1 #LyX 2.4 created this file. For more info see https://www.lyx.org/
5 \save_transient_properties true
6 \origin /systemlyxdir/doc/
9 % DO NOT ALTER THIS PREAMBLE!!!
11 % This preamble is designed to ensure that the file prints
12 % out as advertised. If you mess with this preamble,
13 % parts of this document may not print out as expected. If you
14 % have problems LaTeXing this file, please contact
15 % the documentation team
16 % email: lyx-docs@lists.lyx.org
18 % solves the following problem:
19 % If the dection number consits of too many numerals the section heading
20 % will be printed in the TOC without a space between it and the section number.
21 % As solution more space between the number and the heading is inserted:
22 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
23 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
25 % increase link area for cross-references and autoname them,
26 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
27 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
28 \@ifpackageloaded{babel}{
29 \addto\extrasenglish{%
30 \renewcommand*{\equationautorefname}[1]{}%
31 \renewcommand{\sectionautorefname}{sec.\negthinspace}%
32 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
33 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
37 % don't load packages twice
38 % see first footnote in sec. 9.3
39 \@ifundefined{textcolor}{\usepackage{color}}{}
41 % the pages of the TOC are numbered roman
42 % and a PDF-bookmark for the TOC is added
44 \let\myTOC\tableofcontents
45 \renewcommand{\tableofcontents}{%
47 \pdfbookmark[1]{\contentsname}{}
50 \pagenumbering{arabic}}
52 % add 0.5 mm vertical space for table rows
53 \@ifundefined{extrarowheight} {\usepackage{array}}{}
54 \setlength{\extrarowheight}{0.5mm}
56 % insert additional vertical space of 1.5 mm between footnotes,
58 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
60 % makes caption labels bold
61 \setkomafont{captionlabel}{\bfseries}
63 % enables calculation of values
66 % for multiple columns used in sec. 24.7
72 % for the Fourier transformation symbol
75 % define a color, used in sec.9.3
76 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
78 % declare operators (see sec. 10.4 and sec. 15.2)
79 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
80 \DeclareMathOperator{\sgn}{sgn}
82 % example definitions for sec. 20.1
83 \newcommand{\gr}{\Longrightarrow}
84 \newcommand{\us}[1]{\underline{#1}}
85 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
86 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
87 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
89 % example macro from sec. 19.4
91 %\def\tagform@#1{\maketag@@@{|#1|}}
94 % ------------------------------------
95 % used to check for needed LaTeX packages
98 % check for package undertilde
99 % used for the command \utilde
100 \newboolean{undertilde}
101 \IfFileExists{undertilde.sty}
102 {\usepackage{undertilde}
103 \setboolean{undertilde}{true}}
104 {\setboolean{undertilde}{false}}
106 % check for package eurosym
107 % used for the Euro symbol
109 \IfFileExists{eurosym.sty}
110 {\usepackage[gennarrow]{eurosym}
111 \setboolean{eurosym}{true}}
112 {\setboolean{eurosym}{false}}
114 % check for package braket
115 % used for physical vectors
117 \IfFileExists{braket.sty}
119 \setboolean{braket}{true}}
120 {\setboolean{braket}{false}}
122 % check for package cancel
124 \IfFileExists{cancel.sty}
126 \setboolean{cancel}{true}}
127 {\setboolean{cancel}{false}}
129 % check for package upgreek
131 \IfFileExists{upgreek.sty}
132 {\usepackage{upgreek}
133 \setboolean{upgreek}{true}}
134 {\setboolean{upgreek}{false}}
136 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
137 \use_default_options false
141 \maintain_unincluded_children no
143 \language_package default
146 \font_roman "lmodern" "default"
147 \font_sans "lmss" "default"
148 \font_typewriter "lmtt" "default"
149 \font_math "auto" "auto"
150 \font_default_family default
151 \use_non_tex_fonts false
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155 \font_typewriter_osf false
156 \font_sf_scale 100 100
157 \font_tt_scale 100 100
159 \use_dash_ligatures false
161 \default_output_format pdf2
163 \bibtex_command default
164 \index_command makeindex
165 \float_placement class
166 \float_alignment class
170 \pdf_title "LyX's Math Manual"
171 \pdf_author "LyX Team, Uwe Stöhr"
172 \pdf_subject "LyX-documentation about math"
173 \pdf_keywords "LyX, Mathed"
175 \pdf_bookmarksnumbered true
176 \pdf_bookmarksopen true
177 \pdf_bookmarksopenlevel 1
178 \pdf_breaklinks false
182 \pdf_pdfusetitle false
183 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
186 \use_package amsmath 2
187 \use_package amssymb 2
188 \use_package cancel 1
190 \use_package mathdots 1
191 \use_package mathtools 2
192 \use_package mhchem 1
193 \use_package stackrel 1
194 \use_package stmaryrd 1
195 \use_package undertilde 0
197 \cite_engine_type default
201 \paperorientation portrait
207 \notefontcolor #0000ff
214 \paragraph_separation skip
217 \math_numbering_side default
218 \quotes_style english
222 \paperpagestyle plain
227 \tracking_changes true
228 \output_changes false
230 \postpone_fragile_content false
233 \html_be_strict false
234 \docbook_table_output 0
235 \docbook_mathml_prefix 1
236 \author -563046850 "Jean-Marc LASGOUTTES"
239 \author 47243155 "Jean-Marc"
240 \author 232239728 "Owner"
247 's Detailed Math Manual
251 by the \SpecialChar LyX
256 \begin_layout Plain Layout
258 If you have comments or error corrections,
259 please send them to the \SpecialChar LyX
260 Documentation mailing list:
264 \begin_inset CommandInset href
266 name "lyx-docs@lists.lyx.org"
267 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
279 \begin_inset Note Note
282 \begin_layout Plain Layout
290 \begin_inset Newline newline
294 \begin_inset Newline newline
300 \change_inserted 47243155 1563226038
302 \change_deleted 47243155 1563226038
308 \begin_layout Standard
309 \begin_inset CommandInset toc
310 LatexCommand tableofcontents
317 \begin_layout Standard
318 \begin_inset Note Note
321 \begin_layout Plain Layout
322 To export this document to PDF,
323 PS or DVI the \SpecialChar LaTeX
339 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.
345 if it is not installed,
346 this file cannot be exported.
349 \begin_layout Plain Layout
350 The latest PDF-version of this document can be found here:
351 \begin_inset Newline newline
356 https://wiki.lyx.org/LyX/Manuals#Math
364 \begin_layout Standard
365 \begin_inset Newpage newpage
371 \begin_layout Section
375 \begin_layout Standard
376 This document details \SpecialChar LyX
377 's math features and the \SpecialChar LaTeX
378 -commands used for mathematical characters and constructs.
379 It is oriented toward the use of commands.
380 The user should read the
388 section of the User's Guide before proceeding.
391 \begin_layout Standard
392 Most of the characters and many constructs explained in this manual are also accessible via the menu
396 \SpecialChar menuseparator
412 But everybody who has to write lots of formulas will notice that it is much faster to use commands instead of the math toolbar.
413 Therefore this manual is focused on commands but also mentions the corresponding toolbar buttons when available.
416 \begin_layout Standard
417 Unless specially mentioned,
418 math commands are only available within formulas.
419 To be able to use all of the commands explained in this document,
424 must be checked in the document settings (menu
426 Document\SpecialChar menuseparator
427 Settings\SpecialChar menuseparator
438 \begin_layout Plain Layout
441 Use AMS math package automatically
447 \begin_layout Plain Layout
456 -math when math constructs are found that are supported by \SpecialChar LyX
465 \begin_layout Standard
466 This document doesn't list all
470 \begin_layout Plain Layout
483 \begin_layout Plain Layout
484 A list containing all
488 \begin_layout Plain Layout
497 -math commands is in the file
500 \begin_inset CommandInset href
503 target "https://www.ctan.org/tex-archive/macros/amstex/doc/amsguide.pdf"
511 which is part of every \SpecialChar LaTeX
512 standard installation.
517 for lucidity reasons.
520 \begin_layout Section
524 \begin_layout Standard
525 To create an inline formula
526 \begin_inset Index idx
531 \begin_layout Plain Layout
533 \begin_inset IndexMacro subentry
536 \begin_layout Plain Layout
547 that is embedded in a text line,
548 use one of the shortcuts
554 or the toolbar button
561 \begin_inset Newline newline
564 To create a display style formula
565 \begin_inset Index idx
570 \begin_layout Plain Layout
572 \begin_inset IndexMacro subentry
575 \begin_layout Plain Layout
586 which will appear bigger,
587 has a different format,
588 and will be in a separate paragraph,
589 use one of these shortcuts:
599 \begin_layout Standard
600 To change a display style formula to an inline formula,
601 place the cursor inside the formula and use
602 \change_deleted 5863208 1612729312
606 \change_deleted 5863208 1612729314
610 \change_deleted 5863208 1612729303
618 \change_inserted 5863208 1612729281
622 arg "math-mutate simple"
629 Edit\SpecialChar menuseparator
630 Math\SpecialChar menuseparator
635 \change_inserted 5863208 1612729555
636 Similarly you can use the shortcut
639 arg "math-mutate equation"
642 to change from an inline to a display style formula.
644 \change_deleted 5863208 1612729557
645 The same method is used to change an inline formula to a display style formula.
650 \begin_layout Standard
651 To display parts of an inline formula in the size of a display style formula,
659 \begin_inset Index idx
664 \begin_layout Plain Layout
666 \begin_inset IndexMacro subentry
669 \begin_layout Plain Layout
676 \begin_inset IndexMacro subentry
679 \begin_layout Plain Layout
693 A new blue box will appear in which the desired formula part is inserted.
696 \begin_layout Standard
697 Only inline formulas are allowed inside tables.
700 \begin_layout Standard
702 \change_deleted 232239728 1610897673
707 can be turned on in the menu
709 View\SpecialChar menuseparator
713 When you click there on
714 \begin_inset Quotes eld
718 \begin_inset Quotes erd
721 the toolbar will be shown permanently at the bottom;
722 this state is visualized in the
726 menu with a checkmark.
727 When you click in this state again on
728 \begin_inset Quotes eld
732 \begin_inset Quotes erd
744 is only shown when the cursor is within a formula;
745 this state is visualized by the renaming of the menu entry from
746 \begin_inset Quotes eld
750 \begin_inset Quotes erd
754 \begin_inset Quotes eld
762 \begin_inset Quotes erd
766 \change_inserted 232239728 1610897478
770 \begin_layout Standard
772 \change_inserted 232239728 1610918987
777 visibility is controlled in the menu
779 View\SpecialChar menuseparator
780 Toolbars\SpecialChar menuseparator
784 Three options will be presented,
788 Selecting On will cause the toolbar to be shown permanently at the bottom of the screen.
789 Selecting Off will disable the toolbar.
790 Selecting Automatic will cause the toolbar to automatically appear when the cursor is located within a formula.
791 The active state of the toolbar is indicated by a checkmark next to the current menu selection.
792 \begin_inset Note Note
795 \begin_layout Plain Layout
797 \change_inserted 232239728 1610897730
798 The menu functionality appears to have changed,
799 I rewrote the paragraph for the current functionality
811 \begin_layout Standard
814 \begin_inset Index idx
819 \begin_layout Plain Layout
820 \begin_inset IndexMacro sortkey
823 \begin_layout Plain Layout
835 is invoked by pressing the toolbar button
843 Insert\SpecialChar menuseparator
855 \begin_layout Standard
856 To change the \SpecialChar LaTeX
858 \begin_inset Index idx
863 \begin_layout Plain Layout
864 \begin_inset IndexMacro sortkey
867 \begin_layout Plain Layout
882 Document\SpecialChar menuseparator
883 Settings\SpecialChar menuseparator
893 \begin_layout Standard
895 case differentiations and multiline formulas,
898 Edit\SpecialChar menuseparator
903 Edit\SpecialChar menuseparator
905 \begin_inset space \thinspace{}
909 \begin_inset space \thinspace{}
920 When lines and columns are swapped via the menu,
921 the column or line where the cursor is in is exchanged with the column to the right or the line below,
923 If the cursor is in the last column or row,
924 the exchange is done with the column to the left or the line above.
927 \begin_layout Standard
928 To write text in formulas
932 \begin_layout Plain Layout
933 For multiline formulas the command
941 \begin_inset CommandInset ref
943 reference "subsec:Text-in-multiline"
958 \begin_inset Index idx
963 \begin_layout Plain Layout
965 \begin_inset IndexMacro subentry
968 \begin_layout Plain Layout
980 \begin_inset Index idx
985 \begin_layout Plain Layout
992 This mode is invoked with the shortcut
998 or by the insertion of the command
1005 \begin_inset Index idx
1010 \begin_layout Plain Layout
1012 \begin_inset IndexMacro subentry
1015 \begin_layout Plain Layout
1022 \begin_inset IndexMacro subentry
1025 \begin_layout Plain Layout
1039 The text appears black in \SpecialChar LyX
1040 and can therefore be distinguished from the other formula parts which appear blue.
1042 mathematical text is set upright contrary to other formula parts.
1045 \begin_layout Subsection*
1049 \begin_layout Standard
1050 Most \SpecialChar LaTeX
1051 -commands for math constructs have the following syntax:
1054 \begin_layout Standard
1059 commandname[optional
1070 \begin_layout Standard
1071 A command always starts with a backslash
1072 \begin_inset Quotes gld
1082 \begin_inset Quotes grd
1095 also omit the associated brackets.
1096 The braces around the
1104 are referred to in this document as \SpecialChar TeX
1106 \begin_inset Index idx
1111 \begin_layout Plain Layout
1112 \begin_inset IndexMacro sortkey
1115 \begin_layout Plain Layout
1128 If you append a left brace to a command name inside a formula,
1130 automatically creates a right \SpecialChar TeX
1132 In all other cases standalone \SpecialChar TeX
1133 braces are created in formulas with the command
1140 Normal braces are created by typing
1146 braces appear red in \SpecialChar LyX
1148 normal braces appear blue.
1150 mode a command is not needed to get \SpecialChar TeX
1153 braces don't appear in the output while normal braces do.
1156 \begin_layout Standard
1157 When commands without arguments,
1158 like commands for symbols,
1159 are entered in \SpecialChar TeX
1161 a space character must
1165 be behind the command to end it.
1166 This space doesn't appear in the output.
1167 When the space should appear in the output,
1168 the space must be followed by a
1169 \change_deleted 177693 1654668848
1171 \change_inserted 177693 1654668851
1174 space in normal text.
1177 \begin_layout Standard
1179 \change_deleted 177693 1654668857
1181 \change_inserted 177693 1654668860
1184 space is inserted with
1185 \change_inserted 232239728 1610908934
1187 \change_deleted 5863208 1612729787
1189 \change_inserted 5863208 1612729774
1193 arg "command-alternatives math-space ; space-insert protected"
1197 \change_deleted 232239728 1610908788
1201 arg "command-alternatives space-insert protected; math-space"
1205 \change_inserted 5863208 1612729766
1206 or with the menu selection
1209 \change_inserted 232239728 1610908897
1210 Insert\SpecialChar menuseparator
1211 Formatting\SpecialChar menuseparator
1213 \change_deleted 177693 1654668863
1215 \change_inserted 177693 1654668975
1217 \change_inserted 232239728 1610908897
1221 \change_inserted 5863208 1612729638
1225 \change_deleted 5863208 1612729640
1233 \begin_layout Subsection*
1234 \begin_inset Newpage newpage
1238 \change_deleted 5863208 1612098922
1242 \change_inserted 5863208 1612100879
1243 of Syntax Used in this Manual
1248 \begin_layout Itemize
1250 \begin_inset space \textvisiblespace{}
1253 denotes a space character to be input
1254 \change_inserted 5863208 1612098935
1260 \begin_layout Itemize
1262 \begin_inset Formula $\to$
1265 denotes the usage of the corresponding arrow key on the keyboard.
1270 key can often be used instead of
1271 \begin_inset Formula $\to$
1275 \begin_inset Formula $\downarrow$
1284 \begin_inset Formula $\leftarrow$
1288 \begin_inset Formula $\uparrow$
1294 \begin_layout Subsection*
1298 \begin_layout Standard
1300 \begin_inset Float table
1307 \begin_layout Plain Layout
1309 \begin_inset Caption Standard
1311 \begin_layout Plain Layout
1312 \begin_inset CommandInset label
1314 name "tab:Available-units"
1326 \begin_layout Plain Layout
1328 \begin_inset Tabular
1329 <lyxtabular version="3" rows="13" columns="2">
1330 <features booktabs="true" tabularvalignment="middle">
1331 <column alignment="center" valignment="top">
1332 <column alignment="center" valignment="top" width="0pt">
1334 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1337 \begin_layout Plain Layout
1343 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1346 \begin_layout Plain Layout
1354 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1357 \begin_layout Plain Layout
1363 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1366 \begin_layout Plain Layout
1374 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1377 \begin_layout Plain Layout
1383 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1386 \begin_layout Plain Layout
1394 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1397 \begin_layout Plain Layout
1403 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1406 \begin_layout Plain Layout
1408 \begin_inset space \thinspace{}
1412 \change_deleted 232239728 1610909338
1414 \change_inserted 232239728 1610909338
1418 \begin_inset space \thinspace{}
1428 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1431 \begin_layout Plain Layout
1437 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1440 \begin_layout Plain Layout
1442 \begin_inset space \thinspace{}
1446 \begin_inset space \thinspace{}
1456 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1459 \begin_layout Plain Layout
1465 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1468 \begin_layout Plain Layout
1470 \begin_inset space \thinspace{}
1474 \begin_inset space \thinspace{}
1484 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1487 \begin_layout Plain Layout
1493 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1496 \begin_layout Plain Layout
1498 \begin_inset space \thinspace{}
1502 \begin_inset space \thinspace{}
1512 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1515 \begin_layout Plain Layout
1521 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1524 \begin_layout Plain Layout
1526 \begin_inset space \thinspace{}
1530 \begin_inset space \thinspace{}
1540 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1543 \begin_layout Plain Layout
1549 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1552 \begin_layout Plain Layout
1554 \begin_inset space \thinspace{}
1558 \begin_inset Formula $\approx$
1562 \begin_inset space \thinspace{}
1572 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1575 \begin_layout Plain Layout
1581 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1584 \begin_layout Plain Layout
1586 \begin_inset space \thinspace{}
1590 \begin_inset space \thinspace{}
1600 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1603 \begin_layout Plain Layout
1609 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1612 \begin_layout Plain Layout
1616 \begin_inset Quotes eld
1622 \begin_inset Quotes erd
1632 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1635 \begin_layout Plain Layout
1641 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1644 \begin_layout Plain Layout
1646 \begin_inset Quotes eld
1654 \begin_inset Quotes erd
1664 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1667 \begin_layout Plain Layout
1673 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1676 \begin_layout Plain Layout
1678 \begin_inset space \thinspace{}
1682 \begin_inset Formula $\nicefrac{1}{18}$
1686 \begin_inset space \thinspace{}
1707 \begin_layout Section
1711 \begin_layout Subsection
1713 \begin_inset Index idx
1718 \begin_layout Plain Layout
1725 \begin_inset Index idx
1730 \begin_layout Plain Layout
1737 \begin_inset Index idx
1742 \begin_layout Plain Layout
1744 \begin_inset IndexMacro see
1747 \begin_layout Plain Layout
1759 \begin_inset Index idx
1764 \begin_layout Plain Layout
1766 \begin_inset IndexMacro see
1769 \begin_layout Plain Layout
1783 \begin_layout Standard
1784 Indices are created with an underscore
1785 \begin_inset Quotes eld
1789 \begin_inset Quotes erd
1792 or via the math toolbar button
1795 arg "math-subscript"
1799 exponents with a caret
1800 \begin_inset Quotes eld
1804 \begin_inset Quotes erd
1807 or via the math toolbar button
1810 arg "math-superscript"
1816 \begin_layout Standard
1818 \begin_inset Tabular
1819 <lyxtabular version="3" rows="4" columns="2">
1820 <features booktabs="true" tabularvalignment="middle">
1821 <column alignment="center" valignment="top" width="0pt">
1822 <column alignment="center" valignment="top" width="0pt">
1824 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1827 \begin_layout Plain Layout
1833 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1836 \begin_layout Plain Layout
1844 <cell alignment="center" valignment="top" usebox="none">
1847 \begin_layout Plain Layout
1853 <cell alignment="center" valignment="top" usebox="none">
1856 \begin_layout Plain Layout
1857 \begin_inset Formula $B_{V}$
1866 <row topspace="1.5mm">
1867 <cell alignment="center" valignment="top" usebox="none">
1870 \begin_layout Plain Layout
1876 <cell alignment="center" valignment="top" usebox="none">
1879 \begin_layout Plain Layout
1880 \begin_inset Formula $B^{V}$
1889 <row topspace="1.5mm">
1890 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1893 \begin_layout Plain Layout
1895 \begin_inset space \textvisiblespace{}
1903 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1906 \begin_layout Plain Layout
1907 \begin_inset Formula $B^{A}$
1923 \begin_layout Standard
1924 As the caret is in some languages an accent,
1925 vowels will be accentuated in this case and not set as exponents
1929 \begin_layout Plain Layout
1930 Depending on the keyboard settings used this can also happen for characters other than vowels.
1936 To get exponents in this case,
1941 after the caret as in the last example.
1944 \begin_layout Subsection
1946 \begin_inset CommandInset label
1948 name "subsec:Fractions"
1953 \begin_inset Index idx
1958 \begin_layout Plain Layout
1967 \begin_layout Standard
1968 Fractions are generated with the command
1975 \begin_inset Index idx
1980 \begin_layout Plain Layout
1982 \begin_inset IndexMacro subentry
1985 \begin_layout Plain Layout
1992 \begin_inset IndexMacro subentry
1995 \begin_layout Plain Layout
2008 or via the math toolbar button
2011 arg "math-insert \\frac"
2015 The font size is adjusted automatically,
2016 depending on whether the fraction is in an inline or display style formula.
2017 With the math toolbar button
2020 arg "math-insert \\frac-square"
2023 you can select different fraction types.
2026 \begin_layout Standard
2034 \begin_inset Index idx
2039 \begin_layout Plain Layout
2041 \begin_inset IndexMacro subentry
2044 \begin_layout Plain Layout
2051 \begin_inset IndexMacro subentry
2054 \begin_layout Plain Layout
2067 a fraction can be created that always has the size of a display style formula.
2075 \begin_inset Index idx
2080 \begin_layout Plain Layout
2082 \begin_inset IndexMacro subentry
2085 \begin_layout Plain Layout
2092 \begin_inset IndexMacro subentry
2095 \begin_layout Plain Layout
2108 the fraction appears always with the size of an inline formula.
2112 \begin_layout Standard
2113 A line with the fraction
2114 \begin_inset Formula $\frac{1}{2}$
2117 that was created with the command
2126 \begin_layout Standard
2127 A line with the fraction
2128 \begin_inset Formula $\dfrac{1}{2}$
2131 that was created with the command
2140 \begin_layout Standard
2142 \begin_inset Tabular
2143 <lyxtabular version="3" rows="4" columns="2">
2144 <features booktabs="true" tabularvalignment="middle">
2145 <column alignment="center" valignment="top" width="0pt">
2146 <column alignment="center" valignment="top" width="0pt">
2148 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2151 \begin_layout Plain Layout
2157 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2160 \begin_layout Plain Layout
2167 <row topspace="1.5mm">
2168 <cell alignment="center" valignment="top" usebox="none">
2171 \begin_layout Plain Layout
2175 \begin_inset space \textvisiblespace{}
2179 \begin_inset Formula $\downarrow$
2187 <cell alignment="center" valignment="top" usebox="none">
2190 \begin_layout Plain Layout
2191 \begin_inset Formula $\frac{A}{B}$
2200 <row topspace="2mm">
2201 <cell alignment="center" valignment="top" usebox="none">
2204 \begin_layout Plain Layout
2208 \begin_inset space \textvisiblespace{}
2212 \begin_inset Formula $\downarrow$
2220 <cell alignment="center" valignment="top" usebox="none">
2223 \begin_layout Plain Layout
2224 \begin_inset Formula $\dfrac{A}{B}$
2233 <row topspace="2mm" bottomspace="1mm">
2234 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2237 \begin_layout Plain Layout
2241 \begin_inset space \textvisiblespace{}
2247 \begin_inset space \textvisiblespace{}
2251 \begin_inset Formula $\downarrow$
2255 \begin_inset Formula $\downarrow\downarrow$
2263 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2266 \begin_layout Plain Layout
2267 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
2283 \begin_layout Standard
2284 \begin_inset VSpace bigskip
2288 \begin_inset Newpage newpage
2291 For nested fractions the command
2298 \begin_inset Index idx
2303 \begin_layout Plain Layout
2305 \begin_inset IndexMacro subentry
2308 \begin_layout Plain Layout
2315 \begin_inset IndexMacro subentry
2318 \begin_layout Plain Layout
2333 \begin_inset VSpace -3mm
2339 \begin_layout Standard
2340 \begin_inset Formula
2342 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2343 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2351 \begin_layout Standard
2352 The command for the example above is:
2355 \begin_layout Standard
2361 \begin_inset space \textvisiblespace{}
2365 \begin_inset Formula $\downarrow$
2371 \begin_inset space \textvisiblespace{}
2377 \begin_inset space \textvisiblespace{}
2381 \begin_inset Formula $\downarrow$
2385 \begin_inset Formula $\downarrow$
2391 \begin_layout Standard
2392 \begin_inset VSpace medskip
2398 \begin_layout Standard
2405 always sets the fraction size to that of a displayed formula,
2406 even when it is part of another fraction.
2409 \begin_layout Standard
2410 It is possible to specify the alignment of the numerator.
2417 is used to left align it,
2431 centers the numerator.
2432 These fractions demonstrate the different alignments:
2435 \begin_layout Standard
2438 \begin_inset Formula
2440 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2448 \begin_layout Standard
2449 \begin_inset Note Greyedout
2452 \begin_layout Plain Layout
2470 are not real \SpecialChar LaTeX
2471 commands but represent the command
2475 cfrac[alignment]{numerator}{denominator}
2478 Therefore you cannot use them in \SpecialChar TeX
2487 \begin_layout Standard
2488 \begin_inset VSpace medskip
2491 It is often advantageous to combine
2504 \begin_inset Formula
2506 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2514 \begin_layout Standard
2515 For inline fractions with a sloped fraction stroke you can use the command
2522 \begin_inset Index idx
2527 \begin_layout Plain Layout
2529 \begin_inset IndexMacro subentry
2532 \begin_layout Plain Layout
2539 \begin_inset IndexMacro subentry
2542 \begin_layout Plain Layout
2557 \begin_inset Formula $\nicefrac{5}{31}$
2567 \begin_inset Index idx
2572 \begin_layout Plain Layout
2574 \begin_inset IndexMacro subentry
2577 \begin_layout Plain Layout
2584 \begin_inset IndexMacro subentry
2587 \begin_layout Plain Layout
2602 \begin_inset Formula $\unitfrac{5}{31}$
2605 There is also the command
2611 which allows you to write a fraction in combination with a number:
2613 \begin_inset Formula $\unitfrac[2]{1}{3}$
2619 \begin_layout Standard
2620 \begin_inset Note Greyedout
2623 \begin_layout Plain Layout
2635 is not a real \SpecialChar LaTeX
2636 command but the command
2637 \begin_inset Newline newline
2644 unitfrac[number]{numerator}{denominator}
2647 Therefore you cannot use it in \SpecialChar TeX
2656 \begin_layout Standard
2657 How to define your own fractions where the fraction stroke can be changed is explained in
2658 \begin_inset CommandInset ref
2660 reference "subsec:Self-defined-Fractions"
2668 \begin_layout Standard
2669 Multiline fractions are explained in
2670 \begin_inset CommandInset ref
2672 reference "subsec:Multiline-Fractions"
2680 \begin_layout Subsection
2682 \begin_inset Index idx
2687 \begin_layout Plain Layout
2696 \begin_layout Standard
2697 Square roots are created with
2704 \begin_inset Index idx
2709 \begin_layout Plain Layout
2711 \begin_inset IndexMacro subentry
2714 \begin_layout Plain Layout
2721 \begin_inset IndexMacro subentry
2724 \begin_layout Plain Layout
2737 or the math toolbar button
2740 arg "math-insert \\sqrt"
2744 all other roots with the command
2751 \begin_inset Index idx
2756 \begin_layout Plain Layout
2758 \begin_inset IndexMacro subentry
2761 \begin_layout Plain Layout
2768 \begin_inset IndexMacro subentry
2771 \begin_layout Plain Layout
2784 or with the math toolbar button
2787 arg "math-insert \\root"
2793 \begin_layout Standard
2795 \begin_inset Tabular
2796 <lyxtabular version="3" rows="3" columns="2">
2797 <features booktabs="true" tabularvalignment="middle">
2798 <column alignment="center" valignment="top" width="0pt">
2799 <column alignment="center" valignment="top" width="0pt">
2801 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2804 \begin_layout Plain Layout
2810 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2813 \begin_layout Plain Layout
2820 <row topspace="1mm">
2821 <cell alignment="center" valignment="top" usebox="none">
2824 \begin_layout Plain Layout
2828 \begin_inset space \textvisiblespace{}
2836 <cell alignment="center" valignment="top" usebox="none">
2839 \begin_layout Plain Layout
2840 \begin_inset Formula $\sqrt{A-B}$
2849 <row topspace="1mm">
2850 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2853 \begin_layout Plain Layout
2857 \begin_inset space \textvisiblespace{}
2861 \begin_inset Formula $\downarrow$
2869 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2872 \begin_layout Plain Layout
2873 \begin_inset Formula $\sqrt[3]{A-B}$
2889 \begin_layout Standard
2890 A square root can also be created with
2896 when the root index field is left empty.
2899 \begin_layout Standard
2900 With certain indices the distance to the root is too small,
2901 like in this formula:
2903 \begin_inset Formula $\sqrt[\beta]{B}$
2907 \begin_inset Newline newline
2911 \begin_inset Formula $\beta$
2923 \begin_inset Index idx
2928 \begin_layout Plain Layout
2930 \begin_inset IndexMacro subentry
2933 \begin_layout Plain Layout
2940 \begin_inset IndexMacro subentry
2943 \begin_layout Plain Layout
2963 \begin_inset Index idx
2968 \begin_layout Plain Layout
2970 \begin_inset IndexMacro subentry
2973 \begin_layout Plain Layout
2980 \begin_inset IndexMacro subentry
2983 \begin_layout Plain Layout
2996 are used with the following scheme:
2999 \begin_layout Standard
3013 \begin_layout Standard
3014 Distance is the number of Big Points (unit bp;
3016 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
3020 that the index should be moved to the left or up,
3022 The commands are written to the index.
3023 This way the command
3024 \begin_inset Newline newline
3034 \begin_inset Formula $\to$
3040 \begin_inset Formula $\to$
3046 \begin_inset space \textvisiblespace{}
3050 \begin_inset Formula $\to$
3054 \begin_inset Newline newline
3059 produces a correct typeset formula:
3061 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
3067 \begin_layout Subsection
3068 Binomial Coefficients
3069 \begin_inset Index idx
3074 \begin_layout Plain Layout
3075 Binomial coefficients
3083 \begin_layout Standard
3084 Binomial coefficients are inserted with the command
3091 \begin_inset Index idx
3096 \begin_layout Plain Layout
3098 \begin_inset IndexMacro subentry
3101 \begin_layout Plain Layout
3108 \begin_inset IndexMacro subentry
3111 \begin_layout Plain Layout
3124 or with the submenu of the math toolbar button
3127 arg "math-insert \\frac-square"
3143 there are the commands
3150 \begin_inset Index idx
3155 \begin_layout Plain Layout
3157 \begin_inset IndexMacro subentry
3160 \begin_layout Plain Layout
3167 \begin_inset IndexMacro subentry
3170 \begin_layout Plain Layout
3190 \begin_inset Index idx
3195 \begin_layout Plain Layout
3197 \begin_inset IndexMacro subentry
3200 \begin_layout Plain Layout
3207 \begin_inset IndexMacro subentry
3210 \begin_layout Plain Layout
3224 For other brackets around binomial coefficients there are the commands
3231 \begin_inset Index idx
3236 \begin_layout Plain Layout
3238 \begin_inset IndexMacro subentry
3241 \begin_layout Plain Layout
3248 \begin_inset IndexMacro subentry
3251 \begin_layout Plain Layout
3271 \begin_inset Index idx
3276 \begin_layout Plain Layout
3278 \begin_inset IndexMacro subentry
3281 \begin_layout Plain Layout
3288 \begin_inset IndexMacro subentry
3291 \begin_layout Plain Layout
3307 \begin_layout Standard
3309 \begin_inset Tabular
3310 <lyxtabular version="3" rows="6" columns="2">
3311 <features booktabs="true" tabularvalignment="middle">
3312 <column alignment="center" valignment="top" width="0pt">
3313 <column alignment="center" valignment="top" width="0pt">
3315 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3318 \begin_layout Plain Layout
3324 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3327 \begin_layout Plain Layout
3334 <row topspace="1mm">
3335 <cell alignment="center" valignment="top" usebox="none">
3338 \begin_layout Plain Layout
3342 \begin_inset space \textvisiblespace{}
3346 \begin_inset Formula $\downarrow$
3354 <cell alignment="center" valignment="top" usebox="none">
3357 \begin_layout Plain Layout
3358 \begin_inset Formula $\binom{A}{B}$
3367 <row topspace="2mm">
3368 <cell alignment="center" valignment="top" usebox="none">
3371 \begin_layout Plain Layout
3375 \begin_inset space \textvisiblespace{}
3379 \begin_inset Formula $\downarrow$
3387 <cell alignment="center" valignment="top" usebox="none">
3390 \begin_layout Plain Layout
3391 \begin_inset Formula $\dbinom{A}{B}$
3400 <row topspace="2mm" bottomspace="0.5mm">
3401 <cell alignment="center" valignment="top" usebox="none">
3404 \begin_layout Plain Layout
3408 \begin_inset space \textvisiblespace{}
3412 \begin_inset Formula $\downarrow$
3420 <cell alignment="center" valignment="top" usebox="none">
3423 \begin_layout Plain Layout
3424 \begin_inset Formula $\tbinom{A}{B}$
3433 <row topspace="1mm">
3434 <cell alignment="center" valignment="top" topline="true" usebox="none">
3437 \begin_layout Plain Layout
3441 \begin_inset space \textvisiblespace{}
3445 \begin_inset Formula $\downarrow$
3453 <cell alignment="center" valignment="top" topline="true" usebox="none">
3456 \begin_layout Plain Layout
3457 \begin_inset Formula ${A \brack B}$
3466 <row topspace="2mm" bottomspace="0.5mm">
3467 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3470 \begin_layout Plain Layout
3474 \begin_inset space \textvisiblespace{}
3478 \begin_inset Formula $\downarrow$
3486 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3489 \begin_layout Plain Layout
3490 \begin_inset Formula ${A \brace B}$
3506 \begin_layout Subsection
3507 Case Differentiations
3508 \begin_inset Index idx
3513 \begin_layout Plain Layout
3514 Case differentiations
3522 \begin_layout Standard
3524 \begin_inset Tabular
3525 <lyxtabular version="3" rows="3" columns="2">
3526 <features booktabs="true" tabularvalignment="middle">
3527 <column alignment="center" valignment="top" width="0pt">
3528 <column alignment="center" valignment="top" width="0pt">
3530 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3533 \begin_layout Plain Layout
3539 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3542 \begin_layout Plain Layout
3550 <cell alignment="center" valignment="top" usebox="none">
3553 \begin_layout Plain Layout
3557 \begin_inset space \textvisiblespace{}
3561 \begin_inset Formula $\to$
3565 \begin_inset Index idx
3570 \begin_layout Plain Layout
3572 \begin_inset IndexMacro subentry
3575 \begin_layout Plain Layout
3582 \begin_inset IndexMacro subentry
3585 \begin_layout Plain Layout
3603 <cell alignment="center" valignment="top" usebox="none">
3606 \begin_layout Plain Layout
3607 \begin_inset Formula $\begin{cases}
3617 <row topspace="1.5mm">
3618 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3621 \begin_layout Plain Layout
3625 \begin_inset space \textvisiblespace{}
3631 arg "newline-insert newline"
3639 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3642 \begin_layout Plain Layout
3643 \begin_inset Formula $\begin{cases}
3644 A & \textrm{for }x>0\\
3645 B & \textrm{for }x=0
3662 \begin_layout Standard
3669 or pressing the math toolbar button
3672 arg "math-insert \\cases"
3675 you can create new lines with the shortcut
3678 arg "newline-insert newline"
3681 or the table toolbar button
3684 arg "tabular-feature append-row"
3690 \begin_layout Standard
3697 is also available via the menu
3699 Insert\SpecialChar menuseparator
3700 Math\SpecialChar menuseparator
3706 \begin_layout Subsection
3708 \begin_inset Index idx
3713 \begin_layout Plain Layout
3722 \begin_layout Standard
3730 \begin_inset Index idx
3735 \begin_layout Plain Layout
3737 \begin_inset IndexMacro subentry
3740 \begin_layout Plain Layout
3747 \begin_inset IndexMacro subentry
3750 \begin_layout Plain Layout
3763 every character can be displayed canceled.
3764 The characters are quasi accentuated by a slash.
3767 \begin_layout Standard
3769 \begin_inset Tabular
3770 <lyxtabular version="3" rows="4" columns="2">
3771 <features booktabs="true" tabularvalignment="middle">
3772 <column alignment="center" valignment="top" width="0pt">
3773 <column alignment="center" valignment="top" width="0pt">
3775 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3778 \begin_layout Plain Layout
3784 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3787 \begin_layout Plain Layout
3795 <cell alignment="center" valignment="top" usebox="none">
3798 \begin_layout Plain Layout
3806 <cell alignment="center" valignment="top" usebox="none">
3809 \begin_layout Plain Layout
3810 \begin_inset Formula $\not=$
3820 <cell alignment="center" valignment="top" usebox="none">
3823 \begin_layout Plain Layout
3833 <cell alignment="center" valignment="top" usebox="none">
3836 \begin_layout Plain Layout
3837 \begin_inset Formula $\not\le$
3847 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3850 \begin_layout Plain Layout
3860 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3863 \begin_layout Plain Layout
3864 \begin_inset Formula $\not\parallel$
3880 \begin_layout Standard
3881 The last example shows that not all negations look good.
3882 Therefore there are special commands for some negations (see
3883 \begin_inset CommandInset ref
3885 reference "subsec:Mathematical-Symbols"
3891 \begin_inset CommandInset ref
3893 reference "sec:Relations"
3901 \begin_layout Subsection
3903 \begin_inset CommandInset label
3905 name "subsec:Placeholders"
3910 \begin_inset Index idx
3915 \begin_layout Plain Layout
3922 \begin_inset Index idx
3927 \begin_layout Plain Layout
3929 \begin_inset IndexMacro subentry
3932 \begin_layout Plain Layout
3944 \begin_inset Index idx
3949 \begin_layout Plain Layout
3951 \begin_inset IndexMacro see
3954 \begin_layout Plain Layout
3968 \begin_layout Standard
3970 \begin_inset space \thinspace{}
3974 \begin_inset space \space{}
3981 \begin_layout Plain Layout
3982 Typesetting isotopes and chemical symbols is described in
3983 \begin_inset CommandInset ref
3985 reference "subsec:Chemical-Symbols-and"
3995 the following problem occurs:
3998 \begin_layout Standard
4000 \begin_inset Tabular
4001 <lyxtabular version="3" rows="2" columns="2">
4002 <features booktabs="true" tabularvalignment="middle">
4003 <column alignment="center" valignment="top" width="0pt">
4004 <column alignment="center" valignment="top" width="0pt">
4006 <cell alignment="center" valignment="top" usebox="none">
4009 \begin_layout Plain Layout
4010 Indices created with sub- and superscripts:
4015 <cell alignment="center" valignment="top" usebox="none">
4018 \begin_layout Plain Layout
4019 \begin_inset Formula $_{9}^{19}\mathrm{F}$
4028 <row topspace="1.5mm">
4029 <cell alignment="center" valignment="top" usebox="none">
4032 \begin_layout Plain Layout
4038 <cell alignment="center" valignment="top" usebox="none">
4041 \begin_layout Plain Layout
4042 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
4058 \begin_layout Standard
4059 The shorter index is placed by default below or above the first character of the longer index.
4060 This is corrected using the command
4067 \begin_inset Index idx
4072 \begin_layout Plain Layout
4074 \begin_inset IndexMacro subentry
4077 \begin_layout Plain Layout
4084 \begin_inset IndexMacro subentry
4087 \begin_layout Plain Layout
4100 or the math toolbar button
4101 \begin_inset space \thinspace{}
4108 \begin_layout Plain Layout
4109 Found in the submenu of the toolbar button
4112 arg "math-insert \\space"
4126 to create one or more phantom characters.
4127 When inserting phantom characters a small blue box appears that is superposed with two red arrows.
4128 The arrows indicate the width and height of the box to be created as a placeholder.
4129 Phantom characters are placeholders with the same character size.
4132 \begin_layout Standard
4134 \begin_inset Tabular
4135 <lyxtabular version="3" rows="4" columns="2">
4136 <features booktabs="true" tabularvalignment="middle">
4137 <column alignment="center" valignment="top" width="0pt">
4138 <column alignment="center" valignment="top" width="0pt">
4140 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4143 \begin_layout Plain Layout
4149 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4152 \begin_layout Plain Layout
4159 <row topspace="1.5mm">
4160 <cell alignment="center" valignment="top" usebox="none">
4163 \begin_layout Plain Layout
4165 \begin_inset space \textvisiblespace{}
4171 \begin_inset space \textvisiblespace{}
4175 \begin_inset Formula $\to$
4179 \begin_inset space \textvisiblespace{}
4183 \change_inserted 5863208 1612176450
4187 \begin_inset space \textvisiblespace{}
4197 <cell alignment="center" valignment="top" usebox="none">
4200 \begin_layout Plain Layout
4201 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
4210 <row topspace="1.5mm" bottomspace="0.5mm">
4211 <cell alignment="center" valignment="top" usebox="none">
4214 \begin_layout Plain Layout
4216 \begin_inset space \textvisiblespace{}
4222 \begin_inset space \textvisiblespace{}
4226 \begin_inset Formula $\to$
4230 \begin_inset space \textvisiblespace{}
4234 \change_inserted 5863208 1612707447
4238 \begin_inset space \textvisiblespace{}
4248 <cell alignment="center" valignment="top" usebox="none">
4251 \begin_layout Plain Layout
4252 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
4261 <row topspace="1.5mm" bottomspace="0.5mm">
4262 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4265 \begin_layout Plain Layout
4269 \change_inserted 5863208 1612707546
4271 \begin_inset space \textvisiblespace{}
4277 \change_deleted 5863208 1612707563
4279 \begin_inset space \textvisiblespace{}
4287 \begin_inset space \textvisiblespace{}
4291 \begin_inset Formula $\to$
4295 \begin_inset space \textvisiblespace{}
4303 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4306 \begin_layout Plain Layout
4307 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
4323 \begin_layout Standard
4324 Furthermore there are the commands
4331 \begin_inset Index idx
4336 \begin_layout Plain Layout
4338 \begin_inset IndexMacro subentry
4341 \begin_layout Plain Layout
4348 \begin_inset IndexMacro subentry
4351 \begin_layout Plain Layout
4377 \begin_inset Index idx
4382 \begin_layout Plain Layout
4384 \begin_inset IndexMacro subentry
4387 \begin_layout Plain Layout
4394 \begin_inset IndexMacro subentry
4397 \begin_layout Plain Layout
4423 creates only space for the maximal height of the characters in the box but not for its width.
4430 creates only space for the width of the box content.
4431 Therefore the boxes of both commands have only one red arrow.
4434 \begin_layout Standard
4435 For example the command
4440 \begin_inset space \textvisiblespace{}
4447 creates space for the height of the integral sign,
4451 \begin_layout Plain Layout
4458 creates an integral sign,
4460 \begin_inset CommandInset ref
4462 reference "subsec:Big-Operators"
4472 because this is the larger character.
4473 An example application is in
4474 \begin_inset CommandInset ref
4476 reference "subsec:Multiline-Brackets"
4484 \begin_layout Standard
4485 Placeholders can also be used for text when they are inserted via the menu
4487 Insert\SpecialChar menuseparator
4488 Formatting\SpecialChar menuseparator
4494 \begin_layout Standard
4496 \begin_inset Newline newline
4500 \begin_inset Phantom Phantom
4503 \begin_layout Plain Layout
4512 \begin_layout Subsection
4514 \begin_inset Index idx
4519 \begin_layout Plain Layout
4526 \begin_inset Index idx
4531 \begin_layout Plain Layout
4533 \begin_inset IndexMacro subentry
4536 \begin_layout Plain Layout
4550 \begin_layout Standard
4552 \begin_inset Tabular
4553 <lyxtabular version="3" rows="4" columns="2">
4554 <features booktabs="true" tabularvalignment="middle">
4555 <column alignment="center" valignment="top" width="0pt">
4556 <column alignment="center" valignment="top" width="0pt">
4558 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4561 \begin_layout Plain Layout
4567 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4570 \begin_layout Plain Layout
4577 <row topspace="2mm">
4578 <cell alignment="center" valignment="top" usebox="none">
4581 \begin_layout Plain Layout
4585 \begin_inset space \textvisiblespace{}
4589 \begin_inset Index idx
4594 \begin_layout Plain Layout
4596 \begin_inset IndexMacro subentry
4599 \begin_layout Plain Layout
4606 \begin_inset IndexMacro subentry
4609 \begin_layout Plain Layout
4627 <cell alignment="center" valignment="top" usebox="none">
4630 \begin_layout Plain Layout
4631 \begin_inset Formula $\overline{A+B}$
4640 <row bottomspace="1mm">
4641 <cell alignment="center" valignment="top" usebox="none">
4644 \begin_layout Plain Layout
4648 \begin_inset space \textvisiblespace{}
4652 \begin_inset Index idx
4657 \begin_layout Plain Layout
4659 \begin_inset IndexMacro subentry
4662 \begin_layout Plain Layout
4669 \begin_inset IndexMacro subentry
4672 \begin_layout Plain Layout
4690 <cell alignment="center" valignment="top" usebox="none">
4693 \begin_layout Plain Layout
4694 \begin_inset Formula $\underline{A+B}$
4703 <row topspace="2mm" bottomspace="1mm">
4704 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4707 \begin_layout Plain Layout
4711 \begin_inset space \textvisiblespace{}
4717 \begin_inset space \textvisiblespace{}
4725 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4728 \begin_layout Plain Layout
4729 \begin_inset Formula $\overline{\underline{A+B}}$
4745 \begin_layout Standard
4746 In the last example it doesn't matter if
4761 \begin_layout Standard
4762 To double underline use
4769 \change_deleted 5863208 1612707977
4771 \change_inserted 5863208 1612707993
4772 (or as many times you want).
