1 #LyX 2.4 created this file. For more info see https://www.lyx.org/
5 \save_transient_properties true
6 \origin /systemlyxdir/doc/
9 % DO NOT ALTER THIS PREAMBLE!!!
11 % This preamble is designed to ensure that the file prints
12 % out as advertised. If you mess with this preamble,
13 % parts of this document may not print out as expected. If you
14 % have problems LaTeXing this file, please contact
15 % the documentation team
16 % email: lyx-docs@lists.lyx.org
18 % solves the following problem:
19 % If the dection number consits of too many numerals the section heading
20 % will be printed in the TOC without a space between it and the section number.
21 % As solution more space between the number and the heading is inserted:
22 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
23 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
25 % increase link area for cross-references and autoname them,
26 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
27 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
28 \@ifpackageloaded{babel}{
29 \addto\extrasenglish{%
30 \renewcommand*{\equationautorefname}[1]{}%
31 \renewcommand{\sectionautorefname}{sec.\negthinspace}%
32 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
33 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
37 % don't load packages twice
38 % see first footnote in sec. 9.3
39 \@ifundefined{textcolor}{\usepackage{color}}{}
41 % the pages of the TOC are numbered roman
42 % and a PDF-bookmark for the TOC is added
44 \let\myTOC\tableofcontents
45 \renewcommand{\tableofcontents}{%
47 \pdfbookmark[1]{\contentsname}{}
50 \pagenumbering{arabic}}
52 % add 0.5 mm vertical space for table rows
53 \@ifundefined{extrarowheight} {\usepackage{array}}{}
54 \setlength{\extrarowheight}{0.5mm}
56 % insert additional vertical space of 1.5 mm between footnotes,
58 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
60 % makes caption labels bold
61 \setkomafont{captionlabel}{\bfseries}
63 % enables calculation of values
66 % for multiple columns used in sec. 24.7
72 % for the Fourier transformation symbol
75 % define a color, used in sec.9.3
76 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
78 % declare operators (see sec. 10.4 and sec. 15.2)
79 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
80 \DeclareMathOperator{\sgn}{sgn}
82 % example definitions for sec. 20.1
83 \newcommand{\gr}{\Longrightarrow}
84 \newcommand{\us}[1]{\underline{#1}}
85 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
86 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
87 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
89 % example macro from sec. 19.4
91 %\def\tagform@#1{\maketag@@@{|#1|}}
94 % ------------------------------------
95 % used to check for needed LaTeX packages
98 % check for package undertilde
99 % used for the command \utilde
100 \newboolean{undertilde}
101 \IfFileExists{undertilde.sty}
102 {\usepackage{undertilde}
103 \setboolean{undertilde}{true}}
104 {\setboolean{undertilde}{false}}
106 % check for package eurosym
107 % used for the Euro symbol
109 \IfFileExists{eurosym.sty}
110 {\usepackage[gennarrow]{eurosym}
111 \setboolean{eurosym}{true}}
112 {\setboolean{eurosym}{false}}
114 % check for package braket
115 % used for physical vectors
117 \IfFileExists{braket.sty}
119 \setboolean{braket}{true}}
120 {\setboolean{braket}{false}}
122 % check for package cancel
124 \IfFileExists{cancel.sty}
126 \setboolean{cancel}{true}}
127 {\setboolean{cancel}{false}}
129 % check for package upgreek
131 \IfFileExists{upgreek.sty}
132 {\usepackage{upgreek}
133 \setboolean{upgreek}{true}}
134 {\setboolean{upgreek}{false}}
136 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
137 \use_default_options false
141 \maintain_unincluded_children no
143 \language_package default
146 \font_roman "lmodern" "default"
147 \font_sans "lmss" "default"
148 \font_typewriter "lmtt" "default"
149 \font_math "auto" "auto"
150 \font_default_family default
151 \use_non_tex_fonts false
153 \font_roman_osf false
155 \font_typewriter_osf false
156 \font_sf_scale 100 100
157 \font_tt_scale 100 100
159 \use_dash_ligatures false
161 \default_output_format pdf2
163 \bibtex_command default
164 \index_command makeindex
165 \float_placement class
166 \float_alignment class
170 \pdf_title "LyX's Math Manual"
171 \pdf_author "LyX Team, Uwe Stöhr"
172 \pdf_subject "LyX-documentation about math"
173 \pdf_keywords "LyX, Mathed"
175 \pdf_bookmarksnumbered true
176 \pdf_bookmarksopen true
177 \pdf_bookmarksopenlevel 1
178 \pdf_breaklinks false
182 \pdf_pdfusetitle false
183 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
186 \use_package amsmath 2
187 \use_package amssymb 2
188 \use_package cancel 1
190 \use_package mathdots 1
191 \use_package mathtools 2
192 \use_package mhchem 1
193 \use_package stackrel 1
194 \use_package stmaryrd 1
195 \use_package undertilde 0
197 \cite_engine_type default
201 \paperorientation portrait
207 \notefontcolor #0000ff
214 \paragraph_separation skip
217 \math_numbering_side default
218 \quotes_style english
222 \paperpagestyle plain
227 \tracking_changes true
228 \output_changes false
230 \postpone_fragile_content false
233 \html_be_strict false
234 \docbook_table_output 0
235 \author -563046850 "Jean-Marc LASGOUTTES"
237 \author 47243155 "Jean-Marc"
238 \author 232239728 "Owner"
245 's Detailed Math Manual
249 by the \SpecialChar LyX
254 \begin_layout Plain Layout
256 If you have comments or error corrections, please send them to the \SpecialChar LyX
261 \begin_inset CommandInset href
263 name "lyx-docs@lists.lyx.org"
264 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
276 \begin_inset Note Note
279 \begin_layout Plain Layout
286 \begin_inset Newline newline
290 \begin_inset Newline newline
296 \change_inserted 47243155 1563226038
298 \change_deleted 47243155 1563226038
304 \begin_layout Standard
305 \begin_inset CommandInset toc
306 LatexCommand tableofcontents
313 \begin_layout Standard
314 \begin_inset Note Note
317 \begin_layout Plain Layout
318 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
321 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
328 If they are not installed the document can be exported anyway but the sections
329 where the packages are required will not appear in the output.
334 ; if it is not installed, this file cannot be exported.
337 \begin_layout Plain Layout
338 The latest PDF-version of this document can be found here:
339 \begin_inset Newline newline
344 https://wiki.lyx.org/LyX/Manuals#Math
352 \begin_layout Standard
353 \begin_inset Newpage newpage
359 \begin_layout Section
363 \begin_layout Standard
364 This document details \SpecialChar LyX
365 's math features and the \SpecialChar LaTeX
366 -commands used for mathematical
367 characters and constructs.
368 It is oriented toward the use of commands.
369 The user should read the
377 section of the User's Guide before proceeding.
380 \begin_layout Standard
381 Most of the characters and many constructs explained in this manual are
382 also accessible via the menu
386 \SpecialChar menuseparator
402 But everybody who has to write lots of formulas will notice that it is
403 much faster to use commands instead of the math toolbar.
404 Therefore this manual is focused on commands but also mentions the correspondin
405 g toolbar buttons when available.
408 \begin_layout Standard
409 Unless specially mentioned, math commands are only available within formulas.
410 To be able to use all of the commands explained in this document, the option
415 must be checked in the document settings (menu
417 Document\SpecialChar menuseparator
418 Settings\SpecialChar menuseparator
429 \begin_layout Plain Layout
432 Use AMS math package automatically
438 \begin_layout Plain Layout
447 -math when math constructs are found that are supported by \SpecialChar LyX
456 \begin_layout Standard
457 This document doesn't list all
461 \begin_layout Plain Layout
474 \begin_layout Plain Layout
475 A list containing all
479 \begin_layout Plain Layout
488 -math commands is in the file
491 \begin_inset CommandInset href
494 target "https://www.ctan.org/tex-archive/macros/amstex/doc/amsguide.pdf"
501 , which is part of every \SpecialChar LaTeX
502 standard installation.
507 for lucidity reasons.
510 \begin_layout Section
514 \begin_layout Standard
515 To create an inline formula
516 \begin_inset Index idx
519 \begin_layout Plain Layout
525 that is embedded in a text line, use one of the shortcuts
531 or the toolbar button
538 \begin_inset Newline newline
541 To create a display style formula
542 \begin_inset Index idx
545 \begin_layout Plain Layout
546 Formula ! display style
551 which will appear bigger, has a different format, and will be in a separate
552 paragraph, use one of these shortcuts:
561 \begin_layout Standard
562 To change a display style formula to an inline formula, place the cursor
563 inside the formula and use
564 \change_deleted 5863208 1612729312
568 \change_deleted 5863208 1612729314
572 \change_deleted 5863208 1612729303
580 \change_inserted 5863208 1612729281
584 arg "math-mutate simple"
591 Edit\SpecialChar menuseparator
592 Math\SpecialChar menuseparator
597 \change_inserted 5863208 1612729555
598 Similarly you can use the shortcut
601 arg "math-mutate equation"
604 to change from an inline to a display style formula.
606 \change_deleted 5863208 1612729557
607 The same method is used to change an inline formula to a display style formula.
612 \begin_layout Standard
613 To display parts of an inline formula in the size of a display style formula,
621 \begin_inset Index idx
624 \begin_layout Plain Layout
633 A new blue box will appear in which the desired formula part is inserted.
636 \begin_layout Standard
637 Only inline formulas are allowed inside tables.
640 \begin_layout Standard
642 \change_deleted 232239728 1610897673
647 can be turned on in the menu
649 View\SpecialChar menuseparator
653 When you click there on
654 \begin_inset Quotes eld
658 \begin_inset Quotes erd
661 the toolbar will be shown permanently at the bottom; this state is visualized
666 menu with a checkmark.
667 When you click in this state again on
668 \begin_inset Quotes eld
672 \begin_inset Quotes erd
683 is only shown when the cursor is within a formula; this state is visualized
684 by the renaming of the menu entry from
685 \begin_inset Quotes eld
689 \begin_inset Quotes erd
693 \begin_inset Quotes eld
701 \begin_inset Quotes erd
705 \change_inserted 232239728 1610897478
709 \begin_layout Standard
711 \change_inserted 232239728 1610918987
716 visibility is controlled in the menu
718 View\SpecialChar menuseparator
719 Toolbars\SpecialChar menuseparator
723 Three options will be presented, On, Off, and Automatic.
724 Selecting On will cause the toolbar to be shown permanently at the bottom
726 Selecting Off will disable the toolbar.
727 Selecting Automatic will cause the toolbar to automatically appear when
728 the cursor is located within a formula.
729 The active state of the toolbar is indicated by a checkmark next to the
730 current menu selection.
731 \begin_inset Note Note
734 \begin_layout Plain Layout
736 \change_inserted 232239728 1610897730
737 The menu functionality appears to have changed, I rewrote the paragraph
738 for the current functionality
750 \begin_layout Standard
753 \begin_inset Index idx
756 \begin_layout Plain Layout
763 is invoked by pressing the toolbar button
771 Insert\SpecialChar menuseparator
783 \begin_layout Standard
784 To change the \SpecialChar LaTeX
786 \begin_inset Index idx
789 \begin_layout Plain Layout
798 Document\SpecialChar menuseparator
799 Settings\SpecialChar menuseparator
809 \begin_layout Standard
810 To edit matrices, case differentiations and multiline formulas, use the
813 Edit\SpecialChar menuseparator
818 Edit\SpecialChar menuseparator
820 \begin_inset space \thinspace{}
824 \begin_inset space \thinspace{}
834 When lines and columns are swapped via the menu, the column or line where
835 the cursor is in is exchanged with the column to the right or the line
837 If the cursor is in the last column or row, the exchange is done with the
838 column to the left or the line above.
841 \begin_layout Standard
842 To write text in formulas
846 \begin_layout Plain Layout
847 For multiline formulas the command
854 \begin_inset CommandInset ref
856 reference "subsec:Text-in-multiline"
870 \begin_inset Index idx
873 \begin_layout Plain Layout
880 \begin_inset Index idx
883 \begin_layout Plain Layout
890 This mode is invoked with the shortcut
896 or by the insertion of the command
903 \begin_inset Index idx
906 \begin_layout Plain Layout
915 The text appears black in \SpecialChar LyX
916 and can therefore be distinguished from the
917 other formula parts which appear blue.
918 In the output, mathematical text is set upright contrary to other formula
922 \begin_layout Subsection*
926 \begin_layout Standard
927 Most \SpecialChar LaTeX
928 -commands for math constructs have the following syntax:
931 \begin_layout Standard
947 \begin_layout Standard
948 A command always starts with a backslash
949 \begin_inset Quotes gld
959 \begin_inset Quotes grd
971 s, also omit the associated brackets.
972 The braces around the
980 are referred to in this document as \SpecialChar TeX
982 \begin_inset Index idx
985 \begin_layout Plain Layout
993 If you append a left brace to a command name inside a formula, \SpecialChar LyX
995 creates a right \SpecialChar TeX
997 In all other cases standalone \SpecialChar TeX
998 braces are created in formulas with the
1006 Normal braces are created by typing
1012 braces appear red in \SpecialChar LyX
1013 , normal braces appear blue.
1015 mode a command is not needed to get \SpecialChar TeX
1018 braces don't appear in the output while normal braces do.
1021 \begin_layout Standard
1022 When commands without arguments, like commands for symbols, are entered
1024 mode, a space character must
1028 be behind the command to end it.
1029 This space doesn't appear in the output.
1030 When the space should appear in the output, the space must be followed
1031 by a protected space in normal text.
1034 \begin_layout Standard
1035 A protected space is inserted with
1036 \change_inserted 232239728 1610908934
1038 \change_deleted 5863208 1612729787
1040 \change_inserted 5863208 1612729774
1044 arg "command-alternatives math-space ; space-insert protected"
1048 \change_deleted 232239728 1610908788
1052 arg "command-alternatives space-insert protected; math-space"
1056 \change_inserted 5863208 1612729766
1057 or with the menu selection
1060 \change_inserted 232239728 1610908897
1061 Insert\SpecialChar menuseparator
1062 Formatting\SpecialChar menuseparator
1066 \change_inserted 5863208 1612729638
1070 \change_deleted 5863208 1612729640
1078 \begin_layout Subsection*
1079 \begin_inset Newpage newpage
1083 \change_deleted 5863208 1612098922
1087 \change_inserted 5863208 1612100879
1088 of Syntax Used in this Manual
1093 \begin_layout Itemize
1095 \begin_inset space \textvisiblespace{}
1098 denotes a space character to be input
1099 \change_inserted 5863208 1612098935
1105 \begin_layout Itemize
1107 \begin_inset Formula $\to$
1110 denotes the usage of the corresponding arrow key on the keyboard.
1115 key can often be used instead of
1116 \begin_inset Formula $\to$
1120 \begin_inset Formula $\downarrow$
1128 \begin_inset Formula $\leftarrow$
1132 \begin_inset Formula $\uparrow$
1138 \begin_layout Subsection*
1142 \begin_layout Standard
1144 \begin_inset Float table
1151 \begin_layout Plain Layout
1153 \begin_inset Caption Standard
1155 \begin_layout Plain Layout
1156 \begin_inset CommandInset label
1158 name "tab:Available-units"
1170 \begin_layout Plain Layout
1172 \begin_inset Tabular
1173 <lyxtabular version="3" rows="13" columns="2">
1174 <features booktabs="true" tabularvalignment="middle">
1175 <column alignment="center" valignment="top">
1176 <column alignment="center" valignment="top" width="0pt">
1178 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1181 \begin_layout Plain Layout
1187 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1190 \begin_layout Plain Layout
1198 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1201 \begin_layout Plain Layout
1207 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1210 \begin_layout Plain Layout
1218 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1221 \begin_layout Plain Layout
1227 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1230 \begin_layout Plain Layout
1238 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1241 \begin_layout Plain Layout
1247 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1250 \begin_layout Plain Layout
1252 \begin_inset space \thinspace{}
1256 \change_deleted 232239728 1610909338
1258 \change_inserted 232239728 1610909338
1262 \begin_inset space \thinspace{}
1272 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1275 \begin_layout Plain Layout
1281 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1284 \begin_layout Plain Layout
1286 \begin_inset space \thinspace{}
1290 \begin_inset space \thinspace{}
1300 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1303 \begin_layout Plain Layout
1309 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1312 \begin_layout Plain Layout
1314 \begin_inset space \thinspace{}
1318 \begin_inset space \thinspace{}
1328 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1331 \begin_layout Plain Layout
1337 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1340 \begin_layout Plain Layout
1342 \begin_inset space \thinspace{}
1346 \begin_inset space \thinspace{}
1356 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1359 \begin_layout Plain Layout
1365 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1368 \begin_layout Plain Layout
1370 \begin_inset space \thinspace{}
1374 \begin_inset space \thinspace{}
1384 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1387 \begin_layout Plain Layout
1393 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1396 \begin_layout Plain Layout
1398 \begin_inset space \thinspace{}
1402 \begin_inset Formula $\approx$
1406 \begin_inset space \thinspace{}
1416 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1419 \begin_layout Plain Layout
1425 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1428 \begin_layout Plain Layout
1430 \begin_inset space \thinspace{}
1434 \begin_inset space \thinspace{}
1444 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1447 \begin_layout Plain Layout
1453 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1456 \begin_layout Plain Layout
1460 \begin_inset Quotes eld
1466 \begin_inset Quotes erd
1476 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1479 \begin_layout Plain Layout
1485 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1488 \begin_layout Plain Layout
1490 \begin_inset Quotes eld
1498 \begin_inset Quotes erd
1508 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1511 \begin_layout Plain Layout
1517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1520 \begin_layout Plain Layout
1522 \begin_inset space \thinspace{}
1526 \begin_inset Formula $\nicefrac{1}{18}$
1530 \begin_inset space \thinspace{}
1551 \begin_layout Section
1555 \begin_layout Subsection
1557 \begin_inset Index idx
1560 \begin_layout Plain Layout
1567 \begin_inset Index idx
1570 \begin_layout Plain Layout
1577 \begin_inset Index idx
1580 \begin_layout Plain Layout
1585 \begin_layout Plain Layout
1596 \begin_layout Plain Layout
1609 \begin_inset Index idx
1612 \begin_layout Plain Layout
1617 \begin_layout Plain Layout
1628 \begin_layout Plain Layout
1643 \begin_layout Standard
1644 Indices are created with an underscore
1645 \begin_inset Quotes eld
1649 \begin_inset Quotes erd
1652 or via the math toolbar button
1655 arg "math-subscript"
1658 , exponents with a caret
1659 \begin_inset Quotes eld
1663 \begin_inset Quotes erd
1666 or via the math toolbar button
1669 arg "math-superscript"
1675 \begin_layout Standard
1677 \begin_inset Tabular
1678 <lyxtabular version="3" rows="4" columns="2">
1679 <features booktabs="true" tabularvalignment="middle">
1680 <column alignment="center" valignment="top" width="0pt">
1681 <column alignment="center" valignment="top" width="0pt">
1683 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1686 \begin_layout Plain Layout
1692 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1695 \begin_layout Plain Layout
1703 <cell alignment="center" valignment="top" usebox="none">
1706 \begin_layout Plain Layout
1712 <cell alignment="center" valignment="top" usebox="none">
1715 \begin_layout Plain Layout
1716 \begin_inset Formula $B_{V}$
1725 <row topspace="1.5mm">
1726 <cell alignment="center" valignment="top" usebox="none">
1729 \begin_layout Plain Layout
1735 <cell alignment="center" valignment="top" usebox="none">
1738 \begin_layout Plain Layout
1739 \begin_inset Formula $B^{V}$
1748 <row topspace="1.5mm">
1749 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1752 \begin_layout Plain Layout
1754 \begin_inset space \textvisiblespace{}
1762 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1765 \begin_layout Plain Layout
1766 \begin_inset Formula $B^{A}$
1782 \begin_layout Standard
1783 As the caret is in some languages an accent, vowels will be accentuated
1784 in this case and not set as exponents
1788 \begin_layout Plain Layout
1789 Depending on the keyboard settings used this can also happen for characters
1796 To get exponents in this case, press
1800 after the caret as in the last example.
1803 \begin_layout Subsection
1805 \begin_inset CommandInset label
1807 name "subsec:Fractions"
1812 \begin_inset Index idx
1815 \begin_layout Plain Layout
1824 \begin_layout Standard
1825 Fractions are generated with the command
1832 \begin_inset Index idx
1835 \begin_layout Plain Layout
1843 or via the math toolbar button
1846 arg "math-insert \\frac"
1850 The font size is adjusted automatically, depending on whether the fraction
1851 is in an inline or display style formula.
1852 With the math toolbar button
1855 arg "math-insert \\frac-square"
1858 you can select different fraction types.
1861 \begin_layout Standard
1869 \begin_inset Index idx
1872 \begin_layout Plain Layout
1880 a fraction can be created that always has the size of a display style formula.
1888 \begin_inset Index idx
1891 \begin_layout Plain Layout
1899 the fraction appears always with the size of an inline formula.
1903 \begin_layout Standard
1904 A line with the fraction
1905 \begin_inset Formula $\frac{1}{2}$
1908 that was created with the command
1917 \begin_layout Standard
1918 A line with the fraction
1919 \begin_inset Formula $\dfrac{1}{2}$
1922 that was created with the command
1931 \begin_layout Standard
1933 \begin_inset Tabular
1934 <lyxtabular version="3" rows="4" columns="2">
1935 <features booktabs="true" tabularvalignment="middle">
1936 <column alignment="center" valignment="top" width="0pt">
1937 <column alignment="center" valignment="top" width="0pt">
1939 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1942 \begin_layout Plain Layout
1948 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1951 \begin_layout Plain Layout
1958 <row topspace="1.5mm">
1959 <cell alignment="center" valignment="top" usebox="none">
1962 \begin_layout Plain Layout
1966 \begin_inset space \textvisiblespace{}
1970 \begin_inset Formula $\downarrow$
1978 <cell alignment="center" valignment="top" usebox="none">
1981 \begin_layout Plain Layout
1982 \begin_inset Formula $\frac{A}{B}$
1991 <row topspace="2mm">
1992 <cell alignment="center" valignment="top" usebox="none">
1995 \begin_layout Plain Layout
1999 \begin_inset space \textvisiblespace{}
2003 \begin_inset Formula $\downarrow$
2011 <cell alignment="center" valignment="top" usebox="none">
2014 \begin_layout Plain Layout
2015 \begin_inset Formula $\dfrac{A}{B}$
2024 <row topspace="2mm" bottomspace="1mm">
2025 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2028 \begin_layout Plain Layout
2032 \begin_inset space \textvisiblespace{}
2038 \begin_inset space \textvisiblespace{}
2042 \begin_inset Formula $\downarrow$
2046 \begin_inset Formula $\downarrow\downarrow$
2054 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2057 \begin_layout Plain Layout
2058 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
2074 \begin_layout Standard
2075 \begin_inset VSpace bigskip
2079 \begin_inset Newpage newpage
2082 For nested fractions the command
2089 \begin_inset Index idx
2092 \begin_layout Plain Layout
2102 \begin_inset VSpace -3mm
2108 \begin_layout Standard
2109 \begin_inset Formula
2111 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2112 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2120 \begin_layout Standard
2121 The command for the example above is:
2124 \begin_layout Standard
2130 \begin_inset space \textvisiblespace{}
2134 \begin_inset Formula $\downarrow$
2140 \begin_inset space \textvisiblespace{}
2146 \begin_inset space \textvisiblespace{}
2150 \begin_inset Formula $\downarrow$
2154 \begin_inset Formula $\downarrow$
2160 \begin_layout Standard
2161 \begin_inset VSpace medskip
2167 \begin_layout Standard
2174 always sets the fraction size to that of a displayed formula, even when
2175 it is part of another fraction.
2178 \begin_layout Standard
2179 It is possible to specify the alignment of the numerator.
2186 is used to left align it, the command
2199 centers the numerator.
2200 These fractions demonstrate the different alignments:
2203 \begin_layout Standard
2206 \begin_inset Formula
2208 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2216 \begin_layout Standard
2217 \begin_inset Note Greyedout
2220 \begin_layout Plain Layout
2237 are not real \SpecialChar LaTeX
2238 commands but represent the command
2242 cfrac[alignment]{numerator}{denominator}
2245 Therefore you cannot use them in \SpecialChar TeX
2254 \begin_layout Standard
2255 \begin_inset VSpace medskip
2258 It is often advantageous to combine
2271 \begin_inset Formula
2273 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2281 \begin_layout Standard
2282 For inline fractions with a sloped fraction stroke you can use the command
2290 \begin_inset Index idx
2293 \begin_layout Plain Layout
2302 \begin_inset Formula $\nicefrac{5}{31}$
2312 \begin_inset Index idx
2315 \begin_layout Plain Layout
2324 \begin_inset Formula $\unitfrac{5}{31}$
2327 There is also the command
2333 which allows you to write a fraction in combination with a number:
2334 \begin_inset Formula $\unitfrac[2]{1}{3}$
2340 \begin_layout Standard
2341 \begin_inset Note Greyedout
2344 \begin_layout Plain Layout
2355 is not a real \SpecialChar LaTeX
2356 command but the command
2357 \begin_inset Newline newline
2364 unitfrac[number]{numerator}{denominator}
2367 Therefore you cannot use it in \SpecialChar TeX
2376 \begin_layout Standard
2377 How to define your own fractions where the fraction stroke can be changed
2379 \begin_inset CommandInset ref
2381 reference "subsec:Self-defined-Fractions"
2388 \begin_layout Standard
2389 Multiline fractions are explained in
2390 \begin_inset CommandInset ref
2392 reference "subsec:Multiline-Fractions"
2399 \begin_layout Subsection
2401 \begin_inset Index idx
2404 \begin_layout Plain Layout
2413 \begin_layout Standard
2414 Square roots are created with
2421 \begin_inset Index idx
2424 \begin_layout Plain Layout
2432 or the math toolbar button
2435 arg "math-insert \\sqrt"
2438 , all other roots with the command
2445 \begin_inset Index idx
2448 \begin_layout Plain Layout
2456 or with the math toolbar button
2459 arg "math-insert \\root"
2465 \begin_layout Standard
2467 \begin_inset Tabular
2468 <lyxtabular version="3" rows="3" columns="2">
2469 <features booktabs="true" tabularvalignment="middle">
2470 <column alignment="center" valignment="top" width="0pt">
2471 <column alignment="center" valignment="top" width="0pt">
2473 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2476 \begin_layout Plain Layout
2482 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2485 \begin_layout Plain Layout
2492 <row topspace="1mm">
2493 <cell alignment="center" valignment="top" usebox="none">
2496 \begin_layout Plain Layout
2500 \begin_inset space \textvisiblespace{}
2508 <cell alignment="center" valignment="top" usebox="none">
2511 \begin_layout Plain Layout
2512 \begin_inset Formula $\sqrt{A-B}$
2521 <row topspace="1mm">
2522 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2525 \begin_layout Plain Layout
2529 \begin_inset space \textvisiblespace{}
2533 \begin_inset Formula $\downarrow$
2541 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2544 \begin_layout Plain Layout
2545 \begin_inset Formula $\sqrt[3]{A-B}$
2561 \begin_layout Standard
2562 A square root can also be created with
2568 when the root index field is left empty.
2571 \begin_layout Standard
2572 With certain indices the distance to the root is too small, like in this
2574 \begin_inset Formula $\sqrt[\beta]{B}$
2578 \begin_inset Newline newline
2582 \begin_inset Formula $\beta$
2586 To avoid this, the commands
2593 \begin_inset Index idx
2596 \begin_layout Plain Layout
2611 \begin_inset Index idx
2614 \begin_layout Plain Layout
2622 are used with the following scheme:
2625 \begin_layout Standard
2639 \begin_layout Standard
2640 Distance is the number of Big Points (unit bp;
2641 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2644 ), that the index should be moved to the left or up, resp..
2645 The commands are written to the index.
2646 This way the command
2647 \begin_inset Newline newline
2657 \begin_inset Formula $\to$
2663 \begin_inset Formula $\to$
2669 \begin_inset space \textvisiblespace{}
2673 \begin_inset Formula $\to$
2677 \begin_inset Newline newline
2682 produces a correct typeset formula:
2683 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2689 \begin_layout Subsection
2690 Binomial Coefficients
2691 \begin_inset Index idx
2694 \begin_layout Plain Layout
2695 Binomial coefficients
2703 \begin_layout Standard
2704 Binomial coefficients are inserted with the command
2711 \begin_inset Index idx
2714 \begin_layout Plain Layout
2722 or with the submenu of the math toolbar button
2725 arg "math-insert \\frac-square"
2741 there are the commands
2748 \begin_inset Index idx
2751 \begin_layout Plain Layout
2766 \begin_inset Index idx
2769 \begin_layout Plain Layout
2778 For other brackets around binomial coefficients there are the commands
2786 \begin_inset Index idx
2789 \begin_layout Plain Layout
2804 \begin_inset Index idx
2807 \begin_layout Plain Layout
2818 \begin_layout Standard
2820 \begin_inset Tabular
2821 <lyxtabular version="3" rows="6" columns="2">
2822 <features booktabs="true" tabularvalignment="middle">
2823 <column alignment="center" valignment="top" width="0pt">
2824 <column alignment="center" valignment="top" width="0pt">
2826 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2829 \begin_layout Plain Layout
2835 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2838 \begin_layout Plain Layout
2845 <row topspace="1mm">
2846 <cell alignment="center" valignment="top" usebox="none">
2849 \begin_layout Plain Layout
2853 \begin_inset space \textvisiblespace{}
2857 \begin_inset Formula $\downarrow$
2865 <cell alignment="center" valignment="top" usebox="none">
2868 \begin_layout Plain Layout
2869 \begin_inset Formula $\binom{A}{B}$
2878 <row topspace="2mm">
2879 <cell alignment="center" valignment="top" usebox="none">
2882 \begin_layout Plain Layout
2886 \begin_inset space \textvisiblespace{}
2890 \begin_inset Formula $\downarrow$
2898 <cell alignment="center" valignment="top" usebox="none">
2901 \begin_layout Plain Layout
2902 \begin_inset Formula $\dbinom{A}{B}$
2911 <row topspace="2mm" bottomspace="0.5mm">
2912 <cell alignment="center" valignment="top" usebox="none">
2915 \begin_layout Plain Layout
2919 \begin_inset space \textvisiblespace{}
2923 \begin_inset Formula $\downarrow$
2931 <cell alignment="center" valignment="top" usebox="none">
2934 \begin_layout Plain Layout
2935 \begin_inset Formula $\tbinom{A}{B}$
2944 <row topspace="1mm">
2945 <cell alignment="center" valignment="top" topline="true" usebox="none">
2948 \begin_layout Plain Layout
2952 \begin_inset space \textvisiblespace{}
2956 \begin_inset Formula $\downarrow$
2964 <cell alignment="center" valignment="top" topline="true" usebox="none">
2967 \begin_layout Plain Layout
2968 \begin_inset Formula ${A \brack B}$
2977 <row topspace="2mm" bottomspace="0.5mm">
2978 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2981 \begin_layout Plain Layout
2985 \begin_inset space \textvisiblespace{}
2989 \begin_inset Formula $\downarrow$
2997 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3000 \begin_layout Plain Layout
3001 \begin_inset Formula ${A \brace B}$
3017 \begin_layout Subsection
3018 Case Differentiations
3019 \begin_inset Index idx
3022 \begin_layout Plain Layout
3023 Case differentiations
3031 \begin_layout Standard
3033 \begin_inset Tabular
3034 <lyxtabular version="3" rows="3" columns="2">
3035 <features booktabs="true" tabularvalignment="middle">
3036 <column alignment="center" valignment="top" width="0pt">
3037 <column alignment="center" valignment="top" width="0pt">
3039 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3042 \begin_layout Plain Layout
3048 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3051 \begin_layout Plain Layout
3059 <cell alignment="center" valignment="top" usebox="none">
3062 \begin_layout Plain Layout
3066 \begin_inset space \textvisiblespace{}
3070 \begin_inset Formula $\to$
3074 \begin_inset Index idx
3077 \begin_layout Plain Layout
3090 <cell alignment="center" valignment="top" usebox="none">
3093 \begin_layout Plain Layout
3094 \begin_inset Formula $\begin{cases}
3104 <row topspace="1.5mm">
3105 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3108 \begin_layout Plain Layout
3112 \begin_inset space \textvisiblespace{}
3118 arg "newline-insert newline"
3126 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3129 \begin_layout Plain Layout
3130 \begin_inset Formula $\begin{cases}
3131 A & \textrm{for }x>0\\
3132 B & \textrm{for }x=0
3149 \begin_layout Standard
3156 or pressing the math toolbar button
3159 arg "math-insert \\cases"
3162 you can create new lines with the shortcut
3165 arg "newline-insert newline"
3168 or the table toolbar button
3171 arg "tabular-feature append-row"
3177 \begin_layout Standard
3184 is also available via the menu
3186 Insert\SpecialChar menuseparator
3187 Math\SpecialChar menuseparator
3193 \begin_layout Subsection
3195 \begin_inset Index idx
3198 \begin_layout Plain Layout
3207 \begin_layout Standard
3215 \begin_inset Index idx
3218 \begin_layout Plain Layout
3226 every character can be displayed canceled.
3227 The characters are quasi accentuated by a slash.
3230 \begin_layout Standard
3232 \begin_inset Tabular
3233 <lyxtabular version="3" rows="4" columns="2">
3234 <features booktabs="true" tabularvalignment="middle">
3235 <column alignment="center" valignment="top" width="0pt">
3236 <column alignment="center" valignment="top" width="0pt">
3238 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3241 \begin_layout Plain Layout
3247 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3250 \begin_layout Plain Layout
3258 <cell alignment="center" valignment="top" usebox="none">
3261 \begin_layout Plain Layout
3269 <cell alignment="center" valignment="top" usebox="none">
3272 \begin_layout Plain Layout
3273 \begin_inset Formula $\not=$
3283 <cell alignment="center" valignment="top" usebox="none">
3286 \begin_layout Plain Layout
3296 <cell alignment="center" valignment="top" usebox="none">
3299 \begin_layout Plain Layout
3300 \begin_inset Formula $\not\le$
3310 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3313 \begin_layout Plain Layout
3323 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3326 \begin_layout Plain Layout
3327 \begin_inset Formula $\not\parallel$
3343 \begin_layout Standard
3344 The last example shows that not all negations look good.
3345 Therefore there are special commands for some negations (see
3346 \begin_inset CommandInset ref
3348 reference "subsec:Mathematical-Symbols"
3353 \begin_inset CommandInset ref
3355 reference "sec:Relations"
3362 \begin_layout Subsection
3364 \begin_inset CommandInset label
3366 name "subsec:Placeholders"
3371 \begin_inset Index idx
3374 \begin_layout Plain Layout
3381 \begin_inset Index idx
3384 \begin_layout Plain Layout
3385 Chemical characters ! Isotopes
3391 \begin_inset Index idx
3394 \begin_layout Plain Layout
3399 \begin_layout Plain Layout
3410 \begin_layout Plain Layout
3425 \begin_layout Standard
3427 \begin_inset space \thinspace{}
3431 \begin_inset space \space{}
3438 \begin_layout Plain Layout
3439 Typesetting isotopes and chemical symbols is described in
3440 \begin_inset CommandInset ref
3442 reference "subsec:Chemical-Symbols-and"
3451 the following problem occurs:
3454 \begin_layout Standard
3456 \begin_inset Tabular
3457 <lyxtabular version="3" rows="2" columns="2">
3458 <features booktabs="true" tabularvalignment="middle">
3459 <column alignment="center" valignment="top" width="0pt">
3460 <column alignment="center" valignment="top" width="0pt">
3462 <cell alignment="center" valignment="top" usebox="none">
3465 \begin_layout Plain Layout
3466 Indices created with sub- and superscripts:
3471 <cell alignment="center" valignment="top" usebox="none">
3474 \begin_layout Plain Layout
3475 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3484 <row topspace="1.5mm">
3485 <cell alignment="center" valignment="top" usebox="none">
3488 \begin_layout Plain Layout
3494 <cell alignment="center" valignment="top" usebox="none">
3497 \begin_layout Plain Layout
3498 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3514 \begin_layout Standard
3515 The shorter index is placed by default below or above the first character
3516 of the longer index.
3517 This is corrected using the command
3524 \begin_inset Index idx
3527 \begin_layout Plain Layout
3535 or the math toolbar button
3536 \begin_inset space \thinspace{}
3543 \begin_layout Plain Layout
3544 Found in the submenu of the toolbar button
3547 arg "math-insert \\space"
3561 to create one or more phantom characters.
3562 When inserting phantom characters a small blue box appears that is superposed
3563 with two red arrows.
3564 The arrows indicate the width and height of the box to be created as a
3566 Phantom characters are placeholders with the same character size.
3569 \begin_layout Standard
3571 \begin_inset Tabular
3572 <lyxtabular version="3" rows="4" columns="2">
3573 <features booktabs="true" tabularvalignment="middle">
3574 <column alignment="center" valignment="top" width="0pt">
3575 <column alignment="center" valignment="top" width="0pt">
3577 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3580 \begin_layout Plain Layout
3586 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3589 \begin_layout Plain Layout
3596 <row topspace="1.5mm">
3597 <cell alignment="center" valignment="top" usebox="none">
3600 \begin_layout Plain Layout
3602 \begin_inset space \textvisiblespace{}
3608 \begin_inset space \textvisiblespace{}
3612 \begin_inset Formula $\to$
3616 \begin_inset space \textvisiblespace{}
3620 \change_inserted 5863208 1612176450
3624 \begin_inset space \textvisiblespace{}
3634 <cell alignment="center" valignment="top" usebox="none">
3637 \begin_layout Plain Layout
3638 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3647 <row topspace="1.5mm" bottomspace="0.5mm">
3648 <cell alignment="center" valignment="top" usebox="none">
3651 \begin_layout Plain Layout
3653 \begin_inset space \textvisiblespace{}
3659 \begin_inset space \textvisiblespace{}
3663 \begin_inset Formula $\to$
3667 \begin_inset space \textvisiblespace{}
3671 \change_inserted 5863208 1612707447
3675 \begin_inset space \textvisiblespace{}
3685 <cell alignment="center" valignment="top" usebox="none">
3688 \begin_layout Plain Layout
3689 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3698 <row topspace="1.5mm" bottomspace="0.5mm">
3699 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3702 \begin_layout Plain Layout
3706 \change_inserted 5863208 1612707546
3708 \begin_inset space \textvisiblespace{}
3714 \change_deleted 5863208 1612707563
3716 \begin_inset space \textvisiblespace{}
3724 \begin_inset space \textvisiblespace{}
3728 \begin_inset Formula $\to$
3732 \begin_inset space \textvisiblespace{}
3740 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3743 \begin_layout Plain Layout
3744 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3760 \begin_layout Standard
3761 Furthermore there are the commands
3768 \begin_inset Index idx
3771 \begin_layout Plain Layout
3792 \begin_inset Index idx
3795 \begin_layout Plain Layout
3816 creates only space for the maximal height of the characters in the box
3817 but not for its width.
3824 creates only space for the width of the box content.
3825 Therefore the boxes of both commands have only one red arrow.
3828 \begin_layout Standard
3829 For example the command
3834 \begin_inset space \textvisiblespace{}
3841 creates space for the height of the integral sign,
3845 \begin_layout Plain Layout
3852 creates an integral sign, see
3853 \begin_inset CommandInset ref
3855 reference "subsec:Big-Operators"
3864 because this is the larger character.
3865 An example application is in
3866 \begin_inset CommandInset ref
3868 reference "subsec:Multiline-Brackets"
3875 \begin_layout Standard
3876 Placeholders can also be used for text when they are inserted via the menu
3879 Insert\SpecialChar menuseparator
3880 Formatting\SpecialChar menuseparator
3886 \begin_layout Standard
3888 \begin_inset Newline newline
3892 \begin_inset Phantom Phantom
3895 \begin_layout Plain Layout
3904 \begin_layout Subsection
3906 \begin_inset Index idx
3909 \begin_layout Plain Layout
3916 \begin_inset Index idx
3919 \begin_layout Plain Layout
3920 Formula ! underlined
3928 \begin_layout Standard
3930 \begin_inset Tabular
3931 <lyxtabular version="3" rows="4" columns="2">
3932 <features booktabs="true" tabularvalignment="middle">
3933 <column alignment="center" valignment="top" width="0pt">
3934 <column alignment="center" valignment="top" width="0pt">
3936 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3939 \begin_layout Plain Layout
3945 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3948 \begin_layout Plain Layout
3955 <row topspace="2mm">
3956 <cell alignment="center" valignment="top" usebox="none">
3959 \begin_layout Plain Layout
3963 \begin_inset space \textvisiblespace{}
3967 \begin_inset Index idx
3970 \begin_layout Plain Layout
3983 <cell alignment="center" valignment="top" usebox="none">
3986 \begin_layout Plain Layout
3987 \begin_inset Formula $\overline{A+B}$
3996 <row bottomspace="1mm">
3997 <cell alignment="center" valignment="top" usebox="none">
4000 \begin_layout Plain Layout
4004 \begin_inset space \textvisiblespace{}
4008 \begin_inset Index idx
4011 \begin_layout Plain Layout
4024 <cell alignment="center" valignment="top" usebox="none">
4027 \begin_layout Plain Layout
4028 \begin_inset Formula $\underline{A+B}$
4037 <row topspace="2mm" bottomspace="1mm">
4038 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4041 \begin_layout Plain Layout
4045 \begin_inset space \textvisiblespace{}
4051 \begin_inset space \textvisiblespace{}
4059 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4062 \begin_layout Plain Layout
4063 \begin_inset Formula $\overline{\underline{A+B}}$
4079 \begin_layout Standard
4080 In the last example it doesn't matter if
4095 \begin_layout Standard
4096 To double underline use
4103 \change_deleted 5863208 1612707977
4105 \change_inserted 5863208 1612707993
4106 (or as many times you want).
