is the length 0
33263 \begin_inset space \thinspace{}
33269 \begin_layout Standard
33270 As example the above formula where the command
33273 \begin_layout Standard
33283 \begin_layout Standard
33284 was inserted in \SpecialChar TeX
33289 \begin_layout Plain Layout
33301 \begin_inset Formula
33303 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}\\
33304 \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}}\\
33305 =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}}
33314 \begin_layout Plain Layout
33325 The second line was left aligned using
33334 \begin_layout Subsection
33335 Multiline Formula Parts
33336 \begin_inset CommandInset label
33338 name "subsec:Multiline-Formula-Parts"
33343 \begin_inset Index idx
33348 \begin_layout Plain Layout
33350 \begin_inset IndexMacro subentry
33353 \begin_layout Plain Layout
33360 \begin_inset IndexMacro subentry
33363 \begin_layout Plain Layout
33377 \begin_layout Standard
33378 To display only parts of a formula with multiple lines,
33379 one of the following environments is used:
33399 They can be inserted via the menu
33401 Insert\SpecialChar menuseparator
33404 or by using the commands described in this section.
33407 \begin_layout Standard
33408 The first three have the same properties as the corresponding multiline formula environments,
33409 but it is possible to set additional formula parts beside them.
33411 \begin_inset Formula
33413 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
33414 \Delta E\Delta t & \ge\frac{\hbar}{2}
33416 \right\} \textrm{Uncertainty relations}
33424 \begin_layout Standard
33425 To get this formula,
33426 a displayed formula is created where the command
33433 \begin_inset Index idx
33438 \begin_layout Plain Layout
33440 \begin_inset IndexMacro subentry
33443 \begin_layout Plain Layout
33450 \begin_inset IndexMacro subentry
33453 \begin_layout Plain Layout
33467 A purple box appears around the blue formula box where now columns and lines can be added.
33468 Outside the multiline environment other formula parts can be set,
33472 \begin_layout Standard
33473 The aligned environment is also suitable for long formulas whose lines are horizontally aligned.
33474 Using aligned in a displayed formula has the advantage that the formula number is vertically centered behind the lines.
33475 For example here is formula
33476 \begin_inset CommandInset ref
33478 reference "eq:shortlong"
33483 in the aligned environment:
33484 \begin_inset Formula
33486 \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}|}\\
33487 & -\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}|}
33496 \begin_layout Standard
33497 To use the environments
33519 \begin_inset Index idx
33524 \begin_layout Plain Layout
33526 \begin_inset IndexMacro subentry
33529 \begin_layout Plain Layout
33536 \begin_inset IndexMacro subentry
33539 \begin_layout Plain Layout
33559 \begin_inset Index idx
33564 \begin_layout Plain Layout
33566 \begin_inset IndexMacro subentry
33569 \begin_layout Plain Layout
33576 \begin_inset IndexMacro subentry
33579 \begin_layout Plain Layout
33600 \begin_inset Index idx
33605 \begin_layout Plain Layout
33607 \begin_inset IndexMacro subentry
33610 \begin_layout Plain Layout
33617 \begin_inset IndexMacro subentry
33620 \begin_layout Plain Layout
33635 The split environment has the same properties as the aligned environment but it can only have two columns.
33638 \begin_layout Subsection
33639 Text in Multiline Formulas
33640 \begin_inset CommandInset label
33642 name "subsec:Text-in-multiline"
33647 \begin_inset Index idx
33652 \begin_layout Plain Layout
33654 \begin_inset IndexMacro subentry
33657 \begin_layout Plain Layout
33669 \begin_inset Index idx
33674 \begin_layout Plain Layout
33676 \begin_inset IndexMacro subentry
33679 \begin_layout Plain Layout
33686 \begin_inset IndexMacro subentry
33689 \begin_layout Plain Layout
33703 \begin_layout Standard
33704 In the align environments as well as the multline and gather environment,
33705 text can be inserted that will appear in a separate line and doesn't affect the column alignment.
33714 \begin_inset Index idx
33719 \begin_layout Plain Layout
33721 \begin_inset IndexMacro subentry
33724 \begin_layout Plain Layout
33731 \begin_inset IndexMacro subentry
33734 \begin_layout Plain Layout
33747 is used in the following scheme:
33750 \begin_layout Standard
33758 \begin_layout Standard
33759 The text should not be longer than a line because it cannot be hyphenated.
33760 As \SpecialChar LyX
33761 doesn't yet support
33768 the text is written as mathematical text.
33775 must be at the beginning of a line and will appear in the output above this line.
33776 An example where the text was inserted at the beginning of the second line:
33777 \begin_inset Formula
33779 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
33780 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
33788 \begin_layout Standard
33795 always creates some vertical space between the text and the formula lines.
33796 To avoid this space,
33797 in the document settings under
33800 \begin_inset space ~
33810 \begin_inset Index idx
33815 \begin_layout Plain Layout
33817 \begin_inset IndexMacro subentry
33820 \begin_layout Plain Layout
33834 \begin_inset space ~
33840 Then you can use the command
33847 \begin_inset Index idx
33852 \begin_layout Plain Layout
33854 \begin_inset IndexMacro subentry
33857 \begin_layout Plain Layout
33864 \begin_inset IndexMacro subentry
33867 \begin_layout Plain Layout
33889 \begin_layout Standard
33890 \begin_inset Formula
33892 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
33893 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
33901 \begin_layout Section
33903 \begin_inset Index idx
33908 \begin_layout Plain Layout
33915 \begin_inset Index idx
33920 \begin_layout Plain Layout
33922 \begin_inset IndexMacro subentry
33925 \begin_layout Plain Layout
33932 \begin_inset IndexMacro see
33935 \begin_layout Plain Layout
33949 \begin_layout Subsection
33953 \begin_layout Standard
33954 Numbered formulas can be created with the menu
33956 Insert\SpecialChar menuseparator
33957 Math\SpecialChar menuseparator
33959 \begin_inset space ~
33967 arg "command-sequence math-display; math-number-toggle;"
33971 Existing formulas can be numbered with the menu
33973 Edit\SpecialChar menuseparator
33974 Math\SpecialChar menuseparator
33976 \begin_inset space ~
33980 \begin_inset space ~
33988 arg "math-number-toggle"
33992 The formula number is displayed in \SpecialChar LyX
33993 behind the formula as a number in parentheses.
33995 \change_deleted 232239728 1611410645
33996 The number sign is replaced in the output by the formula number.
33997 \change_deleted 5863208 1612727075
33999 \begin_inset Note Note
34002 \begin_layout Plain Layout
34004 \change_inserted 232239728 1611410697
34005 LyX appears to put the actual formula number in the raw file now
34017 \begin_layout Standard
34018 When numbering is turned on in multiline formulas,
34019 all formulas will be numbered.
34020 But the numbering can be controlled with the menu
34022 Edit\SpecialChar menuseparator
34023 Math\SpecialChar menuseparator
34025 \begin_inset space ~
34029 \begin_inset space ~
34037 arg "math-number-line-toggle"
34040 ) for every formula.
34043 \begin_layout Standard
34044 Except for inline formulas,
34045 all formulas can be numbered with two different styles,
34047 \begin_inset CommandInset ref
34049 reference "sec:Formula-Styles"
34057 \begin_layout Subsection
34059 \begin_inset Index idx
34064 \begin_layout Plain Layout
34066 \begin_inset IndexMacro subentry
34069 \begin_layout Plain Layout
34083 \begin_layout Standard
34084 All labeled formulas can be cross-referenced.
34085 A label is added with the menu
34087 Insert\SpecialChar menuseparator
34090 or the toolbar button
34097 The cursor must be inside a displayed formula.
34098 Alternatively you can right-click on the formula and choose
34103 A dialog pops up displaying the prefix
34109 The label is inserted behind the prefix.
34110 The predefined prefix means
34111 \begin_inset Quotes eld
34115 \begin_inset Quotes erd
34118 and makes it easier to find labels in large documents because it marks it as a formula label to distinguish it from e.
34119 \begin_inset space \thinspace{}
34123 \begin_inset space \space{}
34130 Insert\SpecialChar menuseparator
34133 is used again or you can right-click on a formula and then on
34140 \begin_layout Standard
34141 The name of the label is displayed in \SpecialChar LyX
34142 within parentheses behind the formula number.
34143 A formula with a label is always numbered.
34146 \begin_layout Standard
34147 Cross-references are inserted via the menu
34149 Insert\SpecialChar menuseparator
34152 or with the toolbar button
34155 arg "dialog-show-new-inset ref"
34159 A formula cross-reference appears in the output as formula number.
34160 When in the cross-reference dialog window the format
34165 the cross-reference appears in the output as formula number in parentheses.
34166 \begin_inset Newline newline
34169 By right-clicking on a cross-reference in \SpecialChar LyX
34171 one jumps to the formula that is referenced.
34174 \begin_layout Standard
34175 Here are as examples cross-references to formulas of the following subsections:
34176 \begin_inset Note Note
34179 \begin_layout Plain Layout
34180 Note the different cross-reference types.
34188 \begin_layout Standard
34190 \begin_inset CommandInset ref
34198 \begin_inset CommandInset ref
34207 \begin_inset CommandInset ref
34214 ) big Latin letters are used for the numbering in contrary to (
34215 \begin_inset CommandInset ref
34225 \begin_layout Standard
34226 \begin_inset VSpace medskip
34229 When the argument of
34237 \begin_layout Plain Layout
34245 \begin_inset CommandInset ref
34247 reference "subsec:User-defined-Numbering"
34259 contains a box like in
34260 \begin_inset CommandInset ref
34262 reference "subsec:Paragraph-Boxes"
34268 the formula cannot be referenced.
34271 \begin_layout Subsection
34273 \begin_inset Index idx
34278 \begin_layout Plain Layout
34280 \begin_inset IndexMacro subentry
34283 \begin_layout Plain Layout
34297 \begin_layout Standard
34298 Formulas can be numbered as subequations.
34299 To activate this feature,
34304 to the document in the menu
34306 Document\SpecialChar menuseparator
34307 Settings\SpecialChar menuseparator
34311 To insert subequations use the menu
34313 Insert\SpecialChar menuseparator
34314 Custom Insets\SpecialChar menuseparator
34320 \begin_layout Standard
34321 The equations to be subnumbered are put into the
34327 \begin_inset Formula
34335 \begin_inset VSpace -5mm
34339 \begin_inset Flex Subequations
34342 \begin_layout Plain Layout
34343 \begin_inset Formula
34351 \begin_inset Formula
34366 \begin_layout Standard
34367 Every formula in the
34371 inset will be subnumbered with a,
34376 For multiline formulas every line will be subnumbered.
34379 \begin_layout Standard
34380 Referencing subequations works like normal equations:
34382 \begin_inset CommandInset ref
34391 \begin_inset CommandInset ref
34399 If you want to reference the subequations collectively,
34400 insert a label as first thing in the
34406 \begin_inset CommandInset ref
34408 reference "eq:Here-is-an"
34419 \begin_layout Standard
34420 When inserting subequations,
34421 vertical space is added before the equation.