4777 \begin_layout Standard
4779 \change_deleted 232239728 1610990247
4780 It is possible to place up to 6 lines above or below characters.
4781 \change_deleted 5863208 1612729848
4783 \begin_inset Note Note
4786 \begin_layout Plain Layout
4788 \change_inserted 232239728 1610990434
4789 I put 30 over and under lines in my test so I don't know what the actual maximum is,
4790 but it's greater than 6.
4800 \begin_layout Standard
4801 \begin_inset VSpace bigskip
4804 Custom lines can be created using the command
4811 \begin_inset Index idx
4816 \begin_layout Plain Layout
4818 \begin_inset IndexMacro subentry
4821 \begin_layout Plain Layout
4828 \begin_inset IndexMacro subentry
4831 \begin_layout Plain Layout
4844 which has the following scheme:
4847 \begin_layout Standard
4852 rule[vertical offset]{length}{thickness}
4855 \begin_layout Standard
4856 The optional vertical offset shifts the line upwards (or downwards,
4857 when the value is negative).
4859 \begin_inset CommandInset ref
4861 reference "tab:Available-units"
4866 can be used for the values.
4867 Here are two example lines created with the commands
4868 \begin_inset Newline newline
4875 rule[-2ex]{3cm}{2pt}
4886 \begin_layout Standard
4888 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4894 \begin_layout Standard
4901 can also be used for text when a line is inserted via the menu
4903 Insert\SpecialChar menuseparator
4904 Formatting\SpecialChar menuseparator
4906 \begin_inset space ~
4914 \begin_layout Standard
4916 \begin_inset CommandInset line
4927 \begin_layout Subsection
4929 \begin_inset CommandInset label
4931 name "subsec:Ellipses"
4936 \begin_inset Index idx
4941 \begin_layout Plain Layout
4950 \begin_layout Standard
4951 There are different types of ellipses available.
4955 \begin_layout Plain Layout
4956 In the math toolbar in the submenu of the button
4959 arg "math-insert \\ldots"
4968 dots at the baseline are used (
4975 \begin_inset Index idx
4980 \begin_layout Plain Layout
4982 \begin_inset IndexMacro subentry
4985 \begin_layout Plain Layout
4992 \begin_inset IndexMacro subentry
4995 \begin_layout Plain Layout
5009 while for operations,
5010 dots are needed that are on the same height as the operators (
5017 \begin_inset Index idx
5022 \begin_layout Plain Layout
5024 \begin_inset IndexMacro subentry
5027 \begin_layout Plain Layout
5034 \begin_inset IndexMacro subentry
5037 \begin_layout Plain Layout
5051 When using the command
5058 \begin_inset Index idx
5063 \begin_layout Plain Layout
5065 \begin_inset IndexMacro subentry
5068 \begin_layout Plain Layout
5075 \begin_inset IndexMacro subentry
5078 \begin_layout Plain Layout
5093 decides on the basis of the next character what type is used.
5096 \begin_layout Standard
5098 \begin_inset Tabular
5099 <lyxtabular version="3" rows="9" columns="2">
5100 <features booktabs="true" tabularvalignment="middle">
5101 <column alignment="center" valignment="top" width="0pt">
5102 <column alignment="center" valignment="top" width="0pt">
5104 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5107 \begin_layout Plain Layout
5113 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5116 \begin_layout Plain Layout
5124 <cell alignment="center" valignment="top" usebox="none">
5127 \begin_layout Plain Layout
5129 \begin_inset space \textvisiblespace{}
5135 \begin_inset space \textvisiblespace{}
5143 <cell alignment="center" valignment="top" usebox="none">
5146 \begin_layout Plain Layout
5147 \begin_inset Formula $A_{1},\dots,A_{n}$
5157 <cell alignment="center" valignment="top" usebox="none">
5160 \begin_layout Plain Layout
5162 \begin_inset space \textvisiblespace{}
5168 \begin_inset space \textvisiblespace{}
5176 <cell alignment="center" valignment="top" usebox="none">
5179 \begin_layout Plain Layout
5180 \begin_inset Formula $A_{1}+\dots+A_{n}$
5190 <cell alignment="center" valignment="top" usebox="none">
5193 \begin_layout Plain Layout
5195 \begin_inset space \textvisiblespace{}
5201 \begin_inset space \textvisiblespace{}
5209 <cell alignment="center" valignment="top" usebox="none">
5212 \begin_layout Plain Layout
5213 \begin_inset Formula $A_{1},\ldots,A_{n}$
5223 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5226 \begin_layout Plain Layout
5228 \begin_inset space \textvisiblespace{}
5234 \begin_inset space \textvisiblespace{}
5242 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5245 \begin_layout Plain Layout
5246 \begin_inset Formula $A_{1}+\cdots+A_{n}$
5256 <cell alignment="center" valignment="top" usebox="none">
5259 \begin_layout Plain Layout
5267 <cell alignment="center" valignment="top" usebox="none">
5270 \begin_layout Plain Layout
5271 \begin_inset Formula $\vdots$
5281 <cell alignment="center" valignment="top" usebox="none">
5284 \begin_layout Plain Layout
5292 <cell alignment="center" valignment="top" usebox="none">
5295 \begin_layout Plain Layout
5296 \begin_inset Formula $\ddots$
5306 <cell alignment="center" valignment="top" usebox="none">
5309 \begin_layout Plain Layout
5317 <cell alignment="center" valignment="top" usebox="none">
5320 \begin_layout Plain Layout
5321 \begin_inset Formula $\iddots$
5331 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5334 \begin_layout Plain Layout
5336 \begin_inset space \thinspace{}
5339 matrix with the different dots
5344 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5347 \begin_layout Plain Layout
5348 \begin_inset Formula $\begin{array}{ccc}
5349 A_{11} & \cdots & A_{1m}\\
5350 \vdots & \ddots & \vdots\\
5351 A_{n1} & \cdots & A_{nm}
5368 \begin_layout Standard
5369 The ellipses available in menu
5371 Insert\SpecialChar menuseparator
5373 \begin_inset space ~
5387 \begin_layout Standard
5388 \begin_inset VSpace medskip
5400 Use mathdots package (automatically)
5402 must be set in the document settings under
5405 \begin_inset space ~
5411 \begin_inset Newline newline
5416 Use mathdots package
5418 will improve the appearance of all dots in the documents if their font style or size is not the default.
5421 \begin_layout Standard
5422 \begin_inset VSpace medskip
5425 Specially for matrices there are ellipses that span over several columns.
5426 They are created with the command
5433 \begin_inset Index idx
5438 \begin_layout Plain Layout
5440 \begin_inset IndexMacro subentry
5443 \begin_layout Plain Layout
5450 \begin_inset IndexMacro subentry
5453 \begin_layout Plain Layout
5466 and have the following scheme
5467 \change_inserted 5863208 1612709418
5479 \begin_inset space ~
5489 \begin_layout Standard
5494 hdotsfor[distance]{number of columns}
5497 \begin_layout Standard
5498 The number of columns specifies how many columns should be spanned.
5499 Distance is a factor for the distance between the dots.
5502 \begin_layout Standard
5503 In the following matrix the command
5509 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
5516 \begin_inset Formula
5518 \left(\begin{array}{cccc}
5527 Note that the matrix fields that should be spanned must be empty,
5528 otherwise you get \SpecialChar LaTeX
5532 \begin_layout Standard
5533 \begin_inset VSpace bigskip
5536 Furthermore you can fill with the command
5543 \begin_inset Index idx
5548 \begin_layout Plain Layout
5550 \begin_inset IndexMacro subentry
5553 \begin_layout Plain Layout
5560 \begin_inset IndexMacro subentry
5563 \begin_layout Plain Layout
5576 the rest of a line with dots.
5577 The effect of these commands is the same as with
5585 \begin_inset CommandInset ref
5587 reference "subsec:Variable-Space"
5595 \begin_layout Standard
5596 For example the command
5601 \begin_inset space \textvisiblespace{}
5609 \begin_layout Standard
5610 \begin_inset Formula $A\dotfill B$
5616 \begin_layout Standard
5623 there is for a line the command
5630 \begin_inset Index idx
5635 \begin_layout Plain Layout
5637 \begin_inset IndexMacro subentry
5640 \begin_layout Plain Layout
5647 \begin_inset IndexMacro subentry
5650 \begin_layout Plain Layout
5666 \begin_layout Standard
5667 \begin_inset Formula $A\hrulefill B$
5673 \begin_layout Standard
5674 To use the commands for text,
5675 they have to be inserted in \SpecialChar TeX
5679 \begin_layout Section
5681 \begin_inset CommandInset label
5688 \begin_inset Index idx
5693 \begin_layout Plain Layout
5702 \begin_layout Standard
5703 Matrices can be inserted via the math toolbar button
5706 arg "dialog-show mathmatrix"
5711 Insert\SpecialChar menuseparator
5712 Math\SpecialChar menuseparator
5716 In the matrix dialog you can specify the number of columns and rows,
5717 the alignment and the decoration.
5718 The vertical alignment is only of importance for matrices in inline formulas:
5721 \begin_layout Standard
5722 The first matrix is top
5723 \begin_inset Formula $\begin{array}[t]{cccc}
5732 \begin_inset Formula $\begin{array}{cccc}
5739 and the third bottom
5740 \begin_inset Formula $\begin{array}[b]{cccc}
5750 \begin_layout Standard
5751 The horizontal alignment specifies how the column entries should be aligned.
5752 It is set by entering a letter for every column.
5757 denotes left aligned,
5767 To create for example a 4
5772 \begin_inset space ~
5775 matrix where the first column is left aligned,
5776 the second and third are centered and the last one is right aligned,
5777 one enters for the horizontal alignment
5782 Normally in a matrix all columns are centered,
5783 therefore the default for every column is a
5790 \begin_layout Standard
5791 Horizontal alignment:
5794 \begin_layout Standard
5801 \begin_inset Formula $\begin{array}{lll}
5815 \begin_inset Formula $\begin{array}{ccc}
5829 \begin_inset Formula $\begin{array}{rrr}
5839 \begin_layout Standard
5840 To subsequently add or delete rows and columns,
5841 the math toolbar buttons
5844 arg "tabular-feature append-row"
5851 arg "tabular-feature delete-row"
5856 \begin_inset space \thinspace{}
5862 Edit\SpecialChar menuseparator
5866 New rows can also be created with
5869 arg "newline-insert newline"
5875 \begin_layout Standard
5876 \begin_inset VSpace bigskip
5880 \change_deleted 47243155 1563226130
5882 \change_deleted -563046850 1563190969
5886 \change_inserted -563046850 1563190971
5892 \change_deleted -563046850 1563192602
5894 \change_inserted -563046850 1563192607
5897 parentheses in the selected style around the matrix
5898 \change_inserted -563046850 1563192780
5904 suitable for an inline matrix like this one
5905 \begin_inset Formula $\bigl(\begin{smallmatrix}0 & \textrm{-}\mathrm{i}\\
5907 \end{smallmatrix}\bigr)$
5914 \change_inserted -563046850 1563192943
5915 Here the parentheses have been added manually using commands
5928 \begin_layout Standard
5930 \change_deleted -563046850 1563192735
5935 \change_deleted -563046850 1563192971
5938 be created with the commands
5945 \begin_inset Index idx
5950 \begin_layout Plain Layout
5952 \begin_inset IndexMacro subentry
5955 \begin_layout Plain Layout
5962 \begin_inset IndexMacro subentry
5965 \begin_layout Plain Layout
5985 \begin_inset Index idx
5990 \begin_layout Plain Layout
5992 \begin_inset IndexMacro subentry
5995 \begin_layout Plain Layout
6002 \begin_inset IndexMacro subentry
6005 \begin_layout Plain Layout
6021 \begin_inset space ~
6028 \begin_inset CommandInset ref
6030 reference "subsec:Automatic-Bracket-Size"
6036 or by using the following commands:
6037 \begin_inset VSpace medskip
6043 \begin_layout Standard
6044 \begin_inset space \hfill{}
6048 \begin_inset Tabular
6049 <lyxtabular version="3" rows="4" columns="2">
6050 <features booktabs="true" tabularvalignment="middle">
6051 <column alignment="center" valignment="top" width="0pt">
6052 <column alignment="center" valignment="top">
6054 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6057 \begin_layout Plain Layout
6063 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6066 \begin_layout Plain Layout
6073 <row topspace="1.5mm">
6074 <cell alignment="center" valignment="top" usebox="none">
6077 \begin_layout Plain Layout
6081 \begin_inset space \textvisiblespace{}
6089 \begin_inset space \thinspace{}
6097 <cell alignment="center" valignment="top" usebox="none">
6100 \begin_layout Plain Layout
6101 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
6102 0 & \textrm{-}\mathrm{i}\\
6104 \end{array}\end{bmatrix}$
6113 <row topspace="1.5mm" bottomspace="0.5mm">
6114 <cell alignment="center" valignment="top" usebox="none">
6117 \begin_layout Plain Layout
6121 \begin_inset space \textvisiblespace{}
6129 \begin_inset space \thinspace{}
6137 <cell alignment="center" valignment="top" usebox="none">
6140 \begin_layout Plain Layout
6141 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
6142 0 & \textrm{-}\mathrm{i}\\
6144 \end{array}\end{Bmatrix}$
6154 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6157 \begin_layout Plain Layout
6161 \begin_inset space \textvisiblespace{}
6169 \begin_inset space \thinspace{}
6177 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6180 \begin_layout Plain Layout
6181 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
6182 0 & \textrm{-}\mathrm{i}\\
6184 \end{array}\end{pmatrix}$
6198 \begin_inset space \hfill{}
6202 \begin_inset Tabular
6203 <lyxtabular version="3" rows="4" columns="2">
6204 <features booktabs="true" tabularvalignment="middle">
6205 <column alignment="center" valignment="top" width="0pt">
6206 <column alignment="center" valignment="top">
6208 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6211 \begin_layout Plain Layout
6217 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6220 \begin_layout Plain Layout
6227 <row topspace="1.5mm">
6228 <cell alignment="center" valignment="top" usebox="none">
6231 \begin_layout Plain Layout
6235 \begin_inset space \textvisiblespace{}
6243 \begin_inset space \thinspace{}
6251 <cell alignment="center" valignment="top" usebox="none">
6254 \begin_layout Plain Layout
6255 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
6256 0 & \textrm{-}\mathrm{i}\\
6258 \end{array}\end{vmatrix}$
6267 <row topspace="1.5mm" bottomspace="0.5mm">
6268 <cell alignment="center" valignment="top" usebox="none">
6271 \begin_layout Plain Layout
6275 \begin_inset space \textvisiblespace{}
6283 \begin_inset space \thinspace{}
6291 <cell alignment="center" valignment="top" usebox="none">
6294 \begin_layout Plain Layout
6295 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
6296 0 & \textrm{-}\mathrm{i}\\
6298 \end{array}\end{Vmatrix}$
6308 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6311 \begin_layout Plain Layout
6315 \begin_inset space \textvisiblespace{}
6323 \begin_inset space \thinspace{}
6331 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6334 \begin_layout Plain Layout
6335 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
6336 0 & \textrm{-}\mathrm{i}\\
6338 \end{array}\end{matrix}$
6352 \begin_inset space \hfill{}
6358 \begin_layout Standard
6359 \begin_inset VSpace medskip
6363 \begin_inset space \thinspace{}
6367 \begin_inset space \space{}
6377 a blue box appears between two vertical lines where the matrix is inserted.
6378 \begin_inset Newline newline
6381 Note that decorated matrices ignore the vertical alignment.
6384 \begin_layout Standard
6385 \begin_inset VSpace bigskip
6388 As all multiline formulas are matrices,
6396 \begin_inset Index idx
6401 \begin_layout Plain Layout
6403 \begin_inset IndexMacro subentry
6406 \begin_layout Plain Layout
6413 \begin_inset IndexMacro subentry
6416 \begin_layout Plain Layout
6429 that is described in
6430 \begin_inset CommandInset ref
6432 reference "subsec:Column-Separation"
6437 can also be used to change the column separation of matrices.
6440 \begin_layout Standard
6441 To change the row separation,
6449 \begin_inset Index idx
6454 \begin_layout Plain Layout
6456 \begin_inset IndexMacro subentry
6459 \begin_layout Plain Layout
6466 \begin_inset IndexMacro subentry
6469 \begin_layout Plain Layout
6485 \begin_layout Standard
6492 arraystretch}{stretch factor}
6493 \begin_inset Index idx
6498 \begin_layout Plain Layout
6500 \begin_inset IndexMacro subentry
6503 \begin_layout Plain Layout
6510 \begin_inset IndexMacro subentry
6513 \begin_layout Plain Layout
6529 \begin_layout Standard
6536 assigns the stretch factor to the predefined command
6543 For example to double the row separation,
6544 use a stretch factor of 2.
6545 This is then used for all following matrices.
6546 To restore the original separation,
6547 assign a stretch factor of 1 to
6556 \begin_layout Standard
6558 \change_inserted 47243155 1563226178
6559 Small inline matrices can also be obtained using
6560 \change_deleted 47243155 1563226182
6561 To set matrices into a text line,
6571 \begin_inset Index idx
6576 \begin_layout Plain Layout
6578 \begin_inset IndexMacro subentry
6581 \begin_layout Plain Layout
6588 \begin_inset IndexMacro subentry
6591 \begin_layout Plain Layout
6605 \change_deleted 47243155 1563226186
6609 When it is inserted in a line a blue box with two dashed lines appears.
6610 Adjust the matrix rows and columns as desired.
6613 \begin_layout Standard
6615 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
6617 \end{smallmatrix}\right)$
6621 \change_inserted 47243155 1563226243
6622 with automatic delimiters around it
6627 \begin_layout Section
6628 Brackets and Delimiters
6629 \begin_inset Index idx
6634 \begin_layout Plain Layout
6641 \begin_inset Index idx
6646 \begin_layout Plain Layout
6655 \begin_layout Subsection
6656 Vertical Brackets and Delimiters
6657 \begin_inset Index idx
6662 \begin_layout Plain Layout
6664 \begin_inset IndexMacro subentry
6667 \begin_layout Plain Layout
6681 \begin_layout Standard
6682 \begin_inset space \hfill{}
6686 \begin_inset Tabular
6687 <lyxtabular version="3" rows="9" columns="2">
6688 <features booktabs="true" tabularvalignment="middle">
6689 <column alignment="center" valignment="top" width="0pt">
6690 <column alignment="center" valignment="top" width="0pt">
6692 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6695 \begin_layout Plain Layout
6701 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6704 \begin_layout Plain Layout
6712 <cell alignment="center" valignment="top" usebox="none">
6715 \begin_layout Plain Layout
6721 <cell alignment="center" valignment="top" usebox="none">
6724 \begin_layout Plain Layout
6725 \begin_inset Formula $($
6735 <cell alignment="center" valignment="top" usebox="none">
6738 \begin_layout Plain Layout
6744 <cell alignment="center" valignment="top" usebox="none">
6747 \begin_layout Plain Layout
6748 \begin_inset Formula $\{$
6758 <cell alignment="center" valignment="top" usebox="none">
6761 \begin_layout Plain Layout
6767 <cell alignment="center" valignment="top" usebox="none">
6770 \begin_layout Plain Layout
6771 \begin_inset Formula $[$
6781 <cell alignment="center" valignment="top" usebox="none">
6784 \begin_layout Plain Layout
6792 <cell alignment="center" valignment="top" usebox="none">
6795 \begin_layout Plain Layout
6796 \begin_inset Formula $\langle$
6806 <cell alignment="center" valignment="top" usebox="none">
6809 \begin_layout Plain Layout
6817 <cell alignment="center" valignment="top" usebox="none">
6820 \begin_layout Plain Layout
6821 \begin_inset Formula $\lceil$
6831 <cell alignment="center" valignment="top" usebox="none">
6834 \begin_layout Plain Layout
6842 <cell alignment="center" valignment="top" usebox="none">
6845 \begin_layout Plain Layout
6846 \begin_inset Formula $\lfloor$
6856 <cell alignment="center" valignment="top" usebox="none">
6859 \begin_layout Plain Layout
6865 <cell alignment="center" valignment="top" usebox="none">
6868 \begin_layout Plain Layout
6869 \begin_inset Formula $/$
6879 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6882 \begin_layout Plain Layout
6888 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6891 \begin_layout Plain Layout
6892 \begin_inset Formula $|$
6906 \begin_inset space \hfill{}
6910 \begin_inset Tabular
6911 <lyxtabular version="3" rows="9" columns="2">
6912 <features booktabs="true" tabularvalignment="middle">
6913 <column alignment="center" valignment="top" width="0pt">
6914 <column alignment="center" valignment="top" width="0pt">
6916 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6919 \begin_layout Plain Layout
6925 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6928 \begin_layout Plain Layout
6936 <cell alignment="center" valignment="top" usebox="none">
6939 \begin_layout Plain Layout
6945 <cell alignment="center" valignment="top" usebox="none">
6948 \begin_layout Plain Layout
6949 \begin_inset Formula $)$
6959 <cell alignment="center" valignment="top" usebox="none">
6962 \begin_layout Plain Layout
6968 <cell alignment="center" valignment="top" usebox="none">
6971 \begin_layout Plain Layout
6972 \begin_inset Formula $\}$
6982 <cell alignment="center" valignment="top" usebox="none">
6985 \begin_layout Plain Layout
6991 <cell alignment="center" valignment="top" usebox="none">
6994 \begin_layout Plain Layout
6995 \begin_inset Formula $]$
7005 <cell alignment="center" valignment="top" usebox="none">
7008 \begin_layout Plain Layout
7016 <cell alignment="center" valignment="top" usebox="none">
7019 \begin_layout Plain Layout
7020 \begin_inset Formula $\rangle$
7030 <cell alignment="center" valignment="top" usebox="none">
7033 \begin_layout Plain Layout
7041 <cell alignment="center" valignment="top" usebox="none">
7044 \begin_layout Plain Layout
7045 \begin_inset Formula $\rceil$
7055 <cell alignment="center" valignment="top" usebox="none">
7058 \begin_layout Plain Layout
7066 <cell alignment="center" valignment="top" usebox="none">
7069 \begin_layout Plain Layout
7070 \begin_inset Formula $\rfloor$
7080 <cell alignment="center" valignment="top" usebox="none">
7083 \begin_layout Plain Layout
7093 <cell alignment="center" valignment="top" usebox="none">
7096 \begin_layout Plain Layout
7097 \begin_inset Formula $\backslash$
7107 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7110 \begin_layout Plain Layout
7118 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7121 \begin_layout Plain Layout
7122 \begin_inset Formula $\|$
7136 \begin_inset space \hfill{}
7142 \begin_layout Standard
7145 \begin_inset Note Greyedout
7148 \begin_layout Plain Layout
7162 \begin_inset Index idx
7167 \begin_layout Plain Layout
7169 \begin_inset IndexMacro subentry
7172 \begin_layout Plain Layout
7179 \begin_inset IndexMacro subentry
7182 \begin_layout Plain Layout
7195 must be used for the backslash,
7204 produces a line break there.
7212 \begin_layout Standard
7213 For all characters listed above the size can be adjusted with the commands described in the following two subsections.
7214 When using these commands,
7215 the characters < and > can directly be used instead of the commands
7230 \begin_layout Subsubsection
7232 \begin_inset CommandInset label
7234 name "subsec:Manual-Bracket-Size"
7239 \begin_inset Index idx
7244 \begin_layout Plain Layout
7246 \begin_inset IndexMacro subentry
7249 \begin_layout Plain Layout
7263 \begin_layout Standard
7264 The bracket size can be specified manually by the \SpecialChar LaTeX
7272 \begin_inset Index idx
7277 \begin_layout Plain Layout
7279 \begin_inset IndexMacro subentry
7282 \begin_layout Plain Layout
7289 \begin_inset IndexMacro subentry
7292 \begin_layout Plain Layout
7332 denotes the smallest and
7338 the largest bracket size.
7341 \begin_layout Standard
7342 These commands are used to emphasize levels of brackets:
7345 \begin_layout Standard
7347 \begin_inset Tabular
7348 <lyxtabular version="3" rows="2" columns="2">
7349 <features booktabs="true" tabularvalignment="middle">
7350 <column alignment="center" valignment="top" width="0pt">
7351 <column alignment="center" valignment="top" width="0pt">
7353 <cell alignment="center" valignment="top" usebox="none">
7356 \begin_layout Plain Layout
7357 All brackets in the same size:
7362 <cell alignment="center" valignment="top" usebox="none">
7365 \begin_layout Plain Layout
7366 \begin_inset Formula $((A+B)(A-B))^{C}$
7375 <row topspace="2mm">
7376 <cell alignment="center" valignment="top" usebox="none">
7379 \begin_layout Plain Layout
7385 <cell alignment="center" valignment="top" usebox="none">
7388 \begin_layout Plain Layout
7389 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
7405 \begin_layout Standard
7406 For the second formula the command
7413 \begin_inset space \textvisiblespace{}
7421 \begin_layout Standard
7422 Here is an example containing all bracket sizes:
7425 \begin_layout Standard
7442 \begin_inset space \textvisiblespace{}
7450 \begin_inset space \textvisiblespace{}
7454 \begin_inset space \textvisiblespace{}
7464 \begin_layout Standard
7466 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
7472 \begin_layout Standard
7479 -commands there is a variant,
7487 \begin_inset Index idx
7492 \begin_layout Plain Layout
7494 \begin_inset IndexMacro subentry
7497 \begin_layout Plain Layout
7504 \begin_inset IndexMacro subentry
7507 \begin_layout Plain Layout
7521 that adds a bit more space between the bracket and its content.
7535 \begin_inset Index idx
7540 \begin_layout Plain Layout
7542 \begin_inset IndexMacro subentry
7545 \begin_layout Plain Layout
7552 \begin_inset IndexMacro subentry
7555 \begin_layout Plain Layout
7571 don't add additional space.
7576 at the end of the command
7582 is for a left bracket;
7583 for a right bracket this is replaced by an
7588 A left or right bracket can each be an opening or closing bracket.
7591 \begin_layout Standard
7592 The following table contains comparisons of the variants:
7595 \begin_layout Standard
7597 \begin_inset Tabular
7598 <lyxtabular version="3" rows="5" columns="2">
7599 <features booktabs="true" tabularvalignment="middle">
7600 <column alignment="center" valignment="top" width="0pt">
7601 <column alignment="center" valignment="middle">
7603 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7606 \begin_layout Plain Layout
7612 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7615 \begin_layout Plain Layout
7622 <row topspace="2mm">
7623 <cell alignment="center" valignment="top" usebox="none">
7626 \begin_layout Plain Layout
7636 \begin_inset space \textvisiblespace{}
7646 <cell alignment="center" valignment="top" usebox="none">
7649 \begin_layout Plain Layout
7650 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
7659 <row topspace="2mm">
7660 <cell alignment="center" valignment="top" usebox="none">
7663 \begin_layout Plain Layout
7673 \begin_inset space \textvisiblespace{}
7683 <cell alignment="center" valignment="top" usebox="none">
7686 \begin_layout Plain Layout
7687 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
7696 <row topspace="2mm" bottomspace="0.5mm">
7697 <cell alignment="center" valignment="top" usebox="none">
7700 \begin_layout Plain Layout
7710 \begin_inset space \textvisiblespace{}
7720 <cell alignment="center" valignment="top" usebox="none">
7723 \begin_layout Plain Layout
7724 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
7733 <row topspace="1.5mm" bottomspace="0.5mm">
7734 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7737 \begin_layout Plain Layout
7749 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7752 \begin_layout Plain Layout
7753 \begin_inset Formula $\bigl)\ln(3x)\bigr($
7769 \begin_layout Subsubsection
7770 Automatic Bracket Size
7771 \begin_inset CommandInset label
7773 name "subsec:Automatic-Bracket-Size"
7778 \begin_inset Index idx
7783 \begin_layout Plain Layout
7785 \begin_inset IndexMacro subentry
7788 \begin_layout Plain Layout
7802 \begin_layout Standard
7803 Variably sized brackets can be inserted with the commands
7810 \begin_inset Index idx
7815 \begin_layout Plain Layout
7817 \begin_inset IndexMacro subentry
7820 \begin_layout Plain Layout
7827 \begin_inset IndexMacro subentry
7830 \begin_layout Plain Layout
7850 \begin_inset Index idx
7855 \begin_layout Plain Layout
7857 \begin_inset IndexMacro subentry
7860 \begin_layout Plain Layout
7867 \begin_inset IndexMacro subentry
7870 \begin_layout Plain Layout
7883 or via the math toolbar button
7886 arg "dialog-show mathdelimiter"
7890 The desired bracket must be inserted directly behind the
7903 The bracket size will then automatically be calculated for the output.
7906 \begin_layout Standard
7916 \begin_inset space \textvisiblespace{}
7920 \begin_inset Formula $\downarrow$
7924 \begin_inset space \textvisiblespace{}
7930 \begin_inset Formula
7940 \begin_layout Standard
7952 \begin_inset space \textvisiblespace{}
7956 \begin_inset Formula $\downarrow$
7960 \begin_inset space \textvisiblespace{}
7968 \begin_inset Formula
7970 \ln\left(\frac{A}{C}\right)
7978 \begin_layout Standard
7994 \begin_inset space ~
8000 This has the advantage that you can see in \SpecialChar LyX
8001 immediately the real bracket size and that the matching right bracket will be created too.
8002 \begin_inset Newline newline
8005 The command for the last example would then be:
8017 \begin_inset space \textvisiblespace{}
8021 \begin_inset Formula $\downarrow$
8027 \begin_layout Standard
8028 To omit a left or right bracket,
8029 a dot is inserted for the omitted bracket.
8030 For example the command
8037 \begin_inset space \textvisiblespace{}
8041 \begin_inset Formula $\downarrow$
8045 \begin_inset space \textvisiblespace{}
8055 \begin_inset Formula
8057 \left.\frac{A}{B}\right\}
8076 will be converted by \SpecialChar LyX
8077 to brackets with the correct size when the document is reloaded and an omitted bracket will appear as dashed line.
8080 \begin_layout Standard
8081 \begin_inset VSpace bigskip
8084 Because all popular \SpecialChar LaTeX
8085 distributions use e\SpecialChar TeX
8087 an extension to \SpecialChar LaTeX
8096 \begin_inset Index idx
8101 \begin_layout Plain Layout
8103 \begin_inset IndexMacro subentry
8106 \begin_layout Plain Layout
8113 \begin_inset IndexMacro subentry
8116 \begin_layout Plain Layout
8129 is available for all brackets and limits.
8130 With this command the height of the following character is adapted to the one of the surrounding brackets,
8131 for example in the case of physical vectors:
8132 \begin_inset Formula
8134 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
8139 For physical vectors there is a special \SpecialChar LaTeX
8142 \begin_inset CommandInset ref
8144 reference "subsec:Physical-Vectors"
8152 \begin_layout Subsection
8154 \begin_inset Index idx
8159 \begin_layout Plain Layout
8161 \begin_inset IndexMacro subentry
8164 \begin_layout Plain Layout
8178 \begin_layout Standard
8180 \begin_inset Tabular
8181 <lyxtabular version="3" rows="4" columns="2">
8182 <features booktabs="true" tabularvalignment="middle">
8183 <column alignment="center" valignment="top" width="0pt">
8184 <column alignment="center" valignment="top" width="0pt">
8186 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8189 \begin_layout Plain Layout
8195 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8198 \begin_layout Plain Layout
8206 <cell alignment="center" valignment="top" usebox="none">
8209 \begin_layout Plain Layout
8213 \begin_inset space \textvisiblespace{}
8217 \begin_inset space \textvisiblespace{}
8221 \begin_inset Index idx
8226 \begin_layout Plain Layout
8228 \begin_inset IndexMacro subentry
8231 \begin_layout Plain Layout
8238 \begin_inset IndexMacro subentry
8241 \begin_layout Plain Layout
8259 <cell alignment="center" valignment="top" usebox="none">
8262 \begin_layout Plain Layout
8263 \begin_inset Formula $\overbrace{A+B}^{3}$
8272 <row topspace="2mm">
8273 <cell alignment="center" valignment="top" usebox="none">
8276 \begin_layout Plain Layout
8280 \begin_inset space \textvisiblespace{}
8284 \begin_inset space \textvisiblespace{}
8288 \begin_inset Index idx
8293 \begin_layout Plain Layout
8295 \begin_inset IndexMacro subentry
8298 \begin_layout Plain Layout
8305 \begin_inset IndexMacro subentry
8308 \begin_layout Plain Layout
8326 <cell alignment="center" valignment="top" usebox="none">
8329 \begin_layout Plain Layout
8330 \begin_inset Formula $\underbrace{A+B}_{5}$
8340 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8343 \begin_layout Plain Layout
8347 \begin_inset space \textvisiblespace{}
8353 \begin_inset space \textvisiblespace{}
8357 \begin_inset space \textvisiblespace{}
8361 \begin_inset space \textvisiblespace{}
8365 \begin_inset space \textvisiblespace{}
8369 \begin_inset space \textvisiblespace{}
8373 \begin_inset space \textvisiblespace{}
8381 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8384 \begin_layout Plain Layout
8385 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
8401 \begin_layout Standard
8402 In the last example it doesn't matter if
8417 \begin_layout Standard
8418 \begin_inset VSpace medskip
8424 \begin_layout Standard
8425 If in document settings under
8428 \begin_inset space ~
8433 the option for the package
8438 \begin_inset Index idx
8443 \begin_layout Plain Layout
8445 \begin_inset IndexMacro subentry
8448 \begin_layout Plain Layout
8462 \begin_inset space ~
8468 you will also have access to square brackets:
8471 \begin_layout Standard
8473 \begin_inset Tabular
8474 <lyxtabular version="3" rows="4" columns="2">
8475 <features booktabs="true" tabularvalignment="middle">
8476 <column alignment="center" valignment="top" width="0pt">
8477 <column alignment="center" valignment="top" width="0pt">
8479 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8482 \begin_layout Plain Layout
8488 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8491 \begin_layout Plain Layout
8499 <cell alignment="center" valignment="top" usebox="none">
8502 \begin_layout Plain Layout
8530 \begin_inset space \textvisiblespace{}
8534 \begin_inset Index idx
8539 \begin_layout Plain Layout
8541 \begin_inset IndexMacro subentry
8544 \begin_layout Plain Layout
8551 \begin_inset IndexMacro subentry
8554 \begin_layout Plain Layout
8572 <cell alignment="center" valignment="top" usebox="none">
8575 \begin_layout Plain Layout
8576 \begin_inset Formula $\overbracket{A+B}^{3}$
8585 <row topspace="2mm">
8586 <cell alignment="center" valignment="top" usebox="none">
8589 \begin_layout Plain Layout
8617 \begin_inset space \textvisiblespace{}
8621 \begin_inset Index idx
8626 \begin_layout Plain Layout
8628 \begin_inset IndexMacro subentry
8631 \begin_layout Plain Layout
8638 \begin_inset IndexMacro subentry
8641 \begin_layout Plain Layout
8671 <cell alignment="center" valignment="top" usebox="none">
8674 \begin_layout Plain Layout
8675 \begin_inset Formula $\underbracket{A+B}_{5}$
8685 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8688 \begin_layout Plain Layout
8694 \begin_inset space \textvisiblespace{}
8698 \begin_inset space \textvisiblespace{}
8702 \begin_inset space \textvisiblespace{}
8706 \begin_inset space \textvisiblespace{}
8710 \change_deleted 5863208 1612711596
8712 \begin_inset space \textvisiblespace{}
8722 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8725 \begin_layout Plain Layout
8726 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
8742 \begin_layout Standard
8755 you can change the thickness of the bracket's stroke by specifying the desired thickness in square brackets behind the command:
8758 \begin_layout Standard
8760 \begin_inset Tabular
8761 <lyxtabular version="3" rows="3" columns="2">
8762 <features booktabs="true" tabularvalignment="middle">
8763 <column alignment="center" valignment="top" width="0pt">
8764 <column alignment="center" valignment="top" width="0pt">
8766 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8769 \begin_layout Plain Layout
8775 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8778 \begin_layout Plain Layout
8786 <cell alignment="center" valignment="top" usebox="none">
8789 \begin_layout Plain Layout
8819 \begin_inset space \textvisiblespace{}
8827 <cell alignment="center" valignment="top" usebox="none">
8830 \begin_layout Plain Layout
8831 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
8840 <row topspace="2mm">
8841 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8844 \begin_layout Plain Layout
8874 \begin_inset space \textvisiblespace{}
8882 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8885 \begin_layout Plain Layout
8886 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
8902 \begin_layout Standard
8903 \begin_inset VSpace bigskip
8906 When brackets overlap each other,
8907 multiline formulas as described in
8908 \begin_inset CommandInset ref
8910 reference "sec:Multiline-Formulas"
8916 \begin_inset Formula
8918 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
8919 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
8925 the formula is inserted together with the first brace.
8926 It is important that the space command
8930 \begin_layout Plain Layout
8931 Space commands are explained in
8932 \begin_inset CommandInset ref
8934 reference "subsec:Predefined-Space"
8951 is inserted before the first
8952 \begin_inset Formula $d$
8955 because the brace that ends behind the
8956 \begin_inset Formula $q$
8959 prevents the following
8960 \begin_inset Quotes eld
8964 \begin_inset Quotes erd
8967 from being surrounded by spaces.
8971 \begin_layout Plain Layout
8972 Because a bracket is not handled as a character,
8974 \begin_inset CommandInset ref
8976 reference "subsec:Binary-Operators"
8986 The second brace is inserted in the second row.
8987 As it should begin before the
8988 \begin_inset Formula $b$
9004 \begin_layout Plain Layout
9012 \begin_inset CommandInset ref
9014 reference "subsec:Placeholders"
9024 This space is needed because the
9025 \begin_inset Quotes eld
9029 \begin_inset Quotes erd
9032 is surrounded by spaces in the formula.
9033 The brace is placed under the command
9042 \begin_layout Standard
9043 It gets more complicated when brackets overlap each other above and under the formula as in the following example:
9047 \begin_layout Plain Layout
9059 \begin_inset Formula
9061 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
9062 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
9071 \begin_layout Plain Layout
9082 The first formula row is the same as the second row of the previous example,
9083 with the difference that the brace is above.
9084 The second row contains the formula together with the second brace.
9085 To avoid the space between the upper brace in the first row and the formula,
9086 the row spacing needs to be reduced.
9087 This is not easily done due to a bug in \SpecialChar LyX
9092 \begin_layout Plain Layout
9093 \begin_inset CommandInset href
9095 name "LyX-bug #1505"
9096 target "https://www.lyx.org/trac/ticket/1505"
9106 As a solution for the problem,
9107 the global formula row separation
9114 \begin_inset Index idx
9119 \begin_layout Plain Layout
9121 \begin_inset IndexMacro subentry
9124 \begin_layout Plain Layout
9131 \begin_inset IndexMacro subentry
9134 \begin_layout Plain Layout
9147 must be changed to -6
9148 \begin_inset space \thinspace{}
9151 pt before the formula with the command
9167 is set back after the formula to the standard value of 3
9168 \begin_inset space \thinspace{}
9171 pt using the same command.
9172 More about the row separation in formulas is explained in
9173 \begin_inset CommandInset ref
9175 reference "subsec:Line-Separation"
9183 \begin_layout Section
9185 \begin_inset Index idx
9190 \begin_layout Plain Layout
9199 \begin_layout Standard
9200 Arrows can be inserted via the math toolbar button
9203 arg "math-insert \\leftarrow"
9206 or the commands listed in the following subsections.
9209 \begin_layout Subsection
9211 \begin_inset Index idx
9216 \begin_layout Plain Layout
9218 \begin_inset IndexMacro subentry
9221 \begin_layout Plain Layout
9235 \begin_layout Standard
9236 \begin_inset space \hfill{}
9240 \begin_inset Tabular
9241 <lyxtabular version="3" rows="8" columns="2">
9242 <features booktabs="true" tabularvalignment="middle">
9243 <column alignment="center" valignment="top" width="0pt">
9244 <column alignment="center" valignment="top" width="0pt">
9246 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9249 \begin_layout Plain Layout
9255 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9258 \begin_layout Plain Layout
9266 <cell alignment="center" valignment="top" usebox="none">
9269 \begin_layout Plain Layout
9277 <cell alignment="center" valignment="top" usebox="none">
9280 \begin_layout Plain Layout
9281 \begin_inset Formula $\gets$
9291 <cell alignment="center" valignment="top" usebox="none">
9294 \begin_layout Plain Layout
9302 <cell alignment="center" valignment="top" usebox="none">
9305 \begin_layout Plain Layout
9306 \begin_inset Formula $\Leftarrow$
9316 <cell alignment="center" valignment="top" usebox="none">
9319 \begin_layout Plain Layout
9327 <cell alignment="center" valignment="top" usebox="none">
9330 \begin_layout Plain Layout
9331 \begin_inset Formula $\longleftarrow$
9341 <cell alignment="center" valignment="top" usebox="none">
9344 \begin_layout Plain Layout
9352 <cell alignment="center" valignment="top" usebox="none">
9355 \begin_layout Plain Layout
9356 \begin_inset Formula $\Longleftarrow$
9366 <cell alignment="center" valignment="top" usebox="none">
9369 \begin_layout Plain Layout
9377 <cell alignment="center" valignment="top" usebox="none">
9380 \begin_layout Plain Layout
9381 \begin_inset Formula $\leftharpoonup$
9391 <cell alignment="center" valignment="top" usebox="none">
9394 \begin_layout Plain Layout
9402 <cell alignment="center" valignment="top" usebox="none">
9405 \begin_layout Plain Layout
9406 \begin_inset Formula $\leftharpoondown$
9416 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9419 \begin_layout Plain Layout
9427 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9430 \begin_layout Plain Layout
9431 \begin_inset Formula $\hookleftarrow$
9445 \begin_inset space \hfill{}
9449 \begin_inset Tabular
9450 <lyxtabular version="3" rows="8" columns="2">
9451 <features booktabs="true" tabularvalignment="middle">
9452 <column alignment="center" valignment="top" width="0pt">
9453 <column alignment="center" valignment="top" width="0pt">
9455 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9458 \begin_layout Plain Layout
9464 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9467 \begin_layout Plain Layout
9475 <cell alignment="center" valignment="top" usebox="none">
9478 \begin_layout Plain Layout
9486 <cell alignment="center" valignment="top" usebox="none">
9489 \begin_layout Plain Layout
9490 \begin_inset Formula $\to$
9500 <cell alignment="center" valignment="top" usebox="none">
9503 \begin_layout Plain Layout
9511 <cell alignment="center" valignment="top" usebox="none">
9514 \begin_layout Plain Layout
9515 \begin_inset Formula $\Rightarrow$
9525 <cell alignment="center" valignment="top" usebox="none">
9528 \begin_layout Plain Layout
9536 <cell alignment="center" valignment="top" usebox="none">
9539 \begin_layout Plain Layout
9540 \begin_inset Formula $\longrightarrow$
9550 <cell alignment="center" valignment="top" usebox="none">
9553 \begin_layout Plain Layout
9561 <cell alignment="center" valignment="top" usebox="none">
9564 \begin_layout Plain Layout
9565 \begin_inset Formula $\Longrightarrow$
9575 <cell alignment="center" valignment="top" usebox="none">
9578 \begin_layout Plain Layout
9586 <cell alignment="center" valignment="top" usebox="none">
9589 \begin_layout Plain Layout
9590 \begin_inset Formula $\rightharpoonup$
9600 <cell alignment="center" valignment="top" usebox="none">
9603 \begin_layout Plain Layout
9611 <cell alignment="center" valignment="top" usebox="none">
9614 \begin_layout Plain Layout
9615 \begin_inset Formula $\rightharpoondown$
9625 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9628 \begin_layout Plain Layout
9636 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9639 \begin_layout Plain Layout
9640 \begin_inset Formula $\hookrightarrow$
9654 \begin_inset space \hfill{}
9660 \begin_layout Standard
9661 \begin_inset space \hfill{}
9665 \begin_inset Tabular
9666 <lyxtabular version="3" rows="6" columns="2">
9667 <features booktabs="true" tabularvalignment="middle">
9668 <column alignment="center" valignment="top" width="0pt">
9669 <column alignment="center" valignment="top" width="0pt">
9671 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9674 \begin_layout Plain Layout
9680 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9683 \begin_layout Plain Layout
9691 <cell alignment="center" valignment="top" usebox="none">
9694 \begin_layout Plain Layout
9702 <cell alignment="center" valignment="top" usebox="none">
9705 \begin_layout Plain Layout
9706 \begin_inset Formula $\leftrightarrow$
9716 <cell alignment="center" valignment="top" usebox="none">
9719 \begin_layout Plain Layout
9727 <cell alignment="center" valignment="top" usebox="none">
9730 \begin_layout Plain Layout
9731 \begin_inset Formula $\Leftrightarrow$
9741 <cell alignment="center" valignment="top" usebox="none">
9744 \begin_layout Plain Layout
9752 <cell alignment="center" valignment="top" usebox="none">
9755 \begin_layout Plain Layout
9756 \begin_inset Formula $\longleftrightarrow$
9766 <cell alignment="center" valignment="top" usebox="none">
9769 \begin_layout Plain Layout
9777 <cell alignment="center" valignment="top" usebox="none">
9780 \begin_layout Plain Layout
9781 \begin_inset Formula $\Longleftrightarrow$
9791 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9794 \begin_layout Plain Layout
9802 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9805 \begin_layout Plain Layout
9806 \begin_inset Formula $\rightleftharpoons$
9820 \begin_inset space \hspace{}
9825 \begin_inset space \hfill{}
9829 \begin_inset Tabular
9830 <lyxtabular version="3" rows="5" columns="2">
9831 <features booktabs="true" tabularvalignment="middle">
9832 <column alignment="center" valignment="top" width="0pt">
9833 <column alignment="center" valignment="top" width="0pt">
9835 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9838 \begin_layout Plain Layout
9844 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9847 \begin_layout Plain Layout
9855 <cell alignment="center" valignment="top" usebox="none">
9858 \begin_layout Plain Layout
9866 <cell alignment="center" valignment="top" usebox="none">
9869 \begin_layout Plain Layout
9870 \begin_inset Formula $\mapsto$
9880 <cell alignment="center" valignment="top" usebox="none">
9883 \begin_layout Plain Layout
9891 <cell alignment="center" valignment="top" usebox="none">
9894 \begin_layout Plain Layout
9895 \begin_inset Formula $\longmapsto$
9905 <cell alignment="center" valignment="top" usebox="none">
9908 \begin_layout Plain Layout
9916 <cell alignment="center" valignment="top" usebox="none">
9919 \begin_layout Plain Layout
9920 \begin_inset Formula $\leadsto$
9930 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9933 \begin_layout Plain Layout
9941 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9944 \begin_layout Plain Layout
9945 \begin_inset Formula $\dasharrow$
9959 \begin_inset space \hfill{}
9965 \begin_layout Standard
9966 \begin_inset VSpace medskip
9969 Arrows used as accents such as vector arrows are listed in
9970 \begin_inset CommandInset ref
9972 reference "sec:Accents"
9980 \begin_layout Standard
9981 \begin_inset VSpace bigskip
9985 \begin_inset Index idx
9990 \begin_layout Plain Layout
9992 \begin_inset IndexMacro subentry
9995 \begin_layout Plain Layout
10006 are also available using the commands
10013 \begin_inset Index idx
10018 \begin_layout Plain Layout
10020 \begin_inset IndexMacro subentry
10023 \begin_layout Plain Layout
10030 \begin_inset IndexMacro subentry
10033 \begin_layout Plain Layout
10053 \begin_inset Index idx
10058 \begin_layout Plain Layout
10060 \begin_inset IndexMacro subentry
10063 \begin_layout Plain Layout
10070 \begin_inset IndexMacro subentry
10073 \begin_layout Plain Layout
10087 When inserting one of these commands in a formula,
10088 an arrow with two blue boxes appears indicating where the labels can be inserted.