4111 \begin_layout Standard
4113 \change_deleted 232239728 1610990247
4114 It is possible to place up to 6 lines above or below characters.
4115 \change_deleted 5863208 1612729848
4117 \begin_inset Note Note
4120 \begin_layout Plain Layout
4122 \change_inserted 232239728 1610990434
4123 I put 30 over and under lines in my test so I don't know what the actual
4124 maximum is, but it's greater than 6.
4134 \begin_layout Standard
4135 \begin_inset VSpace bigskip
4138 Custom lines can be created using the command
4145 \begin_inset Index idx
4148 \begin_layout Plain Layout
4156 which has the following scheme:
4159 \begin_layout Standard
4164 rule[vertical offset]{length}{thickness}
4167 \begin_layout Standard
4168 The optional vertical offset shifts the line upwards (or downwards, when
4169 the value is negative).
4171 \begin_inset CommandInset ref
4173 reference "tab:Available-units"
4177 can be used for the values.
4178 Here are two example lines created with the commands
4179 \begin_inset Newline newline
4186 rule[-2ex]{3cm}{2pt}
4197 \begin_layout Standard
4199 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4205 \begin_layout Standard
4212 can also be used for text when a line is inserted via the menu
4214 Insert\SpecialChar menuseparator
4215 Formatting\SpecialChar menuseparator
4217 \begin_inset space ~
4225 \begin_layout Standard
4227 \begin_inset CommandInset line
4238 \begin_layout Subsection
4240 \begin_inset CommandInset label
4242 name "subsec:Ellipses"
4247 \begin_inset Index idx
4250 \begin_layout Plain Layout
4259 \begin_layout Standard
4260 There are different types of ellipses available.
4264 \begin_layout Plain Layout
4265 In the math toolbar in the submenu of the button
4268 arg "math-insert \\ldots"
4276 For listings, dots at the baseline are used (
4283 \begin_inset Index idx
4286 \begin_layout Plain Layout
4294 ), while for operations, dots are needed that are on the same height as
4302 \begin_inset Index idx
4305 \begin_layout Plain Layout
4314 When using the command
4321 \begin_inset Index idx
4324 \begin_layout Plain Layout
4332 , \SpecialChar LaTeX
4333 decides on the basis of the next character what type is used.
4336 \begin_layout Standard
4338 \begin_inset Tabular
4339 <lyxtabular version="3" rows="9" columns="2">
4340 <features booktabs="true" tabularvalignment="middle">
4341 <column alignment="center" valignment="top" width="0pt">
4342 <column alignment="center" valignment="top" width="0pt">
4344 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4347 \begin_layout Plain Layout
4353 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4356 \begin_layout Plain Layout
4364 <cell alignment="center" valignment="top" usebox="none">
4367 \begin_layout Plain Layout
4369 \begin_inset space \textvisiblespace{}
4375 \begin_inset space \textvisiblespace{}
4383 <cell alignment="center" valignment="top" usebox="none">
4386 \begin_layout Plain Layout
4387 \begin_inset Formula $A_{1},\dots,A_{n}$
4397 <cell alignment="center" valignment="top" usebox="none">
4400 \begin_layout Plain Layout
4402 \begin_inset space \textvisiblespace{}
4408 \begin_inset space \textvisiblespace{}
4416 <cell alignment="center" valignment="top" usebox="none">
4419 \begin_layout Plain Layout
4420 \begin_inset Formula $A_{1}+\dots+A_{n}$
4430 <cell alignment="center" valignment="top" usebox="none">
4433 \begin_layout Plain Layout
4435 \begin_inset space \textvisiblespace{}
4441 \begin_inset space \textvisiblespace{}
4449 <cell alignment="center" valignment="top" usebox="none">
4452 \begin_layout Plain Layout
4453 \begin_inset Formula $A_{1},\ldots,A_{n}$
4463 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4466 \begin_layout Plain Layout
4468 \begin_inset space \textvisiblespace{}
4474 \begin_inset space \textvisiblespace{}
4482 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4485 \begin_layout Plain Layout
4486 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4496 <cell alignment="center" valignment="top" usebox="none">
4499 \begin_layout Plain Layout
4507 <cell alignment="center" valignment="top" usebox="none">
4510 \begin_layout Plain Layout
4511 \begin_inset Formula $\vdots$
4521 <cell alignment="center" valignment="top" usebox="none">
4524 \begin_layout Plain Layout
4532 <cell alignment="center" valignment="top" usebox="none">
4535 \begin_layout Plain Layout
4536 \begin_inset Formula $\ddots$
4546 <cell alignment="center" valignment="top" usebox="none">
4549 \begin_layout Plain Layout
4557 <cell alignment="center" valignment="top" usebox="none">
4560 \begin_layout Plain Layout
4561 \begin_inset Formula $\iddots$
4571 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4574 \begin_layout Plain Layout
4576 \begin_inset space \thinspace{}
4579 matrix with the different dots
4584 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4587 \begin_layout Plain Layout
4588 \begin_inset Formula $\begin{array}{ccc}
4589 A_{11} & \cdots & A_{1m}\\
4590 \vdots & \ddots & \vdots\\
4591 A_{n1} & \cdots & A_{nm}
4608 \begin_layout Standard
4609 The ellipses available in menu
4611 Insert\SpecialChar menuseparator
4613 \begin_inset space ~
4627 \begin_layout Standard
4628 \begin_inset VSpace medskip
4639 Use mathdots package (automatically)
4641 must be set in the document settings under
4644 \begin_inset space ~
4650 \begin_inset Newline newline
4655 Use mathdots package
4657 will improve the appearance of all dots in the documents if their font
4658 style or size is not the default.
4661 \begin_layout Standard
4662 \begin_inset VSpace medskip
4665 Specially for matrices there are ellipses that span over several columns.
4666 They are created with the command
4673 \begin_inset Index idx
4676 \begin_layout Plain Layout
4684 and have the following scheme
4685 \change_inserted 5863208 1612709418
4697 \begin_inset space ~
4707 \begin_layout Standard
4712 hdotsfor[distance]{number of columns}
4715 \begin_layout Standard
4716 The number of columns specifies how many columns should be spanned.
4717 Distance is a factor for the distance between the dots.
4720 \begin_layout Standard
4721 In the following matrix the command
4727 was inserted in the first box of the second line to get an ellipsis with
4728 a dot distance twice as long as with the command
4735 \begin_inset Formula
4737 \left(\begin{array}{cccc}
4746 Note that the matrix fields that should be spanned must be empty, otherwise
4747 you get \SpecialChar LaTeX
4751 \begin_layout Standard
4752 \begin_inset VSpace bigskip
4755 Furthermore you can fill with the command
4762 \begin_inset Index idx
4765 \begin_layout Plain Layout
4773 the rest of a line with dots.
4774 The effect of these commands is the same as with
4781 \begin_inset CommandInset ref
4783 reference "subsec:Variable-Space"
4790 \begin_layout Standard
4791 For example the command
4796 \begin_inset space \textvisiblespace{}
4804 \begin_layout Standard
4805 \begin_inset Formula $A\dotfill B$
4811 \begin_layout Standard
4818 there is for a line the command
4825 \begin_inset Index idx
4828 \begin_layout Plain Layout
4839 \begin_layout Standard
4840 \begin_inset Formula $A\hrulefill B$
4846 \begin_layout Standard
4847 To use the commands for text, they have to be inserted in \SpecialChar TeX
4851 \begin_layout Section
4853 \begin_inset CommandInset label
4860 \begin_inset Index idx
4863 \begin_layout Plain Layout
4872 \begin_layout Standard
4873 Matrices can be inserted via the math toolbar button
4876 arg "dialog-show mathmatrix"
4881 Insert\SpecialChar menuseparator
4882 Math\SpecialChar menuseparator
4886 In the matrix dialog you can specify the number of columns and rows, the
4887 alignment and the decoration.
4888 The vertical alignment is only of importance for matrices in inline formulas:
4891 \begin_layout Standard
4892 The first matrix is top
4893 \begin_inset Formula $\begin{array}[t]{cccc}
4901 \begin_inset Formula $\begin{array}{cccc}
4908 and the third bottom
4909 \begin_inset Formula $\begin{array}[b]{cccc}
4919 \begin_layout Standard
4920 The horizontal alignment specifies how the column entries should be aligned.
4921 It is set by entering a letter for every column.
4926 denotes left aligned,
4935 To create for example a 4
4940 \begin_inset space ~
4943 matrix where the first column is left aligned, the second and third are
4944 centered and the last one is right aligned, one enters for the horizontal
4950 Normally in a matrix all columns are centered, therefore the default for
4958 \begin_layout Standard
4959 Horizontal alignment:
4962 \begin_layout Standard
4968 \begin_inset Formula $\begin{array}{lll}
4980 \begin_inset Formula $\begin{array}{ccc}
4992 \begin_inset Formula $\begin{array}{rrr}
5002 \begin_layout Standard
5003 To subsequently add or delete rows and columns, the math toolbar buttons
5007 arg "tabular-feature append-row"
5013 arg "tabular-feature delete-row"
5017 \begin_inset space \thinspace{}
5022 Edit\SpecialChar menuseparator
5026 New rows can also be created with
5029 arg "newline-insert newline"
5035 \begin_layout Standard
5036 \begin_inset VSpace bigskip
5040 \change_deleted 47243155 1563226130
5042 \change_deleted -563046850 1563190969
5046 \change_inserted -563046850 1563190971
5052 \change_deleted -563046850 1563192602
5054 \change_inserted -563046850 1563192607
5057 parentheses in the selected style around the matrix
5058 \change_inserted -563046850 1563192780
5063 style, suitable for an inline matrix like this one
5064 \begin_inset Formula $\bigl(\begin{smallmatrix}0 & \textrm{-}\mathrm{i}\\
5066 \end{smallmatrix}\bigr)$
5073 \change_inserted -563046850 1563192943
5074 Here the parentheses have been added manually using commands
5087 \begin_layout Standard
5089 \change_deleted -563046850 1563192735
5092 Alternatively, parentheses can
5093 \change_deleted -563046850 1563192971
5096 be created with the commands
5103 \begin_inset Index idx
5106 \begin_layout Plain Layout
5121 \begin_inset Index idx
5124 \begin_layout Plain Layout
5135 \begin_inset space ~
5141 \begin_inset CommandInset ref
5143 reference "subsec:Automatic-Bracket-Size"
5147 , or by using the following commands:
5148 \begin_inset VSpace medskip
5154 \begin_layout Standard
5155 \begin_inset space \hfill{}
5159 \begin_inset Tabular
5160 <lyxtabular version="3" rows="4" columns="2">
5161 <features booktabs="true" tabularvalignment="middle">
5162 <column alignment="center" valignment="top" width="0pt">
5163 <column alignment="center" valignment="top">
5165 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5168 \begin_layout Plain Layout
5174 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5177 \begin_layout Plain Layout
5184 <row topspace="1.5mm">
5185 <cell alignment="center" valignment="top" usebox="none">
5188 \begin_layout Plain Layout
5192 \begin_inset space \textvisiblespace{}
5200 \begin_inset space \thinspace{}
5208 <cell alignment="center" valignment="top" usebox="none">
5211 \begin_layout Plain Layout
5212 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
5213 0 & \textrm{-}\mathrm{i}\\
5215 \end{array}\end{bmatrix}$
5224 <row topspace="1.5mm" bottomspace="0.5mm">
5225 <cell alignment="center" valignment="top" usebox="none">
5228 \begin_layout Plain Layout
5232 \begin_inset space \textvisiblespace{}
5240 \begin_inset space \thinspace{}
5248 <cell alignment="center" valignment="top" usebox="none">
5251 \begin_layout Plain Layout
5252 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
5253 0 & \textrm{-}\mathrm{i}\\
5255 \end{array}\end{Bmatrix}$
5265 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5268 \begin_layout Plain Layout
5272 \begin_inset space \textvisiblespace{}
5280 \begin_inset space \thinspace{}
5288 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5291 \begin_layout Plain Layout
5292 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5293 0 & \textrm{-}\mathrm{i}\\
5295 \end{array}\end{pmatrix}$
5309 \begin_inset space \hfill{}
5313 \begin_inset Tabular
5314 <lyxtabular version="3" rows="4" columns="2">
5315 <features booktabs="true" tabularvalignment="middle">
5316 <column alignment="center" valignment="top" width="0pt">
5317 <column alignment="center" valignment="top">
5319 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5322 \begin_layout Plain Layout
5328 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5331 \begin_layout Plain Layout
5338 <row topspace="1.5mm">
5339 <cell alignment="center" valignment="top" usebox="none">
5342 \begin_layout Plain Layout
5346 \begin_inset space \textvisiblespace{}
5354 \begin_inset space \thinspace{}
5362 <cell alignment="center" valignment="top" usebox="none">
5365 \begin_layout Plain Layout
5366 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5367 0 & \textrm{-}\mathrm{i}\\
5369 \end{array}\end{vmatrix}$
5378 <row topspace="1.5mm" bottomspace="0.5mm">
5379 <cell alignment="center" valignment="top" usebox="none">
5382 \begin_layout Plain Layout
5386 \begin_inset space \textvisiblespace{}
5394 \begin_inset space \thinspace{}
5402 <cell alignment="center" valignment="top" usebox="none">
5405 \begin_layout Plain Layout
5406 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5407 0 & \textrm{-}\mathrm{i}\\
5409 \end{array}\end{Vmatrix}$
5419 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5422 \begin_layout Plain Layout
5426 \begin_inset space \textvisiblespace{}
5434 \begin_inset space \thinspace{}
5442 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5445 \begin_layout Plain Layout
5446 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5447 0 & \textrm{-}\mathrm{i}\\
5449 \end{array}\end{matrix}$
5463 \begin_inset space \hfill{}
5469 \begin_layout Standard
5470 \begin_inset VSpace medskip
5474 \begin_inset space \thinspace{}
5478 \begin_inset space \space{}
5487 is inserted, a blue box appears between two vertical lines where the matrix
5489 \begin_inset Newline newline
5492 Note that decorated matrices ignore the vertical alignment.
5495 \begin_layout Standard
5496 \begin_inset VSpace bigskip
5499 As all multiline formulas are matrices, the length
5506 \begin_inset Index idx
5509 \begin_layout Plain Layout
5517 that is described in
5518 \begin_inset CommandInset ref
5520 reference "subsec:Column-Separation"
5524 can also be used to change the column separation of matrices.
5527 \begin_layout Standard
5528 To change the row separation, the command
5535 \begin_inset Index idx
5538 \begin_layout Plain Layout
5549 \begin_layout Standard
5556 arraystretch}{stretch factor}
5557 \begin_inset Index idx
5560 \begin_layout Plain Layout
5571 \begin_layout Standard
5578 assigns the stretch factor to the predefined command
5585 For example to double the row separation, use a stretch factor of 2.
5586 This is then used for all following matrices.
5587 To restore the original separation, assign a stretch factor of 1 to
5596 \begin_layout Standard
5598 \change_inserted 47243155 1563226178
5599 Small inline matrices can also be obtained using
5600 \change_deleted 47243155 1563226182
5601 To set matrices into a text line,
5610 \begin_inset Index idx
5613 \begin_layout Plain Layout
5622 \change_deleted 47243155 1563226186
5626 When it is inserted in a line a blue box with two dashed lines appears.
5627 Adjust the matrix rows and columns as desired.
5630 \begin_layout Standard
5632 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5634 \end{smallmatrix}\right)$
5638 \change_inserted 47243155 1563226243
5639 with automatic delimiters around it
5644 \begin_layout Section
5645 Brackets and Delimiters
5646 \begin_inset Index idx
5649 \begin_layout Plain Layout
5656 \begin_inset Index idx
5659 \begin_layout Plain Layout
5668 \begin_layout Subsection
5669 Vertical Brackets and Delimiters
5670 \begin_inset Index idx
5673 \begin_layout Plain Layout
5682 \begin_layout Standard
5683 \begin_inset space \hfill{}
5687 \begin_inset Tabular
5688 <lyxtabular version="3" rows="9" columns="2">
5689 <features booktabs="true" tabularvalignment="middle">
5690 <column alignment="center" valignment="top" width="0pt">
5691 <column alignment="center" valignment="top" width="0pt">
5693 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5696 \begin_layout Plain Layout
5702 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5705 \begin_layout Plain Layout
5713 <cell alignment="center" valignment="top" usebox="none">
5716 \begin_layout Plain Layout
5722 <cell alignment="center" valignment="top" usebox="none">
5725 \begin_layout Plain Layout
5726 \begin_inset Formula $($
5736 <cell alignment="center" valignment="top" usebox="none">
5739 \begin_layout Plain Layout
5745 <cell alignment="center" valignment="top" usebox="none">
5748 \begin_layout Plain Layout
5749 \begin_inset Formula $\{$
5759 <cell alignment="center" valignment="top" usebox="none">
5762 \begin_layout Plain Layout
5768 <cell alignment="center" valignment="top" usebox="none">
5771 \begin_layout Plain Layout
5772 \begin_inset Formula $[$
5782 <cell alignment="center" valignment="top" usebox="none">
5785 \begin_layout Plain Layout
5793 <cell alignment="center" valignment="top" usebox="none">
5796 \begin_layout Plain Layout
5797 \begin_inset Formula $\langle$
5807 <cell alignment="center" valignment="top" usebox="none">
5810 \begin_layout Plain Layout
5818 <cell alignment="center" valignment="top" usebox="none">
5821 \begin_layout Plain Layout
5822 \begin_inset Formula $\lceil$
5832 <cell alignment="center" valignment="top" usebox="none">
5835 \begin_layout Plain Layout
5843 <cell alignment="center" valignment="top" usebox="none">
5846 \begin_layout Plain Layout
5847 \begin_inset Formula $\lfloor$
5857 <cell alignment="center" valignment="top" usebox="none">
5860 \begin_layout Plain Layout
5866 <cell alignment="center" valignment="top" usebox="none">
5869 \begin_layout Plain Layout
5870 \begin_inset Formula $/$
5880 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5883 \begin_layout Plain Layout
5889 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5892 \begin_layout Plain Layout
5893 \begin_inset Formula $|$
5907 \begin_inset space \hfill{}
5911 \begin_inset Tabular
5912 <lyxtabular version="3" rows="9" columns="2">
5913 <features booktabs="true" tabularvalignment="middle">
5914 <column alignment="center" valignment="top" width="0pt">
5915 <column alignment="center" valignment="top" width="0pt">
5917 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5920 \begin_layout Plain Layout
5926 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5929 \begin_layout Plain Layout
5937 <cell alignment="center" valignment="top" usebox="none">
5940 \begin_layout Plain Layout
5946 <cell alignment="center" valignment="top" usebox="none">
5949 \begin_layout Plain Layout
5950 \begin_inset Formula $)$
5960 <cell alignment="center" valignment="top" usebox="none">
5963 \begin_layout Plain Layout
5969 <cell alignment="center" valignment="top" usebox="none">
5972 \begin_layout Plain Layout
5973 \begin_inset Formula $\}$
5983 <cell alignment="center" valignment="top" usebox="none">
5986 \begin_layout Plain Layout
5992 <cell alignment="center" valignment="top" usebox="none">
5995 \begin_layout Plain Layout
5996 \begin_inset Formula $]$
6006 <cell alignment="center" valignment="top" usebox="none">
6009 \begin_layout Plain Layout
6017 <cell alignment="center" valignment="top" usebox="none">
6020 \begin_layout Plain Layout
6021 \begin_inset Formula $\rangle$
6031 <cell alignment="center" valignment="top" usebox="none">
6034 \begin_layout Plain Layout
6042 <cell alignment="center" valignment="top" usebox="none">
6045 \begin_layout Plain Layout
6046 \begin_inset Formula $\rceil$
6056 <cell alignment="center" valignment="top" usebox="none">
6059 \begin_layout Plain Layout
6067 <cell alignment="center" valignment="top" usebox="none">
6070 \begin_layout Plain Layout
6071 \begin_inset Formula $\rfloor$
6081 <cell alignment="center" valignment="top" usebox="none">
6084 \begin_layout Plain Layout
6094 <cell alignment="center" valignment="top" usebox="none">
6097 \begin_layout Plain Layout
6098 \begin_inset Formula $\backslash$
6108 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6111 \begin_layout Plain Layout
6119 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6122 \begin_layout Plain Layout
6123 \begin_inset Formula $\|$
6137 \begin_inset space \hfill{}
6143 \begin_layout Standard
6146 \begin_inset Note Greyedout
6149 \begin_layout Plain Layout
6162 \begin_inset Index idx
6165 \begin_layout Plain Layout
6173 must be used for the backslash, because the command
6181 produces a line break there.
6189 \begin_layout Standard
6190 For all characters listed above the size can be adjusted with the commands
6191 described in the following two subsections.
6192 When using these commands, the characters < and > can directly be used
6193 instead of the commands
6208 \begin_layout Subsubsection
6210 \begin_inset CommandInset label
6212 name "subsec:Manual-Bracket-Size"
6217 \begin_inset Index idx
6220 \begin_layout Plain Layout
6221 Bracket size ! manual
6229 \begin_layout Standard
6230 The bracket size can be specified manually by the \SpecialChar LaTeX
6238 \begin_inset Index idx
6241 \begin_layout Plain Layout
6274 denotes the smallest and
6280 the largest bracket size.
6283 \begin_layout Standard
6284 These commands are used to emphasize levels of brackets:
6287 \begin_layout Standard
6289 \begin_inset Tabular
6290 <lyxtabular version="3" rows="2" columns="2">
6291 <features booktabs="true" tabularvalignment="middle">
6292 <column alignment="center" valignment="top" width="0pt">
6293 <column alignment="center" valignment="top" width="0pt">
6295 <cell alignment="center" valignment="top" usebox="none">
6298 \begin_layout Plain Layout
6299 All brackets in the same size:
6304 <cell alignment="center" valignment="top" usebox="none">
6307 \begin_layout Plain Layout
6308 \begin_inset Formula $((A+B)(A-B))^{C}$
6317 <row topspace="2mm">
6318 <cell alignment="center" valignment="top" usebox="none">
6321 \begin_layout Plain Layout
6327 <cell alignment="center" valignment="top" usebox="none">
6330 \begin_layout Plain Layout
6331 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6347 \begin_layout Standard
6348 For the second formula the command
6355 \begin_inset space \textvisiblespace{}
6363 \begin_layout Standard
6364 Here is an example containing all bracket sizes:
6367 \begin_layout Standard
6384 \begin_inset space \textvisiblespace{}
6392 \begin_inset space \textvisiblespace{}
6396 \begin_inset space \textvisiblespace{}
6406 \begin_layout Standard
6408 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6414 \begin_layout Standard
6421 -commands there is a variant,
6428 \begin_inset Index idx
6431 \begin_layout Plain Layout
6439 , that adds a bit more space between the bracket and its content.
6453 \begin_inset Index idx
6456 \begin_layout Plain Layout
6466 , don't add additional space.
6471 at the end of the command
6477 is for a left bracket; for a right bracket this is replaced by an
6482 A left or right bracket can each be an opening or closing bracket.
6485 \begin_layout Standard
6486 The following table contains comparisons of the variants:
6489 \begin_layout Standard
6491 \begin_inset Tabular
6492 <lyxtabular version="3" rows="5" columns="2">
6493 <features booktabs="true" tabularvalignment="middle">
6494 <column alignment="center" valignment="top" width="0pt">
6495 <column alignment="center" valignment="middle">
6497 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6500 \begin_layout Plain Layout
6506 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6509 \begin_layout Plain Layout
6516 <row topspace="2mm">
6517 <cell alignment="center" valignment="top" usebox="none">
6520 \begin_layout Plain Layout
6530 \begin_inset space \textvisiblespace{}
6540 <cell alignment="center" valignment="top" usebox="none">
6543 \begin_layout Plain Layout
6544 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6553 <row topspace="2mm">
6554 <cell alignment="center" valignment="top" usebox="none">
6557 \begin_layout Plain Layout
6567 \begin_inset space \textvisiblespace{}
6577 <cell alignment="center" valignment="top" usebox="none">
6580 \begin_layout Plain Layout
6581 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6590 <row topspace="2mm" bottomspace="0.5mm">
6591 <cell alignment="center" valignment="top" usebox="none">
6594 \begin_layout Plain Layout
6604 \begin_inset space \textvisiblespace{}
6614 <cell alignment="center" valignment="top" usebox="none">
6617 \begin_layout Plain Layout
6618 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6627 <row topspace="1.5mm" bottomspace="0.5mm">
6628 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6631 \begin_layout Plain Layout
6643 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6646 \begin_layout Plain Layout
6647 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6663 \begin_layout Subsubsection
6664 Automatic Bracket Size
6665 \begin_inset CommandInset label
6667 name "subsec:Automatic-Bracket-Size"
6672 \begin_inset Index idx
6675 \begin_layout Plain Layout
6676 Bracket size ! automatic
6684 \begin_layout Standard
6685 Variably sized brackets can be inserted with the commands
6692 \begin_inset Index idx
6695 \begin_layout Plain Layout
6710 \begin_inset Index idx
6713 \begin_layout Plain Layout
6721 or via the math toolbar button
6724 arg "dialog-show mathdelimiter"
6728 The desired bracket must be inserted directly behind the
6741 The bracket size will then automatically be calculated for the output.
6744 \begin_layout Standard
6746 normal bracket: The command
6753 \begin_inset space \textvisiblespace{}
6757 \begin_inset Formula $\downarrow$
6761 \begin_inset space \textvisiblespace{}
6767 \begin_inset Formula
6777 \begin_layout Standard
6779 multiline bracket: The command
6788 \begin_inset space \textvisiblespace{}
6792 \begin_inset Formula $\downarrow$
6796 \begin_inset space \textvisiblespace{}
6804 \begin_inset Formula
6806 \ln\left(\frac{A}{C}\right)
6814 \begin_layout Standard
6830 \begin_inset space ~
6836 This has the advantage that you can see in \SpecialChar LyX
6837 immediately the real bracket
6838 size and that the matching right bracket will be created too.
6839 \begin_inset Newline newline
6842 The command for the last example would then be:
6853 \begin_inset space \textvisiblespace{}
6857 \begin_inset Formula $\downarrow$
6863 \begin_layout Standard
6864 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6865 For example the command
6872 \begin_inset space \textvisiblespace{}
6876 \begin_inset Formula $\downarrow$
6880 \begin_inset space \textvisiblespace{}
6890 \begin_inset Formula
6892 \left.\frac{A}{B}\right\}
6911 will be converted by \SpecialChar LyX
6912 to brackets with the correct size when the document
6913 is reloaded and an omitted bracket will appear as dashed line.
6916 \begin_layout Standard
6917 \begin_inset VSpace bigskip
6920 Because all popular \SpecialChar LaTeX
6921 distributions use e\SpecialChar TeX
6922 , an extension to \SpecialChar LaTeX
6931 \begin_inset Index idx
6934 \begin_layout Plain Layout
6942 is available for all brackets and limits.
6943 With this command the height of the following character is adapted to the
6944 one of the surrounding brackets, for example in the case of physical vectors:
6945 \begin_inset Formula
6947 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6952 For physical vectors there is a special \SpecialChar LaTeX
6953 -package, described in
6954 \begin_inset CommandInset ref
6956 reference "subsec:Physical-Vectors"
6963 \begin_layout Subsection
6965 \begin_inset Index idx
6968 \begin_layout Plain Layout
6969 Brackets ! horizontal
6977 \begin_layout Standard
6979 \begin_inset Tabular
6980 <lyxtabular version="3" rows="4" columns="2">
6981 <features booktabs="true" tabularvalignment="middle">
6982 <column alignment="center" valignment="top" width="0pt">
6983 <column alignment="center" valignment="top" width="0pt">
6985 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6988 \begin_layout Plain Layout
6994 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6997 \begin_layout Plain Layout
7005 <cell alignment="center" valignment="top" usebox="none">
7008 \begin_layout Plain Layout
7012 \begin_inset space \textvisiblespace{}
7016 \begin_inset space \textvisiblespace{}
7020 \begin_inset Index idx
7023 \begin_layout Plain Layout
7036 <cell alignment="center" valignment="top" usebox="none">
7039 \begin_layout Plain Layout
7040 \begin_inset Formula $\overbrace{A+B}^{3}$
7049 <row topspace="2mm">
7050 <cell alignment="center" valignment="top" usebox="none">
7053 \begin_layout Plain Layout
7057 \begin_inset space \textvisiblespace{}
7061 \begin_inset space \textvisiblespace{}
7065 \begin_inset Index idx
7068 \begin_layout Plain Layout
7081 <cell alignment="center" valignment="top" usebox="none">
7084 \begin_layout Plain Layout
7085 \begin_inset Formula $\underbrace{A+B}_{5}$
7095 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7098 \begin_layout Plain Layout
7102 \begin_inset space \textvisiblespace{}
7108 \begin_inset space \textvisiblespace{}
7112 \begin_inset space \textvisiblespace{}
7116 \begin_inset space \textvisiblespace{}
7120 \begin_inset space \textvisiblespace{}
7124 \begin_inset space \textvisiblespace{}
7128 \begin_inset space \textvisiblespace{}
7136 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7139 \begin_layout Plain Layout
7140 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7156 \begin_layout Standard
7157 In the last example it doesn't matter if
7172 \begin_layout Standard
7173 \begin_inset VSpace medskip
7179 \begin_layout Standard
7180 If in document settings under
7183 \begin_inset space ~
7188 the option for the package
7193 \begin_inset Index idx
7196 \begin_layout Plain Layout
7197 Packages ! mathtools
7205 \begin_inset space ~
7210 , you will also have access to square brackets:
7213 \begin_layout Standard
7215 \begin_inset Tabular
7216 <lyxtabular version="3" rows="4" columns="2">
7217 <features booktabs="true" tabularvalignment="middle">
7218 <column alignment="center" valignment="top" width="0pt">
7219 <column alignment="center" valignment="top" width="0pt">
7221 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7224 \begin_layout Plain Layout
7230 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7233 \begin_layout Plain Layout
7241 <cell alignment="center" valignment="top" usebox="none">
7244 \begin_layout Plain Layout
7272 \begin_inset space \textvisiblespace{}
7276 \begin_inset Index idx
7279 \begin_layout Plain Layout
7292 <cell alignment="center" valignment="top" usebox="none">
7295 \begin_layout Plain Layout
7296 \begin_inset Formula $\overbracket{A+B}^{3}$
7305 <row topspace="2mm">
7306 <cell alignment="center" valignment="top" usebox="none">
7309 \begin_layout Plain Layout
7337 \begin_inset space \textvisiblespace{}
7341 \begin_inset Index idx
7344 \begin_layout Plain Layout
7369 <cell alignment="center" valignment="top" usebox="none">
7372 \begin_layout Plain Layout
7373 \begin_inset Formula $\underbracket{A+B}_{5}$
7383 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7386 \begin_layout Plain Layout
7392 \begin_inset space \textvisiblespace{}
7396 \begin_inset space \textvisiblespace{}
7400 \begin_inset space \textvisiblespace{}
7404 \begin_inset space \textvisiblespace{}
7408 \change_deleted 5863208 1612711596
7410 \begin_inset space \textvisiblespace{}
7420 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7423 \begin_layout Plain Layout
7424 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7440 \begin_layout Standard
7453 you can change the thickness of the bracket's stroke by specifying the
7454 desired thickness in square brackets behind the command:
7457 \begin_layout Standard
7459 \begin_inset Tabular
7460 <lyxtabular version="3" rows="3" columns="2">
7461 <features booktabs="true" tabularvalignment="middle">
7462 <column alignment="center" valignment="top" width="0pt">
7463 <column alignment="center" valignment="top" width="0pt">
7465 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7468 \begin_layout Plain Layout
7474 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7477 \begin_layout Plain Layout
7485 <cell alignment="center" valignment="top" usebox="none">
7488 \begin_layout Plain Layout
7518 \begin_inset space \textvisiblespace{}
7526 <cell alignment="center" valignment="top" usebox="none">
7529 \begin_layout Plain Layout
7530 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7539 <row topspace="2mm">
7540 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7543 \begin_layout Plain Layout
7573 \begin_inset space \textvisiblespace{}
7581 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7584 \begin_layout Plain Layout
7585 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7601 \begin_layout Standard
7602 \begin_inset VSpace bigskip
7605 When brackets overlap each other, multiline formulas as described in
7606 \begin_inset CommandInset ref
7608 reference "sec:Multiline-Formulas"
7613 \begin_inset Formula
7615 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7616 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7621 In the first row, the formula is inserted together with the first brace.
7622 It is important that the space command
7626 \begin_layout Plain Layout
7627 Space commands are explained in
7628 \begin_inset CommandInset ref
7630 reference "subsec:Predefined-Space"
7645 is inserted before the first
7646 \begin_inset Formula $d$
7649 because the brace that ends behind the
7650 \begin_inset Formula $q$
7653 prevents the following
7654 \begin_inset Quotes eld
7658 \begin_inset Quotes erd
7661 from being surrounded by spaces.
7665 \begin_layout Plain Layout
7666 Because a bracket is not handled as a character, see
7667 \begin_inset CommandInset ref
7669 reference "subsec:Binary-Operators"
7678 The second brace is inserted in the second row.
7679 As it should begin before the
7680 \begin_inset Formula $b$
7695 \begin_layout Plain Layout
7703 \begin_inset CommandInset ref
7705 reference "subsec:Placeholders"
7714 This space is needed because the
7715 \begin_inset Quotes eld
7719 \begin_inset Quotes erd
7722 is surrounded by spaces in the formula.
7723 The brace is placed under the command
7732 \begin_layout Standard
7733 It gets more complicated when brackets overlap each other above and under
7734 the formula as in the following example:
7738 \begin_layout Plain Layout
7750 \begin_inset Formula
7752 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7753 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7762 \begin_layout Plain Layout
7773 The first formula row is the same as the second row of the previous example,
7774 with the difference that the brace is above.
7775 The second row contains the formula together with the second brace.
7776 To avoid the space between the upper brace in the first row and the formula,
7777 the row spacing needs to be reduced.
7778 This is not easily done due to a bug in \SpecialChar LyX
7783 \begin_layout Plain Layout
7784 \begin_inset CommandInset href
7786 name "LyX-bug #1505"
7787 target "https://www.lyx.org/trac/ticket/1505"
7797 As a solution for the problem, the global formula row separation
7804 \begin_inset Index idx
7807 \begin_layout Plain Layout
7815 must be changed to -6
7816 \begin_inset space \thinspace{}
7819 pt before the formula with the command
7835 is set back after the formula to the standard value of 3
7836 \begin_inset space \thinspace{}
7839 pt using the same command.
7840 More about the row separation in formulas is explained in
7841 \begin_inset CommandInset ref
7843 reference "subsec:Line-Separation"
7850 \begin_layout Section
7852 \begin_inset Index idx
7855 \begin_layout Plain Layout
7864 \begin_layout Standard
7865 Arrows can be inserted via the math toolbar button
7868 arg "math-insert \\leftarrow"
7871 or the commands listed in the following subsections.
7874 \begin_layout Subsection
7876 \begin_inset Index idx
7879 \begin_layout Plain Layout
7888 \begin_layout Standard
7889 \begin_inset space \hfill{}
7893 \begin_inset Tabular
7894 <lyxtabular version="3" rows="8" columns="2">
7895 <features booktabs="true" tabularvalignment="middle">
7896 <column alignment="center" valignment="top" width="0pt">
7897 <column alignment="center" valignment="top" width="0pt">
7899 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7902 \begin_layout Plain Layout
7908 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7911 \begin_layout Plain Layout
7919 <cell alignment="center" valignment="top" usebox="none">
7922 \begin_layout Plain Layout
7930 <cell alignment="center" valignment="top" usebox="none">
7933 \begin_layout Plain Layout
7934 \begin_inset Formula $\gets$
7944 <cell alignment="center" valignment="top" usebox="none">
7947 \begin_layout Plain Layout
7955 <cell alignment="center" valignment="top" usebox="none">
7958 \begin_layout Plain Layout
7959 \begin_inset Formula $\Leftarrow$
7969 <cell alignment="center" valignment="top" usebox="none">
7972 \begin_layout Plain Layout
7980 <cell alignment="center" valignment="top" usebox="none">
7983 \begin_layout Plain Layout
7984 \begin_inset Formula $\longleftarrow$
7994 <cell alignment="center" valignment="top" usebox="none">
7997 \begin_layout Plain Layout
8005 <cell alignment="center" valignment="top" usebox="none">
8008 \begin_layout Plain Layout
8009 \begin_inset Formula $\Longleftarrow$
8019 <cell alignment="center" valignment="top" usebox="none">
8022 \begin_layout Plain Layout
8030 <cell alignment="center" valignment="top" usebox="none">
8033 \begin_layout Plain Layout
8034 \begin_inset Formula $\leftharpoonup$
8044 <cell alignment="center" valignment="top" usebox="none">
8047 \begin_layout Plain Layout
8055 <cell alignment="center" valignment="top" usebox="none">
8058 \begin_layout Plain Layout
8059 \begin_inset Formula $\leftharpoondown$
8069 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8072 \begin_layout Plain Layout
8080 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8083 \begin_layout Plain Layout
8084 \begin_inset Formula $\hookleftarrow$
8098 \begin_inset space \hfill{}
8102 \begin_inset Tabular
8103 <lyxtabular version="3" rows="8" columns="2">
8104 <features booktabs="true" tabularvalignment="middle">
8105 <column alignment="center" valignment="top" width="0pt">
8106 <column alignment="center" valignment="top" width="0pt">
8108 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8111 \begin_layout Plain Layout
8117 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8120 \begin_layout Plain Layout
8128 <cell alignment="center" valignment="top" usebox="none">
8131 \begin_layout Plain Layout
8139 <cell alignment="center" valignment="top" usebox="none">
8142 \begin_layout Plain Layout
8143 \begin_inset Formula $\to$
8153 <cell alignment="center" valignment="top" usebox="none">
8156 \begin_layout Plain Layout
8164 <cell alignment="center" valignment="top" usebox="none">
8167 \begin_layout Plain Layout
8168 \begin_inset Formula $\Rightarrow$
8178 <cell alignment="center" valignment="top" usebox="none">
8181 \begin_layout Plain Layout
8189 <cell alignment="center" valignment="top" usebox="none">
8192 \begin_layout Plain Layout
8193 \begin_inset Formula $\longrightarrow$
8203 <cell alignment="center" valignment="top" usebox="none">
8206 \begin_layout Plain Layout
8214 <cell alignment="center" valignment="top" usebox="none">
8217 \begin_layout Plain Layout
8218 \begin_inset Formula $\Longrightarrow$
8228 <cell alignment="center" valignment="top" usebox="none">
8231 \begin_layout Plain Layout
8239 <cell alignment="center" valignment="top" usebox="none">
8242 \begin_layout Plain Layout
8243 \begin_inset Formula $\rightharpoonup$
8253 <cell alignment="center" valignment="top" usebox="none">
8256 \begin_layout Plain Layout
8264 <cell alignment="center" valignment="top" usebox="none">
8267 \begin_layout Plain Layout
8268 \begin_inset Formula $\rightharpoondown$
8278 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8281 \begin_layout Plain Layout
8289 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8292 \begin_layout Plain Layout
8293 \begin_inset Formula $\hookrightarrow$
8307 \begin_inset space \hfill{}
8313 \begin_layout Standard
8314 \begin_inset space \hfill{}
8318 \begin_inset Tabular
8319 <lyxtabular version="3" rows="6" columns="2">
8320 <features booktabs="true" tabularvalignment="middle">
8321 <column alignment="center" valignment="top" width="0pt">
8322 <column alignment="center" valignment="top" width="0pt">
8324 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8327 \begin_layout Plain Layout
8333 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8336 \begin_layout Plain Layout
8344 <cell alignment="center" valignment="top" usebox="none">
8347 \begin_layout Plain Layout
8355 <cell alignment="center" valignment="top" usebox="none">
8358 \begin_layout Plain Layout
8359 \begin_inset Formula $\leftrightarrow$
8369 <cell alignment="center" valignment="top" usebox="none">
8372 \begin_layout Plain Layout
8380 <cell alignment="center" valignment="top" usebox="none">
8383 \begin_layout Plain Layout
8384 \begin_inset Formula $\Leftrightarrow$
8394 <cell alignment="center" valignment="top" usebox="none">
8397 \begin_layout Plain Layout
8405 <cell alignment="center" valignment="top" usebox="none">
8408 \begin_layout Plain Layout
8409 \begin_inset Formula $\longleftrightarrow$
8419 <cell alignment="center" valignment="top" usebox="none">
8422 \begin_layout Plain Layout
8430 <cell alignment="center" valignment="top" usebox="none">
8433 \begin_layout Plain Layout
8434 \begin_inset Formula $\Longleftrightarrow$
8444 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8447 \begin_layout Plain Layout
8455 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8458 \begin_layout Plain Layout
8459 \begin_inset Formula $\rightleftharpoons$
8473 \begin_inset space \hspace{}
8478 \begin_inset space \hfill{}
8482 \begin_inset Tabular
8483 <lyxtabular version="3" rows="5" columns="2">
8484 <features booktabs="true" tabularvalignment="middle">
8485 <column alignment="center" valignment="top" width="0pt">
8486 <column alignment="center" valignment="top" width="0pt">
8488 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8491 \begin_layout Plain Layout
8497 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8500 \begin_layout Plain Layout
8508 <cell alignment="center" valignment="top" usebox="none">
8511 \begin_layout Plain Layout
8519 <cell alignment="center" valignment="top" usebox="none">
8522 \begin_layout Plain Layout
8523 \begin_inset Formula $\mapsto$
8533 <cell alignment="center" valignment="top" usebox="none">
8536 \begin_layout Plain Layout
8544 <cell alignment="center" valignment="top" usebox="none">
8547 \begin_layout Plain Layout
8548 \begin_inset Formula $\longmapsto$
8558 <cell alignment="center" valignment="top" usebox="none">
8561 \begin_layout Plain Layout
8569 <cell alignment="center" valignment="top" usebox="none">
8572 \begin_layout Plain Layout
8573 \begin_inset Formula $\leadsto$
8583 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8586 \begin_layout Plain Layout
8594 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8597 \begin_layout Plain Layout
8598 \begin_inset Formula $\dasharrow$
8612 \begin_inset space \hfill{}
8618 \begin_layout Standard
8619 \begin_inset VSpace medskip
8622 Arrows used as accents such as vector arrows are listed in
8623 \begin_inset CommandInset ref
8625 reference "sec:Accents"
8632 \begin_layout Standard
8633 \begin_inset VSpace bigskip
8637 \begin_inset Index idx
8640 \begin_layout Plain Layout
8646 are also available using the commands
8653 \begin_inset Index idx
8656 \begin_layout Plain Layout
8671 \begin_inset Index idx
8674 \begin_layout Plain Layout
8681 \begin_layout Plain Layout
8696 When inserting one of these commands in a formula, an arrow with two blue
8697 boxes appears indicating where the labels can be inserted.