34424 \begin_inset space \thinspace{}
34427 mm vertical space right before the
34432 If the formula style
34438 \begin_layout Plain Layout
34439 For formula styles see
34440 \begin_inset CommandInset ref
34442 reference "sec:Formula-Styles"
34456 \begin_inset space \thinspace{}
34462 \begin_layout Standard
34463 To get another subnumber instead of small Latin letters,
34464 insert this command as \SpecialChar TeX
34465 code before the equations in the
34472 \begin_layout Standard
34481 theparentequation -
34486 \begin_layout Standard
34493 creates the parent number and
34499 adds a small Roman number as subnumber.
34500 For more information about the customization of the numbering,
34502 \begin_inset CommandInset ref
34504 reference "subsec:Numbering-with-Roman"
34512 \begin_layout Standard
34513 Here is an example of a multiline formula where the numbering is customized and turned off for the second line:
34514 \begin_inset Flex Subequations
34517 \begin_layout Plain Layout
34518 \begin_inset CommandInset label
34520 name "eq:Here-is-an"
34528 \begin_layout Plain Layout
34536 theparentequation -
34544 \begin_inset Formula
34546 A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
34547 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
34548 & = & B^{2}-2BZ+Z^{2}
34561 \begin_layout Subsection
34562 Numbering with Roman Numbers and Letters
34563 \begin_inset CommandInset label
34565 name "subsec:Numbering-with-Roman"
34570 \begin_inset Index idx
34575 \begin_layout Plain Layout
34577 \begin_inset IndexMacro subentry
34580 \begin_layout Plain Layout
34592 \begin_inset Index idx
34597 \begin_layout Plain Layout
34599 \begin_inset IndexMacro subentry
34602 \begin_layout Plain Layout
34616 \begin_layout Standard
34617 Formulas can also be numbered with Roman numbers and Latin letters.
34618 To number with small Roman numbers,
34622 \begin_layout Standard
34634 \begin_layout Standard
34635 is inserted before the formula in \SpecialChar TeX
34644 \begin_inset Index idx
34649 \begin_layout Plain Layout
34651 \begin_inset IndexMacro subentry
34654 \begin_layout Plain Layout
34661 \begin_inset IndexMacro subentry
34664 \begin_layout Plain Layout
34677 redefines the predefined command
34693 \begin_layout Plain Layout
34700 has the same scheme as the command
34707 \begin_inset CommandInset ref
34709 reference "subsec:The-Command-newcommand"
34723 is the formula counter.
34730 is used as prefix for a counter,
34731 the value of the counter is output as Arabic number.
34732 When a formula is numbered,
34734 sets internally the command
34740 behind the formula.
34746 \begin_inset Index idx
34751 \begin_layout Plain Layout
34753 \begin_inset IndexMacro subentry
34756 \begin_layout Plain Layout
34763 \begin_inset IndexMacro subentry
34766 \begin_layout Plain Layout
34781 outputs the counter as small Roman number.
34784 \begin_layout Standard
34785 All formulas behind the command
34795 are now numbered Roman.
34796 To switch to numbering with big Roman numbers,
34797 the command is inserted again,
34811 \begin_inset Index idx
34816 \begin_layout Plain Layout
34818 \begin_inset IndexMacro subentry
34821 \begin_layout Plain Layout
34828 \begin_inset IndexMacro subentry
34831 \begin_layout Plain Layout
34832 \begin_inset IndexMacro sortkey
34835 \begin_layout Plain Layout
34857 \begin_inset Quotes eld
34861 \begin_inset Quotes erd
34864 with small Latin letters there is the command
34871 \begin_inset Index idx
34876 \begin_layout Plain Layout
34878 \begin_inset IndexMacro subentry
34881 \begin_layout Plain Layout
34888 \begin_inset IndexMacro subentry
34891 \begin_layout Plain Layout
34905 for big ones there is the command
34912 \begin_inset Index idx
34917 \begin_layout Plain Layout
34919 \begin_inset IndexMacro subentry
34922 \begin_layout Plain Layout
34929 \begin_inset IndexMacro subentry
34932 \begin_layout Plain Layout
34933 \begin_inset IndexMacro sortkey
34936 \begin_layout Plain Layout
34959 \begin_layout Standard
34960 \begin_inset Note Greyedout
34963 \begin_layout Plain Layout
34969 Only a maximum of 26
34970 \begin_inset space ~
34973 formulas can be numbered with Latin letters in one document.
34981 \begin_layout Standard
34985 \begin_layout Plain Layout
35001 \begin_layout Standard
35002 \begin_inset Formula
35004 A=\textrm{small roman}
35013 \begin_layout Plain Layout
35027 \begin_inset Formula
35029 B=\textrm{big Roman}\label{eq:Rom}
35038 \begin_layout Plain Layout
35052 \begin_inset Formula
35054 C=\textrm{small Latin}
35063 \begin_layout Plain Layout
35077 \begin_inset Formula
35079 D=\textrm{big Latin}\label{eq:Lat}
35087 \begin_layout Standard
35088 To switch back to the default numbering,
35089 insert the command:
35092 \begin_layout Standard
35102 \begin_inset Index idx
35107 \begin_layout Plain Layout
35109 \begin_inset IndexMacro subentry
35112 \begin_layout Plain Layout
35119 \begin_inset IndexMacro subentry
35122 \begin_layout Plain Layout
35138 \begin_layout Standard
35142 \begin_layout Plain Layout
35156 \begin_inset Formula
35166 \begin_layout Standard
35167 \begin_inset VSpace medskip
35171 formulas are numbered serially independent from the numbering style.
35172 When then numbering should start with
35173 \begin_inset Quotes eld
35177 \begin_inset Quotes erd
35180 when the style is changed,
35181 new equation counters have to be defined.
35182 A description of this can be found in the file
35183 \begin_inset CommandInset href
35185 name "Formula-numbering.lyx"
35186 target "run:Formula-numbering.lyx"
35195 \begin_layout Subsection
35196 User-defined Numbering
35197 \begin_inset CommandInset label
35199 name "subsec:User-defined-Numbering"
35204 \begin_inset Index idx
35209 \begin_layout Plain Layout
35211 \begin_inset IndexMacro subentry
35214 \begin_layout Plain Layout
35228 \begin_layout Standard
35229 \begin_inset Note Greyedout
35232 \begin_layout Plain Layout
35238 If the document language is a right-to-left language such as Arabic,
35239 you must add this to the to the \SpecialChar LaTeX
35240 -preamble to be able to use the commands described in this section:
35241 \begin_inset Newline newline
35249 \begin_inset Newline newline
35253 \begin_inset Phantom HPhantom
35256 \begin_layout Plain Layout
35259 \begin_inset space ~
35285 \begin_layout Standard
35286 \begin_inset Index idx
35291 \begin_layout Plain Layout
35293 \begin_inset IndexMacro subentry
35296 \begin_layout Plain Layout
35297 self-defined delimiters
35307 With standard numbering,
35308 parentheses are set around a formula number.
35309 To replace the parentheses for example with vertical bars,
35310 the following line is added to the \SpecialChar LaTeX
35314 \begin_layout Standard
35320 \begin_inset Newline newline
35324 \begin_inset Phantom HPhantom
35327 \begin_layout Plain Layout
35330 \begin_inset space ~
35344 maketag@@@{|#1|}} }
35347 \begin_inset Note Note
35350 \begin_layout Plain Layout
35351 This macro is already declared in the \SpecialChar LaTeX
35352 -preamble for testing.
35354 remove the percent signs at the beginning.
35362 \begin_layout Standard
35363 To use other characters,
35364 the vertical bars besides the
35368 are replaced by one or more characters.
35369 To display only the formula number the vertical bars are omitted.
35372 \begin_layout Standard
35373 \begin_inset VSpace bigskip
35376 When there should be an expression of your choice instead of the consecutive formula number in parentheses behind the formula,
35384 \begin_inset Index idx
35389 \begin_layout Plain Layout
35391 \begin_inset IndexMacro subentry
35394 \begin_layout Plain Layout
35401 \begin_inset IndexMacro subentry
35404 \begin_layout Plain Layout
35418 \begin_inset Formula
35420 A+B=C\tag{something}\label{eq:tag}
35425 In this example the command
35430 \begin_inset space \textvisiblespace{}
35435 was inserted in the formula.
35438 \begin_layout Standard
35444 \begin_inset space \textvisiblespace{}
35449 is inserted instead,
35450 the parentheses are removed:
35451 \begin_inset Formula
35453 A+B=C\tag*{something}
35461 \begin_layout Standard
35462 \begin_inset VSpace bigskip
35465 To restart the formula numbering with new document parts or sections,
35466 the following command is used:
35469 \begin_layout Standard
35474 @addtoreset{equation}{part}
35477 \begin_inset Index idx
35482 \begin_layout Plain Layout
35484 \begin_inset IndexMacro subentry
35487 \begin_layout Plain Layout
35491 \begin_layout Plain Layout
35504 \begin_inset IndexMacro subentry
35507 \begin_layout Plain Layout
35514 \begin_layout Plain Layout
35532 \begin_inset Newline newline
35536 \begin_inset Newline newline
35543 @addtoreset{equation}{section}
35546 \begin_layout Standard
35547 To be able to use these commands in \SpecialChar TeX
35550 \begin_inset Quotes eld
35554 \begin_inset Quotes erd
35557 character has to be made
35558 \begin_inset Quotes eld
35562 \begin_inset Quotes erd
35565 for \SpecialChar LaTeX
35580 So the command sequence in \SpecialChar TeX
35584 \begin_layout Standard
35590 \begin_inset Newline newline
35595 @addtoreset{equation}{section}
35596 \begin_inset Newline newline
35604 \begin_layout Standard
35605 In the \SpecialChar LaTeX
35618 can be omitted as they are automatically internally inserted by \SpecialChar LyX
35622 \begin_layout Standard
35638 \begin_layout Plain Layout
35643 is part of the \SpecialChar LaTeX
35649 \begin_inset Index idx
35654 \begin_layout Plain Layout
35656 \begin_inset IndexMacro subentry
35659 \begin_layout Plain Layout
35670 that is part of every \SpecialChar LaTeX
35671 standard installation.
35677 \begin_inset Index idx
35682 \begin_layout Plain Layout
35684 \begin_inset IndexMacro subentry
35687 \begin_layout Plain Layout
35698 has to be loaded in the \SpecialChar LaTeX
35699 -preamble with the line
35702 \begin_layout Standard
35707 usepackage{remreset}
35710 \begin_layout Standard
35718 \begin_inset Index idx
35723 \begin_layout Plain Layout
35725 \begin_inset IndexMacro subentry
35728 \begin_layout Plain Layout
35732 \begin_layout Plain Layout
35745 \begin_inset IndexMacro subentry
35748 \begin_layout Plain Layout
35755 \begin_layout Plain Layout
35772 can be used with the same scheme as
35781 \begin_layout Standard
35782 \begin_inset VSpace bigskip
35785 Sometimes formulas should be numbered in the following form:
35788 \begin_layout Standard
35791 (section number.formula number)
35794 \begin_layout Standard
35795 The formula number should start with every section with
35796 \begin_inset Quotes eld
35800 \begin_inset Quotes erd
35806 \begin_layout Standard
35807 For this case there is the command
35814 \begin_inset Index idx
35819 \begin_layout Plain Layout
35821 \begin_inset IndexMacro subentry
35824 \begin_layout Plain Layout
35831 \begin_inset IndexMacro subentry
35834 \begin_layout Plain Layout
35848 which is used with the following scheme:
35851 \begin_layout Standard
35856 numberwithin{counter}{sectioning}
35859 \begin_layout Standard
35860 Counter denotes what kind of numbering is affected,
35861 sectioning denotes what the number before the dot is.
