1 #LyX 2.4 created this file. For more info see https://www.lyx.org/
5 \save_transient_properties true
6 \origin /systemlyxdir/doc/
9 % DO NOT ALTER THIS PREAMBLE!!!
11 % This preamble is designed to ensure that the file prints
12 % out as advertised. If you mess with this preamble,
13 % parts of this document may not print out as expected. If you
14 % have problems LaTeXing this file, please contact
15 % the documentation team
16 % email: lyx-docs@lists.lyx.org
18 % solves the following problem:
19 % If the dection number consits of too many numerals the section heading
20 % will be printed in the TOC without a space between it and the section number.
21 % As solution more space between the number and the heading is inserted:
22 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
23 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
25 % increase link area for cross-references and autoname them,
26 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
27 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
28 \@ifpackageloaded{babel}{
29 \addto\extrasenglish{%
30 \renewcommand*{\equationautorefname}[1]{}%
31 \renewcommand{\sectionautorefname}{sec.\negthinspace}%
32 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
33 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
37 % don't load packages twice
38 % see first footnote in sec. 9.3
39 \@ifundefined{textcolor}{\usepackage{color}}{}
41 % the pages of the TOC are numbered roman
42 % and a PDF-bookmark for the TOC is added
44 \let\myTOC\tableofcontents
45 \renewcommand{\tableofcontents}{%
47 \pdfbookmark[1]{\contentsname}{}
50 \pagenumbering{arabic}}
52 % add 0.5 mm vertical space for table rows
53 \@ifundefined{extrarowheight} {\usepackage{array}}{}
54 \setlength{\extrarowheight}{0.5mm}
56 % insert additional vertical space of 1.5 mm between footnotes,
58 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
60 % makes caption labels bold
61 \setkomafont{captionlabel}{\bfseries}
63 % enables calculation of values
66 % for multiple columns used in sec. 24.7
72 % for the Fourier transformation symbol
75 % define a color, used in sec.9.3
76 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
78 % declare operators (see sec. 10.4 and sec. 15.2)
79 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
80 \DeclareMathOperator{\sgn}{sgn}
82 % example definitions for sec. 20.1
83 \newcommand{\gr}{\Longrightarrow}
84 \newcommand{\us}[1]{\underline{#1}}
85 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
86 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
87 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
89 % example macro from sec. 19.4
91 %\def\tagform@#1{\maketag@@@{|#1|}}
94 % ------------------------------------
95 % used to check for needed LaTeX packages
98 % check for package undertilde
99 % used for the command \utilde
100 \newboolean{undertilde}
101 \IfFileExists{undertilde.sty}
102 {\usepackage{undertilde}
103 \setboolean{undertilde}{true}}
104 {\setboolean{undertilde}{false}}
106 % check for package eurosym
107 % used for the Euro symbol
109 \IfFileExists{eurosym.sty}
110 {\usepackage[gennarrow]{eurosym}
111 \setboolean{eurosym}{true}}
112 {\setboolean{eurosym}{false}}
114 % check for package braket
115 % used for physical vectors
117 \IfFileExists{braket.sty}
119 \setboolean{braket}{true}}
120 {\setboolean{braket}{false}}
122 % check for package cancel
124 \IfFileExists{cancel.sty}
126 \setboolean{cancel}{true}}
127 {\setboolean{cancel}{false}}
129 % check for package upgreek
131 \IfFileExists{upgreek.sty}
132 {\usepackage{upgreek}
133 \setboolean{upgreek}{true}}
134 {\setboolean{upgreek}{false}}
136 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
137 \use_default_options false
141 \maintain_unincluded_children no
143 \language_package default
146 \font_roman "lmodern" "default"
147 \font_sans "lmss" "default"
148 \font_typewriter "lmtt" "default"
149 \font_math "auto" "auto"
150 \font_default_family default
151 \use_non_tex_fonts false
153 \font_roman_osf false
155 \font_typewriter_osf false
156 \font_sf_scale 100 100
157 \font_tt_scale 100 100
159 \use_dash_ligatures false
161 \default_output_format pdf2
163 \bibtex_command default
164 \index_command makeindex
165 \float_placement class
166 \float_alignment class
170 \pdf_title "LyX's Math Manual"
171 \pdf_author "LyX Team, Uwe Stöhr"
172 \pdf_subject "LyX-documentation about math"
173 \pdf_keywords "LyX, Mathed"
175 \pdf_bookmarksnumbered true
176 \pdf_bookmarksopen true
177 \pdf_bookmarksopenlevel 1
178 \pdf_breaklinks false
182 \pdf_pdfusetitle false
183 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
186 \use_package amsmath 2
187 \use_package amssymb 2
188 \use_package cancel 1
190 \use_package mathdots 1
191 \use_package mathtools 2
192 \use_package mhchem 1
193 \use_package stackrel 1
194 \use_package stmaryrd 1
195 \use_package undertilde 0