10089 The length of the arrow adapts to the label width.
10092 \begin_layout Standard
10094 \begin_inset Tabular
10095 <lyxtabular version="3" rows="3" columns="2">
10096 <features booktabs="true" tabularvalignment="middle">
10097 <column alignment="center" valignment="top" width="0pt">
10098 <column alignment="center" valignment="top" width="0pt">
10100 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10103 \begin_layout Plain Layout
10109 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10112 \begin_layout Plain Layout
10120 <cell alignment="center" valignment="top" usebox="none">
10123 \begin_layout Plain Layout
10127 \begin_inset space \textvisiblespace{}
10131 \begin_inset Formula $\downarrow$
10135 \begin_inset Formula $\to$
10143 <cell alignment="center" valignment="top" usebox="none">
10146 \begin_layout Plain Layout
10147 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
10156 <row topspace="2mm">
10157 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10160 \begin_layout Plain Layout
10164 \begin_inset space \textvisiblespace{}
10168 \begin_inset Formula $\downarrow$
10172 \begin_inset Formula $\to$
10180 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10183 \begin_layout Plain Layout
10184 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
10200 \begin_layout Standard
10201 \begin_inset VSpace medskip
10207 \begin_layout Standard
10208 If in the document settings under
10211 \begin_inset space ~
10221 \begin_inset Index idx
10226 \begin_layout Plain Layout
10228 \begin_inset IndexMacro subentry
10231 \begin_layout Plain Layout
10245 \begin_inset space ~
10251 you will have access to the following labeled arrows:
10254 \begin_layout Standard
10255 \begin_inset Newpage newpage
10261 \begin_layout Standard
10263 \begin_inset space \hspace*{\fill}
10267 \begin_inset Tabular
10268 <lyxtabular version="3" rows="7" columns="2">
10269 <features booktabs="true" tabularvalignment="middle">
10270 <column alignment="center" valignment="top" width="0pt">
10271 <column alignment="center" valignment="top" width="0pt">
10273 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10276 \begin_layout Plain Layout
10282 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10285 \begin_layout Plain Layout
10293 <cell alignment="center" valignment="top" usebox="none">
10296 \begin_layout Plain Layout
10316 <cell alignment="center" valignment="top" usebox="none">
10319 \begin_layout Plain Layout
10320 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
10329 <row topspace="2mm">
10330 <cell alignment="center" valignment="top" usebox="none">
10333 \begin_layout Plain Layout
10353 <cell alignment="center" valignment="top" usebox="none">
10356 \begin_layout Plain Layout
10357 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
10366 <row topspace="2mm">
10367 <cell alignment="center" valignment="top" usebox="none">
10370 \begin_layout Plain Layout
10390 <cell alignment="center" valignment="top" usebox="none">
10393 \begin_layout Plain Layout
10394 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
10403 <row topspace="2mm">
10404 <cell alignment="center" valignment="top" usebox="none">
10407 \begin_layout Plain Layout
10427 <cell alignment="center" valignment="top" usebox="none">
10430 \begin_layout Plain Layout
10431 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
10440 <row topspace="2mm">
10441 <cell alignment="center" valignment="top" usebox="none">
10444 \begin_layout Plain Layout
10464 <cell alignment="center" valignment="top" usebox="none">
10467 \begin_layout Plain Layout
10468 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
10477 <row topspace="2mm">
10478 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10481 \begin_layout Plain Layout
10501 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10504 \begin_layout Plain Layout
10505 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
10519 \begin_inset space \hspace*{\fill}
10523 \begin_inset Tabular
10524 <lyxtabular version="3" rows="7" columns="2">
10525 <features booktabs="true" tabularvalignment="middle">
10526 <column alignment="center" valignment="top" width="0pt">
10527 <column alignment="center" valignment="top" width="0pt">
10529 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10532 \begin_layout Plain Layout
10538 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10541 \begin_layout Plain Layout
10549 <cell alignment="center" valignment="top" usebox="none">
10552 \begin_layout Plain Layout
10572 <cell alignment="center" valignment="top" usebox="none">
10575 \begin_layout Plain Layout
10576 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
10585 <row topspace="2mm">
10586 <cell alignment="center" valignment="top" usebox="none">
10589 \begin_layout Plain Layout
10609 <cell alignment="center" valignment="top" usebox="none">
10612 \begin_layout Plain Layout
10613 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
10622 <row topspace="2mm">
10623 <cell alignment="center" valignment="top" usebox="none">
10626 \begin_layout Plain Layout
10646 <cell alignment="center" valignment="top" usebox="none">
10649 \begin_layout Plain Layout
10650 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
10659 <row topspace="2mm">
10660 <cell alignment="center" valignment="top" usebox="none">
10663 \begin_layout Plain Layout
10683 <cell alignment="center" valignment="top" usebox="none">
10686 \begin_layout Plain Layout
10687 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
10696 <row topspace="2mm">
10697 <cell alignment="center" valignment="top" usebox="none">
10700 \begin_layout Plain Layout
10720 <cell alignment="center" valignment="top" usebox="none">
10723 \begin_layout Plain Layout
10724 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
10733 <row topspace="2mm">
10734 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10737 \begin_layout Plain Layout
10757 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10760 \begin_layout Plain Layout
10761 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
10775 \begin_inset space \hspace*{\fill}
10781 \begin_layout Standard
10782 The command scheme for all of these arrows is:
10785 \begin_layout Standard
10787 \begin_inset Tabular
10788 <lyxtabular version="3" rows="2" columns="2">
10789 <features booktabs="true" tabularvalignment="middle">
10790 <column alignment="center" valignment="top" width="0pt">
10791 <column alignment="center" valignment="top" width="0pt">
10793 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10796 \begin_layout Plain Layout
10802 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10805 \begin_layout Plain Layout
10812 <row bottomspace="0.5mm">
10813 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10816 \begin_layout Plain Layout
10819 xleftrightarrow[x=a]
10822 \begin_inset Formula $\to$
10830 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10833 \begin_layout Plain Layout
10834 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
10850 \begin_layout Subsection
10851 Vertical and Diagonal Arrows
10852 \begin_inset Index idx
10857 \begin_layout Plain Layout
10859 \begin_inset IndexMacro subentry
10862 \begin_layout Plain Layout
10874 \begin_inset Index idx
10879 \begin_layout Plain Layout
10881 \begin_inset IndexMacro subentry
10884 \begin_layout Plain Layout
10898 \begin_layout Standard
10899 \begin_inset space \hfill{}
10903 \begin_inset Tabular
10904 <lyxtabular version="3" rows="7" columns="2">
10905 <features booktabs="true" tabularvalignment="middle">
10906 <column alignment="center" valignment="top" width="0pt">
10907 <column alignment="center" valignment="top" width="0pt">
10909 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10912 \begin_layout Plain Layout
10918 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10921 \begin_layout Plain Layout
10929 <cell alignment="center" valignment="top" usebox="none">
10932 \begin_layout Plain Layout
10940 <cell alignment="center" valignment="top" usebox="none">
10943 \begin_layout Plain Layout
10944 \begin_inset Formula $\uparrow$
10954 <cell alignment="center" valignment="top" usebox="none">
10957 \begin_layout Plain Layout
10965 <cell alignment="center" valignment="top" usebox="none">
10968 \begin_layout Plain Layout
10969 \begin_inset Formula $\Uparrow$
10979 <cell alignment="center" valignment="top" usebox="none">
10982 \begin_layout Plain Layout
10990 <cell alignment="center" valignment="top" usebox="none">
10993 \begin_layout Plain Layout
10994 \begin_inset Formula $\updownarrow$
11004 <cell alignment="center" valignment="top" usebox="none">
11007 \begin_layout Plain Layout
11015 <cell alignment="center" valignment="top" usebox="none">
11018 \begin_layout Plain Layout
11019 \begin_inset Formula $\Updownarrow$
11029 <cell alignment="center" valignment="top" usebox="none">
11032 \begin_layout Plain Layout
11040 <cell alignment="center" valignment="top" usebox="none">
11043 \begin_layout Plain Layout
11044 \begin_inset Formula $\Downarrow$
11054 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11057 \begin_layout Plain Layout
11065 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11068 \begin_layout Plain Layout
11069 \begin_inset Formula $\downarrow$
11083 \begin_inset space \hfill{}
11087 \begin_inset Tabular
11088 <lyxtabular version="3" rows="5" columns="2">
11089 <features booktabs="true" tabularvalignment="middle">
11090 <column alignment="center" valignment="top" width="0pt">
11091 <column alignment="center" valignment="top" width="0pt">
11093 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11096 \begin_layout Plain Layout
11102 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11105 \begin_layout Plain Layout
11113 <cell alignment="center" valignment="top" usebox="none">
11116 \begin_layout Plain Layout
11124 <cell alignment="center" valignment="top" usebox="none">
11127 \begin_layout Plain Layout
11128 \begin_inset Formula $\nearrow$
11138 <cell alignment="center" valignment="top" usebox="none">
11141 \begin_layout Plain Layout
11149 <cell alignment="center" valignment="top" usebox="none">
11152 \begin_layout Plain Layout
11153 \begin_inset Formula $\searrow$
11163 <cell alignment="center" valignment="top" usebox="none">
11166 \begin_layout Plain Layout
11174 <cell alignment="center" valignment="top" usebox="none">
11177 \begin_layout Plain Layout
11178 \begin_inset Formula $\swarrow$
11188 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11191 \begin_layout Plain Layout
11199 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11202 \begin_layout Plain Layout
11203 \begin_inset Formula $\nwarrow$
11217 \begin_inset space \hfill{}
11223 \begin_layout Standard
11224 \begin_inset VSpace medskip
11227 Vertical arrows can also be used as delimiters together with the commands described in
11228 \begin_inset CommandInset ref
11230 reference "subsec:Manual-Bracket-Size"
11236 \begin_inset CommandInset ref
11238 reference "subsec:Automatic-Bracket-Size"
11246 \begin_layout Section
11248 \begin_inset CommandInset label
11255 \begin_inset Index idx
11260 \begin_layout Plain Layout
11269 \begin_layout Standard
11270 Accents can be inserted via the math toolbar button
11273 arg "math-insert \\hat"
11276 or the commands listed in the following subsections.
11279 \begin_layout Subsection
11280 Accents for One Character
11284 \begin_layout Plain Layout
11297 \begin_layout Plain Layout
11298 For accents in text see
11299 \begin_inset CommandInset ref
11301 reference "subsec:Accents-in-Text"
11315 \begin_layout Plain Layout
11323 \begin_inset Note Note
11326 \begin_layout Plain Layout
11333 is used to avoid that the footnote appears in the PDF-bookmark.
11336 \begin_layout Plain Layout
11344 \begin_inset CommandInset ref
11346 reference "subsec:Formulas-in-Section"
11357 \begin_inset CommandInset label
11359 name "subsec:Accents-for-one"
11364 \begin_inset Index idx
11369 \begin_layout Plain Layout
11371 \begin_inset IndexMacro subentry
11374 \begin_layout Plain Layout
11388 \begin_layout Standard
11389 \begin_inset space \hfill{}
11393 \begin_inset Tabular
11394 <lyxtabular version="3" rows="8" columns="2">
11395 <features booktabs="true" tabularvalignment="middle">
11396 <column alignment="center" valignment="top" width="0pt">
11397 <column alignment="center" valignment="top" width="0pt">
11399 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11402 \begin_layout Plain Layout
11408 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11411 \begin_layout Plain Layout
11418 <row topspace="1.5mm">
11419 <cell alignment="center" valignment="top" usebox="none">
11422 \begin_layout Plain Layout
11426 \begin_inset space \textvisiblespace{}
11434 <cell alignment="center" valignment="top" usebox="none">
11437 \begin_layout Plain Layout
11438 \begin_inset Formula $\dot{A}$
11447 <row topspace="1.5mm">
11448 <cell alignment="center" valignment="top" usebox="none">
11451 \begin_layout Plain Layout
11455 \begin_inset space \textvisiblespace{}
11463 <cell alignment="center" valignment="top" usebox="none">
11466 \begin_layout Plain Layout
11467 \begin_inset Formula $\ddot{A}$
11476 <row topspace="1.5mm">
11477 <cell alignment="center" valignment="top" usebox="none">
11480 \begin_layout Plain Layout
11484 \begin_inset space \textvisiblespace{}
11492 <cell alignment="center" valignment="top" usebox="none">
11495 \begin_layout Plain Layout
11496 \begin_inset Formula $\dddot{A}$
11505 <row topspace="1.5mm">
11506 <cell alignment="center" valignment="top" usebox="none">
11509 \begin_layout Plain Layout
11513 \begin_inset space \textvisiblespace{}
11521 <cell alignment="center" valignment="top" usebox="none">
11524 \begin_layout Plain Layout
11525 \begin_inset Formula $\ddddot{A}$
11534 <row topspace="1.5mm">
11535 <cell alignment="center" valignment="top" usebox="none">
11538 \begin_layout Plain Layout
11542 \begin_inset space \textvisiblespace{}
11546 \begin_inset Index idx
11551 \begin_layout Plain Layout
11562 <cell alignment="center" valignment="top" usebox="none">
11565 \begin_layout Plain Layout
11566 \begin_inset Formula $\vec{A}$
11575 <row topspace="1.5mm">
11576 <cell alignment="center" valignment="top" usebox="none">
11579 \begin_layout Plain Layout
11583 \begin_inset space \textvisiblespace{}
11591 <cell alignment="center" valignment="top" usebox="none">
11594 \begin_layout Plain Layout
11595 \begin_inset Formula $\bar{A}$
11604 <row topspace="1.5mm">
11605 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11608 \begin_layout Plain Layout
11612 \begin_inset space \textvisiblespace{}
11620 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11623 \begin_layout Plain Layout
11624 \begin_inset Formula $\mathring{A}$
11638 \begin_inset space \hfill{}
11642 \begin_inset Tabular
11643 <lyxtabular version="3" rows="7" columns="2">
11644 <features booktabs="true" tabularvalignment="middle">
11645 <column alignment="center" valignment="top" width="0pt">
11646 <column alignment="center" valignment="top" width="0pt">
11648 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11651 \begin_layout Plain Layout
11657 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11660 \begin_layout Plain Layout
11667 <row topspace="1.5mm">
11668 <cell alignment="center" valignment="top" usebox="none">
11671 \begin_layout Plain Layout
11675 \begin_inset space \textvisiblespace{}
11683 <cell alignment="center" valignment="top" usebox="none">
11686 \begin_layout Plain Layout
11687 \begin_inset Formula $\tilde{A}$
11696 <row topspace="1.5mm">
11697 <cell alignment="center" valignment="top" usebox="none">
11700 \begin_layout Plain Layout
11704 \begin_inset space \textvisiblespace{}
11712 <cell alignment="center" valignment="top" usebox="none">
11715 \begin_layout Plain Layout
11716 \begin_inset Formula $\hat{A}$
11725 <row topspace="1.5mm">
11726 <cell alignment="center" valignment="top" usebox="none">
11729 \begin_layout Plain Layout
11733 \begin_inset space \textvisiblespace{}
11741 <cell alignment="center" valignment="top" usebox="none">
11744 \begin_layout Plain Layout
11745 \begin_inset Formula $\check{A}$
11754 <row topspace="1.5mm">
11755 <cell alignment="center" valignment="top" usebox="none">
11758 \begin_layout Plain Layout
11762 \begin_inset space \textvisiblespace{}
11770 <cell alignment="center" valignment="top" usebox="none">
11773 \begin_layout Plain Layout
11774 \begin_inset Formula $\acute{A}$
11783 <row topspace="1.5mm">
11784 <cell alignment="center" valignment="top" usebox="none">
11787 \begin_layout Plain Layout
11791 \begin_inset space \textvisiblespace{}
11799 <cell alignment="center" valignment="top" usebox="none">
11802 \begin_layout Plain Layout
11803 \begin_inset Formula $\grave{A}$
11812 <row topspace="1.5mm">
11813 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11816 \begin_layout Plain Layout
11820 \begin_inset space \textvisiblespace{}
11828 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11831 \begin_layout Plain Layout
11832 \begin_inset Formula $\breve{A}$
11846 \begin_inset space \hfill{}
11852 \begin_layout Standard
11853 \begin_inset VSpace bigskip
11859 \begin_layout Standard
11860 You can directly insert accents such as é in formulas.
11862 will transform them to the corresponding accent command.
11864 \begin_inset Index idx
11869 \begin_layout Plain Layout
11875 however it is better to insert a quotation mark before the vowel.
11876 These two characters are then treated by \SpecialChar LaTeX
11881 character when the formula part with the umlaut is marked as German.
11890 \begin_inset Quotes eld
11894 \begin_inset Quotes erd
11897 umlauts are created as demonstrated in the following example:
11900 \begin_layout Standard
11901 \begin_inset VSpace -2mm
11907 \begin_layout Standard
11909 \begin_inset Tabular
11910 <lyxtabular version="3" rows="3" columns="2">
11911 <features booktabs="true" tabularvalignment="middle">
11912 <column alignment="center" valignment="top" width="0pt">
11913 <column alignment="center" valignment="top">
11915 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11918 \begin_layout Plain Layout
11924 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11927 \begin_layout Plain Layout
11935 <cell alignment="center" valignment="top" usebox="none">
11938 \begin_layout Plain Layout
11939 \begin_inset Quotes grd
11947 <cell alignment="center" valignment="top" usebox="none">
11950 \begin_layout Plain Layout
11951 \begin_inset space \hspace{}
11958 \begin_inset Formula $"i$
11967 <row topspace="1.5mm">
11968 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11971 \begin_layout Plain Layout
11975 \begin_inset space \textvisiblespace{}
11983 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11986 \begin_layout Plain Layout
11987 \begin_inset Formula $\ddot{i}$
12003 \begin_layout Standard
12010 is that umlauts can be directly converted to mathematical text because the accent commands above are
12016 in mathematical text
12019 To convert an accented character to mathematical text,
12020 only the character under the accent may be converted.
12021 This applies for all conversions,
12023 \begin_inset space \thinspace{}
12027 \begin_inset space \space{}
12033 \begin_layout Standard
12034 \begin_inset VSpace bigskip
12040 \begin_layout Standard
12042 also supports a tilde under the character if the \SpecialChar LaTeX
12048 \begin_inset Index idx
12053 \begin_layout Plain Layout
12055 \begin_inset IndexMacro subentry
12058 \begin_layout Plain Layout
12069 is installed on your system:
12072 \begin_layout Standard
12076 \begin_layout Plain Layout
12086 \begin_inset Note Note
12089 \begin_layout Plain Layout
12090 The following table will only be displayed when the \SpecialChar LaTeX
12103 \begin_layout Standard
12106 \begin_inset Tabular
12107 <lyxtabular version="3" rows="2" columns="2">
12108 <features booktabs="true" tabularvalignment="middle">
12109 <column alignment="center" valignment="top" width="0pt">
12110 <column alignment="center" valignment="top" width="0pt">
12112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12115 \begin_layout Plain Layout
12121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12124 \begin_layout Plain Layout
12132 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
12135 \begin_layout Plain Layout
12139 \begin_inset space \textvisiblespace{}
12147 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12150 \begin_layout Plain Layout
12151 \begin_inset Formula $\utilde{A}$
12167 \begin_layout Standard
12171 \begin_layout Plain Layout
12181 \begin_inset Note Note
12184 \begin_layout Plain Layout
12185 The following will be displayed when the \SpecialChar LaTeX
12198 \begin_layout Standard
12199 You need to install the \SpecialChar LaTeX
12204 to see the rest of this subsection in the output.
12207 \begin_layout Standard
12211 \begin_layout Plain Layout
12223 \begin_layout Subsection
12224 Accents for Several Characters
12225 \begin_inset Index idx
12230 \begin_layout Plain Layout
12232 \begin_inset IndexMacro subentry
12235 \begin_layout Plain Layout
12236 for several characters
12249 \begin_layout Standard
12250 \begin_inset space \hfill{}
12254 \begin_inset Tabular
12255 <lyxtabular version="3" rows="5" columns="2">
12256 <features booktabs="true" tabularvalignment="middle">
12257 <column alignment="center" valignment="top" width="0pt">
12258 <column alignment="center" valignment="top" width="0pt">
12260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12263 \begin_layout Plain Layout
12269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12272 \begin_layout Plain Layout
12279 <row topspace="1.5mm">
12280 <cell alignment="center" valignment="top" usebox="none">
12283 \begin_layout Plain Layout
12287 \begin_inset space \textvisiblespace{}
12295 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12298 \begin_layout Plain Layout
12299 \begin_inset Formula $\overleftarrow{A=B}$
12308 <row topspace="1.5mm">
12309 <cell alignment="center" valignment="top" usebox="none">
12312 \begin_layout Plain Layout
12316 \begin_inset space \textvisiblespace{}
12324 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12327 \begin_layout Plain Layout
12328 \begin_inset Formula $\underleftarrow{A=B}$
12337 <row topspace="1.5mm">
12338 <cell alignment="center" valignment="top" usebox="none">
12341 \begin_layout Plain Layout
12345 \begin_inset space \textvisiblespace{}
12353 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12356 \begin_layout Plain Layout
12357 \begin_inset Formula $\overleftrightarrow{A=B}$
12366 <row topspace="1.5mm" bottomspace="1mm">
12367 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12370 \begin_layout Plain Layout
12373 underleftrightarrow
12374 \begin_inset space \textvisiblespace{}
12382 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12385 \begin_layout Plain Layout
12386 \begin_inset Formula $\underleftrightarrow{A=B}$
12400 \begin_inset space \hfill{}
12404 \begin_inset Tabular
12405 <lyxtabular version="3" rows="5" columns="2">
12406 <features booktabs="true" tabularvalignment="middle">
12407 <column alignment="center" valignment="top" width="0pt">
12408 <column alignment="center" valignment="top" width="0pt">
12410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12413 \begin_layout Plain Layout
12419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12422 \begin_layout Plain Layout
12429 <row topspace="1.5mm">
12430 <cell alignment="center" valignment="top" usebox="none">
12433 \begin_layout Plain Layout
12437 \begin_inset space \textvisiblespace{}
12445 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12448 \begin_layout Plain Layout
12449 \begin_inset Formula $\overrightarrow{A=B}$
12458 <row topspace="1.5mm">
12459 <cell alignment="center" valignment="top" usebox="none">
12462 \begin_layout Plain Layout
12466 \begin_inset space \textvisiblespace{}
12474 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12477 \begin_layout Plain Layout
12478 \begin_inset Formula $\underrightarrow{A=B}$
12487 <row topspace="1.5mm">
12488 <cell alignment="center" valignment="top" usebox="none">
12491 \begin_layout Plain Layout
12495 \begin_inset space \textvisiblespace{}
12503 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12506 \begin_layout Plain Layout
12507 \begin_inset Formula $\widetilde{A=B}$
12516 <row topspace="1.5mm" bottomspace="1mm">
12517 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12520 \begin_layout Plain Layout
12524 \begin_inset space \textvisiblespace{}
12532 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12535 \begin_layout Plain Layout
12536 \begin_inset Formula $\widehat{A=B}$
12550 \begin_inset space \hfill{}
12556 \begin_layout Standard
12557 \begin_inset VSpace medskip
12560 Using these commands you can accent as many characters as you like.
12573 will only be set in the output with a length of three characters,
12574 as shown in the following example:
12575 \begin_inset Formula
12577 \widetilde{A+B=C-D}
12585 \begin_layout Standard
12586 It is also possible to accent several characters using the commands
12593 \begin_inset Index idx
12598 \begin_layout Plain Layout
12600 \begin_inset IndexMacro subentry
12603 \begin_layout Plain Layout
12610 \begin_inset IndexMacro subentry
12613 \begin_layout Plain Layout
12633 \begin_inset Index idx
12638 \begin_layout Plain Layout
12640 \begin_inset IndexMacro subentry
12643 \begin_layout Plain Layout
12650 \begin_inset IndexMacro subentry
12653 \begin_layout Plain Layout
12666 described in the previous subsection.
12672 \begin_inset space \textvisiblespace{}
12676 \begin_inset Formula $\downarrow$
12682 \begin_inset Formula
12684 \underset{***}{A=B}
12692 \begin_layout Section
12694 \begin_inset CommandInset label
12696 name "subsec:Space"
12701 \begin_inset Index idx
12706 \begin_layout Plain Layout
12708 \begin_inset IndexMacro subentry
12711 \begin_layout Plain Layout
12725 \begin_layout Subsection
12727 \begin_inset CommandInset label
12729 name "subsec:Predefined-Space"
12734 \begin_inset Index idx
12739 \begin_layout Plain Layout
12741 \begin_inset IndexMacro subentry
12744 \begin_layout Plain Layout
12751 \begin_inset IndexMacro subentry
12754 \begin_layout Plain Layout
12768 \begin_layout Standard
12769 Sometimes it is necessary to insert horizontal space into a formula.
12770 This is done by inserting a
12771 \change_deleted 177693 1654668870
12773 \change_inserted 177693 1654668872
12777 \change_inserted 5863208 1612729962
12781 arg "command-alternatives math-space ; space-insert protected"
12785 \change_deleted 5863208 1612729965
12789 arg "command-alternatives space-insert protected ; math-space"
12793 \begin_inset Note Note
12796 \begin_layout Plain Layout
12798 \change_inserted 232239728 1611160593
12799 What is intended here?
12810 \begin_inset Quotes eld
12816 \begin_inset space \textvisiblespace{}
12822 \begin_inset Quotes erd
12825 appears and by pressing
12829 several times one can select one of eight different space sizes.
12830 The spaces can also be inserted using the math toolbar button
12833 arg "math-insert \\space"
12836 or special commands.
12837 The size can be adjusted at any time by positioning the cursor on the
12840 arg "math-insert \\space"
12847 until the desired size is achieved.
12850 \begin_layout Standard
12853 \begin_inset Tabular
12854 <lyxtabular version="3" rows="6" columns="3">
12855 <features booktabs="true" tabularvalignment="middle">
12856 <column alignment="center" valignment="top">
12857 <column alignment="center" valignment="top" width="15col%">
12858 <column alignment="center" valignment="top">
12860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12863 \begin_layout Plain Layout
12869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12872 \begin_layout Plain Layout
12882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12885 \begin_layout Plain Layout
12893 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12896 \begin_layout Plain Layout
12904 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12907 \begin_layout Plain Layout
12913 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12916 \begin_layout Plain Layout
12917 \begin_inset Formula $A\,B$
12927 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12930 \begin_layout Plain Layout
12938 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12941 \begin_layout Plain Layout
12947 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12950 \begin_layout Plain Layout
12951 \begin_inset Formula $A\:B$
12961 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12964 \begin_layout Plain Layout
12972 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12975 \begin_layout Plain Layout
12981 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12984 \begin_layout Plain Layout
12985 \begin_inset Formula $A\;B$
12995 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12998 \begin_layout Plain Layout
13006 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13009 \begin_layout Plain Layout
13015 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13018 \begin_layout Plain Layout
13019 \begin_inset Formula $A\quad B$
13029 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13032 \begin_layout Plain Layout
13040 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13043 \begin_layout Plain Layout
13049 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13052 \begin_layout Plain Layout
13053 \begin_inset Formula $A\qquad B$
13067 \begin_inset space \hfill{}
13071 \begin_inset Tabular
13072 <lyxtabular version="3" rows="6" columns="3">
13073 <features booktabs="true" tabularvalignment="middle">
13074 <column alignment="center" valignment="top">
13075 <column alignment="center" valignment="top" width="15col%">
13076 <column alignment="center" valignment="top">
13078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13081 \begin_layout Plain Layout
13087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13090 \begin_layout Plain Layout
13100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13103 \begin_layout Plain Layout
13111 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13114 \begin_layout Plain Layout
13122 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13125 \begin_layout Plain Layout
13131 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13134 \begin_layout Plain Layout
13135 \begin_inset Formula $A\hfill B$
13145 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13148 \begin_layout Plain Layout
13156 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13159 \begin_layout Plain Layout
13165 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13168 \begin_layout Plain Layout
13169 \begin_inset Formula $A\hspace*{1em}B$
13179 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13182 \begin_layout Plain Layout
13190 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13193 \begin_layout Plain Layout
13199 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13202 \begin_layout Plain Layout
13203 \begin_inset Formula $A\hspace{1em}B$
13213 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13216 \begin_layout Plain Layout
13220 \begin_inset space \textvisiblespace{}
13228 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13231 \begin_layout Plain Layout
13237 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13240 \begin_layout Plain Layout
13241 \begin_inset Formula $A\ B$
13251 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13254 \begin_layout Plain Layout
13262 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13265 \begin_layout Plain Layout
13271 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13274 \begin_layout Plain Layout
13275 \begin_inset Formula $A\!B$
13291 \begin_layout Standard
13293 \begin_inset space ~
13297 \begin_inset space \thinspace{}
13301 \begin_inset space \thinspace{}
13304 7 are variable spaces which are explained in
13305 \begin_inset CommandInset ref
13307 reference "subsec:Variable-Space"
13314 \begin_inset space ~
13317 9 appears to produce no space.
13318 It is displayed red in \SpecialChar LyX
13319 contrary to the other sizes,
13320 because it is a negative space.
13321 There are two more negative spaces:
13324 \begin_layout Standard
13326 \begin_inset Tabular
13327 <lyxtabular version="3" rows="3" columns="3">
13328 <features booktabs="true" tabularvalignment="middle">
13329 <column alignment="center" valignment="middle" width="6.8cm">
13330 <column alignment="center" valignment="top" width="0pt">
13331 <column alignment="center" valignment="top" width="0pt">
13333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13336 \begin_layout Plain Layout
13342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13345 \begin_layout Plain Layout
13353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13356 \begin_layout Plain Layout
13366 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13369 \begin_layout Plain Layout
13374 keystrokes after inserting the
13375 \change_deleted 177693 1654668881
13377 \change_inserted 177693 1654668883
13385 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13388 \begin_layout Plain Layout
13394 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13397 \begin_layout Plain Layout
13405 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13408 \begin_layout Plain Layout
13414 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13417 \begin_layout Plain Layout
13418 \begin_inset Formula $A\negmedspace B$
13426 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13429 \begin_layout Plain Layout
13430 \begin_inset Formula $A\negthickspace B$
13446 \begin_layout Standard
13447 Negative spaces can lead to characters overlapping each other.
13448 Thus they can be used to enforce ligatures,
13449 which are useful for things such as summation operators:
13452 \begin_layout Standard
13454 \begin_inset Tabular
13455 <lyxtabular version="3" rows="3" columns="2">
13456 <features booktabs="true" tabularvalignment="middle">
13457 <column alignment="center" valignment="top" width="0pt">
13458 <column alignment="center" valignment="top">
13460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13463 \begin_layout Plain Layout
13469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13472 \begin_layout Plain Layout
13480 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13483 \begin_layout Plain Layout
13489 \begin_inset space \textvisiblespace{}
13497 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13500 \begin_layout Plain Layout
13501 \begin_inset Formula $\sum\sum f_{kl}$
13511 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13514 \begin_layout Plain Layout
13522 \begin_inset space \textvisiblespace{}
13530 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13533 \begin_layout Plain Layout
13534 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
13550 \begin_layout Standard
13552 \begin_inset VSpace medskip
13558 \begin_layout Standard
13560 Relational operators,
13561 for example equal or less than signs,
13562 are always surrounded by space.
13564 the operator is placed into a \SpecialChar TeX
13566 The following example demonstrates this:
13569 \begin_layout Standard
13571 \begin_inset Tabular
13572 <lyxtabular version="3" rows="2" columns="2">
13573 <features tabularvalignment="middle">
13574 <column alignment="center" valignment="top" width="0pt">
13575 <column alignment="center" valignment="top" width="0pt">
13577 <cell alignment="center" valignment="top" usebox="none">
13580 \begin_layout Plain Layout
13586 <cell alignment="center" valignment="top" usebox="none">
13589 \begin_layout Plain Layout
13590 \begin_inset Formula $A=B$
13600 <cell alignment="center" valignment="top" usebox="none">
13603 \begin_layout Plain Layout
13604 Equation without space
13609 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
13612 \begin_layout Plain Layout
13613 \begin_inset Formula $A{=}B$
13629 \begin_layout Standard
13631 The command for the last formula is:
13637 \begin_inset Formula $\to$
13643 \begin_layout Standard
13644 \begin_inset VSpace bigskip
13650 \begin_layout Standard
13651 Another example of controlled spaces is physical units.
13652 The space between a value and its unit is smaller than a normal space,
13653 typically a thin space is used.
13655 the smaller space is inserted via the menu
13657 Insert\SpecialChar menuseparator
13658 Formatting\SpecialChar menuseparator
13660 \begin_inset space ~
13668 arg "space-insert thin"
13674 \begin_layout Standard
13675 An example to visualize the difference:
13678 \begin_layout Standard
13679 \begin_inset Tabular
13680 <lyxtabular version="3" rows="2" columns="2">
13681 <features tabularvalignment="middle">
13682 <column alignment="left" valignment="top">
13683 <column alignment="left" valignment="top">
13685 <cell alignment="center" valignment="top" usebox="none">
13688 \begin_layout Plain Layout
13690 \begin_inset Formula $\cdot$
13698 <cell alignment="center" valignment="top" usebox="none">
13701 \begin_layout Plain Layout
13702 Space between value and unit
13709 <cell alignment="center" valignment="top" usebox="none">
13712 \begin_layout Plain Layout
13714 \begin_inset space \thinspace{}
13718 \begin_inset Formula $\cdot$
13726 <cell alignment="center" valignment="top" usebox="none">
13729 \begin_layout Plain Layout
13730 Thin space between value and unit
13743 \begin_layout Subsection
13748 \begin_layout Plain Layout
13761 \begin_layout Plain Layout
13762 For vertical space in formulas see
13763 \begin_inset CommandInset ref
13765 reference "subsec:Line-Separation"
13779 \begin_layout Plain Layout
13787 \begin_inset Note Note
13790 \begin_layout Plain Layout
13793 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
13796 \begin_layout Plain Layout
13799 texorpdfstring is in section
13800 \begin_inset CommandInset ref
13802 reference "subsec:Formulas-in-Section"
13813 \begin_inset CommandInset label
13815 name "subsec:Variable-Space"
13820 \begin_inset Index idx
13825 \begin_layout Plain Layout
13827 \begin_inset IndexMacro subentry
13830 \begin_layout Plain Layout
13837 \begin_inset IndexMacro subentry
13840 \begin_layout Plain Layout
13854 \begin_layout Standard
13855 Space with a defined length can be inserted with the command
13862 \begin_inset Index idx
13867 \begin_layout Plain Layout
13869 \begin_inset IndexMacro subentry
13872 \begin_layout Plain Layout
13879 \begin_inset IndexMacro subentry
13882 \begin_layout Plain Layout
13897 \begin_inset Quotes eld
13903 \begin_inset space \textvisiblespace{}
13909 \begin_inset Quotes erd
13913 the length of which can be specified by left-clicking on the
13914 \begin_inset Quotes eld
13920 \begin_inset space \textvisiblespace{}
13926 \begin_inset Quotes erd
13930 The length may also be negative.
13931 If the space is the first character in a line,
13932 it will ordinarily be omitted.
13933 To force its output use the command
13945 or left-click on the
13946 \begin_inset Quotes eld
13952 \begin_inset space \textvisiblespace{}
13958 \begin_inset Quotes erd
13961 and check the option
13966 \begin_inset Newline newline
13969 To insert as much space as is available,
13977 \begin_inset Index idx
13982 \begin_layout Plain Layout
13984 \begin_inset IndexMacro subentry
13987 \begin_layout Plain Layout
13994 \begin_inset IndexMacro subentry
13997 \begin_layout Plain Layout
14013 \begin_layout Standard
14015 \begin_inset Tabular
14016 <lyxtabular version="3" rows="4" columns="2">
14017 <features booktabs="true" tabularvalignment="middle">
14018 <column alignment="center" valignment="top" width="0pt">
14019 <column alignment="center" valignment="top">
14021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14024 \begin_layout Plain Layout
14032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14035 \begin_layout Plain Layout
14043 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14046 \begin_layout Plain Layout
14050 \begin_inset space \textvisiblespace{}
14056 \begin_inset space \thinspace{}
14064 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14067 \begin_layout Plain Layout
14068 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
14078 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14081 \begin_layout Plain Layout
14085 \begin_inset space \textvisiblespace{}
14091 \begin_inset space \thinspace{}
14099 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14102 \begin_layout Plain Layout
14103 \begin_inset Formula $A\hspace{-1mm}A\not=A$
14113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14116 \begin_layout Plain Layout
14120 \begin_inset space \textvisiblespace{}
14128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14131 \begin_layout Plain Layout
14132 \begin_inset Formula $A=A\hfill B=B$
14148 \begin_layout Standard
14149 In the last example the available space is given by the longest column entry of the table.
14150 In an inline formula the space depends on the length of the line in which
14158 when the line uses the full width,
14159 no space will be created.
14166 only has an effect on displayed formulas when the formula style
14171 (Formula styles are explained in
14172 \begin_inset CommandInset ref
14174 reference "sec:Formula-Styles"
14182 \begin_layout Standard
14190 there are also commands,
14204 that fill the space with a pattern.
14206 \begin_inset CommandInset ref
14208 reference "subsec:Ellipses"
14216 \begin_layout Standard
14218 variable space can be inserted via the menu
14220 Insert\SpecialChar menuseparator
14221 Formatting\SpecialChar menuseparator
14223 \begin_inset space ~
14231 \begin_layout Standard
14232 This is a line with
14233 \begin_inset space \hspace{}
14238 \begin_inset space \thinspace{}
14244 \begin_layout Standard
14245 This is a line with
14246 \begin_inset space \hfill{}
14252 \begin_layout Subsection
14253 Space Besides Inline Formulas
14254 \begin_inset Index idx
14259 \begin_layout Plain Layout
14261 \begin_inset IndexMacro subentry
14264 \begin_layout Plain Layout
14265 besides inline formulas
14278 \begin_layout Standard
14279 The space that surrounds inline formulas can be adjusted with the length
14286 \begin_inset Index idx
14291 \begin_layout Plain Layout
14293 \begin_inset IndexMacro subentry
14296 \begin_layout Plain Layout
14303 \begin_inset IndexMacro subentry
14306 \begin_layout Plain Layout
14320 The value of a length is set with the command
14327 \begin_inset Index idx
14332 \begin_layout Plain Layout
14334 \begin_inset IndexMacro subentry
14337 \begin_layout Plain Layout
14344 \begin_inset IndexMacro subentry
14347 \begin_layout Plain Layout
14360 which has the following scheme:
14363 \begin_layout Standard
14368 setlength{length name}{value}
14371 \begin_layout Standard
14379 \begin_inset space \thinspace{}
14386 \begin_layout Standard
14396 \begin_layout Standard
14397 is inserted in \SpecialChar TeX
14400 \begin_inset space \thinspace{}
14403 mm space will now be set around all inline formulas:
14407 \begin_layout Plain Layout
14421 \begin_layout Standard
14422 This is a line with an inline formula
14423 \begin_inset Formula $A=B$
14427 \begin_inset space \thinspace{}
14430 mm surrounding space.
14434 \begin_layout Plain Layout
14448 \begin_layout Standard
14449 To return to the predefined value,
14456 is set to the value 0
14457 \begin_inset space \thinspace{}
14463 \begin_layout Section
14465 \begin_inset Index idx
14470 \begin_layout Plain Layout
14477 \begin_inset Index idx
14482 \begin_layout Plain Layout
14484 \begin_inset IndexMacro see
14487 \begin_layout Plain Layout
14501 \begin_layout Standard
14502 Boxes for text are described in chapter
14509 \begin_inset space ~
14517 \begin_layout Subsection
14519 \begin_inset CommandInset label
14521 name "subsec:Boxes-with-Frame"
14526 \begin_inset Index idx
14531 \begin_layout Plain Layout
14533 \begin_inset IndexMacro subentry
14536 \begin_layout Plain Layout
14550 \begin_layout Standard
14551 It is possible to frame a formula or part of one with the commands
14558 \begin_inset Index idx
14563 \begin_layout Plain Layout
14565 \begin_inset IndexMacro subentry
14568 \begin_layout Plain Layout
14575 \begin_inset IndexMacro subentry
14578 \begin_layout Plain Layout
14598 \begin_inset Index idx
14603 \begin_layout Plain Layout
14605 \begin_inset IndexMacro subentry
14608 \begin_layout Plain Layout
14615 \begin_inset IndexMacro subentry
14618 \begin_layout Plain Layout
14634 \begin_layout Standard
14635 When one of these commands is inserted in a formula,
14636 a blue box appears within a frame to enter formula parts.
14643 an additional formula has to be created by
14648 because the box content will otherwise be treated as mathematical text.
14656 a new formula is automatically created inside the frame.
14659 \begin_layout Standard
14666 is not suitable to frame displayed formulas because the formula will always be set in the size of the documents text.
14673 is not suitable to frame inline formulas because the formula will always be set in the size of a displayed formula.
14676 \begin_layout Standard
14690 \begin_inset Index idx
14695 \begin_layout Plain Layout
14697 \begin_inset IndexMacro subentry
14700 \begin_layout Plain Layout
14707 \begin_inset IndexMacro subentry
14710 \begin_layout Plain Layout
14723 with which the frame width and the alignment can be specified.
14730 is used in the following scheme:
14733 \begin_layout Standard
14738 framebox[frame width][position]{box content}
14741 \begin_layout Standard
14742 The position can either be
14759 right aligns the formula in the box.
14760 If no position is given the formula will be centered.
14761 \begin_inset Newline newline
14764 If width is not given then position can not be given.
14765 In this case the frame width is adjusted to the box content like for
14774 \begin_layout Standard
14782 a box appears containing three blue boxes.