35864 \begin_layout Standard
35865 Thus in our case the following \SpecialChar LaTeX
35866 preamble or \SpecialChar TeX
35870 \begin_layout Standard
35875 numberwithin{equation}{section}
35878 \begin_layout Standard
35879 This is the result:
35883 \begin_layout Plain Layout
35887 numberwithin{equation}{section}
35893 \begin_inset Formula
35903 \begin_layout Standard
35905 \begin_inset space \thinspace{}
35909 \begin_inset space \space{}
35912 tables so that the number of the part is the sectioning,
35913 \begin_inset Newline newline
35920 numberwithin{table}{part}
35925 \begin_layout Standard
35926 To go back to the standard numbering or to prevent this kind of numbering when it is defined by the document class,
35927 the following command is inserted as \SpecialChar TeX
35928 code or to the \SpecialChar LaTeX
35932 \begin_layout Standard
35942 \begin_inset Index idx
35947 \begin_layout Plain Layout
35949 \begin_inset IndexMacro subentry
35952 \begin_layout Plain Layout
35959 \begin_inset IndexMacro subentry
35962 \begin_layout Plain Layout
35981 \begin_layout Plain Layout
35997 \begin_inset Newline newline
36005 \begin_inset Newline newline
36017 \begin_layout Standard
36024 internally uses the command
36032 and would also need to be reverted.
36036 \begin_layout Plain Layout
36043 \begin_layout Plain Layout
36047 @removefromreset{equation}{section}
36050 \begin_layout Plain Layout
36062 \begin_layout Section
36063 Chemical Symbols and Equations
36064 \begin_inset CommandInset label
36066 name "subsec:Chemical-Symbols-and"
36071 \begin_inset Index idx
36076 \begin_layout Plain Layout
36077 Chemical characters
36078 \begin_inset IndexMacro subentry
36081 \begin_layout Plain Layout
36093 \begin_inset Index idx
36098 \begin_layout Plain Layout
36105 \begin_inset Index idx
36110 \begin_layout Plain Layout
36112 \begin_inset IndexMacro subentry
36115 \begin_layout Plain Layout
36129 \begin_layout Standard
36130 An example text from chemistry:
36133 \begin_layout Quote
36135 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
36138 -ion reacts with two
36139 \begin_inset Formula $\mathrm{Na^{+}}$
36142 -ions to sodium sulfate
36143 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
36147 The chemical equation for this is:
36148 \begin_inset Formula
36150 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
36158 \begin_layout Standard
36159 Chemical equations can be created as formulas.
36160 To avoid the symbols appearing in italic,
36161 everything is highlighted and changed by the shortcut
36167 to the upright font style.
36171 \begin_layout Plain Layout
36177 \begin_inset CommandInset ref
36179 reference "subsec:Font-Styles"
36192 \begin_layout Standard
36193 A more convenient way to typeset chemical formulas is to use the command
36200 \begin_inset Index idx
36205 \begin_layout Plain Layout
36207 \begin_inset IndexMacro subentry
36210 \begin_layout Plain Layout
36217 \begin_inset IndexMacro subentry
36220 \begin_layout Plain Layout
36233 which is available when the \SpecialChar LaTeX
36239 \begin_inset Index idx
36244 \begin_layout Plain Layout
36246 \begin_inset IndexMacro subentry
36249 \begin_layout Plain Layout
36267 in a formula a new blue box appears where chemical formulas can be inserted in an intuitive way.
36270 \begin_layout Standard
36272 \begin_inset Tabular
36273 <lyxtabular version="3" rows="10" columns="2">
36274 <features booktabs="true" tabularvalignment="middle">
36275 <column alignment="center" valignment="top" width="0pt">
36276 <column alignment="center" valignment="top">
36278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36281 \begin_layout Plain Layout
36287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36290 \begin_layout Plain Layout
36298 <cell alignment="center" valignment="top" leftline="true" usebox="none">
36301 \begin_layout Plain Layout
36305 \begin_inset space \textvisiblespace{}
36313 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
36316 \begin_layout Plain Layout
36317 \begin_inset Formula $\ce{H2CO3}$
36326 <row topspace="1.5mm">
36327 <cell alignment="center" valignment="top" usebox="none">
36330 \begin_layout Plain Layout
36334 \begin_inset space \textvisiblespace{}
36342 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
36345 \begin_layout Plain Layout
36346 \begin_inset Formula $\ce{SO4^{2-}}$
36355 <row topspace="1.5mm">
36356 <cell alignment="center" valignment="top" usebox="none">
36359 \begin_layout Plain Layout
36363 \begin_inset space \textvisiblespace{}
36371 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
36374 \begin_layout Plain Layout
36375 \begin_inset Formula $\ce{(NH4)2S}$
36384 <row topspace="1.5mm">
36385 <cell alignment="center" valignment="top" usebox="none">
36388 \begin_layout Plain Layout
36392 \begin_inset space \textvisiblespace{}
36400 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
36403 \begin_layout Plain Layout
36404 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
36413 <row topspace="1.5mm">
36414 <cell alignment="center" valignment="top" usebox="none">
36417 \begin_layout Plain Layout
36421 \begin_inset space \textvisiblespace{}
36427 \begin_inset space \textvisiblespace{}
36433 \begin_inset space \textvisiblespace{}
36441 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
36444 \begin_layout Plain Layout
36445 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
36454 <row topspace="1.5mm">
36455 <cell alignment="center" valignment="top" usebox="none">
36458 \begin_layout Plain Layout
36462 \begin_inset space \textvisiblespace{}
36466 \begin_inset Formula $\downarrow$
36470 \begin_inset Formula $\to$
36478 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
36481 \begin_layout Plain Layout
36482 \begin_inset Formula $\ce{_{90}^{227}Th+}$
36492 <cell alignment="center" valignment="top" leftline="true" usebox="none">
36495 \begin_layout Plain Layout
36499 \begin_inset space \textvisiblespace{}
36505 \begin_inset space \textvisiblespace{}
36511 \begin_inset space \textvisiblespace{}
36519 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
36522 \begin_layout Plain Layout
36523 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
36533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36536 \begin_layout Plain Layout
36540 \begin_inset space \textvisiblespace{}
36544 \begin_inset space \textvisiblespace{}
36548 \begin_inset space \textvisiblespace{}
36552 \begin_inset space \textvisiblespace{}
36556 \begin_inset space \textvisiblespace{}
36564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36567 \begin_layout Plain Layout
36568 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
36577 <row topspace="1.5mm">
36578 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
36581 \begin_layout Plain Layout
36585 \begin_inset space \textvisiblespace{}
36589 \begin_inset space \textvisiblespace{}
36593 \begin_inset space \textvisiblespace{}
36597 \begin_inset space \textvisiblespace{}
36605 \begin_inset space \textvisiblespace{}
36613 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
36616 \begin_layout Plain Layout
36617 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
36633 \begin_layout Standard
36634 \begin_inset Note Greyedout
36637 \begin_layout Plain Layout
36643 It is not possible in \SpecialChar LyX
36644 to use the character ^ to get an up-arrow as described in the
36649 One instead uses a negative thin space followed by the command
36657 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
36668 \begin_layout Standard
36675 the command for equation
36676 \begin_inset space ~
36680 \begin_inset CommandInset ref
36682 reference "eq:chem-reaction"
36688 \begin_inset Newline newline
36696 \begin_inset space \textvisiblespace{}
36700 \begin_inset space \textvisiblespace{}
36704 \begin_inset space \textvisiblespace{}
36708 \begin_inset space \textvisiblespace{}
36712 \begin_inset space \textvisiblespace{}
36716 \begin_inset space \textvisiblespace{}
36722 \begin_layout Standard
36723 To create multiline chemical equations first a multiline formula is created as described in
36724 \begin_inset CommandInset ref
36726 reference "sec:Multiline-Formulas"
36732 Afterwards the command
36738 is used in every small blue box of the formula.
36740 \begin_inset CommandInset ref
36742 reference "eq:TEOS-reaction-1"
36748 \begin_inset CommandInset ref
36750 reference "eq:TEOS-reaction-2"
36755 are an example of a multi-stage chemical reaction where every equation has its own number.
36756 \begin_inset Formula
36758 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
36759 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
36767 \begin_layout Standard
36778 package provides the command
36785 \begin_inset Index idx
36790 \begin_layout Plain Layout
36792 \begin_inset IndexMacro subentry
36795 \begin_layout Plain Layout
36802 \begin_inset IndexMacro subentry
36805 \begin_layout Plain Layout
36818 that is used for special cases.
36819 For more information about
36825 and more examples have a look at the documentation of
36831 \begin_inset CommandInset citation
36841 \begin_layout Section
36845 \begin_layout Standard
36847 supports two types of commutative diagrams:
36856 and are explained below.
36859 \begin_layout Subsection
36861 \begin_inset Index idx
36866 \begin_layout Plain Layout
36868 \begin_inset IndexMacro subentry
36871 \begin_layout Plain Layout
36885 \begin_layout Standard
36886 Diagrams of this type visualize relations by vertical and horizontal lines or arrows:
36887 \begin_inset Formula
36889 \begin{CD}A@>>>B@>>>C\\
36900 \begin_layout Standard
36907 \begin_inset Index idx
36912 \begin_layout Plain Layout
36914 \begin_inset IndexMacro subentry
36917 \begin_layout Plain Layout
36924 \begin_inset IndexMacro subentry
36927 \begin_layout Plain Layout
36942 is inserted to a formula.
36943 A blue box appears with two dashed lines where additional commands can be inserted.
36947 arg "newline-insert newline"
36950 a new line is created.
36951 Horizontal relations are inserted in odd formula lines,
36952 vertical in even formula lines.
36955 \begin_layout Standard
36956 To create the relations use the following commands:
36959 \begin_layout Itemize
36964 creates a left arrow,
36976 \begin_layout Itemize
36981 creates an up arrow,
36990 a vertical equal sign
36993 \begin_layout Itemize
36999 is a placeholder for non-existent relations
37002 \begin_layout Standard
37003 All arrows can be labeled as follows:
37006 \begin_layout Itemize
37007 If text inserted between the first and second < or >,
37009 it is placed above the arrow.
37010 When it is inserted between the second and third one,
37011 it appears under the arrow.
37014 \begin_layout Itemize
37015 When text for vertical arrows is inserted between the first and second A or V,
37017 it is placed left beside the arrow.
37018 When it is inserted between the second and third one,
37019 it appears right beside the arrow.