8698 The length of the arrow adapts to the label width.
8701 \begin_layout Standard
8703 \begin_inset Tabular
8704 <lyxtabular version="3" rows="3" columns="2">
8705 <features booktabs="true" tabularvalignment="middle">
8706 <column alignment="center" valignment="top" width="0pt">
8707 <column alignment="center" valignment="top" width="0pt">
8709 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8712 \begin_layout Plain Layout
8718 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8721 \begin_layout Plain Layout
8729 <cell alignment="center" valignment="top" usebox="none">
8732 \begin_layout Plain Layout
8736 \begin_inset space \textvisiblespace{}
8740 \begin_inset Formula $\downarrow$
8744 \begin_inset Formula $\to$
8752 <cell alignment="center" valignment="top" usebox="none">
8755 \begin_layout Plain Layout
8756 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8765 <row topspace="2mm">
8766 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8769 \begin_layout Plain Layout
8773 \begin_inset space \textvisiblespace{}
8777 \begin_inset Formula $\downarrow$
8781 \begin_inset Formula $\to$
8789 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8792 \begin_layout Plain Layout
8793 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8809 \begin_layout Standard
8810 \begin_inset VSpace medskip
8816 \begin_layout Standard
8817 If in the document settings under
8820 \begin_inset space ~
8830 \begin_inset Index idx
8833 \begin_layout Plain Layout
8834 Packages ! mathtools
8842 \begin_inset space ~
8847 is set, you will have access to the following labeled arrows:
8850 \begin_layout Standard
8851 \begin_inset Newpage newpage
8857 \begin_layout Standard
8859 \begin_inset space \hspace*{\fill}
8863 \begin_inset Tabular
8864 <lyxtabular version="3" rows="7" columns="2">
8865 <features booktabs="true" tabularvalignment="middle">
8866 <column alignment="center" valignment="top" width="0pt">
8867 <column alignment="center" valignment="top" width="0pt">
8869 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8872 \begin_layout Plain Layout
8878 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8881 \begin_layout Plain Layout
8889 <cell alignment="center" valignment="top" usebox="none">
8892 \begin_layout Plain Layout
8912 <cell alignment="center" valignment="top" usebox="none">
8915 \begin_layout Plain Layout
8916 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8925 <row topspace="2mm">
8926 <cell alignment="center" valignment="top" usebox="none">
8929 \begin_layout Plain Layout
8949 <cell alignment="center" valignment="top" usebox="none">
8952 \begin_layout Plain Layout
8953 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8962 <row topspace="2mm">
8963 <cell alignment="center" valignment="top" usebox="none">
8966 \begin_layout Plain Layout
8986 <cell alignment="center" valignment="top" usebox="none">
8989 \begin_layout Plain Layout
8990 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8999 <row topspace="2mm">
9000 <cell alignment="center" valignment="top" usebox="none">
9003 \begin_layout Plain Layout
9023 <cell alignment="center" valignment="top" usebox="none">
9026 \begin_layout Plain Layout
9027 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
9036 <row topspace="2mm">
9037 <cell alignment="center" valignment="top" usebox="none">
9040 \begin_layout Plain Layout
9060 <cell alignment="center" valignment="top" usebox="none">
9063 \begin_layout Plain Layout
9064 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
9073 <row topspace="2mm">
9074 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9077 \begin_layout Plain Layout
9097 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9100 \begin_layout Plain Layout
9101 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
9115 \begin_inset space \hspace*{\fill}
9119 \begin_inset Tabular
9120 <lyxtabular version="3" rows="7" columns="2">
9121 <features booktabs="true" tabularvalignment="middle">
9122 <column alignment="center" valignment="top" width="0pt">
9123 <column alignment="center" valignment="top" width="0pt">
9125 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9128 \begin_layout Plain Layout
9134 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9137 \begin_layout Plain Layout
9145 <cell alignment="center" valignment="top" usebox="none">
9148 \begin_layout Plain Layout
9168 <cell alignment="center" valignment="top" usebox="none">
9171 \begin_layout Plain Layout
9172 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
9181 <row topspace="2mm">
9182 <cell alignment="center" valignment="top" usebox="none">
9185 \begin_layout Plain Layout
9205 <cell alignment="center" valignment="top" usebox="none">
9208 \begin_layout Plain Layout
9209 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
9218 <row topspace="2mm">
9219 <cell alignment="center" valignment="top" usebox="none">
9222 \begin_layout Plain Layout
9242 <cell alignment="center" valignment="top" usebox="none">
9245 \begin_layout Plain Layout
9246 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
9255 <row topspace="2mm">
9256 <cell alignment="center" valignment="top" usebox="none">
9259 \begin_layout Plain Layout
9279 <cell alignment="center" valignment="top" usebox="none">
9282 \begin_layout Plain Layout
9283 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9292 <row topspace="2mm">
9293 <cell alignment="center" valignment="top" usebox="none">
9296 \begin_layout Plain Layout
9316 <cell alignment="center" valignment="top" usebox="none">
9319 \begin_layout Plain Layout
9320 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9329 <row topspace="2mm">
9330 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9333 \begin_layout Plain Layout
9353 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9356 \begin_layout Plain Layout
9357 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9371 \begin_inset space \hspace*{\fill}
9377 \begin_layout Standard
9378 The command scheme for all of these arrows is:
9381 \begin_layout Standard
9383 \begin_inset Tabular
9384 <lyxtabular version="3" rows="2" columns="2">
9385 <features booktabs="true" tabularvalignment="middle">
9386 <column alignment="center" valignment="top" width="0pt">
9387 <column alignment="center" valignment="top" width="0pt">
9389 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9392 \begin_layout Plain Layout
9398 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9401 \begin_layout Plain Layout
9408 <row bottomspace="0.5mm">
9409 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9412 \begin_layout Plain Layout
9415 xleftrightarrow[x=a]
9418 \begin_inset Formula $\to$
9426 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9429 \begin_layout Plain Layout
9430 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9446 \begin_layout Subsection
9447 Vertical and Diagonal Arrows
9448 \begin_inset Index idx
9451 \begin_layout Plain Layout
9458 \begin_inset Index idx
9461 \begin_layout Plain Layout
9470 \begin_layout Standard
9471 \begin_inset space \hfill{}
9475 \begin_inset Tabular
9476 <lyxtabular version="3" rows="7" columns="2">
9477 <features booktabs="true" tabularvalignment="middle">
9478 <column alignment="center" valignment="top" width="0pt">
9479 <column alignment="center" valignment="top" width="0pt">
9481 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9484 \begin_layout Plain Layout
9490 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9493 \begin_layout Plain Layout
9501 <cell alignment="center" valignment="top" usebox="none">
9504 \begin_layout Plain Layout
9512 <cell alignment="center" valignment="top" usebox="none">
9515 \begin_layout Plain Layout
9516 \begin_inset Formula $\uparrow$
9526 <cell alignment="center" valignment="top" usebox="none">
9529 \begin_layout Plain Layout
9537 <cell alignment="center" valignment="top" usebox="none">
9540 \begin_layout Plain Layout
9541 \begin_inset Formula $\Uparrow$
9551 <cell alignment="center" valignment="top" usebox="none">
9554 \begin_layout Plain Layout
9562 <cell alignment="center" valignment="top" usebox="none">
9565 \begin_layout Plain Layout
9566 \begin_inset Formula $\updownarrow$
9576 <cell alignment="center" valignment="top" usebox="none">
9579 \begin_layout Plain Layout
9587 <cell alignment="center" valignment="top" usebox="none">
9590 \begin_layout Plain Layout
9591 \begin_inset Formula $\Updownarrow$
9601 <cell alignment="center" valignment="top" usebox="none">
9604 \begin_layout Plain Layout
9612 <cell alignment="center" valignment="top" usebox="none">
9615 \begin_layout Plain Layout
9616 \begin_inset Formula $\Downarrow$
9626 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9629 \begin_layout Plain Layout
9637 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9640 \begin_layout Plain Layout
9641 \begin_inset Formula $\downarrow$
9655 \begin_inset space \hfill{}
9659 \begin_inset Tabular
9660 <lyxtabular version="3" rows="5" columns="2">
9661 <features booktabs="true" tabularvalignment="middle">
9662 <column alignment="center" valignment="top" width="0pt">
9663 <column alignment="center" valignment="top" width="0pt">
9665 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9668 \begin_layout Plain Layout
9674 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9677 \begin_layout Plain Layout
9685 <cell alignment="center" valignment="top" usebox="none">
9688 \begin_layout Plain Layout
9696 <cell alignment="center" valignment="top" usebox="none">
9699 \begin_layout Plain Layout
9700 \begin_inset Formula $\nearrow$
9710 <cell alignment="center" valignment="top" usebox="none">
9713 \begin_layout Plain Layout
9721 <cell alignment="center" valignment="top" usebox="none">
9724 \begin_layout Plain Layout
9725 \begin_inset Formula $\searrow$
9735 <cell alignment="center" valignment="top" usebox="none">
9738 \begin_layout Plain Layout
9746 <cell alignment="center" valignment="top" usebox="none">
9749 \begin_layout Plain Layout
9750 \begin_inset Formula $\swarrow$
9760 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9763 \begin_layout Plain Layout
9771 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9774 \begin_layout Plain Layout
9775 \begin_inset Formula $\nwarrow$
9789 \begin_inset space \hfill{}
9795 \begin_layout Standard
9796 \begin_inset VSpace medskip
9799 Vertical arrows can also be used as delimiters together with the commands
9801 \begin_inset CommandInset ref
9803 reference "subsec:Manual-Bracket-Size"
9808 \begin_inset CommandInset ref
9810 reference "subsec:Automatic-Bracket-Size"
9817 \begin_layout Section
9819 \begin_inset CommandInset label
9826 \begin_inset Index idx
9829 \begin_layout Plain Layout
9838 \begin_layout Standard
9839 Accents can be inserted via the math toolbar button
9842 arg "math-insert \\hat"
9845 or the commands listed in the following subsections.
9848 \begin_layout Subsection
9849 Accents for One Character
9853 \begin_layout Plain Layout
9866 \begin_layout Plain Layout
9867 For accents in text see
9868 \begin_inset CommandInset ref
9870 reference "subsec:Accents-in-Text"
9883 \begin_layout Plain Layout
9891 \begin_inset Note Note
9894 \begin_layout Plain Layout
9901 is used to avoid that the footnote appears in the PDF-bookmark.
9904 \begin_layout Plain Layout
9912 \begin_inset CommandInset ref
9914 reference "subsec:Formulas-in-Section"
9924 \begin_inset CommandInset label
9926 name "subsec:Accents-for-one"
9931 \begin_inset Index idx
9934 \begin_layout Plain Layout
9935 Accents ! for one character
9943 \begin_layout Standard
9944 \begin_inset space \hfill{}
9948 \begin_inset Tabular
9949 <lyxtabular version="3" rows="8" columns="2">
9950 <features booktabs="true" tabularvalignment="middle">
9951 <column alignment="center" valignment="top" width="0pt">
9952 <column alignment="center" valignment="top" width="0pt">
9954 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9957 \begin_layout Plain Layout
9963 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9966 \begin_layout Plain Layout
9973 <row topspace="1.5mm">
9974 <cell alignment="center" valignment="top" usebox="none">
9977 \begin_layout Plain Layout
9981 \begin_inset space \textvisiblespace{}
9989 <cell alignment="center" valignment="top" usebox="none">
9992 \begin_layout Plain Layout
9993 \begin_inset Formula $\dot{A}$
10002 <row topspace="1.5mm">
10003 <cell alignment="center" valignment="top" usebox="none">
10006 \begin_layout Plain Layout
10010 \begin_inset space \textvisiblespace{}
10018 <cell alignment="center" valignment="top" usebox="none">
10021 \begin_layout Plain Layout
10022 \begin_inset Formula $\ddot{A}$
10031 <row topspace="1.5mm">
10032 <cell alignment="center" valignment="top" usebox="none">
10035 \begin_layout Plain Layout
10039 \begin_inset space \textvisiblespace{}
10047 <cell alignment="center" valignment="top" usebox="none">
10050 \begin_layout Plain Layout
10051 \begin_inset Formula $\dddot{A}$
10060 <row topspace="1.5mm">
10061 <cell alignment="center" valignment="top" usebox="none">
10064 \begin_layout Plain Layout
10068 \begin_inset space \textvisiblespace{}
10076 <cell alignment="center" valignment="top" usebox="none">
10079 \begin_layout Plain Layout
10080 \begin_inset Formula $\ddddot{A}$
10089 <row topspace="1.5mm">
10090 <cell alignment="center" valignment="top" usebox="none">
10093 \begin_layout Plain Layout
10097 \begin_inset space \textvisiblespace{}
10101 \begin_inset Index idx
10104 \begin_layout Plain Layout
10115 <cell alignment="center" valignment="top" usebox="none">
10118 \begin_layout Plain Layout
10119 \begin_inset Formula $\vec{A}$
10128 <row topspace="1.5mm">
10129 <cell alignment="center" valignment="top" usebox="none">
10132 \begin_layout Plain Layout
10136 \begin_inset space \textvisiblespace{}
10144 <cell alignment="center" valignment="top" usebox="none">
10147 \begin_layout Plain Layout
10148 \begin_inset Formula $\bar{A}$
10157 <row topspace="1.5mm">
10158 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10161 \begin_layout Plain Layout
10165 \begin_inset space \textvisiblespace{}
10173 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10176 \begin_layout Plain Layout
10177 \begin_inset Formula $\mathring{A}$
10191 \begin_inset space \hfill{}
10195 \begin_inset Tabular
10196 <lyxtabular version="3" rows="7" columns="2">
10197 <features booktabs="true" tabularvalignment="middle">
10198 <column alignment="center" valignment="top" width="0pt">
10199 <column alignment="center" valignment="top" width="0pt">
10201 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10204 \begin_layout Plain Layout
10210 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10213 \begin_layout Plain Layout
10220 <row topspace="1.5mm">
10221 <cell alignment="center" valignment="top" usebox="none">
10224 \begin_layout Plain Layout
10228 \begin_inset space \textvisiblespace{}
10236 <cell alignment="center" valignment="top" usebox="none">
10239 \begin_layout Plain Layout
10240 \begin_inset Formula $\tilde{A}$
10249 <row topspace="1.5mm">
10250 <cell alignment="center" valignment="top" usebox="none">
10253 \begin_layout Plain Layout
10257 \begin_inset space \textvisiblespace{}
10265 <cell alignment="center" valignment="top" usebox="none">
10268 \begin_layout Plain Layout
10269 \begin_inset Formula $\hat{A}$
10278 <row topspace="1.5mm">
10279 <cell alignment="center" valignment="top" usebox="none">
10282 \begin_layout Plain Layout
10286 \begin_inset space \textvisiblespace{}
10294 <cell alignment="center" valignment="top" usebox="none">
10297 \begin_layout Plain Layout
10298 \begin_inset Formula $\check{A}$
10307 <row topspace="1.5mm">
10308 <cell alignment="center" valignment="top" usebox="none">
10311 \begin_layout Plain Layout
10315 \begin_inset space \textvisiblespace{}
10323 <cell alignment="center" valignment="top" usebox="none">
10326 \begin_layout Plain Layout
10327 \begin_inset Formula $\acute{A}$
10336 <row topspace="1.5mm">
10337 <cell alignment="center" valignment="top" usebox="none">
10340 \begin_layout Plain Layout
10344 \begin_inset space \textvisiblespace{}
10352 <cell alignment="center" valignment="top" usebox="none">
10355 \begin_layout Plain Layout
10356 \begin_inset Formula $\grave{A}$
10365 <row topspace="1.5mm">
10366 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10369 \begin_layout Plain Layout
10373 \begin_inset space \textvisiblespace{}
10381 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10384 \begin_layout Plain Layout
10385 \begin_inset Formula $\breve{A}$
10399 \begin_inset space \hfill{}
10405 \begin_layout Standard
10406 \begin_inset VSpace bigskip
10412 \begin_layout Standard
10413 You can directly insert accents such as é in formulas.
10415 will transform them to the corresponding accent command.
10417 \begin_inset Index idx
10420 \begin_layout Plain Layout
10426 however it is better to insert a quotation mark before the vowel.
10427 These two characters are then treated by \SpecialChar LaTeX
10432 character when the formula part with the umlaut is marked as German.
10440 \begin_inset Quotes eld
10444 \begin_inset Quotes erd
10447 umlauts are created as demonstrated in the following example:
10450 \begin_layout Standard
10451 \begin_inset VSpace -2mm
10457 \begin_layout Standard
10459 \begin_inset Tabular
10460 <lyxtabular version="3" rows="3" columns="2">
10461 <features booktabs="true" tabularvalignment="middle">
10462 <column alignment="center" valignment="top" width="0pt">
10463 <column alignment="center" valignment="top">
10465 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10468 \begin_layout Plain Layout
10474 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10477 \begin_layout Plain Layout
10485 <cell alignment="center" valignment="top" usebox="none">
10488 \begin_layout Plain Layout
10489 \begin_inset Quotes grd
10497 <cell alignment="center" valignment="top" usebox="none">
10500 \begin_layout Plain Layout
10501 \begin_inset space \hspace{}
10508 \begin_inset Formula $"i$
10517 <row topspace="1.5mm">
10518 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10521 \begin_layout Plain Layout
10525 \begin_inset space \textvisiblespace{}
10533 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10536 \begin_layout Plain Layout
10537 \begin_inset Formula $\ddot{i}$
10553 \begin_layout Standard
10560 is that umlauts can be directly converted to mathematical text because
10561 the accent commands above are
10567 in mathematical text
10570 To convert an accented character to mathematical text, only the character
10571 under the accent may be converted.
10572 This applies for all conversions, e.
10573 \begin_inset space \thinspace{}
10577 \begin_inset space \space{}
10583 \begin_layout Standard
10584 \begin_inset VSpace bigskip
10590 \begin_layout Standard
10592 also supports a tilde under the character if the \SpecialChar LaTeX
10598 \begin_inset Index idx
10601 \begin_layout Plain Layout
10602 Packages ! undertilde
10607 is installed on your system:
10610 \begin_layout Standard
10614 \begin_layout Plain Layout
10624 \begin_inset Note Note
10627 \begin_layout Plain Layout
10628 The following table will only be displayed when the \SpecialChar LaTeX
10641 \begin_layout Standard
10644 \begin_inset Tabular
10645 <lyxtabular version="3" rows="2" columns="2">
10646 <features booktabs="true" tabularvalignment="middle">
10647 <column alignment="center" valignment="top" width="0pt">
10648 <column alignment="center" valignment="top" width="0pt">
10650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10653 \begin_layout Plain Layout
10659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10662 \begin_layout Plain Layout
10670 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10673 \begin_layout Plain Layout
10677 \begin_inset space \textvisiblespace{}
10685 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10688 \begin_layout Plain Layout
10689 \begin_inset Formula $\utilde{A}$
10705 \begin_layout Standard
10709 \begin_layout Plain Layout
10719 \begin_inset Note Note
10722 \begin_layout Plain Layout
10723 The following will be displayed when the \SpecialChar LaTeX
10736 \begin_layout Standard
10737 You need to install the \SpecialChar LaTeX
10742 to see the rest of this subsection in the output.
10745 \begin_layout Standard
10749 \begin_layout Plain Layout
10761 \begin_layout Subsection
10762 Accents for Several Characters
10763 \begin_inset Index idx
10766 \begin_layout Plain Layout
10767 Accents ! for several characters
10775 \begin_layout Standard
10776 \begin_inset space \hfill{}
10780 \begin_inset Tabular
10781 <lyxtabular version="3" rows="5" columns="2">
10782 <features booktabs="true" tabularvalignment="middle">
10783 <column alignment="center" valignment="top" width="0pt">
10784 <column alignment="center" valignment="top" width="0pt">
10786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10789 \begin_layout Plain Layout
10795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10798 \begin_layout Plain Layout
10805 <row topspace="1.5mm">
10806 <cell alignment="center" valignment="top" usebox="none">
10809 \begin_layout Plain Layout
10813 \begin_inset space \textvisiblespace{}
10821 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10824 \begin_layout Plain Layout
10825 \begin_inset Formula $\overleftarrow{A=B}$
10834 <row topspace="1.5mm">
10835 <cell alignment="center" valignment="top" usebox="none">
10838 \begin_layout Plain Layout
10842 \begin_inset space \textvisiblespace{}
10850 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10853 \begin_layout Plain Layout
10854 \begin_inset Formula $\underleftarrow{A=B}$
10863 <row topspace="1.5mm">
10864 <cell alignment="center" valignment="top" usebox="none">
10867 \begin_layout Plain Layout
10871 \begin_inset space \textvisiblespace{}
10879 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10882 \begin_layout Plain Layout
10883 \begin_inset Formula $\overleftrightarrow{A=B}$
10892 <row topspace="1.5mm" bottomspace="1mm">
10893 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10896 \begin_layout Plain Layout
10899 underleftrightarrow
10900 \begin_inset space \textvisiblespace{}
10908 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10911 \begin_layout Plain Layout
10912 \begin_inset Formula $\underleftrightarrow{A=B}$
10926 \begin_inset space \hfill{}
10930 \begin_inset Tabular
10931 <lyxtabular version="3" rows="5" columns="2">
10932 <features booktabs="true" tabularvalignment="middle">
10933 <column alignment="center" valignment="top" width="0pt">
10934 <column alignment="center" valignment="top" width="0pt">
10936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10939 \begin_layout Plain Layout
10945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10948 \begin_layout Plain Layout
10955 <row topspace="1.5mm">
10956 <cell alignment="center" valignment="top" usebox="none">
10959 \begin_layout Plain Layout
10963 \begin_inset space \textvisiblespace{}
10971 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10974 \begin_layout Plain Layout
10975 \begin_inset Formula $\overrightarrow{A=B}$
10984 <row topspace="1.5mm">
10985 <cell alignment="center" valignment="top" usebox="none">
10988 \begin_layout Plain Layout
10992 \begin_inset space \textvisiblespace{}
11000 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11003 \begin_layout Plain Layout
11004 \begin_inset Formula $\underrightarrow{A=B}$
11013 <row topspace="1.5mm">
11014 <cell alignment="center" valignment="top" usebox="none">
11017 \begin_layout Plain Layout
11021 \begin_inset space \textvisiblespace{}
11029 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11032 \begin_layout Plain Layout
11033 \begin_inset Formula $\widetilde{A=B}$
11042 <row topspace="1.5mm" bottomspace="1mm">
11043 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11046 \begin_layout Plain Layout
11050 \begin_inset space \textvisiblespace{}
11058 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11061 \begin_layout Plain Layout
11062 \begin_inset Formula $\widehat{A=B}$
11076 \begin_inset space \hfill{}
11082 \begin_layout Standard
11083 \begin_inset VSpace medskip
11086 Using these commands you can accent as many characters as you like.
11099 will only be set in the output with a length of three characters, as shown
11100 in the following example:
11101 \begin_inset Formula
11103 \widetilde{A+B=C-D}
11111 \begin_layout Standard
11112 It is also possible to accent several characters using the commands
11119 \begin_inset Index idx
11122 \begin_layout Plain Layout
11137 \begin_inset Index idx
11140 \begin_layout Plain Layout
11148 described in the previous subsection.
11154 \begin_inset space \textvisiblespace{}
11158 \begin_inset Formula $\downarrow$
11164 \begin_inset Formula
11166 \underset{***}{A=B}
11174 \begin_layout Section
11176 \begin_inset CommandInset label
11178 name "subsec:Space"
11183 \begin_inset Index idx
11186 \begin_layout Plain Layout
11195 \begin_layout Subsection
11197 \begin_inset CommandInset label
11199 name "subsec:Predefined-Space"
11204 \begin_inset Index idx
11207 \begin_layout Plain Layout
11208 Space ! horizontal ! predefined
11216 \begin_layout Standard
11217 Sometimes it is necessary to insert horizontal space into a formula.
11218 This is done by inserting a protected space (shortcut
11219 \change_inserted 5863208 1612729962
11223 arg "command-alternatives math-space ; space-insert protected"
11227 \change_deleted 5863208 1612729965
11231 arg "command-alternatives space-insert protected ; math-space"
11235 \begin_inset Note Note
11238 \begin_layout Plain Layout
11240 \change_inserted 232239728 1611160593
11241 What is intended here?
11252 \begin_inset Quotes eld
11258 \begin_inset space \textvisiblespace{}
11264 \begin_inset Quotes erd
11267 appears and by pressing
11271 several times one can select one of eight different space sizes.
11272 The spaces can also be inserted using the math toolbar button
11275 arg "math-insert \\space"
11278 or special commands.
11279 The size can be adjusted at any time by positioning the cursor on the
11282 arg "math-insert \\space"
11289 until the desired size is achieved.
11292 \begin_layout Standard
11295 \begin_inset Tabular
11296 <lyxtabular version="3" rows="6" columns="3">
11297 <features booktabs="true" tabularvalignment="middle">
11298 <column alignment="center" valignment="top">
11299 <column alignment="center" valignment="top" width="15col%">
11300 <column alignment="center" valignment="top">
11302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11305 \begin_layout Plain Layout
11311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11314 \begin_layout Plain Layout
11324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11327 \begin_layout Plain Layout
11335 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11338 \begin_layout Plain Layout
11346 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11349 \begin_layout Plain Layout
11355 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11358 \begin_layout Plain Layout
11359 \begin_inset Formula $A\,B$
11369 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11372 \begin_layout Plain Layout
11380 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11383 \begin_layout Plain Layout
11389 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11392 \begin_layout Plain Layout
11393 \begin_inset Formula $A\:B$
11403 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11406 \begin_layout Plain Layout
11414 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11417 \begin_layout Plain Layout
11423 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11426 \begin_layout Plain Layout
11427 \begin_inset Formula $A\;B$
11437 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11440 \begin_layout Plain Layout
11448 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11451 \begin_layout Plain Layout
11457 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11460 \begin_layout Plain Layout
11461 \begin_inset Formula $A\quad B$
11471 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11474 \begin_layout Plain Layout
11482 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11485 \begin_layout Plain Layout
11491 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11494 \begin_layout Plain Layout
11495 \begin_inset Formula $A\qquad B$
11509 \begin_inset space \hfill{}
11513 \begin_inset Tabular
11514 <lyxtabular version="3" rows="6" columns="3">
11515 <features booktabs="true" tabularvalignment="middle">
11516 <column alignment="center" valignment="top">
11517 <column alignment="center" valignment="top" width="15col%">
11518 <column alignment="center" valignment="top">
11520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11523 \begin_layout Plain Layout
11529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11532 \begin_layout Plain Layout
11542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11545 \begin_layout Plain Layout
11553 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11556 \begin_layout Plain Layout
11564 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11567 \begin_layout Plain Layout
11573 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11576 \begin_layout Plain Layout
11577 \begin_inset Formula $A\hfill B$
11587 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11590 \begin_layout Plain Layout
11598 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11601 \begin_layout Plain Layout
11607 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11610 \begin_layout Plain Layout
11611 \begin_inset Formula $A\hspace*{1em}B$
11621 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11624 \begin_layout Plain Layout
11632 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11635 \begin_layout Plain Layout
11641 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11644 \begin_layout Plain Layout
11645 \begin_inset Formula $A\hspace{1em}B$
11655 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11658 \begin_layout Plain Layout
11662 \begin_inset space \textvisiblespace{}
11670 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11673 \begin_layout Plain Layout
11679 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11682 \begin_layout Plain Layout
11683 \begin_inset Formula $A\ B$
11693 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11696 \begin_layout Plain Layout
11704 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11707 \begin_layout Plain Layout
11713 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11716 \begin_layout Plain Layout
11717 \begin_inset Formula $A\!B$
11733 \begin_layout Standard
11735 \begin_inset space ~
11739 \begin_inset space \thinspace{}
11743 \begin_inset space \thinspace{}
11746 7 are variable spaces which are explained in
11747 \begin_inset CommandInset ref
11749 reference "subsec:Variable-Space"
11755 \begin_inset space ~
11758 9 appears to produce no space.
11759 It is displayed red in \SpecialChar LyX
11760 contrary to the other sizes, because it is a negative
11762 There are two more negative spaces:
11765 \begin_layout Standard
11767 \begin_inset Tabular
11768 <lyxtabular version="3" rows="3" columns="3">
11769 <features booktabs="true" tabularvalignment="middle">
11770 <column alignment="center" valignment="middle" width="6.8cm">
11771 <column alignment="center" valignment="top" width="0pt">
11772 <column alignment="center" valignment="top" width="0pt">
11774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11777 \begin_layout Plain Layout
11783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11786 \begin_layout Plain Layout
11794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11797 \begin_layout Plain Layout
11807 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11810 \begin_layout Plain Layout
11815 keystrokes after inserting the protected space
11820 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11823 \begin_layout Plain Layout
11829 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11832 \begin_layout Plain Layout
11840 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11843 \begin_layout Plain Layout
11849 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11852 \begin_layout Plain Layout
11853 \begin_inset Formula $A\negmedspace B$
11861 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11864 \begin_layout Plain Layout
11865 \begin_inset Formula $A\negthickspace B$
11881 \begin_layout Standard
11882 Negative spaces can lead to characters overlapping each other.
11883 Thus they can be used to enforce ligatures, which are useful for things
11884 such as summation operators:
11887 \begin_layout Standard
11889 \begin_inset Tabular
11890 <lyxtabular version="3" rows="3" columns="2">
11891 <features booktabs="true" tabularvalignment="middle">
11892 <column alignment="center" valignment="top" width="0pt">
11893 <column alignment="center" valignment="top">
11895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11898 \begin_layout Plain Layout
11904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11907 \begin_layout Plain Layout
11915 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11918 \begin_layout Plain Layout
11924 \begin_inset space \textvisiblespace{}
11932 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11935 \begin_layout Plain Layout
11936 \begin_inset Formula $\sum\sum f_{kl}$
11946 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11949 \begin_layout Plain Layout
11957 \begin_inset space \textvisiblespace{}
11965 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11968 \begin_layout Plain Layout
11969 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11985 \begin_layout Standard
11987 \begin_inset VSpace medskip
11993 \begin_layout Standard
11995 Relational operators, for example equal or less than signs, are always surrounde
11997 To suppress this, the operator is placed into a \SpecialChar TeX
11999 The following example demonstrates this:
12002 \begin_layout Standard
12004 \begin_inset Tabular
12005 <lyxtabular version="3" rows="2" columns="2">
12006 <features tabularvalignment="middle">
12007 <column alignment="center" valignment="top" width="0pt">
12008 <column alignment="center" valignment="top" width="0pt">
12010 <cell alignment="center" valignment="top" usebox="none">
12013 \begin_layout Plain Layout
12019 <cell alignment="center" valignment="top" usebox="none">
12022 \begin_layout Plain Layout
12023 \begin_inset Formula $A=B$
12033 <cell alignment="center" valignment="top" usebox="none">
12036 \begin_layout Plain Layout
12037 Equation without space
12042 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
12045 \begin_layout Plain Layout
12046 \begin_inset Formula $A{=}B$
12062 \begin_layout Standard
12064 The command for the last formula is:
12069 \begin_inset Formula $\to$
12075 \begin_layout Standard
12076 \begin_inset VSpace bigskip
12082 \begin_layout Standard
12083 Another example of controlled spaces is physical units.
12084 The space between a value and its unit is smaller than a normal space,
12085 typically a thin space is used.
12086 For units in text, the smaller space is inserted via the menu
12088 Insert\SpecialChar menuseparator
12089 Formatting\SpecialChar menuseparator
12091 \begin_inset space ~
12099 arg "space-insert thin"
12105 \begin_layout Standard
12106 An example to visualize the difference:
12109 \begin_layout Standard
12110 \begin_inset Tabular
12111 <lyxtabular version="3" rows="2" columns="2">
12112 <features tabularvalignment="middle">
12113 <column alignment="left" valignment="top">
12114 <column alignment="left" valignment="top">
12116 <cell alignment="center" valignment="top" usebox="none">
12119 \begin_layout Plain Layout
12121 \begin_inset Formula $\cdot$
12129 <cell alignment="center" valignment="top" usebox="none">
12132 \begin_layout Plain Layout
12133 Space between value and unit
12140 <cell alignment="center" valignment="top" usebox="none">
12143 \begin_layout Plain Layout
12145 \begin_inset space \thinspace{}
12149 \begin_inset Formula $\cdot$
12157 <cell alignment="center" valignment="top" usebox="none">
12160 \begin_layout Plain Layout
12161 Thin space between value and unit
12174 \begin_layout Subsection
12179 \begin_layout Plain Layout
12192 \begin_layout Plain Layout
12193 For vertical space in formulas see
12194 \begin_inset CommandInset ref
12196 reference "subsec:Line-Separation"
12209 \begin_layout Plain Layout
12217 \begin_inset Note Note
12220 \begin_layout Plain Layout
12223 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12226 \begin_layout Plain Layout
12229 texorpdfstring is in section
12230 \begin_inset CommandInset ref
12232 reference "subsec:Formulas-in-Section"
12242 \begin_inset CommandInset label
12244 name "subsec:Variable-Space"
12249 \begin_inset Index idx
12252 \begin_layout Plain Layout
12253 Space ! horizontal ! variable
12261 \begin_layout Standard
12262 Space with a defined length can be inserted with the command
12269 \begin_inset Index idx
12272 \begin_layout Plain Layout
12282 \begin_inset Quotes eld
12288 \begin_inset space \textvisiblespace{}
12294 \begin_inset Quotes erd
12297 will appear, the length of which can be specified by left-clicking on the
12299 \begin_inset Quotes eld
12305 \begin_inset space \textvisiblespace{}
12311 \begin_inset Quotes erd
12315 The length may also be negative.
12316 If the space is the first character in a line, it will ordinarily be omitted.
12317 To force its output use the command
12329 or left-click on the
12330 \begin_inset Quotes eld
12336 \begin_inset space \textvisiblespace{}
12342 \begin_inset Quotes erd
12345 and check the option
12350 \begin_inset Newline newline
12353 To insert as much space as is available, the command
12360 \begin_inset Index idx
12363 \begin_layout Plain Layout
12374 \begin_layout Standard
12376 \begin_inset Tabular
12377 <lyxtabular version="3" rows="4" columns="2">
12378 <features booktabs="true" tabularvalignment="middle">
12379 <column alignment="center" valignment="top" width="0pt">
12380 <column alignment="center" valignment="top">
12382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12385 \begin_layout Plain Layout
12393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12396 \begin_layout Plain Layout
12404 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12407 \begin_layout Plain Layout
12411 \begin_inset space \textvisiblespace{}
12417 \begin_inset space \thinspace{}
12425 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12428 \begin_layout Plain Layout
12429 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12439 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12442 \begin_layout Plain Layout
12446 \begin_inset space \textvisiblespace{}
12452 \begin_inset space \thinspace{}
12460 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12463 \begin_layout Plain Layout
12464 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12477 \begin_layout Plain Layout
12481 \begin_inset space \textvisiblespace{}
12489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12492 \begin_layout Plain Layout
12493 \begin_inset Formula $A=A\hfill B=B$
12509 \begin_layout Standard
12510 In the last example the available space is given by the longest column entry
12512 In an inline formula the space depends on the length of the line in which
12520 Thus, when the line uses the full width, no space will be created.
12527 only has an effect on displayed formulas when the formula style
12532 (Formula styles are explained in
12533 \begin_inset CommandInset ref
12535 reference "sec:Formula-Styles"
12542 \begin_layout Standard
12549 , there are also commands,
12561 that fill the space with a pattern.
12563 \begin_inset CommandInset ref
12565 reference "subsec:Ellipses"
12572 \begin_layout Standard
12573 For text, variable space can be inserted via the menu
12575 Insert\SpecialChar menuseparator
12576 Formatting\SpecialChar menuseparator
12578 \begin_inset space ~
12586 \begin_layout Standard
12587 This is a line with
12588 \begin_inset space \hspace{}
12593 \begin_inset space \thinspace{}
12599 \begin_layout Standard
12600 This is a line with
12601 \begin_inset space \hfill{}
12607 \begin_layout Subsection
12608 Space Besides Inline Formulas
12609 \begin_inset Index idx
12612 \begin_layout Plain Layout
12613 Space ! besides inline formulas
12621 \begin_layout Standard
12622 The space that surrounds inline formulas can be adjusted with the length
12630 \begin_inset Index idx
12633 \begin_layout Plain Layout
12642 The value of a length is set with the command
12649 \begin_inset Index idx
12652 \begin_layout Plain Layout
12660 which has the following scheme:
12663 \begin_layout Standard
12668 setlength{length name}{value}
12671 \begin_layout Standard
12679 \begin_inset space \thinspace{}
12685 \begin_layout Standard
12695 \begin_layout Standard
12696 is inserted in \SpecialChar TeX
12699 \begin_inset space \thinspace{}
12702 mm space will now be set around all inline formulas:
12706 \begin_layout Plain Layout
12720 \begin_layout Standard
12721 This is a line with an inline formula
12722 \begin_inset Formula $A=B$
12726 \begin_inset space \thinspace{}
12729 mm surrounding space.
12733 \begin_layout Plain Layout
12747 \begin_layout Standard
12748 To return to the predefined value,
12754 is set to the value 0
12755 \begin_inset space \thinspace{}
12761 \begin_layout Section
12763 \begin_inset Index idx
12766 \begin_layout Plain Layout
12773 \begin_inset Index idx
12776 \begin_layout Plain Layout
12781 \begin_layout Plain Layout
12792 \begin_layout Plain Layout
12807 \begin_layout Standard
12808 Boxes for text are described in chapter
12815 \begin_inset space ~
12823 \begin_layout Subsection
12825 \begin_inset CommandInset label
12827 name "subsec:Boxes-with-Frame"
12832 \begin_inset Index idx
12835 \begin_layout Plain Layout
12844 \begin_layout Standard
12845 It is possible to frame a formula or part of one with the commands
12852 \begin_inset Index idx
12855 \begin_layout Plain Layout
12870 \begin_inset Index idx
12873 \begin_layout Plain Layout
12884 \begin_layout Standard
12885 When one of these commands is inserted in a formula, a blue box appears
12886 within a frame to enter formula parts.
12893 an additional formula has to be created by
12897 within this box, because the box content will otherwise be treated as mathemati
12905 is used, a new formula is automatically created inside the frame.
12908 \begin_layout Standard
12915 is not suitable to frame displayed formulas because the formula will always
12916 be set in the size of the documents text.
12923 is not suitable to frame inline formulas because the formula will always
12924 be set in the size of a displayed formula.
12927 \begin_layout Standard
12941 \begin_inset Index idx
12944 \begin_layout Plain Layout
12952 with which the frame width and the alignment can be specified.
12959 is used in the following scheme:
12962 \begin_layout Standard
12967 framebox[frame width][position]{box content}
12970 \begin_layout Standard
12971 The position can either be
12988 right aligns the formula in the box.
12989 If no position is given the formula will be centered.
12990 \begin_inset Newline newline
12993 If width is not given then position can not be given.
12994 In this case the frame width is adjusted to the box content like for
13003 \begin_layout Standard
13010 is inserted, a box appears containing three blue boxes.
13011 The first two boxes are surrounded by brackets and denote the two optional
13013 The third box is for formula parts like for
13022 \begin_layout Standard
13024 \begin_inset Tabular
13025 <lyxtabular version="3" rows="5" columns="2">
13026 <features booktabs="true" tabularvalignment="middle">
13027 <column alignment="center" valignment="top" width="0pt">
13028 <column alignment="center" valignment="top">
13030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13033 \begin_layout Plain Layout
13039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13042 \begin_layout Plain Layout
13049 <row topspace="1.5mm">
13050 <cell alignment="center" valignment="top" usebox="none">
13053 \begin_layout Plain Layout
13057 \begin_inset space \textvisiblespace{}
13067 \begin_inset space \textvisiblespace{}
13075 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13078 \begin_layout Plain Layout
13079 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
13088 <row topspace="1.5mm">
13089 <cell alignment="center" valignment="top" usebox="none">
13092 \begin_layout Plain Layout
13096 \begin_inset space \textvisiblespace{}
13102 \begin_inset space \textvisiblespace{}
13110 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13113 \begin_layout Plain Layout
13114 \begin_inset Formula $\boxed{\int A=B}$
13123 <row topspace="1.5mm">
13124 <cell alignment="center" valignment="top" usebox="none">
13127 \begin_layout Plain Layout
13131 \begin_inset space \textvisiblespace{}
13139 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13142 \begin_layout Plain Layout
13143 \begin_inset Formula $A+\fbox{B}$
13152 <row topspace="1.5mm" bottomspace="1mm">
13153 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13156 \begin_layout Plain Layout
13160 \begin_inset space \textvisiblespace{}
13164 \begin_inset Formula $\to$
13168 \begin_inset Formula $\to$
13178 \begin_inset space \textvisiblespace{}
13182 \begin_inset Formula $\downarrow$
13190 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13193 \begin_layout Plain Layout
13194 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13210 \begin_layout Standard
13211 To adjust the frame thickness the following commands are inserted in \SpecialChar TeX
13213 before the formula:
13216 \begin_layout Standard
13226 \begin_inset Quotes eld
13230 \begin_inset Quotes erd
13244 \begin_inset Quotes eld
13248 \begin_inset Quotes erd
13254 \begin_layout Standard
13255 \begin_inset Quotes eld
13259 \begin_inset Quotes erd
13262 specifies the minimum distance between the frame and the first character
13264 An example of this is given in the following framed formula:
13268 \begin_layout Plain Layout
13280 \begin_inset Formula
13287 Before this formula the commands
13290 \begin_layout Standard
13312 \begin_layout Standard
13313 were inserted in \SpecialChar TeX
13315 These values are then used for all following boxes.
13318 \begin_layout Standard
13319 To return to the standard frame size, the command
13322 \begin_layout Standard
13347 \begin_layout Plain Layout
13361 \begin_layout Standard
13362 is inserted in \SpecialChar TeX
13363 mode before the next formula.