14783 The first two boxes are surrounded by brackets and denote the two optional arguments.
14784 The third box is for formula parts like for
14793 \begin_layout Standard
14795 \begin_inset Tabular
14796 <lyxtabular version="3" rows="5" columns="2">
14797 <features booktabs="true" tabularvalignment="middle">
14798 <column alignment="center" valignment="top" width="0pt">
14799 <column alignment="center" valignment="top">
14801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14804 \begin_layout Plain Layout
14810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14813 \begin_layout Plain Layout
14820 <row topspace="1.5mm">
14821 <cell alignment="center" valignment="top" usebox="none">
14824 \begin_layout Plain Layout
14828 \begin_inset space \textvisiblespace{}
14838 \begin_inset space \textvisiblespace{}
14846 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14849 \begin_layout Plain Layout
14850 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
14859 <row topspace="1.5mm">
14860 <cell alignment="center" valignment="top" usebox="none">
14863 \begin_layout Plain Layout
14867 \begin_inset space \textvisiblespace{}
14873 \begin_inset space \textvisiblespace{}
14881 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14884 \begin_layout Plain Layout
14885 \begin_inset Formula $\boxed{\int A=B}$
14894 <row topspace="1.5mm">
14895 <cell alignment="center" valignment="top" usebox="none">
14898 \begin_layout Plain Layout
14902 \begin_inset space \textvisiblespace{}
14910 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14913 \begin_layout Plain Layout
14914 \begin_inset Formula $A+\fbox{B}$
14923 <row topspace="1.5mm" bottomspace="1mm">
14924 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
14927 \begin_layout Plain Layout
14931 \begin_inset space \textvisiblespace{}
14935 \begin_inset Formula $\to$
14939 \begin_inset Formula $\to$
14949 \begin_inset space \textvisiblespace{}
14953 \begin_inset Formula $\downarrow$
14961 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
14964 \begin_layout Plain Layout
14965 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
14981 \begin_layout Standard
14982 To adjust the frame thickness the following commands are inserted in \SpecialChar TeX
14983 mode before the formula:
14986 \begin_layout Standard
14996 \begin_inset Quotes eld
15000 \begin_inset Quotes erd
15014 \begin_inset Quotes eld
15018 \begin_inset Quotes erd
15024 \begin_layout Standard
15025 \begin_inset Quotes eld
15029 \begin_inset Quotes erd
15032 specifies the minimum distance between the frame and the first character in the box.
15033 An example of this is given in the following framed formula:
15037 \begin_layout Plain Layout
15049 \begin_inset Formula
15056 Before this formula the commands
15059 \begin_layout Standard
15081 \begin_layout Standard
15082 were inserted in \SpecialChar TeX
15084 These values are then used for all following boxes.
15087 \begin_layout Standard
15088 To return to the standard frame size,
15092 \begin_layout Standard
15117 \begin_layout Plain Layout
15131 \begin_layout Standard
15132 is inserted in \SpecialChar TeX
15133 mode before the next formula.
15136 \begin_layout Subsection
15137 Boxes Without Frame
15138 \begin_inset CommandInset label
15140 name "subsec:Boxes-without-Frame"
15145 \begin_inset Index idx
15150 \begin_layout Plain Layout
15152 \begin_inset IndexMacro subentry
15155 \begin_layout Plain Layout
15169 \begin_layout Standard
15170 For boxes without a frame the following box commands:
15178 \begin_inset Index idx
15183 \begin_layout Plain Layout
15185 \begin_inset IndexMacro subentry
15188 \begin_layout Plain Layout
15195 \begin_inset IndexMacro subentry
15198 \begin_layout Plain Layout
15219 \begin_inset Index idx
15224 \begin_layout Plain Layout
15226 \begin_inset IndexMacro subentry
15229 \begin_layout Plain Layout
15236 \begin_inset IndexMacro subentry
15239 \begin_layout Plain Layout
15259 \begin_inset Index idx
15264 \begin_layout Plain Layout
15266 \begin_inset IndexMacro subentry
15269 \begin_layout Plain Layout
15276 \begin_inset IndexMacro subentry
15279 \begin_layout Plain Layout
15295 \begin_layout Standard
15302 a box can be super- or subscripted.
15303 But in contrary to normal super- and subscripting,
15304 the characters in the box keep their font size.
15311 is used in the following scheme:
15314 \begin_layout Standard
15319 raisebox{height}{box content}
15322 \begin_layout Standard
15323 When the box contains a formula,
15324 an extra formula is needed like for
15333 \begin_layout Standard
15336 \begin_inset Note Greyedout
15339 \begin_layout Plain Layout
15351 this extra formula is created by pressing
15355 twice instead of once because \SpecialChar LyX
15356 doesn't yet support
15370 \begin_layout Standard
15372 \begin_inset Tabular
15373 <lyxtabular version="3" rows="4" columns="2">
15374 <features booktabs="true" tabularvalignment="middle">
15375 <column alignment="center" valignment="top" width="0pt">
15376 <column alignment="center" valignment="top">
15378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15381 \begin_layout Plain Layout
15387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15390 \begin_layout Plain Layout
15398 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15401 \begin_layout Plain Layout
15405 \begin_inset Formula $\to$
15411 \begin_inset Formula $\to$
15419 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15422 \begin_layout Plain Layout
15423 \begin_inset Formula $H\raisebox{2mm}{al}lo$
15433 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15436 \begin_layout Plain Layout
15440 \begin_inset Formula $\to$
15446 \begin_inset Formula $\to$
15454 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15457 \begin_layout Plain Layout
15458 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
15468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15471 \begin_layout Plain Layout
15475 \begin_inset Formula $\to$
15491 \begin_inset space \textvisiblespace{}
15499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15502 \begin_layout Plain Layout
15503 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
15519 \begin_layout Standard
15545 except that there is no frame.
15548 \begin_layout Subsection
15550 \begin_inset CommandInset label
15552 name "subsec:Colored-Boxes"
15557 \begin_inset Index idx
15562 \begin_layout Plain Layout
15564 \begin_inset IndexMacro subentry
15567 \begin_layout Plain Layout
15581 \begin_layout Standard
15582 To be able to use all commands explained in this section,
15583 the \SpecialChar LaTeX
15592 \begin_layout Plain Layout
15593 The \SpecialChar LaTeX
15598 is part of every \SpecialChar LaTeX
15599 standard installation.
15605 \begin_inset Index idx
15610 \begin_layout Plain Layout
15612 \begin_inset IndexMacro subentry
15615 \begin_layout Plain Layout
15626 must be loaded in the \SpecialChar LaTeX
15627 -preamble with the line
15631 \begin_layout Plain Layout
15632 When text is colored somewhere in the document with a predefined color,
15634 loads the \SpecialChar LaTeX
15640 Thus it is possible that the package is loaded twice,
15641 but this does not cause problems.
15647 \begin_inset Note Note
15650 \begin_layout Plain Layout
15651 To avoid that the package is loaded twice,
15652 a macro was inserted to the \SpecialChar LaTeX
15661 \begin_layout Standard
15669 \begin_layout Standard
15670 \begin_inset VSpace medskip
15673 To create color boxes,
15681 \begin_inset Index idx
15686 \begin_layout Plain Layout
15688 \begin_inset IndexMacro subentry
15691 \begin_layout Plain Layout
15698 \begin_inset IndexMacro subentry
15701 \begin_layout Plain Layout
15714 is used in the following scheme:
15717 \begin_layout Standard
15722 colorbox{color}{box content}
15725 \begin_layout Standard
15726 The box content can also be a box and a
15732 can also be part of another box (see the 2nd and 3rd example).
15733 When the box should contain a formula,
15734 an extra formula has to be created,
15735 the same way as for
15745 \begin_layout Plain Layout
15746 This also applies for the command
15760 \begin_layout Standard
15761 One of the following predefined colors can be chosen:
15764 \begin_layout Standard
15802 \begin_inset VSpace smallskip
15808 \begin_layout Standard
15810 \begin_inset Tabular
15811 <lyxtabular version="3" rows="4" columns="2">
15812 <features booktabs="true" tabularvalignment="middle">
15813 <column alignment="center" valignment="top" width="0pt">
15814 <column alignment="center" valignment="top">
15816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15819 \begin_layout Plain Layout
15825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15828 \begin_layout Plain Layout
15836 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15839 \begin_layout Plain Layout
15843 \begin_inset Formula $\to$
15853 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15856 \begin_layout Plain Layout
15857 \begin_inset Formula $\colorbox{yellow}{A=B}$
15866 <row topspace="1.5mm">
15867 <cell alignment="center" valignment="top" usebox="none">
15870 \begin_layout Plain Layout
15874 \begin_inset Formula $\to$
15882 \begin_inset space \textvisiblespace{}
15886 \change_inserted 232239728 1611182042
15888 \begin_inset Formula $\gets\gets$
15898 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15901 \begin_layout Plain Layout
15902 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
15911 <row topspace="1.5mm" bottomspace="1mm">
15912 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15915 \begin_layout Plain Layout
15919 \begin_inset space \textvisiblespace{}
15923 \change_inserted 232239728 1611182036
15925 \begin_inset Formula $\gets\gets$
15933 \begin_inset Formula $\to$
15949 \begin_inset space \textvisiblespace{}
15957 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15960 \begin_layout Plain Layout
15961 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
15975 \begin_inset VSpace smallskip
15981 \begin_layout Standard
15988 only colors the box background,
15989 not the characters in the box.
15990 To color all characters,
15991 the whole formula is highlighted and the desired color is chosen in the
15994 \begin_inset space ~
16000 The dialog can be called with the toolbar button
16003 arg "dialog-show character"
16008 Edit\SpecialChar menuseparator
16010 \begin_inset space ~
16013 Properties\SpecialChar menuseparator
16017 The formula number will have the same color as the formula.
16018 If a different color for the formula number is desired,
16019 the color must be changed within the formula.
16022 \begin_layout Standard
16026 \begin_layout Standard
16029 \begin_inset Formula
16031 \int A=B\label{eq:red}
16039 \begin_inset Formula
16041 \textcolor{red}{\int A=B}\label{eq:redgreen}
16049 \begin_layout Standard
16051 \begin_inset CommandInset ref
16058 is completely colored red.
16059 \begin_inset Newline newline
16063 \begin_inset CommandInset ref
16065 reference "eq:redgreen"
16070 was first completely colored green to set the color for the formula number.
16071 Subsequently the formula characters were colored red.
16074 \begin_layout Standard
16075 \begin_inset VSpace bigskip
16078 To color the frame different than the rest of the box,
16086 \begin_inset Index idx
16091 \begin_layout Plain Layout
16093 \begin_inset IndexMacro subentry
16096 \begin_layout Plain Layout
16103 \begin_inset IndexMacro subentry
16106 \begin_layout Plain Layout
16119 is used in the following scheme:
16122 \begin_layout Standard
16127 fcolorbox{frame color}{color}{box content}
16130 \begin_layout Standard
16137 is an extension of the command
16144 The frame width is set,
16169 \begin_layout Plain Layout
16181 \begin_inset Formula
16183 \fcolorbox{cyan}{magenta}{A=B}
16192 \begin_layout Plain Layout
16206 \begin_layout Standard
16207 This formula was created with the command
16208 \begin_inset Newline newline
16216 \begin_inset Formula $\to$
16222 \begin_inset Formula $\to$
16232 \begin_layout Standard
16233 \begin_inset VSpace bigskip
16236 To use colors other than predefined ones,
16237 they must be defined first.
16240 \begin_layout Standard
16241 One can for example define the color
16242 \begin_inset Quotes eld
16250 \begin_inset Quotes erd
16253 with the \SpecialChar LaTeX
16257 \begin_layout Standard
16262 definecolor{darkgreen}{cmyk}{0.5,
16280 \begin_inset Index idx
16285 \begin_layout Plain Layout
16287 \begin_inset IndexMacro subentry
16290 \begin_layout Plain Layout
16297 \begin_inset IndexMacro subentry
16300 \begin_layout Plain Layout
16316 \begin_layout Standard
16321 is the color space denoting the colors
16340 The four comma separated numbers are the portion factors for the corresponding colors of the color space.
16341 The factors can be in the range of 0
16342 \begin_inset space \thinspace{}
16346 \begin_inset space \thinspace{}
16359 can also be used for definitions.
16378 so there are three portion factors for the corresponding colors.
16379 Furthermore there is the color space
16383 with one portion factor for the gray value.
16386 \begin_layout Standard
16387 As an example here is a framed box with the newly defined color
16391 where the characters have been colored
16396 \begin_inset Formula
16398 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
16406 \begin_layout Standard
16407 Self-defined colors can also be used for text with the help of the command
16414 \begin_inset Index idx
16419 \begin_layout Plain Layout
16421 \begin_inset IndexMacro subentry
16424 \begin_layout Plain Layout
16438 \begin_layout Standard
16442 \begin_layout Plain Layout
16446 textcolor{darkgreen}{
16452 \begin_inset Quotes eld
16456 \begin_inset Quotes erd
16463 \begin_layout Plain Layout
16473 \begin_layout Standard
16481 \begin_inset Index idx
16486 \begin_layout Plain Layout
16488 \begin_inset IndexMacro subentry
16491 \begin_layout Plain Layout
16498 \begin_inset IndexMacro subentry
16501 \begin_layout Plain Layout
16514 is used in the scheme
16518 textcolor{color}{characters to color}
16523 \begin_layout Subsection
16525 \begin_inset CommandInset label
16527 name "subsec:Paragraph-Boxes"
16532 \begin_inset Index idx
16537 \begin_layout Plain Layout
16539 \begin_inset IndexMacro subentry
16542 \begin_layout Plain Layout
16556 \begin_layout Standard
16557 A box that can contain several lines and paragraphs,
16558 a so-called paragraph box (parbox),
16559 can be created with the menu
16561 Insert\SpecialChar menuseparator
16564 or the toolbar button
16573 \begin_layout Standard
16574 The following example shows a framed parbox in a line:
16577 \begin_layout Standard
16578 \begin_inset VSpace medskip
16582 \begin_inset Box Boxed
16592 height_special "totalheight"
16597 backgroundcolor "none"
16600 \begin_layout Plain Layout
16601 This is a paragraph box.
16603 \begin_inset space \thinspace{}
16606 cm long and can also contain formulas:
16608 \begin_inset Formula $\int A\,\mathrm{d}s=C$
16619 \begin_layout Standard
16620 \begin_inset VSpace medskip
16626 \begin_layout Standard
16627 Such a box is created by right-clicking on the gray box inset.
16628 A dialog pops up showing the box properties.
16648 \begin_inset space \thinspace{}
16654 Vertical Box Alignment
16660 \begin_layout Standard
16661 \begin_inset VSpace medskip
16664 In \SpecialChar LaTeX
16665 a parbox is created with the command
16672 \begin_inset Index idx
16677 \begin_layout Plain Layout
16679 \begin_inset IndexMacro subentry
16682 \begin_layout Plain Layout
16689 \begin_inset IndexMacro subentry
16692 \begin_layout Plain Layout
16705 which has the following scheme:
16708 \begin_layout Standard
16713 parbox[position]{width}{box content}
16716 \begin_layout Standard
16731 \begin_inset Quotes eld
16735 \begin_inset Quotes erd
16738 means that the box is aligned within the surrounding text with its last line.
16744 \begin_inset Quotes eld
16748 \begin_inset Quotes erd
16751 this is done with the first line.
16752 When no position is given,
16753 the box will be vertically centered,
16761 \begin_inset space ~
16766 manual for examples.
16769 \begin_layout Standard
16770 \begin_inset VSpace bigskip
16773 To frame formulas completely,
16774 including the formula number,
16775 the formula must be set into a parbox.
16791 is inserted in \SpecialChar TeX
16792 mode before the formula.
16800 \begin_inset Index idx
16805 \begin_layout Plain Layout
16807 \begin_inset IndexMacro subentry
16810 \begin_layout Plain Layout
16817 \begin_inset IndexMacro subentry
16820 \begin_layout Plain Layout
16833 is the line width set for the document.
16834 Because the frame is outside the parbox,
16835 two times the frame separation and the frame thickness must be subtracted from the line width.
16836 To be able to multiply and subtract in arguments,
16837 the \SpecialChar LaTeX
16846 \begin_layout Plain Layout
16851 is part of every \SpecialChar LaTeX
16852 standard installation.
16858 \begin_inset Index idx
16863 \begin_layout Plain Layout
16865 \begin_inset IndexMacro subentry
16868 \begin_layout Plain Layout
16879 must be loaded in the \SpecialChar LaTeX
16880 -preamble with the line
16883 \begin_layout Standard
16891 \begin_layout Standard
16892 Behind the formula both boxes are closed by entering
16896 in \SpecialChar TeX
16898 Here is an example:
16902 \begin_layout Plain Layout
16916 \begin_layout Standard
16920 \begin_layout Plain Layout
16938 \begin_inset Formula
16940 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
16949 \begin_layout Plain Layout
16960 \begin_layout Plain Layout
16974 \begin_layout Standard
16975 \begin_inset VSpace medskip
16978 As a parbox is used as the argument of
16985 there is in this case no difference between
17000 \begin_layout Standard
17001 \begin_inset VSpace bigskip
17004 Paragraph boxes are very useful to comment formulas directly.
17012 is used in combination with the command
17026 \begin_inset CommandInset ref
17028 reference "subsec:User-defined-Numbering"
17036 \begin_layout Standard
17037 An example of a formula commented with
17046 \begin_layout Standard
17050 \begin_layout Plain Layout
17063 This is a description.
17064 It is distinctly separated from the formula and multiline.
17068 \begin_layout Plain Layout
17080 \begin_layout Standard
17081 Such a formula must be inserted completely in \SpecialChar TeX
17082 mode because \SpecialChar LyX
17083 does not yet support the command
17090 The formula is created with the following command sequence:
17093 \begin_layout Standard
17106 is inserted in \SpecialChar TeX
17111 \begin_layout Plain Layout
17112 When the formula style
17125 can also be replaced by
17132 (formula styles see
17133 \begin_inset CommandInset ref
17135 reference "sec:Formula-Styles"
17145 Then the description follows as normal text and finally
17151 is inserted in \SpecialChar TeX
17165 create a displayed formula.
17168 \begin_layout Standard
17175 can be seen in this example that was
17176 \begin_inset Quotes eld
17180 \begin_inset Quotes erd
17183 using the mathematical textmode:
17184 \begin_inset Formula
17186 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
17194 \begin_layout Section
17196 \begin_inset Index idx
17201 \begin_layout Plain Layout
17210 \begin_layout Subsection
17212 \begin_inset CommandInset label
17214 name "subsec:Big-Operators"
17219 \begin_inset Index idx
17224 \begin_layout Plain Layout
17226 \begin_inset IndexMacro subentry
17229 \begin_layout Plain Layout
17241 \begin_inset Index idx
17246 \begin_layout Plain Layout
17253 \begin_inset Index idx
17258 \begin_layout Plain Layout
17267 \begin_layout Standard
17268 To be able to use all of the integral operators listed here,
17277 must be set in the document settings under
17280 \begin_inset space ~
17288 \begin_layout Standard
17289 \begin_inset space \hfill{}
17293 \begin_inset Tabular
17294 <lyxtabular version="3" rows="11" columns="2">
17295 <features booktabs="true" tabularvalignment="middle">
17296 <column alignment="center" valignment="top" width="0pt">
17297 <column alignment="center" valignment="top" width="0pt">
17299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17302 \begin_layout Plain Layout
17308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17311 \begin_layout Plain Layout
17319 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17322 \begin_layout Plain Layout
17326 \begin_inset Index idx
17331 \begin_layout Plain Layout
17333 \begin_inset IndexMacro subentry
17336 \begin_layout Plain Layout
17343 \begin_inset IndexMacro subentry
17346 \begin_layout Plain Layout
17364 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17367 \begin_layout Plain Layout
17368 \begin_inset Formula $\int$
17378 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17381 \begin_layout Plain Layout
17389 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17392 \begin_layout Plain Layout
17393 \begin_inset Formula $\oint$
17403 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17406 \begin_layout Plain Layout
17414 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17417 \begin_layout Plain Layout
17418 \begin_inset Formula $\ointctrclockwise$
17428 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17431 \begin_layout Plain Layout
17439 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17442 \begin_layout Plain Layout
17443 \begin_inset Formula $\ointclockwise$
17453 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17456 \begin_layout Plain Layout
17464 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17467 \begin_layout Plain Layout
17468 \begin_inset Formula $\sqint$
17478 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17481 \begin_layout Plain Layout
17489 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17492 \begin_layout Plain Layout
17494 \begin_inset Formula $\fint$
17504 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17507 \begin_layout Plain Layout
17515 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17518 \begin_layout Plain Layout
17520 \begin_inset Formula $\landupint$
17530 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17533 \begin_layout Plain Layout
17541 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17544 \begin_layout Plain Layout
17546 \begin_inset Formula $\landdownint$
17556 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17559 \begin_layout Plain Layout
17567 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17570 \begin_layout Plain Layout
17571 \begin_inset Formula $\bigcap$
17581 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17584 \begin_layout Plain Layout
17592 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17595 \begin_layout Plain Layout
17596 \begin_inset Formula $\bigcup$
17610 \begin_inset space \hfill{}
17614 \begin_inset Tabular
17615 <lyxtabular version="3" rows="11" columns="2">
17616 <features booktabs="true" tabularvalignment="middle">
17617 <column alignment="center" valignment="top" width="0pt">
17618 <column alignment="center" valignment="top" width="0pt">
17620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17623 \begin_layout Plain Layout
17629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17632 \begin_layout Plain Layout
17640 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17643 \begin_layout Plain Layout
17647 \begin_inset Index idx
17652 \begin_layout Plain Layout
17654 \begin_inset IndexMacro subentry
17657 \begin_layout Plain Layout
17664 \begin_inset IndexMacro subentry
17667 \begin_layout Plain Layout
17685 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17688 \begin_layout Plain Layout
17689 \begin_inset Formula $\sum$
17699 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17702 \begin_layout Plain Layout
17706 \begin_inset Index idx
17711 \begin_layout Plain Layout
17713 \begin_inset IndexMacro subentry
17716 \begin_layout Plain Layout
17723 \begin_inset IndexMacro subentry
17726 \begin_layout Plain Layout
17744 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17747 \begin_layout Plain Layout
17748 \begin_inset Formula $\prod$
17758 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17761 \begin_layout Plain Layout
17769 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17772 \begin_layout Plain Layout
17773 \begin_inset Formula $\coprod$
17783 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17786 \begin_layout Plain Layout
17794 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17797 \begin_layout Plain Layout
17798 \begin_inset Formula $\bigodot$
17808 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17811 \begin_layout Plain Layout
17819 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17822 \begin_layout Plain Layout
17823 \begin_inset Formula $\bigotimes$
17833 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17836 \begin_layout Plain Layout
17844 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17847 \begin_layout Plain Layout
17848 \begin_inset Formula $\bigoplus$
17858 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17861 \begin_layout Plain Layout
17869 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17872 \begin_layout Plain Layout
17873 \begin_inset Formula $\bigwedge$
17883 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17886 \begin_layout Plain Layout
17894 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17897 \begin_layout Plain Layout
17898 \begin_inset Formula $\bigvee$
17908 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17911 \begin_layout Plain Layout
17919 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17922 \begin_layout Plain Layout
17923 \begin_inset Formula $\bigsqcup$
17933 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17936 \begin_layout Plain Layout
17944 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17947 \begin_layout Plain Layout
17948 \begin_inset Formula $\biguplus$
17962 \begin_inset space \hfill{}
17968 \begin_layout Standard
17969 All big operators can also be inserted via the math toolbar button
17972 arg "math-insert \\intop"
17978 \begin_layout Standard
17979 The operators are called big because they are bigger than the sometimes equal looking binary operators.
17980 All big operators can have limits as described in the next subsection.
17983 \begin_layout Standard
17984 For all integral operators there is a second version available,
18004 These operators differ in the style the operator limits are displayed,
18006 \begin_inset CommandInset ref
18008 reference "subsec:Operator-Limits"
18016 \begin_layout Subsubsection*
18017 Advice for Integrals
18020 \begin_layout Standard
18025 in an integral is an operator that has to be set upright.
18026 This is done by highlighting the
18030 and using the keyboard shortcut
18040 \begin_layout Plain Layout
18046 \begin_inset CommandInset ref
18048 reference "subsec:Font-Styles"
18059 Also the smallest space is inserted before the
18064 as this is usual for operators.
18068 \begin_layout Standard
18071 \begin_inset Formula $\int A(x)dx$
18075 \begin_inset Newline newline
18079 \begin_inset Phantom HPhantom
18082 \begin_layout Plain Layout
18090 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
18096 \begin_layout Standard
18097 The following commands exist for multiple integrals:
18098 \begin_inset VSpace medskip
18104 \begin_layout Standard
18105 \begin_inset space \hfill{}
18109 \begin_inset Tabular
18110 <lyxtabular version="3" rows="4" columns="2">
18111 <features booktabs="true" tabularvalignment="middle">
18112 <column alignment="center" valignment="top" width="0pt">
18113 <column alignment="center" valignment="top" width="0pt">
18115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18118 \begin_layout Plain Layout
18124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18127 \begin_layout Plain Layout
18134 <row bottomspace="1mm">
18135 <cell alignment="center" valignment="top" usebox="none">
18138 \begin_layout Plain Layout
18146 <cell alignment="center" valignment="top" usebox="none">
18149 \begin_layout Plain Layout
18150 \begin_inset Formula $\iint$
18159 <row bottomspace="1mm">
18160 <cell alignment="center" valignment="top" usebox="none">
18163 \begin_layout Plain Layout
18171 <cell alignment="center" valignment="top" usebox="none">
18174 \begin_layout Plain Layout
18175 \begin_inset Formula $\oiint$
18184 <row bottomspace="1mm">
18185 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18188 \begin_layout Plain Layout
18196 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18199 \begin_layout Plain Layout
18200 \begin_inset Formula $\sqiint$
18214 \begin_inset space \hfill{}
18218 \begin_inset Tabular
18219 <lyxtabular version="3" rows="4" columns="2">
18220 <features booktabs="true" tabularvalignment="middle">
18221 <column alignment="center" valignment="top" width="0pt">
18222 <column alignment="center" valignment="top" width="0pt">
18224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18227 \begin_layout Plain Layout
18233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18236 \begin_layout Plain Layout
18243 <row bottomspace="1mm">
18244 <cell alignment="center" valignment="top" usebox="none">
18247 \begin_layout Plain Layout
18255 <cell alignment="center" valignment="top" usebox="none">
18258 \begin_layout Plain Layout
18259 \begin_inset Formula $\iiint$
18268 <row bottomspace="1mm">
18269 <cell alignment="center" valignment="top" usebox="none">
18272 \begin_layout Plain Layout
18280 <cell alignment="center" valignment="top" usebox="none">
18283 \begin_layout Plain Layout
18284 \begin_inset Formula $\iiiint$
18293 <row bottomspace="1mm">
18294 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18297 \begin_layout Plain Layout
18305 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18308 \begin_layout Plain Layout
18309 \begin_inset Formula $\dotsint$
18323 \begin_inset space \hfill{}
18329 \begin_layout Subsection
18331 \begin_inset CommandInset label
18333 name "subsec:Operator-Limits"
18338 \begin_inset Index idx
18343 \begin_layout Plain Layout
18345 \begin_inset IndexMacro subentry
18348 \begin_layout Plain Layout
18362 \begin_layout Standard
18363 Limits are created by super- and subscripts:
18366 \begin_layout Standard
18368 \begin_inset Tabular
18369 <lyxtabular version="3" rows="2" columns="2">
18370 <features booktabs="true" tabularvalignment="middle">
18371 <column alignment="center" valignment="top" width="0pt">
18372 <column alignment="center" valignment="top" width="0pt">
18374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18377 \begin_layout Plain Layout
18383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18386 \begin_layout Plain Layout
18394 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18397 \begin_layout Plain Layout
18403 \begin_inset space \textvisiblespace{}
18407 \begin_inset Formula $\to$
18411 \begin_inset Formula $\to$
18419 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18422 \begin_layout Plain Layout
18423 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
18439 \begin_layout Standard
18440 Limits of inline formulas are set on the right side of the operator.
18441 Limits in displayed formulas are set above or below the operator,
18442 except for integral limits.
18445 \begin_layout Standard
18446 To force the limits to be set beside the operator,
18447 the cursor is placed directly behind the operator and the limits type is changed with the menu
18449 Edit\SpecialChar menuseparator
18450 Math\SpecialChar menuseparator
18469 \begin_layout Standard
18470 The default displayed formulas limits type is this:
18471 \begin_inset Formula
18473 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
18478 This is how it looks when the limits type is changed to
18485 \begin_inset Formula
18487 \sum\nolimits_{x=0}^{\infty}\frac{1}{x^{2}}
18493 except those ending with
18511 the limits by default are set beside the operator.
18512 But for multiple integrals the limits are often set below the operator.
18513 In the following example the limits type was set to
18517 and so set below the integrals:
18518 \begin_inset Formula
18520 \iiint\limits_{V}X\,\mathrm{d}V=U\label{eq:VolInt}
18526 \change_deleted 5863208 1612725771
18528 \begin_inset Note Note
18531 \begin_layout Plain Layout
18533 \change_inserted 232239728 1611193306
18534 This integral did not have its limits set to Display in the original document
18546 \begin_layout Standard
18547 \begin_inset VSpace medskip
18550 To specify conditions for limits,
18558 \begin_inset Index idx
18563 \begin_layout Plain Layout
18565 \begin_inset IndexMacro subentry
18568 \begin_layout Plain Layout
18575 \begin_inset IndexMacro subentry
18578 \begin_layout Plain Layout
18598 \begin_inset Index idx
18603 \begin_layout Plain Layout
18605 \begin_inset IndexMacro subentry
18608 \begin_layout Plain Layout
18615 \begin_inset IndexMacro subentry
18618 \begin_layout Plain Layout
18632 To create this expression
18633 \begin_inset Formula
18635 \sum_{\begin{subarray}{c}
18637 \\k\,\in\,\mathbb{N}
18638 \end{subarray}}^{n}k^{-2}\label{eq:substack}
18646 \begin_layout Standard
18647 the following must be done:
18648 \begin_inset Newline newline
18660 \begin_inset space \textvisiblespace{}
18666 The cursor is now in a blue box under the summation operator.
18672 \begin_inset space \textvisiblespace{}
18678 The blue box is now within a purple box and now multiple limit lines can be written.
18679 A new line is created by inserting a line break (
18682 arg "newline-insert newline"
18687 \begin_inset Newline newline
18692 0<k<1000 Ctrl+Return
18693 \begin_inset Newline newline
18699 a new box appears below for the new limit line.
18702 \begin_layout Standard
18703 The alignment of the lines can be changed to left aligned with the
18713 Edit\SpecialChar menuseparator
18717 To get right alignment,
18723 \begin_inset space \textvisiblespace{}
18728 is inserted at the beginning of the line.
18731 \begin_layout Standard
18744 with the difference that the lines are always centered.
18747 \begin_layout Standard
18748 \begin_inset VSpace bigskip
18752 \begin_inset CommandInset ref
18754 reference "eq:substack"
18759 there can be too much space beside an operator.
18760 This occurs because the characters following the operator are set beside the limits.
18761 To avoid this the command
18768 \begin_inset Index idx
18773 \begin_layout Plain Layout
18775 \begin_inset IndexMacro subentry
18778 \begin_layout Plain Layout
18785 \begin_inset IndexMacro subentry
18788 \begin_layout Plain Layout
18808 \begin_inset Index idx
18813 \begin_layout Plain Layout
18815 \begin_inset IndexMacro subentry
18818 \begin_layout Plain Layout
18829 in the document settings under
18832 \begin_inset space ~
18840 \begin_inset space ~
18852 sets the space besides the operator to 0
18853 \begin_inset space \thinspace{}
18857 \begin_inset Newline newline
18861 \begin_inset CommandInset ref
18863 reference "eq:substack"
18869 one uses the command
18872 \begin_layout Standard
18880 \begin_layout Standard
18881 and inserts the operator with its limits into the braces.
18882 Behind the brace one continues the formula:
18883 \begin_inset Formula
18885 \smashoperator{\sum_{\begin{subarray}{c}
18887 \\k\,\in\,\mathbb{N}
18888 \end{subarray}}^{n}}k^{-2}
18896 \begin_layout Standard
18897 It is possible to set the space of only one side of the operator to 0
18898 \begin_inset space \thinspace{}
18902 To do this write either
18921 stands for the left and
18925 for the right side of the operator.
18926 Here is an example of the possible
18935 \begin_layout Standard
18936 \begin_inset Formula
18938 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}
18946 \begin_layout Standard
18947 \begin_inset VSpace bigskip
18953 \begin_layout Standard
18954 When several consecutive operators have limits the typesetting of the limits looks often imperfect in the output,
18956 \begin_inset Formula
18958 \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}
18963 To improve the typesetting,
18964 in the document settings under
18967 \begin_inset space ~
18977 \begin_inset Index idx
18982 \begin_layout Plain Layout
18984 \begin_inset IndexMacro subentry
18987 \begin_layout Plain Layout
19002 \begin_inset space ~
19008 Then insert the command
19015 \begin_inset Index idx
19020 \begin_layout Plain Layout
19022 \begin_inset IndexMacro subentry
19025 \begin_layout Plain Layout
19032 \begin_inset IndexMacro subentry
19035 \begin_layout Plain Layout
19048 directly before the first operator.
19049 The example will then look like this:
19050 \begin_inset Formula
19052 \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}
19060 \begin_layout Standard
19061 \begin_inset VSpace bigskip
19064 How to use one limit for several operators is described in
19065 \begin_inset CommandInset ref
19067 reference "subsec:Self-defined-Operators"
19075 \begin_layout Subsection
19076 Decoration for Operators
19077 \begin_inset Index idx
19082 \begin_layout Plain Layout
19084 \begin_inset IndexMacro subentry
19087 \begin_layout Plain Layout
19101 \begin_layout Standard
19109 \begin_inset Index idx
19114 \begin_layout Plain Layout
19116 \begin_inset IndexMacro subentry
19119 \begin_layout Plain Layout
19126 \begin_inset IndexMacro subentry
19129 \begin_layout Plain Layout
19149 \begin_inset Index idx
19154 \begin_layout Plain Layout
19156 \begin_inset IndexMacro subentry
19159 \begin_layout Plain Layout
19166 \begin_inset IndexMacro subentry
19169 \begin_layout Plain Layout
19182 characters can be placed above or below an operator respectively.
19190 \begin_inset Index idx
19195 \begin_layout Plain Layout
19197 \begin_inset IndexMacro subentry
19200 \begin_layout Plain Layout
19207 \begin_inset IndexMacro subentry
19210 \begin_layout Plain Layout
19223 characters can be set before and behind a big operator.
19226 \begin_layout Standard
19228 \begin_inset space ~
19240 \begin_layout Itemize
19247 is used to set characters at the corners of the operator
19250 \begin_layout Itemize
19257 is used to set characters before and/or behind the operator (this variant represents \SpecialChar LaTeX
19267 \begin_layout Itemize
19274 is used to set characters at the left corners and/or behind the operator
19277 \begin_layout Itemize
19284 is used to set characters at the right corners and/or before the operator
19287 \begin_layout Standard
19288 For example the command
19293 \begin_inset space \textvisiblespace{}
19299 \begin_inset space \textvisiblespace{}
19303 \begin_inset Formula $\to$
19307 \begin_inset Formula $\to$
19311 \begin_inset space \textvisiblespace{}
19321 \begin_inset Formula
19323 \sideset{}{'}\sum_{k=1}^{n}
19331 \begin_layout Standard
19332 \begin_inset Note Greyedout
19335 \begin_layout Plain Layout
19343 can only be used to decorate big operators,
19344 binary operators are not allowed.
19352 \begin_layout Standard
19365 can also be used to decorate symbols and characters.
19372 \begin_inset space \textvisiblespace{}
19378 \begin_inset space \textvisiblespace{}
19384 \begin_inset Formula $\uparrow$
19392 \begin_inset Formula
19394 \overset{a}{\maltese}
19402 \begin_layout Subsection
19404 \begin_inset CommandInset label
19406 name "subsec:Binary-Operators"
19411 \begin_inset Index idx
19416 \begin_layout Plain Layout
19418 \begin_inset IndexMacro subentry
19421 \begin_layout Plain Layout
19435 \begin_layout Standard
19436 Binary operators are surrounded by space when there is a character before and after them.
19437 \begin_inset VSpace medskip
19443 \begin_layout Standard
19444 \begin_inset Tabular
19445 <lyxtabular version="3" rows="13" columns="2">
19446 <features booktabs="true" tabularvalignment="middle">
19447 <column alignment="center" valignment="top" width="0pt">
19448 <column alignment="center" valignment="top" width="0pt">
19450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19453 \begin_layout Plain Layout
19455 \begin_inset Note Note
19458 \begin_layout Plain Layout
19465 is only used as spacer.
19475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19478 \begin_layout Plain Layout
19486 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19489 \begin_layout Plain Layout
19495 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19498 \begin_layout Plain Layout
19499 \begin_inset Formula $+$
19509 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19512 \begin_layout Plain Layout
19518 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19521 \begin_layout Plain Layout
19522 \begin_inset Formula $-$
19532 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19535 \begin_layout Plain Layout
19543 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19546 \begin_layout Plain Layout
19547 \begin_inset Formula $\pm$
19557 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19560 \begin_layout Plain Layout
19568 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19571 \begin_layout Plain Layout
19572 \begin_inset Formula $\mp$
19582 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19585 \begin_layout Plain Layout
19593 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19596 \begin_layout Plain Layout
19597 \begin_inset Formula $\cdot$
19607 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19610 \begin_layout Plain Layout
19618 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19621 \begin_layout Plain Layout
19622 \begin_inset Formula $\times$
19632 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19635 \begin_layout Plain Layout
19643 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19646 \begin_layout Plain Layout
19647 \begin_inset Formula $\div$
19657 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19660 \begin_layout Plain Layout
19664 \begin_layout Plain Layout
19677 \begin_layout Plain Layout
19689 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19692 \begin_layout Plain Layout
19693 \begin_inset Formula $*$
19703 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19706 \begin_layout Plain Layout
19714 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19717 \begin_layout Plain Layout
19718 \begin_inset Formula $\star$
19728 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19731 \begin_layout Plain Layout
19739 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19742 \begin_layout Plain Layout
19743 \begin_inset Formula $\circ$
19753 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19756 \begin_layout Plain Layout
19764 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19767 \begin_layout Plain Layout
19768 \begin_inset Formula $\diamond$
19778 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19781 \begin_layout Plain Layout
19789 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19792 \begin_layout Plain Layout
19793 \begin_inset Formula $\bullet$
19807 \begin_inset space \hfill{}
19811 \begin_inset Tabular
19812 <lyxtabular version="3" rows="13" columns="2">
19813 <features booktabs="true" tabularvalignment="middle">
19814 <column alignment="center" valignment="top" width="0pt">
19815 <column alignment="center" valignment="top" width="0pt">
19817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19820 \begin_layout Plain Layout
19826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19829 \begin_layout Plain Layout
19837 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19840 \begin_layout Plain Layout
19848 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19851 \begin_layout Plain Layout
19852 \begin_inset Formula $\nabla$
19862 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19865 \begin_layout Plain Layout
19873 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19876 \begin_layout Plain Layout
19877 \begin_inset Formula $\bigtriangledown$
19887 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19890 \begin_layout Plain Layout
19898 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19901 \begin_layout Plain Layout
19902 \begin_inset Formula $\bigtriangleup$
19912 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19915 \begin_layout Plain Layout
19923 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19926 \begin_layout Plain Layout
19927 \begin_inset Formula $\Box$
19937 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19940 \begin_layout Plain Layout
19948 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19951 \begin_layout Plain Layout
19952 \begin_inset Formula $\cap$
19962 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19965 \begin_layout Plain Layout
19973 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19976 \begin_layout Plain Layout
19977 \begin_inset Formula $\cup$
19987 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19990 \begin_layout Plain Layout
19998 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20001 \begin_layout Plain Layout
20002 \begin_inset Formula $\dagger$
20012 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20015 \begin_layout Plain Layout
20023 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20026 \begin_layout Plain Layout
20027 \begin_inset Formula $\ddagger$
20037 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20040 \begin_layout Plain Layout
20048 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20051 \begin_layout Plain Layout
20052 \begin_inset Formula $\wr$
20062 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20065 \begin_layout Plain Layout
20073 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20076 \begin_layout Plain Layout
20077 \begin_inset Formula $\bigcirc$
20087 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20090 \begin_layout Plain Layout
20098 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20101 \begin_layout Plain Layout
20102 \begin_inset Formula $\wedge$
20112 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20115 \begin_layout Plain Layout
20123 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20126 \begin_layout Plain Layout
20127 \begin_inset Formula $\vee$
20141 \begin_inset space \hfill{}
20145 \begin_inset Tabular
20146 <lyxtabular version="3" rows="13" columns="2">
20147 <features booktabs="true" tabularvalignment="middle">
20148 <column alignment="center" valignment="top" width="0pt">
20149 <column alignment="center" valignment="top" width="0pt">
20151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20154 \begin_layout Plain Layout
20160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20163 \begin_layout Plain Layout
20171 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20174 \begin_layout Plain Layout
20182 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20185 \begin_layout Plain Layout
20186 \begin_inset Formula $\oplus$
20196 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20199 \begin_layout Plain Layout
20207 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20210 \begin_layout Plain Layout
20211 \begin_inset Formula $\ominus$
20221 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20224 \begin_layout Plain Layout
20232 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20235 \begin_layout Plain Layout
20236 \begin_inset Formula $\otimes$
20246 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20249 \begin_layout Plain Layout
20257 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20260 \begin_layout Plain Layout
20261 \begin_inset Formula $\oslash$
20271 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20274 \begin_layout Plain Layout
20282 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20285 \begin_layout Plain Layout
20286 \begin_inset Formula $\odot$
20296 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20299 \begin_layout Plain Layout
20307 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20310 \begin_layout Plain Layout
20311 \begin_inset Formula $\amalg$
20321 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20324 \begin_layout Plain Layout
20332 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20335 \begin_layout Plain Layout
20336 \begin_inset Formula $\uplus$
20346 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20349 \begin_layout Plain Layout
20357 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20360 \begin_layout Plain Layout
20361 \begin_inset Formula $\setminus$
20371 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20374 \begin_layout Plain Layout
20382 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20385 \begin_layout Plain Layout
20386 \begin_inset Formula $\sqcap$
20396 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20399 \begin_layout Plain Layout
20407 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20410 \begin_layout Plain Layout
20411 \begin_inset Formula $\sqcup$
20421 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20424 \begin_layout Plain Layout
20432 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20435 \begin_layout Plain Layout
20436 \begin_inset Formula $\triangleleft$
20446 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20449 \begin_layout Plain Layout
20457 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20460 \begin_layout Plain Layout
20461 \begin_inset Formula $\triangleright$
20477 \begin_layout Standard
20478 All binary operators can also be inserted via the math toolbar button
20481 arg "math-insert \\pm"
20487 \begin_layout Standard
20488 To typeset the Laplace operator,
20506 \begin_inset Formula $\nabla^{2}$
20509 ) can also be used instead of
20518 \begin_layout Standard
20525 Insert\SpecialChar menuseparator
20537 \begin_layout Subsection
20538 Self-defined Operators
20539 \begin_inset CommandInset label
20541 name "subsec:Self-defined-Operators"
20546 \begin_inset Index idx
20551 \begin_layout Plain Layout
20553 \begin_inset IndexMacro subentry
20556 \begin_layout Plain Layout
20570 \begin_layout Standard
20571 With the help of the command
20575 DeclareMathOperator
20578 \begin_inset Index idx
20583 \begin_layout Plain Layout
20585 \begin_inset IndexMacro subentry
20588 \begin_layout Plain Layout
20595 \begin_inset IndexMacro subentry
20598 \begin_layout Plain Layout
20599 \begin_inset IndexMacro sortkey
20602 \begin_layout Plain Layout
20612 DeclareMathOperator
20623 custom operators can be defined in the \SpecialChar LaTeX
20625 Its command scheme is:
20628 \begin_layout Standard
20633 DeclareMathOperator{new command}{display}
20636 \begin_layout Standard
20637 Display can be characters or symbols that define how the operator looks in the output.
20638 To define a big operator a * is set behind the command.
20639 All self-defined big operators can have limits as described in
20640 \begin_inset CommandInset ref
20642 reference "subsec:Operator-Limits"
20650 \begin_layout Standard
20651 For example the \SpecialChar LaTeX
20655 \begin_layout Standard
20660 DeclareMathOperator*{
20667 \begin_layout Standard
20668 defines the command
20675 that inserts a big operator consisting of the black lozenge symbol from
20676 \begin_inset CommandInset ref
20678 reference "subsec:Miscellaneous-Symbols"
20684 \begin_inset Formula
20686 \Lozenge_{n=1}^{\infty}
20691 The command for this formula is:
20703 \begin_inset Formula $\to$
20709 \begin_layout Standard
20710 \begin_inset VSpace bigskip
20713 When self-defined operators are not used several times in the document,
20714 they can also be defined with the commands
20721 \begin_inset Index idx
20726 \begin_layout Plain Layout
20728 \begin_inset IndexMacro subentry
20731 \begin_layout Plain Layout
20738 \begin_inset IndexMacro subentry
20741 \begin_layout Plain Layout
20761 \begin_inset Index idx
20766 \begin_layout Plain Layout
20768 \begin_inset IndexMacro subentry
20771 \begin_layout Plain Layout
20778 \begin_inset IndexMacro subentry
20781 \begin_layout Plain Layout
20795 which have the following scheme:
20798 \begin_layout Standard
20812 \begin_layout Standard
20819 defines big operators,
20829 \begin_layout Standard
20836 can be used to use one limit for several operators:
20839 \begin_layout Standard
20840 \begin_inset Formula
20842 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
20850 \begin_layout Standard
20851 The command for the formula above is:
20852 \begin_inset Newline newline
20868 \begin_inset space \textvisiblespace{}
20874 \begin_inset Formula $\to$
20880 \begin_inset space \textvisiblespace{}
20888 \begin_layout Section
20890 \begin_inset Index idx
20895 \begin_layout Plain Layout
20904 \begin_layout Subsection
20906 \begin_inset CommandInset label
20908 name "subsec:Font-Styles"
20913 \begin_inset Index idx
20918 \begin_layout Plain Layout
20920 \begin_inset IndexMacro subentry
20923 \begin_layout Plain Layout
20937 \begin_layout Standard
20938 Latin letters in formulas can be set in one of the following font styles:
20941 \begin_layout Standard
20943 \begin_inset Tabular
20944 <lyxtabular version="3" rows="6" columns="3">
20945 <features booktabs="true" tabularvalignment="middle">
20946 <column alignment="center" valignment="top" width="0pt">
20947 <column alignment="center" valignment="top">
20948 <column alignment="center" valignment="top">
20950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20953 \begin_layout Plain Layout
20959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20962 \begin_layout Plain Layout
20968 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
20971 \begin_layout Plain Layout
20979 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20982 \begin_layout Plain Layout
20988 \begin_inset space \textvisiblespace{}
20998 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21001 \begin_layout Plain Layout
21002 \begin_inset Formula $\mathbb{ABC}$
21010 <cell alignment="center" valignment="top" usebox="none">
21013 \begin_layout Plain Layout
21021 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21024 \begin_layout Plain Layout
21030 \begin_inset space \textvisiblespace{}
21040 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21043 \begin_layout Plain Layout
21044 \begin_inset Formula $\mathbf{AbC}$
21052 <cell alignment="center" valignment="top" usebox="none">
21055 \begin_layout Plain Layout
21068 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21071 \begin_layout Plain Layout
21077 \begin_inset space \textvisiblespace{}
21087 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21090 \begin_layout Plain Layout
21091 \begin_inset Formula $\boldsymbol{AbC}$
21099 <cell alignment="center" valignment="top" usebox="none">
21102 \begin_layout Plain Layout
21105 arg "font-boldsymbol"
21115 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21118 \begin_layout Plain Layout
21124 \begin_inset space \textvisiblespace{}
21134 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21137 \begin_layout Plain Layout
21138 \begin_inset Formula $\mathcal{ABC}$
21146 <cell alignment="center" valignment="top" usebox="none">
21149 \begin_layout Plain Layout
21157 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21160 \begin_layout Plain Layout
21166 \begin_inset space \textvisiblespace{}
21176 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21179 \begin_layout Plain Layout
21180 \begin_inset Formula $\mathfrak{AbC}$
21188 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
21191 \begin_layout Plain Layout
21205 \begin_layout Standard
21207 \begin_inset Tabular
21208 <lyxtabular version="3" rows="6" columns="3">
21209 <features booktabs="true" tabularvalignment="middle">
21210 <column alignment="center" valignment="top" width="0pt">
21211 <column alignment="center" valignment="top">
21212 <column alignment="center" valignment="top">
21214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21217 \begin_layout Plain Layout
21223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21226 \begin_layout Plain Layout
21232 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
21235 \begin_layout Plain Layout
21243 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21246 \begin_layout Plain Layout
21252 \begin_inset space \textvisiblespace{}
21262 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21265 \begin_layout Plain Layout
21266 \begin_inset Formula $\mathit{AbC}$
21274 <cell alignment="center" valignment="top" usebox="none">
21277 \begin_layout Plain Layout
21285 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21288 \begin_layout Plain Layout
21294 \begin_inset space \textvisiblespace{}
21304 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21307 \begin_layout Plain Layout
21308 \begin_inset Formula $\mathrm{AbC}$
21316 <cell alignment="center" valignment="top" usebox="none">
21319 \begin_layout Plain Layout
21332 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21335 \begin_layout Plain Layout
21341 \begin_inset space \textvisiblespace{}
21351 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21354 \begin_layout Plain Layout
21355 \begin_inset Formula $\mathsf{AbC}$
21363 <cell alignment="center" valignment="top" usebox="none">
21366 \begin_layout Plain Layout
21379 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21382 \begin_layout Plain Layout
21388 \begin_inset space \textvisiblespace{}
21398 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21401 \begin_layout Plain Layout
21402 \begin_inset Formula $\mathtt{AbC}$
21410 <cell alignment="center" valignment="top" usebox="none">
21413 \begin_layout Plain Layout
21416 arg "font-typewriter"
21426 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21429 \begin_layout Plain Layout
21435 \begin_inset space \textvisiblespace{}
21445 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21448 \begin_layout Plain Layout
21449 \begin_inset Formula $\mathscr{ABC}$
21457 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
21460 \begin_layout Plain Layout
21474 \begin_layout Standard
21475 \begin_inset Note Greyedout
21478 \begin_layout Plain Layout
21503 can only be used for big letters.