37020 If the text contains an A or V,
37021 these letters must be set into a \SpecialChar TeX
37025 \begin_layout Standard
37026 As example a diagram with all possible relations:
37029 \begin_layout Standard
37030 \begin_inset Formula
37032 \begin{CD}A@>j>>B@>>k>C@=F\\
37043 \begin_layout Standard
37044 The command for this is:
37045 \begin_inset Newline newline
37053 \begin_inset space \textvisiblespace{}
37056 A@>j>>B@>>k>C@=F Ctrl+Return
37057 \begin_inset Newline newline
37061 \begin_inset Phantom HPhantom
37064 \begin_layout Plain Layout
37070 \begin_inset space \textvisiblespace{}
37083 \begin_inset Formula $\to$
37089 \begin_inset Newline newline
37093 \begin_inset Phantom HPhantom
37096 \begin_layout Plain Layout
37102 \begin_inset space \textvisiblespace{}
37113 \begin_layout Subsection
37115 \begin_inset Index idx
37120 \begin_layout Plain Layout
37122 \begin_inset IndexMacro subentry
37125 \begin_layout Plain Layout
37139 \begin_layout Standard
37140 To be able to use xymatrices,
37141 the \SpecialChar LaTeX
37147 A xymatrix is created by inserting the command
37154 Then you are able to add new matrix columns and rows like for normal matrices,
37156 \begin_inset CommandInset ref
37158 reference "sec:Matrices"
37166 \begin_layout Standard
37167 Contrary to amscd diagrams,
37168 xymatrices support diagonal and curved arrows,
37170 The commands used to create commutative diagrams and decorations are explained in detail in the
37176 Help\SpecialChar menuseparator
37178 \begin_inset space ~
37186 \begin_layout Subsection
37192 \begin_inset Index idx
37197 \begin_layout Plain Layout
37199 \begin_inset IndexMacro subentry
37202 \begin_layout Plain Layout
37216 \begin_layout Standard
37222 the \SpecialChar LaTeX
37232 -diagram is created by inserting the command
37239 Then you will be able to add new matrix columns and rows like for normal matrices,
37241 \begin_inset CommandInset ref
37243 reference "sec:Matrices"
37251 \begin_layout Standard
37252 Examples of how to create
37256 diagrams in \SpecialChar LyX
37261 manual that you find in the menu
37263 Help\SpecialChar menuseparator
37265 \begin_inset space ~
37273 \begin_layout Section
37274 User-defined Commands
37275 \begin_inset Index idx
37280 \begin_layout Plain Layout
37281 User-defined commands
37289 \begin_layout Standard
37290 \begin_inset Note Greyedout
37293 \begin_layout Plain Layout
37299 The names of user-defined commands and macros may only consist of Latin letters.
37307 \begin_layout Subsection
37311 \begin_inset CommandInset label
37313 name "subsec:The-Command-newcommand"
37318 \begin_inset Index idx
37323 \begin_layout Plain Layout
37324 User-defined commands
37325 \begin_inset IndexMacro subentry
37328 \begin_layout Plain Layout
37342 \begin_inset Index idx
37347 \begin_layout Plain Layout
37349 \begin_inset IndexMacro subentry
37352 \begin_layout Plain Layout
37359 \begin_inset IndexMacro subentry
37362 \begin_layout Plain Layout
37378 \begin_layout Standard
37379 Many \SpecialChar LaTeX
37380 -commands are too long to be used frequently.
37381 But it is possible to define with the command
37387 new shorter commands.
37390 \begin_layout Standard
37391 The command scheme of
37400 \begin_layout Standard
37405 newcommand{new command name}[number of arguments][optional
37410 \begin_inset Newline newline
37414 \begin_inset Phantom HPhantom
37417 \begin_layout Plain Layout
37427 {command definition}
37430 \begin_layout Standard
37431 \begin_inset Note Greyedout
37434 \begin_layout Plain Layout
37440 Verify that the name of the new command is not already used in your document or by the \SpecialChar LaTeX
37441 -packages that you use.
37442 If you for example define the command
37455 you will get an error message because
37461 is already defined as command for
37462 \begin_inset Quotes eld
37466 \begin_inset Formula $\le$
37470 \begin_inset Quotes erd
37481 \begin_layout Standard
37482 The number of arguments is an integer in the range 0
37483 \begin_inset space \thinspace{}
37487 \begin_inset space \thinspace{}
37490 9 and specifies how many arguments the new command should have.
37491 With the optional value a value for an optional argument can be predefined.
37501 rgument of the new command is automatically an optional one.
37504 \begin_layout Standard
37505 Here are some examples:
37508 \begin_layout Itemize
37509 To define the command
37522 the \SpecialChar LaTeX
37524 \begin_inset VSpace medskip
37528 \begin_inset Newline newline
37542 \begin_layout Itemize
37543 To define the command
37556 the argument (that should be underlined) must be taken into account.
37557 For this the preamble line is:
37558 \begin_inset VSpace medskip
37562 \begin_inset Newline newline
37576 \begin_inset VSpace medskip
37580 \begin_inset Newline newline
37587 acts as argument placeholder,
37592 behind it denotes that it is the placeholder for the first argument.
37595 \begin_layout Itemize
37603 \begin_inset space \thinspace{}
37607 \begin_inset space \space{}
37617 \begin_inset VSpace medskip
37621 \begin_inset Newline newline
37632 framebox#1#2{$#3$}}
37635 \begin_inset VSpace medskip
37639 \begin_inset Newline newline
37642 The two Dollar signs creates the extra formula needed for
37650 \begin_inset CommandInset ref
37652 reference "subsec:Boxes-with-Frame"
37660 \begin_layout Itemize
37661 To create a new command for
37667 where the color for the box need not be specified,
37668 the argument for the color is defined optional:
37669 \begin_inset VSpace medskip
37673 \begin_inset Newline newline
37684 fcolorbox{#2}{#1}{$#3$}}
37687 \begin_inset VSpace medskip
37691 \begin_inset Newline newline
37694 When the color is not specified when using
37701 the predefined color
37708 \begin_layout Standard
37709 A test of the new defined commands:
37712 \begin_layout Standard
37714 \begin_inset Tabular
37715 <lyxtabular version="3" rows="6" columns="2">
37716 <features booktabs="true" tabularvalignment="middle">
37717 <column alignment="center" valignment="top" width="0pt">
37718 <column alignment="center" valignment="top">
37720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37723 \begin_layout Plain Layout
37729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37732 \begin_layout Plain Layout
37740 <cell alignment="center" valignment="top" leftline="true" usebox="none">
37743 \begin_layout Plain Layout
37747 \begin_inset space \textvisiblespace{}
37755 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
37758 \begin_layout Plain Layout
37759 \begin_inset Formula $A\gr B$
37769 <cell alignment="center" valignment="top" leftline="true" usebox="none">
37772 \begin_layout Plain Layout
37780 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
37783 \begin_layout Plain Layout
37784 \begin_inset Formula $\us{ABcd}$
37793 <row topspace="1mm">
37794 <cell alignment="center" valignment="top" usebox="none">
37797 \begin_layout Plain Layout
37801 \begin_inset Formula $\to$
37807 \begin_inset Formula $\to$
37815 \begin_inset space \textvisiblespace{}
37823 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
37826 \begin_layout Plain Layout
37827 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
37836 <row topspace="1.5mm">
37837 <cell alignment="center" valignment="top" usebox="none">
37840 \begin_layout Plain Layout
37844 \begin_inset Formula $\to$
37852 \begin_inset space \textvisiblespace{}
37860 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
37863 \begin_layout Plain Layout
37864 \begin_inset Formula $\cb{red}{\int A=B}$
37873 <row topspace="1.5mm" bottomspace="1mm">
37874 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37877 \begin_layout Plain Layout
37883 \begin_inset Formula $\to$
37891 \begin_inset space \textvisiblespace{}
37899 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
37902 \begin_layout Plain Layout
37903 \begin_inset Formula $\cb[green]{red}{\int A=B}$
37917 \change_inserted -584632292 1686503213
37921 \begin_layout Standard
37923 \change_inserted -584632292 1686503316
37925 commands defined in the preamble do not display `nicely' in LyX itself.
37926 Most such commands can be defined in LyX using `math macros',
37928 which we are about to explain,
37929 and these do display nicely.
37934 \begin_layout Subsection
37936 \begin_inset Index idx
37941 \begin_layout Plain Layout
37942 User-defined commands!
37949 \begin_inset Index idx
37954 \begin_layout Plain Layout
37963 \begin_layout Standard
37964 User-defined commands are especially convenient for complex expressions.
37965 For example if you are dealing with a document that has quadratic equations,
37966 the same solution type occurs several times.
37967 The general form of a quadratic equation is
37968 \begin_inset Formula
37970 0=\lambda^{2}+p\lambda+q
37975 The general form of the solution is
37976 \begin_inset Formula
37978 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
37986 \begin_layout Standard
37987 To define a command for the solution formula where only the three parameters
37988 \begin_inset Formula $\lambda$
37993 \begin_inset Formula $p$
37997 \begin_inset Formula $q$
38000 need to be specified and the index of
38001 \begin_inset Formula $\lambda$
38004 can be given optionally,
38005 the \SpecialChar LaTeX
38007 \begin_inset Newline newline
38023 \begin_inset Newline newline
38027 \begin_inset Phantom HPhantom
38030 \begin_layout Plain Layout
38044 frac{#3^{2}}{4}-#4}}
38047 \begin_layout Standard
38048 To create with this the solution formula,
38050 \begin_inset Newline newline
38060 \begin_inset Formula $\to$
38066 \begin_inset Formula $\to$
38073 is inserted to a formula
38078 \begin_layout Standard
38079 The definition of the new command is unintuitive because one has to know the schemes of all used \SpecialChar LaTeX
38082 \begin_inset space \thinspace{}
38086 \begin_inset space \space{}
38089 that a fraction is inserted in \SpecialChar LaTeX
38094 frac{numerator}{denominator}
38097 Furthermore one can easily forget a brace in the definition and cannot see in \SpecialChar LyX
38098 what the new command is doing.
38099 To avoid these problems \SpecialChar LyX
38100 offers the possibility to use math macros instead of the command
38109 \begin_layout Standard
38110 A math macro is created by using the menu
38112 Insert\SpecialChar menuseparator
38113 Math\SpecialChar menuseparator
38116 or the toolbar button
38119 arg "math-macro newmacroname_newcommand"
38123 The math macro toolbar appears together with the following box where the macro is defined:
38124 \begin_inset Newline newline
38128 \begin_inset space \hspace*{\fill}
38132 \begin_inset Graphics
38133 filename clipart/macrobox.png
38139 \begin_inset space \hspace*{\fill}
38143 \begin_inset Newline newline
38147 \begin_inset FormulaMacro
38148 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
38153 newmacroname is the default name of the macro that should be changed to something sensible.
38154 The wanted formula is inserted in the first blue box.
38155 An argument placeholder is inserted with the command
38163 \begin_inset space \thinspace{}
38167 \begin_inset space \space{}
38176 or by using the macro toolbar button
38179 arg "math-macro-add-param"
38183 Argument placeholders are displayed red.
38185 \begin_inset space ~
38188 arguments are possible.
38189 Optional arguments are created with the toolbar button
38192 arg "math-macro-add-optional-param"
38196 The first non-optional argument can be transformed to an optional one with the toolbar button
38199 arg "math-macro-make-optional"
38203 In the second blue box the appearance of the macro in \SpecialChar LyX
38205 Normally you want to see it as it is defined,
38206 so the box is kept empty.
38207 But when you have created a macro that needs lot of space on the screen,
38208 you can insert in the box for example
38209 \begin_inset Newline newline
38243 \begin_inset Newline newline
38248 For the macro only the arguments with the macro name in front of them will then be displayed in \SpecialChar LyX
38250 leading to a better overview.