13366 \begin_layout Subsection
13367 Boxes Without Frame
13368 \begin_inset CommandInset label
13370 name "subsec:Boxes-without-Frame"
13375 \begin_inset Index idx
13378 \begin_layout Plain Layout
13379 Boxes ! without frame
13387 \begin_layout Standard
13388 For boxes without a frame the following box commands:
13395 \begin_inset Index idx
13398 \begin_layout Plain Layout
13413 \begin_inset Index idx
13416 \begin_layout Plain Layout
13431 \begin_inset Index idx
13434 \begin_layout Plain Layout
13445 \begin_layout Standard
13452 a box can be super- or subscripted.
13453 But in contrary to normal super- and subscripting, the characters in the
13454 box keep their font size.
13461 is used in the following scheme:
13464 \begin_layout Standard
13469 raisebox{height}{box content}
13472 \begin_layout Standard
13473 When the box contains a formula, an extra formula is needed like for
13482 \begin_layout Standard
13485 \begin_inset Note Greyedout
13488 \begin_layout Plain Layout
13499 this extra formula is created by pressing
13503 twice instead of once because \SpecialChar LyX
13504 doesn't yet support
13518 \begin_layout Standard
13520 \begin_inset Tabular
13521 <lyxtabular version="3" rows="4" columns="2">
13522 <features booktabs="true" tabularvalignment="middle">
13523 <column alignment="center" valignment="top" width="0pt">
13524 <column alignment="center" valignment="top">
13526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13529 \begin_layout Plain Layout
13535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13538 \begin_layout Plain Layout
13546 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13549 \begin_layout Plain Layout
13553 \begin_inset Formula $\to$
13559 \begin_inset Formula $\to$
13567 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13570 \begin_layout Plain Layout
13571 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13581 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13584 \begin_layout Plain Layout
13588 \begin_inset Formula $\to$
13594 \begin_inset Formula $\to$
13602 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13605 \begin_layout Plain Layout
13606 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13619 \begin_layout Plain Layout
13623 \begin_inset Formula $\to$
13639 \begin_inset space \textvisiblespace{}
13647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13650 \begin_layout Plain Layout
13651 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13667 \begin_layout Standard
13692 , except that there is no frame.
13695 \begin_layout Subsection
13697 \begin_inset CommandInset label
13699 name "subsec:Colored-Boxes"
13704 \begin_inset Index idx
13707 \begin_layout Plain Layout
13716 \begin_layout Standard
13717 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13726 \begin_layout Plain Layout
13727 The \SpecialChar LaTeX
13732 is part of every \SpecialChar LaTeX
13733 standard installation.
13739 \begin_inset Index idx
13742 \begin_layout Plain Layout
13748 must be loaded in the \SpecialChar LaTeX
13749 -preamble with the line
13753 \begin_layout Plain Layout
13754 When text is colored somewhere in the document with a predefined color,
13756 loads the \SpecialChar LaTeX
13762 Thus it is possible that the package is loaded twice, but this does not
13769 \begin_inset Note Note
13772 \begin_layout Plain Layout
13773 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13782 \begin_layout Standard
13790 \begin_layout Standard
13791 \begin_inset VSpace medskip
13794 To create color boxes, the command
13801 \begin_inset Index idx
13804 \begin_layout Plain Layout
13812 is used in the following scheme:
13815 \begin_layout Standard
13820 colorbox{color}{box content}
13823 \begin_layout Standard
13824 The box content can also be a box and a
13830 can also be part of another box (see the 2nd and 3rd example).
13831 When the box should contain a formula, an extra formula has to be created,
13832 the same way as for
13842 \begin_layout Plain Layout
13843 This also applies for the command
13857 \begin_layout Standard
13858 One of the following predefined colors can be chosen:
13861 \begin_layout Standard
13893 \begin_inset VSpace smallskip
13899 \begin_layout Standard
13901 \begin_inset Tabular
13902 <lyxtabular version="3" rows="4" columns="2">
13903 <features booktabs="true" tabularvalignment="middle">
13904 <column alignment="center" valignment="top" width="0pt">
13905 <column alignment="center" valignment="top">
13907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13910 \begin_layout Plain Layout
13916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13919 \begin_layout Plain Layout
13927 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13930 \begin_layout Plain Layout
13934 \begin_inset Formula $\to$
13944 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13947 \begin_layout Plain Layout
13948 \begin_inset Formula $\colorbox{yellow}{A=B}$
13957 <row topspace="1.5mm">
13958 <cell alignment="center" valignment="top" usebox="none">
13961 \begin_layout Plain Layout
13965 \begin_inset Formula $\to$
13973 \begin_inset space \textvisiblespace{}
13977 \change_inserted 232239728 1611182042
13979 \begin_inset Formula $\gets\gets$
13989 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13992 \begin_layout Plain Layout
13993 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
14002 <row topspace="1.5mm" bottomspace="1mm">
14003 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
14006 \begin_layout Plain Layout
14010 \begin_inset space \textvisiblespace{}
14014 \change_inserted 232239728 1611182036
14016 \begin_inset Formula $\gets\gets$
14024 \begin_inset Formula $\to$
14040 \begin_inset space \textvisiblespace{}
14048 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
14051 \begin_layout Plain Layout
14052 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
14066 \begin_inset VSpace smallskip
14072 \begin_layout Standard
14079 only colors the box background, not the characters in the box.
14080 To color all characters, the whole formula is highlighted and the desired
14081 color is chosen in the
14084 \begin_inset space ~
14090 The dialog can be called with the toolbar button
14093 arg "dialog-show character"
14098 Edit\SpecialChar menuseparator
14100 \begin_inset space ~
14103 Properties\SpecialChar menuseparator
14107 The formula number will have the same color as the formula.
14108 If a different color for the formula number is desired, the color must
14109 be changed within the formula.
14112 \begin_layout Standard
14116 \begin_layout Standard
14119 \begin_inset Formula
14121 \int A=B\label{eq:red}
14129 \begin_inset Formula
14131 \textcolor{red}{\int A=B}\label{eq:redgreen}
14139 \begin_layout Standard
14141 \begin_inset CommandInset ref
14147 is completely colored red.
14148 \begin_inset Newline newline
14152 \begin_inset CommandInset ref
14154 reference "eq:redgreen"
14158 was first completely colored green to set the color for the formula number.
14159 Subsequently the formula characters were colored red.
14162 \begin_layout Standard
14163 \begin_inset VSpace bigskip
14166 To color the frame different than the rest of the box, the command
14173 \begin_inset Index idx
14176 \begin_layout Plain Layout
14184 is used in the following scheme:
14187 \begin_layout Standard
14192 fcolorbox{frame color}{color}{box content}
14195 \begin_layout Standard
14202 is an extension of the command
14209 The frame width is set, like for
14232 \begin_layout Plain Layout
14244 \begin_inset Formula
14246 \fcolorbox{cyan}{magenta}{A=B}
14255 \begin_layout Plain Layout
14269 \begin_layout Standard
14270 This formula was created with the command
14271 \begin_inset Newline newline
14279 \begin_inset Formula $\to$
14285 \begin_inset Formula $\to$
14295 \begin_layout Standard
14296 \begin_inset VSpace bigskip
14299 To use colors other than predefined ones, they must be defined first.
14302 \begin_layout Standard
14303 One can for example define the color
14304 \begin_inset Quotes eld
14312 \begin_inset Quotes erd
14315 with the \SpecialChar LaTeX
14319 \begin_layout Standard
14324 definecolor{darkgreen}{cmyk}{0.5,
14339 \begin_inset Index idx
14342 \begin_layout Plain Layout
14353 \begin_layout Standard
14358 is the color space denoting the colors
14375 The four comma separated numbers are the portion factors for the corresponding
14376 colors of the color space.
14377 The factors can be in the range of 0
14378 \begin_inset space \thinspace{}
14382 \begin_inset space \thinspace{}
14394 can also be used for definitions.
14411 , so there are three portion factors for the corresponding colors.
14412 Furthermore there is the color space
14416 with one portion factor for the gray value.
14419 \begin_layout Standard
14420 As an example here is a framed box with the newly defined color
14424 where the characters have been colored
14429 \begin_inset Formula
14431 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14439 \begin_layout Standard
14440 Self-defined colors can also be used for text with the help of the command
14448 \begin_inset Index idx
14451 \begin_layout Plain Layout
14460 \begin_layout Standard
14464 \begin_layout Plain Layout
14468 textcolor{darkgreen}{
14474 \begin_inset Quotes eld
14478 \begin_inset Quotes erd
14485 \begin_layout Plain Layout
14495 \begin_layout Standard
14503 \begin_inset Index idx
14506 \begin_layout Plain Layout
14514 is used in the scheme
14518 textcolor{color}{characters to color}
14523 \begin_layout Subsection
14525 \begin_inset CommandInset label
14527 name "subsec:Paragraph-Boxes"
14532 \begin_inset Index idx
14535 \begin_layout Plain Layout
14536 Boxes ! as paragraph
14544 \begin_layout Standard
14545 A box that can contain several lines and paragraphs, a so-called paragraph
14546 box (parbox), can be created with the menu
14548 Insert\SpecialChar menuseparator
14551 or the toolbar button
14560 \begin_layout Standard
14561 The following example shows a framed parbox in a line:
14564 \begin_layout Standard
14565 \begin_inset VSpace medskip
14569 \begin_inset Box Boxed
14579 height_special "totalheight"
14584 backgroundcolor "none"
14587 \begin_layout Plain Layout
14588 This is a paragraph box.
14590 \begin_inset space \thinspace{}
14593 cm long and can also contain formulas:
14594 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14605 \begin_layout Standard
14606 \begin_inset VSpace medskip
14612 \begin_layout Standard
14613 Such a box is created by right-clicking on the gray box inset.
14614 A dialog pops up showing the box properties.
14628 \begin_inset space \thinspace{}
14633 Vertical Box Alignment
14638 \begin_layout Standard
14639 \begin_inset VSpace medskip
14642 In \SpecialChar LaTeX
14643 a parbox is created with the command
14650 \begin_inset Index idx
14653 \begin_layout Plain Layout
14661 which has the following scheme:
14664 \begin_layout Standard
14669 parbox[position]{width}{box content}
14672 \begin_layout Standard
14687 \begin_inset Quotes eld
14691 \begin_inset Quotes erd
14694 means that the box is aligned within the surrounding text with its last
14701 \begin_inset Quotes eld
14705 \begin_inset Quotes erd
14708 this is done with the first line.
14709 When no position is given, the box will be vertically centered, see section
14717 \begin_inset space ~
14722 manual for examples.
14725 \begin_layout Standard
14726 \begin_inset VSpace bigskip
14729 To frame formulas completely, including the formula number, the formula
14730 must be set into a parbox.
14731 To do this, the command
14745 is inserted in \SpecialChar TeX
14746 mode before the formula.
14754 \begin_inset Index idx
14757 \begin_layout Plain Layout
14765 is the line width set for the document.
14766 Because the frame is outside the parbox, two times the frame separation
14767 and the frame thickness must be subtracted from the line width.
14768 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14777 \begin_layout Plain Layout
14782 is part of every \SpecialChar LaTeX
14783 standard installation.
14789 \begin_inset Index idx
14792 \begin_layout Plain Layout
14798 must be loaded in the \SpecialChar LaTeX
14799 -preamble with the line
14802 \begin_layout Standard
14810 \begin_layout Standard
14811 Behind the formula both boxes are closed by entering
14815 in \SpecialChar TeX
14817 Here is an example:
14821 \begin_layout Plain Layout
14835 \begin_layout Standard
14839 \begin_layout Plain Layout
14857 \begin_inset Formula
14859 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14868 \begin_layout Plain Layout
14879 \begin_layout Plain Layout
14893 \begin_layout Standard
14894 \begin_inset VSpace medskip
14897 As a parbox is used as the argument of
14903 , there is in this case no difference between
14918 \begin_layout Standard
14919 \begin_inset VSpace bigskip
14922 Paragraph boxes are very useful to comment formulas directly.
14929 is used in combination with the command
14943 \begin_inset CommandInset ref
14945 reference "subsec:User-defined-Numbering"
14952 \begin_layout Standard
14953 An example of a formula commented with
14962 \begin_layout Standard
14966 \begin_layout Plain Layout
14979 This is a description.
14980 It is distinctly separated from the formula and multiline.
14984 \begin_layout Plain Layout
14996 \begin_layout Standard
14997 Such a formula must be inserted completely in \SpecialChar TeX
14998 mode because \SpecialChar LyX
15000 support the command
15007 The formula is created with the following command sequence:
15010 \begin_layout Standard
15023 is inserted in \SpecialChar TeX
15028 \begin_layout Plain Layout
15029 When the formula style
15041 can also be replaced by
15048 (formula styles see
15049 \begin_inset CommandInset ref
15051 reference "sec:Formula-Styles"
15060 Then the description follows as normal text and finally
15066 is inserted in \SpecialChar TeX
15080 create a displayed formula.
15083 \begin_layout Standard
15090 can be seen in this example that was
15091 \begin_inset Quotes eld
15095 \begin_inset Quotes erd
15098 using the mathematical textmode:
15099 \begin_inset Formula
15101 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
15109 \begin_layout Section
15111 \begin_inset Index idx
15114 \begin_layout Plain Layout
15123 \begin_layout Subsection
15125 \begin_inset CommandInset label
15127 name "subsec:Big-Operators"
15132 \begin_inset Index idx
15135 \begin_layout Plain Layout
15142 \begin_inset Index idx
15145 \begin_layout Plain Layout
15152 \begin_inset Index idx
15155 \begin_layout Plain Layout
15164 \begin_layout Standard
15165 To be able to use all of the integral operators listed here, the
15173 must be set in the document settings under
15176 \begin_inset space ~
15184 \begin_layout Standard
15185 \begin_inset space \hfill{}
15189 \begin_inset Tabular
15190 <lyxtabular version="3" rows="11" columns="2">
15191 <features booktabs="true" tabularvalignment="middle">
15192 <column alignment="center" valignment="top" width="0pt">
15193 <column alignment="center" valignment="top" width="0pt">
15195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15198 \begin_layout Plain Layout
15204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15207 \begin_layout Plain Layout
15215 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15218 \begin_layout Plain Layout
15222 \begin_inset Index idx
15225 \begin_layout Plain Layout
15238 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15241 \begin_layout Plain Layout
15242 \begin_inset Formula $\int$
15252 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15255 \begin_layout Plain Layout
15263 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15266 \begin_layout Plain Layout
15267 \begin_inset Formula $\oint$
15277 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15280 \begin_layout Plain Layout
15288 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15291 \begin_layout Plain Layout
15292 \begin_inset Formula $\ointctrclockwise$
15302 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15305 \begin_layout Plain Layout
15313 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15316 \begin_layout Plain Layout
15317 \begin_inset Formula $\ointclockwise$
15327 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15330 \begin_layout Plain Layout
15338 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15341 \begin_layout Plain Layout
15342 \begin_inset Formula $\sqint$
15352 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15355 \begin_layout Plain Layout
15363 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15366 \begin_layout Plain Layout
15368 \begin_inset Formula $\fint$
15378 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15381 \begin_layout Plain Layout
15389 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15392 \begin_layout Plain Layout
15394 \begin_inset Formula $\landupint$
15404 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15407 \begin_layout Plain Layout
15415 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15418 \begin_layout Plain Layout
15420 \begin_inset Formula $\landdownint$
15430 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15433 \begin_layout Plain Layout
15441 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15444 \begin_layout Plain Layout
15445 \begin_inset Formula $\bigcap$
15455 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15458 \begin_layout Plain Layout
15466 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15469 \begin_layout Plain Layout
15470 \begin_inset Formula $\bigcup$
15484 \begin_inset space \hfill{}
15488 \begin_inset Tabular
15489 <lyxtabular version="3" rows="11" columns="2">
15490 <features booktabs="true" tabularvalignment="middle">
15491 <column alignment="center" valignment="top" width="0pt">
15492 <column alignment="center" valignment="top" width="0pt">
15494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15497 \begin_layout Plain Layout
15503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15506 \begin_layout Plain Layout
15514 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15517 \begin_layout Plain Layout
15521 \begin_inset Index idx
15524 \begin_layout Plain Layout
15537 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15540 \begin_layout Plain Layout
15541 \begin_inset Formula $\sum$
15551 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15554 \begin_layout Plain Layout
15558 \begin_inset Index idx
15561 \begin_layout Plain Layout
15568 \begin_layout Plain Layout
15587 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15590 \begin_layout Plain Layout
15591 \begin_inset Formula $\prod$
15601 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15604 \begin_layout Plain Layout
15612 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15615 \begin_layout Plain Layout
15616 \begin_inset Formula $\coprod$
15626 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15629 \begin_layout Plain Layout
15637 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15640 \begin_layout Plain Layout
15641 \begin_inset Formula $\bigodot$
15651 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15654 \begin_layout Plain Layout
15662 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15665 \begin_layout Plain Layout
15666 \begin_inset Formula $\bigotimes$
15676 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15679 \begin_layout Plain Layout
15687 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15690 \begin_layout Plain Layout
15691 \begin_inset Formula $\bigoplus$
15701 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15704 \begin_layout Plain Layout
15712 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15715 \begin_layout Plain Layout
15716 \begin_inset Formula $\bigwedge$
15726 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15729 \begin_layout Plain Layout
15737 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15740 \begin_layout Plain Layout
15741 \begin_inset Formula $\bigvee$
15751 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15754 \begin_layout Plain Layout
15762 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15765 \begin_layout Plain Layout
15766 \begin_inset Formula $\bigsqcup$
15776 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15779 \begin_layout Plain Layout
15787 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15790 \begin_layout Plain Layout
15791 \begin_inset Formula $\biguplus$
15805 \begin_inset space \hfill{}
15811 \begin_layout Standard
15812 All big operators can also be inserted via the math toolbar button
15815 arg "math-insert \\intop"
15821 \begin_layout Standard
15822 The operators are called big because they are bigger than the sometimes
15823 equal looking binary operators.
15824 All big operators can have limits as described in the next subsection.
15827 \begin_layout Standard
15828 For all integral operators there is a second version available, ending in
15846 These operators differ in the style the operator limits are displayed,
15848 \begin_inset CommandInset ref
15850 reference "subsec:Operator-Limits"
15857 \begin_layout Subsubsection*
15858 Advice for Integrals
15861 \begin_layout Standard
15866 in an integral is an operator that has to be set upright.
15867 This is done by highlighting the
15871 and using the keyboard shortcut
15881 \begin_layout Plain Layout
15887 \begin_inset CommandInset ref
15889 reference "subsec:Font-Styles"
15899 Also the smallest space is inserted before the
15903 , as this is usual for operators.
15907 \begin_layout Standard
15909 \begin_inset Formula $\int A(x)dx$
15913 \begin_inset Newline newline
15917 \begin_inset Phantom HPhantom
15920 \begin_layout Plain Layout
15927 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15933 \begin_layout Standard
15934 The following commands exist for multiple integrals:
15935 \begin_inset VSpace medskip
15941 \begin_layout Standard
15942 \begin_inset space \hfill{}
15946 \begin_inset Tabular
15947 <lyxtabular version="3" rows="4" columns="2">
15948 <features booktabs="true" tabularvalignment="middle">
15949 <column alignment="center" valignment="top" width="0pt">
15950 <column alignment="center" valignment="top" width="0pt">
15952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15955 \begin_layout Plain Layout
15961 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15964 \begin_layout Plain Layout
15971 <row bottomspace="1mm">
15972 <cell alignment="center" valignment="top" usebox="none">
15975 \begin_layout Plain Layout
15983 <cell alignment="center" valignment="top" usebox="none">
15986 \begin_layout Plain Layout
15987 \begin_inset Formula $\iint$
15996 <row bottomspace="1mm">
15997 <cell alignment="center" valignment="top" usebox="none">
16000 \begin_layout Plain Layout
16008 <cell alignment="center" valignment="top" usebox="none">
16011 \begin_layout Plain Layout
16012 \begin_inset Formula $\oiint$
16021 <row bottomspace="1mm">
16022 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16025 \begin_layout Plain Layout
16033 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16036 \begin_layout Plain Layout
16037 \begin_inset Formula $\sqiint$
16051 \begin_inset space \hfill{}
16055 \begin_inset Tabular
16056 <lyxtabular version="3" rows="4" columns="2">
16057 <features booktabs="true" tabularvalignment="middle">
16058 <column alignment="center" valignment="top" width="0pt">
16059 <column alignment="center" valignment="top" width="0pt">
16061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16064 \begin_layout Plain Layout
16070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16073 \begin_layout Plain Layout
16080 <row bottomspace="1mm">
16081 <cell alignment="center" valignment="top" usebox="none">
16084 \begin_layout Plain Layout
16092 <cell alignment="center" valignment="top" usebox="none">
16095 \begin_layout Plain Layout
16096 \begin_inset Formula $\iiint$
16105 <row bottomspace="1mm">
16106 <cell alignment="center" valignment="top" usebox="none">
16109 \begin_layout Plain Layout
16117 <cell alignment="center" valignment="top" usebox="none">
16120 \begin_layout Plain Layout
16121 \begin_inset Formula $\iiiint$
16130 <row bottomspace="1mm">
16131 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16134 \begin_layout Plain Layout
16142 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16145 \begin_layout Plain Layout
16146 \begin_inset Formula $\dotsint$
16160 \begin_inset space \hfill{}
16166 \begin_layout Subsection
16168 \begin_inset CommandInset label
16170 name "subsec:Operator-Limits"
16175 \begin_inset Index idx
16178 \begin_layout Plain Layout
16187 \begin_layout Standard
16188 Limits are created by super- and subscripts:
16191 \begin_layout Standard
16193 \begin_inset Tabular
16194 <lyxtabular version="3" rows="2" columns="2">
16195 <features booktabs="true" tabularvalignment="middle">
16196 <column alignment="center" valignment="top" width="0pt">
16197 <column alignment="center" valignment="top" width="0pt">
16199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16202 \begin_layout Plain Layout
16208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16211 \begin_layout Plain Layout
16219 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16222 \begin_layout Plain Layout
16228 \begin_inset space \textvisiblespace{}
16232 \begin_inset Formula $\to$
16236 \begin_inset Formula $\to$
16244 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16247 \begin_layout Plain Layout
16248 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
16264 \begin_layout Standard
16265 Limits of inline formulas are set on the right side of the operator.
16266 Limits in displayed formulas are set above or below the operator, except
16267 for integral limits.
16270 \begin_layout Standard
16271 To force the limits to be set beside the operator, the cursor is placed
16272 directly behind the operator and the limits type is changed with the menu
16275 Edit\SpecialChar menuseparator
16276 Math\SpecialChar menuseparator
16295 \begin_layout Standard
16296 The default displayed formulas limits type is this:
16297 \begin_inset Formula
16299 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16304 This is how it looks when the limits type is changed to
16311 \begin_inset Formula
16313 \sum\nolimits_{x=0}^{\infty}\frac{1}{x^{2}}
16318 For integrals, except those ending with
16334 etc., the limits by default are set beside the operator.
16335 But for multiple integrals the limits are often set below the operator.
16336 In the following example the limits type was set to
16340 and so set below the integrals:
16341 \begin_inset Formula
16343 \iiint\limits_{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16349 \change_deleted 5863208 1612725771
16351 \begin_inset Note Note
16354 \begin_layout Plain Layout
16356 \change_inserted 232239728 1611193306
16357 This integral did not have its limits set to Display in the original document
16369 \begin_layout Standard
16370 \begin_inset VSpace medskip
16373 To specify conditions for limits, the commands
16380 \begin_inset Index idx
16383 \begin_layout Plain Layout
16398 \begin_inset Index idx
16401 \begin_layout Plain Layout
16410 To create this expression
16411 \begin_inset Formula
16413 \sum_{\begin{subarray}{c}
16417 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16425 \begin_layout Standard
16426 the following must be done:
16427 \begin_inset Newline newline
16439 \begin_inset space \textvisiblespace{}
16445 The cursor is now in a blue box under the summation operator.
16451 \begin_inset space \textvisiblespace{}
16457 The blue box is now within a purple box and now multiple limit lines can
16459 A new line is created by inserting a line break (
16462 arg "newline-insert newline"
16467 \begin_inset Newline newline
16472 0<k<1000 Ctrl+Return
16473 \begin_inset Newline newline
16478 is typed in, a new box appears below for the new limit line.
16481 \begin_layout Standard
16482 The alignment of the lines can be changed to left aligned with the
16492 Edit\SpecialChar menuseparator
16496 To get right alignment,
16501 \begin_inset space \textvisiblespace{}
16506 is inserted at the beginning of the line.
16509 \begin_layout Standard
16522 with the difference that the lines are always centered.
16525 \begin_layout Standard
16526 \begin_inset VSpace bigskip
16530 \begin_inset CommandInset ref
16532 reference "eq:substack"
16536 there can be too much space beside an operator.
16537 This occurs because the characters following the operator are set beside
16539 To avoid this the command
16546 \begin_inset Index idx
16549 \begin_layout Plain Layout
16558 To use it, set the package
16563 \begin_inset Index idx
16566 \begin_layout Plain Layout
16567 Packages ! mathtools
16572 in the document settings under
16575 \begin_inset space ~
16583 \begin_inset space ~
16595 sets the space besides the operator to 0
16596 \begin_inset space \thinspace{}
16600 \begin_inset Newline newline
16604 \begin_inset CommandInset ref
16606 reference "eq:substack"
16610 , one uses the command
16613 \begin_layout Standard
16621 \begin_layout Standard
16622 and inserts the operator with its limits into the braces.
16623 Behind the brace one continues the formula:
16624 \begin_inset Formula
16626 \smashoperator{\sum_{\begin{subarray}{c}
16630 \end{subarray}}^{n}}k^{-2}
16638 \begin_layout Standard
16639 It is possible to set the space of only one side of the operator to 0
16640 \begin_inset space \thinspace{}
16644 To do this write either
16663 stands for the left and
16667 for the right side of the operator.
16668 Here is an example of the possible
16677 \begin_layout Standard
16678 \begin_inset Formula
16680 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}
16688 \begin_layout Standard
16689 \begin_inset VSpace bigskip
16695 \begin_layout Standard
16696 When several consecutive operators have limits the typesetting of the limits
16697 looks often imperfect in the output, for example:
16698 \begin_inset Formula
16700 \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}
16705 To improve the typesetting, in the document settings under
16708 \begin_inset space ~
16718 \begin_inset Index idx
16721 \begin_layout Plain Layout
16722 Packages ! mathtools
16727 , set the option to
16730 \begin_inset space ~
16736 Then insert the command
16743 \begin_inset Index idx
16746 \begin_layout Plain Layout
16754 directly before the first operator.
16755 The example will then look like this:
16756 \begin_inset Formula
16758 \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}
16766 \begin_layout Standard
16767 \begin_inset VSpace bigskip
16770 How to use one limit for several operators is described in
16771 \begin_inset CommandInset ref
16773 reference "subsec:Self-defined-Operators"
16780 \begin_layout Subsection
16781 Decoration for Operators
16782 \begin_inset Index idx
16785 \begin_layout Plain Layout
16786 Operators ! Decoration
16794 \begin_layout Standard
16802 \begin_inset Index idx
16805 \begin_layout Plain Layout
16820 \begin_inset Index idx
16823 \begin_layout Plain Layout
16831 characters can be placed above or below an operator respectively.
16839 \begin_inset Index idx
16842 \begin_layout Plain Layout
16850 characters can be set before and behind a big operator.
16853 \begin_layout Standard
16855 \begin_inset space ~
16867 \begin_layout Itemize
16874 is used to set characters at the corners of the operator
16877 \begin_layout Itemize
16884 is used to set characters before and/or behind the operator (this variant
16885 represents \SpecialChar LaTeX
16895 \begin_layout Itemize
16902 is used to set characters at the left corners and/or behind the operator
16905 \begin_layout Itemize
16912 is used to set characters at the right corners and/or before the operator
16915 \begin_layout Standard
16916 For example the command
16921 \begin_inset space \textvisiblespace{}
16927 \begin_inset space \textvisiblespace{}
16931 \begin_inset Formula $\to$
16935 \begin_inset Formula $\to$
16939 \begin_inset space \textvisiblespace{}
16949 \begin_inset Formula
16951 \sideset{}{'}\sum_{k=1}^{n}
16959 \begin_layout Standard
16960 \begin_inset Note Greyedout
16963 \begin_layout Plain Layout
16970 can only be used to decorate big operators, binary operators are not allowed.
16978 \begin_layout Standard
16991 can also be used to decorate symbols and characters.
16992 For example, the command
16997 \begin_inset space \textvisiblespace{}
17003 \begin_inset space \textvisiblespace{}
17009 \begin_inset Formula $\uparrow$
17017 \begin_inset Formula
17019 \overset{a}{\maltese}
17027 \begin_layout Subsection
17029 \begin_inset CommandInset label
17031 name "subsec:Binary-Operators"
17036 \begin_inset Index idx
17039 \begin_layout Plain Layout
17048 \begin_layout Standard
17049 Binary operators are surrounded by space when there is a character before
17051 \begin_inset VSpace medskip
17057 \begin_layout Standard
17058 \begin_inset Tabular
17059 <lyxtabular version="3" rows="13" columns="2">
17060 <features booktabs="true" tabularvalignment="middle">
17061 <column alignment="center" valignment="top" width="0pt">
17062 <column alignment="center" valignment="top" width="0pt">
17064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17067 \begin_layout Plain Layout
17069 \begin_inset Note Note
17072 \begin_layout Plain Layout
17079 is only used as spacer.
17089 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17092 \begin_layout Plain Layout
17100 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17103 \begin_layout Plain Layout
17109 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17112 \begin_layout Plain Layout
17113 \begin_inset Formula $+$
17123 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17126 \begin_layout Plain Layout
17132 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17135 \begin_layout Plain Layout
17136 \begin_inset Formula $-$
17146 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17149 \begin_layout Plain Layout
17157 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17160 \begin_layout Plain Layout
17161 \begin_inset Formula $\pm$
17171 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17174 \begin_layout Plain Layout
17182 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17185 \begin_layout Plain Layout
17186 \begin_inset Formula $\mp$
17196 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17199 \begin_layout Plain Layout
17207 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17210 \begin_layout Plain Layout
17211 \begin_inset Formula $\cdot$
17221 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17224 \begin_layout Plain Layout
17232 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17235 \begin_layout Plain Layout
17236 \begin_inset Formula $\times$
17246 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17249 \begin_layout Plain Layout
17257 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17260 \begin_layout Plain Layout
17261 \begin_inset Formula $\div$
17271 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17274 \begin_layout Plain Layout
17278 \begin_layout Plain Layout
17291 \begin_layout Plain Layout
17303 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17306 \begin_layout Plain Layout
17307 \begin_inset Formula $*$
17317 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17320 \begin_layout Plain Layout
17328 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17331 \begin_layout Plain Layout
17332 \begin_inset Formula $\star$
17342 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17345 \begin_layout Plain Layout
17353 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17356 \begin_layout Plain Layout
17357 \begin_inset Formula $\circ$
17367 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17370 \begin_layout Plain Layout
17378 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17381 \begin_layout Plain Layout
17382 \begin_inset Formula $\diamond$
17392 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17395 \begin_layout Plain Layout
17403 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17406 \begin_layout Plain Layout
17407 \begin_inset Formula $\bullet$
17421 \begin_inset space \hfill{}
17425 \begin_inset Tabular
17426 <lyxtabular version="3" rows="13" columns="2">
17427 <features booktabs="true" tabularvalignment="middle">
17428 <column alignment="center" valignment="top" width="0pt">
17429 <column alignment="center" valignment="top" width="0pt">
17431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17434 \begin_layout Plain Layout
17440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17443 \begin_layout Plain Layout
17451 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17454 \begin_layout Plain Layout
17462 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17465 \begin_layout Plain Layout
17466 \begin_inset Formula $\nabla$
17476 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17479 \begin_layout Plain Layout
17487 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17490 \begin_layout Plain Layout
17491 \begin_inset Formula $\bigtriangledown$
17501 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17504 \begin_layout Plain Layout
17512 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17515 \begin_layout Plain Layout
17516 \begin_inset Formula $\bigtriangleup$
17526 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17529 \begin_layout Plain Layout
17537 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17540 \begin_layout Plain Layout
17541 \begin_inset Formula $\Box$
17551 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17554 \begin_layout Plain Layout
17562 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17565 \begin_layout Plain Layout
17566 \begin_inset Formula $\cap$
17576 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17579 \begin_layout Plain Layout
17587 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17590 \begin_layout Plain Layout
17591 \begin_inset Formula $\cup$
17601 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17604 \begin_layout Plain Layout
17612 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17615 \begin_layout Plain Layout
17616 \begin_inset Formula $\dagger$
17626 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17629 \begin_layout Plain Layout
17637 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17640 \begin_layout Plain Layout
17641 \begin_inset Formula $\ddagger$
17651 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17654 \begin_layout Plain Layout
17662 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17665 \begin_layout Plain Layout
17666 \begin_inset Formula $\wr$
17676 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17679 \begin_layout Plain Layout
17687 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17690 \begin_layout Plain Layout
17691 \begin_inset Formula $\bigcirc$
17701 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17704 \begin_layout Plain Layout
17712 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17715 \begin_layout Plain Layout
17716 \begin_inset Formula $\wedge$
17726 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17729 \begin_layout Plain Layout
17737 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17740 \begin_layout Plain Layout
17741 \begin_inset Formula $\vee$
17755 \begin_inset space \hfill{}
17759 \begin_inset Tabular
17760 <lyxtabular version="3" rows="13" columns="2">
17761 <features booktabs="true" tabularvalignment="middle">
17762 <column alignment="center" valignment="top" width="0pt">
17763 <column alignment="center" valignment="top" width="0pt">
17765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17768 \begin_layout Plain Layout
17774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17777 \begin_layout Plain Layout
17785 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17788 \begin_layout Plain Layout
17796 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17799 \begin_layout Plain Layout
17800 \begin_inset Formula $\oplus$
17810 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17813 \begin_layout Plain Layout
17821 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17824 \begin_layout Plain Layout
17825 \begin_inset Formula $\ominus$
17835 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17838 \begin_layout Plain Layout
17846 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17849 \begin_layout Plain Layout
17850 \begin_inset Formula $\otimes$
17860 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17863 \begin_layout Plain Layout
17871 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17874 \begin_layout Plain Layout
17875 \begin_inset Formula $\oslash$
17885 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17888 \begin_layout Plain Layout
17896 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17899 \begin_layout Plain Layout
17900 \begin_inset Formula $\odot$
17910 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17913 \begin_layout Plain Layout
17921 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17924 \begin_layout Plain Layout
17925 \begin_inset Formula $\amalg$
17935 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17938 \begin_layout Plain Layout
17946 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17949 \begin_layout Plain Layout
17950 \begin_inset Formula $\uplus$
17960 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17963 \begin_layout Plain Layout
17971 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17974 \begin_layout Plain Layout
17975 \begin_inset Formula $\setminus$
17985 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17988 \begin_layout Plain Layout
17996 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17999 \begin_layout Plain Layout
18000 \begin_inset Formula $\sqcap$
18010 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18013 \begin_layout Plain Layout
18021 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18024 \begin_layout Plain Layout
18025 \begin_inset Formula $\sqcup$
18035 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18038 \begin_layout Plain Layout
18046 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18049 \begin_layout Plain Layout
18050 \begin_inset Formula $\triangleleft$
18060 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18063 \begin_layout Plain Layout
18071 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18074 \begin_layout Plain Layout
18075 \begin_inset Formula $\triangleright$
18091 \begin_layout Standard
18092 All binary operators can also be inserted via the math toolbar button
18095 arg "math-insert \\pm"
18101 \begin_layout Standard
18102 To typeset the Laplace operator,
18119 \begin_inset Formula $\nabla^{2}$
18122 ) can also be used instead of
18131 \begin_layout Standard
18138 Insert\SpecialChar menuseparator
18150 \begin_layout Subsection
18151 Self-defined Operators
18152 \begin_inset CommandInset label
18154 name "subsec:Self-defined-Operators"
18159 \begin_inset Index idx
18162 \begin_layout Plain Layout
18163 Operators ! self-defined
18171 \begin_layout Standard
18172 With the help of the command
18176 DeclareMathOperator
18179 \begin_inset Index idx
18182 \begin_layout Plain Layout
18187 DeclareMathOperator
18192 , custom operators can be defined in the \SpecialChar LaTeX
18194 Its command scheme is:
18197 \begin_layout Standard
18202 DeclareMathOperator{new command}{display}
18205 \begin_layout Standard
18206 Display can be characters or symbols that define how the operator looks
18208 To define a big operator a * is set behind the command.
18209 All self-defined big operators can have limits as described in
18210 \begin_inset CommandInset ref
18212 reference "subsec:Operator-Limits"
18219 \begin_layout Standard
18220 For example the \SpecialChar LaTeX
18224 \begin_layout Standard
18229 DeclareMathOperator*{
18236 \begin_layout Standard
18237 defines the command
18243 , that inserts a big operator consisting of the black lozenge symbol from
18245 \begin_inset CommandInset ref
18247 reference "subsec:Miscellaneous-Symbols"
18252 \begin_inset Formula
18254 \Lozenge_{n=1}^{\infty}
18259 The command for this formula is:
18270 \begin_inset Formula $\to$
18276 \begin_layout Standard
18277 \begin_inset VSpace bigskip
18280 When self-defined operators are not used several times in the document,
18281 they can also be defined with the commands
18288 \begin_inset Index idx
18291 \begin_layout Plain Layout
18306 \begin_inset Index idx
18309 \begin_layout Plain Layout
18317 , which have the following scheme:
18320 \begin_layout Standard
18334 \begin_layout Standard
18341 defines big operators,
18350 \begin_layout Standard
18357 can be used to use one limit for several operators:
18360 \begin_layout Standard
18361 \begin_inset Formula
18363 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18371 \begin_layout Standard
18372 The command for the formula above is:
18373 \begin_inset Newline newline
18389 \begin_inset space \textvisiblespace{}
18395 \begin_inset Formula $\to$
18401 \begin_inset space \textvisiblespace{}
18409 \begin_layout Section
18411 \begin_inset Index idx
18414 \begin_layout Plain Layout
18423 \begin_layout Subsection
18425 \begin_inset CommandInset label
18427 name "subsec:Font-Styles"
18432 \begin_inset Index idx
18435 \begin_layout Plain Layout
18444 \begin_layout Standard
18445 Latin letters in formulas can be set in one of the following font styles:
18448 \begin_layout Standard
18450 \begin_inset Tabular
18451 <lyxtabular version="3" rows="6" columns="3">
18452 <features booktabs="true" tabularvalignment="middle">
18453 <column alignment="center" valignment="top" width="0pt">
18454 <column alignment="center" valignment="top">
18455 <column alignment="center" valignment="top">
18457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18460 \begin_layout Plain Layout
18466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18469 \begin_layout Plain Layout
18475 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18478 \begin_layout Plain Layout
18486 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18489 \begin_layout Plain Layout
18495 \begin_inset space \textvisiblespace{}
18505 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18508 \begin_layout Plain Layout
18509 \begin_inset Formula $\mathbb{ABC}$
18517 <cell alignment="center" valignment="top" usebox="none">
18520 \begin_layout Plain Layout
18528 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18531 \begin_layout Plain Layout
18537 \begin_inset space \textvisiblespace{}
18547 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18550 \begin_layout Plain Layout
18551 \begin_inset Formula $\mathbf{AbC}$
18559 <cell alignment="center" valignment="top" usebox="none">
18562 \begin_layout Plain Layout
18575 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18578 \begin_layout Plain Layout
18584 \begin_inset space \textvisiblespace{}
18594 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18597 \begin_layout Plain Layout
18598 \begin_inset Formula $\boldsymbol{AbC}$
18606 <cell alignment="center" valignment="top" usebox="none">
18609 \begin_layout Plain Layout
18612 arg "font-boldsymbol"
18622 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18625 \begin_layout Plain Layout
18631 \begin_inset space \textvisiblespace{}
18641 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18644 \begin_layout Plain Layout
18645 \begin_inset Formula $\mathcal{ABC}$
18653 <cell alignment="center" valignment="top" usebox="none">
18656 \begin_layout Plain Layout
18664 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18667 \begin_layout Plain Layout
18673 \begin_inset space \textvisiblespace{}
18683 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18686 \begin_layout Plain Layout
18687 \begin_inset Formula $\mathfrak{AbC}$
18695 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18698 \begin_layout Plain Layout
18712 \begin_layout Standard
18714 \begin_inset Tabular
18715 <lyxtabular version="3" rows="6" columns="3">
18716 <features booktabs="true" tabularvalignment="middle">
18717 <column alignment="center" valignment="top" width="0pt">
18718 <column alignment="center" valignment="top">
18719 <column alignment="center" valignment="top">
18721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18724 \begin_layout Plain Layout
18730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18733 \begin_layout Plain Layout
18739 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18742 \begin_layout Plain Layout
18750 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18753 \begin_layout Plain Layout
18759 \begin_inset space \textvisiblespace{}
18769 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18772 \begin_layout Plain Layout
18773 \begin_inset Formula $\mathit{AbC}$
18781 <cell alignment="center" valignment="top" usebox="none">
18784 \begin_layout Plain Layout
18792 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18795 \begin_layout Plain Layout
18801 \begin_inset space \textvisiblespace{}
18811 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18814 \begin_layout Plain Layout
18815 \begin_inset Formula $\mathrm{AbC}$
18823 <cell alignment="center" valignment="top" usebox="none">
18826 \begin_layout Plain Layout
18839 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18842 \begin_layout Plain Layout
18848 \begin_inset space \textvisiblespace{}
18858 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18861 \begin_layout Plain Layout
18862 \begin_inset Formula $\mathsf{AbC}$
18870 <cell alignment="center" valignment="top" usebox="none">
18873 \begin_layout Plain Layout
18886 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18889 \begin_layout Plain Layout
18895 \begin_inset space \textvisiblespace{}
18905 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18908 \begin_layout Plain Layout
18909 \begin_inset Formula $\mathtt{AbC}$
18917 <cell alignment="center" valignment="top" usebox="none">
18920 \begin_layout Plain Layout
18923 arg "font-typewriter"
18933 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18936 \begin_layout Plain Layout
18942 \begin_inset space \textvisiblespace{}
18952 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18955 \begin_layout Plain Layout
18956 \begin_inset Formula $\mathscr{ABC}$
18964 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18967 \begin_layout Plain Layout
18981 \begin_layout Standard
18982 \begin_inset Note Greyedout
18985 \begin_layout Plain Layout
19008 can only be used for big letters.