21511 \begin_layout Standard
21521 \begin_layout Standard
21522 The style commands also work for letters in mathematical constructs:
21523 \begin_inset Formula
21525 \mathfrak{A=\frac{b}{C}}
21533 \begin_layout Standard
21534 Characters in mathematical text don't appear in a math font style but in the text font style
21541 Note that their style can't be set correctly via the text style dialog.
21542 This is a known bug in \SpecialChar LyX
21547 \begin_layout Plain Layout
21548 \begin_inset CommandInset href
21550 name "LyX-bug #4629"
21551 target "https://www.lyx.org/trac/ticket/4629"
21564 \begin_layout Standard
21565 Instead of the style commands,
21568 Edit\SpecialChar menuseparator
21569 Math\SpecialChar menuseparator
21573 or the toolbar button,
21577 arg "math-insert \\font"
21583 \begin_layout Subsection
21585 \begin_inset CommandInset label
21587 name "subsec:Bold-Formulas"
21592 \begin_inset Index idx
21597 \begin_layout Plain Layout
21599 \begin_inset IndexMacro subentry
21602 \begin_layout Plain Layout
21616 \begin_layout Standard
21617 To make a complete formula bold,
21624 from the previous subsection cannot be used because it doesn't work for small Greek letters.
21625 Additionally it always prints Latin letters upright,
21626 as in the following equation:
21629 \begin_layout Standard
21630 \begin_inset Formula
21632 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
21640 \begin_layout Standard
21641 To display the formula correctly,
21649 \begin_inset Formula
21651 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
21656 It is also possible to set the formula in a
21658 boldmath environment
21661 This environment is created by inserting the command
21668 \begin_inset Index idx
21673 \begin_layout Plain Layout
21675 \begin_inset IndexMacro subentry
21678 \begin_layout Plain Layout
21685 \begin_inset IndexMacro subentry
21688 \begin_layout Plain Layout
21701 in \SpecialChar TeX
21703 To end the environment,
21711 \begin_inset Index idx
21716 \begin_layout Plain Layout
21718 \begin_inset IndexMacro subentry
21721 \begin_layout Plain Layout
21728 \begin_inset IndexMacro subentry
21731 \begin_layout Plain Layout
21744 is inserted in \SpecialChar TeX
21749 \begin_layout Plain Layout
21759 \begin_inset Formula
21761 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
21770 \begin_layout Plain Layout
21782 \begin_layout Subsection
21784 \begin_inset Index idx
21789 \begin_layout Plain Layout
21791 \begin_inset IndexMacro subentry
21794 \begin_layout Plain Layout
21808 \begin_layout Standard
21809 Formulas can be colored like normal text:
21810 Highlight a formula or a formula part and use the
21815 Here is a formula in magenta:
21816 \begin_inset Formula
21818 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
21826 \begin_layout Standard
21827 You can also define your own colors as described in
21828 \begin_inset CommandInset ref
21830 reference "subsec:Colored-Boxes"
21836 They can be used with the \SpecialChar TeX
21844 \begin_inset Index idx
21849 \begin_layout Plain Layout
21851 \begin_inset IndexMacro subentry
21854 \begin_layout Plain Layout
21861 \begin_inset IndexMacro subentry
21864 \begin_layout Plain Layout
21880 \begin_layout Standard
21885 textcolor{color}{characters or formula}
21888 \begin_layout Standard
21889 The following example was colored completely dark green and partly red:
21892 \begin_layout Standard
21896 \begin_layout Plain Layout
21900 textcolor{darkgreen}{
21906 \begin_inset Formula
21908 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
21917 \begin_layout Plain Layout
21927 \begin_layout Standard
21928 Due to a bug in \SpecialChar LyX
21929 only complete formulas can be colored with self-defined colors.
21933 \begin_layout Plain Layout
21934 \begin_inset CommandInset href
21936 name "LyX-bug #5269"
21937 target "https://www.lyx.org/trac/ticket/5269"
21950 \begin_layout Subsection
21952 \begin_inset CommandInset label
21954 name "subsec:Font-Sizes"
21959 \begin_inset Index idx
21964 \begin_layout Plain Layout
21966 \begin_inset IndexMacro subentry
21969 \begin_layout Plain Layout
21983 \begin_layout Standard
21984 As with characters in text,
21985 the following size commands are available for formula characters:
21988 \begin_layout Standard
22038 \begin_inset Newline newline
22061 \begin_layout Standard
22062 The font size produced by the commands depends on the document's original font size,
22063 which corresponds to the command
22070 The other commands produce character sizes smaller or larger than
22077 There are however limits to how small or large the font size can be changed.
22078 If for example the document font size is 12
22079 \begin_inset space \thinspace{}
22089 switches to the same size as
22098 \begin_layout Standard
22099 A size command is inserted in \SpecialChar TeX
22100 mode before a formula and sets the size for all of the following formulas and text characters.
22101 To switch back to the initial size,
22108 is inserted behind the formula,
22109 again in \SpecialChar TeX
22113 \begin_layout Standard
22114 Size can also be changed within a formula using the following size commands or the toolbar button
22117 arg "math-insert \\style"
22123 \begin_layout Standard
22126 \begin_inset Tabular
22127 <lyxtabular version="3" rows="5" columns="2">
22128 <features booktabs="true" tabularvalignment="middle">
22129 <column alignment="center" valignment="top" width="0pt">
22130 <column alignment="center" valignment="top">
22132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22135 \begin_layout Plain Layout
22141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22144 \begin_layout Plain Layout
22152 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22155 \begin_layout Plain Layout
22159 \begin_inset Index idx
22164 \begin_layout Plain Layout
22166 \begin_inset IndexMacro subentry
22169 \begin_layout Plain Layout
22176 \begin_inset IndexMacro subentry
22179 \begin_layout Plain Layout
22197 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22200 \begin_layout Plain Layout
22201 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
22210 <row topspace="1mm">
22211 <cell alignment="center" valignment="top" usebox="none">
22214 \begin_layout Plain Layout
22222 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22225 \begin_layout Plain Layout
22226 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
22236 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22239 \begin_layout Plain Layout
22247 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22250 \begin_layout Plain Layout
22251 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
22261 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22264 \begin_layout Plain Layout
22272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22275 \begin_layout Plain Layout
22276 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
22292 \begin_layout Standard
22293 After entering these commands,
22294 a blue box appears in which the formula parts are inserted.
22297 \begin_layout Standard
22298 There is another method for changing the font size,
22299 although it only works for symbols or letters in mathematical text.
22301 one of the above text size commands is inserted into mathematical text.
22302 All characters until the end of the mathematical text or until another size command will have the selected size.
22304 \begin_inset VSpace -2mm
22310 \begin_layout Standard
22314 \begin_layout Plain Layout
22324 \begin_inset Formula
22326 A=\frac{B}{c}\cdot\maltese
22332 \begin_inset Formula
22334 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
22343 \begin_layout Plain Layout
22353 \begin_inset VSpace medskip
22356 Before the first formula the command
22363 The command for the second formula is:
22364 \begin_inset Newline newline
22372 \begin_inset space \textvisiblespace{}
22378 \begin_inset space \textvisiblespace{}
22384 \begin_inset space \textvisiblespace{}
22390 \begin_inset space \textvisiblespace{}
22394 \begin_inset Formula $\to$
22398 \begin_inset Formula $\to$
22402 \begin_inset Newline newline
22406 \begin_inset space \hspace*{}
22417 \begin_inset space \textvisiblespace{}
22423 \begin_inset space \textvisiblespace{}
22429 \begin_inset space \textvisiblespace{}
22435 \begin_layout Standard
22436 If a symbol cannot be displayed in different sizes,
22437 it will always be displayed in the default size.
22440 \begin_layout Section
22442 \begin_inset Index idx
22447 \begin_layout Plain Layout
22456 \begin_layout Standard
22457 Greek letters can be inserted via the toolbar button
22460 arg "math-insert \\alpha"
22463 as well as by command.
22464 All international typesetting norms purport that Greek letters in math have to be typeset italic/slanted.
22466 like French or Russian,
22467 they are nevertheless sometimes typeset upright.
22470 \begin_layout Subsection
22472 \begin_inset Index idx
22477 \begin_layout Plain Layout
22479 \begin_inset IndexMacro subentry
22482 \begin_layout Plain Layout
22496 \begin_layout Standard
22497 \begin_inset space \hfill{}
22501 \begin_inset Tabular
22502 <lyxtabular version="3" rows="11" columns="2">
22503 <features booktabs="true" tabularvalignment="middle">
22504 <column alignment="center" valignment="top" width="0pt">
22505 <column alignment="center" valignment="top" width="0pt">
22507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22510 \begin_layout Plain Layout
22516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22519 \begin_layout Plain Layout
22527 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22530 \begin_layout Plain Layout
22538 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22541 \begin_layout Plain Layout
22542 \begin_inset Formula $\alpha$
22552 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22555 \begin_layout Plain Layout
22563 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22566 \begin_layout Plain Layout
22567 \begin_inset Formula $\beta$
22577 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22580 \begin_layout Plain Layout
22588 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22591 \begin_layout Plain Layout
22592 \begin_inset Formula $\gamma$
22602 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22605 \begin_layout Plain Layout
22613 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22616 \begin_layout Plain Layout
22617 \begin_inset Formula $\delta$
22627 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22630 \begin_layout Plain Layout
22638 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22641 \begin_layout Plain Layout
22642 \begin_inset Formula $\epsilon$
22652 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22655 \begin_layout Plain Layout
22663 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22666 \begin_layout Plain Layout
22667 \begin_inset Formula $\varepsilon$
22677 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22680 \begin_layout Plain Layout
22688 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22691 \begin_layout Plain Layout
22692 \begin_inset Formula $\zeta$
22702 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22705 \begin_layout Plain Layout
22713 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22716 \begin_layout Plain Layout
22717 \begin_inset Formula $\eta$
22727 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22730 \begin_layout Plain Layout
22738 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22741 \begin_layout Plain Layout
22742 \begin_inset Formula $\theta$
22752 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22755 \begin_layout Plain Layout
22763 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22766 \begin_layout Plain Layout
22767 \begin_inset Formula $\vartheta$
22781 \begin_inset space \hfill{}
22785 \begin_inset Tabular
22786 <lyxtabular version="3" rows="12" columns="2">
22787 <features booktabs="true" tabularvalignment="middle">
22788 <column alignment="center" valignment="top" width="0pt">
22789 <column alignment="center" valignment="top" width="0pt">
22791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22794 \begin_layout Plain Layout
22800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22803 \begin_layout Plain Layout
22811 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22814 \begin_layout Plain Layout
22822 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22825 \begin_layout Plain Layout
22826 \begin_inset Formula $\iota$
22836 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22839 \begin_layout Plain Layout
22847 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22850 \begin_layout Plain Layout
22851 \begin_inset Formula $\kappa$
22861 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22864 \begin_layout Plain Layout
22872 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22875 \begin_layout Plain Layout
22876 \begin_inset Formula $\varkappa$
22886 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22889 \begin_layout Plain Layout
22897 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22900 \begin_layout Plain Layout
22901 \begin_inset Formula $\lambda$
22911 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22914 \begin_layout Plain Layout
22922 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22925 \begin_layout Plain Layout
22926 \begin_inset Formula $\mu$
22936 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22939 \begin_layout Plain Layout
22947 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22950 \begin_layout Plain Layout
22951 \begin_inset Formula $\nu$
22961 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22964 \begin_layout Plain Layout
22972 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22975 \begin_layout Plain Layout
22976 \begin_inset Formula $\xi$
22986 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22989 \begin_layout Plain Layout
22995 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22998 \begin_layout Plain Layout
22999 \begin_inset Formula $o$
23009 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23012 \begin_layout Plain Layout
23020 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23023 \begin_layout Plain Layout
23024 \begin_inset Formula $\pi$
23034 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23037 \begin_layout Plain Layout
23045 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23048 \begin_layout Plain Layout
23049 \begin_inset Formula $\varpi$
23059 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23062 \begin_layout Plain Layout
23070 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23073 \begin_layout Plain Layout
23074 \begin_inset Formula $\rho$
23088 \begin_inset space \hfill{}
23092 \begin_inset Tabular
23093 <lyxtabular version="3" rows="11" columns="2">
23094 <features booktabs="true" tabularvalignment="middle">
23095 <column alignment="center" valignment="top" width="0pt">
23096 <column alignment="center" valignment="top" width="0pt">
23098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23101 \begin_layout Plain Layout
23107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23110 \begin_layout Plain Layout
23118 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23121 \begin_layout Plain Layout
23129 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23132 \begin_layout Plain Layout
23133 \begin_inset Formula $\varrho$
23143 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23146 \begin_layout Plain Layout
23154 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23157 \begin_layout Plain Layout
23158 \begin_inset Formula $\sigma$
23168 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23171 \begin_layout Plain Layout
23179 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23182 \begin_layout Plain Layout
23183 \begin_inset Formula $\varsigma$
23193 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23196 \begin_layout Plain Layout
23204 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23207 \begin_layout Plain Layout
23208 \begin_inset Formula $\tau$
23218 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23221 \begin_layout Plain Layout
23229 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23232 \begin_layout Plain Layout
23233 \begin_inset Formula $\upsilon$
23243 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23246 \begin_layout Plain Layout
23254 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23257 \begin_layout Plain Layout
23258 \begin_inset Formula $\phi$
23268 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23271 \begin_layout Plain Layout
23279 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23282 \begin_layout Plain Layout
23283 \begin_inset Formula $\varphi$
23293 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23296 \begin_layout Plain Layout
23304 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23307 \begin_layout Plain Layout
23308 \begin_inset Formula $\chi$
23318 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23321 \begin_layout Plain Layout
23329 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23332 \begin_layout Plain Layout
23333 \begin_inset Formula $\psi$
23343 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23346 \begin_layout Plain Layout
23354 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23357 \begin_layout Plain Layout
23358 \begin_inset Formula $\omega$
23372 \begin_inset space \hfill{}
23378 \begin_layout Standard
23379 \begin_inset VSpace medskip
23385 \begin_layout Standard
23386 Creating upright Greek letters is explained in
23387 \begin_inset CommandInset ref
23389 reference "subsec:Upright-small-Greek"
23397 \begin_layout Subsection
23399 \begin_inset Index idx
23404 \begin_layout Plain Layout
23406 \begin_inset IndexMacro subentry
23409 \begin_layout Plain Layout
23423 \begin_layout Standard
23424 \begin_inset space \hfill{}
23428 \begin_inset Tabular
23429 <lyxtabular version="3" rows="7" columns="2">
23430 <features booktabs="true" tabularvalignment="middle">
23431 <column alignment="center" valignment="top" width="0pt">
23432 <column alignment="center" valignment="top" width="0pt">
23434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23437 \begin_layout Plain Layout
23443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23446 \begin_layout Plain Layout
23454 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23457 \begin_layout Plain Layout
23465 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23468 \begin_layout Plain Layout
23469 \begin_inset Formula $\Gamma$
23479 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23482 \begin_layout Plain Layout
23490 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23493 \begin_layout Plain Layout
23494 \begin_inset Formula $\Delta$
23504 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23507 \begin_layout Plain Layout
23515 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23518 \begin_layout Plain Layout
23519 \begin_inset Formula $\Theta$
23529 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23532 \begin_layout Plain Layout
23540 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23543 \begin_layout Plain Layout
23544 \begin_inset Formula $\Lambda$
23554 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23557 \begin_layout Plain Layout
23565 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23568 \begin_layout Plain Layout
23569 \begin_inset Formula $\Xi$
23579 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23582 \begin_layout Plain Layout
23590 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23593 \begin_layout Plain Layout
23594 \begin_inset Formula $\Pi$
23608 \begin_inset space \hfill{}
23612 \begin_inset Tabular
23613 <lyxtabular version="3" rows="6" columns="2">
23614 <features booktabs="true" tabularvalignment="middle">
23615 <column alignment="center" valignment="top" width="0pt">
23616 <column alignment="center" valignment="top" width="0pt">
23618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23621 \begin_layout Plain Layout
23627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23630 \begin_layout Plain Layout
23638 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23641 \begin_layout Plain Layout
23649 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23652 \begin_layout Plain Layout
23653 \begin_inset Formula $\Sigma$
23663 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23666 \begin_layout Plain Layout
23674 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23677 \begin_layout Plain Layout
23678 \begin_inset Formula $\Upsilon$
23688 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23691 \begin_layout Plain Layout
23699 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23702 \begin_layout Plain Layout
23703 \begin_inset Formula $\Phi$
23713 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23716 \begin_layout Plain Layout
23724 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23727 \begin_layout Plain Layout
23728 \begin_inset Formula $\Psi$
23738 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23741 \begin_layout Plain Layout
23749 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23752 \begin_layout Plain Layout
23753 \begin_inset Formula $\Omega$
23767 \begin_inset space \hfill{}
23773 \begin_layout Standard
23774 \begin_inset VSpace medskip
23777 The big Greek letters appearing upright is caused by a design bug in \SpecialChar TeX
23779 To create correct italic big letters,
23780 begin every command with
23785 For example the command
23792 \begin_inset Formula $\varGamma$
23796 Another way is to load the package
23804 \begin_layout Plain Layout
23809 is part of the \SpecialChar LaTeX
23815 \begin_inset Index idx
23820 \begin_layout Plain Layout
23822 \begin_inset IndexMacro subentry
23825 \begin_layout Plain Layout
23842 \begin_inset Index idx
23847 \begin_layout Plain Layout
23849 \begin_inset IndexMacro subentry
23852 \begin_layout Plain Layout
23863 with the \SpecialChar LaTeX
23867 \begin_layout Standard
23872 usepackage{fixmath}
23875 \begin_layout Standard
23876 Then all big Greek letters in a document will automatically be typeset italic.
23879 \begin_layout Subsection
23881 \begin_inset Index idx
23886 \begin_layout Plain Layout
23888 \begin_inset IndexMacro subentry
23891 \begin_layout Plain Layout
23905 \begin_layout Standard
23906 Greek letters cannot be set with different font styles like Latin letters.
23907 They can only be made bold with the command
23914 \begin_inset Index idx
23919 \begin_layout Plain Layout
23921 \begin_inset IndexMacro subentry
23924 \begin_layout Plain Layout
23931 \begin_inset IndexMacro subentry
23934 \begin_layout Plain Layout
23950 \begin_layout Standard
23952 \begin_inset Tabular
23953 <lyxtabular version="3" rows="3" columns="2">
23954 <features booktabs="true" tabularvalignment="middle">
23955 <column alignment="center" valignment="top" width="0pt">
23956 <column alignment="center" valignment="top">
23958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23961 \begin_layout Plain Layout
23967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23970 \begin_layout Plain Layout
23978 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23981 \begin_layout Plain Layout
23993 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23996 \begin_layout Plain Layout
23997 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
24007 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24010 \begin_layout Plain Layout
24022 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24025 \begin_layout Plain Layout
24026 \begin_inset Formula $\theta\boldsymbol{\theta}$
24042 \begin_layout Section
24047 \begin_layout Plain Layout
24060 \begin_layout Plain Layout
24061 A list with all symbols of most of the \SpecialChar LaTeX
24062 -packages can be found in
24063 \begin_inset CommandInset citation
24079 \begin_layout Plain Layout
24087 \begin_inset Note Note
24090 \begin_layout Plain Layout
24093 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
24096 \begin_layout Plain Layout
24099 texorpdfstring is in section
24100 \begin_inset CommandInset ref
24102 reference "subsec:Formulas-in-Section"
24113 \begin_inset Index idx
24118 \begin_layout Plain Layout
24127 \begin_layout Standard
24128 Many of the symbols listed in this section can also be inserted via the toolbar buttons
24131 arg "math-insert \\nabla"
24137 arg "math-insert \\digamma"
24143 \begin_layout Subsection
24144 Mathematical Symbols
24145 \begin_inset CommandInset label
24147 name "subsec:Mathematical-Symbols"
24152 \begin_inset Index idx
24157 \begin_layout Plain Layout
24159 \begin_inset IndexMacro subentry
24162 \begin_layout Plain Layout
24176 \begin_layout Standard
24177 \begin_inset Tabular
24178 <lyxtabular version="3" rows="10" columns="2">
24179 <features booktabs="true" tabularvalignment="middle">
24180 <column alignment="center" valignment="top" width="0pt">
24181 <column alignment="center" valignment="top" width="0pt">
24183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24186 \begin_layout Plain Layout
24192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24195 \begin_layout Plain Layout
24203 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24206 \begin_layout Plain Layout
24214 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24217 \begin_layout Plain Layout
24218 \begin_inset Formula $\neg$
24228 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24231 \begin_layout Plain Layout
24239 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24242 \begin_layout Plain Layout
24243 \begin_inset Formula $\Im$
24253 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24256 \begin_layout Plain Layout
24264 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24267 \begin_layout Plain Layout
24268 \begin_inset Formula $\Re$
24278 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24281 \begin_layout Plain Layout
24289 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24292 \begin_layout Plain Layout
24293 \begin_inset Formula $\aleph$
24303 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24306 \begin_layout Plain Layout
24314 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24317 \begin_layout Plain Layout
24318 \begin_inset Formula $\partial$
24328 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24331 \begin_layout Plain Layout
24339 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24342 \begin_layout Plain Layout
24343 \begin_inset Formula $\infty$
24353 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24356 \begin_layout Plain Layout
24364 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24367 \begin_layout Plain Layout
24368 \begin_inset Formula $\wp$
24378 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24381 \begin_layout Plain Layout
24389 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24392 \begin_layout Plain Layout
24393 \begin_inset Formula $\imath$
24403 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24406 \begin_layout Plain Layout
24414 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24417 \begin_layout Plain Layout
24418 \begin_inset Formula $\jmath$
24432 \begin_inset space \hfill{}
24436 \begin_inset Tabular
24437 <lyxtabular version="3" rows="10" columns="2">
24438 <features booktabs="true" tabularvalignment="middle">
24439 <column alignment="center" valignment="top" width="0pt">
24440 <column alignment="center" valignment="top" width="0pt">
24442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24445 \begin_layout Plain Layout
24451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24454 \begin_layout Plain Layout
24456 \begin_inset Note Note
24459 \begin_layout Plain Layout
24466 is only used as spacer.
24478 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24481 \begin_layout Plain Layout
24489 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24492 \begin_layout Plain Layout
24493 \begin_inset Formula $\forall$
24503 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24506 \begin_layout Plain Layout
24514 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24517 \begin_layout Plain Layout
24518 \begin_inset Formula $\exists$
24528 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24531 \begin_layout Plain Layout
24539 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24542 \begin_layout Plain Layout
24543 \begin_inset Formula $\nexists$
24553 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24556 \begin_layout Plain Layout
24564 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24567 \begin_layout Plain Layout
24568 \begin_inset Formula $\emptyset$
24578 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24581 \begin_layout Plain Layout
24589 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24592 \begin_layout Plain Layout
24593 \begin_inset Formula $\varnothing$
24603 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24606 \begin_layout Plain Layout
24614 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24617 \begin_layout Plain Layout
24618 \begin_inset Formula $\dag$
24628 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24631 \begin_layout Plain Layout
24639 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24642 \begin_layout Plain Layout
24643 \begin_inset Formula $\ddag$
24653 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24656 \begin_layout Plain Layout
24664 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24667 \begin_layout Plain Layout
24671 \begin_layout Plain Layout
24681 \begin_inset Formula $\complement$
24688 \begin_layout Plain Layout
24702 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24705 \begin_layout Plain Layout
24713 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24716 \begin_layout Plain Layout
24717 \begin_inset Formula $\Bbbk$
24731 \begin_inset space \hfill{}
24735 \begin_inset Tabular
24736 <lyxtabular version="3" rows="10" columns="2">
24737 <features booktabs="true" tabularvalignment="middle">
24738 <column alignment="center" valignment="top" width="0pt">
24739 <column alignment="center" valignment="top" width="0pt">
24741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24744 \begin_layout Plain Layout
24750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24753 \begin_layout Plain Layout
24761 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24764 \begin_layout Plain Layout
24772 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24775 \begin_layout Plain Layout
24776 \begin_inset Formula $\prime$
24786 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24789 \begin_layout Plain Layout
24797 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24800 \begin_layout Plain Layout
24801 \begin_inset Formula $\backprime$
24811 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24814 \begin_layout Plain Layout
24822 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24825 \begin_layout Plain Layout
24826 \begin_inset Formula $\mho$
24836 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24839 \begin_layout Plain Layout
24847 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24850 \begin_layout Plain Layout
24851 \begin_inset Formula $\triangle$
24861 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24864 \begin_layout Plain Layout
24872 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24875 \begin_layout Plain Layout
24876 \begin_inset Formula $\angle$
24886 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24889 \begin_layout Plain Layout
24897 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24900 \begin_layout Plain Layout
24901 \begin_inset Formula $\measuredangle$
24911 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24914 \begin_layout Plain Layout
24922 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24925 \begin_layout Plain Layout
24926 \begin_inset Formula $\sphericalangle$
24936 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24939 \begin_layout Plain Layout
24947 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24950 \begin_layout Plain Layout
24951 \begin_inset Formula $\top$
24961 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24964 \begin_layout Plain Layout
24972 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24975 \begin_layout Plain Layout
24976 \begin_inset Formula $\bot$
24992 \begin_layout Subsection
24993 Miscellaneous Symbols
24994 \begin_inset CommandInset label
24996 name "subsec:Miscellaneous-Symbols"
25001 \begin_inset Index idx
25006 \begin_layout Plain Layout
25008 \begin_inset IndexMacro subentry
25011 \begin_layout Plain Layout
25025 \begin_layout Standard
25028 \begin_inset Tabular
25029 <lyxtabular version="3" rows="10" columns="2">
25030 <features booktabs="true" tabularvalignment="middle">
25031 <column alignment="center" valignment="top" width="0pt">
25032 <column alignment="center" valignment="top" width="0pt">
25034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25037 \begin_layout Plain Layout
25043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25046 \begin_layout Plain Layout
25054 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25057 \begin_layout Plain Layout
25065 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25068 \begin_layout Plain Layout
25069 \begin_inset Formula $\flat$
25079 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25082 \begin_layout Plain Layout
25090 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25093 \begin_layout Plain Layout
25094 \begin_inset Formula $\natural$
25104 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25107 \begin_layout Plain Layout
25115 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25118 \begin_layout Plain Layout
25119 \begin_inset Formula $\sharp$
25129 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25132 \begin_layout Plain Layout
25140 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25143 \begin_layout Plain Layout
25144 \begin_inset Formula $\surd$
25154 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25157 \begin_layout Plain Layout
25165 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25168 \begin_layout Plain Layout
25169 \begin_inset Formula $\checkmark$
25179 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25182 \begin_layout Plain Layout
25190 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25193 \begin_layout Plain Layout
25194 \begin_inset Formula $\yen$
25204 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25207 \begin_layout Plain Layout
25215 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25218 \begin_layout Plain Layout
25219 \begin_inset Formula $\pounds$
25229 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25232 \begin_layout Plain Layout
25238 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25241 \begin_layout Plain Layout
25242 \begin_inset Formula $\$$
25252 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25255 \begin_layout Plain Layout
25261 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25264 \begin_layout Plain Layout
25265 \begin_inset Formula $§$
25279 \begin_inset space \hfill{}
25283 \begin_inset Tabular
25284 <lyxtabular version="3" rows="10" columns="2">
25285 <features booktabs="true" tabularvalignment="middle">
25286 <column alignment="center" valignment="top" width="0pt">
25287 <column alignment="center" valignment="top">
25289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25292 \begin_layout Plain Layout
25298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25301 \begin_layout Plain Layout
25309 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25312 \begin_layout Plain Layout
25320 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25323 \begin_layout Plain Layout
25324 \begin_inset Formula $\hbar$
25334 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25337 \begin_layout Plain Layout
25345 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25348 \begin_layout Plain Layout
25349 \begin_inset Formula $\hslash$
25359 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25362 \begin_layout Plain Layout
25370 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25373 \begin_layout Plain Layout
25374 \begin_inset Formula $\clubsuit$
25384 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25387 \begin_layout Plain Layout
25395 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25398 \begin_layout Plain Layout
25399 \begin_inset Formula $\spadesuit$
25409 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25412 \begin_layout Plain Layout
25420 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25423 \begin_layout Plain Layout
25424 \begin_inset Formula $\bigstar$
25434 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25437 \begin_layout Plain Layout
25445 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25448 \begin_layout Plain Layout
25449 \begin_inset Formula $\blacklozenge$
25459 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25462 \begin_layout Plain Layout
25470 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25473 \begin_layout Plain Layout
25474 \begin_inset Formula $\blacktriangle$
25484 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25487 \begin_layout Plain Layout
25495 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25498 \begin_layout Plain Layout
25499 \begin_inset Formula $\blacktriangledown$
25509 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25512 \begin_layout Plain Layout
25520 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25523 \begin_layout Plain Layout
25524 \begin_inset Formula $\bullet$
25538 \begin_inset space \hfill{}
25542 \begin_inset Tabular
25543 <lyxtabular version="3" rows="10" columns="2">
25544 <features booktabs="true" tabularvalignment="middle">
25545 <column alignment="center" valignment="top" width="0pt">
25546 <column alignment="center" valignment="top" width="0pt">
25548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25551 \begin_layout Plain Layout
25557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25560 \begin_layout Plain Layout
25568 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25571 \begin_layout Plain Layout
25579 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25582 \begin_layout Plain Layout
25583 \begin_inset Formula $\diamondsuit$
25593 <cell alignment="center" valignment="top" rightline="true" usebox="none">
25596 \begin_layout Plain Layout
25604 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25607 \begin_layout Plain Layout
25608 \begin_inset Formula $\Diamond$
25618 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25621 \begin_layout Plain Layout
25629 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25632 \begin_layout Plain Layout
25633 \begin_inset Formula $\heartsuit$
25643 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25646 \begin_layout Plain Layout
25654 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25657 \begin_layout Plain Layout
25658 \begin_inset Formula $\P$
25668 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25671 \begin_layout Plain Layout
25679 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25682 \begin_layout Plain Layout
25683 \begin_inset Formula $\copyright$
25693 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25696 \begin_layout Plain Layout
25704 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25707 \begin_layout Plain Layout
25708 \begin_inset Formula $\circledR$
25718 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25721 \begin_layout Plain Layout
25729 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25732 \begin_layout Plain Layout
25733 \begin_inset Formula $\maltese$
25743 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25746 \begin_layout Plain Layout
25754 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25757 \begin_layout Plain Layout
25758 \begin_inset Formula $\diagup$
25768 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25771 \begin_layout Plain Layout
25779 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25782 \begin_layout Plain Layout
25783 \begin_inset Formula $\diagdown$
25799 \begin_layout Standard
25800 \begin_inset VSpace medskip
25806 \begin_layout Standard
25807 Some symbols can be displayed in different sizes,
25809 \begin_inset CommandInset ref
25811 reference "subsec:Font-Sizes"
25819 \begin_layout Subsection
25821 \begin_inset Index idx
25826 \begin_layout Plain Layout
25828 \begin_inset IndexMacro subentry
25831 \begin_layout Plain Layout
25843 \begin_inset Index idx
25848 \begin_layout Plain Layout
25849 \begin_inset IndexMacro sortkey
25852 \begin_layout Plain Layout
25864 \begin_layout Plain Layout
25881 \begin_layout Standard
25882 To use the Euro symbol in formulas,
25883 the \SpecialChar LaTeX
25889 \begin_inset Index idx
25894 \begin_layout Plain Layout
25896 \begin_inset IndexMacro subentry
25899 \begin_layout Plain Layout
25910 must be installed and loaded with the \SpecialChar LaTeX
25914 \begin_layout Standard
25919 usepackage[gennarrow]{eurosym}
25922 \begin_layout Standard
25923 The Euro symbol can now be inserted with the command
25930 \begin_inset Index idx
25935 \begin_layout Plain Layout
25937 \begin_inset IndexMacro subentry
25940 \begin_layout Plain Layout
25947 \begin_inset IndexMacro subentry
25950 \begin_layout Plain Layout
25966 \begin_layout Standard
25967 The Euro symbol can directly be inserted with the € key in mathematical text,
25984 can also be inserted in \SpecialChar TeX
25986 The official currency symbol can then be inserted with the command
25993 \begin_inset Index idx
25998 \begin_layout Plain Layout
26000 \begin_inset IndexMacro subentry
26003 \begin_layout Plain Layout
26010 \begin_inset IndexMacro subentry
26013 \begin_layout Plain Layout
26027 which is also only available in \SpecialChar TeX
26031 \begin_layout Standard
26035 \begin_layout Plain Layout
26045 \begin_inset Note Note
26048 \begin_layout Plain Layout
26049 The following table will only be displayed when the \SpecialChar LaTeX
26062 \begin_layout Standard
26063 An overview about the different Euro symbols:
26066 \begin_layout Standard
26068 \begin_inset Tabular
26069 <lyxtabular version="3" rows="4" columns="3">
26070 <features booktabs="true" tabularvalignment="middle">
26071 <column alignment="center" valignment="top" width="0pt">
26072 <column alignment="center" valignment="top" width="0pt">
26073 <column alignment="center" valignment="top" width="0pt">
26075 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
26078 \begin_layout Plain Layout
26082 \begin_layout Plain Layout
26086 cmidrule[0.08em]{2-3}
26096 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26099 \begin_layout Plain Layout
26105 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26108 \begin_layout Plain Layout
26116 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26119 \begin_layout Plain Layout
26125 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26128 \begin_layout Plain Layout
26136 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26139 \begin_layout Plain Layout
26140 \begin_inset Formula $\euro$
26150 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26153 \begin_layout Plain Layout
26159 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26162 \begin_layout Plain Layout
26168 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26171 \begin_layout Plain Layout
26172 \begin_inset Formula $\mbox{€}$
26182 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26185 \begin_layout Plain Layout
26192 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26195 \begin_layout Plain Layout
26203 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26206 \begin_layout Plain Layout
26210 \begin_layout Plain Layout
26230 \begin_inset Note Note
26233 \begin_layout Plain Layout
26240 is used here only for table borders.
26250 manual for details.
26258 \begin_layout Standard
26262 \begin_layout Plain Layout
26272 \begin_inset Note Note
26275 \begin_layout Plain Layout
26276 The following will be displayed when the \SpecialChar LaTeX
26289 \begin_layout Standard
26290 You need to install the \SpecialChar LaTeX
26295 to see the rest of this subsection in the output.
26298 \begin_layout Standard
26302 \begin_layout Plain Layout
26314 \begin_layout Section
26316 \begin_inset CommandInset label
26318 name "sec:Relations"
26323 \begin_inset Index idx
26328 \begin_layout Plain Layout
26335 \begin_inset Index idx
26340 \begin_layout Plain Layout
26342 \begin_inset IndexMacro see
26345 \begin_layout Plain Layout
26359 \begin_layout Standard
26360 All of the following relations can also be inserted via the toolbar button
26363 arg "math-insert \\leq"
26369 \begin_layout Standard
26370 \begin_inset Tabular
26371 <lyxtabular version="3" rows="17" columns="2">
26372 <features booktabs="true" tabularvalignment="middle">
26373 <column alignment="center" valignment="top" width="0pt">
26374 <column alignment="center" valignment="top" width="0pt">
26376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26379 \begin_layout Plain Layout
26385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26388 \begin_layout Plain Layout
26396 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26399 \begin_layout Plain Layout
26405 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26408 \begin_layout Plain Layout
26409 \begin_inset Formula $<$
26419 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26422 \begin_layout Plain Layout
26430 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26433 \begin_layout Plain Layout
26434 \begin_inset Formula $\le$
26444 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26447 \begin_layout Plain Layout
26455 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26458 \begin_layout Plain Layout
26459 \begin_inset Formula $\ll$
26469 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26472 \begin_layout Plain Layout
26480 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26483 \begin_layout Plain Layout
26484 \begin_inset Formula $\prec$
26494 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26497 \begin_layout Plain Layout
26505 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26508 \begin_layout Plain Layout
26509 \begin_inset Formula $\preceq$
26519 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26522 \begin_layout Plain Layout
26530 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26533 \begin_layout Plain Layout
26534 \begin_inset Formula $\subset$
26544 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26547 \begin_layout Plain Layout
26555 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26558 \begin_layout Plain Layout
26559 \begin_inset Formula $\subseteq$
26569 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26572 \begin_layout Plain Layout
26580 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26583 \begin_layout Plain Layout
26584 \begin_inset Formula $\sqsubseteq$
26594 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26597 \begin_layout Plain Layout
26605 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26608 \begin_layout Plain Layout
26609 \begin_inset Formula $\in$
26619 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26622 \begin_layout Plain Layout
26630 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26633 \begin_layout Plain Layout
26634 \begin_inset Formula $\vdash$
26644 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26647 \begin_layout Plain Layout
26655 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26658 \begin_layout Plain Layout
26659 \begin_inset Formula $\smile$
26669 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26672 \begin_layout Plain Layout
26680 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26683 \begin_layout Plain Layout
26684 \begin_inset Formula $\lhd$
26694 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26697 \begin_layout Plain Layout
26705 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26708 \begin_layout Plain Layout
26709 \begin_inset Formula $\unlhd$
26719 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26722 \begin_layout Plain Layout
26730 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26733 \begin_layout Plain Layout
26734 \begin_inset Formula $\gtrless$
26744 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26747 \begin_layout Plain Layout
26755 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26758 \begin_layout Plain Layout
26759 \begin_inset Formula $\mid$
26769 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26772 \begin_layout Plain Layout
26780 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26783 \begin_layout Plain Layout
26784 \begin_inset Formula $\nmid$
26798 \begin_inset space \hfill{}
26802 \begin_inset Tabular
26803 <lyxtabular version="3" rows="17" columns="2">
26804 <features booktabs="true" tabularvalignment="middle">
26805 <column alignment="center" valignment="top" width="0pt">
26806 <column alignment="center" valignment="top" width="0pt">
26808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26811 \begin_layout Plain Layout
26817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26820 \begin_layout Plain Layout
26828 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26831 \begin_layout Plain Layout
26837 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26840 \begin_layout Plain Layout
26841 \begin_inset Formula $=$
26851 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26854 \begin_layout Plain Layout
26862 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26865 \begin_layout Plain Layout
26866 \begin_inset Formula $\not=$
26876 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26879 \begin_layout Plain Layout
26887 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26890 \begin_layout Plain Layout
26891 \begin_inset Formula $\equiv$
26901 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26904 \begin_layout Plain Layout
26912 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26915 \begin_layout Plain Layout
26916 \begin_inset Formula $\sim$
26926 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26929 \begin_layout Plain Layout
26937 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26940 \begin_layout Plain Layout
26941 \begin_inset Formula $\simeq$
26951 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26954 \begin_layout Plain Layout
26962 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26965 \begin_layout Plain Layout
26966 \begin_inset Formula $\approx$
26976 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26979 \begin_layout Plain Layout
26987 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26990 \begin_layout Plain Layout
26991 \begin_inset Formula $\cong$
27001 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27004 \begin_layout Plain Layout
27012 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27015 \begin_layout Plain Layout
27016 \begin_inset Formula $\bowtie$
27026 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27029 \begin_layout Plain Layout
27037 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27040 \begin_layout Plain Layout
27041 \begin_inset Formula $\notin$
27051 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27054 \begin_layout Plain Layout
27062 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27065 \begin_layout Plain Layout
27066 \begin_inset Formula $\perp$
27076 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27079 \begin_layout Plain Layout
27087 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27090 \begin_layout Plain Layout
27091 \begin_inset Formula $\propto$
27101 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27104 \begin_layout Plain Layout
27112 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27115 \begin_layout Plain Layout
27116 \begin_inset Formula $\asymp$
27126 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27129 \begin_layout Plain Layout
27137 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27140 \begin_layout Plain Layout
27141 \begin_inset Formula $\doteq$
27151 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27154 \begin_layout Plain Layout
27162 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27165 \begin_layout Plain Layout
27166 \begin_inset Formula $\circeq$
27176 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27179 \begin_layout Plain Layout
27187 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27190 \begin_layout Plain Layout
27191 \begin_inset Formula $\models$
27201 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27204 \begin_layout Plain Layout
27212 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27215 \begin_layout Plain Layout
27216 \begin_inset Formula $\widehat{=}$
27230 \begin_inset space \hfill{}
27234 \begin_inset Tabular
27235 <lyxtabular version="3" rows="17" columns="2">
27236 <features booktabs="true" tabularvalignment="middle">
27237 <column alignment="center" valignment="top" width="0pt">
27238 <column alignment="center" valignment="top" width="0pt">
27240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27243 \begin_layout Plain Layout
27249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27252 \begin_layout Plain Layout
27260 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27263 \begin_layout Plain Layout
27269 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27272 \begin_layout Plain Layout
27273 \begin_inset Formula $>$
27283 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27286 \begin_layout Plain Layout
27294 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27297 \begin_layout Plain Layout
27298 \begin_inset Formula $\ge$
27308 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27311 \begin_layout Plain Layout
27319 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27322 \begin_layout Plain Layout
27323 \begin_inset Formula $\gg$
27333 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27336 \begin_layout Plain Layout
27344 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27347 \begin_layout Plain Layout
27348 \begin_inset Formula $\succ$
27358 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27361 \begin_layout Plain Layout
27369 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27372 \begin_layout Plain Layout
27373 \begin_inset Formula $\succeq$
27383 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27386 \begin_layout Plain Layout
27394 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27397 \begin_layout Plain Layout
27398 \begin_inset Formula $\supset$
27408 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27411 \begin_layout Plain Layout
27419 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27422 \begin_layout Plain Layout
27423 \begin_inset Formula $\supseteq$
27433 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27436 \begin_layout Plain Layout
27444 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27447 \begin_layout Plain Layout
27448 \begin_inset Formula $\sqsupseteq$
27458 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27461 \begin_layout Plain Layout
27469 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27472 \begin_layout Plain Layout
27473 \begin_inset Formula $\ni$
27483 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27486 \begin_layout Plain Layout
27494 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27497 \begin_layout Plain Layout
27498 \begin_inset Formula $\dashv$
27508 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27511 \begin_layout Plain Layout
27519 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27522 \begin_layout Plain Layout
27523 \begin_inset Formula $\frown$
27533 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27536 \begin_layout Plain Layout
27544 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27547 \begin_layout Plain Layout
27548 \begin_inset Formula $\rhd$
27558 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27561 \begin_layout Plain Layout
27569 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27572 \begin_layout Plain Layout
27573 \begin_inset Formula $\unrhd$
27583 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27586 \begin_layout Plain Layout
27594 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27597 \begin_layout Plain Layout
27598 \begin_inset Formula $\lessgtr$
27608 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27611 \begin_layout Plain Layout
27619 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27622 \begin_layout Plain Layout
27623 \begin_inset Formula $\parallel$
27633 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27636 \begin_layout Plain Layout
27644 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27647 \begin_layout Plain Layout
27648 \begin_inset Formula $\nparallel$
27664 \begin_layout Standard
27665 \begin_inset VSpace medskip
27680 are bigger than the equal looking operators
27696 \begin_layout Standard
27698 supports also many special relations.