38251 The formula appears in the output as defined in the first box.
38252 \begin_inset Newline newline
38255 The appearance of macros in formulas can furthermore be changed for single macros by setting the cursor in the macro and using the menu
38257 View\SpecialChar menuseparator
38259 \begin_inset space ~
38263 \begin_inset space ~
38271 \begin_layout Standard
38273 the macro name is inserted as command to a formula,
38281 Our macro looks in \SpecialChar LyX
38283 \begin_inset Newline newline
38287 \begin_inset space \hspace*{\fill}
38291 \begin_inset Graphics
38292 filename clipart/macrouse.png
38298 \begin_inset space \hspace*{\fill}
38302 \begin_inset Newline newline
38305 Here is our macro example with the arguments
38306 \begin_inset Formula $x$
38311 \begin_inset Formula $\ln(x)$
38315 \begin_inset Formula $B$
38321 \begin_layout Standard
38322 \begin_inset Formula
38332 \begin_layout Standard
38336 Tools\SpecialChar menuseparator
38337 Preferences\SpecialChar menuseparator
38338 Editing\SpecialChar menuseparator
38341 different styles to edit macros.
38342 To find the style that suits you best,
38343 choose a style and set the cursor in a macro formula to see the difference.
38346 \begin_layout Standard
38347 A math macro is transformed internally to a
38353 command when exporting the document.
38360 command is not placed in the \SpecialChar LaTeX
38362 therefore macros can only be used in formulas that are in the document below the macro definition box.
38365 \begin_layout Standard
38366 Math macros can also be directly created from a
38373 When writing for example the command
38376 \begin_inset Newline newline
38385 xleftarrow[#2]{#1}}
38386 \begin_inset Newline newline
38391 in \SpecialChar LyX
38393 highlighting it completely and using the shortcut
38398 the command will be transformed to a math macro.
38399 Using this method you need to be careful that the
38405 command is typed correctly,
38406 otherwise you get a faulty macro leading to \SpecialChar LaTeX
38410 \begin_layout Standard
38411 Math macros currently have the problem that further formulas in macro definitions are handled wrong.
38412 Therefore the example
38419 \begin_inset CommandInset ref
38421 reference "subsec:The-Command-newcommand"
38426 cannot be created as macro.
38429 \begin_layout Standard
38430 When the cursor is in a macro definition box,
38431 you will see the macro toolbar in \SpecialChar LyX
38435 \begin_layout Standard
38436 \begin_inset VSpace defskip
38442 \begin_layout Standard
38443 \begin_inset Graphics
38444 filename clipart/MacroToolbar.png
38449 \begin_inset Index idx
38454 \begin_layout Plain Layout
38456 \begin_inset IndexMacro subentry
38459 \begin_layout Plain Layout
38473 \begin_layout Standard
38474 \begin_inset VSpace defskip
38480 \begin_layout Standard
38481 The macro toolbar contains from left to right the following buttons:
38484 \begin_layout Standard
38485 \begin_inset VSpace defskip
38491 \begin_layout Standard
38492 \begin_inset Tabular
38493 <lyxtabular version="3" rows="9" columns="2">
38494 <features islongtable="true" longtabularalignment="center">
38495 <column alignment="left" valignment="top">
38496 <column alignment="left" valignment="top" width="85col%">
38497 <row interlinespace="2.5mm">
38498 <cell alignment="center" valignment="top" usebox="none">
38501 \begin_layout Plain Layout
38504 arg "math-macro-remove-param"
38512 <cell alignment="center" valignment="top" usebox="none">
38515 \begin_layout Plain Layout
38518 Edit\SpecialChar menuseparator
38519 Math\SpecialChar menuseparator
38521 \begin_inset space ~
38524 Definition\SpecialChar menuseparator
38525 Remove Last Argument
38531 <row interlinespace="2.5mm">
38532 <cell alignment="center" valignment="top" usebox="none">
38535 \begin_layout Plain Layout
38538 arg "math-macro-add-param"
38546 <cell alignment="center" valignment="top" usebox="none">
38549 \begin_layout Plain Layout
38552 Edit\SpecialChar menuseparator
38553 Math\SpecialChar menuseparator
38555 \begin_inset space ~
38558 Definition\SpecialChar menuseparator
38565 <row interlinespace="2.5mm">
38566 <cell alignment="center" valignment="top" usebox="none">
38569 \begin_layout Plain Layout
38572 arg "math-macro-make-optional"
38580 <cell alignment="center" valignment="top" usebox="none">
38583 \begin_layout Plain Layout
38586 Edit\SpecialChar menuseparator
38587 Math\SpecialChar menuseparator
38589 \begin_inset space ~
38592 Definition\SpecialChar menuseparator
38593 Transform First Non-Optional to
38594 \begin_inset Newline newline
38598 \begin_inset Phantom HPhantom
38601 \begin_layout Plain Layout
38604 Edit\SpecialChar menuseparator
38605 Math\SpecialChar menuseparator
38607 \begin_inset space ~
38610 Definition\SpecialChar menuseparator
38622 <row interlinespace="2.5mm">
38623 <cell alignment="center" valignment="top" usebox="none">
38626 \begin_layout Plain Layout
38629 arg "math-macro-make-nonoptional"
38637 <cell alignment="center" valignment="top" usebox="none">
38640 \begin_layout Plain Layout
38643 Edit\SpecialChar menuseparator
38644 Math\SpecialChar menuseparator
38646 \begin_inset space ~
38649 Definition\SpecialChar menuseparator
38650 Transform Last Optional to
38651 \begin_inset Newline newline
38655 \begin_inset Phantom HPhantom
38658 \begin_layout Plain Layout
38661 Edit\SpecialChar menuseparator
38662 Math\SpecialChar menuseparator
38664 \begin_inset space ~
38667 Definition\SpecialChar menuseparator
38673 Non-Optional Argument
38679 <row interlinespace="2.5mm">
38680 <cell alignment="center" valignment="top" usebox="none">
38683 \begin_layout Plain Layout
38686 arg "math-macro-remove-optional-param"
38694 <cell alignment="center" valignment="top" usebox="none">
38697 \begin_layout Plain Layout
38700 Edit\SpecialChar menuseparator
38701 Math\SpecialChar menuseparator
38703 \begin_inset space ~
38706 Definition\SpecialChar menuseparator
38707 Remove Optional Argument
38713 <row interlinespace="2.5mm">
38714 <cell alignment="center" valignment="top" usebox="none">
38717 \begin_layout Plain Layout
38720 arg "math-macro-add-optional-param"
38728 <cell alignment="center" valignment="top" usebox="none">
38731 \begin_layout Plain Layout
38734 Edit\SpecialChar menuseparator
38735 Math\SpecialChar menuseparator
38737 \begin_inset space ~
38740 Definition\SpecialChar menuseparator
38741 Insert Optional Argument
38747 <row interlinespace="2.5mm">
38748 <cell alignment="center" valignment="top" usebox="none">
38751 \begin_layout Plain Layout
38754 arg "math-macro-remove-greedy-param"
38762 <cell alignment="center" valignment="top" usebox="none">
38765 \begin_layout Plain Layout
38768 Edit\SpecialChar menuseparator
38769 Math\SpecialChar menuseparator
38771 \begin_inset space ~
38774 Definition\SpecialChar menuseparator
38775 Remove Last Argument
38776 \begin_inset Newline newline
38780 \begin_inset Phantom HPhantom
38783 \begin_layout Plain Layout
38786 Edit\SpecialChar menuseparator
38787 Math\SpecialChar menuseparator
38789 \begin_inset space ~
38792 Definition\SpecialChar menuseparator
38798 Spitting Out To The Right
38804 <row interlinespace="2.5mm">
38805 <cell alignment="center" valignment="top" usebox="none">
38808 \begin_layout Plain Layout
38811 arg "math-macro-append-greedy-param"
38819 <cell alignment="center" valignment="top" usebox="none">
38822 \begin_layout Plain Layout
38825 Edit\SpecialChar menuseparator
38826 Math\SpecialChar menuseparator
38828 \begin_inset space ~
38831 Definition\SpecialChar menuseparator
38833 \begin_inset Newline newline
38837 \begin_inset Phantom HPhantom
38840 \begin_layout Plain Layout
38843 Edit\SpecialChar menuseparator
38844 Math\SpecialChar menuseparator
38846 \begin_inset space ~
38849 Definition\SpecialChar menuseparator
38855 Eating From The Right
38861 <row interlinespace="2.5mm">
38862 <cell alignment="center" valignment="top" usebox="none">
38865 \begin_layout Plain Layout
38868 arg "math-macro-add-greedy-optional-param"
38876 <cell alignment="center" valignment="top" usebox="none">
38879 \begin_layout Plain Layout
38882 Edit\SpecialChar menuseparator
38883 Math\SpecialChar menuseparator
38885 \begin_inset space ~
38888 Definition\SpecialChar menuseparator
38889 Append Optional Argument
38890 \begin_inset Newline newline
38894 \begin_inset Phantom HPhantom
38897 \begin_layout Plain Layout
38900 Edit\SpecialChar menuseparator
38901 Math\SpecialChar menuseparator
38903 \begin_inset space ~
38906 Definition\SpecialChar menuseparator
38912 Eating From The Right
38923 \change_inserted -584632292 1686503329
38927 \begin_layout Subsection
38929 \change_inserted -584632292 1686503341
38930 Math Macros for External Commands
38933 \begin_layout Standard
38935 \change_inserted -584632292 1686503466
38937 you may need to use a LaTeX package which defines a math command that is not natively supported in LyX.
38938 This is easy enough to do:
38939 Just include the package in the preamble and type out the command in math.
38940 As with commands defined in the preamble,
38942 the display in LyX will not be `nice'.
38945 \begin_layout Standard
38947 \change_inserted -584632292 1686503786
38949 this problem has been solved.
38950 Just define a math macro with empty LaTeX slot!
38951 The LyX part will be used for display,
38952 but no corresponding LaTeX will be output.
38955 \begin_inset Flex Code
38958 \begin_layout Plain Layout
38960 \change_inserted -584632292 1686503714
38968 package defines a Godelnum macro that puts a single argument into corner quotes.
38969 To get a nice LyX display of this macro,
38973 \begin_layout Standard
38975 \change_inserted -584632292 1686503742
38976 \begin_inset FormulaMacro
38977 \newcommand{\Godelnum}[1]{}
38978 {\ulcorner#1\urcorner}
38984 \begin_layout Standard
38986 \change_inserted -584632292 1686503753
38989 can be used for commands defined in the preamble.
38994 \begin_layout Section
38995 Computer Algebra Systems
38998 \begin_layout Standard
39000 offers the exchange between mathematical expressions written in \SpecialChar LyX
39001 's math editor and external applications or user defined scripts.
39002 Currently supported applications are
39021 Note that the set of supported mathematical constructs is limited only to very simple cases.
39024 \begin_layout Subsection
39028 \begin_layout Standard
39029 Write some expression in a formula,
39032 Edit\SpecialChar menuseparator
39033 Math\SpecialChar menuseparator
39034 Use Computer Algebra System
39036 menu and choose the application you have installed on the computer.
39037 After that the result of computation should show on the right side of the expression together with the
39038 \begin_inset Quotes eld
39042 \begin_inset Quotes erd
39048 \begin_layout Standard
39049 Here are few simple examples (with results from
39053 ) to show what kind of computations can be performed:
39056 \begin_layout Itemize
39057 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
39063 \begin_layout Itemize
39064 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
39070 \begin_layout Itemize
39071 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
39077 \begin_layout Itemize
39078 \begin_inset Formula $\int\left(\frac{1}{1+x^{3}}\right)dx=-\frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\,x-1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log\left(x+1\right)}{3}$
39082 \begin_inset Newline newline
39086 \begin_inset Note Greyedout
39089 \begin_layout Plain Layout
39095 One needs to use proper delimiter insets
39096 \begin_inset Formula $\left(\right)$
39099 instead of simple '(' ')' characters.