19016 \begin_layout Standard
19026 \begin_layout Standard
19027 The style commands also work for letters in mathematical constructs:
19028 \begin_inset Formula
19030 \mathfrak{A=\frac{b}{C}}
19038 \begin_layout Standard
19039 Characters in mathematical text don't appear in a math font style but in
19040 the text font style
19047 Note that their style can't be set correctly via the text style dialog.
19048 This is a known bug in \SpecialChar LyX
19053 \begin_layout Plain Layout
19054 \begin_inset CommandInset href
19056 name "LyX-bug #4629"
19057 target "https://www.lyx.org/trac/ticket/4629"
19070 \begin_layout Standard
19071 Instead of the style commands,
19073 Edit\SpecialChar menuseparator
19074 Math\SpecialChar menuseparator
19077 dialog, or the toolbar button,
19080 arg "math-insert \\font"
19086 \begin_layout Subsection
19088 \begin_inset CommandInset label
19090 name "subsec:Bold-Formulas"
19095 \begin_inset Index idx
19098 \begin_layout Plain Layout
19107 \begin_layout Standard
19108 To make a complete formula bold, the command
19114 from the previous subsection cannot be used because it doesn't work for
19115 small Greek letters.
19116 Additionally it always prints Latin letters upright, as in the following
19120 \begin_layout Standard
19121 \begin_inset Formula
19123 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
19131 \begin_layout Standard
19132 To display the formula correctly, the command
19139 \begin_inset Formula
19141 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
19146 It is also possible to set the formula in a
19148 boldmath environment
19151 This environment is created by inserting the command
19158 \begin_inset Index idx
19161 \begin_layout Plain Layout
19169 in \SpecialChar TeX
19171 To end the environment, the command
19178 \begin_inset Index idx
19181 \begin_layout Plain Layout
19189 is inserted in \SpecialChar TeX
19194 \begin_layout Plain Layout
19204 \begin_inset Formula
19206 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
19215 \begin_layout Plain Layout
19227 \begin_layout Subsection
19229 \begin_inset Index idx
19232 \begin_layout Plain Layout
19241 \begin_layout Standard
19242 Formulas can be colored like normal text: Highlight a formula or a formula
19248 Here is a formula in magenta:
19249 \begin_inset Formula
19251 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19259 \begin_layout Standard
19260 You can also define your own colors as described in
19261 \begin_inset CommandInset ref
19263 reference "subsec:Colored-Boxes"
19268 They can be used with the \SpecialChar TeX
19276 \begin_inset Index idx
19279 \begin_layout Plain Layout
19290 \begin_layout Standard
19295 textcolor{color}{characters or formula}
19298 \begin_layout Standard
19299 The following example was colored completely dark green and partly red:
19302 \begin_layout Standard
19306 \begin_layout Plain Layout
19310 textcolor{darkgreen}{
19316 \begin_inset Formula
19318 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19327 \begin_layout Plain Layout
19337 \begin_layout Standard
19338 Due to a bug in \SpecialChar LyX
19339 only complete formulas can be colored with self-defined
19344 \begin_layout Plain Layout
19345 \begin_inset CommandInset href
19347 name "LyX-bug #5269"
19348 target "https://www.lyx.org/trac/ticket/5269"
19361 \begin_layout Subsection
19363 \begin_inset CommandInset label
19365 name "subsec:Font-Sizes"
19370 \begin_inset Index idx
19373 \begin_layout Plain Layout
19382 \begin_layout Standard
19383 As with characters in text, the following size commands are available for
19384 formula characters:
19387 \begin_layout Standard
19431 \begin_inset Newline newline
19453 \begin_layout Standard
19454 The font size produced by the commands depends on the document's original
19455 font size, which corresponds to the command
19462 The other commands produce character sizes smaller or larger than
19469 There are however limits to how small or large the font size can be changed.
19470 If for example the document font size is 12
19471 \begin_inset space \thinspace{}
19480 switches to the same size as
19489 \begin_layout Standard
19490 A size command is inserted in \SpecialChar TeX
19491 mode before a formula and sets the size for
19492 all of the following formulas and text characters.
19493 To switch back to the initial size, the command
19499 is inserted behind the formula, again in \SpecialChar TeX
19503 \begin_layout Standard
19504 Size can also be changed within a formula using the following size commands
19505 or the toolbar button
19508 arg "math-insert \\style"
19514 \begin_layout Standard
19517 \begin_inset Tabular
19518 <lyxtabular version="3" rows="5" columns="2">
19519 <features booktabs="true" tabularvalignment="middle">
19520 <column alignment="center" valignment="top" width="0pt">
19521 <column alignment="center" valignment="top">
19523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19526 \begin_layout Plain Layout
19532 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19535 \begin_layout Plain Layout
19543 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19546 \begin_layout Plain Layout
19550 \begin_inset Index idx
19553 \begin_layout Plain Layout
19566 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19569 \begin_layout Plain Layout
19570 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19579 <row topspace="1mm">
19580 <cell alignment="center" valignment="top" usebox="none">
19583 \begin_layout Plain Layout
19591 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19594 \begin_layout Plain Layout
19595 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19605 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19608 \begin_layout Plain Layout
19616 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19619 \begin_layout Plain Layout
19620 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19630 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19633 \begin_layout Plain Layout
19641 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19644 \begin_layout Plain Layout
19645 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19661 \begin_layout Standard
19662 After entering these commands, a blue box appears in which the formula parts
19666 \begin_layout Standard
19667 There is another method for changing the font size, although it only works
19668 for symbols or letters in mathematical text.
19669 To use it, one of the above text size commands is inserted into mathematical
19671 All characters until the end of the mathematical text or until another
19672 size command will have the selected size.
19674 \begin_inset VSpace -2mm
19680 \begin_layout Standard
19684 \begin_layout Plain Layout
19694 \begin_inset Formula
19696 A=\frac{B}{c}\cdot\maltese
19702 \begin_inset Formula
19704 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19713 \begin_layout Plain Layout
19723 \begin_inset VSpace medskip
19726 Before the first formula the command
19733 The command for the second formula is:
19734 \begin_inset Newline newline
19742 \begin_inset space \textvisiblespace{}
19748 \begin_inset space \textvisiblespace{}
19754 \begin_inset space \textvisiblespace{}
19760 \begin_inset space \textvisiblespace{}
19764 \begin_inset Formula $\to$
19768 \begin_inset Formula $\to$
19772 \begin_inset Newline newline
19776 \begin_inset space \hspace*{}
19787 \begin_inset space \textvisiblespace{}
19793 \begin_inset space \textvisiblespace{}
19799 \begin_inset space \textvisiblespace{}
19805 \begin_layout Standard
19806 If a symbol cannot be displayed in different sizes, it will always be displayed
19807 in the default size.
19810 \begin_layout Section
19812 \begin_inset Index idx
19815 \begin_layout Plain Layout
19824 \begin_layout Standard
19825 Greek letters can be inserted via the toolbar button
19828 arg "math-insert \\alpha"
19831 as well as by command.
19832 All international typesetting norms purport that Greek letters in math
19833 have to be typeset italic/slanted.
19834 In some languages, like French or Russian, they are nevertheless sometimes
19838 \begin_layout Subsection
19840 \begin_inset Index idx
19843 \begin_layout Plain Layout
19844 Greek letters ! small
19852 \begin_layout Standard
19853 \begin_inset space \hfill{}
19857 \begin_inset Tabular
19858 <lyxtabular version="3" rows="11" columns="2">
19859 <features booktabs="true" tabularvalignment="middle">
19860 <column alignment="center" valignment="top" width="0pt">
19861 <column alignment="center" valignment="top" width="0pt">
19863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19866 \begin_layout Plain Layout
19872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19875 \begin_layout Plain Layout
19883 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19886 \begin_layout Plain Layout
19894 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19897 \begin_layout Plain Layout
19898 \begin_inset Formula $\alpha$
19908 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19911 \begin_layout Plain Layout
19919 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19922 \begin_layout Plain Layout
19923 \begin_inset Formula $\beta$
19933 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19936 \begin_layout Plain Layout
19944 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19947 \begin_layout Plain Layout
19948 \begin_inset Formula $\gamma$
19958 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19961 \begin_layout Plain Layout
19969 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19972 \begin_layout Plain Layout
19973 \begin_inset Formula $\delta$
19983 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19986 \begin_layout Plain Layout
19994 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19997 \begin_layout Plain Layout
19998 \begin_inset Formula $\epsilon$
20008 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20011 \begin_layout Plain Layout
20019 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20022 \begin_layout Plain Layout
20023 \begin_inset Formula $\varepsilon$
20033 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20036 \begin_layout Plain Layout
20044 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20047 \begin_layout Plain Layout
20048 \begin_inset Formula $\zeta$
20058 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20061 \begin_layout Plain Layout
20069 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20072 \begin_layout Plain Layout
20073 \begin_inset Formula $\eta$
20083 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20086 \begin_layout Plain Layout
20094 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20097 \begin_layout Plain Layout
20098 \begin_inset Formula $\theta$
20108 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20111 \begin_layout Plain Layout
20119 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20122 \begin_layout Plain Layout
20123 \begin_inset Formula $\vartheta$
20137 \begin_inset space \hfill{}
20141 \begin_inset Tabular
20142 <lyxtabular version="3" rows="12" columns="2">
20143 <features booktabs="true" tabularvalignment="middle">
20144 <column alignment="center" valignment="top" width="0pt">
20145 <column alignment="center" valignment="top" width="0pt">
20147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20150 \begin_layout Plain Layout
20156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20159 \begin_layout Plain Layout
20167 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20170 \begin_layout Plain Layout
20178 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20181 \begin_layout Plain Layout
20182 \begin_inset Formula $\iota$
20192 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20195 \begin_layout Plain Layout
20203 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20206 \begin_layout Plain Layout
20207 \begin_inset Formula $\kappa$
20217 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20220 \begin_layout Plain Layout
20228 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20231 \begin_layout Plain Layout
20232 \begin_inset Formula $\varkappa$
20242 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20245 \begin_layout Plain Layout
20253 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20256 \begin_layout Plain Layout
20257 \begin_inset Formula $\lambda$
20267 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20270 \begin_layout Plain Layout
20278 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20281 \begin_layout Plain Layout
20282 \begin_inset Formula $\mu$
20292 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20295 \begin_layout Plain Layout
20303 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20306 \begin_layout Plain Layout
20307 \begin_inset Formula $\nu$
20317 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20320 \begin_layout Plain Layout
20328 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20331 \begin_layout Plain Layout
20332 \begin_inset Formula $\xi$
20342 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20345 \begin_layout Plain Layout
20351 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20354 \begin_layout Plain Layout
20355 \begin_inset Formula $o$
20365 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20368 \begin_layout Plain Layout
20376 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20379 \begin_layout Plain Layout
20380 \begin_inset Formula $\pi$
20390 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20393 \begin_layout Plain Layout
20401 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20404 \begin_layout Plain Layout
20405 \begin_inset Formula $\varpi$
20415 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20418 \begin_layout Plain Layout
20426 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20429 \begin_layout Plain Layout
20430 \begin_inset Formula $\rho$
20444 \begin_inset space \hfill{}
20448 \begin_inset Tabular
20449 <lyxtabular version="3" rows="11" columns="2">
20450 <features booktabs="true" tabularvalignment="middle">
20451 <column alignment="center" valignment="top" width="0pt">
20452 <column alignment="center" valignment="top" width="0pt">
20454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20457 \begin_layout Plain Layout
20463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20466 \begin_layout Plain Layout
20474 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20477 \begin_layout Plain Layout
20485 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20488 \begin_layout Plain Layout
20489 \begin_inset Formula $\varrho$
20499 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20502 \begin_layout Plain Layout
20510 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20513 \begin_layout Plain Layout
20514 \begin_inset Formula $\sigma$
20524 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20527 \begin_layout Plain Layout
20535 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20538 \begin_layout Plain Layout
20539 \begin_inset Formula $\varsigma$
20549 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20552 \begin_layout Plain Layout
20560 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20563 \begin_layout Plain Layout
20564 \begin_inset Formula $\tau$
20574 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20577 \begin_layout Plain Layout
20585 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20588 \begin_layout Plain Layout
20589 \begin_inset Formula $\upsilon$
20599 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20602 \begin_layout Plain Layout
20610 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20613 \begin_layout Plain Layout
20614 \begin_inset Formula $\phi$
20624 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20627 \begin_layout Plain Layout
20635 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20638 \begin_layout Plain Layout
20639 \begin_inset Formula $\varphi$
20649 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20652 \begin_layout Plain Layout
20660 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20663 \begin_layout Plain Layout
20664 \begin_inset Formula $\chi$
20674 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20677 \begin_layout Plain Layout
20685 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20688 \begin_layout Plain Layout
20689 \begin_inset Formula $\psi$
20699 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20702 \begin_layout Plain Layout
20710 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20713 \begin_layout Plain Layout
20714 \begin_inset Formula $\omega$
20728 \begin_inset space \hfill{}
20734 \begin_layout Standard
20735 \begin_inset VSpace medskip
20741 \begin_layout Standard
20742 Creating upright Greek letters is explained in
20743 \begin_inset CommandInset ref
20745 reference "subsec:Upright-small-Greek"
20752 \begin_layout Subsection
20754 \begin_inset Index idx
20757 \begin_layout Plain Layout
20758 Greek letters ! big
20766 \begin_layout Standard
20767 \begin_inset space \hfill{}
20771 \begin_inset Tabular
20772 <lyxtabular version="3" rows="7" columns="2">
20773 <features booktabs="true" tabularvalignment="middle">
20774 <column alignment="center" valignment="top" width="0pt">
20775 <column alignment="center" valignment="top" width="0pt">
20777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20780 \begin_layout Plain Layout
20786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20789 \begin_layout Plain Layout
20797 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20800 \begin_layout Plain Layout
20808 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20811 \begin_layout Plain Layout
20812 \begin_inset Formula $\Gamma$
20822 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20825 \begin_layout Plain Layout
20833 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20836 \begin_layout Plain Layout
20837 \begin_inset Formula $\Delta$
20847 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20850 \begin_layout Plain Layout
20858 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20861 \begin_layout Plain Layout
20862 \begin_inset Formula $\Theta$
20872 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20875 \begin_layout Plain Layout
20883 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20886 \begin_layout Plain Layout
20887 \begin_inset Formula $\Lambda$
20897 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20900 \begin_layout Plain Layout
20908 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20911 \begin_layout Plain Layout
20912 \begin_inset Formula $\Xi$
20922 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20925 \begin_layout Plain Layout
20933 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20936 \begin_layout Plain Layout
20937 \begin_inset Formula $\Pi$
20951 \begin_inset space \hfill{}
20955 \begin_inset Tabular
20956 <lyxtabular version="3" rows="6" columns="2">
20957 <features booktabs="true" tabularvalignment="middle">
20958 <column alignment="center" valignment="top" width="0pt">
20959 <column alignment="center" valignment="top" width="0pt">
20961 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20964 \begin_layout Plain Layout
20970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20973 \begin_layout Plain Layout
20981 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20984 \begin_layout Plain Layout
20992 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20995 \begin_layout Plain Layout
20996 \begin_inset Formula $\Sigma$
21006 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21009 \begin_layout Plain Layout
21017 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21020 \begin_layout Plain Layout
21021 \begin_inset Formula $\Upsilon$
21031 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21034 \begin_layout Plain Layout
21042 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21045 \begin_layout Plain Layout
21046 \begin_inset Formula $\Phi$
21056 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21059 \begin_layout Plain Layout
21067 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21070 \begin_layout Plain Layout
21071 \begin_inset Formula $\Psi$
21081 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21084 \begin_layout Plain Layout
21092 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21095 \begin_layout Plain Layout
21096 \begin_inset Formula $\Omega$
21110 \begin_inset space \hfill{}
21116 \begin_layout Standard
21117 \begin_inset VSpace medskip
21120 The big Greek letters appearing upright is caused by a design bug in \SpecialChar TeX
21122 To create correct italic big letters, begin every command with
21127 For example the command
21134 \begin_inset Formula $\varGamma$
21138 Another way is to load the package
21146 \begin_layout Plain Layout
21151 is part of the \SpecialChar LaTeX
21157 \begin_inset Index idx
21160 \begin_layout Plain Layout
21165 \begin_layout Plain Layout
21185 \begin_inset Index idx
21188 \begin_layout Plain Layout
21194 with the \SpecialChar LaTeX
21198 \begin_layout Standard
21203 usepackage{fixmath}
21206 \begin_layout Standard
21207 Then all big Greek letters in a document will automatically be typeset italic.
21210 \begin_layout Subsection
21212 \begin_inset Index idx
21215 \begin_layout Plain Layout
21216 Greek letters ! bold
21224 \begin_layout Standard
21225 Greek letters cannot be set with different font styles like Latin letters.
21226 They can only be made bold with the command
21233 \begin_inset Index idx
21236 \begin_layout Plain Layout
21247 \begin_layout Standard
21249 \begin_inset Tabular
21250 <lyxtabular version="3" rows="3" columns="2">
21251 <features booktabs="true" tabularvalignment="middle">
21252 <column alignment="center" valignment="top" width="0pt">
21253 <column alignment="center" valignment="top">
21255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21258 \begin_layout Plain Layout
21264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21267 \begin_layout Plain Layout
21275 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21278 \begin_layout Plain Layout
21290 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21293 \begin_layout Plain Layout
21294 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21304 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21307 \begin_layout Plain Layout
21319 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21322 \begin_layout Plain Layout
21323 \begin_inset Formula $\theta\boldsymbol{\theta}$
21339 \begin_layout Section
21344 \begin_layout Plain Layout
21357 \begin_layout Plain Layout
21358 A list with all symbols of most of the \SpecialChar LaTeX
21359 -packages can be found in
21360 \begin_inset CommandInset citation
21376 \begin_layout Plain Layout
21384 \begin_inset Note Note
21387 \begin_layout Plain Layout
21390 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21393 \begin_layout Plain Layout
21396 texorpdfstring is in section
21397 \begin_inset CommandInset ref
21399 reference "subsec:Formulas-in-Section"
21409 \begin_inset Index idx
21412 \begin_layout Plain Layout
21421 \begin_layout Standard
21422 Many of the symbols listed in this section can also be inserted via the
21426 arg "math-insert \\nabla"
21432 arg "math-insert \\digamma"
21438 \begin_layout Subsection
21439 Mathematical Symbols
21440 \begin_inset CommandInset label
21442 name "subsec:Mathematical-Symbols"
21447 \begin_inset Index idx
21450 \begin_layout Plain Layout
21451 Symbols ! mathematical
21459 \begin_layout Standard
21460 \begin_inset Tabular
21461 <lyxtabular version="3" rows="10" columns="2">
21462 <features booktabs="true" tabularvalignment="middle">
21463 <column alignment="center" valignment="top" width="0pt">
21464 <column alignment="center" valignment="top" width="0pt">
21466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21469 \begin_layout Plain Layout
21475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21478 \begin_layout Plain Layout
21486 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21489 \begin_layout Plain Layout
21497 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21500 \begin_layout Plain Layout
21501 \begin_inset Formula $\neg$
21511 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21514 \begin_layout Plain Layout
21522 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21525 \begin_layout Plain Layout
21526 \begin_inset Formula $\Im$
21536 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21539 \begin_layout Plain Layout
21547 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21550 \begin_layout Plain Layout
21551 \begin_inset Formula $\Re$
21561 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21564 \begin_layout Plain Layout
21572 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21575 \begin_layout Plain Layout
21576 \begin_inset Formula $\aleph$
21586 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21589 \begin_layout Plain Layout
21597 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21600 \begin_layout Plain Layout
21601 \begin_inset Formula $\partial$
21611 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21614 \begin_layout Plain Layout
21622 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21625 \begin_layout Plain Layout
21626 \begin_inset Formula $\infty$
21636 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21639 \begin_layout Plain Layout
21647 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21650 \begin_layout Plain Layout
21651 \begin_inset Formula $\wp$
21661 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21664 \begin_layout Plain Layout
21672 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21675 \begin_layout Plain Layout
21676 \begin_inset Formula $\imath$
21686 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21689 \begin_layout Plain Layout
21697 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21700 \begin_layout Plain Layout
21701 \begin_inset Formula $\jmath$
21715 \begin_inset space \hfill{}
21719 \begin_inset Tabular
21720 <lyxtabular version="3" rows="10" columns="2">
21721 <features booktabs="true" tabularvalignment="middle">
21722 <column alignment="center" valignment="top" width="0pt">
21723 <column alignment="center" valignment="top" width="0pt">
21725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21728 \begin_layout Plain Layout
21734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21737 \begin_layout Plain Layout
21739 \begin_inset Note Note
21742 \begin_layout Plain Layout
21749 is only used as spacer.
21761 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21764 \begin_layout Plain Layout
21772 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21775 \begin_layout Plain Layout
21776 \begin_inset Formula $\forall$
21786 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21789 \begin_layout Plain Layout
21797 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21800 \begin_layout Plain Layout
21801 \begin_inset Formula $\exists$
21811 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21814 \begin_layout Plain Layout
21822 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21825 \begin_layout Plain Layout
21826 \begin_inset Formula $\nexists$
21836 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21839 \begin_layout Plain Layout
21847 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21850 \begin_layout Plain Layout
21851 \begin_inset Formula $\emptyset$
21861 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21864 \begin_layout Plain Layout
21872 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21875 \begin_layout Plain Layout
21876 \begin_inset Formula $\varnothing$
21886 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21889 \begin_layout Plain Layout
21897 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21900 \begin_layout Plain Layout
21901 \begin_inset Formula $\dag$
21911 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21914 \begin_layout Plain Layout
21922 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21925 \begin_layout Plain Layout
21926 \begin_inset Formula $\ddag$
21936 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21939 \begin_layout Plain Layout
21947 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21950 \begin_layout Plain Layout
21954 \begin_layout Plain Layout
21964 \begin_inset Formula $\complement$
21971 \begin_layout Plain Layout
21985 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21988 \begin_layout Plain Layout
21996 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21999 \begin_layout Plain Layout
22000 \begin_inset Formula $\Bbbk$
22014 \begin_inset space \hfill{}
22018 \begin_inset Tabular
22019 <lyxtabular version="3" rows="10" columns="2">
22020 <features booktabs="true" tabularvalignment="middle">
22021 <column alignment="center" valignment="top" width="0pt">
22022 <column alignment="center" valignment="top" width="0pt">
22024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22027 \begin_layout Plain Layout
22033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22036 \begin_layout Plain Layout
22044 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22047 \begin_layout Plain Layout
22055 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22058 \begin_layout Plain Layout
22059 \begin_inset Formula $\prime$
22069 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22072 \begin_layout Plain Layout
22080 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22083 \begin_layout Plain Layout
22084 \begin_inset Formula $\backprime$
22094 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22097 \begin_layout Plain Layout
22105 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22108 \begin_layout Plain Layout
22109 \begin_inset Formula $\mho$
22119 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22122 \begin_layout Plain Layout
22130 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22133 \begin_layout Plain Layout
22134 \begin_inset Formula $\triangle$
22144 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22147 \begin_layout Plain Layout
22155 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22158 \begin_layout Plain Layout
22159 \begin_inset Formula $\angle$
22169 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22172 \begin_layout Plain Layout
22180 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22183 \begin_layout Plain Layout
22184 \begin_inset Formula $\measuredangle$
22194 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22197 \begin_layout Plain Layout
22205 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22208 \begin_layout Plain Layout
22209 \begin_inset Formula $\sphericalangle$
22219 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22222 \begin_layout Plain Layout
22230 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22233 \begin_layout Plain Layout
22234 \begin_inset Formula $\top$
22244 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22247 \begin_layout Plain Layout
22255 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22258 \begin_layout Plain Layout
22259 \begin_inset Formula $\bot$
22275 \begin_layout Subsection
22276 Miscellaneous Symbols
22277 \begin_inset CommandInset label
22279 name "subsec:Miscellaneous-Symbols"
22284 \begin_inset Index idx
22287 \begin_layout Plain Layout
22288 Symbols ! miscellaneous
22296 \begin_layout Standard
22299 \begin_inset Tabular
22300 <lyxtabular version="3" rows="10" columns="2">
22301 <features booktabs="true" tabularvalignment="middle">
22302 <column alignment="center" valignment="top" width="0pt">
22303 <column alignment="center" valignment="top" width="0pt">
22305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22308 \begin_layout Plain Layout
22314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22317 \begin_layout Plain Layout
22325 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22328 \begin_layout Plain Layout
22336 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22339 \begin_layout Plain Layout
22340 \begin_inset Formula $\flat$
22350 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22353 \begin_layout Plain Layout
22361 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22364 \begin_layout Plain Layout
22365 \begin_inset Formula $\natural$
22375 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22378 \begin_layout Plain Layout
22386 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22389 \begin_layout Plain Layout
22390 \begin_inset Formula $\sharp$
22400 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22403 \begin_layout Plain Layout
22411 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22414 \begin_layout Plain Layout
22415 \begin_inset Formula $\surd$
22425 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22428 \begin_layout Plain Layout
22436 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22439 \begin_layout Plain Layout
22440 \begin_inset Formula $\checkmark$
22450 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22453 \begin_layout Plain Layout
22461 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22464 \begin_layout Plain Layout
22465 \begin_inset Formula $\yen$
22475 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22478 \begin_layout Plain Layout
22486 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22489 \begin_layout Plain Layout
22490 \begin_inset Formula $\pounds$
22500 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22503 \begin_layout Plain Layout
22509 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22512 \begin_layout Plain Layout
22513 \begin_inset Formula $\$$
22523 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22526 \begin_layout Plain Layout
22532 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22535 \begin_layout Plain Layout
22536 \begin_inset Formula $§$
22550 \begin_inset space \hfill{}
22554 \begin_inset Tabular
22555 <lyxtabular version="3" rows="10" columns="2">
22556 <features booktabs="true" tabularvalignment="middle">
22557 <column alignment="center" valignment="top" width="0pt">
22558 <column alignment="center" valignment="top">
22560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22563 \begin_layout Plain Layout
22569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22572 \begin_layout Plain Layout
22580 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22583 \begin_layout Plain Layout
22591 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22594 \begin_layout Plain Layout
22595 \begin_inset Formula $\hbar$
22605 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22608 \begin_layout Plain Layout
22616 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22619 \begin_layout Plain Layout
22620 \begin_inset Formula $\hslash$
22630 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22633 \begin_layout Plain Layout
22641 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22644 \begin_layout Plain Layout
22645 \begin_inset Formula $\clubsuit$
22655 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22658 \begin_layout Plain Layout
22666 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22669 \begin_layout Plain Layout
22670 \begin_inset Formula $\spadesuit$
22680 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22683 \begin_layout Plain Layout
22691 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22694 \begin_layout Plain Layout
22695 \begin_inset Formula $\bigstar$
22705 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22708 \begin_layout Plain Layout
22716 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22719 \begin_layout Plain Layout
22720 \begin_inset Formula $\blacklozenge$
22730 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22733 \begin_layout Plain Layout
22741 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22744 \begin_layout Plain Layout
22745 \begin_inset Formula $\blacktriangle$
22755 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22758 \begin_layout Plain Layout
22766 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22769 \begin_layout Plain Layout
22770 \begin_inset Formula $\blacktriangledown$
22780 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22783 \begin_layout Plain Layout
22791 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22794 \begin_layout Plain Layout
22795 \begin_inset Formula $\bullet$
22809 \begin_inset space \hfill{}
22813 \begin_inset Tabular
22814 <lyxtabular version="3" rows="10" columns="2">
22815 <features booktabs="true" tabularvalignment="middle">
22816 <column alignment="center" valignment="top" width="0pt">
22817 <column alignment="center" valignment="top" width="0pt">
22819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22822 \begin_layout Plain Layout
22828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22831 \begin_layout Plain Layout
22839 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22842 \begin_layout Plain Layout
22850 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22853 \begin_layout Plain Layout
22854 \begin_inset Formula $\diamondsuit$
22864 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22867 \begin_layout Plain Layout
22875 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22878 \begin_layout Plain Layout
22879 \begin_inset Formula $\Diamond$
22889 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22892 \begin_layout Plain Layout
22900 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22903 \begin_layout Plain Layout
22904 \begin_inset Formula $\heartsuit$
22914 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22917 \begin_layout Plain Layout
22925 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22928 \begin_layout Plain Layout
22929 \begin_inset Formula $\P$
22939 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22942 \begin_layout Plain Layout
22950 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22953 \begin_layout Plain Layout
22954 \begin_inset Formula $\copyright$
22964 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22967 \begin_layout Plain Layout
22975 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22978 \begin_layout Plain Layout
22979 \begin_inset Formula $\circledR$
22989 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22992 \begin_layout Plain Layout
23000 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23003 \begin_layout Plain Layout
23004 \begin_inset Formula $\maltese$
23014 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23017 \begin_layout Plain Layout
23025 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23028 \begin_layout Plain Layout
23029 \begin_inset Formula $\diagup$
23039 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23042 \begin_layout Plain Layout
23050 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23053 \begin_layout Plain Layout
23054 \begin_inset Formula $\diagdown$
23070 \begin_layout Standard
23071 \begin_inset VSpace medskip
23077 \begin_layout Standard
23078 Some symbols can be displayed in different sizes, see
23079 \begin_inset CommandInset ref
23081 reference "subsec:Font-Sizes"
23088 \begin_layout Subsection
23090 \begin_inset Index idx
23093 \begin_layout Plain Layout
23094 Symbols ! Euro-symbol
23100 \begin_inset Index idx
23103 \begin_layout Plain Layout
23110 \begin_layout Plain Layout
23127 \begin_layout Standard
23128 To use the Euro symbol in formulas, the \SpecialChar LaTeX
23134 \begin_inset Index idx
23137 \begin_layout Plain Layout
23143 must be installed and loaded with the \SpecialChar LaTeX
23147 \begin_layout Standard
23152 usepackage[gennarrow]{eurosym}
23155 \begin_layout Standard
23156 The Euro symbol can now be inserted with the command
23163 \begin_inset Index idx
23166 \begin_layout Plain Layout
23177 \begin_layout Standard
23178 The Euro symbol can directly be inserted with the € key in mathematical
23179 text, without having
23194 can also be inserted in \SpecialChar TeX
23196 The official currency symbol can then be inserted with the command
23203 \begin_inset Index idx
23206 \begin_layout Plain Layout
23214 , which is also only available in \SpecialChar TeX
23218 \begin_layout Standard
23222 \begin_layout Plain Layout
23232 \begin_inset Note Note
23235 \begin_layout Plain Layout
23236 The following table will only be displayed when the \SpecialChar LaTeX
23249 \begin_layout Standard
23250 An overview about the different Euro symbols:
23253 \begin_layout Standard
23255 \begin_inset Tabular
23256 <lyxtabular version="3" rows="4" columns="3">
23257 <features booktabs="true" tabularvalignment="middle">
23258 <column alignment="center" valignment="top" width="0pt">
23259 <column alignment="center" valignment="top" width="0pt">
23260 <column alignment="center" valignment="top" width="0pt">
23262 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
23265 \begin_layout Plain Layout
23269 \begin_layout Plain Layout
23273 cmidrule[0.08em]{2-3}
23283 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23286 \begin_layout Plain Layout
23292 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23295 \begin_layout Plain Layout
23303 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23306 \begin_layout Plain Layout
23312 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23315 \begin_layout Plain Layout
23323 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23326 \begin_layout Plain Layout
23327 \begin_inset Formula $\euro$
23337 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23340 \begin_layout Plain Layout
23346 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23349 \begin_layout Plain Layout
23355 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23358 \begin_layout Plain Layout
23359 \begin_inset Formula $\mbox{€}$
23369 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23372 \begin_layout Plain Layout
23379 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23382 \begin_layout Plain Layout
23390 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23393 \begin_layout Plain Layout
23397 \begin_layout Plain Layout
23417 \begin_inset Note Note
23420 \begin_layout Plain Layout
23427 is used here only for table borders.
23437 manual for details.
23445 \begin_layout Standard
23449 \begin_layout Plain Layout
23459 \begin_inset Note Note
23462 \begin_layout Plain Layout
23463 The following will be displayed when the \SpecialChar LaTeX
23476 \begin_layout Standard
23477 You need to install the \SpecialChar LaTeX
23482 to see the rest of this subsection in the output.
23485 \begin_layout Standard
23489 \begin_layout Plain Layout
23501 \begin_layout Section
23503 \begin_inset CommandInset label
23505 name "sec:Relations"
23510 \begin_inset Index idx
23513 \begin_layout Plain Layout
23520 \begin_inset Index idx
23523 \begin_layout Plain Layout
23528 \begin_layout Plain Layout
23539 \begin_layout Plain Layout
23554 \begin_layout Standard
23555 All of the following relations can also be inserted via the toolbar button
23559 arg "math-insert \\leq"
23565 \begin_layout Standard
23566 \begin_inset Tabular
23567 <lyxtabular version="3" rows="17" columns="2">
23568 <features booktabs="true" tabularvalignment="middle">
23569 <column alignment="center" valignment="top" width="0pt">
23570 <column alignment="center" valignment="top" width="0pt">
23572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23575 \begin_layout Plain Layout
23581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23584 \begin_layout Plain Layout
23592 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23595 \begin_layout Plain Layout
23601 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23604 \begin_layout Plain Layout
23605 \begin_inset Formula $<$
23615 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23618 \begin_layout Plain Layout
23626 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23629 \begin_layout Plain Layout
23630 \begin_inset Formula $\le$
23640 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23643 \begin_layout Plain Layout
23651 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23654 \begin_layout Plain Layout
23655 \begin_inset Formula $\ll$
23665 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23668 \begin_layout Plain Layout
23676 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23679 \begin_layout Plain Layout
23680 \begin_inset Formula $\prec$
23690 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23693 \begin_layout Plain Layout
23701 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23704 \begin_layout Plain Layout
23705 \begin_inset Formula $\preceq$
23715 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23718 \begin_layout Plain Layout
23726 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23729 \begin_layout Plain Layout
23730 \begin_inset Formula $\subset$
23740 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23743 \begin_layout Plain Layout
23751 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23754 \begin_layout Plain Layout
23755 \begin_inset Formula $\subseteq$
23765 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23768 \begin_layout Plain Layout
23776 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23779 \begin_layout Plain Layout
23780 \begin_inset Formula $\sqsubseteq$
23790 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23793 \begin_layout Plain Layout
23801 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23804 \begin_layout Plain Layout
23805 \begin_inset Formula $\in$
23815 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23818 \begin_layout Plain Layout
23826 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23829 \begin_layout Plain Layout
23830 \begin_inset Formula $\vdash$
23840 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23843 \begin_layout Plain Layout
23851 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23854 \begin_layout Plain Layout
23855 \begin_inset Formula $\smile$
23865 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23868 \begin_layout Plain Layout
23876 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23879 \begin_layout Plain Layout
23880 \begin_inset Formula $\lhd$
23890 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23893 \begin_layout Plain Layout
23901 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23904 \begin_layout Plain Layout
23905 \begin_inset Formula $\unlhd$
23915 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23918 \begin_layout Plain Layout
23926 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23929 \begin_layout Plain Layout
23930 \begin_inset Formula $\gtrless$
23940 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23943 \begin_layout Plain Layout
23951 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23954 \begin_layout Plain Layout
23955 \begin_inset Formula $\mid$
23965 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23968 \begin_layout Plain Layout
23976 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23979 \begin_layout Plain Layout
23980 \begin_inset Formula $\nmid$
23994 \begin_inset space \hfill{}
23998 \begin_inset Tabular
23999 <lyxtabular version="3" rows="17" columns="2">
24000 <features booktabs="true" tabularvalignment="middle">
24001 <column alignment="center" valignment="top" width="0pt">
24002 <column alignment="center" valignment="top" width="0pt">
24004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24007 \begin_layout Plain Layout
24013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24016 \begin_layout Plain Layout
24024 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24027 \begin_layout Plain Layout
24033 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24036 \begin_layout Plain Layout
24037 \begin_inset Formula $=$
24047 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24050 \begin_layout Plain Layout
24058 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24061 \begin_layout Plain Layout
24062 \begin_inset Formula $\not=$
24072 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24075 \begin_layout Plain Layout
24083 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24086 \begin_layout Plain Layout
24087 \begin_inset Formula $\equiv$
24097 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24100 \begin_layout Plain Layout
24108 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24111 \begin_layout Plain Layout
24112 \begin_inset Formula $\sim$
24122 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24125 \begin_layout Plain Layout
24133 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24136 \begin_layout Plain Layout
24137 \begin_inset Formula $\simeq$
24147 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24150 \begin_layout Plain Layout
24158 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24161 \begin_layout Plain Layout
24162 \begin_inset Formula $\approx$
24172 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24175 \begin_layout Plain Layout
24183 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24186 \begin_layout Plain Layout
24187 \begin_inset Formula $\cong$
24197 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24200 \begin_layout Plain Layout
24208 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24211 \begin_layout Plain Layout
24212 \begin_inset Formula $\bowtie$
24222 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24225 \begin_layout Plain Layout
24233 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24236 \begin_layout Plain Layout
24237 \begin_inset Formula $\notin$
24247 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24250 \begin_layout Plain Layout
24258 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24261 \begin_layout Plain Layout
24262 \begin_inset Formula $\perp$
24272 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24275 \begin_layout Plain Layout
24283 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24286 \begin_layout Plain Layout
24287 \begin_inset Formula $\propto$
24297 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24300 \begin_layout Plain Layout
24308 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24311 \begin_layout Plain Layout
24312 \begin_inset Formula $\asymp$
24322 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24325 \begin_layout Plain Layout
24333 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24336 \begin_layout Plain Layout
24337 \begin_inset Formula $\doteq$
24347 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24350 \begin_layout Plain Layout
24358 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24361 \begin_layout Plain Layout
24362 \begin_inset Formula $\circeq$
24372 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24375 \begin_layout Plain Layout
24383 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24386 \begin_layout Plain Layout
24387 \begin_inset Formula $\models$
24397 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24400 \begin_layout Plain Layout
24408 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24411 \begin_layout Plain Layout
24412 \begin_inset Formula $\widehat{=}$
24426 \begin_inset space \hfill{}
24430 \begin_inset Tabular
24431 <lyxtabular version="3" rows="17" columns="2">
24432 <features booktabs="true" tabularvalignment="middle">
24433 <column alignment="center" valignment="top" width="0pt">
24434 <column alignment="center" valignment="top" width="0pt">
24436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24439 \begin_layout Plain Layout
24445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24448 \begin_layout Plain Layout
24456 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24459 \begin_layout Plain Layout
24465 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24468 \begin_layout Plain Layout
24469 \begin_inset Formula $>$
24479 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24482 \begin_layout Plain Layout
24490 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24493 \begin_layout Plain Layout
24494 \begin_inset Formula $\ge$
24504 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24507 \begin_layout Plain Layout
24515 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24518 \begin_layout Plain Layout
24519 \begin_inset Formula $\gg$
24529 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24532 \begin_layout Plain Layout
24540 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24543 \begin_layout Plain Layout
24544 \begin_inset Formula $\succ$
24554 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24557 \begin_layout Plain Layout
24565 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24568 \begin_layout Plain Layout
24569 \begin_inset Formula $\succeq$
24579 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24582 \begin_layout Plain Layout
24590 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24593 \begin_layout Plain Layout
24594 \begin_inset Formula $\supset$
24604 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24607 \begin_layout Plain Layout
24615 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24618 \begin_layout Plain Layout
24619 \begin_inset Formula $\supseteq$
24629 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24632 \begin_layout Plain Layout
24640 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24643 \begin_layout Plain Layout
24644 \begin_inset Formula $\sqsupseteq$
24654 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24657 \begin_layout Plain Layout
24665 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24668 \begin_layout Plain Layout
24669 \begin_inset Formula $\ni$
24679 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24682 \begin_layout Plain Layout
24690 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24693 \begin_layout Plain Layout
24694 \begin_inset Formula $\dashv$
24704 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24707 \begin_layout Plain Layout
24715 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24718 \begin_layout Plain Layout
24719 \begin_inset Formula $\frown$
24729 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24732 \begin_layout Plain Layout
24740 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24743 \begin_layout Plain Layout
24744 \begin_inset Formula $\rhd$
24754 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24757 \begin_layout Plain Layout
24765 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24768 \begin_layout Plain Layout
24769 \begin_inset Formula $\unrhd$
24779 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24782 \begin_layout Plain Layout
24790 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24793 \begin_layout Plain Layout
24794 \begin_inset Formula $\lessgtr$
24804 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24807 \begin_layout Plain Layout
24815 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24818 \begin_layout Plain Layout
24819 \begin_inset Formula $\parallel$
24829 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24832 \begin_layout Plain Layout
24840 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24843 \begin_layout Plain Layout
24844 \begin_inset Formula $\nparallel$
24860 \begin_layout Standard
24861 \begin_inset VSpace medskip
24876 are bigger than the equal looking operators
24891 \begin_layout Standard
24893 supports also many special relations.