27699 Use the toolbar button
27702 arg "math-insert \\leqq"
27705 to see a list of these relations.
27708 \begin_layout Standard
27709 Contrary to symbols,
27710 relations are always surrounded by space.
27713 \begin_layout Standard
27714 Relations with labels can be created with the command
27721 \begin_inset Index idx
27726 \begin_layout Plain Layout
27728 \begin_inset IndexMacro subentry
27731 \begin_layout Plain Layout
27738 \begin_inset IndexMacro subentry
27741 \begin_layout Plain Layout
27757 \begin_layout Standard
27759 \begin_inset Tabular
27760 <lyxtabular version="3" rows="2" columns="2">
27761 <features booktabs="true" tabularvalignment="middle">
27762 <column alignment="center" valignment="top" width="0pt">
27763 <column alignment="center" valignment="top">
27765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27768 \begin_layout Plain Layout
27774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27777 \begin_layout Plain Layout
27784 <row topspace="1.5mm">
27785 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27788 \begin_layout Plain Layout
27792 \begin_inset space \textvisiblespace{}
27800 \begin_inset space \textvisiblespace{}
27804 \begin_inset Formula $\downarrow$
27810 \begin_inset space \textvisiblespace{}
27814 \begin_inset space \textvisiblespace{}
27822 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27825 \begin_layout Plain Layout
27826 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
27842 \begin_layout Section
27846 \begin_layout Subsection
27847 Predefined Functions
27848 \begin_inset CommandInset label
27850 name "subsec:Predefined-Functions"
27855 \begin_inset Index idx
27860 \begin_layout Plain Layout
27862 \begin_inset IndexMacro subentry
27865 \begin_layout Plain Layout
27879 \begin_layout Standard
27885 in mathematical expressions,
27886 but not function names,
27888 \begin_inset Formula $sin$
27891 could be misunderstood as
27892 \begin_inset Formula $s\cdot i\cdot n$
27896 Also predefined functions are separated a bit from the character in front of them.
27897 They are inserted as commands starting with a backslash before their name.
27900 \begin_layout Standard
27902 \begin_inset Tabular
27903 <lyxtabular version="3" rows="2" columns="2">
27904 <features booktabs="true" tabularvalignment="middle">
27905 <column alignment="center" valignment="top" width="0pt">
27906 <column alignment="center" valignment="top" width="0pt">
27908 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
27911 \begin_layout Plain Layout
27917 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
27920 \begin_layout Plain Layout
27928 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27931 \begin_layout Plain Layout
27937 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
27940 \begin_layout Plain Layout
27941 \begin_inset Formula $Asin(x)+B$
27955 \begin_inset space \quad{}
27959 \begin_inset Tabular
27960 <lyxtabular version="3" rows="2" columns="2">
27961 <features booktabs="true" tabularvalignment="middle">
27962 <column alignment="center" valignment="top" width="0pt">
27963 <column alignment="center" valignment="top" width="0pt">
27965 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
27968 \begin_layout Plain Layout
27974 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
27977 \begin_layout Plain Layout
27985 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27988 \begin_layout Plain Layout
27996 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27999 \begin_layout Plain Layout
28000 \begin_inset Formula $A\sin(x)+B$
28016 \begin_layout Standard
28017 The following functions are predefined:
28020 \begin_layout Standard
28021 \begin_inset VSpace -2mm
28027 \begin_layout Standard
28029 \begin_inset Tabular
28030 <lyxtabular version="3" rows="9" columns="4">
28031 <features booktabs="true" tabularvalignment="middle">
28032 <column alignment="center" valignment="top" width="0pt">
28033 <column alignment="center" valignment="top" width="0pt">
28034 <column alignment="center" valignment="top" width="0pt">
28035 <column alignment="center" valignment="top" width="0pt">
28037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28040 \begin_layout Plain Layout
28046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28049 \begin_layout Plain Layout
28055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28058 \begin_layout Plain Layout
28064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
28067 \begin_layout Plain Layout
28075 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28078 \begin_layout Plain Layout
28086 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28089 \begin_layout Plain Layout
28097 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28100 \begin_layout Plain Layout
28108 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28111 \begin_layout Plain Layout
28121 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28124 \begin_layout Plain Layout
28132 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28135 \begin_layout Plain Layout
28143 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28146 \begin_layout Plain Layout
28154 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28157 \begin_layout Plain Layout
28167 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28170 \begin_layout Plain Layout
28178 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28181 \begin_layout Plain Layout
28189 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28192 \begin_layout Plain Layout
28200 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28203 \begin_layout Plain Layout
28213 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28216 \begin_layout Plain Layout
28224 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28227 \begin_layout Plain Layout
28235 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28238 \begin_layout Plain Layout
28246 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28249 \begin_layout Plain Layout
28259 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28262 \begin_layout Plain Layout
28270 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28273 \begin_layout Plain Layout
28281 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28284 \begin_layout Plain Layout
28292 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28295 \begin_layout Plain Layout
28305 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28308 \begin_layout Plain Layout
28316 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28319 \begin_layout Plain Layout
28327 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28330 \begin_layout Plain Layout
28338 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28341 \begin_layout Plain Layout
28351 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28354 \begin_layout Plain Layout
28362 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28365 \begin_layout Plain Layout
28373 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28376 \begin_layout Plain Layout
28384 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28387 \begin_layout Plain Layout
28397 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
28400 \begin_layout Plain Layout
28408 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
28411 \begin_layout Plain Layout
28419 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
28422 \begin_layout Plain Layout
28430 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
28433 \begin_layout Plain Layout
28449 \begin_layout Standard
28450 They can also be inserted with the math toolbar button
28453 arg "math-insert \\functions"
28459 \begin_layout Subsection
28460 Self-defined Functions
28461 \begin_inset Index idx
28466 \begin_layout Plain Layout
28468 \begin_inset IndexMacro subentry
28471 \begin_layout Plain Layout
28485 \begin_layout Standard
28486 To use a function that is not predefined,
28487 for instance the sign function sgn(x),
28488 there are two possibilities:
28491 \begin_layout Itemize
28492 Define the function by inserting the following line in the \SpecialChar LaTeX
28497 \begin_layout Plain Layout
28502 DeclareMathOperator
28505 \begin_inset CommandInset ref
28507 reference "subsec:Self-defined-Operators"
28518 \begin_inset Newline newline
28522 \begin_inset VSpace -3mm
28526 \begin_inset Newline newline
28533 DeclareMathOperator{
28538 \begin_inset Index idx
28543 \begin_layout Plain Layout
28545 \begin_inset IndexMacro subentry
28548 \begin_layout Plain Layout
28555 \begin_inset IndexMacro subentry
28558 \begin_layout Plain Layout
28559 \begin_inset IndexMacro sortkey
28562 \begin_layout Plain Layout
28572 DeclareMathOperator
28583 \begin_inset Newline newline
28587 \begin_inset VSpace -2mm
28591 \begin_inset Newline newline
28594 Now the newly defined function can be called with the command
28603 \begin_layout Itemize
28604 Write the formula as usual,
28605 mark the formula name,
28606 in our example the letters
28611 and change it to mathematical text.
28613 insert a space between the prefactor and function.
28616 \begin_layout Standard
28617 The result is the same with both methods as with a predefined function
28621 \begin_layout Plain Layout
28622 In \SpecialChar LyX
28623 self-defined functions are displayed red,
28624 predefined ones black.
28632 \begin_layout Standard
28634 \begin_inset Tabular
28635 <lyxtabular version="3" rows="3" columns="2">
28636 <features booktabs="true" tabularvalignment="middle">
28637 <column alignment="center" valignment="top" width="0pt">
28638 <column alignment="center" valignment="top" width="0pt">
28640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28643 \begin_layout Plain Layout
28649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
28652 \begin_layout Plain Layout
28660 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28663 \begin_layout Plain Layout
28671 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28674 \begin_layout Plain Layout
28675 \begin_inset Formula $A\sgn(x)+B$
28685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28688 \begin_layout Plain Layout
28692 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
28700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
28703 \begin_layout Plain Layout
28704 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
28720 \begin_layout Standard
28721 The first method is more suitable when the self-defined function will be used several times.
28724 \begin_layout Subsection
28726 \begin_inset Index idx
28731 \begin_layout Plain Layout
28740 \begin_layout Standard
28742 in addition to the commands
28749 \begin_inset Index idx
28754 \begin_layout Plain Layout
28756 \begin_inset IndexMacro subentry
28759 \begin_layout Plain Layout
28766 \begin_inset IndexMacro subentry
28769 \begin_layout Plain Layout
28795 the following functions are defined:
28798 \begin_layout Standard
28800 \begin_inset Tabular
28801 <lyxtabular version="3" rows="5" columns="2">
28802 <features booktabs="true" tabularvalignment="middle">
28803 <column alignment="center" valignment="top" width="0pt">
28804 <column alignment="center" valignment="top" width="0pt">
28806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28809 \begin_layout Plain Layout
28815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
28818 \begin_layout Plain Layout
28826 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28829 \begin_layout Plain Layout
28837 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28840 \begin_layout Plain Layout
28841 \begin_inset Formula $\varliminf$
28850 <row topspace="1.5mm">
28851 <cell alignment="center" valignment="top" usebox="none">
28854 \begin_layout Plain Layout
28862 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28865 \begin_layout Plain Layout
28866 \begin_inset Formula $\varlimsup$
28875 <row topspace="1.5mm">
28876 <cell alignment="center" valignment="top" usebox="none">
28879 \begin_layout Plain Layout
28887 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28890 \begin_layout Plain Layout
28891 \begin_inset Formula $\varprojlim$
28900 <row topspace="1.5mm" bottomspace="1mm">
28901 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
28904 \begin_layout Plain Layout
28912 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
28915 \begin_layout Plain Layout
28916 \begin_inset Formula $\varinjlim$
28932 \begin_layout Standard
28933 \begin_inset VSpace medskip
28936 The limit is created by inserting a subscript.
28937 It is set right beside the function in an inline formula:
28940 \begin_layout Standard
28942 \begin_inset Tabular
28943 <lyxtabular version="3" rows="2" columns="2">
28944 <features booktabs="true" tabularvalignment="middle">
28945 <column alignment="center" valignment="top" width="0pt">
28946 <column alignment="center" valignment="top" width="0pt">
28948 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
28951 \begin_layout Plain Layout
28957 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
28960 \begin_layout Plain Layout
28968 <cell alignment="center" valignment="top" usebox="none">
28971 \begin_layout Plain Layout
28977 \begin_inset space \textvisiblespace{}
28981 \begin_inset space \textvisiblespace{}
28989 <cell alignment="center" valignment="top" usebox="none">
28992 \begin_layout Plain Layout
28993 \begin_inset Formula $\lim_{x\to A}x=B$
29009 \begin_layout Standard
29010 In a displayed formula the limit is set below the formula,
29012 \begin_inset Formula
29022 \begin_layout Standard
29023 \begin_inset VSpace medskip
29029 \begin_layout Standard
29030 How to adjust the typesetting of the limits see
29031 \begin_inset CommandInset ref
29033 reference "subsec:Operator-Limits"
29041 \begin_layout Subsection
29043 \begin_inset Index idx
29048 \begin_layout Plain Layout
29050 \begin_inset IndexMacro subentry
29053 \begin_layout Plain Layout
29067 \begin_layout Standard
29068 The modulo-function is special,
29069 because it exists in four variants.
29070 The variants in a displayed formula are:
29071 \begin_inset Formula
29073 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
29074 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
29075 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
29076 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
29077 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
29085 \begin_layout Standard
29086 In an inline formula less space is set before the function names for all variants.
29087 By default the modulo-functions take only the first character following the command into account.
29088 To use more than one character,
29089 put them in \SpecialChar TeX
29091 \begin_inset Formula
29093 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
29094 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
29095 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
29103 \begin_layout Section
29105 \begin_inset Index idx
29110 \begin_layout Plain Layout
29119 \begin_layout Standard
29120 The characters ^ and _ would normally create a superscript and subscript,
29122 To get these characters you have to insert them with a leading
29127 \begin_layout Standard
29130 \begin_inset Tabular
29131 <lyxtabular version="3" rows="3" columns="2">
29132 <features booktabs="true" tabularvalignment="middle">
29133 <column alignment="left" valignment="top" width="0pt">
29134 <column alignment="block" valignment="top">
29136 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
29139 \begin_layout Plain Layout
29145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
29148 \begin_layout Plain Layout
29156 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29159 \begin_layout Plain Layout
29163 \begin_inset space \textvisiblespace{}
29171 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29174 \begin_layout Plain Layout
29175 \begin_inset Formula $\mathcircumflex$
29185 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
29188 \begin_layout Plain Layout
29196 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
29199 \begin_layout Plain Layout
29200 \begin_inset Formula $\_$
29216 \begin_layout Subsection
29217 Special Characters in Mathematical Text
29220 \begin_layout Standard
29221 The following commands can only be used in mathematical text or in \SpecialChar TeX
29225 \begin_layout Standard
29226 \begin_inset space \hfill{}
29230 \begin_inset Tabular
29231 <lyxtabular version="3" rows="8" columns="2">
29232 <features booktabs="true" tabularvalignment="middle">
29233 <column alignment="left" valignment="top" width="0pt">
29234 <column alignment="block" valignment="top">
29236 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
29239 \begin_layout Plain Layout
29245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
29248 \begin_layout Plain Layout
29256 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29259 \begin_layout Plain Layout
29267 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29270 \begin_layout Plain Layout
29271 \begin_inset Formula $\textrm{œ}$
29281 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29284 \begin_layout Plain Layout
29292 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29295 \begin_layout Plain Layout
29296 \begin_inset Formula $\textrm{Œ}$
29306 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29309 \begin_layout Plain Layout
29317 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29320 \begin_layout Plain Layout
29321 \begin_inset Formula $\textrm{æ}$
29331 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29334 \begin_layout Plain Layout
29342 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29345 \begin_layout Plain Layout
29346 \begin_inset Formula $\textrm{Æ}$
29356 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29359 \begin_layout Plain Layout
29367 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29370 \begin_layout Plain Layout
29371 \begin_inset Formula $\textrm{å}$
29381 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29384 \begin_layout Plain Layout
29392 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29395 \begin_layout Plain Layout
29396 \begin_inset Formula $\textrm{Å}$
29406 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
29409 \begin_layout Plain Layout
29417 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
29420 \begin_layout Plain Layout
29421 \begin_inset Formula $\textrm{ı}$
29435 \begin_inset space \hfill{}
29439 \begin_inset Tabular
29440 <lyxtabular version="3" rows="8" columns="2">
29441 <features booktabs="true" tabularvalignment="middle">
29442 <column alignment="left" valignment="top" width="0pt">
29443 <column alignment="center" valignment="top">
29445 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
29448 \begin_layout Plain Layout
29450 \begin_inset Note Note
29453 \begin_layout Plain Layout
29455 \begin_inset space \thinspace{}
29458 mm is used for separation,
29459 because otherwise the output will be ¡ and ¿ respectively.
29469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
29472 \begin_layout Plain Layout
29480 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29483 \begin_layout Plain Layout
29491 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29494 \begin_layout Plain Layout
29495 \begin_inset Formula $\textrm{ø}$
29505 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29508 \begin_layout Plain Layout
29516 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29519 \begin_layout Plain Layout
29520 \begin_inset Formula $\textrm{Ø}$
29530 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29533 \begin_layout Plain Layout
29541 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29544 \begin_layout Plain Layout
29545 \begin_inset Formula $\textrm{ł}$
29555 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29558 \begin_layout Plain Layout
29566 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29569 \begin_layout Plain Layout
29570 \begin_inset Formula $\textrm{Ł}$
29580 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29583 \begin_layout Plain Layout
29585 \begin_inset space \hspace{}
29590 \begin_inset space \textvisiblespace{}
29598 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29601 \begin_layout Plain Layout
29602 \begin_inset Formula $\textrm{!`}$
29612 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29615 \begin_layout Plain Layout
29617 \begin_inset space \hspace{}
29622 \begin_inset space \textvisiblespace{}
29630 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29633 \begin_layout Plain Layout
29634 \begin_inset Formula $\textrm{?`}$
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 $\textrm{ȷ}$
29673 \begin_inset space \hfill{}
29679 \begin_layout Standard
29681 \begin_inset Formula $\textrm{Å}$
29685 \begin_inset Formula $\textrm{Ø}$
29688 can also be inserted via the math toolbar button
29691 arg "math-insert \\digamma"
29697 \begin_layout Standard
29701 \begin_inset space \hspace{}
29710 \begin_inset space \hspace{}
29716 are exceptions because they can be inserted in \SpecialChar LyX
29720 \begin_layout Subsection
29722 \begin_inset CommandInset label
29724 name "subsec:Accents-in-Text"
29729 \begin_inset Index idx
29734 \begin_layout Plain Layout
29736 \begin_inset IndexMacro subentry
29739 \begin_layout Plain Layout
29753 \begin_layout Standard
29754 Any letter can be accented with the following commands.
29755 The commands must be inserted in \SpecialChar TeX
29759 \begin_layout Standard
29760 \begin_inset space \hfill{}
29764 \begin_inset Tabular
29765 <lyxtabular version="3" rows="8" columns="2">
29766 <features booktabs="true" tabularvalignment="middle">
29767 <column alignment="left" valignment="top" width="0pt">
29768 <column alignment="block" valignment="top">
29770 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
29773 \begin_layout Plain Layout
29779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
29782 \begin_layout Plain Layout
29790 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29793 \begin_layout Plain Layout
29797 \begin_inset Quotes grd
29805 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29808 \begin_layout Plain Layout
29812 \begin_layout Plain Layout
29828 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29831 \begin_layout Plain Layout
29839 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29842 \begin_layout Plain Layout
29846 \begin_layout Plain Layout
29862 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29865 \begin_layout Plain Layout
29869 \begin_inset space \textvisiblespace{}
29877 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29880 \begin_layout Plain Layout
29884 \begin_layout Plain Layout
29900 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29903 \begin_layout Plain Layout
29911 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29914 \begin_layout Plain Layout
29918 \begin_layout Plain Layout
29934 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29937 \begin_layout Plain Layout
29941 \begin_inset space \textvisiblespace{}
29949 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29952 \begin_layout Plain Layout
29956 \begin_layout Plain Layout
29972 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29975 \begin_layout Plain Layout
29979 \begin_inset space \textvisiblespace{}
29987 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29990 \begin_layout Plain Layout
29994 \begin_layout Plain Layout
30010 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
30013 \begin_layout Plain Layout
30017 \begin_inset space \textvisiblespace{}
30025 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
30028 \begin_layout Plain Layout
30032 \begin_layout Plain Layout
30052 \begin_inset space \hfill{}
30056 \begin_inset Tabular
30057 <lyxtabular version="3" rows="8" columns="2">
30058 <features booktabs="true" tabularvalignment="middle">
30059 <column alignment="left" valignment="top" width="0pt">
30060 <column alignment="center" valignment="top">
30062 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30065 \begin_layout Plain Layout
30071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30074 \begin_layout Plain Layout
30082 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30085 \begin_layout Plain Layout
30089 \begin_inset space \textvisiblespace{}
30097 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30100 \begin_layout Plain Layout
30104 \begin_layout Plain Layout
30120 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30123 \begin_layout Plain Layout
30131 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30134 \begin_layout Plain Layout
30138 \begin_layout Plain Layout
30154 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30157 \begin_layout Plain Layout
30161 \begin_inset Index idx
30166 \begin_layout Plain Layout
30177 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30180 \begin_layout Plain Layout
30184 \begin_layout Plain Layout
30200 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30203 \begin_layout Plain Layout
30211 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30214 \begin_layout Plain Layout
30218 \begin_layout Plain Layout
30234 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30237 \begin_layout Plain Layout
30241 \begin_inset space \textvisiblespace{}
30249 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30252 \begin_layout Plain Layout
30256 \begin_layout Plain Layout
30272 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30275 \begin_layout Plain Layout
30279 \begin_inset space \textvisiblespace{}
30287 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30290 \begin_layout Plain Layout
30294 \begin_layout Plain Layout
30310 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30313 \begin_layout Plain Layout
30317 \begin_inset space \textvisiblespace{}
30325 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30328 \begin_layout Plain Layout
30332 \begin_layout Plain Layout
30352 \begin_inset space \hfill{}
30358 \begin_layout Standard
30359 \begin_inset VSpace medskip
30368 also two different characters can be accented.
30374 \begin_inset space \textvisiblespace{}
30384 \begin_layout Plain Layout
30396 \begin_layout Standard
30410 can in combination with vowels be directly inserted with the keyboard without using \SpecialChar TeX
30412 The same applies for the tilde
30416 \begin_layout Plain Layout
30417 This only applies for keyboards where the tilde is defined as accent.
30426 in combination with
30443 \begin_layout Standard
30492 and accents that are inserted directly with the keyboard are also available in mathematical text.
30493 For the other accents there are special math commands used in formulas,
30495 \begin_inset CommandInset ref
30497 reference "subsec:Accents-for-one"
30505 \begin_layout Standard
30506 \begin_inset VSpace bigskip
30516 \begin_inset Index idx
30521 \begin_layout Plain Layout
30523 \begin_inset IndexMacro subentry
30526 \begin_layout Plain Layout
30533 \begin_inset IndexMacro subentry
30536 \begin_layout Plain Layout
30549 any number or letter can be set into a circle,
30550 quasi accented with a circle,
30551 similar to the copyright symbol.
30554 \begin_layout Standard
30556 \begin_inset Tabular
30557 <lyxtabular version="3" rows="3" columns="2">
30558 <features booktabs="true" tabularvalignment="middle">
30559 <column alignment="center" valignment="top" width="0pt">
30560 <column alignment="center" valignment="top">
30562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30565 \begin_layout Plain Layout
30571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30574 \begin_layout Plain Layout
30582 <cell alignment="center" valignment="top" leftline="true" usebox="none">
30585 \begin_layout Plain Layout
30593 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30596 \begin_layout Plain Layout
30600 \begin_layout Plain Layout
30615 <row topspace="1mm">
30616 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
30619 \begin_layout Plain Layout
30630 raisebox{-1.5pt}{W}}
30635 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
30638 \begin_layout Plain Layout
30642 \begin_layout Plain Layout
30672 \begin_layout Standard
30673 One has to take care that the character fits into the circle.
30684 \begin_layout Plain Layout
30686 \begin_inset CommandInset ref
30688 reference "subsec:Font-Sizes"
30698 specifies the size of the circle.
30709 \begin_layout Plain Layout
30711 \begin_inset CommandInset ref
30713 reference "subsec:Boxes-without-Frame"
30723 the character can be centered.
30726 \begin_layout Subsection
30728 \begin_inset Index idx
30733 \begin_layout Plain Layout
30742 \begin_layout Standard
30743 Old-style figures (also known as old-style numerals) are created with the command
30750 \begin_inset Index idx
30755 \begin_layout Plain Layout
30757 \begin_inset IndexMacro subentry
30760 \begin_layout Plain Layout
30767 \begin_inset IndexMacro subentry
30770 \begin_layout Plain Layout
30784 The command can be used in formulas and in \SpecialChar TeX
30786 The command scheme is:
30789 \begin_layout Standard
30794 oldstylenums{number}
30797 \begin_layout Standard
30802 oldstylenums{0123456789}
30806 \begin_inset Formula $\oldstylenums{0123456789}$
30812 \begin_layout Section
30814 \begin_inset CommandInset label
30816 name "sec:Formula-Styles"
30821 \begin_inset Index idx
30826 \begin_layout Plain Layout
30828 \begin_inset IndexMacro subentry
30831 \begin_layout Plain Layout
30845 \begin_layout Itemize
30846 There are two different alignment styles:
30850 \begin_layout Description
30851 Centered is the predefined standard.
30854 \begin_layout Description
30855 Indented can be set using the menu
30857 Document\SpecialChar menuseparator
30863 \begin_inset space ~
30869 \begin_layout Standard
30875 the indentation can be adjusted.
30876 The default value depends on the document class.
30880 \begin_layout Itemize
30881 Two different numbering styles are available in the menu
30883 Document\SpecialChar menuseparator
30889 \begin_inset space ~
30898 \begin_layout Description
30899 Right is in most cases the default.
30902 \begin_layout Description
30907 \begin_layout Standard
30908 The chosen styles are used for all displayed formulas of the document.
30910 centered and indented formulas should be created in a document,
30916 The indented formulas are then set in a flalign environment,
30918 \begin_inset CommandInset ref
30920 reference "subsec:Flalign-Environment"
30928 \begin_layout Section
30930 \begin_inset CommandInset label
30932 name "sec:Multiline-Formulas"
30937 \begin_inset Index idx
30942 \begin_layout Plain Layout
30944 \begin_inset IndexMacro subentry
30947 \begin_layout Plain Layout
30961 \begin_layout Subsection
30965 \begin_layout Standard
30966 In \SpecialChar LyX
30968 multiline formulas are created by pressing
30971 arg "newline-insert newline"
30975 This creates either an
30979 that is described in
30980 \begin_inset CommandInset ref
30982 reference "subsec:Standard-align-Environment"
30988 when automatically loading of the package
30992 is disabled in the document settings,
30995 eqnarray environment
30997 that is described in
30998 \begin_inset CommandInset ref
31000 reference "subsec:Eqnarray-Environment"
31006 The align environment is recommended as it provides a typographically correct output in all cases.
31009 \begin_layout Standard
31010 There are other multiline formula environments that can be created via the menu
31012 Insert\SpecialChar menuseparator
31016 These environments are described in the following sections.
31019 \begin_layout Standard
31020 In all multiline formula environments a new line is created by pressing
31023 arg "newline-insert newline"
31027 To add or delete lines,
31028 use the math toolbar buttons
31031 arg "tabular-feature append-row"
31037 arg "tabular-feature delete-row"
31043 Edit\SpecialChar menuseparator
31049 \begin_layout Subsubsection
31051 \begin_inset CommandInset label
31053 name "subsec:Line-Separation"
31058 \begin_inset Index idx
31063 \begin_layout Plain Layout
31065 \begin_inset IndexMacro subentry
31068 \begin_layout Plain Layout
31075 \begin_inset IndexMacro subentry
31078 \begin_layout Plain Layout
31092 \begin_layout Standard
31093 Sometimes there is not enough space in multiline formulas between the lines:
31094 \begin_inset Formula
31096 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}\\
31097 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
31105 \begin_layout Standard
31106 In \SpecialChar LaTeX
31107 additional line space is specified as an optional argument of the new line command.
31108 This is not yet possible in \SpecialChar LyX
31113 \begin_layout Plain Layout
31115 \begin_inset CommandInset href
31117 name "LyX-bug #1505"
31118 target "https://www.lyx.org/trac/ticket/1505"
31129 therefore the whole formula must be inserted in \SpecialChar TeX
31131 To add in our example space,
31140 is inserted at the end of the first line.
31146 \begin_layout Plain Layout
31153 \begin_layout Plain Layout
31155 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = &
31157 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
31164 \begin_layout Plain Layout
31168 left(B^{2}+x_{0}^{2}
31176 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
31181 \begin_layout Plain Layout
31193 \begin_layout Standard
31194 \begin_inset VSpace bigskip
31197 To set the line separation for all lines in a formula,
31205 \begin_inset Index idx
31210 \begin_layout Plain Layout
31212 \begin_inset IndexMacro subentry
31215 \begin_layout Plain Layout
31222 \begin_inset IndexMacro subentry
31225 \begin_layout Plain Layout
31241 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
31252 \begin_inset space \thinspace{}
31257 \begin_inset space \thinspace{}
31260 mm of additional line separation as in the previous example,
31264 \begin_layout Standard
31274 \begin_layout Standard
31275 is inserted in \SpecialChar TeX
31276 mode before the formula.
31277 This requires that the \SpecialChar LaTeX
31286 \begin_layout Plain Layout
31291 is part of every \SpecialChar LaTeX
31292 standard installation.
31298 \begin_inset Index idx
31303 \begin_layout Plain Layout
31305 \begin_inset IndexMacro subentry
31308 \begin_layout Plain Layout
31319 was loaded in \SpecialChar LaTeX
31320 -preamble with the line
31323 \begin_layout Standard
31331 \begin_layout Standard
31337 \begin_layout Plain Layout
31349 \begin_inset Formula
31351 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}\\
31352 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
31360 \begin_layout Standard
31364 \begin_layout Plain Layout
31381 to its original value,
31388 is set to the value 3
31389 \begin_inset space \thinspace{}
31395 \begin_layout Subsubsection
31397 \begin_inset CommandInset label
31399 name "subsec:Column-Separation"
31404 \begin_inset Index idx
31409 \begin_layout Plain Layout
31411 \begin_inset IndexMacro subentry
31414 \begin_layout Plain Layout
31421 \begin_inset IndexMacro subentry
31424 \begin_layout Plain Layout
31438 \begin_layout Standard
31439 Multiline formulas form a matrix.
31440 A formula in the eqnarray environment for example is a matrix with three columns.
31441 By changing the column separation in this environment,
31442 the space beside the relation sign can be changed.
31445 \begin_layout Standard
31446 The column separation is specified with the length
31453 \begin_inset Index idx
31458 \begin_layout Plain Layout
31460 \begin_inset IndexMacro subentry
31463 \begin_layout Plain Layout
31470 \begin_inset IndexMacro subentry
31473 \begin_layout Plain Layout
31486 according to the formula:
31487 column separation = 2
31488 \begin_inset space \thinspace{}
31496 \change_deleted 5863208 1612730022
31500 \begin_inset Note Note
31503 \begin_layout Plain Layout
31505 \change_inserted 232239728 1611406079
31506 How does units play into this?
31507 (cm/in/pt) Is the 2 unitless and the result takes on the units of the input value?
31517 \begin_inset Newline newline
31524 \begin_layout Standard
31534 \begin_layout Standard
31535 inserted in \SpecialChar TeX
31537 sets all following formula column separations to 2
31538 \begin_inset space \thinspace{}
31542 To return to the predefined distance,
31550 \begin_inset space \thinspace{}
31556 \begin_layout Standard
31558 \begin_inset space \thinspace{}
31561 cm column separation:
31565 \begin_layout Plain Layout
31577 \begin_inset Formula
31585 A formula with the predefined column separation for matrices of 10
31586 \begin_inset space \thinspace{}
31593 \begin_layout Plain Layout
31605 \begin_inset Formula
31616 \begin_layout Standard
31617 \begin_inset Newpage newpage
31623 \begin_layout Subsubsection
31625 \begin_inset Index idx
31630 \begin_layout Plain Layout
31632 \begin_inset IndexMacro subentry
31635 \begin_layout Plain Layout
31649 \begin_layout Standard
31650 Long formulas can be typeset using these methods:
31653 \begin_layout Itemize
31654 If one side of an equation is much shorter than the line width,
31655 this is chosen for the left side and the right side is typeset over two lines:
31656 \begin_inset Formula
31658 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 \\
31659 & & -\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}
31664 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.
31665 Thus it would not be surrounded by space and could not be distinguished from the fraction bar.
31668 \begin_inset space \thinspace{}
31671 pt space was inserted behind the minus sign with the command
31681 \begin_layout Plain Layout
31689 \begin_inset CommandInset ref
31691 reference "subsec:Variable-Space"
31702 \begin_inset Index idx
31707 \begin_layout Plain Layout
31709 \begin_inset IndexMacro subentry
31712 \begin_layout Plain Layout
31719 \begin_inset IndexMacro subentry
31722 \begin_layout Plain Layout
31738 \begin_layout Itemize
31739 When both sides of the equation are long,
31747 \begin_inset Index idx
31752 \begin_layout Plain Layout
31754 \begin_inset IndexMacro subentry
31757 \begin_layout Plain Layout
31764 \begin_inset IndexMacro subentry
31767 \begin_layout Plain Layout
31781 It is inserted in the first column of the first line and causes all further insertions to overwrite the following columns:
31782 \begin_inset Formula
31784 \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 \\
31785 & & -\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 \\
31786 & & =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}
31791 After the insertion of
31798 the cursor is in a purple box that is shifted a bit to the left from the blue one.
31799 The formula is inserted there.
31800 \begin_inset Newline newline
31803 The content of additional lines is inserted in the second or another formula column.
31804 The greater the insertion column number ,
31805 the larger the indentation.
31806 \begin_inset VSpace medskip
31810 \begin_inset Newline newline
31814 \begin_inset Note Greyedout
31817 \begin_layout Plain Layout
31818 Note the following when using
31827 \begin_layout Itemize
31828 The formula doesn't use the full page width.
31830 \begin_inset space \thinspace{}
31834 \begin_inset space \space{}
31838 \begin_inset Formula $-B^{2}$
31841 is added to the first line in the above example,
31842 it would have been outside the page margin.
31843 To better use the width,
31844 negative space can be inserted at the beginning of the first line.
31847 \begin_layout Itemize
31848 Due to a bug in \SpecialChar LyX
31849 the cursor cannot be set with the mouse in the first line.
31853 \begin_layout Plain Layout
31854 \begin_inset CommandInset href
31856 name "LyX-bug #1429"
31857 target "https://www.lyx.org/trac/ticket/1429"
31867 One can only set the cursor at the beginning of the line and move it with the arrow keys.
31875 \begin_layout Itemize
31876 Other methods to set long formulas are offered by the environments described in
31877 \begin_inset CommandInset ref
31879 reference "subsec:Multline-Environment"
31885 \begin_inset CommandInset ref
31887 reference "subsec:Multiline-Formula-Parts"
31895 \begin_layout Subsubsection
31896 Multiline Fractions
31897 \begin_inset CommandInset label
31899 name "subsec:Multiline-Fractions"
31904 \begin_inset Index idx
31909 \begin_layout Plain Layout
31911 \begin_inset IndexMacro subentry
31914 \begin_layout Plain Layout
31928 \begin_layout Standard
31929 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.
31930 It is then necessary to add a line break within the fraction.
31931 This can be done using the command
31938 \begin_inset Index idx
31943 \begin_layout Plain Layout
31945 \begin_inset IndexMacro subentry
31948 \begin_layout Plain Layout
31955 \begin_inset IndexMacro subentry
31958 \begin_layout Plain Layout
31973 go to the document settings under
31976 \begin_inset space ~
31986 \begin_inset Index idx
31991 \begin_layout Plain Layout
31993 \begin_inset IndexMacro subentry
31996 \begin_layout Plain Layout
32007 and set its option to
32010 \begin_inset space ~
32025 \begin_layout Standard
32030 splitfrac{first line}{second line}
32033 \begin_layout Standard
32034 and is used for either the denominator or numerator:
32037 \begin_layout Standard
32038 \begin_inset Formula
32040 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}
32045 The command for the first numerator above is:
32048 \begin_layout Standard
32053 splitfrac{xy+xy+xy+xy+xy
32054 \begin_inset space \textvisiblespace{}
32062 \begin_layout Subsubsection
32064 \begin_inset CommandInset label
32066 name "subsec:Multiline-Brackets"
32071 \begin_inset Index idx
32076 \begin_layout Plain Layout
32078 \begin_inset IndexMacro subentry
32081 \begin_layout Plain Layout
32082 for multiline expressions
32095 \begin_layout Standard
32096 For brackets spanning multiple lines the following problem occurs:
32097 \begin_inset Formula
32099 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
32100 & & \left.\cdots+B-D\right]
32108 \begin_layout Standard
32109 The closing bracket is smaller than the opening bracket because brackets with variable size may not span multiple lines.
32112 \begin_layout Standard
32113 To set the bracket size for the second line correctly,
32114 the first line is ended with
32121 \begin_inset Index idx
32126 \begin_layout Plain Layout
32128 \begin_inset IndexMacro subentry
32131 \begin_layout Plain Layout
32138 \begin_inset IndexMacro subentry
32141 \begin_layout Plain Layout
32154 and the second line with
32162 \begin_layout Plain Layout
32176 \begin_inset CommandInset ref
32178 reference "subsec:Automatic-Bracket-Size"
32191 \begin_inset Index idx
32196 \begin_layout Plain Layout
32198 \begin_inset IndexMacro subentry
32201 \begin_layout Plain Layout
32208 \begin_inset IndexMacro subentry
32211 \begin_layout Plain Layout
32239 \begin_inset space \textvisiblespace{}
32249 \begin_inset space \textvisiblespace{}
32259 \begin_inset space \textvisiblespace{}
32265 \begin_inset Formula $\downarrow$
32271 \begin_inset Index idx
32276 \begin_layout Plain Layout
32278 \begin_inset IndexMacro subentry
32281 \begin_layout Plain Layout
32288 \begin_inset IndexMacro subentry
32291 \begin_layout Plain Layout
32305 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.
32308 \begin_layout Standard
32309 The result is this:
32310 \begin_inset Formula
32312 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
32313 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
32321 \begin_layout Subsection
32325 \begin_layout Standard
32326 Align environments can be used for every kind of multiline formulas.
32327 They are especially useful to set several formulas side by side.
32330 \begin_layout Standard
32331 Align environments consist of columns.
32332 The odd columns are right aligned,
32333 the even ones left aligned.
32334 Every line in an Align environment can be numbered.
32337 \begin_layout Standard
32338 Align environments are created via the menu
32340 Insert\SpecialChar menuseparator
32346 Edit\SpecialChar menuseparator
32347 Math\SpecialChar menuseparator
32348 Change Formula Type
32350 pre-existing formulas can be converted to Align environments.
32353 \begin_layout Standard
32354 To add or delete columns,
32355 use the math toolbar buttons
32358 arg "tabular-feature append-column"
32364 arg "tabular-feature delete-column"
32370 Edit\SpecialChar menuseparator
32376 \begin_layout Subsubsection
32377 Standard Align Environment
32378 \begin_inset CommandInset label
32380 name "subsec:Standard-align-Environment"
32385 \begin_inset Index idx
32390 \begin_layout Plain Layout
32392 \begin_inset IndexMacro subentry
32395 \begin_layout Plain Layout
32402 \begin_inset IndexMacro subentry
32405 \begin_layout Plain Layout
32419 \begin_layout Standard
32420 This align environment is created by pressing
32423 arg "newline-insert newline"
32426 in a formula or by the menu
32428 Insert\SpecialChar menuseparator
32429 Math\SpecialChar menuseparator
32430 AMS align Environment
32435 \begin_layout Standard
32436 An example for two formulas set side by side,
32437 that are created with a four column align environment:
32438 \begin_inset Formula
32440 A & =\sin(B) & C & =D\\
32441 C & \ne A & B & \ne D
32447 the formulas in this environment are placed so as if there would be a
32455 \begin_layout Plain Layout
32463 \begin_inset CommandInset ref
32465 reference "subsec:Variable-Space"
32477 before the first and after every even column.
32478 When the formula style
32484 \begin_layout Plain Layout
32485 For formula styles see
32486 \begin_inset CommandInset ref
32488 reference "sec:Formula-Styles"
32501 the formula is set without the
32507 before the first column.
32510 \begin_layout Subsubsection
32511 Alignat Environment
32512 \begin_inset Index idx
32517 \begin_layout Plain Layout
32519 \begin_inset IndexMacro subentry
32522 \begin_layout Plain Layout
32529 \begin_inset IndexMacro subentry
32532 \begin_layout Plain Layout
32533 alignat environment
32546 \begin_layout Standard
32547 The alignat environment has no predefined column separation.
32548 It can be inserted manually with the spaces that are described in
32549 \begin_inset CommandInset ref
32551 reference "subsec:Space"
32559 \begin_layout Standard
32560 The above example is shown in the alignat environment where 1
32561 \begin_inset space \thinspace{}
32564 cm space was inserted at the beginning of the second formula:
32565 \begin_inset Formula
32566 \begin{alignat*}{2}
32567 A & =\sin(B) & \hspace{1cm}C & =D\\
32568 C & \ne A & B & \ne D
32573 Because the column separation can be set separately for every column,
32574 this environment is especially suitable to set three or more formulas side by side.
32577 \begin_layout Subsubsection
32578 Flalign Environment
32579 \begin_inset CommandInset label
32581 name "subsec:Flalign-Environment"
32586 \begin_inset Index idx
32591 \begin_layout Plain Layout
32593 \begin_inset IndexMacro subentry
32596 \begin_layout Plain Layout
32603 \begin_inset IndexMacro subentry
32606 \begin_layout Plain Layout
32607 flalign environment
32620 \begin_layout Standard
32621 In this environment the first column is always set to the left as much as possible and the last one to the right.
32623 \begin_inset Formula
32625 A & =1 & B & =2 & C & =3\\
32626 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
32634 \begin_layout Standard
32635 By creating a flalign environment with an odd number of columns where an empty \SpecialChar TeX
32636 brace is inserted in the last column,
32637 several formulas in a document can be set to the left,
32638 although the formula style
32643 As example the indented formula
32644 \begin_inset CommandInset ref
32646 reference "eq:VolInt"
32652 \begin_inset Formula
32654 \hspace{30pt}\iiint_{V}X\,\mathrm{d}V & =U & {}
32659 The first two columns contain the formula.
32660 To indent it as with the formula style
32666 \begin_inset space \thinspace{}
32669 pt space was inserted at the beginning of the first column.
32672 \begin_layout Subsection
32673 Eqnarray Environment
32674 \begin_inset CommandInset label
32676 name "subsec:Eqnarray-Environment"
32681 \begin_inset Index idx
32686 \begin_layout Plain Layout
32688 \begin_inset IndexMacro subentry
32691 \begin_layout Plain Layout
32698 \begin_inset IndexMacro subentry
32701 \begin_layout Plain Layout
32702 eqnarray environment
32715 \begin_layout Standard
32716 When this environment is created,
32717 three blue boxes appear.
32718 The content of the first box is right aligned,
32719 the content of the last box left aligned.
32720 The content of the middle box appears centered and a bit smaller because it is intended for relational characters only.
32721 \begin_inset Formula
32723 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
32733 \begin_layout Subsection
32735 \begin_inset Index idx
32740 \begin_layout Plain Layout
32742 \begin_inset IndexMacro subentry
32745 \begin_layout Plain Layout
32752 \begin_inset IndexMacro subentry
32755 \begin_layout Plain Layout
32769 \begin_layout Standard
32770 This environment consists of one centered column.
32771 Every line can be numbered.
32772 \begin_inset Formula
32783 \begin_layout Subsection
32784 Multline Environment
32785 \begin_inset CommandInset label
32787 name "subsec:Multline-Environment"
32792 \begin_inset Index idx
32797 \begin_layout Plain Layout
32799 \begin_inset IndexMacro subentry
32802 \begin_layout Plain Layout
32809 \begin_inset IndexMacro subentry
32812 \begin_layout Plain Layout
32813 multline environment
32826 \begin_layout Standard
32827 The multline environment consists,
32828 like the gather environment,
32830 But the first line is left aligned,
32831 the last one right aligned.
32832 All other lines are centered.
32833 Therefore this environment is suitable for long formulas.
32834 Using example formula
32835 \begin_inset CommandInset ref
32837 reference "eq:lefteqn"
32842 in the multline environment:
32843 \begin_inset Formula
32845 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}\\
32846 -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}\\
32847 =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}}
32855 \begin_layout Standard
32857 only the last line of a multline environment appears numbered when the document numbering is on the right .
32858 If the document numbering is on the left then only the first line will appear numbered.
32862 \begin_layout Plain Layout
32863 For numbering styles see
32864 \begin_inset CommandInset ref
32866 reference "sec:Formula-Styles"
32879 \begin_layout Standard
32887 \begin_inset Index idx
32892 \begin_layout Plain Layout
32894 \begin_inset IndexMacro subentry
32897 \begin_layout Plain Layout
32904 \begin_inset IndexMacro subentry
32907 \begin_layout Plain Layout
32927 \begin_inset Index idx
32932 \begin_layout Plain Layout
32934 \begin_inset IndexMacro subentry
32937 \begin_layout Plain Layout
32944 \begin_inset IndexMacro subentry
32947 \begin_layout Plain Layout
32960 a centered line can be right or left aligned,
32962 The commands are used as follows:
32965 \begin_layout Standard
32970 shoveright{line content}
32976 shoveleft{line content}
32979 \begin_layout Standard
32980 \begin_inset VSpace medskip
32990 \begin_inset Index idx
32995 \begin_layout Plain Layout
32997 \begin_inset IndexMacro subentry
33000 \begin_layout Plain Layout
33007 \begin_inset IndexMacro subentry
33010 \begin_layout Plain Layout
33023 specifies the distance of the first line from the left page margin.
33024 Predefined is the length 0
33025 \begin_inset space \thinspace{}
33031 \begin_layout Standard
33032 As example the above formula where the command
33035 \begin_layout Standard
33045 \begin_layout Standard
33046 was inserted in \SpecialChar TeX
33051 \begin_layout Plain Layout
33063 \begin_inset Formula
33065 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}\\
33066 \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}}\\
33067 =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}}
33076 \begin_layout Plain Layout
33087 The second line was left aligned using
33096 \begin_layout Subsection
33097 Multiline Formula Parts
33098 \begin_inset CommandInset label
33100 name "subsec:Multiline-Formula-Parts"
33105 \begin_inset Index idx
33110 \begin_layout Plain Layout
33112 \begin_inset IndexMacro subentry
33115 \begin_layout Plain Layout
33122 \begin_inset IndexMacro subentry
33125 \begin_layout Plain Layout
33139 \begin_layout Standard
33140 To display only parts of a formula with multiple lines,
33141 one of the following environments is used:
33161 They can be inserted via the menu
33163 Insert\SpecialChar menuseparator
33166 or by using the commands described in this section.