39107 \begin_layout Itemize
39108 \begin_inset Formula $\det\left[\begin{array}{ccc}
39112 \end{array}\right]=-56$
39118 \begin_layout Itemize
39119 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
39125 \begin_layout Itemize
39126 \begin_inset Formula $powerseries\left(-\log\left(5-x\right),x,1\right)=\sum_{{\mathit{i}_{2}}=0}^{\infty}{\frac{4^{-{\mathit{i}_{2}}-1}\,\left(x-1\right)^{{\mathit{i}_{2}}+1}}{{\mathit{i}_{2}}+1}}-\log4$
39132 \begin_layout Itemize
39133 \begin_inset Formula $solve\left(x_{1}+y_{1}^{3}=y_{1}+x_{1}^{2},x_{1}\right)=\left[x_{1}=-\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}-1}{2},x_{1}=\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}+1}{2}\right]$
39139 \begin_layout Subsection
39143 \begin_layout Standard
39144 Currently there is no keyboard shortcut for calling the algebra applications.
39145 One can easily bind a shortcut to the
39159 \begin_inset space \thinspace{}
39163 \begin_inset space \space{}
39170 key inside the math editor.
39175 one would use this shortcut definition command:
39178 \begin_layout Standard
39181 command-alternatives paragraph-break;math-extern maxima
39184 \begin_layout Section
39186 \begin_inset Index idx
39191 \begin_layout Plain Layout
39200 \begin_layout Subsection
39202 \begin_inset Index idx
39207 \begin_layout Plain Layout
39209 \begin_inset IndexMacro subentry
39212 \begin_layout Plain Layout
39226 \begin_layout Standard
39227 Negative numbers often look ugly in formulas because the minus sign before the number is set with the same length as the minus operator sign.
39228 When writing the negative number in normal text,
39229 the minus sign appears correctly.
39232 \begin_layout Standard
39234 the problem disappears when converting the minus sign to mathematical text.
39237 \begin_layout Standard
39238 An example to visualize the problem:
39241 \begin_layout Standard
39243 \begin_inset Tabular
39244 <lyxtabular version="3" rows="3" columns="2">
39245 <features booktabs="true" tabularvalignment="middle">
39246 <column alignment="right" valignment="top" width="0pt">
39247 <column alignment="left" valignment="top">
39249 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
39252 \begin_layout Plain Layout
39258 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
39261 \begin_layout Plain Layout
39269 <cell alignment="right" valignment="top" leftline="true" usebox="none">
39272 \begin_layout Plain Layout
39278 <cell alignment="center" valignment="top" rightline="true" usebox="none">
39281 \begin_layout Plain Layout
39282 \begin_inset Formula $x=-2$
39292 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
39295 \begin_layout Plain Layout
39301 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
39304 \begin_layout Plain Layout
39305 \begin_inset Formula $x=\textrm{-}2$
39321 \begin_layout Subsection
39322 Comma as decimal Separator
39323 \begin_inset Index idx
39328 \begin_layout Plain Layout
39337 \begin_layout Standard
39338 In \SpecialChar LaTeX
39339 a comma inside a formula is used,
39340 according to the English convention,
39341 as number group separator.
39342 So there will be space added behind all commas in formulas.
39345 \begin_layout Standard
39347 the comma is highlighted and changed to mathematical text (shortcut
39356 \begin_layout Standard
39357 To use all formula commas in the document as decimal separator,
39366 \begin_layout Plain Layout
39371 is part of the \SpecialChar LaTeX
39377 \begin_inset Index idx
39382 \begin_layout Plain Layout
39384 \begin_inset IndexMacro subentry
39387 \begin_layout Plain Layout
39404 \begin_inset Index idx
39409 \begin_layout Plain Layout
39411 \begin_inset IndexMacro subentry
39414 \begin_layout Plain Layout
39425 is loaded with the \SpecialChar LaTeX
39429 \begin_layout Standard
39437 \begin_layout Subsection
39439 \begin_inset CommandInset label
39441 name "subsec:Physical-Vectors"
39446 \begin_inset Index idx
39451 \begin_layout Plain Layout
39453 \begin_inset IndexMacro subentry
39456 \begin_layout Plain Layout
39470 \begin_layout Standard
39471 Predefined vectors are offered by the \SpecialChar LaTeX
39477 \begin_inset Index idx
39482 \begin_layout Plain Layout
39484 \begin_inset IndexMacro subentry
39487 \begin_layout Plain Layout
39498 that is loaded with the \SpecialChar LaTeX
39502 \begin_layout Standard
39510 \begin_layout Standard
39514 \begin_layout Plain Layout
39524 \begin_inset Note Note
39527 \begin_layout Plain Layout
39528 The following table will only be displayed when the \SpecialChar LaTeX
39541 \begin_layout Standard
39542 The following commands are defined:
39545 \begin_layout Standard
39547 \begin_inset Tabular
39548 <lyxtabular version="3" rows="4" columns="2">
39549 <features booktabs="true" tabularvalignment="middle">
39550 <column alignment="center" valignment="top" width="0pt">
39551 <column alignment="center" valignment="top">
39553 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
39556 \begin_layout Plain Layout
39562 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
39565 \begin_layout Plain Layout
39573 <cell alignment="center" valignment="top" usebox="none">
39576 \begin_layout Plain Layout
39586 <cell alignment="center" valignment="top" usebox="none">
39589 \begin_layout Plain Layout
39590 \begin_inset Formula $\Bra{\psi}$
39600 <cell alignment="center" valignment="top" usebox="none">
39603 \begin_layout Plain Layout
39613 <cell alignment="center" valignment="top" usebox="none">
39616 \begin_layout Plain Layout
39617 \begin_inset Formula $\Ket{\psi}$
39627 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
39630 \begin_layout Plain Layout
39642 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
39645 \begin_layout Plain Layout
39646 \begin_inset Formula $\Braket{\psi|\phi}$
39662 \begin_layout Standard
39669 assures that all vertical bars are set in the size of the surrounding brackets:
39670 \begin_inset Formula
39672 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
39681 \begin_layout Plain Layout
39691 \begin_inset Note Note
39694 \begin_layout Plain Layout
39695 The following will be displayed when the \SpecialChar LaTeX
39708 \begin_layout Standard
39709 You need to install the \SpecialChar LaTeX
39714 to see the rest of this subsection in the output.
39717 \begin_layout Standard
39721 \begin_layout Plain Layout
39733 \begin_layout Standard
39740 can also be achieved using the command
39747 that is described in
39748 \begin_inset CommandInset ref
39750 reference "subsec:Automatic-Bracket-Size"
39758 \begin_layout Subsection
39759 Self-defined Fractions
39760 \begin_inset CommandInset label
39762 name "subsec:Self-defined-Fractions"
39767 \begin_inset Index idx
39772 \begin_layout Plain Layout
39774 \begin_inset IndexMacro subentry
39777 \begin_layout Plain Layout
39791 \begin_layout Standard
39792 To define custom commands for fractions,
39800 \begin_inset Index idx
39805 \begin_layout Plain Layout
39807 \begin_inset IndexMacro subentry
39810 \begin_layout Plain Layout
39817 \begin_inset IndexMacro subentry
39820 \begin_layout Plain Layout
39833 is used in the following scheme:
39836 \begin_layout Standard
39849 bracket}{fraction bar thickness}{style}
39850 \begin_inset Newline newline
39854 \begin_inset Phantom HPhantom
39857 \begin_layout Plain Layout
39867 {numerator}{denominator}
39870 \begin_layout Standard
39871 The style is a number in the range of 0
39872 \begin_inset space \thinspace{}
39876 \begin_inset space \thinspace{}
39882 \begin_layout Standard
39884 \begin_inset Tabular
39885 <lyxtabular version="3" rows="5" columns="2">
39886 <features booktabs="true" tabularvalignment="middle">
39887 <column alignment="center" valignment="top" width="0pt">
39888 <column alignment="center" valignment="top">
39890 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
39893 \begin_layout Plain Layout
39899 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
39902 \begin_layout Plain Layout
39910 <cell alignment="center" valignment="top" usebox="none">
39913 \begin_layout Plain Layout
39919 <cell alignment="center" valignment="top" usebox="none">
39922 \begin_layout Plain Layout
39923 display style formula
39930 <cell alignment="center" valignment="top" usebox="none">
39933 \begin_layout Plain Layout
39939 <cell alignment="center" valignment="top" usebox="none">
39942 \begin_layout Plain Layout
39950 <cell alignment="center" valignment="top" usebox="none">
39953 \begin_layout Plain Layout
39959 <cell alignment="center" valignment="top" usebox="none">
39962 \begin_layout Plain Layout
39970 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
39973 \begin_layout Plain Layout
39979 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
39982 \begin_layout Plain Layout
39996 \begin_layout Standard
39997 When no style is given,
39998 the size is adjusted to the surrounding environment like for the command
40007 \begin_layout Standard
40008 When no fraction bar thickness is given,
40009 the predefined value of 0.4
40010 \begin_inset space \thinspace{}
40016 \begin_layout Standard
40017 \begin_inset VSpace medskip
40034 \begin_inset CommandInset ref
40036 reference "subsec:Fractions"
40041 are defined with the commands
40044 \begin_layout Standard
40053 genfrac{}{}{}{0}{#1}{#2}}
40056 \begin_layout Standard
40060 \begin_layout Standard
40069 genfrac{(}{)}{0pt}{1}{#1}{#2}}
40072 \begin_layout Standard
40073 \begin_inset VSpace medskip
40076 To define a fraction where the fraction bar thickness can be given as optional argument,
40077 the following line is inserted to the \SpecialChar LaTeX
40081 \begin_layout Standard
40090 genfrac{}{}{#1}{}{#2}{#3}}
40093 \begin_layout Standard
40095 \begin_inset Formula
40097 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
40098 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
40104 the distance of the numerator and the denominator to the fraction bar is round about three times the bar thickness.