24894 Use the toolbar button
24897 arg "math-insert \\leqq"
24900 to see a list of these relations.
24903 \begin_layout Standard
24904 Contrary to symbols, relations are always surrounded by space.
24907 \begin_layout Standard
24908 Relations with labels can be created with the command
24915 \begin_inset Index idx
24918 \begin_layout Plain Layout
24929 \begin_layout Standard
24931 \begin_inset Tabular
24932 <lyxtabular version="3" rows="2" columns="2">
24933 <features booktabs="true" tabularvalignment="middle">
24934 <column alignment="center" valignment="top" width="0pt">
24935 <column alignment="center" valignment="top">
24937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24940 \begin_layout Plain Layout
24946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24949 \begin_layout Plain Layout
24956 <row topspace="1.5mm">
24957 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24960 \begin_layout Plain Layout
24964 \begin_inset space \textvisiblespace{}
24972 \begin_inset space \textvisiblespace{}
24976 \begin_inset Formula $\downarrow$
24982 \begin_inset space \textvisiblespace{}
24986 \begin_inset space \textvisiblespace{}
24994 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24997 \begin_layout Plain Layout
24998 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
25014 \begin_layout Section
25018 \begin_layout Subsection
25019 Predefined Functions
25020 \begin_inset CommandInset label
25022 name "subsec:Predefined-Functions"
25027 \begin_inset Index idx
25030 \begin_layout Plain Layout
25031 Functions ! predefined
25039 \begin_layout Standard
25040 In general, variables are set
25044 in mathematical expressions, but not function names, because
25045 \begin_inset Formula $sin$
25048 could be misunderstood as
25049 \begin_inset Formula $s\cdot i\cdot n$
25053 Also predefined functions are separated a bit from the character in front
25055 They are inserted as commands starting with a backslash before their name.
25058 \begin_layout Standard
25060 \begin_inset Tabular
25061 <lyxtabular version="3" rows="2" columns="2">
25062 <features booktabs="true" tabularvalignment="middle">
25063 <column alignment="center" valignment="top" width="0pt">
25064 <column alignment="center" valignment="top" width="0pt">
25066 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
25069 \begin_layout Plain Layout
25075 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
25078 \begin_layout Plain Layout
25086 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25089 \begin_layout Plain Layout
25095 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
25098 \begin_layout Plain Layout
25099 \begin_inset Formula $Asin(x)+B$
25113 \begin_inset space \quad{}
25117 \begin_inset Tabular
25118 <lyxtabular version="3" rows="2" columns="2">
25119 <features booktabs="true" tabularvalignment="middle">
25120 <column alignment="center" valignment="top" width="0pt">
25121 <column alignment="center" valignment="top" width="0pt">
25123 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
25126 \begin_layout Plain Layout
25132 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
25135 \begin_layout Plain Layout
25143 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25146 \begin_layout Plain Layout
25154 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25157 \begin_layout Plain Layout
25158 \begin_inset Formula $A\sin(x)+B$
25174 \begin_layout Standard
25175 The following functions are predefined:
25178 \begin_layout Standard
25179 \begin_inset VSpace -2mm
25185 \begin_layout Standard
25187 \begin_inset Tabular
25188 <lyxtabular version="3" rows="9" columns="4">
25189 <features booktabs="true" tabularvalignment="middle">
25190 <column alignment="center" valignment="top" width="0pt">
25191 <column alignment="center" valignment="top" width="0pt">
25192 <column alignment="center" valignment="top" width="0pt">
25193 <column alignment="center" valignment="top" width="0pt">
25195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25198 \begin_layout Plain Layout
25204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25207 \begin_layout Plain Layout
25213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25216 \begin_layout Plain Layout
25222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25225 \begin_layout Plain Layout
25233 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25236 \begin_layout Plain Layout
25244 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25247 \begin_layout Plain Layout
25255 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25258 \begin_layout Plain Layout
25266 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25269 \begin_layout Plain Layout
25279 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25282 \begin_layout Plain Layout
25290 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25293 \begin_layout Plain Layout
25301 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25304 \begin_layout Plain Layout
25312 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25315 \begin_layout Plain Layout
25325 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25328 \begin_layout Plain Layout
25336 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25339 \begin_layout Plain Layout
25347 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25350 \begin_layout Plain Layout
25358 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25361 \begin_layout Plain Layout
25371 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25374 \begin_layout Plain Layout
25382 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25385 \begin_layout Plain Layout
25393 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25396 \begin_layout Plain Layout
25404 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25407 \begin_layout Plain Layout
25417 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25420 \begin_layout Plain Layout
25428 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25431 \begin_layout Plain Layout
25439 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25442 \begin_layout Plain Layout
25450 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25453 \begin_layout Plain Layout
25463 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25466 \begin_layout Plain Layout
25474 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25477 \begin_layout Plain Layout
25485 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25488 \begin_layout Plain Layout
25496 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25499 \begin_layout Plain Layout
25509 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25512 \begin_layout Plain Layout
25520 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25523 \begin_layout Plain Layout
25531 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25534 \begin_layout Plain Layout
25542 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25545 \begin_layout Plain Layout
25555 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25558 \begin_layout Plain Layout
25566 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25569 \begin_layout Plain Layout
25577 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25580 \begin_layout Plain Layout
25588 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25591 \begin_layout Plain Layout
25607 \begin_layout Standard
25608 They can also be inserted with the math toolbar button
25611 arg "math-insert \\functions"
25617 \begin_layout Subsection
25618 Self-defined Functions
25619 \begin_inset Index idx
25622 \begin_layout Plain Layout
25623 Functions ! self-defined
25631 \begin_layout Standard
25632 To use a function that is not predefined, for instance the sign function
25633 sgn(x), there are two possibilities:
25636 \begin_layout Itemize
25637 Define the function by inserting the following line in the \SpecialChar LaTeX
25642 \begin_layout Plain Layout
25647 DeclareMathOperator
25650 \begin_inset CommandInset ref
25652 reference "subsec:Self-defined-Operators"
25662 \begin_inset Newline newline
25666 \begin_inset VSpace -3mm
25670 \begin_inset Newline newline
25677 DeclareMathOperator{
25682 \begin_inset Index idx
25685 \begin_layout Plain Layout
25690 DeclareMathOperator
25696 \begin_inset Newline newline
25700 \begin_inset VSpace -2mm
25704 \begin_inset Newline newline
25707 Now the newly defined function can be called with the command
25716 \begin_layout Itemize
25717 Write the formula as usual, mark the formula name, in our example the letters
25722 , and change it to mathematical text.
25723 Finally, insert a space between the prefactor and function.
25726 \begin_layout Standard
25727 The result is the same with both methods as with a predefined function
25731 \begin_layout Plain Layout
25732 In \SpecialChar LyX
25733 self-defined functions are displayed red, predefined ones black.
25741 \begin_layout Standard
25743 \begin_inset Tabular
25744 <lyxtabular version="3" rows="3" columns="2">
25745 <features booktabs="true" tabularvalignment="middle">
25746 <column alignment="center" valignment="top" width="0pt">
25747 <column alignment="center" valignment="top" width="0pt">
25749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25752 \begin_layout Plain Layout
25758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25761 \begin_layout Plain Layout
25769 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25772 \begin_layout Plain Layout
25780 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25783 \begin_layout Plain Layout
25784 \begin_inset Formula $A\sgn(x)+B$
25794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25797 \begin_layout Plain Layout
25801 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25812 \begin_layout Plain Layout
25813 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25829 \begin_layout Standard
25830 The first method is more suitable when the self-defined function will be
25831 used several times.
25834 \begin_layout Subsection
25836 \begin_inset Index idx
25839 \begin_layout Plain Layout
25848 \begin_layout Standard
25849 For limits, in addition to the commands
25856 \begin_inset Index idx
25859 \begin_layout Plain Layout
25879 the following functions are defined:
25882 \begin_layout Standard
25884 \begin_inset Tabular
25885 <lyxtabular version="3" rows="5" columns="2">
25886 <features booktabs="true" tabularvalignment="middle">
25887 <column alignment="center" valignment="top" width="0pt">
25888 <column alignment="center" valignment="top" width="0pt">
25890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25893 \begin_layout Plain Layout
25899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25902 \begin_layout Plain Layout
25910 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25913 \begin_layout Plain Layout
25921 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25924 \begin_layout Plain Layout
25925 \begin_inset Formula $\varliminf$
25934 <row topspace="1.5mm">
25935 <cell alignment="center" valignment="top" usebox="none">
25938 \begin_layout Plain Layout
25946 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25949 \begin_layout Plain Layout
25950 \begin_inset Formula $\varlimsup$
25959 <row topspace="1.5mm">
25960 <cell alignment="center" valignment="top" usebox="none">
25963 \begin_layout Plain Layout
25971 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25974 \begin_layout Plain Layout
25975 \begin_inset Formula $\varprojlim$
25984 <row topspace="1.5mm" bottomspace="1mm">
25985 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25988 \begin_layout Plain Layout
25996 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25999 \begin_layout Plain Layout
26000 \begin_inset Formula $\varinjlim$
26016 \begin_layout Standard
26017 \begin_inset VSpace medskip
26020 The limit is created by inserting a subscript.
26021 It is set right beside the function in an inline formula:
26024 \begin_layout Standard
26026 \begin_inset Tabular
26027 <lyxtabular version="3" rows="2" columns="2">
26028 <features booktabs="true" tabularvalignment="middle">
26029 <column alignment="center" valignment="top" width="0pt">
26030 <column alignment="center" valignment="top" width="0pt">
26032 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
26035 \begin_layout Plain Layout
26041 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
26044 \begin_layout Plain Layout
26052 <cell alignment="center" valignment="top" usebox="none">
26055 \begin_layout Plain Layout
26061 \begin_inset space \textvisiblespace{}
26065 \begin_inset space \textvisiblespace{}
26073 <cell alignment="center" valignment="top" usebox="none">
26076 \begin_layout Plain Layout
26077 \begin_inset Formula $\lim_{x\to A}x=B$
26093 \begin_layout Standard
26094 In a displayed formula the limit is set below the formula, as usual:
26095 \begin_inset Formula
26105 \begin_layout Standard
26106 \begin_inset VSpace medskip
26112 \begin_layout Standard
26113 How to adjust the typesetting of the limits see
26114 \begin_inset CommandInset ref
26116 reference "subsec:Operator-Limits"
26123 \begin_layout Subsection
26125 \begin_inset Index idx
26128 \begin_layout Plain Layout
26129 Functions ! modulo-
26137 \begin_layout Standard
26138 The modulo-function is special, because it exists in four variants.
26139 The variants in a displayed formula are:
26140 \begin_inset Formula
26142 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26143 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
26144 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
26145 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
26146 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
26154 \begin_layout Standard
26155 In an inline formula less space is set before the function names for all
26157 By default the modulo-functions take only the first character following
26158 the command into account.
26159 To use more than one character, put them in \SpecialChar TeX
26161 \begin_inset Formula
26163 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26164 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
26165 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26173 \begin_layout Section
26175 \begin_inset Index idx
26178 \begin_layout Plain Layout
26187 \begin_layout Standard
26188 The characters ^ and _ would normally create a superscript and subscript,
26190 To get these characters you have to insert them with a leading
26195 \begin_layout Standard
26198 \begin_inset Tabular
26199 <lyxtabular version="3" rows="3" columns="2">
26200 <features booktabs="true" tabularvalignment="middle">
26201 <column alignment="left" valignment="top" width="0pt">
26202 <column alignment="block" valignment="top">
26204 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26207 \begin_layout Plain Layout
26213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26216 \begin_layout Plain Layout
26224 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26227 \begin_layout Plain Layout
26231 \begin_inset space \textvisiblespace{}
26239 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26242 \begin_layout Plain Layout
26243 \begin_inset Formula $\mathcircumflex$
26253 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26256 \begin_layout Plain Layout
26264 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26267 \begin_layout Plain Layout
26268 \begin_inset Formula $\_$
26284 \begin_layout Subsection
26285 Special Characters in Mathematical Text
26288 \begin_layout Standard
26289 The following commands can only be used in mathematical text or in \SpecialChar TeX
26293 \begin_layout Standard
26294 \begin_inset space \hfill{}
26298 \begin_inset Tabular
26299 <lyxtabular version="3" rows="8" columns="2">
26300 <features booktabs="true" tabularvalignment="middle">
26301 <column alignment="left" valignment="top" width="0pt">
26302 <column alignment="block" valignment="top">
26304 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26307 \begin_layout Plain Layout
26313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26316 \begin_layout Plain Layout
26324 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26327 \begin_layout Plain Layout
26335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26338 \begin_layout Plain Layout
26339 \begin_inset Formula $\textrm{œ}$
26349 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26352 \begin_layout Plain Layout
26360 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26363 \begin_layout Plain Layout
26364 \begin_inset Formula $\textrm{Œ}$
26374 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26377 \begin_layout Plain Layout
26385 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26388 \begin_layout Plain Layout
26389 \begin_inset Formula $\textrm{æ}$
26399 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26402 \begin_layout Plain Layout
26410 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26413 \begin_layout Plain Layout
26414 \begin_inset Formula $\textrm{Æ}$
26424 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26427 \begin_layout Plain Layout
26435 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26438 \begin_layout Plain Layout
26439 \begin_inset Formula $\textrm{å}$
26449 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26452 \begin_layout Plain Layout
26460 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26463 \begin_layout Plain Layout
26464 \begin_inset Formula $\textrm{Å}$
26474 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26477 \begin_layout Plain Layout
26485 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26488 \begin_layout Plain Layout
26489 \begin_inset Formula $\textrm{ı}$
26503 \begin_inset space \hfill{}
26507 \begin_inset Tabular
26508 <lyxtabular version="3" rows="8" columns="2">
26509 <features booktabs="true" tabularvalignment="middle">
26510 <column alignment="left" valignment="top" width="0pt">
26511 <column alignment="center" valignment="top">
26513 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26516 \begin_layout Plain Layout
26518 \begin_inset Note Note
26521 \begin_layout Plain Layout
26523 \begin_inset space \thinspace{}
26526 mm is used for separation, because otherwise the output will be ¡ and ¿
26537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26540 \begin_layout Plain Layout
26548 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26551 \begin_layout Plain Layout
26559 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26562 \begin_layout Plain Layout
26563 \begin_inset Formula $\textrm{ø}$
26573 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26576 \begin_layout Plain Layout
26584 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26587 \begin_layout Plain Layout
26588 \begin_inset Formula $\textrm{Ø}$
26598 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26601 \begin_layout Plain Layout
26609 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26612 \begin_layout Plain Layout
26613 \begin_inset Formula $\textrm{ł}$
26623 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26626 \begin_layout Plain Layout
26634 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26637 \begin_layout Plain Layout
26638 \begin_inset Formula $\textrm{Ł}$
26648 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26651 \begin_layout Plain Layout
26653 \begin_inset space \hspace{}
26658 \begin_inset space \textvisiblespace{}
26666 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26669 \begin_layout Plain Layout
26670 \begin_inset Formula $\textrm{!`}$
26680 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26683 \begin_layout Plain Layout
26685 \begin_inset space \hspace{}
26690 \begin_inset space \textvisiblespace{}
26698 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26701 \begin_layout Plain Layout
26702 \begin_inset Formula $\textrm{?`}$
26712 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26715 \begin_layout Plain Layout
26723 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26726 \begin_layout Plain Layout
26727 \begin_inset Formula $\textrm{ȷ}$
26741 \begin_inset space \hfill{}
26747 \begin_layout Standard
26749 \begin_inset Formula $\textrm{Å}$
26753 \begin_inset Formula $\textrm{Ø}$
26756 can also be inserted via the math toolbar button
26759 arg "math-insert \\digamma"
26765 \begin_layout Standard
26769 \begin_inset space \hspace{}
26778 \begin_inset space \hspace{}
26784 are exceptions because they can be inserted in \SpecialChar LyX
26788 \begin_layout Subsection
26790 \begin_inset CommandInset label
26792 name "subsec:Accents-in-Text"
26797 \begin_inset Index idx
26800 \begin_layout Plain Layout
26809 \begin_layout Standard
26810 Any letter can be accented with the following commands.
26811 The commands must be inserted in \SpecialChar TeX
26815 \begin_layout Standard
26816 \begin_inset space \hfill{}
26820 \begin_inset Tabular
26821 <lyxtabular version="3" rows="8" columns="2">
26822 <features booktabs="true" tabularvalignment="middle">
26823 <column alignment="left" valignment="top" width="0pt">
26824 <column alignment="block" valignment="top">
26826 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26829 \begin_layout Plain Layout
26835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26838 \begin_layout Plain Layout
26846 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26849 \begin_layout Plain Layout
26853 \begin_inset Quotes grd
26861 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26864 \begin_layout Plain Layout
26868 \begin_layout Plain Layout
26884 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26887 \begin_layout Plain Layout
26895 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26898 \begin_layout Plain Layout
26902 \begin_layout Plain Layout
26918 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26921 \begin_layout Plain Layout
26925 \begin_inset space \textvisiblespace{}
26933 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26936 \begin_layout Plain Layout
26940 \begin_layout Plain Layout
26956 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26959 \begin_layout Plain Layout
26967 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26970 \begin_layout Plain Layout
26974 \begin_layout Plain Layout
26990 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26993 \begin_layout Plain Layout
26997 \begin_inset space \textvisiblespace{}
27005 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27008 \begin_layout Plain Layout
27012 \begin_layout Plain Layout
27028 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27031 \begin_layout Plain Layout
27035 \begin_inset space \textvisiblespace{}
27043 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27046 \begin_layout Plain Layout
27050 \begin_layout Plain Layout
27066 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
27069 \begin_layout Plain Layout
27073 \begin_inset space \textvisiblespace{}
27081 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27084 \begin_layout Plain Layout
27088 \begin_layout Plain Layout
27108 \begin_inset space \hfill{}
27112 \begin_inset Tabular
27113 <lyxtabular version="3" rows="8" columns="2">
27114 <features booktabs="true" tabularvalignment="middle">
27115 <column alignment="left" valignment="top" width="0pt">
27116 <column alignment="center" valignment="top">
27118 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27121 \begin_layout Plain Layout
27127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27130 \begin_layout Plain Layout
27138 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27141 \begin_layout Plain Layout
27145 \begin_inset space \textvisiblespace{}
27153 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27156 \begin_layout Plain Layout
27160 \begin_layout Plain Layout
27176 <cell alignment="left" 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
27194 \begin_layout Plain Layout
27210 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27213 \begin_layout Plain Layout
27217 \begin_inset Index idx
27220 \begin_layout Plain Layout
27231 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27234 \begin_layout Plain Layout
27238 \begin_layout Plain Layout
27254 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27257 \begin_layout Plain Layout
27265 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27268 \begin_layout Plain Layout
27272 \begin_layout Plain Layout
27288 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27291 \begin_layout Plain Layout
27295 \begin_inset space \textvisiblespace{}
27303 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27306 \begin_layout Plain Layout
27310 \begin_layout Plain Layout
27326 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27329 \begin_layout Plain Layout
27333 \begin_inset space \textvisiblespace{}
27341 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27344 \begin_layout Plain Layout
27348 \begin_layout Plain Layout
27364 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27367 \begin_layout Plain Layout
27371 \begin_inset space \textvisiblespace{}
27379 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27382 \begin_layout Plain Layout
27386 \begin_layout Plain Layout
27406 \begin_inset space \hfill{}
27412 \begin_layout Standard
27413 \begin_inset VSpace medskip
27422 also two different characters can be accented.
27428 \begin_inset space \textvisiblespace{}
27437 \begin_layout Plain Layout
27449 \begin_layout Standard
27462 can in combination with vowels be directly inserted with the keyboard without
27463 using \SpecialChar TeX
27465 The same applies for the tilde
27469 \begin_layout Plain Layout
27470 This only applies for keyboards where the tilde is defined as accent.
27479 in combination with
27494 \begin_layout Standard
27537 and accents that are inserted directly with the keyboard are also available
27538 in mathematical text.
27539 For the other accents there are special math commands used in formulas,
27541 \begin_inset CommandInset ref
27543 reference "subsec:Accents-for-one"
27550 \begin_layout Standard
27551 \begin_inset VSpace bigskip
27561 \begin_inset Index idx
27564 \begin_layout Plain Layout
27572 any number or letter can be set into a circle, quasi accented with a circle,
27573 similar to the copyright symbol.
27576 \begin_layout Standard
27578 \begin_inset Tabular
27579 <lyxtabular version="3" rows="3" columns="2">
27580 <features booktabs="true" tabularvalignment="middle">
27581 <column alignment="center" valignment="top" width="0pt">
27582 <column alignment="center" valignment="top">
27584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27587 \begin_layout Plain Layout
27593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27596 \begin_layout Plain Layout
27604 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27607 \begin_layout Plain Layout
27615 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27618 \begin_layout Plain Layout
27622 \begin_layout Plain Layout
27637 <row topspace="1mm">
27638 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27641 \begin_layout Plain Layout
27652 raisebox{-1.5pt}{W}}
27657 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27660 \begin_layout Plain Layout
27664 \begin_layout Plain Layout
27694 \begin_layout Standard
27695 One has to take care that the character fits into the circle.
27706 \begin_layout Plain Layout
27708 \begin_inset CommandInset ref
27710 reference "subsec:Font-Sizes"
27719 specifies the size of the circle.
27730 \begin_layout Plain Layout
27732 \begin_inset CommandInset ref
27734 reference "subsec:Boxes-without-Frame"
27743 the character can be centered.
27746 \begin_layout Subsection
27748 \begin_inset Index idx
27751 \begin_layout Plain Layout
27760 \begin_layout Standard
27761 Old-style figures (also known as old-style numerals) are created with the
27769 \begin_inset Index idx
27772 \begin_layout Plain Layout
27781 The command can be used in formulas and in \SpecialChar TeX
27783 The command scheme is:
27786 \begin_layout Standard
27791 oldstylenums{number}
27794 \begin_layout Standard
27799 oldstylenums{0123456789}
27802 \begin_inset Formula $\oldstylenums{0123456789}$
27808 \begin_layout Section
27810 \begin_inset CommandInset label
27812 name "sec:Formula-Styles"
27817 \begin_inset Index idx
27820 \begin_layout Plain Layout
27829 \begin_layout Itemize
27830 There are two different alignment styles:
27834 \begin_layout Description
27835 Centered is the predefined standard.
27838 \begin_layout Description
27839 Indented can be set using the menu
27841 Document\SpecialChar menuseparator
27847 \begin_inset space ~
27853 \begin_layout Standard
27858 is used, the indentation can be adjusted.
27859 The default value depends on the document class.
27863 \begin_layout Itemize
27864 Two different numbering styles are available in the menu
27866 Document\SpecialChar menuseparator
27872 \begin_inset space ~
27881 \begin_layout Description
27882 Right is in most cases the default.
27885 \begin_layout Description
27890 \begin_layout Standard
27891 The chosen styles are used for all displayed formulas of the document.
27892 When both, centered and indented formulas should be created in a document,
27898 The indented formulas are then set in a flalign environment, see
27899 \begin_inset CommandInset ref
27901 reference "subsec:Flalign-Environment"
27908 \begin_layout Section
27910 \begin_inset CommandInset label
27912 name "sec:Multiline-Formulas"
27917 \begin_inset Index idx
27920 \begin_layout Plain Layout
27921 Formula ! multiline
27929 \begin_layout Subsection
27933 \begin_layout Standard
27934 In \SpecialChar LyX
27935 , multiline formulas are created by pressing
27938 arg "newline-insert newline"
27942 This creates either an
27946 that is described in
27947 \begin_inset CommandInset ref
27949 reference "subsec:Standard-align-Environment"
27953 or, when automatically loading of the package
27957 is disabled in the document settings, an
27959 eqnarray environment
27961 that is described in
27962 \begin_inset CommandInset ref
27964 reference "subsec:Eqnarray-Environment"
27969 The align environment is recommended as it provides a typographically correct
27970 output in all cases.
27973 \begin_layout Standard
27974 There are other multiline formula environments that can be created via the
27977 Insert\SpecialChar menuseparator
27981 These environments are described in the following sections.
27984 \begin_layout Standard
27985 In all multiline formula environments a new line is created by pressing
27989 arg "newline-insert newline"
27993 To add or delete lines, use the math toolbar buttons
27996 arg "tabular-feature append-row"
28002 arg "tabular-feature delete-row"
28005 respectively, or the menu option
28007 Edit\SpecialChar menuseparator
28013 \begin_layout Subsubsection
28015 \begin_inset CommandInset label
28017 name "subsec:Line-Separation"
28022 \begin_inset Index idx
28025 \begin_layout Plain Layout
28026 Formula ! multiline ! Line separation
28034 \begin_layout Standard
28035 Sometimes there is not enough space in multiline formulas between the lines:
28036 \begin_inset Formula
28038 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}\\
28039 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
28047 \begin_layout Standard
28048 In \SpecialChar LaTeX
28049 additional line space is specified as an optional argument of the new
28051 This is not yet possible in \SpecialChar LyX
28056 \begin_layout Plain Layout
28058 \begin_inset CommandInset href
28060 name "LyX-bug #1505"
28061 target "https://www.lyx.org/trac/ticket/1505"
28071 , therefore the whole formula must be inserted in \SpecialChar TeX
28073 To add in our example space, the command
28081 is inserted at the end of the first line.
28086 \begin_layout Plain Layout
28093 \begin_layout Plain Layout
28095 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28098 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28105 \begin_layout Plain Layout
28109 left(B^{2}+x_{0}^{2}
28117 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28122 \begin_layout Plain Layout
28134 \begin_layout Standard
28135 \begin_inset VSpace bigskip
28138 To set the line separation for all lines in a formula, the length of
28145 \begin_inset Index idx
28148 \begin_layout Plain Layout
28158 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
28169 \begin_inset space \thinspace{}
28174 \begin_inset space \thinspace{}
28177 mm of additional line separation as in the previous example, the command
28180 \begin_layout Standard
28190 \begin_layout Standard
28191 is inserted in \SpecialChar TeX
28192 mode before the formula.
28193 This requires that the \SpecialChar LaTeX
28202 \begin_layout Plain Layout
28207 is part of every \SpecialChar LaTeX
28208 standard installation.
28214 \begin_inset Index idx
28217 \begin_layout Plain Layout
28223 was loaded in \SpecialChar LaTeX
28224 -preamble with the line
28227 \begin_layout Standard
28235 \begin_layout Standard
28240 \begin_layout Plain Layout
28252 \begin_inset Formula
28254 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}\\
28255 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
28263 \begin_layout Standard
28267 \begin_layout Plain Layout
28284 to its original value,
28290 is set to the value 3
28291 \begin_inset space \thinspace{}
28297 \begin_layout Subsubsection
28299 \begin_inset CommandInset label
28301 name "subsec:Column-Separation"
28306 \begin_inset Index idx
28309 \begin_layout Plain Layout
28310 Formula ! multiline ! Column separation
28318 \begin_layout Standard
28319 Multiline formulas form a matrix.
28320 A formula in the eqnarray environment for example is a matrix with three
28322 By changing the column separation in this environment, the space beside
28323 the relation sign can be changed.
28326 \begin_layout Standard
28327 The column separation is specified with the length
28334 \begin_inset Index idx
28337 \begin_layout Plain Layout
28345 according to the formula: column separation = 2
28346 \begin_inset space \thinspace{}
28354 \change_deleted 5863208 1612730022
28358 \begin_inset Note Note
28361 \begin_layout Plain Layout
28363 \change_inserted 232239728 1611406079
28364 How does units play into this? (cm/in/pt) Is the 2 unitless and the result
28365 takes on the units of the input value?
28375 \begin_inset Newline newline
28381 \begin_layout Standard
28391 \begin_layout Standard
28392 inserted in \SpecialChar TeX
28393 mode, sets all following formula column separations to 2
28394 \begin_inset space \thinspace{}
28398 To return to the predefined distance,
28405 \begin_inset space \thinspace{}
28411 \begin_layout Standard
28413 \begin_inset space \thinspace{}
28416 cm column separation:
28420 \begin_layout Plain Layout
28432 \begin_inset Formula
28440 A formula with the predefined column separation for matrices of 10
28441 \begin_inset space \thinspace{}
28448 \begin_layout Plain Layout
28460 \begin_inset Formula
28471 \begin_layout Standard
28472 \begin_inset Newpage newpage
28478 \begin_layout Subsubsection
28480 \begin_inset Index idx
28483 \begin_layout Plain Layout
28492 \begin_layout Standard
28493 Long formulas can be typeset using these methods:
28496 \begin_layout Itemize
28497 If one side of an equation is much shorter than the line width, this is
28498 chosen for the left side and the right side is typeset over two lines:
28499 \begin_inset Formula
28501 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 \\
28502 & & -\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}
28507 The minus sign at the beginning of the second line does normally not appear
28508 as an operator because it is the first character of the line.
28509 Thus it would not be surrounded by space and could not be distinguished
28510 from the fraction bar.
28512 \begin_inset space \thinspace{}
28515 pt space was inserted behind the minus sign with the command
28525 \begin_layout Plain Layout
28533 \begin_inset CommandInset ref
28535 reference "subsec:Variable-Space"
28545 \begin_inset Index idx
28548 \begin_layout Plain Layout
28559 \begin_layout Itemize
28560 When both sides of the equation are long, the command
28567 \begin_inset Index idx
28570 \begin_layout Plain Layout
28579 It is inserted in the first column of the first line and causes all further
28580 insertions to overwrite the following columns:
28581 \begin_inset Formula
28583 \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 \\
28584 & & -\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 \\
28585 & & =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}
28590 After the insertion of
28596 , the cursor is in a purple box that is shifted a bit to the left from the
28598 The formula is inserted there.
28599 \begin_inset Newline newline
28602 The content of additional lines is inserted in the second or another formula
28604 The greater the insertion column number , the larger the indentation.
28605 \begin_inset VSpace medskip
28609 \begin_inset Newline newline
28613 \begin_inset Note Greyedout
28616 \begin_layout Plain Layout
28617 Note the following when using
28626 \begin_layout Itemize
28627 The formula doesn't use the full page width.
28629 \begin_inset space \thinspace{}
28633 \begin_inset space \space{}
28637 \begin_inset Formula $-B^{2}$
28640 is added to the first line in the above example, it would have been outside
28642 To better use the width, negative space can be inserted at the beginning
28646 \begin_layout Itemize
28647 Due to a bug in \SpecialChar LyX
28648 the cursor cannot be set with the mouse in the first line.
28652 \begin_layout Plain Layout
28653 \begin_inset CommandInset href
28655 name "LyX-bug #1429"
28656 target "https://www.lyx.org/trac/ticket/1429"
28666 One can only set the cursor at the beginning of the line and move it with
28675 \begin_layout Itemize
28676 Other methods to set long formulas are offered by the environments described
28678 \begin_inset CommandInset ref
28680 reference "subsec:Multline-Environment"
28685 \begin_inset CommandInset ref
28687 reference "subsec:Multiline-Formula-Parts"
28694 \begin_layout Subsubsection
28695 Multiline Fractions
28696 \begin_inset CommandInset label
28698 name "subsec:Multiline-Fractions"
28703 \begin_inset Index idx
28706 \begin_layout Plain Layout
28707 Fractions ! multiline
28715 \begin_layout Standard
28716 There are cases where the denominator and/or the numerator of a fraction
28717 is so long that the fraction does not fit on one line.
28718 It is then necessary to add a line break within the fraction.
28719 This can be done using the command
28726 \begin_inset Index idx
28729 \begin_layout Plain Layout
28738 To activate it, go to the document settings under
28741 \begin_inset space ~
28751 \begin_inset Index idx
28754 \begin_layout Plain Layout
28755 Packages ! mathtools
28760 and set its option to
28763 \begin_inset space ~
28778 \begin_layout Standard
28783 splitfrac{first line}{second line}
28786 \begin_layout Standard
28787 and is used for either the denominator or numerator:
28790 \begin_layout Standard
28791 \begin_inset Formula
28793 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}
28798 The command for the first numerator above is:
28801 \begin_layout Standard
28806 splitfrac{xy+xy+xy+xy+xy
28807 \begin_inset space \textvisiblespace{}
28815 \begin_layout Subsubsection
28817 \begin_inset CommandInset label
28819 name "subsec:Multiline-Brackets"
28824 \begin_inset Index idx
28827 \begin_layout Plain Layout
28828 Brackets ! for multiline expressions
28836 \begin_layout Standard
28837 For brackets spanning multiple lines the following problem occurs:
28838 \begin_inset Formula
28840 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28841 & & \left.\cdots+B-D\right]
28849 \begin_layout Standard
28850 The closing bracket is smaller than the opening bracket because brackets
28851 with variable size may not span multiple lines.
28854 \begin_layout Standard
28855 To set the bracket size for the second line correctly, the first line is
28863 \begin_inset Index idx
28866 \begin_layout Plain Layout
28874 and the second line with
28882 \begin_layout Plain Layout
28896 \begin_inset CommandInset ref
28898 reference "subsec:Automatic-Bracket-Size"
28910 \begin_inset Index idx
28913 \begin_layout Plain Layout
28936 \begin_inset space \textvisiblespace{}
28946 \begin_inset space \textvisiblespace{}
28956 \begin_inset space \textvisiblespace{}
28962 \begin_inset Formula $\downarrow$
28968 \begin_inset Index idx
28971 \begin_layout Plain Layout
28979 is inserted, because the multiplication operator with its limits is the
28980 largest symbol in the first line and this should be the size for the bracket
28981 in the second line.
28984 \begin_layout Standard
28985 The result is this:
28986 \begin_inset Formula
28988 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28989 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28997 \begin_layout Subsection
29001 \begin_layout Standard
29002 Align environments can be used for every kind of multiline formulas.
29003 They are especially useful to set several formulas side by side.
29006 \begin_layout Standard
29007 Align environments consist of columns.
29008 The odd columns are right aligned, the even ones left aligned.
29009 Every line in an Align environment can be numbered.
29012 \begin_layout Standard
29013 Align environments are created via the menu
29015 Insert\SpecialChar menuseparator
29021 Edit\SpecialChar menuseparator
29022 Math\SpecialChar menuseparator
29023 Change Formula Type
29025 pre-existing formulas can be converted to Align environments.
29028 \begin_layout Standard
29029 To add or delete columns, use the math toolbar buttons
29032 arg "tabular-feature append-column"
29038 arg "tabular-feature delete-column"
29041 respectively, or the menu option
29043 Edit\SpecialChar menuseparator
29049 \begin_layout Subsubsection
29050 Standard Align Environment
29051 \begin_inset CommandInset label
29053 name "subsec:Standard-align-Environment"
29058 \begin_inset Index idx
29061 \begin_layout Plain Layout
29062 Formula ! multiline ! align environment
29070 \begin_layout Standard
29071 This align environment is created by pressing
29074 arg "newline-insert newline"
29077 in a formula or by the menu
29079 Insert\SpecialChar menuseparator
29080 Math\SpecialChar menuseparator
29081 AMS align Environment
29086 \begin_layout Standard
29087 An example for two formulas set side by side, that are created with a four
29088 column align environment:
29089 \begin_inset Formula
29091 A & =\sin(B) & C & =D\\
29092 C & \ne A & B & \ne D
29097 As it can be seen, the formulas in this environment are placed so as if
29106 \begin_layout Plain Layout
29114 \begin_inset CommandInset ref
29116 reference "subsec:Variable-Space"
29127 before the first and after every even column.
29128 When the formula style
29134 \begin_layout Plain Layout
29135 For formula styles see
29136 \begin_inset CommandInset ref
29138 reference "sec:Formula-Styles"
29149 is used, the formula is set without the
29155 before the first column.
29158 \begin_layout Subsubsection
29159 Alignat Environment
29160 \begin_inset Index idx
29163 \begin_layout Plain Layout
29164 Formula ! multiline ! alignat environment
29172 \begin_layout Standard
29173 The alignat environment has no predefined column separation.
29174 It can be inserted manually with the spaces that are described in
29175 \begin_inset CommandInset ref
29177 reference "subsec:Space"
29184 \begin_layout Standard
29185 The above example is shown in the alignat environment where 1
29186 \begin_inset space \thinspace{}
29189 cm space was inserted at the beginning of the second formula:
29190 \begin_inset Formula
29191 \begin{alignat*}{2}
29192 A & =\sin(B) & \hspace{1cm}C & =D\\
29193 C & \ne A & B & \ne D
29198 Because the column separation can be set separately for every column, this
29199 environment is especially suitable to set three or more formulas side by
29203 \begin_layout Subsubsection
29204 Flalign Environment
29205 \begin_inset CommandInset label
29207 name "subsec:Flalign-Environment"
29212 \begin_inset Index idx
29215 \begin_layout Plain Layout
29216 Formula ! multiline ! flalign environment
29224 \begin_layout Standard
29225 In this environment the first column is always set to the left as much as
29226 possible and the last one to the right.
29228 \begin_inset Formula
29230 A & =1 & B & =2 & C & =3\\
29231 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29239 \begin_layout Standard
29240 By creating a flalign environment with an odd number of columns where an
29241 empty \SpecialChar TeX
29242 brace is inserted in the last column, several formulas in a document
29243 can be set to the left, although the formula style
29248 As example the indented formula
29249 \begin_inset CommandInset ref
29251 reference "eq:VolInt"
29256 \begin_inset Formula
29258 \hspace{30pt}\iiint_{V}X\,\mathrm{d}V & =U & {}
29263 The first two columns contain the formula.
29264 To indent it as with the formula style
29269 \begin_inset space \thinspace{}
29272 pt space was inserted at the beginning of the first column.
29275 \begin_layout Subsection
29276 Eqnarray Environment
29277 \begin_inset CommandInset label
29279 name "subsec:Eqnarray-Environment"
29284 \begin_inset Index idx
29287 \begin_layout Plain Layout
29288 Formula ! multiline ! eqnarray environment
29296 \begin_layout Standard
29297 When this environment is created, three blue boxes appear.
29298 The content of the first box is right aligned, the content of the last
29300 The content of the middle box appears centered and a bit smaller because
29301 it is intended for relational characters only.
29302 \begin_inset Formula
29304 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29314 \begin_layout Subsection
29316 \begin_inset Index idx
29319 \begin_layout Plain Layout
29320 Formula ! multiline ! gather environment
29328 \begin_layout Standard
29329 This environment consists of one centered column.
29330 Every line can be numbered.
29331 \begin_inset Formula
29342 \begin_layout Subsection
29343 Multline Environment
29344 \begin_inset CommandInset label
29346 name "subsec:Multline-Environment"
29351 \begin_inset Index idx
29354 \begin_layout Plain Layout
29355 Formula ! multiline ! multline environment
29363 \begin_layout Standard
29364 The multline environment consists, like the gather environment, of one column.
29365 But the first line is left aligned, the last one right aligned.
29366 All other lines are centered.
29367 Therefore this environment is suitable for long formulas.
29368 Using example formula
29369 \begin_inset CommandInset ref
29371 reference "eq:lefteqn"
29375 in the multline environment:
29376 \begin_inset Formula
29378 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}\\
29379 -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}\\
29380 =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}}
29388 \begin_layout Standard
29389 In the output, only the last line of a multline environment appears numbered
29390 when the document numbering is on the right .
29391 If the document numbering is on the left then only the first line will
29396 \begin_layout Plain Layout
29397 For numbering styles see
29398 \begin_inset CommandInset ref
29400 reference "sec:Formula-Styles"
29412 \begin_layout Standard
29420 \begin_inset Index idx
29423 \begin_layout Plain Layout
29438 \begin_inset Index idx
29441 \begin_layout Plain Layout
29449 a centered line can be right or left aligned, respectively.
29450 The commands are used as follows:
29453 \begin_layout Standard
29458 shoveright{line content}
29464 shoveleft{line content}
29467 \begin_layout Standard
29468 \begin_inset VSpace medskip
29478 \begin_inset Index idx
29481 \begin_layout Plain Layout
29489 specifies the distance of the first line from the left page margin.
29490 Predefined is the length 0
29491 \begin_inset space \thinspace{}
29497 \begin_layout Standard
29498 As example the above formula where the command
29501 \begin_layout Standard
29511 \begin_layout Standard
29512 was inserted in \SpecialChar TeX
29517 \begin_layout Plain Layout
29529 \begin_inset Formula
29531 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}\\
29532 \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}}\\
29533 =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}}
29542 \begin_layout Plain Layout
29553 The second line was left aligned using
29562 \begin_layout Subsection
29563 Multiline Formula Parts
29564 \begin_inset CommandInset label
29566 name "subsec:Multiline-Formula-Parts"
29571 \begin_inset Index idx
29574 \begin_layout Plain Layout
29575 Formula ! multiline ! formula parts
29583 \begin_layout Standard
29584 To display only parts of a formula with multiple lines, one of the following
29585 environments is used:
29602 They can be inserted via the menu
29604 Insert\SpecialChar menuseparator
29607 or by using the commands described in this section.
29610 \begin_layout Standard
29611 The first three have the same properties as the corresponding multiline
29612 formula environments, but it is possible to set additional formula parts
29615 \begin_inset Formula
29617 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29618 \Delta E\Delta t & \ge\frac{\hbar}{2}
29620 \right\} \textrm{Uncertainty relations}
29628 \begin_layout Standard
29629 To get this formula, a displayed formula is created where the command
29636 \begin_inset Index idx
29639 \begin_layout Plain Layout
29648 A purple box appears around the blue formula box where now columns and
29649 lines can be added.