33169 \begin_layout Standard
33170 The first three have the same properties as the corresponding multiline formula environments,
33171 but it is possible to set additional formula parts beside them.
33173 \begin_inset Formula
33175 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
33176 \Delta E\Delta t & \ge\frac{\hbar}{2}
33178 \right\} \textrm{Uncertainty relations}
33186 \begin_layout Standard
33187 To get this formula,
33188 a displayed formula is created where the command
33195 \begin_inset Index idx
33200 \begin_layout Plain Layout
33202 \begin_inset IndexMacro subentry
33205 \begin_layout Plain Layout
33212 \begin_inset IndexMacro subentry
33215 \begin_layout Plain Layout
33229 A purple box appears around the blue formula box where now columns and lines can be added.
33230 Outside the multiline environment other formula parts can be set,
33234 \begin_layout Standard
33235 The aligned environment is also suitable for long formulas whose lines are horizontally aligned.
33236 Using aligned in a displayed formula has the advantage that the formula number is vertically centered behind the lines.
33237 For example here is formula
33238 \begin_inset CommandInset ref
33240 reference "eq:shortlong"
33245 in the aligned environment:
33246 \begin_inset Formula
33248 \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}|}\\
33249 & -\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}|}
33258 \begin_layout Standard
33259 To use the environments
33281 \begin_inset Index idx
33286 \begin_layout Plain Layout
33288 \begin_inset IndexMacro subentry
33291 \begin_layout Plain Layout
33298 \begin_inset IndexMacro subentry
33301 \begin_layout Plain Layout
33321 \begin_inset Index idx
33326 \begin_layout Plain Layout
33328 \begin_inset IndexMacro subentry
33331 \begin_layout Plain Layout
33338 \begin_inset IndexMacro subentry
33341 \begin_layout Plain Layout
33362 \begin_inset Index idx
33367 \begin_layout Plain Layout
33369 \begin_inset IndexMacro subentry
33372 \begin_layout Plain Layout
33379 \begin_inset IndexMacro subentry
33382 \begin_layout Plain Layout
33397 The split environment has the same properties as the aligned environment but it can only have two columns.
33400 \begin_layout Subsection
33401 Text in Multiline Formulas
33402 \begin_inset CommandInset label
33404 name "subsec:Text-in-multiline"
33409 \begin_inset Index idx
33414 \begin_layout Plain Layout
33416 \begin_inset IndexMacro subentry
33419 \begin_layout Plain Layout
33431 \begin_inset Index idx
33436 \begin_layout Plain Layout
33438 \begin_inset IndexMacro subentry
33441 \begin_layout Plain Layout
33448 \begin_inset IndexMacro subentry
33451 \begin_layout Plain Layout
33465 \begin_layout Standard
33466 In the align environments as well as the multline and gather environment,
33467 text can be inserted that will appear in a separate line and doesn't affect the column alignment.
33476 \begin_inset Index idx
33481 \begin_layout Plain Layout
33483 \begin_inset IndexMacro subentry
33486 \begin_layout Plain Layout
33493 \begin_inset IndexMacro subentry
33496 \begin_layout Plain Layout
33509 is used in the following scheme:
33512 \begin_layout Standard
33520 \begin_layout Standard
33521 The text should not be longer than a line because it cannot be hyphenated.
33522 As \SpecialChar LyX
33523 doesn't yet support
33530 the text is written as mathematical text.
33537 must be at the beginning of a line and will appear in the output above this line.
33538 An example where the text was inserted at the beginning of the second line:
33539 \begin_inset Formula
33541 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
33542 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
33550 \begin_layout Standard
33557 always creates some vertical space between the text and the formula lines.
33558 To avoid this space,
33559 in the document settings under
33562 \begin_inset space ~
33572 \begin_inset Index idx
33577 \begin_layout Plain Layout
33579 \begin_inset IndexMacro subentry
33582 \begin_layout Plain Layout
33596 \begin_inset space ~
33602 Then you can use the command
33609 \begin_inset Index idx
33614 \begin_layout Plain Layout
33616 \begin_inset IndexMacro subentry
33619 \begin_layout Plain Layout
33626 \begin_inset IndexMacro subentry
33629 \begin_layout Plain Layout
33651 \begin_layout Standard
33652 \begin_inset Formula
33654 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
33655 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
33663 \begin_layout Section
33665 \begin_inset Index idx
33670 \begin_layout Plain Layout
33677 \begin_inset Index idx
33682 \begin_layout Plain Layout
33684 \begin_inset IndexMacro subentry
33687 \begin_layout Plain Layout
33694 \begin_inset IndexMacro see
33697 \begin_layout Plain Layout
33711 \begin_layout Subsection
33715 \begin_layout Standard
33716 Numbered formulas can be created with the menu
33718 Insert\SpecialChar menuseparator
33719 Math\SpecialChar menuseparator
33721 \begin_inset space ~
33729 arg "command-sequence math-display; math-number-toggle;"
33733 Existing formulas can be numbered with the menu
33735 Edit\SpecialChar menuseparator
33736 Math\SpecialChar menuseparator
33738 \begin_inset space ~
33742 \begin_inset space ~
33750 arg "math-number-toggle"
33754 The formula number is displayed in \SpecialChar LyX
33755 behind the formula as a number in parentheses.
33757 \change_deleted 232239728 1611410645
33758 The number sign is replaced in the output by the formula number.
33759 \change_deleted 5863208 1612727075
33761 \begin_inset Note Note
33764 \begin_layout Plain Layout
33766 \change_inserted 232239728 1611410697
33767 LyX appears to put the actual formula number in the raw file now
33779 \begin_layout Standard
33780 When numbering is turned on in multiline formulas,
33781 all formulas will be numbered.
33782 But the numbering can be controlled with the menu
33784 Edit\SpecialChar menuseparator
33785 Math\SpecialChar menuseparator
33787 \begin_inset space ~
33791 \begin_inset space ~
33799 arg "math-number-line-toggle"
33802 ) for every formula.
33805 \begin_layout Standard
33806 Except for inline formulas,
33807 all formulas can be numbered with two different styles,
33809 \begin_inset CommandInset ref
33811 reference "sec:Formula-Styles"
33819 \begin_layout Subsection
33821 \begin_inset Index idx
33826 \begin_layout Plain Layout
33828 \begin_inset IndexMacro subentry
33831 \begin_layout Plain Layout
33845 \begin_layout Standard
33846 All labeled formulas can be cross-referenced.
33847 A label is added with the menu
33849 Insert\SpecialChar menuseparator
33852 or the toolbar button
33859 The cursor must be inside a displayed formula.
33860 Alternatively you can right-click on the formula and choose
33865 A dialog pops up displaying the prefix
33871 The label is inserted behind the prefix.
33872 The predefined prefix means
33873 \begin_inset Quotes eld
33877 \begin_inset Quotes erd
33880 and makes it easier to find labels in large documents because it marks it as a formula label to distinguish it from e.
33881 \begin_inset space \thinspace{}
33885 \begin_inset space \space{}
33892 Insert\SpecialChar menuseparator
33895 is used again or you can right-click on a formula and then on
33902 \begin_layout Standard
33903 The name of the label is displayed in \SpecialChar LyX
33904 within parentheses behind the formula number.
33905 A formula with a label is always numbered.
33908 \begin_layout Standard
33909 Cross-references are inserted via the menu
33911 Insert\SpecialChar menuseparator
33914 or with the toolbar button
33917 arg "dialog-show-new-inset ref"
33921 A formula cross-reference appears in the output as formula number.
33922 When in the cross-reference dialog window the format
33927 the cross-reference appears in the output as formula number in parentheses.
33928 \begin_inset Newline newline
33931 By right-clicking on a cross-reference in \SpecialChar LyX
33933 one jumps to the formula that is referenced.
33936 \begin_layout Standard
33937 Here are as examples cross-references to formulas of the following subsections:
33938 \begin_inset Note Note
33941 \begin_layout Plain Layout
33942 Note the different cross-reference types.
33950 \begin_layout Standard
33952 \begin_inset CommandInset ref
33960 \begin_inset CommandInset ref
33969 \begin_inset CommandInset ref
33976 ) big Latin letters are used for the numbering in contrary to (
33977 \begin_inset CommandInset ref
33987 \begin_layout Standard
33988 \begin_inset VSpace medskip
33991 When the argument of
33999 \begin_layout Plain Layout
34007 \begin_inset CommandInset ref
34009 reference "subsec:User-defined-Numbering"
34021 contains a box like in
34022 \begin_inset CommandInset ref
34024 reference "subsec:Paragraph-Boxes"
34030 the formula cannot be referenced.
34033 \begin_layout Subsection
34035 \begin_inset Index idx
34040 \begin_layout Plain Layout
34042 \begin_inset IndexMacro subentry
34045 \begin_layout Plain Layout
34059 \begin_layout Standard
34060 Formulas can be numbered as subequations.
34061 To activate this feature,
34066 to the document in the menu
34068 Document\SpecialChar menuseparator
34069 Settings\SpecialChar menuseparator
34073 To insert subequations use the menu
34075 Insert\SpecialChar menuseparator
34076 Custom Insets\SpecialChar menuseparator
34082 \begin_layout Standard
34083 The equations to be subnumbered are put into the
34089 \begin_inset Formula
34097 \begin_inset VSpace -5mm
34101 \begin_inset Flex Subequations
34104 \begin_layout Plain Layout
34105 \begin_inset Formula
34113 \begin_inset Formula
34128 \begin_layout Standard
34129 Every formula in the
34133 inset will be subnumbered with a,
34138 For multiline formulas every line will be subnumbered.
34141 \begin_layout Standard
34142 Referencing subequations works like normal equations:
34144 \begin_inset CommandInset ref
34153 \begin_inset CommandInset ref
34161 If you want to reference the subequations collectively,
34162 insert a label as first thing in the
34168 \begin_inset CommandInset ref
34170 reference "eq:Here-is-an"
34181 \begin_layout Standard
34182 When inserting subequations,
34183 vertical space is added before the equation.
34186 \begin_inset space \thinspace{}
34189 mm vertical space right before the
34194 If the formula style
34200 \begin_layout Plain Layout
34201 For formula styles see
34202 \begin_inset CommandInset ref
34204 reference "sec:Formula-Styles"
34218 \begin_inset space \thinspace{}
34224 \begin_layout Standard
34225 To get another subnumber instead of small Latin letters,
34226 insert this command as \SpecialChar TeX
34227 code before the equations in the
34234 \begin_layout Standard
34243 theparentequation -
34248 \begin_layout Standard
34255 creates the parent number and
34261 adds a small Roman number as subnumber.
34262 For more information about the customization of the numbering,
34264 \begin_inset CommandInset ref
34266 reference "subsec:Numbering-with-Roman"
34274 \begin_layout Standard
34275 Here is an example of a multiline formula where the numbering is customized and turned off for the second line:
34276 \begin_inset Flex Subequations
34279 \begin_layout Plain Layout
34280 \begin_inset CommandInset label
34282 name "eq:Here-is-an"
34290 \begin_layout Plain Layout
34298 theparentequation -
34306 \begin_inset Formula
34308 A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
34309 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
34310 & = & B^{2}-2BZ+Z^{2}
34323 \begin_layout Subsection
34324 Numbering with Roman Numbers and Letters
34325 \begin_inset CommandInset label
34327 name "subsec:Numbering-with-Roman"
34332 \begin_inset Index idx
34337 \begin_layout Plain Layout
34339 \begin_inset IndexMacro subentry
34342 \begin_layout Plain Layout
34354 \begin_inset Index idx
34359 \begin_layout Plain Layout
34361 \begin_inset IndexMacro subentry
34364 \begin_layout Plain Layout
34378 \begin_layout Standard
34379 Formulas can also be numbered with Roman numbers and Latin letters.
34380 To number with small Roman numbers,
34384 \begin_layout Standard
34396 \begin_layout Standard
34397 is inserted before the formula in \SpecialChar TeX
34406 \begin_inset Index idx
34411 \begin_layout Plain Layout
34413 \begin_inset IndexMacro subentry
34416 \begin_layout Plain Layout
34423 \begin_inset IndexMacro subentry
34426 \begin_layout Plain Layout
34439 redefines the predefined command
34455 \begin_layout Plain Layout
34462 has the same scheme as the command
34469 \begin_inset CommandInset ref
34471 reference "subsec:The-Command-newcommand"
34485 is the formula counter.
34492 is used as prefix for a counter,
34493 the value of the counter is output as Arabic number.
34494 When a formula is numbered,
34496 sets internally the command
34502 behind the formula.
34508 \begin_inset Index idx
34513 \begin_layout Plain Layout
34515 \begin_inset IndexMacro subentry
34518 \begin_layout Plain Layout
34525 \begin_inset IndexMacro subentry
34528 \begin_layout Plain Layout
34543 outputs the counter as small Roman number.
34546 \begin_layout Standard
34547 All formulas behind the command
34557 are now numbered Roman.
34558 To switch to numbering with big Roman numbers,
34559 the command is inserted again,
34573 \begin_inset Index idx
34578 \begin_layout Plain Layout
34580 \begin_inset IndexMacro subentry
34583 \begin_layout Plain Layout
34590 \begin_inset IndexMacro subentry
34593 \begin_layout Plain Layout
34594 \begin_inset IndexMacro sortkey
34597 \begin_layout Plain Layout
34619 \begin_inset Quotes eld
34623 \begin_inset Quotes erd
34626 with small Latin letters there is the command
34633 \begin_inset Index idx
34638 \begin_layout Plain Layout
34640 \begin_inset IndexMacro subentry
34643 \begin_layout Plain Layout
34650 \begin_inset IndexMacro subentry
34653 \begin_layout Plain Layout
34667 for big ones there is the command
34674 \begin_inset Index idx
34679 \begin_layout Plain Layout
34681 \begin_inset IndexMacro subentry
34684 \begin_layout Plain Layout
34691 \begin_inset IndexMacro subentry
34694 \begin_layout Plain Layout
34695 \begin_inset IndexMacro sortkey
34698 \begin_layout Plain Layout
34721 \begin_layout Standard
34722 \begin_inset Note Greyedout
34725 \begin_layout Plain Layout
34731 Only a maximum of 26
34732 \begin_inset space ~
34735 formulas can be numbered with Latin letters in one document.
34743 \begin_layout Standard
34747 \begin_layout Plain Layout
34763 \begin_layout Standard
34764 \begin_inset Formula
34766 A=\textrm{small roman}
34775 \begin_layout Plain Layout
34789 \begin_inset Formula
34791 B=\textrm{big Roman}\label{eq:Rom}
34800 \begin_layout Plain Layout
34814 \begin_inset Formula
34816 C=\textrm{small Latin}
34825 \begin_layout Plain Layout
34839 \begin_inset Formula
34841 D=\textrm{big Latin}\label{eq:Lat}
34849 \begin_layout Standard
34850 To switch back to the default numbering,
34851 insert the command:
34854 \begin_layout Standard
34864 \begin_inset Index idx
34869 \begin_layout Plain Layout
34871 \begin_inset IndexMacro subentry
34874 \begin_layout Plain Layout
34881 \begin_inset IndexMacro subentry
34884 \begin_layout Plain Layout
34900 \begin_layout Standard
34904 \begin_layout Plain Layout
34918 \begin_inset Formula
34928 \begin_layout Standard
34929 \begin_inset VSpace medskip
34933 formulas are numbered serially independent from the numbering style.
34934 When then numbering should start with
34935 \begin_inset Quotes eld
34939 \begin_inset Quotes erd
34942 when the style is changed,
34943 new equation counters have to be defined.
34944 A description of this can be found in the file
34945 \begin_inset CommandInset href
34947 name "Formula-numbering.lyx"
34948 target "run:Formula-numbering.lyx"
34956 \begin_layout Subsection
34957 User-defined Numbering
34958 \begin_inset CommandInset label
34960 name "subsec:User-defined-Numbering"
34965 \begin_inset Index idx
34970 \begin_layout Plain Layout
34972 \begin_inset IndexMacro subentry
34975 \begin_layout Plain Layout
34989 \begin_layout Standard
34990 \begin_inset Note Greyedout
34993 \begin_layout Plain Layout
34999 If the document language is a right-to-left language such as Arabic,
35000 you must add this to the to the \SpecialChar LaTeX
35001 -preamble to be able to use the commands described in this section:
35002 \begin_inset Newline newline
35010 \begin_inset Newline newline
35014 \begin_inset Phantom HPhantom
35017 \begin_layout Plain Layout
35020 \begin_inset space ~
35046 \begin_layout Standard
35047 \begin_inset Index idx
35052 \begin_layout Plain Layout
35054 \begin_inset IndexMacro subentry
35057 \begin_layout Plain Layout
35058 self-defined delimiters
35068 With standard numbering,
35069 parentheses are set around a formula number.
35070 To replace the parentheses for example with vertical bars,
35071 the following line is added to the \SpecialChar LaTeX
35075 \begin_layout Standard
35081 \begin_inset Newline newline
35085 \begin_inset Phantom HPhantom
35088 \begin_layout Plain Layout
35091 \begin_inset space ~
35105 maketag@@@{|#1|}} }
35108 \begin_inset Note Note
35111 \begin_layout Plain Layout
35112 This macro is already declared in the \SpecialChar LaTeX
35113 -preamble for testing.
35115 remove the percent signs at the beginning.
35123 \begin_layout Standard
35124 To use other characters,
35125 the vertical bars besides the
35129 are replaced by one or more characters.
35130 To display only the formula number the vertical bars are omitted.
35133 \begin_layout Standard
35134 \begin_inset VSpace bigskip
35137 When there should be an expression of your choice instead of the consecutive formula number in parentheses behind the formula,
35145 \begin_inset Index idx
35150 \begin_layout Plain Layout
35152 \begin_inset IndexMacro subentry
35155 \begin_layout Plain Layout
35162 \begin_inset IndexMacro subentry
35165 \begin_layout Plain Layout
35179 \begin_inset Formula
35181 A+B=C\tag{something}\label{eq:tag}
35186 In this example the command
35191 \begin_inset space \textvisiblespace{}
35196 was inserted in the formula.
35199 \begin_layout Standard
35205 \begin_inset space \textvisiblespace{}
35210 is inserted instead,
35211 the parentheses are removed:
35212 \begin_inset Formula
35214 A+B=C\tag*{something}
35222 \begin_layout Standard
35223 \begin_inset VSpace bigskip
35226 To restart the formula numbering with new document parts or sections,
35227 the following command is used:
35230 \begin_layout Standard
35235 @addtoreset{equation}{part}
35238 \begin_inset Index idx
35243 \begin_layout Plain Layout
35245 \begin_inset IndexMacro subentry
35248 \begin_layout Plain Layout
35252 \begin_layout Plain Layout
35265 \begin_inset IndexMacro subentry
35268 \begin_layout Plain Layout
35275 \begin_layout Plain Layout
35293 \begin_inset Newline newline
35297 \begin_inset Newline newline
35304 @addtoreset{equation}{section}
35307 \begin_layout Standard
35308 To be able to use these commands in \SpecialChar TeX
35311 \begin_inset Quotes eld
35315 \begin_inset Quotes erd
35318 character has to be made
35319 \begin_inset Quotes eld
35323 \begin_inset Quotes erd
35326 for \SpecialChar LaTeX
35341 So the command sequence in \SpecialChar TeX
35345 \begin_layout Standard
35351 \begin_inset Newline newline
35356 @addtoreset{equation}{section}
35357 \begin_inset Newline newline
35365 \begin_layout Standard
35366 In the \SpecialChar LaTeX
35379 can be omitted as they are automatically internally inserted by \SpecialChar LyX
35383 \begin_layout Standard
35399 \begin_layout Plain Layout
35404 is part of the \SpecialChar LaTeX
35410 \begin_inset Index idx
35415 \begin_layout Plain Layout
35417 \begin_inset IndexMacro subentry
35420 \begin_layout Plain Layout
35431 that is part of every \SpecialChar LaTeX
35432 standard installation.
35438 \begin_inset Index idx
35443 \begin_layout Plain Layout
35445 \begin_inset IndexMacro subentry
35448 \begin_layout Plain Layout
35459 has to be loaded in the \SpecialChar LaTeX
35460 -preamble with the line
35463 \begin_layout Standard
35468 usepackage{remreset}
35471 \begin_layout Standard
35479 \begin_inset Index idx
35484 \begin_layout Plain Layout
35486 \begin_inset IndexMacro subentry
35489 \begin_layout Plain Layout
35493 \begin_layout Plain Layout
35506 \begin_inset IndexMacro subentry
35509 \begin_layout Plain Layout
35516 \begin_layout Plain Layout
35533 can be used with the same scheme as
35542 \begin_layout Standard
35543 \begin_inset VSpace bigskip
35546 Sometimes formulas should be numbered in the following form:
35549 \begin_layout Standard
35552 (section number.formula number)
35555 \begin_layout Standard
35556 The formula number should start with every section with
35557 \begin_inset Quotes eld
35561 \begin_inset Quotes erd
35567 \begin_layout Standard
35568 For this case there is the command
35575 \begin_inset Index idx
35580 \begin_layout Plain Layout
35582 \begin_inset IndexMacro subentry
35585 \begin_layout Plain Layout
35592 \begin_inset IndexMacro subentry
35595 \begin_layout Plain Layout
35609 which is used with the following scheme:
35612 \begin_layout Standard
35617 numberwithin{counter}{sectioning}
35620 \begin_layout Standard
35621 Counter denotes what kind of numbering is affected,
35622 sectioning denotes what the number before the dot is.
35625 \begin_layout Standard
35626 Thus in our case the following \SpecialChar LaTeX
35627 preamble or \SpecialChar TeX
35631 \begin_layout Standard
35636 numberwithin{equation}{section}
35639 \begin_layout Standard
35640 This is the result:
35644 \begin_layout Plain Layout
35648 numberwithin{equation}{section}
35654 \begin_inset Formula
35664 \begin_layout Standard
35666 \begin_inset space \thinspace{}
35670 \begin_inset space \space{}
35673 tables so that the number of the part is the sectioning,
35674 \begin_inset Newline newline
35681 numberwithin{table}{part}
35686 \begin_layout Standard
35687 To go back to the standard numbering or to prevent this kind of numbering when it is defined by the document class,
35688 the following command is inserted as \SpecialChar TeX
35689 code or to the \SpecialChar LaTeX
35693 \begin_layout Standard
35703 \begin_inset Index idx
35708 \begin_layout Plain Layout
35710 \begin_inset IndexMacro subentry
35713 \begin_layout Plain Layout
35720 \begin_inset IndexMacro subentry
35723 \begin_layout Plain Layout
35742 \begin_layout Plain Layout
35758 \begin_inset Newline newline
35766 \begin_inset Newline newline
35778 \begin_layout Standard
35785 internally uses the command
35793 and would also need to be reverted.
35797 \begin_layout Plain Layout
35804 \begin_layout Plain Layout
35808 @removefromreset{equation}{section}
35811 \begin_layout Plain Layout
35823 \begin_layout Section
35824 Chemical Symbols and Equations
35825 \begin_inset CommandInset label
35827 name "subsec:Chemical-Symbols-and"
35832 \begin_inset Index idx
35837 \begin_layout Plain Layout
35838 Chemical characters
35839 \begin_inset IndexMacro subentry
35842 \begin_layout Plain Layout
35854 \begin_inset Index idx
35859 \begin_layout Plain Layout
35866 \begin_inset Index idx
35871 \begin_layout Plain Layout
35873 \begin_inset IndexMacro subentry
35876 \begin_layout Plain Layout
35890 \begin_layout Standard
35891 An example text from chemistry:
35894 \begin_layout Quote
35896 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
35899 -ion reacts with two
35900 \begin_inset Formula $\mathrm{Na^{+}}$
35903 -ions to sodium sulfate
35904 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
35908 The chemical equation for this is:
35909 \begin_inset Formula
35911 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
35919 \begin_layout Standard
35920 Chemical equations can be created as formulas.
35921 To avoid the symbols appearing in italic,
35922 everything is highlighted and changed by the shortcut
35928 to the upright font style.
35932 \begin_layout Plain Layout
35938 \begin_inset CommandInset ref
35940 reference "subsec:Font-Styles"
35953 \begin_layout Standard
35954 A more convenient way to typeset chemical formulas is to use the command
35961 \begin_inset Index idx
35966 \begin_layout Plain Layout
35968 \begin_inset IndexMacro subentry
35971 \begin_layout Plain Layout
35978 \begin_inset IndexMacro subentry
35981 \begin_layout Plain Layout
35994 which is available when the \SpecialChar LaTeX
36000 \begin_inset Index idx
36005 \begin_layout Plain Layout
36007 \begin_inset IndexMacro subentry
36010 \begin_layout Plain Layout
36028 in a formula a new blue box appears where chemical formulas can be inserted in an intuitive way.
36031 \begin_layout Standard
36033 \begin_inset Tabular
36034 <lyxtabular version="3" rows="10" columns="2">
36035 <features booktabs="true" tabularvalignment="middle">
36036 <column alignment="center" valignment="top" width="0pt">
36037 <column alignment="center" valignment="top">
36039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36042 \begin_layout Plain Layout
36048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36051 \begin_layout Plain Layout
36059 <cell alignment="center" valignment="top" leftline="true" usebox="none">
36062 \begin_layout Plain Layout
36066 \begin_inset space \textvisiblespace{}
36074 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
36077 \begin_layout Plain Layout
36078 \begin_inset Formula $\ce{H2CO3}$
36087 <row topspace="1.5mm">
36088 <cell alignment="center" valignment="top" usebox="none">
36091 \begin_layout Plain Layout
36095 \begin_inset space \textvisiblespace{}
36103 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
36106 \begin_layout Plain Layout
36107 \begin_inset Formula $\ce{SO4^{2-}}$
36116 <row topspace="1.5mm">
36117 <cell alignment="center" valignment="top" usebox="none">
36120 \begin_layout Plain Layout
36124 \begin_inset space \textvisiblespace{}
36132 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
36135 \begin_layout Plain Layout
36136 \begin_inset Formula $\ce{(NH4)2S}$
36145 <row topspace="1.5mm">
36146 <cell alignment="center" valignment="top" usebox="none">
36149 \begin_layout Plain Layout
36153 \begin_inset space \textvisiblespace{}
36161 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
36164 \begin_layout Plain Layout
36165 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
36174 <row topspace="1.5mm">
36175 <cell alignment="center" valignment="top" usebox="none">
36178 \begin_layout Plain Layout
36182 \begin_inset space \textvisiblespace{}
36188 \begin_inset space \textvisiblespace{}
36194 \begin_inset space \textvisiblespace{}
36202 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
36205 \begin_layout Plain Layout
36206 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
36215 <row topspace="1.5mm">
36216 <cell alignment="center" valignment="top" usebox="none">
36219 \begin_layout Plain Layout
36223 \begin_inset space \textvisiblespace{}
36227 \begin_inset Formula $\downarrow$
36231 \begin_inset Formula $\to$
36239 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
36242 \begin_layout Plain Layout
36243 \begin_inset Formula $\ce{_{90}^{227}Th+}$
36253 <cell alignment="center" valignment="top" leftline="true" usebox="none">
36256 \begin_layout Plain Layout
36260 \begin_inset space \textvisiblespace{}
36266 \begin_inset space \textvisiblespace{}
36272 \begin_inset space \textvisiblespace{}
36280 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
36283 \begin_layout Plain Layout
36284 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
36294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36297 \begin_layout Plain Layout
36301 \begin_inset space \textvisiblespace{}
36305 \begin_inset space \textvisiblespace{}
36309 \begin_inset space \textvisiblespace{}
36313 \begin_inset space \textvisiblespace{}
36317 \begin_inset space \textvisiblespace{}
36325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36328 \begin_layout Plain Layout
36329 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
36338 <row topspace="1.5mm">
36339 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
36342 \begin_layout Plain Layout
36346 \begin_inset space \textvisiblespace{}
36350 \begin_inset space \textvisiblespace{}
36354 \begin_inset space \textvisiblespace{}
36358 \begin_inset space \textvisiblespace{}
36366 \begin_inset space \textvisiblespace{}
36374 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
36377 \begin_layout Plain Layout
36378 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
36394 \begin_layout Standard
36395 \begin_inset Note Greyedout
36398 \begin_layout Plain Layout
36404 It is not possible in \SpecialChar LyX
36405 to use the character ^ to get an up-arrow as described in the
36410 One instead uses a negative thin space followed by the command
36418 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
36429 \begin_layout Standard
36436 the command for equation
36437 \begin_inset space ~
36441 \begin_inset CommandInset ref
36443 reference "eq:chem-reaction"
36449 \begin_inset Newline newline
36457 \begin_inset space \textvisiblespace{}
36461 \begin_inset space \textvisiblespace{}
36465 \begin_inset space \textvisiblespace{}
36469 \begin_inset space \textvisiblespace{}
36473 \begin_inset space \textvisiblespace{}
36477 \begin_inset space \textvisiblespace{}
36483 \begin_layout Standard
36484 To create multiline chemical equations first a multiline formula is created as described in
36485 \begin_inset CommandInset ref
36487 reference "sec:Multiline-Formulas"
36493 Afterwards the command
36499 is used in every small blue box of the formula.
36501 \begin_inset CommandInset ref
36503 reference "eq:TEOS-reaction-1"
36509 \begin_inset CommandInset ref
36511 reference "eq:TEOS-reaction-2"
36516 are an example of a multi-stage chemical reaction where every equation has its own number.
36517 \begin_inset Formula
36519 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
36520 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
36528 \begin_layout Standard
36539 package provides the command
36546 \begin_inset Index idx
36551 \begin_layout Plain Layout
36553 \begin_inset IndexMacro subentry
36556 \begin_layout Plain Layout
36563 \begin_inset IndexMacro subentry
36566 \begin_layout Plain Layout
36579 that is used for special cases.
36580 For more information about
36586 and more examples have a look at the documentation of
36592 \begin_inset CommandInset citation
36602 \begin_layout Section
36606 \begin_layout Standard
36608 supports two types of commutative diagrams:
36617 and are explained below.
36620 \begin_layout Subsection
36622 \begin_inset Index idx
36627 \begin_layout Plain Layout
36629 \begin_inset IndexMacro subentry
36632 \begin_layout Plain Layout
36646 \begin_layout Standard
36647 Diagrams of this type visualize relations by vertical and horizontal lines or arrows:
36648 \begin_inset Formula
36650 \begin{CD}A@>>>B@>>>C\\
36661 \begin_layout Standard
36668 \begin_inset Index idx
36673 \begin_layout Plain Layout
36675 \begin_inset IndexMacro subentry
36678 \begin_layout Plain Layout
36685 \begin_inset IndexMacro subentry
36688 \begin_layout Plain Layout
36703 is inserted to a formula.
36704 A blue box appears with two dashed lines where additional commands can be inserted.
36708 arg "newline-insert newline"
36711 a new line is created.
36712 Horizontal relations are inserted in odd formula lines,
36713 vertical in even formula lines.
36716 \begin_layout Standard
36717 To create the relations use the following commands:
36720 \begin_layout Itemize
36725 creates a left arrow,
36737 \begin_layout Itemize
36742 creates an up arrow,
36751 a vertical equal sign
36754 \begin_layout Itemize
36760 is a placeholder for non-existent relations
36763 \begin_layout Standard
36764 All arrows can be labeled as follows:
36767 \begin_layout Itemize
36768 If text inserted between the first and second < or >,
36770 it is placed above the arrow.
36771 When it is inserted between the second and third one,
36772 it appears under the arrow.
36775 \begin_layout Itemize
36776 When text for vertical arrows is inserted between the first and second A or V,
36778 it is placed left beside the arrow.
36779 When it is inserted between the second and third one,
36780 it appears right beside the arrow.
36781 If the text contains an A or V,
36782 these letters must be set into a \SpecialChar TeX
36786 \begin_layout Standard
36787 As example a diagram with all possible relations:
36790 \begin_layout Standard
36791 \begin_inset Formula
36793 \begin{CD}A@>j>>B@>>k>C@=F\\
36804 \begin_layout Standard
36805 The command for this is:
36806 \begin_inset Newline newline
36814 \begin_inset space \textvisiblespace{}
36817 A@>j>>B@>>k>C@=F Ctrl+Return
36818 \begin_inset Newline newline
36822 \begin_inset Phantom HPhantom
36825 \begin_layout Plain Layout
36831 \begin_inset space \textvisiblespace{}
36844 \begin_inset Formula $\to$
36850 \begin_inset Newline newline
36854 \begin_inset Phantom HPhantom
36857 \begin_layout Plain Layout
36863 \begin_inset space \textvisiblespace{}
36874 \begin_layout Subsection
36876 \begin_inset Index idx
36881 \begin_layout Plain Layout
36883 \begin_inset IndexMacro subentry
36886 \begin_layout Plain Layout
36900 \begin_layout Standard
36901 To be able to use xymatrices,
36902 the \SpecialChar LaTeX
36908 A xymatrix is created by inserting the command
36915 Then you are able to add new matrix columns and rows like for normal matrices,
36917 \begin_inset CommandInset ref
36919 reference "sec:Matrices"
36927 \begin_layout Standard
36928 Contrary to amscd diagrams,
36929 xymatrices support diagonal and curved arrows,
36931 The commands used to create commutative diagrams and decorations are explained in detail in the
36937 Help\SpecialChar menuseparator
36939 \begin_inset space ~
36947 \begin_layout Subsection
36953 \begin_inset Index idx
36958 \begin_layout Plain Layout
36960 \begin_inset IndexMacro subentry
36963 \begin_layout Plain Layout
36977 \begin_layout Standard
36983 the \SpecialChar LaTeX
36993 -diagram is created by inserting the command
37000 Then you will be able to add new matrix columns and rows like for normal matrices,
37002 \begin_inset CommandInset ref
37004 reference "sec:Matrices"
37012 \begin_layout Standard
37013 Examples of how to create
37017 diagrams in \SpecialChar LyX
37022 manual that you find in the menu
37024 Help\SpecialChar menuseparator
37026 \begin_inset space ~
37034 \begin_layout Section
37035 User-defined Commands
37036 \begin_inset Index idx
37041 \begin_layout Plain Layout
37042 User-defined commands
37050 \begin_layout Standard
37051 \begin_inset Note Greyedout
37054 \begin_layout Plain Layout
37060 The names of user-defined commands and macros may only consist of Latin letters.
37068 \begin_layout Subsection
37072 \begin_inset CommandInset label
37074 name "subsec:The-Command-newcommand"
37079 \begin_inset Index idx
37084 \begin_layout Plain Layout
37085 User-defined commands
37086 \begin_inset IndexMacro subentry
37089 \begin_layout Plain Layout
37103 \begin_inset Index idx
37108 \begin_layout Plain Layout
37110 \begin_inset IndexMacro subentry
37113 \begin_layout Plain Layout
37120 \begin_inset IndexMacro subentry
37123 \begin_layout Plain Layout
37139 \begin_layout Standard
37140 Many \SpecialChar LaTeX
37141 -commands are too long to be used frequently.
37142 But it is possible to define with the command
37148 new shorter commands.
37151 \begin_layout Standard
37152 The command scheme of
37161 \begin_layout Standard
37166 newcommand{new command name}[number of arguments][optional
37171 \begin_inset Newline newline
37175 \begin_inset Phantom HPhantom
37178 \begin_layout Plain Layout
37188 {command definition}
37191 \begin_layout Standard
37192 \begin_inset Note Greyedout
37195 \begin_layout Plain Layout
37201 Verify that the name of the new command is not already used in your document or by the \SpecialChar LaTeX
37202 -packages that you use.
37203 If you for example define the command
37216 you will get an error message because
37222 is already defined as command for
37223 \begin_inset Quotes eld
37227 \begin_inset Formula $\le$
37231 \begin_inset Quotes erd
37242 \begin_layout Standard
37243 The number of arguments is an integer in the range 0
37244 \begin_inset space \thinspace{}
37248 \begin_inset space \thinspace{}
37251 9 and specifies how many arguments the new command should have.
37252 With the optional value a value for an optional argument can be predefined.
37262 rgument of the new command is automatically an optional one.
37265 \begin_layout Standard
37266 Here are some examples:
37269 \begin_layout Itemize
37270 To define the command
37283 the \SpecialChar LaTeX
37285 \begin_inset VSpace medskip
37289 \begin_inset Newline newline
37303 \begin_layout Itemize
37304 To define the command
37317 the argument (that should be underlined) must be taken into account.
37318 For this the preamble line is:
37319 \begin_inset VSpace medskip
37323 \begin_inset Newline newline
37337 \begin_inset VSpace medskip
37341 \begin_inset Newline newline
37348 acts as argument placeholder,
37353 behind it denotes that it is the placeholder for the first argument.
37356 \begin_layout Itemize
37364 \begin_inset space \thinspace{}
37368 \begin_inset space \space{}
37378 \begin_inset VSpace medskip
37382 \begin_inset Newline newline
37393 framebox#1#2{$#3$}}
37396 \begin_inset VSpace medskip
37400 \begin_inset Newline newline
37403 The two Dollar signs creates the extra formula needed for
37411 \begin_inset CommandInset ref
37413 reference "subsec:Boxes-with-Frame"
37421 \begin_layout Itemize
37422 To create a new command for
37428 where the color for the box need not be specified,
37429 the argument for the color is defined optional:
37430 \begin_inset VSpace medskip
37434 \begin_inset Newline newline
37445 fcolorbox{#2}{#1}{$#3$}}
37448 \begin_inset VSpace medskip
37452 \begin_inset Newline newline
37455 When the color is not specified when using
37462 the predefined color
37469 \begin_layout Standard
37470 A test of the new defined commands:
37473 \begin_layout Standard
37475 \begin_inset Tabular
37476 <lyxtabular version="3" rows="6" columns="2">
37477 <features booktabs="true" tabularvalignment="middle">
37478 <column alignment="center" valignment="top" width="0pt">
37479 <column alignment="center" valignment="top">
37481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37484 \begin_layout Plain Layout
37490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37493 \begin_layout Plain Layout
37501 <cell alignment="center" valignment="top" leftline="true" usebox="none">
37504 \begin_layout Plain Layout
37508 \begin_inset space \textvisiblespace{}
37516 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
37519 \begin_layout Plain Layout
37520 \begin_inset Formula $A\gr B$
37530 <cell alignment="center" valignment="top" leftline="true" usebox="none">
37533 \begin_layout Plain Layout
37541 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
37544 \begin_layout Plain Layout
37545 \begin_inset Formula $\us{ABcd}$
37554 <row topspace="1mm">
37555 <cell alignment="center" valignment="top" usebox="none">
37558 \begin_layout Plain Layout
37562 \begin_inset Formula $\to$
37568 \begin_inset Formula $\to$
37576 \begin_inset space \textvisiblespace{}
37584 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
37587 \begin_layout Plain Layout
37588 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
37597 <row topspace="1.5mm">
37598 <cell alignment="center" valignment="top" usebox="none">
37601 \begin_layout Plain Layout
37605 \begin_inset Formula $\to$
37613 \begin_inset space \textvisiblespace{}
37621 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
37624 \begin_layout Plain Layout
37625 \begin_inset Formula $\cb{red}{\int A=B}$
37634 <row topspace="1.5mm" bottomspace="1mm">
37635 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37638 \begin_layout Plain Layout
37644 \begin_inset Formula $\to$
37652 \begin_inset space \textvisiblespace{}
37660 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
37663 \begin_layout Plain Layout
37664 \begin_inset Formula $\cb[green]{red}{\int A=B}$
37680 \begin_layout Subsection
37682 \begin_inset Index idx
37687 \begin_layout Plain Layout
37688 User-defined commands!
37695 \begin_inset Index idx
37700 \begin_layout Plain Layout
37709 \begin_layout Standard
37710 User-defined commands are especially convenient for complex expressions.
37711 For example if you are dealing with a document that has quadratic equations,
37712 the same solution type occurs several times.
37713 The general form of a quadratic equation is
37714 \begin_inset Formula
37716 0=\lambda^{2}+p\lambda+q
37721 The general form of the solution is
37722 \begin_inset Formula
37724 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
37732 \begin_layout Standard
37733 To define a command for the solution formula where only the three parameters
37734 \begin_inset Formula $\lambda$
37739 \begin_inset Formula $p$
37743 \begin_inset Formula $q$
37746 need to be specified and the index of
37747 \begin_inset Formula $\lambda$
37750 can be given optionally,
37751 the \SpecialChar LaTeX
37753 \begin_inset Newline newline
37769 \begin_inset Newline newline
37773 \begin_inset Phantom HPhantom
37776 \begin_layout Plain Layout
37790 frac{#3^{2}}{4}-#4}}
37793 \begin_layout Standard
37794 To create with this the solution formula,
37796 \begin_inset Newline newline
37806 \begin_inset Formula $\to$
37812 \begin_inset Formula $\to$
37819 is inserted to a formula
37824 \begin_layout Standard
37825 The definition of the new command is unintuitive because one has to know the schemes of all used \SpecialChar LaTeX
37828 \begin_inset space \thinspace{}
37832 \begin_inset space \space{}
37835 that a fraction is inserted in \SpecialChar LaTeX
37840 frac{numerator}{denominator}
37843 Furthermore one can easily forget a brace in the definition and cannot see in \SpecialChar LyX
37844 what the new command is doing.
37845 To avoid these problems \SpecialChar LyX
37846 offers the possibility to use math macros instead of the command
37855 \begin_layout Standard
37856 A math macro is created by using the menu
37858 Insert\SpecialChar menuseparator
37859 Math\SpecialChar menuseparator
37862 or the toolbar button
37865 arg "math-macro newmacroname_newcommand"
37869 The math macro toolbar appears together with the following box where the macro is defined:
37870 \begin_inset Newline newline
37874 \begin_inset space \hspace*{\fill}
37878 \begin_inset Graphics
37879 filename clipart/macrobox.png
37885 \begin_inset space \hspace*{\fill}
37889 \begin_inset Newline newline
37893 \begin_inset FormulaMacro
37894 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
37899 newmacroname is the default name of the macro that should be changed to something sensible.
37900 The wanted formula is inserted in the first blue box.
37901 An argument placeholder is inserted with the command
37909 \begin_inset space \thinspace{}
37913 \begin_inset space \space{}
37922 or by using the macro toolbar button
37925 arg "math-macro-add-param"
37929 Argument placeholders are displayed red.
37931 \begin_inset space ~
37934 arguments are possible.
37935 Optional arguments are created with the toolbar button
37938 arg "math-macro-add-optional-param"
37942 The first non-optional argument can be transformed to an optional one with the toolbar button
37945 arg "math-macro-make-optional"
37949 In the second blue box the appearance of the macro in \SpecialChar LyX
37951 Normally you want to see it as it is defined,
37952 so the box is kept empty.
37953 But when you have created a macro that needs lot of space on the screen,
37954 you can insert in the box for example
37955 \begin_inset Newline newline
37989 \begin_inset Newline newline
37994 For the macro only the arguments with the macro name in front of them will then be displayed in \SpecialChar LyX
37996 leading to a better overview.
37997 The formula appears in the output as defined in the first box.
37998 \begin_inset Newline newline
38001 The appearance of macros in formulas can furthermore be changed for single macros by setting the cursor in the macro and using the menu
38003 View\SpecialChar menuseparator
38005 \begin_inset space ~
38009 \begin_inset space ~
38017 \begin_layout Standard
38019 the macro name is inserted as command to a formula,
38027 Our macro looks in \SpecialChar LyX
38029 \begin_inset Newline newline
38033 \begin_inset space \hspace*{\fill}
38037 \begin_inset Graphics
38038 filename clipart/macrouse.png
38044 \begin_inset space \hspace*{\fill}
38048 \begin_inset Newline newline
38051 Here is our macro example with the arguments
38052 \begin_inset Formula $x$
38057 \begin_inset Formula $\ln(x)$
38061 \begin_inset Formula $B$
38067 \begin_layout Standard
38068 \begin_inset Formula
38078 \begin_layout Standard
38082 Tools\SpecialChar menuseparator
38083 Preferences\SpecialChar menuseparator
38084 Editing\SpecialChar menuseparator
38087 different styles to edit macros.
38088 To find the style that suits you best,
38089 choose a style and set the cursor in a macro formula to see the difference.
38092 \begin_layout Standard
38093 A math macro is transformed internally to a
38099 command when exporting the document.
38106 command is not placed in the \SpecialChar LaTeX
38108 therefore macros can only be used in formulas that are in the document below the macro definition box.
38111 \begin_layout Standard
38112 Math macros can also be directly created from a
38119 When writing for example the command
38122 \begin_inset Newline newline
38131 xleftarrow[#2]{#1}}
38132 \begin_inset Newline newline
38137 in \SpecialChar LyX
38139 highlighting it completely and using the shortcut
38144 the command will be transformed to a math macro.
38145 Using this method you need to be careful that the
38151 command is typed correctly,
38152 otherwise you get a faulty macro leading to \SpecialChar LaTeX
38156 \begin_layout Standard
38157 Math macros currently have the problem that further formulas in macro definitions are handled wrong.
38158 Therefore the example
38165 \begin_inset CommandInset ref
38167 reference "subsec:The-Command-newcommand"
38172 cannot be created as macro.