40107 \begin_layout Subsection
40109 \begin_inset Index idx
40114 \begin_layout Plain Layout
40116 \begin_inset IndexMacro subentry
40119 \begin_layout Plain Layout
40133 \begin_layout Standard
40134 There are four ways to cancel formulas or parts of formulas:
40137 \begin_layout Standard
40141 \begin_layout Plain Layout
40151 \begin_inset Note Note
40154 \begin_layout Plain Layout
40155 The following table will only be displayed when the \SpecialChar LaTeX
40168 \begin_layout Standard
40170 \begin_inset Tabular
40171 <lyxtabular version="3" rows="5" columns="2">
40172 <features booktabs="true" tabularvalignment="middle">
40173 <column alignment="center" valignment="top" width="0pt">
40174 <column alignment="center" valignment="top">
40176 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
40179 \begin_layout Plain Layout
40185 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
40188 \begin_layout Plain Layout
40196 <cell alignment="center" valignment="top" usebox="none">
40199 \begin_layout Plain Layout
40203 \begin_inset space \textvisiblespace{}
40209 \begin_inset space \textvisiblespace{}
40217 <cell alignment="center" valignment="top" usebox="none">
40220 \begin_layout Plain Layout
40221 \begin_inset Formula $\cancel{\int A=B}$
40230 <row topspace="1.5mm">
40231 <cell alignment="center" valignment="top" usebox="none">
40234 \begin_layout Plain Layout
40238 \begin_inset space \textvisiblespace{}
40244 \begin_inset space \textvisiblespace{}
40252 <cell alignment="center" valignment="top" usebox="none">
40255 \begin_layout Plain Layout
40256 \begin_inset Formula $\bcancel{\int A=B}$
40265 <row topspace="1.5mm">
40266 <cell alignment="center" valignment="top" usebox="none">
40269 \begin_layout Plain Layout
40273 \begin_inset space \textvisiblespace{}
40279 \begin_inset space \textvisiblespace{}
40287 <cell alignment="center" valignment="top" usebox="none">
40290 \begin_layout Plain Layout
40291 \begin_inset Formula $\xcancel{\int A=B}$
40301 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
40304 \begin_layout Plain Layout
40308 \begin_inset space \textvisiblespace{}
40314 \begin_inset space \textvisiblespace{}
40318 \begin_inset Formula $\to$
40326 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
40329 \begin_layout Plain Layout
40330 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
40346 \begin_layout Standard
40353 is especially suitable to visualize the reduction of fractions within formulas:
40354 \begin_inset Formula
40356 \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}}}
40364 \begin_layout Standard
40365 To change the size of
40372 \begin_inset Quotes eld
40376 \begin_inset Quotes erd
40379 value one can add the \SpecialChar LaTeX
40383 \begin_layout Standard
40388 PassOptionsToPackage{option}{cancel}
40391 \begin_layout Standard
40400 which leads to the same size as for the canceled value,
40405 which makes is it a bit smaller than normal.
40408 \begin_layout Standard
40409 To color the cancellation bar one adds this command as \SpecialChar TeX
40413 \begin_layout Standard
40425 \begin_layout Standard
40430 can be replaced by a color of your choice.
40433 \begin_layout Standard
40437 \begin_layout Plain Layout
40453 \begin_layout Standard
40454 \begin_inset Formula
40456 \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}}}
40464 \begin_layout Standard
40468 \begin_layout Plain Layout
40482 \begin_inset Note Note
40485 \begin_layout Plain Layout
40494 \begin_layout Standard
40495 For further customizations,
40496 see the documentation of the package
40502 \begin_inset CommandInset citation
40510 \begin_inset Index idx
40515 \begin_layout Plain Layout
40517 \begin_inset IndexMacro subentry
40520 \begin_layout Plain Layout
40534 \begin_layout Standard
40538 \begin_layout Plain Layout
40548 \begin_inset Note Note
40551 \begin_layout Plain Layout
40552 The following will be displayed when the \SpecialChar LaTeX
40565 \begin_layout Standard
40566 You need to install the \SpecialChar LaTeX
40571 to see the rest of this subsection in the output.
40574 \begin_layout Standard
40578 \begin_layout Plain Layout
40590 \begin_layout Subsection
40591 Formulas in Section Headings
40592 \begin_inset CommandInset label
40594 name "subsec:Formulas-in-Section"
40599 \begin_inset Index idx
40604 \begin_layout Plain Layout
40606 \begin_inset IndexMacro subentry
40609 \begin_layout Plain Layout
40610 in section headings
40623 \begin_layout Standard
40624 When formulas are used in section headings,
40625 the following has to be taken into account:
40628 \begin_layout Standard
40629 \begin_inset Note Greyedout
40632 \begin_layout Plain Layout
40638 \begin_inset Index idx
40643 \begin_layout Plain Layout
40645 \begin_inset IndexMacro subentry
40648 \begin_layout Plain Layout
40659 support is enabled in the document settings dialog under
40662 \begin_inset space ~
40668 PDF-bookmarks are created for every section heading in the table of contents.
40669 If a section heading contains formulas,
40670 they are incorrectly displayed in the bookmark text,
40671 because formulas in bookmarks infringe the PDF conventions.
40679 \begin_layout Standard
40680 Both problems can be solved by inserting at the end of the section heading a short title with the menu
40682 Insert\SpecialChar menuseparator
40684 \begin_inset space ~
40690 Short titles are used as alternative for multiline section headings to keep the table of contents clearly arranged.
40691 Only the short title appears in the table of contents and therefore also in the PDF-bookmark.
40694 \begin_layout Standard
40695 When formulas should be used in the table of contents but
40700 one can use the following command in \SpecialChar TeX
40704 \begin_layout Standard
40709 texorpdfstring{part}{alternative}
40710 \begin_inset Index idx
40715 \begin_layout Plain Layout
40717 \begin_inset IndexMacro subentry
40720 \begin_layout Plain Layout
40727 \begin_inset IndexMacro subentry
40730 \begin_layout Plain Layout
40746 \begin_layout Standard
40747 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
40748 This can be characters,
40751 but also cross-references.
40752 The alternative is used instead of the part for the bookmark.
40755 \begin_layout Standard
40756 Here are two example headings:
40757 \begin_inset VSpace -3mm
40764 \begin_layout Plain Layout
40776 \begin_layout Subsubsection
40777 Heading without formula in table of contents
40778 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
40782 \begin_inset Argument 1
40785 \begin_layout Plain Layout
40786 Heading without formula in table of contents
40794 \begin_layout Subsubsection
40795 Heading with formula in table of contents
40799 \begin_layout Plain Layout
40809 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
40816 \begin_layout Plain Layout
40826 \begin_layout Standard
40830 \begin_layout Plain Layout
40839 In the first heading a short title was used,
40849 \begin_layout Standard
40850 To get the same formatting as for the other headings,
40851 the complete heading was set into a
40859 \begin_layout Plain Layout
40861 \begin_inset CommandInset ref
40863 reference "subsec:Bold-Formulas"
40876 \begin_layout Subsection
40877 Formulas in multi-column Text
40878 \begin_inset Index idx
40883 \begin_layout Plain Layout
40885 \begin_inset IndexMacro subentry
40888 \begin_layout Plain Layout
40889 in multi-column text
40902 \begin_layout Standard
40903 Formulas in multi-column text are often too wide to fit into a column and thus need to be set over the whole page width.
40904 This is done by using the \SpecialChar LaTeX
40913 \begin_layout Plain Layout
40918 is part of every \SpecialChar LaTeX
40919 standard installation.
40925 \begin_inset Index idx
40930 \begin_layout Plain Layout
40932 \begin_inset IndexMacro subentry
40935 \begin_layout Plain Layout
40947 that is loaded with the \SpecialChar LaTeX
40951 \begin_layout Standard
40956 usepackage{multicol}
40959 \begin_layout Standard
40960 \begin_inset Note Greyedout
40963 \begin_layout Plain Layout
40964 Note that in this case the setting
40967 \begin_inset space ~
40974 Document\SpecialChar menuseparator
40980 \begin_inset space ~
41000 \begin_layout Standard
41001 Before the multi-column text the command
41004 \begin_layout Standard
41009 begin{multicols}{column number}
41012 \begin_layout Standard
41013 is written in \SpecialChar TeX
41015 The column number is a number in the range of 2
41016 \begin_inset space \thinspace{}
41020 \begin_inset space \thinspace{}
41024 Before the formula the multi-column text is ended by inserting the command
41027 \begin_layout Standard
41035 \begin_layout Standard
41036 in \SpecialChar TeX
41040 \begin_layout Standard
41041 Due to the command some space is automatically added before the formula.
41044 \begin_inset space \thinspace{}
41047 mm vertical space is inserted before the formula.
41048 When the formula style
41054 \begin_layout Plain Layout
41055 For formula styles see
41056 \begin_inset CommandInset ref
41058 reference "sec:Formula-Styles"
41072 \begin_inset space \thinspace{}
41075 mm space is inserted instead.
41078 \begin_layout Standard
41079 As example a multi-column text with a displayed formula:
41082 \begin_layout Standard
41088 \begin_layout Plain Layout
41092 begin{multicols}{2}
41097 Das Spektrum wird fouriertransformiert.
41098 Die Fouriertransformation wird verwendet,
41099 um die überlagerten Signale (Netzwerk,
41100 Lösungsmittel) zu trennen.
41101 Nachdem wir die Phasenverschiebung bestimmen konnten,
41102 interessiert uns nun das Aussehen des Ausgangssignals.
41103 Im Experiment haben wir es mit sehr vielen Teilchen zu tun,
41104 so dass man über alle Phasen integrieren muss.
41106 \begin_inset Formula $S$
41109 unser normiertes Ausgangssignal und
41110 \begin_inset Formula $P$
41113 die Phasenverteilungsfunktion,
41114 so ergibt sich die Beziehung
41118 \begin_layout Plain Layout
41128 \begin_inset VSpace -6mm
41132 \begin_inset Formula
41134 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
41143 \begin_layout Plain Layout
41147 begin{multicols}{2}
41153 \begin_inset Formula $S_{0}$
41156 das Signal ohne Gradient ist und die Normierungsbedingung
41157 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
41161 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
41163 \begin_inset Formula $\nicefrac{\pi}{2}$
41167 \begin_inset space \thinspace{}
41170 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren,
41171 wodurch sich das Signal zusätzlich abschwächt.
41172 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
41173 \begin_inset Formula $T_{2}$
41179 \begin_layout Standard
41185 \begin_layout Plain Layout
41197 \begin_layout Subsection
41198 Formulas with Description of Variables
41199 \begin_inset Index idx
41204 \begin_layout Plain Layout
41206 \begin_inset IndexMacro subentry
41209 \begin_layout Plain Layout
41210 with description of variables
41223 \begin_layout Standard
41224 To describe variables within a formula,
41226 \begin_inset CommandInset ref
41228 reference "eq:within"
41239 \begin_inset Formula $n$
41243 \begin_inset space ~
41246 matrix is used with left aligned columns for the
41247 \begin_inset Formula $n$
41254 \begin_layout Plain Layout
41256 \begin_inset CommandInset ref
41258 reference "sec:Matrices"
41268 To set the description in a smaller size,
41269 before the matrix e.
41270 \begin_inset space \thinspace{}
41274 \begin_inset space \space{}
41287 \begin_layout Plain Layout
41289 \begin_inset CommandInset ref
41291 reference "subsec:Font-Sizes"
41304 \begin_layout Standard
41305 When the formula style
41311 \begin_layout Plain Layout
41312 For formula styles see
41313 \begin_inset CommandInset ref
41315 reference "sec:Formula-Styles"
41338 \begin_layout Plain Layout
41345 only works in formulas with the style
41351 \begin_inset CommandInset ref
41353 reference "subsec:Variable-Space"
41363 is inserted before and after the matrix to have the same separation of the matrix from the equation and the side margin.
41366 \begin_layout Standard
41367 When the formula style
41372 the method described in
41373 \begin_inset CommandInset ref
41375 reference "subsec:Flalign-Environment"
41380 is used to indent formulas.