29650 Outside the multiline environment other formula parts can be set, like
29654 \begin_layout Standard
29655 The aligned environment is also suitable for long formulas whose lines are
29656 horizontally aligned.
29657 Using aligned in a displayed formula has the advantage that the formula
29658 number is vertically centered behind the lines.
29659 For example here is formula
29660 \begin_inset CommandInset ref
29662 reference "eq:shortlong"
29666 in the aligned environment:
29667 \begin_inset Formula
29669 \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}|}\\
29670 & -\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}|}
29679 \begin_layout Standard
29680 To use the environments
29699 \begin_inset Index idx
29702 \begin_layout Plain Layout
29717 \begin_inset Index idx
29720 \begin_layout Plain Layout
29735 \begin_inset Index idx
29738 \begin_layout Plain Layout
29746 are inserted, respectively.
29747 The split environment has the same properties as the aligned environment
29748 but it can only have two columns.
29751 \begin_layout Subsection
29752 Text in Multiline Formulas
29753 \begin_inset CommandInset label
29755 name "subsec:Text-in-multiline"
29760 \begin_inset Index idx
29763 \begin_layout Plain Layout
29770 \begin_inset Index idx
29773 \begin_layout Plain Layout
29774 Formula ! multiline ! text
29782 \begin_layout Standard
29783 In the align environments as well as the multline and gather environment,
29784 text can be inserted that will appear in a separate line and doesn't affect
29785 the column alignment.
29786 To do this, the command
29793 \begin_inset Index idx
29796 \begin_layout Plain Layout
29804 is used in the following scheme:
29807 \begin_layout Standard
29815 \begin_layout Standard
29816 The text should not be longer than a line because it cannot be hyphenated.
29817 As \SpecialChar LyX
29818 doesn't yet support
29824 directly, the text is written as mathematical text.
29831 must be at the beginning of a line and will appear in the output above
29833 An example where the text was inserted at the beginning of the second line:
29834 \begin_inset Formula
29836 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29837 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29845 \begin_layout Standard
29852 always creates some vertical space between the text and the formula lines.
29853 To avoid this space, in the document settings under
29856 \begin_inset space ~
29866 \begin_inset Index idx
29869 \begin_layout Plain Layout
29870 Packages ! mathtools
29878 \begin_inset space ~
29884 Then you can use the command
29891 \begin_inset Index idx
29894 \begin_layout Plain Layout
29911 \begin_layout Standard
29912 \begin_inset Formula
29914 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29915 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29923 \begin_layout Section
29925 \begin_inset Index idx
29928 \begin_layout Plain Layout
29935 \begin_inset Index idx
29938 \begin_layout Plain Layout
29939 Formula ! numbering|see
29943 \begin_layout Plain Layout
29954 \begin_layout Plain Layout
29969 \begin_layout Subsection
29973 \begin_layout Standard
29974 Numbered formulas can be created with the menu
29976 Insert\SpecialChar menuseparator
29977 Math\SpecialChar menuseparator
29979 \begin_inset space ~
29987 arg "command-sequence math-display; math-number-toggle;"
29991 Existing formulas can be numbered with the menu
29993 Edit\SpecialChar menuseparator
29994 Math\SpecialChar menuseparator
29996 \begin_inset space ~
30000 \begin_inset space ~
30008 arg "math-number-toggle"
30012 The formula number is displayed in \SpecialChar LyX
30013 behind the formula as a number in parenthes
30016 \change_deleted 232239728 1611410645
30017 The number sign is replaced in the output by the formula number.
30018 \change_deleted 5863208 1612727075
30020 \begin_inset Note Note
30023 \begin_layout Plain Layout
30025 \change_inserted 232239728 1611410697
30026 LyX appears to put the actual formula number in the raw file now
30038 \begin_layout Standard
30039 When numbering is turned on in multiline formulas, all formulas will be
30041 But the numbering can be controlled with the menu
30043 Edit\SpecialChar menuseparator
30044 Math\SpecialChar menuseparator
30046 \begin_inset space ~
30050 \begin_inset space ~
30058 arg "math-number-line-toggle"
30061 ) for every formula.
30064 \begin_layout Standard
30065 Except for inline formulas, all formulas can be numbered with two different
30067 \begin_inset CommandInset ref
30069 reference "sec:Formula-Styles"
30076 \begin_layout Subsection
30078 \begin_inset Index idx
30081 \begin_layout Plain Layout
30082 Cross-references ! to formulas
30090 \begin_layout Standard
30091 All labeled formulas can be cross-referenced.
30092 A label is added with the menu
30094 Insert\SpecialChar menuseparator
30097 or the toolbar button
30104 The cursor must be inside a displayed formula.
30105 Alternatively you can right-click on the formula and choose
30110 A dialog pops up displaying the prefix
30115 The label is inserted behind the prefix.
30116 The predefined prefix means
30117 \begin_inset Quotes eld
30121 \begin_inset Quotes erd
30124 and makes it easier to find labels in large documents because it marks
30125 it as a formula label to distinguish it from e.
30126 \begin_inset space \thinspace{}
30130 \begin_inset space \space{}
30134 To change a label, the menu
30136 Insert\SpecialChar menuseparator
30139 is used again or you can right-click on a formula and then on
30146 \begin_layout Standard
30147 The name of the label is displayed in \SpecialChar LyX
30148 within parentheses behind the formula
30150 A formula with a label is always numbered.
30153 \begin_layout Standard
30154 Cross-references are inserted via the menu
30156 Insert\SpecialChar menuseparator
30159 or with the toolbar button
30162 arg "dialog-show-new-inset ref"
30166 A formula cross-reference appears in the output as formula number.
30167 When in the cross-reference dialog window the format
30171 is chosen, the cross-reference appears in the output as formula number
30173 \begin_inset Newline newline
30176 By right-clicking on a cross-reference in \SpecialChar LyX
30177 , one jumps to the formula that
30181 \begin_layout Standard
30182 Here are as examples cross-references to formulas of the following subsections:
30183 \begin_inset Note Note
30186 \begin_layout Plain Layout
30187 Note the different cross-reference types.
30195 \begin_layout Standard
30197 \begin_inset CommandInset ref
30204 \begin_inset CommandInset ref
30212 \begin_inset CommandInset ref
30218 ) big Latin letters are used for the numbering in contrary to (
30219 \begin_inset CommandInset ref
30228 \begin_layout Standard
30229 \begin_inset VSpace medskip
30232 When the argument of
30240 \begin_layout Plain Layout
30248 \begin_inset CommandInset ref
30250 reference "subsec:User-defined-Numbering"
30261 contains a box like in
30262 \begin_inset CommandInset ref
30264 reference "subsec:Paragraph-Boxes"
30268 , the formula cannot be referenced.
30271 \begin_layout Subsection
30273 \begin_inset Index idx
30276 \begin_layout Plain Layout
30277 Formula numbering ! subnumbering
30285 \begin_layout Standard
30286 Formulas can be numbered as subequations.
30287 To activate this feature, add the module
30291 to the document in the menu
30293 Document\SpecialChar menuseparator
30294 Settings\SpecialChar menuseparator
30298 To insert subequations use the menu
30300 Insert\SpecialChar menuseparator
30301 Custom Insets\SpecialChar menuseparator
30307 \begin_layout Standard
30308 The equations to be subnumbered are put into the
30314 \begin_inset Formula
30322 \begin_inset VSpace -5mm
30326 \begin_inset Flex Subequations
30329 \begin_layout Plain Layout
30330 \begin_inset Formula
30338 \begin_inset Formula
30353 \begin_layout Standard
30354 Every formula in the
30358 inset will be subnumbered with a, b, c, \SpecialChar ldots
30360 For multiline formulas every line will be subnumbered.
30363 \begin_layout Standard
30364 Referencing subequations works like normal equations:
30365 \begin_inset CommandInset ref
30372 \begin_inset CommandInset ref
30379 If you want to reference the subequations collectively, insert a label
30380 as first thing in the
30386 \begin_inset CommandInset ref
30388 reference "eq:Here-is-an"
30398 \begin_layout Standard
30399 When inserting subequations, vertical space is added before the equation.
30400 To remove this, insert -5
30401 \begin_inset space \thinspace{}
30404 mm vertical space right before the
30409 If the formula style
30415 \begin_layout Plain Layout
30416 For formula styles see
30417 \begin_inset CommandInset ref
30419 reference "sec:Formula-Styles"
30431 \begin_inset space \thinspace{}
30437 \begin_layout Standard
30438 To get another subnumber instead of small Latin letters, insert this command
30439 as \SpecialChar TeX
30440 code before the equations in the
30447 \begin_layout Standard
30456 theparentequation -
30461 \begin_layout Standard
30468 creates the parent number and
30474 adds a small Roman number as subnumber.
30475 For more information about the customization of the numbering, see
30476 \begin_inset CommandInset ref
30478 reference "subsec:Numbering-with-Roman"
30485 \begin_layout Standard
30486 Here is an example of a multiline formula where the numbering is customized
30487 and turned off for the second line:
30488 \begin_inset Flex Subequations
30491 \begin_layout Plain Layout
30492 \begin_inset CommandInset label
30494 name "eq:Here-is-an"
30502 \begin_layout Plain Layout
30510 theparentequation -
30518 \begin_inset Formula
30520 A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
30521 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30522 & = & B^{2}-2BZ+Z^{2}
30535 \begin_layout Subsection
30536 Numbering with Roman Numbers and Letters
30537 \begin_inset CommandInset label
30539 name "subsec:Numbering-with-Roman"
30544 \begin_inset Index idx
30547 \begin_layout Plain Layout
30548 Formula numbering ! with letters
30554 \begin_inset Index idx
30557 \begin_layout Plain Layout
30558 Formula numbering ! with Roman numbers
30566 \begin_layout Standard
30567 Formulas can also be numbered with Roman numbers and Latin letters.
30568 To number with small Roman numbers, the command
30571 \begin_layout Standard
30583 \begin_layout Standard
30584 is inserted before the formula in \SpecialChar TeX
30593 \begin_inset Index idx
30596 \begin_layout Plain Layout
30604 redefines the predefined command
30620 \begin_layout Plain Layout
30627 has the same scheme as the command
30634 \begin_inset CommandInset ref
30636 reference "subsec:The-Command-newcommand"
30649 is the formula counter.
30656 is used as prefix for a counter, the value of the counter is output as
30658 When a formula is numbered, \SpecialChar LaTeX
30659 sets internally the command
30665 behind the formula.
30671 \begin_inset Index idx
30674 \begin_layout Plain Layout
30684 outputs the counter as small Roman number.
30687 \begin_layout Standard
30688 All formulas behind the command
30698 are now numbered Roman.
30699 To switch to numbering with big Roman numbers, the command is inserted
30713 \begin_inset Index idx
30716 \begin_layout Plain Layout
30728 \begin_inset Quotes eld
30732 \begin_inset Quotes erd
30735 with small Latin letters there is the command
30742 \begin_inset Index idx
30745 \begin_layout Plain Layout
30753 , for big ones there is the command
30760 \begin_inset Index idx
30763 \begin_layout Plain Layout
30776 \begin_layout Standard
30777 \begin_inset Note Greyedout
30780 \begin_layout Plain Layout
30785 Only a maximum of 26
30786 \begin_inset space ~
30789 formulas can be numbered with Latin letters in one document.
30797 \begin_layout Standard
30801 \begin_layout Plain Layout
30817 \begin_layout Standard
30818 \begin_inset Formula
30820 A=\textrm{small roman}
30829 \begin_layout Plain Layout
30843 \begin_inset Formula
30845 B=\textrm{big Roman}\label{eq:Rom}
30854 \begin_layout Plain Layout
30868 \begin_inset Formula
30870 C=\textrm{small Latin}
30879 \begin_layout Plain Layout
30893 \begin_inset Formula
30895 D=\textrm{big Latin}\label{eq:Lat}
30903 \begin_layout Standard
30904 To switch back to the default numbering, insert the command:
30907 \begin_layout Standard
30917 \begin_inset Index idx
30920 \begin_layout Plain Layout
30931 \begin_layout Standard
30935 \begin_layout Plain Layout
30949 \begin_inset Formula
30959 \begin_layout Standard
30960 \begin_inset VSpace medskip
30963 As you see, formulas are numbered serially independent from the numbering
30965 When then numbering should start with
30966 \begin_inset Quotes eld
30970 \begin_inset Quotes erd
30973 when the style is changed, new equation counters have to be defined.
30974 A description of this can be found in the file
30975 \begin_inset CommandInset href
30977 name "Formula-numbering.lyx"
30978 target "run:Formula-numbering.lyx"
30986 \begin_layout Subsection
30987 User-defined Numbering
30988 \begin_inset CommandInset label
30990 name "subsec:User-defined-Numbering"
30995 \begin_inset Index idx
30998 \begin_layout Plain Layout
30999 Formula numbering ! user-defined
31007 \begin_layout Standard
31008 \begin_inset Note Greyedout
31011 \begin_layout Plain Layout
31016 If the document language is a right-to-left language such as Arabic, you
31017 must add this to the to the \SpecialChar LaTeX
31018 -preamble to be able to use the commands described
31020 \begin_inset Newline newline
31028 \begin_inset Newline newline
31032 \begin_inset Phantom HPhantom
31035 \begin_layout Plain Layout
31038 \begin_inset space ~
31064 \begin_layout Standard
31065 \begin_inset Index idx
31068 \begin_layout Plain Layout
31069 Formula numbering ! self-defined delimiters
31074 With standard numbering, parentheses are set around a formula number.
31075 To replace the parentheses for example with vertical bars, the following
31076 line is added to the \SpecialChar LaTeX
31080 \begin_layout Standard
31086 \begin_inset Newline newline
31090 \begin_inset Phantom HPhantom
31093 \begin_layout Plain Layout
31096 \begin_inset space ~
31110 maketag@@@{|#1|}} }
31113 \begin_inset Note Note
31116 \begin_layout Plain Layout
31117 This macro is already declared in the \SpecialChar LaTeX
31118 -preamble for testing.
31119 To activate it, remove the percent signs at the beginning.
31127 \begin_layout Standard
31128 To use other characters, the vertical bars besides the
31132 are replaced by one or more characters.
31133 To display only the formula number the vertical bars are omitted.
31136 \begin_layout Standard
31137 \begin_inset VSpace bigskip
31140 When there should be an expression of your choice instead of the consecutive
31141 formula number in parentheses behind the formula, the command
31148 \begin_inset Index idx
31151 \begin_layout Plain Layout
31160 \begin_inset Formula
31162 A+B=C\tag{something}\label{eq:tag}
31167 In this example the command
31172 \begin_inset space \textvisiblespace{}
31177 was inserted in the formula.
31180 \begin_layout Standard
31186 \begin_inset space \textvisiblespace{}
31191 is inserted instead, the parentheses are removed:
31192 \begin_inset Formula
31194 A+B=C\tag*{something}
31202 \begin_layout Standard
31203 \begin_inset VSpace bigskip
31206 To restart the formula numbering with new document parts or sections, the
31207 following command is used:
31210 \begin_layout Standard
31215 @addtoreset{equation}{part}
31218 \begin_inset Index idx
31221 \begin_layout Plain Layout
31226 \begin_layout Plain Layout
31237 \begin_layout Plain Layout
31250 \begin_layout Plain Layout
31261 \begin_layout Plain Layout
31274 \begin_inset Newline newline
31278 \begin_inset Newline newline
31285 @addtoreset{equation}{section}
31288 \begin_layout Standard
31289 To be able to use these commands in \SpecialChar TeX
31291 \begin_inset Quotes eld
31295 \begin_inset Quotes erd
31298 character has to be made
31299 \begin_inset Quotes eld
31303 \begin_inset Quotes erd
31306 for \SpecialChar LaTeX
31321 So the command sequence in \SpecialChar TeX
31325 \begin_layout Standard
31331 \begin_inset Newline newline
31336 @addtoreset{equation}{section}
31337 \begin_inset Newline newline
31345 \begin_layout Standard
31346 In the \SpecialChar LaTeX
31359 can be omitted as they are automatically internally inserted by \SpecialChar LyX
31363 \begin_layout Standard
31378 \begin_layout Plain Layout
31383 is part of the \SpecialChar LaTeX
31389 \begin_inset Index idx
31392 \begin_layout Plain Layout
31393 Packages ! carlisle
31398 that is part of every \SpecialChar LaTeX
31399 standard installation.
31405 \begin_inset Index idx
31408 \begin_layout Plain Layout
31409 Packages ! remreset
31414 has to be loaded in the \SpecialChar LaTeX
31415 -preamble with the line
31418 \begin_layout Standard
31423 usepackage{remreset}
31426 \begin_layout Standard
31434 \begin_inset Index idx
31437 \begin_layout Plain Layout
31442 \begin_layout Plain Layout
31453 \begin_layout Plain Layout
31466 \begin_layout Plain Layout
31477 \begin_layout Plain Layout
31489 can be used with the same scheme as
31498 \begin_layout Standard
31499 \begin_inset VSpace bigskip
31502 Sometimes formulas should be numbered in the following form:
31505 \begin_layout Standard
31508 (section number.formula number)
31511 \begin_layout Standard
31512 The formula number should start with every section with
31513 \begin_inset Quotes eld
31517 \begin_inset Quotes erd
31523 \begin_layout Standard
31524 For this case there is the command
31531 \begin_inset Index idx
31534 \begin_layout Plain Layout
31542 , which is used with the following scheme:
31545 \begin_layout Standard
31550 numberwithin{counter}{sectioning}
31553 \begin_layout Standard
31554 Counter denotes what kind of numbering is affected, sectioning denotes what
31555 the number before the dot is.
31558 \begin_layout Standard
31559 Thus in our case the following \SpecialChar LaTeX
31560 preamble or \SpecialChar TeX
31564 \begin_layout Standard
31569 numberwithin{equation}{section}
31572 \begin_layout Standard
31573 This is the result:
31577 \begin_layout Plain Layout
31581 numberwithin{equation}{section}
31587 \begin_inset Formula
31597 \begin_layout Standard
31599 \begin_inset space \thinspace{}
31603 \begin_inset space \space{}
31606 tables so that the number of the part is the sectioning,
31607 \begin_inset Newline newline
31614 numberwithin{table}{part}
31619 \begin_layout Standard
31620 To go back to the standard numbering or to prevent this kind of numbering
31621 when it is defined by the document class, the following command is inserted
31622 as \SpecialChar TeX
31623 code or to the \SpecialChar LaTeX
31627 \begin_layout Standard
31637 \begin_inset Index idx
31640 \begin_layout Plain Layout
31654 \begin_layout Plain Layout
31670 \begin_inset Newline newline
31678 \begin_inset Newline newline
31690 \begin_layout Standard
31697 internally uses the command
31703 , described above, and would also need to be reverted.
31707 \begin_layout Plain Layout
31714 \begin_layout Plain Layout
31718 @removefromreset{equation}{section}
31721 \begin_layout Plain Layout
31733 \begin_layout Section
31734 Chemical Symbols and Equations
31735 \begin_inset CommandInset label
31737 name "subsec:Chemical-Symbols-and"
31742 \begin_inset Index idx
31745 \begin_layout Plain Layout
31746 Chemical characters ! Symbols
31752 \begin_inset Index idx
31755 \begin_layout Plain Layout
31762 \begin_inset Index idx
31765 \begin_layout Plain Layout
31774 \begin_layout Standard
31775 An example text from chemistry:
31778 \begin_layout Quote
31780 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31783 -ion reacts with two
31784 \begin_inset Formula $\mathrm{Na^{+}}$
31787 -ions to sodium sulfate
31788 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31792 The chemical equation for this is:
31793 \begin_inset Formula
31795 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31803 \begin_layout Standard
31804 Chemical equations can be created as formulas.
31805 To avoid the symbols appearing in italic, everything is highlighted and
31806 changed by the shortcut
31812 to the upright font style.
31816 \begin_layout Plain Layout
31822 \begin_inset CommandInset ref
31824 reference "subsec:Font-Styles"
31836 \begin_layout Standard
31837 A more convenient way to typeset chemical formulas is to use the command
31845 \begin_inset Index idx
31848 \begin_layout Plain Layout
31856 which is available when the \SpecialChar LaTeX
31862 \begin_inset Index idx
31865 \begin_layout Plain Layout
31878 in a formula a new blue box appears where chemical formulas can be inserted
31879 in an intuitive way.
31882 \begin_layout Standard
31884 \begin_inset Tabular
31885 <lyxtabular version="3" rows="10" columns="2">
31886 <features booktabs="true" tabularvalignment="middle">
31887 <column alignment="center" valignment="top" width="0pt">
31888 <column alignment="center" valignment="top">
31890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31893 \begin_layout Plain Layout
31899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31902 \begin_layout Plain Layout
31910 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31913 \begin_layout Plain Layout
31917 \begin_inset space \textvisiblespace{}
31925 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31928 \begin_layout Plain Layout
31929 \begin_inset Formula $\ce{H2CO3}$
31938 <row topspace="1.5mm">
31939 <cell alignment="center" valignment="top" usebox="none">
31942 \begin_layout Plain Layout
31946 \begin_inset space \textvisiblespace{}
31954 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31957 \begin_layout Plain Layout
31958 \begin_inset Formula $\ce{SO4^{2-}}$
31967 <row topspace="1.5mm">
31968 <cell alignment="center" valignment="top" usebox="none">
31971 \begin_layout Plain Layout
31975 \begin_inset space \textvisiblespace{}
31983 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31986 \begin_layout Plain Layout
31987 \begin_inset Formula $\ce{(NH4)2S}$
31996 <row topspace="1.5mm">
31997 <cell alignment="center" valignment="top" usebox="none">
32000 \begin_layout Plain Layout
32004 \begin_inset space \textvisiblespace{}
32012 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32015 \begin_layout Plain Layout
32016 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
32025 <row topspace="1.5mm">
32026 <cell alignment="center" valignment="top" usebox="none">
32029 \begin_layout Plain Layout
32033 \begin_inset space \textvisiblespace{}
32039 \begin_inset space \textvisiblespace{}
32045 \begin_inset space \textvisiblespace{}
32053 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32056 \begin_layout Plain Layout
32057 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
32066 <row topspace="1.5mm">
32067 <cell alignment="center" valignment="top" usebox="none">
32070 \begin_layout Plain Layout
32074 \begin_inset space \textvisiblespace{}
32078 \begin_inset Formula $\downarrow$
32082 \begin_inset Formula $\to$
32090 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32093 \begin_layout Plain Layout
32094 \begin_inset Formula $\ce{_{90}^{227}Th+}$
32104 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32107 \begin_layout Plain Layout
32111 \begin_inset space \textvisiblespace{}
32117 \begin_inset space \textvisiblespace{}
32123 \begin_inset space \textvisiblespace{}
32131 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32134 \begin_layout Plain Layout
32135 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
32145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32148 \begin_layout Plain Layout
32152 \begin_inset space \textvisiblespace{}
32156 \begin_inset space \textvisiblespace{}
32160 \begin_inset space \textvisiblespace{}
32164 \begin_inset space \textvisiblespace{}
32168 \begin_inset space \textvisiblespace{}
32176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32179 \begin_layout Plain Layout
32180 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
32189 <row topspace="1.5mm">
32190 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
32193 \begin_layout Plain Layout
32197 \begin_inset space \textvisiblespace{}
32201 \begin_inset space \textvisiblespace{}
32205 \begin_inset space \textvisiblespace{}
32209 \begin_inset space \textvisiblespace{}
32217 \begin_inset space \textvisiblespace{}
32225 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
32228 \begin_layout Plain Layout
32229 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
32245 \begin_layout Standard
32246 \begin_inset Note Greyedout
32249 \begin_layout Plain Layout
32254 It is not possible in \SpecialChar LyX
32255 to use the character ^ to get an up-arrow as described
32261 One instead uses a negative thin space followed by the command
32268 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32279 \begin_layout Standard
32286 the command for equation
32287 \begin_inset space ~
32291 \begin_inset CommandInset ref
32293 reference "eq:chem-reaction"
32298 \begin_inset Newline newline
32306 \begin_inset space \textvisiblespace{}
32310 \begin_inset space \textvisiblespace{}
32314 \begin_inset space \textvisiblespace{}
32318 \begin_inset space \textvisiblespace{}
32322 \begin_inset space \textvisiblespace{}
32326 \begin_inset space \textvisiblespace{}
32332 \begin_layout Standard
32333 To create multiline chemical equations first a multiline formula is created
32335 \begin_inset CommandInset ref
32337 reference "sec:Multiline-Formulas"
32342 Afterwards the command
32348 is used in every small blue box of the formula.
32350 \begin_inset CommandInset ref
32352 reference "eq:TEOS-reaction-1"
32357 \begin_inset CommandInset ref
32359 reference "eq:TEOS-reaction-2"
32363 are an example of a multi-stage chemical reaction where every equation
32364 has its own number.
32365 \begin_inset Formula
32367 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32368 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32376 \begin_layout Standard
32387 package provides the command
32394 \begin_inset Index idx
32397 \begin_layout Plain Layout
32405 that is used for special cases.
32406 For more information about
32412 and more examples have a look at the documentation of
32417 \begin_inset CommandInset citation
32427 \begin_layout Section
32431 \begin_layout Standard
32433 supports two types of commutative diagrams:
32441 and are explained below.
32444 \begin_layout Subsection
32446 \begin_inset Index idx
32449 \begin_layout Plain Layout
32458 \begin_layout Standard
32459 Diagrams of this type visualize relations by vertical and horizontal lines
32461 \begin_inset Formula
32463 \begin{CD}A@>>>B@>>>C\\
32474 \begin_layout Standard
32475 To create them, the command
32480 \begin_inset Index idx
32483 \begin_layout Plain Layout
32493 is inserted to a formula.
32494 A blue box appears with two dashed lines where additional commands can
32499 arg "newline-insert newline"
32502 a new line is created.
32503 Horizontal relations are inserted in odd formula lines, vertical in even
32507 \begin_layout Standard
32508 To create the relations use the following commands:
32511 \begin_layout Itemize
32516 creates a left arrow,
32527 \begin_layout Itemize
32532 creates an up arrow,
32540 a vertical equal sign
32543 \begin_layout Itemize
32549 is a placeholder for non-existent relations
32552 \begin_layout Standard
32553 All arrows can be labeled as follows:
32556 \begin_layout Itemize
32557 If text inserted between the first and second < or >, resp., it is placed
32559 When it is inserted between the second and third one, it appears under
32563 \begin_layout Itemize
32564 When text for vertical arrows is inserted between the first and second A
32565 or V, resp., it is placed left beside the arrow.
32566 When it is inserted between the second and third one, it appears right
32568 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32572 \begin_layout Standard
32573 As example a diagram with all possible relations:
32576 \begin_layout Standard
32577 \begin_inset Formula
32579 \begin{CD}A@>j>>B@>>k>C@=F\\
32590 \begin_layout Standard
32591 The command for this is:
32592 \begin_inset Newline newline
32600 \begin_inset space \textvisiblespace{}
32603 A@>j>>B@>>k>C@=F Ctrl+Return
32604 \begin_inset Newline newline
32608 \begin_inset Phantom HPhantom
32611 \begin_layout Plain Layout
32617 \begin_inset space \textvisiblespace{}
32630 \begin_inset Formula $\to$
32636 \begin_inset Newline newline
32640 \begin_inset Phantom HPhantom
32643 \begin_layout Plain Layout
32649 \begin_inset space \textvisiblespace{}
32660 \begin_layout Subsection
32662 \begin_inset Index idx
32665 \begin_layout Plain Layout
32666 Diagrams ! xymatrix
32674 \begin_layout Standard
32675 To be able to use xymatrices, the \SpecialChar LaTeX
32681 A xymatrix is created by inserting the command
32688 Then you are able to add new matrix columns and rows like for normal matrices,
32690 \begin_inset CommandInset ref
32692 reference "sec:Matrices"
32699 \begin_layout Standard
32700 Contrary to amscd diagrams, xymatrices support diagonal and curved arrows,
32702 The commands used to create commutative diagrams and decorations are explained
32709 Help\SpecialChar menuseparator
32711 \begin_inset space ~
32719 \begin_layout Subsection
32725 \begin_inset Index idx
32728 \begin_layout Plain Layout
32737 \begin_layout Standard
32742 -diagrams, the \SpecialChar LaTeX
32752 -diagram is created by inserting the command
32759 Then you will be able to add new matrix columns and rows like for normal
32761 \begin_inset CommandInset ref
32763 reference "sec:Matrices"
32770 \begin_layout Standard
32771 Examples of how to create
32775 diagrams in \SpecialChar LyX
32780 manual that you find in the menu
32782 Help\SpecialChar menuseparator
32784 \begin_inset space ~
32792 \begin_layout Section
32793 User-defined Commands
32794 \begin_inset Index idx
32797 \begin_layout Plain Layout
32798 User-defined commands
32806 \begin_layout Standard
32807 \begin_inset Note Greyedout
32810 \begin_layout Plain Layout
32815 The names of user-defined commands and macros may only consist of Latin
32824 \begin_layout Subsection
32828 \begin_inset CommandInset label
32830 name "subsec:The-Command-newcommand"
32835 \begin_inset Index idx
32838 \begin_layout Plain Layout
32839 User-defined commands !
32847 \begin_inset Index idx
32850 \begin_layout Plain Layout
32861 \begin_layout Standard
32862 Many \SpecialChar LaTeX
32863 -commands are too long to be used frequently.
32864 But it is possible to define with the command
32870 new shorter commands.
32873 \begin_layout Standard
32874 The command scheme of
32883 \begin_layout Standard
32888 newcommand{new command name}[number of arguments][optional
32893 \begin_inset Newline newline
32897 \begin_inset Phantom HPhantom
32900 \begin_layout Plain Layout
32910 {command definition}
32913 \begin_layout Standard
32914 \begin_inset Note Greyedout
32917 \begin_layout Plain Layout
32922 Verify that the name of the new command is not already used in your document
32923 or by the \SpecialChar LaTeX
32924 -packages that you use.
32925 If you for example define the command
32937 , you will get an error message because
32943 is already defined as command for
32944 \begin_inset Quotes eld
32948 \begin_inset Formula $\le$
32952 \begin_inset Quotes erd
32963 \begin_layout Standard
32964 The number of arguments is an integer in the range 0
32965 \begin_inset space \thinspace{}
32969 \begin_inset space \thinspace{}
32972 9 and specifies how many arguments the new command should have.
32973 With the optional value a value for an optional argument can be predefined.
32974 When this is done, the
32982 rgument of the new command is automatically an optional one.
32985 \begin_layout Standard
32986 Here are some examples:
32989 \begin_layout Itemize
32990 To define the command
33002 , the \SpecialChar LaTeX
33004 \begin_inset VSpace medskip
33008 \begin_inset Newline newline
33022 \begin_layout Itemize
33023 To define the command
33035 , the argument (that should be underlined) must be taken into account.
33036 For this the preamble line is:
33037 \begin_inset VSpace medskip
33041 \begin_inset Newline newline
33055 \begin_inset VSpace medskip
33059 \begin_inset Newline newline
33066 acts as argument placeholder, the
33070 behind it denotes that it is the placeholder for the first argument.
33073 \begin_layout Itemize
33081 \begin_inset space \thinspace{}
33085 \begin_inset space \space{}
33095 \begin_inset VSpace medskip
33099 \begin_inset Newline newline
33110 framebox#1#2{$#3$}}
33113 \begin_inset VSpace medskip
33117 \begin_inset Newline newline
33120 The two Dollar signs creates the extra formula needed for
33127 \begin_inset CommandInset ref
33129 reference "subsec:Boxes-with-Frame"
33136 \begin_layout Itemize
33137 To create a new command for
33143 where the color for the box need not be specified, the argument for the
33144 color is defined optional:
33145 \begin_inset VSpace medskip
33149 \begin_inset Newline newline
33160 fcolorbox{#2}{#1}{$#3$}}
33163 \begin_inset VSpace medskip
33167 \begin_inset Newline newline
33170 When the color is not specified when using
33176 , the predefined color
33183 \begin_layout Standard
33184 A test of the new defined commands:
33187 \begin_layout Standard
33189 \begin_inset Tabular
33190 <lyxtabular version="3" rows="6" columns="2">
33191 <features booktabs="true" tabularvalignment="middle">
33192 <column alignment="center" valignment="top" width="0pt">
33193 <column alignment="center" valignment="top">
33195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33198 \begin_layout Plain Layout
33204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33207 \begin_layout Plain Layout
33215 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33218 \begin_layout Plain Layout
33222 \begin_inset space \textvisiblespace{}
33230 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33233 \begin_layout Plain Layout
33234 \begin_inset Formula $A\gr B$
33244 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33247 \begin_layout Plain Layout
33255 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33258 \begin_layout Plain Layout
33259 \begin_inset Formula $\us{ABcd}$
33268 <row topspace="1mm">
33269 <cell alignment="center" valignment="top" usebox="none">
33272 \begin_layout Plain Layout
33276 \begin_inset Formula $\to$
33282 \begin_inset Formula $\to$
33290 \begin_inset space \textvisiblespace{}
33298 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33301 \begin_layout Plain Layout
33302 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33311 <row topspace="1.5mm">
33312 <cell alignment="center" valignment="top" usebox="none">
33315 \begin_layout Plain Layout
33319 \begin_inset Formula $\to$
33327 \begin_inset space \textvisiblespace{}
33335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33338 \begin_layout Plain Layout
33339 \begin_inset Formula $\cb{red}{\int A=B}$
33348 <row topspace="1.5mm" bottomspace="1mm">
33349 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33352 \begin_layout Plain Layout
33358 \begin_inset Formula $\to$
33366 \begin_inset space \textvisiblespace{}
33374 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33377 \begin_layout Plain Layout
33378 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33394 \begin_layout Subsection
33396 \begin_inset Index idx
33399 \begin_layout Plain Layout
33400 User-defined commands! Math macros
33406 \begin_inset Index idx
33409 \begin_layout Plain Layout
33418 \begin_layout Standard
33419 User-defined commands are especially convenient for complex expressions.
33420 For example if you are dealing with a document that has quadratic equations,
33421 the same solution type occurs several times.
33422 The general form of a quadratic equation is
33423 \begin_inset Formula
33425 0=\lambda^{2}+p\lambda+q
33430 The general form of the solution is
33431 \begin_inset Formula
33433 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33441 \begin_layout Standard
33442 To define a command for the solution formula where only the three parameters
33444 \begin_inset Formula $\lambda$
33448 \begin_inset Formula $p$
33452 \begin_inset Formula $q$
33455 need to be specified and the index of
33456 \begin_inset Formula $\lambda$
33459 can be given optionally, the \SpecialChar LaTeX
33461 \begin_inset Newline newline
33477 \begin_inset Newline newline
33481 \begin_inset Phantom HPhantom
33484 \begin_layout Plain Layout
33498 frac{#3^{2}}{4}-#4}}
33501 \begin_layout Standard
33502 To create with this the solution formula, the command
33503 \begin_inset Newline newline
33513 \begin_inset Formula $\to$
33519 \begin_inset Formula $\to$
33526 is inserted to a formula
33531 \begin_layout Standard
33532 The definition of the new command is unintuitive because one has to know
33533 the schemes of all used \SpecialChar LaTeX
33535 \begin_inset space \thinspace{}
33539 \begin_inset space \space{}
33542 that a fraction is inserted in \SpecialChar LaTeX
33547 frac{numerator}{denominator}
33550 Furthermore one can easily forget a brace in the definition and cannot
33551 see in \SpecialChar LyX
33552 what the new command is doing.
33553 To avoid these problems \SpecialChar LyX
33554 offers the possibility to use math macros instead
33564 \begin_layout Standard
33565 A math macro is created by using the menu
33567 Insert\SpecialChar menuseparator
33568 Math\SpecialChar menuseparator
33571 or the toolbar button
33574 arg "math-macro newmacroname_newcommand"
33578 The math macro toolbar appears together with the following box where the
33580 \begin_inset Newline newline
33584 \begin_inset space \hspace*{\fill}
33588 \begin_inset Graphics
33589 filename clipart/macrobox.png
33595 \begin_inset space \hspace*{\fill}
33599 \begin_inset Newline newline
33603 \begin_inset FormulaMacro
33604 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33609 newmacroname is the default name of the macro that should be changed to
33610 something sensible.
33611 The wanted formula is inserted in the first blue box.
33612 An argument placeholder is inserted with the command
33619 \begin_inset space \thinspace{}
33623 \begin_inset space \space{}
33632 or by using the macro toolbar button
33635 arg "math-macro-add-param"
33639 Argument placeholders are displayed red.
33641 \begin_inset space ~
33644 arguments are possible.
33645 Optional arguments are created with the toolbar button
33648 arg "math-macro-add-optional-param"
33652 The first non-optional argument can be transformed to an optional one with
33656 arg "math-macro-make-optional"
33660 In the second blue box the appearance of the macro in \SpecialChar LyX
33662 Normally you want to see it as it is defined, so the box is kept empty.
33663 But when you have created a macro that needs lot of space on the screen,
33664 you can insert in the box for example
33665 \begin_inset Newline newline
33695 \begin_inset Newline newline
33700 For the macro only the arguments with the macro name in front of them will
33701 then be displayed in \SpecialChar LyX
33702 , leading to a better overview.
33703 The formula appears in the output as defined in the first box.
33704 \begin_inset Newline newline
33707 The appearance of macros in formulas can furthermore be changed for single
33708 macros by setting the cursor in the macro and using the menu
33710 View\SpecialChar menuseparator
33712 \begin_inset space ~
33716 \begin_inset space ~
33724 \begin_layout Standard
33725 To use a macro, the macro name is inserted as command to a formula, in our
33733 Our macro looks in \SpecialChar LyX
33735 \begin_inset Newline newline
33739 \begin_inset space \hspace*{\fill}
33743 \begin_inset Graphics
33744 filename clipart/macrouse.png
33750 \begin_inset space \hspace*{\fill}
33754 \begin_inset Newline newline
33757 Here is our macro example with the arguments
33758 \begin_inset Formula $x$
33762 \begin_inset Formula $\ln(x)$
33766 \begin_inset Formula $B$
33772 \begin_layout Standard
33773 \begin_inset Formula
33783 \begin_layout Standard
33787 Tools\SpecialChar menuseparator
33788 Preferences\SpecialChar menuseparator
33789 Editing\SpecialChar menuseparator
33792 different styles to edit macros.
33793 To find the style that suits you best, choose a style and set the cursor
33794 in a macro formula to see the difference.
33797 \begin_layout Standard
33798 A math macro is transformed internally to a
33804 command when exporting the document.
33811 command is not placed in the \SpecialChar LaTeX
33812 -preamble, therefore macros can only be used
33813 in formulas that are in the document below the macro definition box.
33816 \begin_layout Standard
33817 Math macros can also be directly created from a
33824 When writing for example the command
33827 \begin_inset Newline newline
33836 xleftarrow[#2]{#1}}
33837 \begin_inset Newline newline
33842 in \SpecialChar LyX
33843 as normal text, highlighting it completely and using the shortcut
33847 , the command will be transformed to a math macro.
33848 Using this method you need to be careful that the
33854 command is typed correctly, otherwise you get a faulty macro leading to
33859 \begin_layout Standard
33860 Math macros currently have the problem that further formulas in macro definition
33861 s are handled wrong.
33862 Therefore the example
33869 \begin_inset CommandInset ref
33871 reference "subsec:The-Command-newcommand"
33875 cannot be created as macro.