38175 \begin_layout Standard
38176 When the cursor is in a macro definition box,
38177 you will see the macro toolbar in \SpecialChar LyX
38181 \begin_layout Standard
38182 \begin_inset VSpace defskip
38188 \begin_layout Standard
38189 \begin_inset Graphics
38190 filename clipart/MacroToolbar.png
38195 \begin_inset Index idx
38200 \begin_layout Plain Layout
38202 \begin_inset IndexMacro subentry
38205 \begin_layout Plain Layout
38219 \begin_layout Standard
38220 \begin_inset VSpace defskip
38226 \begin_layout Standard
38227 The macro toolbar contains from left to right the following buttons:
38230 \begin_layout Standard
38231 \begin_inset VSpace defskip
38237 \begin_layout Standard
38238 \begin_inset Tabular
38239 <lyxtabular version="3" rows="9" columns="2">
38240 <features islongtable="true" longtabularalignment="center">
38241 <column alignment="left" valignment="top">
38242 <column alignment="left" valignment="top" width="85col%">
38243 <row interlinespace="2.5mm">
38244 <cell alignment="center" valignment="top" usebox="none">
38247 \begin_layout Plain Layout
38250 arg "math-macro-remove-param"
38258 <cell alignment="center" valignment="top" usebox="none">
38261 \begin_layout Plain Layout
38264 Edit\SpecialChar menuseparator
38265 Math\SpecialChar menuseparator
38267 \begin_inset space ~
38270 Definition\SpecialChar menuseparator
38271 Remove Last Argument
38277 <row interlinespace="2.5mm">
38278 <cell alignment="center" valignment="top" usebox="none">
38281 \begin_layout Plain Layout
38284 arg "math-macro-add-param"
38292 <cell alignment="center" valignment="top" usebox="none">
38295 \begin_layout Plain Layout
38298 Edit\SpecialChar menuseparator
38299 Math\SpecialChar menuseparator
38301 \begin_inset space ~
38304 Definition\SpecialChar menuseparator
38311 <row interlinespace="2.5mm">
38312 <cell alignment="center" valignment="top" usebox="none">
38315 \begin_layout Plain Layout
38318 arg "math-macro-make-optional"
38326 <cell alignment="center" valignment="top" usebox="none">
38329 \begin_layout Plain Layout
38332 Edit\SpecialChar menuseparator
38333 Math\SpecialChar menuseparator
38335 \begin_inset space ~
38338 Definition\SpecialChar menuseparator
38339 Transform First Non-Optional to
38340 \begin_inset Newline newline
38344 \begin_inset Phantom HPhantom
38347 \begin_layout Plain Layout
38350 Edit\SpecialChar menuseparator
38351 Math\SpecialChar menuseparator
38353 \begin_inset space ~
38356 Definition\SpecialChar menuseparator
38368 <row interlinespace="2.5mm">
38369 <cell alignment="center" valignment="top" usebox="none">
38372 \begin_layout Plain Layout
38375 arg "math-macro-make-nonoptional"
38383 <cell alignment="center" valignment="top" usebox="none">
38386 \begin_layout Plain Layout
38389 Edit\SpecialChar menuseparator
38390 Math\SpecialChar menuseparator
38392 \begin_inset space ~
38395 Definition\SpecialChar menuseparator
38396 Transform Last Optional to
38397 \begin_inset Newline newline
38401 \begin_inset Phantom HPhantom
38404 \begin_layout Plain Layout
38407 Edit\SpecialChar menuseparator
38408 Math\SpecialChar menuseparator
38410 \begin_inset space ~
38413 Definition\SpecialChar menuseparator
38419 Non-Optional Argument
38425 <row interlinespace="2.5mm">
38426 <cell alignment="center" valignment="top" usebox="none">
38429 \begin_layout Plain Layout
38432 arg "math-macro-remove-optional-param"
38440 <cell alignment="center" valignment="top" usebox="none">
38443 \begin_layout Plain Layout
38446 Edit\SpecialChar menuseparator
38447 Math\SpecialChar menuseparator
38449 \begin_inset space ~
38452 Definition\SpecialChar menuseparator
38453 Remove Optional Argument
38459 <row interlinespace="2.5mm">
38460 <cell alignment="center" valignment="top" usebox="none">
38463 \begin_layout Plain Layout
38466 arg "math-macro-add-optional-param"
38474 <cell alignment="center" valignment="top" usebox="none">
38477 \begin_layout Plain Layout
38480 Edit\SpecialChar menuseparator
38481 Math\SpecialChar menuseparator
38483 \begin_inset space ~
38486 Definition\SpecialChar menuseparator
38487 Insert Optional Argument
38493 <row interlinespace="2.5mm">
38494 <cell alignment="center" valignment="top" usebox="none">
38497 \begin_layout Plain Layout
38500 arg "math-macro-remove-greedy-param"
38508 <cell alignment="center" valignment="top" usebox="none">
38511 \begin_layout Plain Layout
38514 Edit\SpecialChar menuseparator
38515 Math\SpecialChar menuseparator
38517 \begin_inset space ~
38520 Definition\SpecialChar menuseparator
38521 Remove Last Argument
38522 \begin_inset Newline newline
38526 \begin_inset Phantom HPhantom
38529 \begin_layout Plain Layout
38532 Edit\SpecialChar menuseparator
38533 Math\SpecialChar menuseparator
38535 \begin_inset space ~
38538 Definition\SpecialChar menuseparator
38544 Spitting Out To The Right
38550 <row interlinespace="2.5mm">
38551 <cell alignment="center" valignment="top" usebox="none">
38554 \begin_layout Plain Layout
38557 arg "math-macro-append-greedy-param"
38565 <cell alignment="center" valignment="top" usebox="none">
38568 \begin_layout Plain Layout
38571 Edit\SpecialChar menuseparator
38572 Math\SpecialChar menuseparator
38574 \begin_inset space ~
38577 Definition\SpecialChar menuseparator
38579 \begin_inset Newline newline
38583 \begin_inset Phantom HPhantom
38586 \begin_layout Plain Layout
38589 Edit\SpecialChar menuseparator
38590 Math\SpecialChar menuseparator
38592 \begin_inset space ~
38595 Definition\SpecialChar menuseparator
38601 Eating From The Right
38607 <row interlinespace="2.5mm">
38608 <cell alignment="center" valignment="top" usebox="none">
38611 \begin_layout Plain Layout
38614 arg "math-macro-add-greedy-optional-param"
38622 <cell alignment="center" valignment="top" usebox="none">
38625 \begin_layout Plain Layout
38628 Edit\SpecialChar menuseparator
38629 Math\SpecialChar menuseparator
38631 \begin_inset space ~
38634 Definition\SpecialChar menuseparator
38635 Append Optional Argument
38636 \begin_inset Newline newline
38640 \begin_inset Phantom HPhantom
38643 \begin_layout Plain Layout
38646 Edit\SpecialChar menuseparator
38647 Math\SpecialChar menuseparator
38649 \begin_inset space ~
38652 Definition\SpecialChar menuseparator
38658 Eating From The Right
38671 \begin_layout Section
38672 Computer Algebra Systems
38675 \begin_layout Standard
38677 offers the exchange between mathematical expressions written in \SpecialChar LyX
38678 's math editor and external applications or user defined scripts.
38679 Currently supported applications are
38698 Note that the set of supported mathematical constructs is limited only to very simple cases.
38701 \begin_layout Subsection
38705 \begin_layout Standard
38706 Write some expression in a formula,
38709 Edit\SpecialChar menuseparator
38710 Math\SpecialChar menuseparator
38711 Use Computer Algebra System
38713 menu and choose the application you have installed on the computer.
38714 After that the result of computation should show on the right side of the expression together with the
38715 \begin_inset Quotes eld
38719 \begin_inset Quotes erd
38725 \begin_layout Standard
38726 Here are few simple examples (with results from
38730 ) to show what kind of computations can be performed:
38733 \begin_layout Itemize
38734 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
38740 \begin_layout Itemize
38741 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
38747 \begin_layout Itemize
38748 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
38754 \begin_layout Itemize
38755 \begin_inset Formula $\int\left(\frac{1}{1+x^{3}}\right)dx=-\frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\,x-1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log\left(x+1\right)}{3}$
38759 \begin_inset Newline newline
38763 \begin_inset Note Greyedout
38766 \begin_layout Plain Layout
38772 One needs to use proper delimiter insets
38773 \begin_inset Formula $\left(\right)$
38776 instead of simple '(' ')' characters.
38784 \begin_layout Itemize
38785 \begin_inset Formula $\det\left[\begin{array}{ccc}
38789 \end{array}\right]=-56$
38795 \begin_layout Itemize
38796 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
38802 \begin_layout Itemize
38803 \begin_inset Formula $powerseries\left(-\log\left(5-x\right),x,1\right)=\sum_{{\mathit{i}_{2}}=0}^{\infty}{\frac{4^{-{\mathit{i}_{2}}-1}\,\left(x-1\right)^{{\mathit{i}_{2}}+1}}{{\mathit{i}_{2}}+1}}-\log4$
38809 \begin_layout Itemize
38810 \begin_inset Formula $solve\left(x_{1}+y_{1}^{3}=y_{1}+x_{1}^{2},x_{1}\right)=\left[x_{1}=-\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}-1}{2},x_{1}=\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}+1}{2}\right]$
38816 \begin_layout Subsection
38820 \begin_layout Standard
38821 Currently there is no keyboard shortcut for calling the algebra applications.
38822 One can easily bind a shortcut to the
38836 \begin_inset space \thinspace{}
38840 \begin_inset space \space{}
38847 key inside the math editor.
38852 one would use this shortcut definition command:
38855 \begin_layout Standard
38858 command-alternatives paragraph-break;math-extern maxima
38861 \begin_layout Section
38863 \begin_inset Index idx
38868 \begin_layout Plain Layout
38877 \begin_layout Subsection
38879 \begin_inset Index idx
38884 \begin_layout Plain Layout
38886 \begin_inset IndexMacro subentry
38889 \begin_layout Plain Layout
38903 \begin_layout Standard
38904 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.
38905 When writing the negative number in normal text,
38906 the minus sign appears correctly.
38909 \begin_layout Standard
38911 the problem disappears when converting the minus sign to mathematical text.
38914 \begin_layout Standard
38915 An example to visualize the problem:
38918 \begin_layout Standard
38920 \begin_inset Tabular
38921 <lyxtabular version="3" rows="3" columns="2">
38922 <features booktabs="true" tabularvalignment="middle">
38923 <column alignment="right" valignment="top" width="0pt">
38924 <column alignment="left" valignment="top">
38926 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
38929 \begin_layout Plain Layout
38935 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
38938 \begin_layout Plain Layout
38946 <cell alignment="right" valignment="top" leftline="true" usebox="none">
38949 \begin_layout Plain Layout
38955 <cell alignment="center" valignment="top" rightline="true" usebox="none">
38958 \begin_layout Plain Layout
38959 \begin_inset Formula $x=-2$
38969 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
38972 \begin_layout Plain Layout
38978 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
38981 \begin_layout Plain Layout
38982 \begin_inset Formula $x=\textrm{-}2$
38998 \begin_layout Subsection
38999 Comma as decimal Separator
39000 \begin_inset Index idx
39005 \begin_layout Plain Layout
39014 \begin_layout Standard
39015 In \SpecialChar LaTeX
39016 a comma inside a formula is used,
39017 according to the English convention,
39018 as number group separator.
39019 So there will be space added behind all commas in formulas.
39022 \begin_layout Standard
39024 the comma is highlighted and changed to mathematical text (shortcut
39033 \begin_layout Standard
39034 To use all formula commas in the document as decimal separator,
39043 \begin_layout Plain Layout
39048 is part of the \SpecialChar LaTeX
39054 \begin_inset Index idx
39059 \begin_layout Plain Layout
39061 \begin_inset IndexMacro subentry
39064 \begin_layout Plain Layout
39081 \begin_inset Index idx
39086 \begin_layout Plain Layout
39088 \begin_inset IndexMacro subentry
39091 \begin_layout Plain Layout
39102 is loaded with the \SpecialChar LaTeX
39106 \begin_layout Standard
39114 \begin_layout Subsection
39116 \begin_inset CommandInset label
39118 name "subsec:Physical-Vectors"
39123 \begin_inset Index idx
39128 \begin_layout Plain Layout
39130 \begin_inset IndexMacro subentry
39133 \begin_layout Plain Layout
39147 \begin_layout Standard
39148 Predefined vectors are offered by the \SpecialChar LaTeX
39154 \begin_inset Index idx
39159 \begin_layout Plain Layout
39161 \begin_inset IndexMacro subentry
39164 \begin_layout Plain Layout
39175 that is loaded with the \SpecialChar LaTeX
39179 \begin_layout Standard
39187 \begin_layout Standard
39191 \begin_layout Plain Layout
39201 \begin_inset Note Note
39204 \begin_layout Plain Layout
39205 The following table will only be displayed when the \SpecialChar LaTeX
39218 \begin_layout Standard
39219 The following commands are defined:
39222 \begin_layout Standard
39224 \begin_inset Tabular
39225 <lyxtabular version="3" rows="4" columns="2">
39226 <features booktabs="true" tabularvalignment="middle">
39227 <column alignment="center" valignment="top" width="0pt">
39228 <column alignment="center" valignment="top">
39230 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
39233 \begin_layout Plain Layout
39239 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
39242 \begin_layout Plain Layout
39250 <cell alignment="center" valignment="top" usebox="none">
39253 \begin_layout Plain Layout
39263 <cell alignment="center" valignment="top" usebox="none">
39266 \begin_layout Plain Layout
39267 \begin_inset Formula $\Bra{\psi}$
39277 <cell alignment="center" valignment="top" usebox="none">
39280 \begin_layout Plain Layout
39290 <cell alignment="center" valignment="top" usebox="none">
39293 \begin_layout Plain Layout
39294 \begin_inset Formula $\Ket{\psi}$
39304 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
39307 \begin_layout Plain Layout
39319 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
39322 \begin_layout Plain Layout
39323 \begin_inset Formula $\Braket{\psi|\phi}$
39339 \begin_layout Standard
39346 assures that all vertical bars are set in the size of the surrounding brackets:
39347 \begin_inset Formula
39349 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
39358 \begin_layout Plain Layout
39368 \begin_inset Note Note
39371 \begin_layout Plain Layout
39372 The following will be displayed when the \SpecialChar LaTeX
39385 \begin_layout Standard
39386 You need to install the \SpecialChar LaTeX
39391 to see the rest of this subsection in the output.
39394 \begin_layout Standard
39398 \begin_layout Plain Layout
39410 \begin_layout Standard
39417 can also be achieved using the command
39424 that is described in
39425 \begin_inset CommandInset ref
39427 reference "subsec:Automatic-Bracket-Size"
39435 \begin_layout Subsection
39436 Self-defined Fractions
39437 \begin_inset CommandInset label
39439 name "subsec:Self-defined-Fractions"
39444 \begin_inset Index idx
39449 \begin_layout Plain Layout
39451 \begin_inset IndexMacro subentry
39454 \begin_layout Plain Layout
39468 \begin_layout Standard
39469 To define custom commands for fractions,
39477 \begin_inset Index idx
39482 \begin_layout Plain Layout
39484 \begin_inset IndexMacro subentry
39487 \begin_layout Plain Layout
39494 \begin_inset IndexMacro subentry
39497 \begin_layout Plain Layout
39510 is used in the following scheme:
39513 \begin_layout Standard
39526 bracket}{fraction bar thickness}{style}
39527 \begin_inset Newline newline
39531 \begin_inset Phantom HPhantom
39534 \begin_layout Plain Layout
39544 {numerator}{denominator}
39547 \begin_layout Standard
39548 The style is a number in the range of 0
39549 \begin_inset space \thinspace{}
39553 \begin_inset space \thinspace{}
39559 \begin_layout Standard
39561 \begin_inset Tabular
39562 <lyxtabular version="3" rows="5" columns="2">
39563 <features booktabs="true" tabularvalignment="middle">
39564 <column alignment="center" valignment="top" width="0pt">
39565 <column alignment="center" valignment="top">
39567 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
39570 \begin_layout Plain Layout
39576 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
39579 \begin_layout Plain Layout
39587 <cell alignment="center" valignment="top" usebox="none">
39590 \begin_layout Plain Layout
39596 <cell alignment="center" valignment="top" usebox="none">
39599 \begin_layout Plain Layout
39600 display style formula
39607 <cell alignment="center" valignment="top" usebox="none">
39610 \begin_layout Plain Layout
39616 <cell alignment="center" valignment="top" usebox="none">
39619 \begin_layout Plain Layout
39627 <cell alignment="center" valignment="top" usebox="none">
39630 \begin_layout Plain Layout
39636 <cell alignment="center" valignment="top" usebox="none">
39639 \begin_layout Plain Layout
39647 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
39650 \begin_layout Plain Layout
39656 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
39659 \begin_layout Plain Layout
39673 \begin_layout Standard
39674 When no style is given,
39675 the size is adjusted to the surrounding environment like for the command
39684 \begin_layout Standard
39685 When no fraction bar thickness is given,
39686 the predefined value of 0.4
39687 \begin_inset space \thinspace{}
39693 \begin_layout Standard
39694 \begin_inset VSpace medskip
39711 \begin_inset CommandInset ref
39713 reference "subsec:Fractions"
39718 are defined with the commands
39721 \begin_layout Standard
39730 genfrac{}{}{}{0}{#1}{#2}}
39733 \begin_layout Standard
39737 \begin_layout Standard
39746 genfrac{(}{)}{0pt}{1}{#1}{#2}}
39749 \begin_layout Standard
39750 \begin_inset VSpace medskip
39753 To define a fraction where the fraction bar thickness can be given as optional argument,
39754 the following line is inserted to the \SpecialChar LaTeX
39758 \begin_layout Standard
39767 genfrac{}{}{#1}{}{#2}{#3}}
39770 \begin_layout Standard
39772 \begin_inset Formula
39774 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
39775 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
39781 the distance of the numerator and the denominator to the fraction bar is round about three times the bar thickness.
39784 \begin_layout Subsection
39786 \begin_inset Index idx
39791 \begin_layout Plain Layout
39793 \begin_inset IndexMacro subentry
39796 \begin_layout Plain Layout
39810 \begin_layout Standard
39811 There are four ways to cancel formulas or parts of formulas:
39814 \begin_layout Standard
39818 \begin_layout Plain Layout
39828 \begin_inset Note Note
39831 \begin_layout Plain Layout
39832 The following table will only be displayed when the \SpecialChar LaTeX
39845 \begin_layout Standard
39847 \begin_inset Tabular
39848 <lyxtabular version="3" rows="5" columns="2">
39849 <features booktabs="true" tabularvalignment="middle">
39850 <column alignment="center" valignment="top" width="0pt">
39851 <column alignment="center" valignment="top">
39853 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
39856 \begin_layout Plain Layout
39862 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
39865 \begin_layout Plain Layout
39873 <cell alignment="center" valignment="top" usebox="none">
39876 \begin_layout Plain Layout
39880 \begin_inset space \textvisiblespace{}
39886 \begin_inset space \textvisiblespace{}
39894 <cell alignment="center" valignment="top" usebox="none">
39897 \begin_layout Plain Layout
39898 \begin_inset Formula $\cancel{\int A=B}$
39907 <row topspace="1.5mm">
39908 <cell alignment="center" valignment="top" usebox="none">
39911 \begin_layout Plain Layout
39915 \begin_inset space \textvisiblespace{}
39921 \begin_inset space \textvisiblespace{}
39929 <cell alignment="center" valignment="top" usebox="none">
39932 \begin_layout Plain Layout
39933 \begin_inset Formula $\bcancel{\int A=B}$
39942 <row topspace="1.5mm">
39943 <cell alignment="center" valignment="top" usebox="none">
39946 \begin_layout Plain Layout
39950 \begin_inset space \textvisiblespace{}
39956 \begin_inset space \textvisiblespace{}
39964 <cell alignment="center" valignment="top" usebox="none">
39967 \begin_layout Plain Layout
39968 \begin_inset Formula $\xcancel{\int A=B}$
39978 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
39981 \begin_layout Plain Layout
39985 \begin_inset space \textvisiblespace{}
39991 \begin_inset space \textvisiblespace{}
39995 \begin_inset Formula $\to$
40003 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
40006 \begin_layout Plain Layout
40007 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
40023 \begin_layout Standard
40030 is especially suitable to visualize the reduction of fractions within formulas:
40031 \begin_inset Formula
40033 \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}}}
40041 \begin_layout Standard
40042 To change the size of
40049 \begin_inset Quotes eld
40053 \begin_inset Quotes erd
40056 value one can add the \SpecialChar LaTeX
40060 \begin_layout Standard
40065 PassOptionsToPackage{option}{cancel}
40068 \begin_layout Standard
40077 which leads to the same size as for the canceled value,
40082 which makes is it a bit smaller than normal.
40085 \begin_layout Standard
40086 To color the cancellation bar one adds this command as \SpecialChar TeX
40090 \begin_layout Standard
40102 \begin_layout Standard
40107 can be replaced by a color of your choice.
40110 \begin_layout Standard
40114 \begin_layout Plain Layout
40130 \begin_layout Standard
40131 \begin_inset Formula
40133 \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}}}
40141 \begin_layout Standard
40145 \begin_layout Plain Layout
40159 \begin_inset Note Note
40162 \begin_layout Plain Layout
40171 \begin_layout Standard
40172 For further customizations,
40173 see the documentation of the package
40179 \begin_inset CommandInset citation
40187 \begin_inset Index idx
40192 \begin_layout Plain Layout
40194 \begin_inset IndexMacro subentry
40197 \begin_layout Plain Layout
40211 \begin_layout Standard
40215 \begin_layout Plain Layout
40225 \begin_inset Note Note
40228 \begin_layout Plain Layout
40229 The following will be displayed when the \SpecialChar LaTeX
40242 \begin_layout Standard
40243 You need to install the \SpecialChar LaTeX
40248 to see the rest of this subsection in the output.
40251 \begin_layout Standard
40255 \begin_layout Plain Layout
40267 \begin_layout Subsection
40268 Formulas in Section Headings
40269 \begin_inset CommandInset label
40271 name "subsec:Formulas-in-Section"
40276 \begin_inset Index idx
40281 \begin_layout Plain Layout
40283 \begin_inset IndexMacro subentry
40286 \begin_layout Plain Layout
40287 in section headings
40300 \begin_layout Standard
40301 When formulas are used in section headings,
40302 the following has to be taken into account:
40305 \begin_layout Standard
40306 \begin_inset Note Greyedout
40309 \begin_layout Plain Layout
40315 \begin_inset Index idx
40320 \begin_layout Plain Layout
40322 \begin_inset IndexMacro subentry
40325 \begin_layout Plain Layout
40336 support is enabled in the document settings dialog under
40339 \begin_inset space ~
40345 PDF-bookmarks are created for every section heading in the table of contents.
40346 If a section heading contains formulas,
40347 they are incorrectly displayed in the bookmark text,
40348 because formulas in bookmarks infringe the PDF conventions.
40356 \begin_layout Standard
40357 Both problems can be solved by inserting at the end of the section heading a short title with the menu
40359 Insert\SpecialChar menuseparator
40361 \begin_inset space ~
40367 Short titles are used as alternative for multiline section headings to keep the table of contents clearly arranged.
40368 Only the short title appears in the table of contents and therefore also in the PDF-bookmark.
40371 \begin_layout Standard
40372 When formulas should be used in the table of contents but
40377 one can use the following command in \SpecialChar TeX
40381 \begin_layout Standard
40386 texorpdfstring{part}{alternative}
40387 \begin_inset Index idx
40392 \begin_layout Plain Layout
40394 \begin_inset IndexMacro subentry
40397 \begin_layout Plain Layout
40404 \begin_inset IndexMacro subentry
40407 \begin_layout Plain Layout
40423 \begin_layout Standard
40424 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
40425 This can be characters,
40428 but also cross-references.
40429 The alternative is used instead of the part for the bookmark.
40432 \begin_layout Standard
40433 Here are two example headings:
40434 \begin_inset VSpace -3mm
40441 \begin_layout Plain Layout
40453 \begin_layout Subsubsection
40454 Heading without formula in table of contents
40455 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
40459 \begin_inset Argument 1
40462 \begin_layout Plain Layout
40463 Heading without formula in table of contents
40471 \begin_layout Subsubsection
40472 Heading with formula in table of contents
40476 \begin_layout Plain Layout
40486 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
40493 \begin_layout Plain Layout
40503 \begin_layout Standard
40507 \begin_layout Plain Layout
40516 In the first heading a short title was used,
40526 \begin_layout Standard
40527 To get the same formatting as for the other headings,
40528 the complete heading was set into a
40536 \begin_layout Plain Layout
40538 \begin_inset CommandInset ref
40540 reference "subsec:Bold-Formulas"
40553 \begin_layout Subsection
40554 Formulas in multi-column Text
40555 \begin_inset Index idx
40560 \begin_layout Plain Layout
40562 \begin_inset IndexMacro subentry
40565 \begin_layout Plain Layout
40566 in multi-column text
40579 \begin_layout Standard
40580 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.
40581 This is done by using the \SpecialChar LaTeX
40590 \begin_layout Plain Layout
40595 is part of every \SpecialChar LaTeX
40596 standard installation.
40602 \begin_inset Index idx
40607 \begin_layout Plain Layout
40609 \begin_inset IndexMacro subentry
40612 \begin_layout Plain Layout
40624 that is loaded with the \SpecialChar LaTeX
40628 \begin_layout Standard
40633 usepackage{multicol}
40636 \begin_layout Standard
40637 \begin_inset Note Greyedout
40640 \begin_layout Plain Layout
40641 Note that in this case the setting
40644 \begin_inset space ~
40651 Document\SpecialChar menuseparator
40657 \begin_inset space ~
40677 \begin_layout Standard
40678 Before the multi-column text the command
40681 \begin_layout Standard
40686 begin{multicols}{column number}
40689 \begin_layout Standard
40690 is written in \SpecialChar TeX
40692 The column number is a number in the range of 2
40693 \begin_inset space \thinspace{}
40697 \begin_inset space \thinspace{}
40701 Before the formula the multi-column text is ended by inserting the command
40704 \begin_layout Standard
40712 \begin_layout Standard
40713 in \SpecialChar TeX
40717 \begin_layout Standard
40718 Due to the command some space is automatically added before the formula.
40721 \begin_inset space \thinspace{}
40724 mm vertical space is inserted before the formula.
40725 When the formula style
40731 \begin_layout Plain Layout
40732 For formula styles see
40733 \begin_inset CommandInset ref
40735 reference "sec:Formula-Styles"
40749 \begin_inset space \thinspace{}
40752 mm space is inserted instead.
40755 \begin_layout Standard
40756 As example a multi-column text with a displayed formula:
40759 \begin_layout Standard
40765 \begin_layout Plain Layout
40769 begin{multicols}{2}
40774 Das Spektrum wird fouriertransformiert.
40775 Die Fouriertransformation wird verwendet,
40776 um die überlagerten Signale (Netzwerk,
40777 Lösungsmittel) zu trennen.
40778 Nachdem wir die Phasenverschiebung bestimmen konnten,
40779 interessiert uns nun das Aussehen des Ausgangssignals.
40780 Im Experiment haben wir es mit sehr vielen Teilchen zu tun,
40781 so dass man über alle Phasen integrieren muss.
40783 \begin_inset Formula $S$
40786 unser normiertes Ausgangssignal und
40787 \begin_inset Formula $P$
40790 die Phasenverteilungsfunktion,
40791 so ergibt sich die Beziehung
40795 \begin_layout Plain Layout
40805 \begin_inset VSpace -6mm
40809 \begin_inset Formula
40811 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
40820 \begin_layout Plain Layout
40824 begin{multicols}{2}
40830 \begin_inset Formula $S_{0}$
40833 das Signal ohne Gradient ist und die Normierungsbedingung
40834 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
40838 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
40840 \begin_inset Formula $\nicefrac{\pi}{2}$
40844 \begin_inset space \thinspace{}
40847 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren,
40848 wodurch sich das Signal zusätzlich abschwächt.
40849 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
40850 \begin_inset Formula $T_{2}$
40856 \begin_layout Standard
40862 \begin_layout Plain Layout
40874 \begin_layout Subsection
40875 Formulas with Description of Variables
40876 \begin_inset Index idx
40881 \begin_layout Plain Layout
40883 \begin_inset IndexMacro subentry
40886 \begin_layout Plain Layout
40887 with description of variables
40900 \begin_layout Standard
40901 To describe variables within a formula,
40903 \begin_inset CommandInset ref
40905 reference "eq:within"
40916 \begin_inset Formula $n$
40920 \begin_inset space ~
40923 matrix is used with left aligned columns for the
40924 \begin_inset Formula $n$
40931 \begin_layout Plain Layout
40933 \begin_inset CommandInset ref
40935 reference "sec:Matrices"
40945 To set the description in a smaller size,
40946 before the matrix e.
40947 \begin_inset space \thinspace{}
40951 \begin_inset space \space{}
40964 \begin_layout Plain Layout
40966 \begin_inset CommandInset ref
40968 reference "subsec:Font-Sizes"
40981 \begin_layout Standard
40982 When the formula style
40988 \begin_layout Plain Layout
40989 For formula styles see
40990 \begin_inset CommandInset ref
40992 reference "sec:Formula-Styles"
41015 \begin_layout Plain Layout
41022 only works in formulas with the style
41028 \begin_inset CommandInset ref
41030 reference "subsec:Variable-Space"
41040 is inserted before and after the matrix to have the same separation of the matrix from the equation and the side margin.
41043 \begin_layout Standard
41044 When the formula style
41049 the method described in
41050 \begin_inset CommandInset ref
41052 reference "subsec:Flalign-Environment"
41057 is used to indent formulas.
41059 \begin_inset CommandInset ref
41061 reference "eq:within"
41066 consists of five columns where in the first two columns contain the equation,
41067 the third the matrix and the last one an empty \SpecialChar TeX
41069 \begin_inset Formula
41071 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
41072 \rho & \textrm{density}\\
41073 V & \textrm{volume}\\
41074 g & \textrm{gravitational acceleration}
41075 \end{array} & & {}\label{eq:within}
41083 \begin_layout Subsection
41084 Upright small Greek Letters
41085 \begin_inset CommandInset label
41087 name "subsec:Upright-small-Greek"
41092 \begin_inset Index idx
41097 \begin_layout Plain Layout
41099 \begin_inset IndexMacro subentry
41102 \begin_layout Plain Layout
41116 \begin_layout Standard
41117 Most of the math fonts only provide italic small Greek letters.
41118 But for symbols of elementary particles like pions and neutrinos,
41119 upright Greek letters are needed.
41128 \begin_layout Plain Layout
41133 is part of the \SpecialChar LaTeX
41139 \begin_inset Index idx
41144 \begin_layout Plain Layout
41146 \begin_inset IndexMacro subentry
41149 \begin_layout Plain Layout
41166 \begin_inset Index idx
41171 \begin_layout Plain Layout
41173 \begin_inset IndexMacro subentry
41176 \begin_layout Plain Layout
41187 that is loaded with the \SpecialChar LaTeX
41191 \begin_layout Standard
41196 usepackage{upgreek}
41199 \begin_layout Standard
41205 \begin_layout Plain Layout
41215 \begin_inset Note Note
41218 \begin_layout Plain Layout
41219 The following table will only be displayed when the \SpecialChar LaTeX
41229 They are created when the command for a small Greek letter is started with
41234 For example the command
41242 \begin_inset Formula $\uptau$
41248 \begin_layout Standard
41249 With these commands reactions of elementary particles can be typeset:
41250 \begin_inset Formula
41252 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
41260 \begin_layout Standard
41261 The upright letters are more bold and wider than the italic ones.
41262 They should therefore not be used for units like
41263 \begin_inset Quotes eld
41267 \begin_inset Quotes erd
41273 \begin_layout Standard
41277 \begin_layout Plain Layout
41287 \begin_inset Note Note
41290 \begin_layout Plain Layout
41291 The following will be displayed when the \SpecialChar LaTeX
41304 \begin_layout Standard
41305 You need to install the \SpecialChar LaTeX
41310 to see the rest of this subsection in the output.
41313 \begin_layout Standard
41317 \begin_layout Plain Layout
41329 \begin_layout Subsection
41330 Text Characters in Formulas
41331 \begin_inset Index idx
41336 \begin_layout Plain Layout
41338 \begin_inset IndexMacro subentry
41341 \begin_layout Plain Layout
41355 \begin_layout Standard
41356 In some cases you might want to insert text characters directly into formulas.
41357 For example the centered dot · is often used in formulas like
41358 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
41362 One would have to insert the command
41372 \begin_layout Plain Layout
41374 \begin_inset CommandInset ref
41376 reference "subsec:Binary-Operators"
41387 because this character is defined in all encodings as a text character.
41388 But the encoding can be changed by this \SpecialChar LaTeX
41392 \begin_layout Standard
41397 Declare Inputtext{183}{
41407 f\SpecialChar ligaturebreak
41411 \begin_layout Standard
41412 The character encoding (menu
41414 Document\SpecialChar menuseparator
41415 Settings\SpecialChar menuseparator
41418 ) specifies what character appears when a keyboard key is pressed.
41419 When the key for the character '·' is pressed,
41420 internally the command
41427 But this command is not available in a formula so that you would get \SpecialChar LaTeX
41429 With the changed encoding the correct command is chosen automatically,
41430 depending on if the character was inserted into a formula or not.
41433 \begin_layout Standard
41434 The encoding of several characters is saved in definition files.
41435 For example the encoding
41439 is defined in the file
41443 which is in the installation folder of \SpecialChar LaTeX
41445 Encodings should only be changed via the \SpecialChar LaTeX
41446 -preamble and not in the definition files.
41447 Otherwise documents could not be edited by other \SpecialChar LyX
41448 users working on other computers.
41451 \begin_layout Standard
41452 \begin_inset VSpace medskip
41455 Besides the centered dot,
41456 in this document the degree sign ° is defined with the following \SpecialChar LaTeX
41457 -preamble line so that it can be directly inserted into a formula:
41460 \begin_layout Standard
41465 DeclareInputtext{176}{
41475 f\SpecialChar ligaturebreak
41479 \begin_layout Subsection
41481 -comments in formulas
41482 \begin_inset Index idx
41487 \begin_layout Plain Layout
41497 \begin_layout Standard
41498 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
41499 source code of your file with the menu
41501 Insert\SpecialChar menuseparator
41502 Note\SpecialChar menuseparator
41506 This is not possible in a formula but you can insert \SpecialChar LaTeX
41507 -comments with the command
41510 \begin_layout Standard
41518 \begin_layout Standard
41519 This creates a box in which you can write your comment.
41520 Due to a bug in \SpecialChar LyX
41525 \begin_layout Plain Layout
41526 \begin_inset CommandInset href
41528 name "LyX-bug #9002"
41529 target "https://www.lyx.org/trac/ticket/9002"
41539 you cannot write normal text inside the comment,
41540 even when you use mathematical text,
41541 you will see its \SpecialChar LaTeX
41542 -commands in the \SpecialChar LaTeX
41544 \begin_inset Newline newline
41547 This a formula with a \SpecialChar LaTeX
41549 \begin_inset Formula
41551 A=B%\text{This is the comment}
41559 \begin_layout Standard
41560 \begin_inset Newpage newpage
41566 \begin_layout Section
41569 \begin_inset Index idx
41574 \begin_layout Plain Layout
41583 \begin_layout Standard
41584 This section is a summary of the most important typographic rules,
41585 listed in ISO norms.
41589 \begin_layout Plain Layout
41590 This collection was partly taken from the German semi-official dictionary called
41591 \begin_inset Quotes eld
41595 \begin_inset Quotes erd
41599 \begin_inset CommandInset citation
41606 that lists some of the ISO rules.
41607 More rules are listed in
41608 \begin_inset CommandInset citation
41623 \begin_layout Itemize
41632 \begin_layout Plain Layout
41633 Done with font styles,
41635 \begin_inset CommandInset ref
41637 reference "subsec:Font-Styles"
41648 no matter if they appear in italic text:
41650 \begin_inset space \thinspace{}
41654 \begin_inset Newline newline
41657 Between the value and the unit is the smallest space,
41659 \begin_inset CommandInset ref
41661 reference "subsec:Predefined-Space"
41667 \begin_inset Newline newline
41670 This convention is automatically fulfilled when the command
41677 When it is entered in a formula,
41679 In the first one the value is inserted,
41680 in the second one the unit,
41681 and the result is as above:
41683 \begin_inset Formula $\unit[30]{km/h}$
41687 \begin_inset space \thinspace{}
41697 is not a real \SpecialChar LaTeX
41698 command but the command
41705 therefore you cannot use it in \SpecialChar TeX
41709 \begin_layout Itemize
41710 Percent and perthousand signs are set like physical units:
41711 \begin_inset Newline newline
41715 \begin_inset space \thinspace{}
41721 \begin_layout Itemize
41722 The degree sign follows the value directly:
41724 except when it is used in units:
41726 \begin_inset space \thinspace{}
41732 \begin_layout Itemize
41733 In numbers with more than four digits the smallest space is inserted before every third digit to group them:
41744 \begin_inset space \thinspace{}
41748 \begin_inset space \thinspace{}
41754 \begin_layout Itemize
41755 For dimensions like 120×90×40
41756 \begin_inset space \thinspace{}
41759 cm the multiplication sign
41760 \begin_inset Quotes eld
41764 \begin_inset Quotes erd
41768 It is available either via the command
41776 Insert\SpecialChar menuseparator
41777 Special Character\SpecialChar menuseparator
41783 \begin_layout Itemize
41784 Functions with names consisting of several letters are set upright to avoid confusions,
41786 \begin_inset CommandInset ref
41788 reference "subsec:Predefined-Functions"
41796 \begin_layout Itemize
41797 Indices consisting of several letters,
41800 \begin_inset Formula $E_{\mathrm{kin}}$
41804 \begin_inset Newline newline
41807 Components of matrices are set italic:
41809 \begin_inset Formula $\hat{H}_{kl}$
41815 \begin_layout Itemize
41816 The differentiation/integration operator 'd',
41817 the Euler's number 'e' and the imaginary unit 'i' should be set upright,
41818 to avoid mixing them up with other variables.
41821 \begin_layout Itemize
41822 The character that denotes a
41826 transformation is inserted either by the command
41831 \begin_inset space \textvisiblespace{}
41838 Insert\SpecialChar menuseparator
41839 Special Character\SpecialChar menuseparator
41840 Symbols\SpecialChar menuseparator
41842 \begin_inset space ~
41849 \begin_inset Formula $\mathscr{F}$
41855 \begin_layout Standard
41856 \begin_inset Newpage newpage
41862 \begin_layout Section
41864 \begin_inset Index idx
41869 \begin_layout Plain Layout
41878 \begin_layout Standard
41879 Some characters and symbols can be created with several commands.
41880 Here is a list of the synonym commands:
41883 \begin_layout Standard
41884 \begin_inset VSpace bigskip
41888 \begin_inset space \hfill{}
41892 \begin_inset Tabular
41893 <lyxtabular version="3" rows="12" columns="2">
41894 <features booktabs="true" tabularvalignment="middle">
41895 <column alignment="center" valignment="top" width="0pt">
41896 <column alignment="center" valignment="top" width="0pt">
41898 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
41901 \begin_layout Plain Layout
41907 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
41910 \begin_layout Plain Layout
41918 <cell alignment="center" valignment="top" usebox="none">
41921 \begin_layout Plain Layout
41929 <cell alignment="center" valignment="top" usebox="none">
41932 \begin_layout Plain Layout
41940 <cell alignment="center" valignment="top" usebox="none">
41943 \begin_layout Plain Layout
41951 <cell alignment="center" valignment="top" usebox="none">
41954 \begin_layout Plain Layout
41964 <cell alignment="center" valignment="top" usebox="none">
41967 \begin_layout Plain Layout
41975 <cell alignment="center" valignment="top" usebox="none">
41978 \begin_layout Plain Layout
41988 <cell alignment="center" valignment="top" usebox="none">
41991 \begin_layout Plain Layout
41999 <cell alignment="center" valignment="top" usebox="none">
42002 \begin_layout Plain Layout
42010 <cell alignment="center" valignment="top" usebox="none">
42013 \begin_layout Plain Layout
42021 <cell alignment="center" valignment="top" usebox="none">
42024 \begin_layout Plain Layout
42032 <cell alignment="center" valignment="top" usebox="none">
42035 \begin_layout Plain Layout
42043 <cell alignment="center" valignment="top" usebox="none">
42046 \begin_layout Plain Layout
42056 <cell alignment="center" valignment="top" usebox="none">
42059 \begin_layout Plain Layout
42067 <cell alignment="center" valignment="top" usebox="none">
42070 \begin_layout Plain Layout
42080 <cell alignment="center" valignment="top" usebox="none">
42083 \begin_layout Plain Layout
42091 <cell alignment="center" valignment="top" usebox="none">
42094 \begin_layout Plain Layout
42104 <cell alignment="center" valignment="top" usebox="none">
42107 \begin_layout Plain Layout
42115 <cell alignment="center" valignment="top" usebox="none">
42118 \begin_layout Plain Layout
42128 <cell alignment="center" valignment="top" usebox="none">
42131 \begin_layout Plain Layout
42139 <cell alignment="center" valignment="top" usebox="none">
42142 \begin_layout Plain Layout
42150 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
42153 \begin_layout Plain Layout
42161 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
42164 \begin_layout Plain Layout
42176 \begin_inset space \hfill{}
42180 \begin_inset Tabular
42181 <lyxtabular version="3" rows="12" columns="2">
42182 <features booktabs="true" tabularvalignment="middle">
42183 <column alignment="center" valignment="top" width="0pt">
42184 <column alignment="center" valignment="top" width="0pt">
42186 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
42189 \begin_layout Plain Layout
42195 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
42198 \begin_layout Plain Layout
42206 <cell alignment="center" valignment="top" usebox="none">
42209 \begin_layout Plain Layout
42217 <cell alignment="center" valignment="top" usebox="none">
42220 \begin_layout Plain Layout
42232 <cell alignment="center" valignment="top" usebox="none">
42235 \begin_layout Plain Layout
42243 <cell alignment="center" valignment="top" usebox="none">
42246 \begin_layout Plain Layout
42256 <cell alignment="center" valignment="top" usebox="none">
42259 \begin_layout Plain Layout
42267 <cell alignment="center" valignment="top" usebox="none">
42270 \begin_layout Plain Layout
42280 <cell alignment="center" valignment="top" usebox="none">
42283 \begin_layout Plain Layout
42291 <cell alignment="center" valignment="top" usebox="none">
42294 \begin_layout Plain Layout
42302 <cell alignment="center" valignment="top" usebox="none">
42305 \begin_layout Plain Layout
42313 <cell alignment="center" valignment="top" usebox="none">
42316 \begin_layout Plain Layout
42324 <cell alignment="center" valignment="top" usebox="none">
42327 \begin_layout Plain Layout
42335 <cell alignment="center" valignment="top" usebox="none">
42338 \begin_layout Plain Layout
42348 <cell alignment="center" valignment="top" usebox="none">
42351 \begin_layout Plain Layout
42359 <cell alignment="center" valignment="top" usebox="none">
42362 \begin_layout Plain Layout
42372 <cell alignment="center" valignment="top" usebox="none">
42375 \begin_layout Plain Layout
42383 <cell alignment="center" valignment="top" usebox="none">
42386 \begin_layout Plain Layout
42396 <cell alignment="center" valignment="top" usebox="none">
42399 \begin_layout Plain Layout
42407 <cell alignment="center" valignment="top" usebox="none">
42410 \begin_layout Plain Layout
42420 <cell alignment="center" valignment="top" usebox="none">
42423 \begin_layout Plain Layout
42431 <cell alignment="center" valignment="top" usebox="none">
42434 \begin_layout Plain Layout
42444 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
42447 \begin_layout Plain Layout
42455 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
42458 \begin_layout Plain Layout
42472 \begin_inset space \hfill{}
42476 \begin_inset CommandInset href
42479 target "https://ctan.org/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
42487 \begin_layout Standard
42488 \begin_inset Newpage newpage
42494 \begin_layout Bibliography
42495 \begin_inset CommandInset bibitem
42496 LatexCommand bibitem
42512 The \SpecialChar LaTeX
42520 \begin_layout Bibliography
42521 \begin_inset CommandInset bibitem
42522 LatexCommand bibitem
42529 \change_inserted 5863208 1612728717
42531 \begin_inset CommandInset href
42534 target "http://mirrors.ctan.org/obsolete/info/math/voss/mathmode/Mathmode.pdf"
42540 \change_deleted 5863208 1612728717
42542 \begin_inset CommandInset href
42545 target "https://www.tug.org/~hvoss/PDF/mathmode.pdf"
42552 of \SpecialChar LaTeX
42554 \change_deleted 5863208 1612728849
42556 \begin_inset Note Note
42559 \begin_layout Plain Layout
42561 \change_inserted 232239728 1611367909
42574 \begin_layout Bibliography
42575 \begin_inset CommandInset bibitem
42576 LatexCommand bibitem
42583 \change_inserted 5863208 1612728836
42585 \begin_inset CommandInset href
42588 target "http://tug.ctan.org/info/amslatex/english/amsldoc.pdf"
42594 \change_deleted 5863208 1612728836
42596 \begin_inset CommandInset href
42599 target "https://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/amsldoc.pdf"
42610 \begin_layout Plain Layout
42619 -\SpecialChar LaTeX
42621 \change_deleted 5863208 1612728851
42623 \begin_inset Note Note
42626 \begin_layout Plain Layout
42628 \change_inserted 232239728 1611367919
42641 \begin_layout Bibliography
42642 \begin_inset CommandInset bibitem
42643 LatexCommand bibitem
42650 \change_inserted 5863208 1612728963
42652 \begin_inset CommandInset href
42655 target "http://tug.ctan.org/info/symbols/comprehensive/symbols-a4.pdf"
42661 \change_deleted 5863208 1612728963
42663 \begin_inset CommandInset href
42666 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
42673 of all symbols available with \SpecialChar LaTeX
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42712 of the \SpecialChar LaTeX
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42759 of the \SpecialChar LaTeX
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42806 of the \SpecialChar LaTeX
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42879 for reviewing manuscripts
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