41382 \begin_inset CommandInset ref
41384 reference "eq:within"
41389 consists of five columns where in the first two columns contain the equation,
41390 the third the matrix and the last one an empty \SpecialChar TeX
41392 \begin_inset Formula
41394 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
41395 \rho & \textrm{density}\\
41396 V & \textrm{volume}\\
41397 g & \textrm{gravitational acceleration}
41398 \end{array} & & {}\label{eq:within}
41406 \begin_layout Subsection
41407 Upright small Greek Letters
41408 \begin_inset CommandInset label
41410 name "subsec:Upright-small-Greek"
41415 \begin_inset Index idx
41420 \begin_layout Plain Layout
41422 \begin_inset IndexMacro subentry
41425 \begin_layout Plain Layout
41439 \begin_layout Standard
41440 Most of the math fonts only provide italic small Greek letters.
41441 But for symbols of elementary particles like pions and neutrinos,
41442 upright Greek letters are needed.
41451 \begin_layout Plain Layout
41456 is part of the \SpecialChar LaTeX
41462 \begin_inset Index idx
41467 \begin_layout Plain Layout
41469 \begin_inset IndexMacro subentry
41472 \begin_layout Plain Layout
41489 \begin_inset Index idx
41494 \begin_layout Plain Layout
41496 \begin_inset IndexMacro subentry
41499 \begin_layout Plain Layout
41510 that is loaded with the \SpecialChar LaTeX
41514 \begin_layout Standard
41519 usepackage{upgreek}
41522 \begin_layout Standard
41528 \begin_layout Plain Layout
41538 \begin_inset Note Note
41541 \begin_layout Plain Layout
41542 The following table will only be displayed when the \SpecialChar LaTeX
41552 They are created when the command for a small Greek letter is started with
41557 For example the command
41565 \begin_inset Formula $\uptau$
41571 \begin_layout Standard
41572 With these commands reactions of elementary particles can be typeset:
41573 \begin_inset Formula
41575 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
41583 \begin_layout Standard
41584 The upright letters are more bold and wider than the italic ones.
41585 They should therefore not be used for units like
41586 \begin_inset Quotes eld
41590 \begin_inset Quotes erd
41596 \begin_layout Standard
41600 \begin_layout Plain Layout
41610 \begin_inset Note Note
41613 \begin_layout Plain Layout
41614 The following will be displayed when the \SpecialChar LaTeX
41627 \begin_layout Standard
41628 You need to install the \SpecialChar LaTeX
41633 to see the rest of this subsection in the output.
41636 \begin_layout Standard
41640 \begin_layout Plain Layout
41652 \begin_layout Subsection
41653 Text Characters in Formulas
41654 \begin_inset Index idx
41659 \begin_layout Plain Layout
41661 \begin_inset IndexMacro subentry
41664 \begin_layout Plain Layout
41678 \begin_layout Standard
41679 In some cases you might want to insert text characters directly into formulas.
41680 For example the centered dot · is often used in formulas like
41681 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
41685 One would have to insert the command
41695 \begin_layout Plain Layout
41697 \begin_inset CommandInset ref
41699 reference "subsec:Binary-Operators"
41710 because this character is defined in all encodings as a text character.
41711 But the encoding can be changed by this \SpecialChar LaTeX
41715 \begin_layout Standard
41720 Declare Inputtext{183}{
41730 f\SpecialChar ligaturebreak
41734 \begin_layout Standard
41735 The character encoding (menu
41737 Document\SpecialChar menuseparator
41738 Settings\SpecialChar menuseparator
41741 ) specifies what character appears when a keyboard key is pressed.
41742 When the key for the character '·' is pressed,
41743 internally the command
41750 But this command is not available in a formula so that you would get \SpecialChar LaTeX
41752 With the changed encoding the correct command is chosen automatically,
41753 depending on if the character was inserted into a formula or not.
41756 \begin_layout Standard
41757 The encoding of several characters is saved in definition files.
41758 For example the encoding
41762 is defined in the file
41766 which is in the installation folder of \SpecialChar LaTeX
41768 Encodings should only be changed via the \SpecialChar LaTeX
41769 -preamble and not in the definition files.
41770 Otherwise documents could not be edited by other \SpecialChar LyX
41771 users working on other computers.
41774 \begin_layout Standard
41775 \begin_inset VSpace medskip
41778 Besides the centered dot,
41779 in this document the degree sign ° is defined with the following \SpecialChar LaTeX
41780 -preamble line so that it can be directly inserted into a formula:
41783 \begin_layout Standard
41788 DeclareInputtext{176}{
41798 f\SpecialChar ligaturebreak
41802 \begin_layout Subsection
41804 -comments in formulas
41805 \begin_inset Index idx
41810 \begin_layout Plain Layout
41820 \begin_layout Standard
41821 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
41822 source code of your file with the menu
41824 Insert\SpecialChar menuseparator
41825 Note\SpecialChar menuseparator
41829 This is not possible in a formula but you can insert \SpecialChar LaTeX
41830 -comments with the command
41833 \begin_layout Standard
41841 \begin_layout Standard
41842 This creates a box in which you can write your comment.
41843 Due to a bug in \SpecialChar LyX
41848 \begin_layout Plain Layout
41849 \begin_inset CommandInset href
41851 name "LyX-bug #9002"
41852 target "https://www.lyx.org/trac/ticket/9002"
41862 you cannot write normal text inside the comment,
41863 even when you use mathematical text,
41864 you will see its \SpecialChar LaTeX
41865 -commands in the \SpecialChar LaTeX
41867 \begin_inset Newline newline
41870 This a formula with a \SpecialChar LaTeX
41872 \begin_inset Formula
41874 A=B%\text{This is the comment}
41882 \begin_layout Standard
41883 \begin_inset Newpage newpage
41889 \begin_layout Section
41892 \begin_inset Index idx
41897 \begin_layout Plain Layout
41906 \begin_layout Standard
41907 This section is a summary of the most important typographic rules,
41908 listed in ISO norms.
41912 \begin_layout Plain Layout
41913 This collection was partly taken from the German semi-official dictionary called
41914 \begin_inset Quotes eld
41918 \begin_inset Quotes erd
41922 \begin_inset CommandInset citation
41929 that lists some of the ISO rules.
41930 More rules are listed in
41931 \begin_inset CommandInset citation
41946 \begin_layout Itemize
41955 \begin_layout Plain Layout
41956 Done with font styles,
41958 \begin_inset CommandInset ref
41960 reference "subsec:Font-Styles"
41971 no matter if they appear in italic text:
41973 \begin_inset space \thinspace{}
41977 \begin_inset Newline newline
41980 Between the value and the unit is the smallest space,
41982 \begin_inset CommandInset ref
41984 reference "subsec:Predefined-Space"
41990 \begin_inset Newline newline
41993 This convention is automatically fulfilled when the command
42000 When it is entered in a formula,
42002 In the first one the value is inserted,
42003 in the second one the unit,
42004 and the result is as above:
42006 \begin_inset Formula $\unit[30]{km/h}$
42010 \begin_inset space \thinspace{}
42020 is not a real \SpecialChar LaTeX
42021 command but the command
42028 therefore you cannot use it in \SpecialChar TeX
42032 \begin_layout Itemize
42033 Percent and perthousand signs are set like physical units:
42034 \begin_inset Newline newline
42038 \begin_inset space \thinspace{}
42044 \begin_layout Itemize
42045 The degree sign follows the value directly:
42047 except when it is used in units:
42049 \begin_inset space \thinspace{}
42055 \begin_layout Itemize
42056 In numbers with more than four digits the smallest space is inserted before every third digit to group them:
42067 \begin_inset space \thinspace{}
42071 \begin_inset space \thinspace{}
42077 \begin_layout Itemize
42078 For dimensions like 120×90×40
42079 \begin_inset space \thinspace{}
42082 cm the multiplication sign
42083 \begin_inset Quotes eld
42087 \begin_inset Quotes erd
42091 It is available either via the command
42099 Insert\SpecialChar menuseparator
42100 Special Character\SpecialChar menuseparator
42106 \begin_layout Itemize
42107 Functions with names consisting of several letters are set upright to avoid confusions,
42109 \begin_inset CommandInset ref
42111 reference "subsec:Predefined-Functions"
42119 \begin_layout Itemize
42120 Indices consisting of several letters,
42123 \begin_inset Formula $E_{\mathrm{kin}}$
42127 \begin_inset Newline newline
42130 Components of matrices are set italic:
42132 \begin_inset Formula $\hat{H}_{kl}$
42138 \begin_layout Itemize
42139 The differentiation/integration operator 'd',
42140 the Euler's number 'e' and the imaginary unit 'i' should be set upright,
42141 to avoid mixing them up with other variables.
42144 \begin_layout Itemize
42145 The character that denotes a
42149 transformation is inserted either by the command
42154 \begin_inset space \textvisiblespace{}
42161 Insert\SpecialChar menuseparator
42162 Special Character\SpecialChar menuseparator
42163 Symbols\SpecialChar menuseparator
42165 \begin_inset space ~
42172 \begin_inset Formula $\mathscr{F}$
42178 \begin_layout Standard
42179 \begin_inset Newpage newpage
42185 \begin_layout Section
42187 \begin_inset Index idx
42192 \begin_layout Plain Layout
42201 \begin_layout Standard
42202 Some characters and symbols can be created with several commands.
42203 Here is a list of the synonym commands:
42206 \begin_layout Standard
42207 \begin_inset VSpace bigskip
42211 \begin_inset space \hfill{}
42215 \begin_inset Tabular
42216 <lyxtabular version="3" rows="12" columns="2">
42217 <features booktabs="true" tabularvalignment="middle">
42218 <column alignment="center" valignment="top" width="0pt">
42219 <column alignment="center" valignment="top" width="0pt">
42221 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
42224 \begin_layout Plain Layout
42230 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
42233 \begin_layout Plain Layout
42241 <cell alignment="center" valignment="top" usebox="none">
42244 \begin_layout Plain Layout
42252 <cell alignment="center" valignment="top" usebox="none">
42255 \begin_layout Plain Layout
42263 <cell alignment="center" valignment="top" usebox="none">
42266 \begin_layout Plain Layout
42274 <cell alignment="center" valignment="top" usebox="none">
42277 \begin_layout Plain Layout
42287 <cell alignment="center" valignment="top" usebox="none">
42290 \begin_layout Plain Layout
42298 <cell alignment="center" valignment="top" usebox="none">
42301 \begin_layout Plain Layout
42311 <cell alignment="center" valignment="top" usebox="none">
42314 \begin_layout Plain Layout
42322 <cell alignment="center" valignment="top" usebox="none">
42325 \begin_layout Plain Layout
42333 <cell alignment="center" valignment="top" usebox="none">
42336 \begin_layout Plain Layout
42344 <cell alignment="center" valignment="top" usebox="none">
42347 \begin_layout Plain Layout
42355 <cell alignment="center" valignment="top" usebox="none">
42358 \begin_layout Plain Layout
42366 <cell alignment="center" valignment="top" usebox="none">
42369 \begin_layout Plain Layout
42379 <cell alignment="center" valignment="top" usebox="none">
42382 \begin_layout Plain Layout
42390 <cell alignment="center" valignment="top" usebox="none">
42393 \begin_layout Plain Layout
42403 <cell alignment="center" valignment="top" usebox="none">
42406 \begin_layout Plain Layout
42414 <cell alignment="center" valignment="top" usebox="none">
42417 \begin_layout Plain Layout
42427 <cell alignment="center" valignment="top" usebox="none">
42430 \begin_layout Plain Layout
42438 <cell alignment="center" valignment="top" usebox="none">
42441 \begin_layout Plain Layout
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