33878 \begin_layout Standard
33879 When the cursor is in a macro definition box, you will see the macro toolbar
33880 in \SpecialChar LyX
33884 \begin_layout Standard
33885 \begin_inset VSpace defskip
33891 \begin_layout Standard
33892 \begin_inset Graphics
33893 filename clipart/MacroToolbar.png
33898 \begin_inset Index idx
33901 \begin_layout Plain Layout
33910 \begin_layout Standard
33911 \begin_inset VSpace defskip
33917 \begin_layout Standard
33918 The macro toolbar contains from left to right the following buttons:
33921 \begin_layout Standard
33922 \begin_inset VSpace defskip
33928 \begin_layout Standard
33929 \begin_inset Tabular
33930 <lyxtabular version="3" rows="9" columns="2">
33931 <features islongtable="true" longtabularalignment="center">
33932 <column alignment="left" valignment="top">
33933 <column alignment="left" valignment="top" width="85col%">
33934 <row interlinespace="2.5mm">
33935 <cell alignment="center" valignment="top" usebox="none">
33938 \begin_layout Plain Layout
33941 arg "math-macro-remove-param"
33949 <cell alignment="center" valignment="top" usebox="none">
33952 \begin_layout Plain Layout
33955 Edit\SpecialChar menuseparator
33956 Math\SpecialChar menuseparator
33958 \begin_inset space ~
33961 Definition\SpecialChar menuseparator
33962 Remove Last Argument
33968 <row interlinespace="2.5mm">
33969 <cell alignment="center" valignment="top" usebox="none">
33972 \begin_layout Plain Layout
33975 arg "math-macro-add-param"
33983 <cell alignment="center" valignment="top" usebox="none">
33986 \begin_layout Plain Layout
33989 Edit\SpecialChar menuseparator
33990 Math\SpecialChar menuseparator
33992 \begin_inset space ~
33995 Definition\SpecialChar menuseparator
34002 <row interlinespace="2.5mm">
34003 <cell alignment="center" valignment="top" usebox="none">
34006 \begin_layout Plain Layout
34009 arg "math-macro-make-optional"
34017 <cell alignment="center" valignment="top" usebox="none">
34020 \begin_layout Plain Layout
34023 Edit\SpecialChar menuseparator
34024 Math\SpecialChar menuseparator
34026 \begin_inset space ~
34029 Definition\SpecialChar menuseparator
34030 Transform First Non-Optional to
34031 \begin_inset Newline newline
34035 \begin_inset Phantom HPhantom
34038 \begin_layout Plain Layout
34041 Edit\SpecialChar menuseparator
34042 Math\SpecialChar menuseparator
34044 \begin_inset space ~
34047 Definition\SpecialChar menuseparator
34059 <row interlinespace="2.5mm">
34060 <cell alignment="center" valignment="top" usebox="none">
34063 \begin_layout Plain Layout
34066 arg "math-macro-make-nonoptional"
34074 <cell alignment="center" valignment="top" usebox="none">
34077 \begin_layout Plain Layout
34080 Edit\SpecialChar menuseparator
34081 Math\SpecialChar menuseparator
34083 \begin_inset space ~
34086 Definition\SpecialChar menuseparator
34087 Transform Last Optional to
34088 \begin_inset Newline newline
34092 \begin_inset Phantom HPhantom
34095 \begin_layout Plain Layout
34098 Edit\SpecialChar menuseparator
34099 Math\SpecialChar menuseparator
34101 \begin_inset space ~
34104 Definition\SpecialChar menuseparator
34110 Non-Optional Argument
34116 <row interlinespace="2.5mm">
34117 <cell alignment="center" valignment="top" usebox="none">
34120 \begin_layout Plain Layout
34123 arg "math-macro-remove-optional-param"
34131 <cell alignment="center" valignment="top" usebox="none">
34134 \begin_layout Plain Layout
34137 Edit\SpecialChar menuseparator
34138 Math\SpecialChar menuseparator
34140 \begin_inset space ~
34143 Definition\SpecialChar menuseparator
34144 Remove Optional Argument
34150 <row interlinespace="2.5mm">
34151 <cell alignment="center" valignment="top" usebox="none">
34154 \begin_layout Plain Layout
34157 arg "math-macro-add-optional-param"
34165 <cell alignment="center" valignment="top" usebox="none">
34168 \begin_layout Plain Layout
34171 Edit\SpecialChar menuseparator
34172 Math\SpecialChar menuseparator
34174 \begin_inset space ~
34177 Definition\SpecialChar menuseparator
34178 Insert Optional Argument
34184 <row interlinespace="2.5mm">
34185 <cell alignment="center" valignment="top" usebox="none">
34188 \begin_layout Plain Layout
34191 arg "math-macro-remove-greedy-param"
34199 <cell alignment="center" valignment="top" usebox="none">
34202 \begin_layout Plain Layout
34205 Edit\SpecialChar menuseparator
34206 Math\SpecialChar menuseparator
34208 \begin_inset space ~
34211 Definition\SpecialChar menuseparator
34212 Remove Last Argument
34213 \begin_inset Newline newline
34217 \begin_inset Phantom HPhantom
34220 \begin_layout Plain Layout
34223 Edit\SpecialChar menuseparator
34224 Math\SpecialChar menuseparator
34226 \begin_inset space ~
34229 Definition\SpecialChar menuseparator
34235 Spitting Out To The Right
34241 <row interlinespace="2.5mm">
34242 <cell alignment="center" valignment="top" usebox="none">
34245 \begin_layout Plain Layout
34248 arg "math-macro-append-greedy-param"
34256 <cell alignment="center" valignment="top" usebox="none">
34259 \begin_layout Plain Layout
34262 Edit\SpecialChar menuseparator
34263 Math\SpecialChar menuseparator
34265 \begin_inset space ~
34268 Definition\SpecialChar menuseparator
34270 \begin_inset Newline newline
34274 \begin_inset Phantom HPhantom
34277 \begin_layout Plain Layout
34280 Edit\SpecialChar menuseparator
34281 Math\SpecialChar menuseparator
34283 \begin_inset space ~
34286 Definition\SpecialChar menuseparator
34292 Eating From The Right
34298 <row interlinespace="2.5mm">
34299 <cell alignment="center" valignment="top" usebox="none">
34302 \begin_layout Plain Layout
34305 arg "math-macro-add-greedy-optional-param"
34313 <cell alignment="center" valignment="top" usebox="none">
34316 \begin_layout Plain Layout
34319 Edit\SpecialChar menuseparator
34320 Math\SpecialChar menuseparator
34322 \begin_inset space ~
34325 Definition\SpecialChar menuseparator
34326 Append Optional Argument
34327 \begin_inset Newline newline
34331 \begin_inset Phantom HPhantom
34334 \begin_layout Plain Layout
34337 Edit\SpecialChar menuseparator
34338 Math\SpecialChar menuseparator
34340 \begin_inset space ~
34343 Definition\SpecialChar menuseparator
34349 Eating From The Right
34362 \begin_layout Section
34363 Computer Algebra Systems
34366 \begin_layout Standard
34368 offers the exchange between mathematical expressions written in \SpecialChar LyX
34370 editor and external applications or user defined scripts.
34371 Currently supported applications are
34388 Note that the set of supported mathematical constructs is limited only
34389 to very simple cases.
34392 \begin_layout Subsection
34396 \begin_layout Standard
34397 Write some expression in a formula, go to the
34399 Edit\SpecialChar menuseparator
34400 Math\SpecialChar menuseparator
34401 Use Computer Algebra System
34403 menu and choose the application you have installed on the computer.
34404 After that the result of computation should show on the right side of the
34405 expression together with the
34406 \begin_inset Quotes eld
34410 \begin_inset Quotes erd
34416 \begin_layout Standard
34417 Here are few simple examples (with results from
34421 ) to show what kind of computations can be performed:
34424 \begin_layout Itemize
34425 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34431 \begin_layout Itemize
34432 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34438 \begin_layout Itemize
34439 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34445 \begin_layout Itemize
34446 \begin_inset Formula $\int\left(\frac{1}{1+x^{3}}\right)dx=-\frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\,x-1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log\left(x+1\right)}{3}$
34450 \begin_inset Newline newline
34454 \begin_inset Note Greyedout
34457 \begin_layout Plain Layout
34462 One needs to use proper delimiter insets
34463 \begin_inset Formula $\left(\right)$
34466 instead of simple '(' ')' characters.
34474 \begin_layout Itemize
34475 \begin_inset Formula $\det\left[\begin{array}{ccc}
34479 \end{array}\right]=-56$
34485 \begin_layout Itemize
34486 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34492 \begin_layout Itemize
34493 \begin_inset Formula $powerseries\left(-\log\left(5-x\right),x,1\right)=\sum_{{\mathit{i}_{2}}=0}^{\infty}{\frac{4^{-{\mathit{i}_{2}}-1}\,\left(x-1\right)^{{\mathit{i}_{2}}+1}}{{\mathit{i}_{2}}+1}}-\log4$
34499 \begin_layout Itemize
34500 \begin_inset Formula $solve\left(x_{1}+y_{1}^{3}=y_{1}+x_{1}^{2},x_{1}\right)=\left[x_{1}=-\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}-1}{2},x_{1}=\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}+1}{2}\right]$
34506 \begin_layout Subsection
34510 \begin_layout Standard
34511 Currently there is no keyboard shortcut for calling the algebra applications.
34512 One can easily bind a shortcut to the
34526 \begin_inset space \thinspace{}
34530 \begin_inset space \space{}
34537 key inside the math editor.
34542 one would use this shortcut definition command:
34545 \begin_layout Standard
34548 command-alternatives paragraph-break;math-extern maxima
34551 \begin_layout Section
34553 \begin_inset Index idx
34556 \begin_layout Plain Layout
34565 \begin_layout Subsection
34567 \begin_inset Index idx
34570 \begin_layout Plain Layout
34579 \begin_layout Standard
34580 Negative numbers often look ugly in formulas because the minus sign before
34581 the number is set with the same length as the minus operator sign.
34582 When writing the negative number in normal text, the minus sign appears
34586 \begin_layout Standard
34587 Thus, the problem disappears when converting the minus sign to mathematical
34591 \begin_layout Standard
34592 An example to visualize the problem:
34595 \begin_layout Standard
34597 \begin_inset Tabular
34598 <lyxtabular version="3" rows="3" columns="2">
34599 <features booktabs="true" tabularvalignment="middle">
34600 <column alignment="right" valignment="top" width="0pt">
34601 <column alignment="left" valignment="top">
34603 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34606 \begin_layout Plain Layout
34612 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34615 \begin_layout Plain Layout
34623 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34626 \begin_layout Plain Layout
34632 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34635 \begin_layout Plain Layout
34636 \begin_inset Formula $x=-2$
34646 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34649 \begin_layout Plain Layout
34655 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34658 \begin_layout Plain Layout
34659 \begin_inset Formula $x=\textrm{-}2$
34675 \begin_layout Subsection
34676 Comma as decimal Separator
34677 \begin_inset Index idx
34680 \begin_layout Plain Layout
34689 \begin_layout Standard
34690 In \SpecialChar LaTeX
34691 a comma inside a formula is used, according to the English convention,
34692 as number group separator.
34693 So there will be space added behind all commas in formulas.
34696 \begin_layout Standard
34697 To avoid this, the comma is highlighted and changed to mathematical text
34707 \begin_layout Standard
34708 To use all formula commas in the document as decimal separator, the file
34717 \begin_layout Plain Layout
34722 is part of the \SpecialChar LaTeX
34728 \begin_inset Index idx
34731 \begin_layout Plain Layout
34736 \begin_layout Plain Layout
34756 \begin_inset Index idx
34759 \begin_layout Plain Layout
34765 is loaded with the \SpecialChar LaTeX
34769 \begin_layout Standard
34777 \begin_layout Subsection
34779 \begin_inset CommandInset label
34781 name "subsec:Physical-Vectors"
34786 \begin_inset Index idx
34789 \begin_layout Plain Layout
34798 \begin_layout Standard
34799 Predefined vectors are offered by the \SpecialChar LaTeX
34805 \begin_inset Index idx
34808 \begin_layout Plain Layout
34814 that is loaded with the \SpecialChar LaTeX
34818 \begin_layout Standard
34826 \begin_layout Standard
34830 \begin_layout Plain Layout
34840 \begin_inset Note Note
34843 \begin_layout Plain Layout
34844 The following table will only be displayed when the \SpecialChar LaTeX
34857 \begin_layout Standard
34858 The following commands are defined:
34861 \begin_layout Standard
34863 \begin_inset Tabular
34864 <lyxtabular version="3" rows="4" columns="2">
34865 <features booktabs="true" tabularvalignment="middle">
34866 <column alignment="center" valignment="top" width="0pt">
34867 <column alignment="center" valignment="top">
34869 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34872 \begin_layout Plain Layout
34878 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34881 \begin_layout Plain Layout
34889 <cell alignment="center" valignment="top" usebox="none">
34892 \begin_layout Plain Layout
34902 <cell alignment="center" valignment="top" usebox="none">
34905 \begin_layout Plain Layout
34906 \begin_inset Formula $\Bra{\psi}$
34916 <cell alignment="center" valignment="top" usebox="none">
34919 \begin_layout Plain Layout
34929 <cell alignment="center" valignment="top" usebox="none">
34932 \begin_layout Plain Layout
34933 \begin_inset Formula $\Ket{\psi}$
34943 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34946 \begin_layout Plain Layout
34958 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34961 \begin_layout Plain Layout
34962 \begin_inset Formula $\Braket{\psi|\phi}$
34978 \begin_layout Standard
34985 assures that all vertical bars are set in the size of the surrounding brackets:
34986 \begin_inset Formula
34988 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34997 \begin_layout Plain Layout
35007 \begin_inset Note Note
35010 \begin_layout Plain Layout
35011 The following will be displayed when the \SpecialChar LaTeX
35024 \begin_layout Standard
35025 You need to install the \SpecialChar LaTeX
35030 to see the rest of this subsection in the output.
35033 \begin_layout Standard
35037 \begin_layout Plain Layout
35049 \begin_layout Standard
35056 can also be achieved using the command
35062 , that is described in
35063 \begin_inset CommandInset ref
35065 reference "subsec:Automatic-Bracket-Size"
35072 \begin_layout Subsection
35073 Self-defined Fractions
35074 \begin_inset CommandInset label
35076 name "subsec:Self-defined-Fractions"
35081 \begin_inset Index idx
35084 \begin_layout Plain Layout
35085 Fractions ! self-defined
35093 \begin_layout Standard
35094 To define custom commands for fractions, the command
35101 \begin_inset Index idx
35104 \begin_layout Plain Layout
35111 \begin_layout Plain Layout
35125 is used in the following scheme:
35128 \begin_layout Standard
35141 bracket}{fraction bar thickness}{style}
35142 \begin_inset Newline newline
35146 \begin_inset Phantom HPhantom
35149 \begin_layout Plain Layout
35159 {numerator}{denominator}
35162 \begin_layout Standard
35163 The style is a number in the range of 0
35164 \begin_inset space \thinspace{}
35168 \begin_inset space \thinspace{}
35174 \begin_layout Standard
35176 \begin_inset Tabular
35177 <lyxtabular version="3" rows="5" columns="2">
35178 <features booktabs="true" tabularvalignment="middle">
35179 <column alignment="center" valignment="top" width="0pt">
35180 <column alignment="center" valignment="top">
35182 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35185 \begin_layout Plain Layout
35191 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35194 \begin_layout Plain Layout
35202 <cell alignment="center" valignment="top" usebox="none">
35205 \begin_layout Plain Layout
35211 <cell alignment="center" valignment="top" usebox="none">
35214 \begin_layout Plain Layout
35215 display style formula
35222 <cell alignment="center" valignment="top" usebox="none">
35225 \begin_layout Plain Layout
35231 <cell alignment="center" valignment="top" usebox="none">
35234 \begin_layout Plain Layout
35242 <cell alignment="center" valignment="top" usebox="none">
35245 \begin_layout Plain Layout
35251 <cell alignment="center" valignment="top" usebox="none">
35254 \begin_layout Plain Layout
35262 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35265 \begin_layout Plain Layout
35271 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35274 \begin_layout Plain Layout
35288 \begin_layout Standard
35289 When no style is given, the size is adjusted to the surrounding environment
35290 like for the command
35299 \begin_layout Standard
35300 When no fraction bar thickness is given, the predefined value of 0.4
35301 \begin_inset space \thinspace{}
35307 \begin_layout Standard
35308 \begin_inset VSpace medskip
35311 For example, the commands
35324 \begin_inset CommandInset ref
35326 reference "subsec:Fractions"
35330 are defined with the commands
35333 \begin_layout Standard
35342 genfrac{}{}{}{0}{#1}{#2}}
35345 \begin_layout Standard
35349 \begin_layout Standard
35358 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35361 \begin_layout Standard
35362 \begin_inset VSpace medskip
35365 To define a fraction where the fraction bar thickness can be given as optional
35366 argument, the following line is inserted to the \SpecialChar LaTeX
35370 \begin_layout Standard
35379 genfrac{}{}{#1}{}{#2}{#3}}
35382 \begin_layout Standard
35384 \begin_inset Formula
35386 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35387 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35392 As one can see, the distance of the numerator and the denominator to the
35393 fraction bar is round about three times the bar thickness.
35396 \begin_layout Subsection
35398 \begin_inset Index idx
35401 \begin_layout Plain Layout
35410 \begin_layout Standard
35411 There are four ways to cancel formulas or parts of formulas:
35414 \begin_layout Standard
35418 \begin_layout Plain Layout
35428 \begin_inset Note Note
35431 \begin_layout Plain Layout
35432 The following table will only be displayed when the \SpecialChar LaTeX
35445 \begin_layout Standard
35447 \begin_inset Tabular
35448 <lyxtabular version="3" rows="5" columns="2">
35449 <features booktabs="true" tabularvalignment="middle">
35450 <column alignment="center" valignment="top" width="0pt">
35451 <column alignment="center" valignment="top">
35453 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35456 \begin_layout Plain Layout
35462 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35465 \begin_layout Plain Layout
35473 <cell alignment="center" valignment="top" usebox="none">
35476 \begin_layout Plain Layout
35480 \begin_inset space \textvisiblespace{}
35486 \begin_inset space \textvisiblespace{}
35494 <cell alignment="center" valignment="top" usebox="none">
35497 \begin_layout Plain Layout
35498 \begin_inset Formula $\cancel{\int A=B}$
35507 <row topspace="1.5mm">
35508 <cell alignment="center" valignment="top" usebox="none">
35511 \begin_layout Plain Layout
35515 \begin_inset space \textvisiblespace{}
35521 \begin_inset space \textvisiblespace{}
35529 <cell alignment="center" valignment="top" usebox="none">
35532 \begin_layout Plain Layout
35533 \begin_inset Formula $\bcancel{\int A=B}$
35542 <row topspace="1.5mm">
35543 <cell alignment="center" valignment="top" usebox="none">
35546 \begin_layout Plain Layout
35550 \begin_inset space \textvisiblespace{}
35556 \begin_inset space \textvisiblespace{}
35564 <cell alignment="center" valignment="top" usebox="none">
35567 \begin_layout Plain Layout
35568 \begin_inset Formula $\xcancel{\int A=B}$
35578 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35581 \begin_layout Plain Layout
35585 \begin_inset space \textvisiblespace{}
35591 \begin_inset space \textvisiblespace{}
35595 \begin_inset Formula $\to$
35603 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35606 \begin_layout Plain Layout
35607 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35623 \begin_layout Standard
35630 is especially suitable to visualize the reduction of fractions within formulas:
35631 \begin_inset Formula
35633 \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}}}
35641 \begin_layout Standard
35642 To change the size of
35649 \begin_inset Quotes eld
35653 \begin_inset Quotes erd
35656 value one can add the \SpecialChar LaTeX
35660 \begin_layout Standard
35665 PassOptionsToPackage{option}{cancel}
35668 \begin_layout Standard
35677 which leads to the same size as for the canceled value, or
35681 which makes is it a bit smaller than normal.
35684 \begin_layout Standard
35685 To color the cancellation bar one adds this command as \SpecialChar TeX
35689 \begin_layout Standard
35701 \begin_layout Standard
35706 can be replaced by a color of your choice.
35709 \begin_layout Standard
35713 \begin_layout Plain Layout
35729 \begin_layout Standard
35730 \begin_inset Formula
35732 \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}}}
35740 \begin_layout Standard
35744 \begin_layout Plain Layout
35758 \begin_inset Note Note
35761 \begin_layout Plain Layout
35770 \begin_layout Standard
35771 For further customizations, see the documentation of the package
35776 \begin_inset CommandInset citation
35784 \begin_inset Index idx
35787 \begin_layout Plain Layout
35796 \begin_layout Standard
35800 \begin_layout Plain Layout
35810 \begin_inset Note Note
35813 \begin_layout Plain Layout
35814 The following will be displayed when the \SpecialChar LaTeX
35827 \begin_layout Standard
35828 You need to install the \SpecialChar LaTeX
35833 to see the rest of this subsection in the output.
35836 \begin_layout Standard
35840 \begin_layout Plain Layout
35852 \begin_layout Subsection
35853 Formulas in Section Headings
35854 \begin_inset CommandInset label
35856 name "subsec:Formulas-in-Section"
35861 \begin_inset Index idx
35864 \begin_layout Plain Layout
35865 Formula ! in section headings
35873 \begin_layout Standard
35874 When formulas are used in section headings, the following has to be taken
35878 \begin_layout Standard
35879 \begin_inset Note Greyedout
35882 \begin_layout Plain Layout
35888 \begin_inset Index idx
35891 \begin_layout Plain Layout
35892 Packages ! hyperref
35897 support is enabled in the document settings dialog under
35900 \begin_inset space ~
35905 , PDF-bookmarks are created for every section heading in the table of contents.
35906 If a section heading contains formulas, they are incorrectly displayed
35907 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35916 \begin_layout Standard
35917 Both problems can be solved by inserting at the end of the section heading
35918 a short title with the menu
35920 Insert\SpecialChar menuseparator
35922 \begin_inset space ~
35928 Short titles are used as alternative for multiline section headings to
35929 keep the table of contents clearly arranged.
35930 Only the short title appears in the table of contents and therefore also
35931 in the PDF-bookmark.
35934 \begin_layout Standard
35935 When formulas should be used in the table of contents but
35939 is used, one can use the following command in \SpecialChar TeX
35943 \begin_layout Standard
35948 texorpdfstring{part}{alternative}
35949 \begin_inset Index idx
35952 \begin_layout Plain Layout
35963 \begin_layout Standard
35964 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35965 This can be characters, formulas, footnotes, but also cross-references.
35966 The alternative is used instead of the part for the bookmark.
35969 \begin_layout Standard
35970 Here are two example headings:
35971 \begin_inset VSpace -3mm
35978 \begin_layout Plain Layout
35990 \begin_layout Subsubsection
35991 Heading without formula in table of contents
35992 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35996 \begin_inset Argument 1
35999 \begin_layout Plain Layout
36000 Heading without formula in table of contents
36008 \begin_layout Subsubsection
36009 Heading with formula in table of contents
36013 \begin_layout Plain Layout
36023 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36030 \begin_layout Plain Layout
36040 \begin_layout Standard
36044 \begin_layout Plain Layout
36053 In the first heading a short title was used, in the second one
36062 \begin_layout Standard
36063 To get the same formatting as for the other headings, the complete heading
36072 \begin_layout Plain Layout
36074 \begin_inset CommandInset ref
36076 reference "subsec:Bold-Formulas"
36088 \begin_layout Subsection
36089 Formulas in multi-column Text
36090 \begin_inset Index idx
36093 \begin_layout Plain Layout
36094 Formula ! in multi-column text
36102 \begin_layout Standard
36103 Formulas in multi-column text are often too wide to fit into a column and
36104 thus need to be set over the whole page width.
36105 This is done by using the \SpecialChar LaTeX
36114 \begin_layout Plain Layout
36119 is part of every \SpecialChar LaTeX
36120 standard installation.
36126 \begin_inset Index idx
36129 \begin_layout Plain Layout
36130 Packages ! multicol
36135 , that is loaded with the \SpecialChar LaTeX
36139 \begin_layout Standard
36144 usepackage{multicol}
36147 \begin_layout Standard
36148 \begin_inset Note Greyedout
36151 \begin_layout Plain Layout
36152 Note that in this case the setting
36155 \begin_inset space ~
36162 Document\SpecialChar menuseparator
36168 \begin_inset space ~
36188 \begin_layout Standard
36189 Before the multi-column text the command
36192 \begin_layout Standard
36197 begin{multicols}{column number}
36200 \begin_layout Standard
36201 is written in \SpecialChar TeX
36203 The column number is a number in the range of 2
36204 \begin_inset space \thinspace{}
36208 \begin_inset space \thinspace{}
36212 Before the formula the multi-column text is ended by inserting the command
36215 \begin_layout Standard
36223 \begin_layout Standard
36224 in \SpecialChar TeX
36228 \begin_layout Standard
36229 Due to the command some space is automatically added before the formula.
36230 To correct this, -6
36231 \begin_inset space \thinspace{}
36234 mm vertical space is inserted before the formula.
36235 When the formula style
36241 \begin_layout Plain Layout
36242 For formula styles see
36243 \begin_inset CommandInset ref
36245 reference "sec:Formula-Styles"
36257 \begin_inset space \thinspace{}
36260 mm space is inserted instead.
36263 \begin_layout Standard
36264 As example a multi-column text with a displayed formula:
36267 \begin_layout Standard
36273 \begin_layout Plain Layout
36277 begin{multicols}{2}
36282 Das Spektrum wird fouriertransformiert.
36283 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36284 , Lösungsmittel) zu trennen.
36285 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36286 nun das Aussehen des Ausgangssignals.
36287 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36288 über alle Phasen integrieren muss.
36290 \begin_inset Formula $S$
36293 unser normiertes Ausgangssignal und
36294 \begin_inset Formula $P$
36297 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36301 \begin_layout Plain Layout
36311 \begin_inset VSpace -6mm
36315 \begin_inset Formula
36317 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36326 \begin_layout Plain Layout
36330 begin{multicols}{2}
36336 \begin_inset Formula $S_{0}$
36339 das Signal ohne Gradient ist und die Normierungsbedingung
36340 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36344 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36346 \begin_inset Formula $\nicefrac{\pi}{2}$
36350 \begin_inset space \thinspace{}
36353 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36354 das Signal zusätzlich abschwächt.
36355 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36357 \begin_inset Formula $T_{2}$
36363 \begin_layout Standard
36369 \begin_layout Plain Layout
36381 \begin_layout Subsection
36382 Formulas with Description of Variables
36383 \begin_inset Index idx
36386 \begin_layout Plain Layout
36387 Formula ! with description of variables
36395 \begin_layout Standard
36396 To describe variables within a formula, like in formula
36397 \begin_inset CommandInset ref
36399 reference "eq:within"
36408 \begin_inset Formula $n$
36412 \begin_inset space ~
36415 matrix is used with left aligned columns for the
36416 \begin_inset Formula $n$
36423 \begin_layout Plain Layout
36425 \begin_inset CommandInset ref
36427 reference "sec:Matrices"
36436 To set the description in a smaller size, before the matrix e.
36437 \begin_inset space \thinspace{}
36441 \begin_inset space \space{}
36454 \begin_layout Plain Layout
36456 \begin_inset CommandInset ref
36458 reference "subsec:Font-Sizes"
36470 \begin_layout Standard
36471 When the formula style
36477 \begin_layout Plain Layout
36478 For formula styles see
36479 \begin_inset CommandInset ref
36481 reference "sec:Formula-Styles"
36502 \begin_layout Plain Layout
36509 only works in formulas with the style
36514 \begin_inset CommandInset ref
36516 reference "subsec:Variable-Space"
36525 is inserted before and after the matrix to have the same separation of
36526 the matrix from the equation and the side margin.
36529 \begin_layout Standard
36530 When the formula style
36534 is used, the method described in
36535 \begin_inset CommandInset ref
36537 reference "subsec:Flalign-Environment"
36541 is used to indent formulas.
36543 \begin_inset CommandInset ref
36545 reference "eq:within"
36549 consists of five columns where in the first two columns contain the equation,
36550 the third the matrix and the last one an empty \SpecialChar TeX
36552 \begin_inset Formula
36554 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36555 \rho & \textrm{density}\\
36556 V & \textrm{volume}\\
36557 g & \textrm{gravitational acceleration}
36558 \end{array} & & {}\label{eq:within}
36566 \begin_layout Subsection
36567 Upright small Greek Letters
36568 \begin_inset CommandInset label
36570 name "subsec:Upright-small-Greek"
36575 \begin_inset Index idx
36578 \begin_layout Plain Layout
36579 Greek letters ! upright
36587 \begin_layout Standard
36588 Most of the math fonts only provide italic small Greek letters.
36589 But for symbols of elementary particles like pions and neutrinos, upright
36590 Greek letters are needed.
36599 \begin_layout Plain Layout
36604 is part of the \SpecialChar LaTeX
36610 \begin_inset Index idx
36613 \begin_layout Plain Layout
36618 \begin_layout Plain Layout
36638 \begin_inset Index idx
36641 \begin_layout Plain Layout
36647 that is loaded with the \SpecialChar LaTeX
36651 \begin_layout Standard
36656 usepackage{upgreek}
36659 \begin_layout Standard
36665 \begin_layout Plain Layout
36675 \begin_inset Note Note
36678 \begin_layout Plain Layout
36679 The following table will only be displayed when the \SpecialChar LaTeX
36689 They are created when the command for a small Greek letter is started with
36695 For example the command
36702 \begin_inset Formula $\uptau$
36708 \begin_layout Standard
36709 With these commands reactions of elementary particles can be typeset:
36710 \begin_inset Formula
36712 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36720 \begin_layout Standard
36721 The upright letters are more bold and wider than the italic ones.
36722 They should therefore not be used for units like
36723 \begin_inset Quotes eld
36727 \begin_inset Quotes erd
36733 \begin_layout Standard
36737 \begin_layout Plain Layout
36747 \begin_inset Note Note
36750 \begin_layout Plain Layout
36751 The following will be displayed when the \SpecialChar LaTeX
36764 \begin_layout Standard
36765 You need to install the \SpecialChar LaTeX
36770 to see the rest of this subsection in the output.
36773 \begin_layout Standard
36777 \begin_layout Plain Layout
36789 \begin_layout Subsection
36790 Text Characters in Formulas
36791 \begin_inset Index idx
36794 \begin_layout Plain Layout
36803 \begin_layout Standard
36804 In some cases you might want to insert text characters directly into formulas.
36805 For example the centered dot · is often used in formulas like
36806 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36810 One would have to insert the command
36820 \begin_layout Plain Layout
36822 \begin_inset CommandInset ref
36824 reference "subsec:Binary-Operators"
36833 all the time, because this character is defined in all encodings as a text
36835 But the encoding can be changed by this \SpecialChar LaTeX
36839 \begin_layout Standard
36844 Declare Inputtext{183}{
36854 f\SpecialChar ligaturebreak
36858 \begin_layout Standard
36859 The character encoding (menu
36861 Document\SpecialChar menuseparator
36862 Settings\SpecialChar menuseparator
36865 ) specifies what character appears when a keyboard key is pressed.
36866 When the key for the character '·' is pressed, internally the command
36873 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36875 With the changed encoding the correct command is chosen automatically,
36876 depending on if the character was inserted into a formula or not.
36879 \begin_layout Standard
36880 The encoding of several characters is saved in definition files.
36881 For example the encoding
36885 is defined in the file
36889 which is in the installation folder of \SpecialChar LaTeX
36891 Encodings should only be changed via the \SpecialChar LaTeX
36892 -preamble and not in the definition
36894 Otherwise documents could not be edited by other \SpecialChar LyX
36895 users working on other
36899 \begin_layout Standard
36900 \begin_inset VSpace medskip
36903 Besides the centered dot, in this document the degree sign ° is defined
36904 with the following \SpecialChar LaTeX
36905 -preamble line so that it can be directly inserted into
36909 \begin_layout Standard
36914 DeclareInputtext{176}{
36924 f\SpecialChar ligaturebreak
36928 \begin_layout Subsection
36930 -comments in formulas
36931 \begin_inset Index idx
36934 \begin_layout Plain Layout
36944 \begin_layout Standard
36945 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36947 code of your file with the menu
36949 Insert\SpecialChar menuseparator
36950 Note\SpecialChar menuseparator
36954 This is not possible in a formula but you can insert \SpecialChar LaTeX
36959 \begin_layout Standard
36967 \begin_layout Standard
36968 This creates a box in which you can write your comment.
36969 Due to a bug in \SpecialChar LyX
36974 \begin_layout Plain Layout
36975 \begin_inset CommandInset href
36977 name "LyX-bug #9002"
36978 target "https://www.lyx.org/trac/ticket/9002"
36988 you cannot write normal text inside the comment, even when you use mathematical
36989 text, you will see its \SpecialChar LaTeX
36990 -commands in the \SpecialChar LaTeX
36992 \begin_inset Newline newline
36995 This a formula with a \SpecialChar LaTeX
36997 \begin_inset Formula
36999 A=B%\text{This is the comment}
37007 \begin_layout Standard
37008 \begin_inset Newpage newpage
37014 \begin_layout Section
37017 \begin_inset Index idx
37020 \begin_layout Plain Layout
37029 \begin_layout Standard
37030 This section is a summary of the most important typographic rules, listed
37035 \begin_layout Plain Layout
37036 This collection was partly taken from the German semi-official dictionary
37038 \begin_inset Quotes eld
37042 \begin_inset Quotes erd
37046 \begin_inset CommandInset citation
37053 that lists some of the ISO rules.
37054 More rules are listed in
37055 \begin_inset CommandInset citation
37070 \begin_layout Itemize
37079 \begin_layout Plain Layout
37080 Done with font styles, see
37081 \begin_inset CommandInset ref
37083 reference "subsec:Font-Styles"
37092 , no matter if they appear in italic text: 30
37093 \begin_inset space \thinspace{}
37097 \begin_inset Newline newline
37100 Between the value and the unit is the smallest space, see
37101 \begin_inset CommandInset ref
37103 reference "subsec:Predefined-Space"
37108 \begin_inset Newline newline
37111 This convention is automatically fulfilled when the command
37118 When it is entered in a formula, two boxes appear.
37119 In the first one the value is inserted, in the second one the unit, and
37120 the result is as above:
37121 \begin_inset Formula $\unit[30]{km/h}$
37125 \begin_inset space \thinspace{}
37135 is not a real \SpecialChar LaTeX
37136 command but the command
37142 , therefore you cannot use it in \SpecialChar TeX
37146 \begin_layout Itemize
37147 Percent and perthousand signs are set like physical units:
37148 \begin_inset Newline newline
37152 \begin_inset space \thinspace{}
37158 \begin_layout Itemize
37159 The degree sign follows the value directly: 15°, except when it is used
37161 \begin_inset space \thinspace{}
37167 \begin_layout Itemize
37168 In numbers with more than four digits the smallest space is inserted before
37169 every third digit to group them:
37179 \begin_inset space \thinspace{}
37183 \begin_inset space \thinspace{}
37189 \begin_layout Itemize
37190 For dimensions like 120×90×40
37191 \begin_inset space \thinspace{}
37194 cm the multiplication sign
37195 \begin_inset Quotes eld
37199 \begin_inset Quotes erd
37203 It is available either via the command
37211 Insert\SpecialChar menuseparator
37212 Special Character\SpecialChar menuseparator
37218 \begin_layout Itemize
37219 Functions with names consisting of several letters are set upright to avoid
37221 \begin_inset CommandInset ref
37223 reference "subsec:Predefined-Functions"
37230 \begin_layout Itemize
37231 Indices consisting of several letters, are set upright:
37232 \begin_inset Formula $E_{\mathrm{kin}}$
37236 \begin_inset Newline newline
37239 Components of matrices are set italic:
37240 \begin_inset Formula $\hat{H}_{kl}$
37246 \begin_layout Itemize
37247 The differentiation/integration operator 'd', the Euler's number 'e' and
37248 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37252 \begin_layout Itemize
37253 The character that denotes a
37257 transformation is inserted either by the command
37262 \begin_inset space \textvisiblespace{}
37269 Insert\SpecialChar menuseparator
37270 Special Character\SpecialChar menuseparator
37271 Symbols\SpecialChar menuseparator
37273 \begin_inset space ~
37279 \begin_inset Formula $\mathscr{F}$
37285 \begin_layout Standard
37286 \begin_inset Newpage newpage
37292 \begin_layout Section
37294 \begin_inset Index idx
37297 \begin_layout Plain Layout
37306 \begin_layout Standard
37307 Some characters and symbols can be created with several commands.
37308 Here is a list of the synonym commands:
37311 \begin_layout Standard
37312 \begin_inset VSpace bigskip
37316 \begin_inset space \hfill{}
37320 \begin_inset Tabular
37321 <lyxtabular version="3" rows="12" columns="2">
37322 <features booktabs="true" tabularvalignment="middle">
37323 <column alignment="center" valignment="top" width="0pt">
37324 <column alignment="center" valignment="top" width="0pt">
37326 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37329 \begin_layout Plain Layout
37335 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37338 \begin_layout Plain Layout
37346 <cell alignment="center" valignment="top" usebox="none">
37349 \begin_layout Plain Layout
37357 <cell alignment="center" valignment="top" usebox="none">
37360 \begin_layout Plain Layout
37368 <cell alignment="center" valignment="top" usebox="none">
37371 \begin_layout Plain Layout
37379 <cell alignment="center" valignment="top" usebox="none">
37382 \begin_layout Plain Layout
37392 <cell alignment="center" valignment="top" usebox="none">
37395 \begin_layout Plain Layout
37403 <cell alignment="center" valignment="top" usebox="none">
37406 \begin_layout Plain Layout
37416 <cell alignment="center" valignment="top" usebox="none">
37419 \begin_layout Plain Layout
37427 <cell alignment="center" valignment="top" usebox="none">
37430 \begin_layout Plain Layout
37438 <cell alignment="center" valignment="top" usebox="none">
37441 \begin_layout Plain Layout
37449 <cell alignment="center" valignment="top" usebox="none">
37452 \begin_layout Plain Layout
37460 <cell alignment="center" valignment="top" usebox="none">
37463 \begin_layout Plain Layout
37471 <cell alignment="center" valignment="top" usebox="none">
37474 \begin_layout Plain Layout
37484 <cell alignment="center" valignment="top" usebox="none">
37487 \begin_layout Plain Layout
37495 <cell alignment="center" valignment="top" usebox="none">
37498 \begin_layout Plain Layout
37508 <cell alignment="center" valignment="top" usebox="none">
37511 \begin_layout Plain Layout
37519 <cell alignment="center" valignment="top" usebox="none">
37522 \begin_layout Plain Layout
37532 <cell alignment="center" valignment="top" usebox="none">
37535 \begin_layout Plain Layout
37543 <cell alignment="center" valignment="top" usebox="none">
37546 \begin_layout Plain Layout
37556 <cell alignment="center" valignment="top" usebox="none">
37559 \begin_layout Plain Layout
37567 <cell alignment="center" valignment="top" usebox="none">
37570 \begin_layout Plain Layout
37578 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37581 \begin_layout Plain Layout
37589 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37592 \begin_layout Plain Layout
37604 \begin_inset space \hfill{}
37608 \begin_inset Tabular
37609 <lyxtabular version="3" rows="12" columns="2">
37610 <features booktabs="true" tabularvalignment="middle">
37611 <column alignment="center" valignment="top" width="0pt">
37612 <column alignment="center" valignment="top" width="0pt">
37614 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37617 \begin_layout Plain Layout
37623 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37626 \begin_layout Plain Layout
37634 <cell alignment="center" valignment="top" usebox="none">
37637 \begin_layout Plain Layout
37645 <cell alignment="center" valignment="top" usebox="none">
37648 \begin_layout Plain Layout
37660 <cell alignment="center" valignment="top" usebox="none">
37663 \begin_layout Plain Layout
37671 <cell alignment="center" valignment="top" usebox="none">
37674 \begin_layout Plain Layout
37684 <cell alignment="center" valignment="top" usebox="none">
37687 \begin_layout Plain Layout
37695 <cell alignment="center" valignment="top" usebox="none">
37698 \begin_layout Plain Layout
37708 <cell alignment="center" valignment="top" usebox="none">
37711 \begin_layout Plain Layout
37719 <cell alignment="center" valignment="top" usebox="none">
37722 \begin_layout Plain Layout
37730 <cell alignment="center" valignment="top" usebox="none">
37733 \begin_layout Plain Layout
37741 <cell alignment="center" valignment="top" usebox="none">
37744 \begin_layout Plain Layout
37752 <cell alignment="center" valignment="top" usebox="none">
37755 \begin_layout Plain Layout
37763 <cell alignment="center" valignment="top" usebox="none">
37766 \begin_layout Plain Layout
37776 <cell alignment="center" valignment="top" usebox="none">
37779 \begin_layout Plain Layout
37787 <cell alignment="center" valignment="top" usebox="none">
37790 \begin_layout Plain Layout
37800 <cell alignment="center" valignment="top" usebox="none">
37803 \begin_layout Plain Layout
37811 <cell alignment="center" valignment="top" usebox="none">
37814 \begin_layout Plain Layout
37824 <cell alignment="center" valignment="top" usebox="none">
37827 \begin_layout Plain Layout
37835 <cell alignment="center" valignment="top" usebox="none">
37838 \begin_layout Plain Layout
37848 <cell alignment="center" valignment="top" usebox="none">
37851 \begin_layout Plain Layout
37859 <cell alignment="center" valignment="top" usebox="none">
37862 \begin_layout Plain Layout
37872 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37875 \begin_layout Plain Layout
37883 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37886 \begin_layout Plain Layout
37900 \begin_inset space \hfill{}
37904 \begin_inset CommandInset href
37907 target "https://ctan.org/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37915 \begin_layout Standard
37916 \begin_inset Newpage newpage
37922 \begin_layout Bibliography
37923 \begin_inset CommandInset bibitem
37924 LatexCommand bibitem
37938 The \SpecialChar LaTeX
37942 Addison Wesley, 2004
37945 \begin_layout Bibliography
37946 \begin_inset CommandInset bibitem
37947 LatexCommand bibitem
37954 \change_inserted 5863208 1612728717
37956 \begin_inset CommandInset href
37959 target "http://mirrors.ctan.org/obsolete/info/math/voss/mathmode/Mathmode.pdf"
37965 \change_deleted 5863208 1612728717
37967 \begin_inset CommandInset href
37970 target "https://www.tug.org/~hvoss/PDF/mathmode.pdf"
37977 of \SpecialChar LaTeX
37979 \change_deleted 5863208 1612728849
37981 \begin_inset Note Note
37984 \begin_layout Plain Layout
37986 \change_inserted 232239728 1611367909
37999 \begin_layout Bibliography
38000 \begin_inset CommandInset bibitem
38001 LatexCommand bibitem
38008 \change_inserted 5863208 1612728836
38010 \begin_inset CommandInset href
38013 target "http://tug.ctan.org/info/amslatex/english/amsldoc.pdf"
38019 \change_deleted 5863208 1612728836
38021 \begin_inset CommandInset href
38024 target "https://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/amsldoc.pdf"
38035 \begin_layout Plain Layout
38044 -\SpecialChar LaTeX
38046 \change_deleted 5863208 1612728851
38048 \begin_inset Note Note
38051 \begin_layout Plain Layout
38053 \change_inserted 232239728 1611367919
38066 \begin_layout Bibliography
38067 \begin_inset CommandInset bibitem
38068 LatexCommand bibitem
38075 \change_inserted 5863208 1612728963
38077 \begin_inset CommandInset href
38080 target "http://tug.ctan.org/info/symbols/comprehensive/symbols-a4.pdf"
38086 \change_deleted 5863208 1612728963
38088 \begin_inset CommandInset href
38091 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
38098 of all symbols available with \SpecialChar LaTeX
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38172 of the \SpecialChar LaTeX
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38182 Packages ! hyperref
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38246 Auflage, Dudenverlag, 2000
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38261 target "https://www.nist.gov/physical-measurement-laboratory/special-publication-811"
38266 for reviewing manuscripts
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