197 \cite_engine_type default
201 \paperorientation portrait
207 \notefontcolor #0000ff
214 \paragraph_separation skip
217 \math_numbering_side default
218 \quotes_style english
222 \paperpagestyle plain
227 \tracking_changes true
228 \output_changes false
230 \postpone_fragile_content false
233 \html_be_strict false
234 \docbook_table_output 0
235 \docbook_mathml_prefix 1
236 \author -563046850 "Jean-Marc LASGOUTTES"
239 \author 47243155 "Jean-Marc"
240 \author 232239728 "Owner"
247 's Detailed Math Manual
251 by the \SpecialChar LyX
256 \begin_layout Plain Layout
258 If you have comments or error corrections, please send them to the \SpecialChar LyX
263 \begin_inset CommandInset href
265 name "lyx-docs@lists.lyx.org"
266 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
278 \begin_inset Note Note
281 \begin_layout Plain Layout
288 \begin_inset Newline newline
292 \begin_inset Newline newline
298 \change_inserted 47243155 1563226038
300 \change_deleted 47243155 1563226038
306 \begin_layout Standard
307 \begin_inset CommandInset toc
308 LatexCommand tableofcontents
315 \begin_layout Standard
316 \begin_inset Note Note
319 \begin_layout Plain Layout
320 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
323 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
330 If they are not installed the document can be exported anyway but the sections
331 where the packages are required will not appear in the output.
336 ; if it is not installed, this file cannot be exported.
339 \begin_layout Plain Layout
340 The latest PDF-version of this document can be found here:
341 \begin_inset Newline newline
346 https://wiki.lyx.org/LyX/Manuals#Math
354 \begin_layout Standard
355 \begin_inset Newpage newpage
361 \begin_layout Section
365 \begin_layout Standard
366 This document details \SpecialChar LyX
367 's math features and the \SpecialChar LaTeX
368 -commands used for mathematical
369 characters and constructs.
370 It is oriented toward the use of commands.
371 The user should read the
379 section of the User's Guide before proceeding.
382 \begin_layout Standard
383 Most of the characters and many constructs explained in this manual are
384 also accessible via the menu
388 \SpecialChar menuseparator
404 But everybody who has to write lots of formulas will notice that it is
405 much faster to use commands instead of the math toolbar.
406 Therefore this manual is focused on commands but also mentions the correspondin
407 g toolbar buttons when available.
410 \begin_layout Standard
411 Unless specially mentioned, math commands are only available within formulas.
412 To be able to use all of the commands explained in this document, the option
417 must be checked in the document settings (menu
419 Document\SpecialChar menuseparator
420 Settings\SpecialChar menuseparator
431 \begin_layout Plain Layout
434 Use AMS math package automatically
440 \begin_layout Plain Layout
449 -math when math constructs are found that are supported by \SpecialChar LyX
458 \begin_layout Standard
459 This document doesn't list all
463 \begin_layout Plain Layout
476 \begin_layout Plain Layout
477 A list containing all
481 \begin_layout Plain Layout
490 -math commands is in the file
493 \begin_inset CommandInset href
496 target "https://www.ctan.org/tex-archive/macros/amstex/doc/amsguide.pdf"
503 , which is part of every \SpecialChar LaTeX
504 standard installation.
509 for lucidity reasons.
512 \begin_layout Section
516 \begin_layout Standard
517 To create an inline formula
518 \begin_inset Index idx
523 \begin_layout Plain Layout
525 \begin_inset IndexMacro subentry
528 \begin_layout Plain Layout
539 that is embedded in a text line, use one of the shortcuts
545 or the toolbar button
552 \begin_inset Newline newline
555 To create a display style formula
556 \begin_inset Index idx
561 \begin_layout Plain Layout
563 \begin_inset IndexMacro subentry
566 \begin_layout Plain Layout
577 which will appear bigger, has a different format, and will be in a separate
578 paragraph, use one of these shortcuts:
587 \begin_layout Standard
588 To change a display style formula to an inline formula, place the cursor
589 inside the formula and use
590 \change_deleted 5863208 1612729312
594 \change_deleted 5863208 1612729314
598 \change_deleted 5863208 1612729303
606 \change_inserted 5863208 1612729281
610 arg "math-mutate simple"
617 Edit\SpecialChar menuseparator
618 Math\SpecialChar menuseparator
623 \change_inserted 5863208 1612729555
624 Similarly you can use the shortcut
627 arg "math-mutate equation"
630 to change from an inline to a display style formula.
632 \change_deleted 5863208 1612729557
633 The same method is used to change an inline formula to a display style formula.
638 \begin_layout Standard
639 To display parts of an inline formula in the size of a display style formula,
647 \begin_inset Index idx
652 \begin_layout Plain Layout
654 \begin_inset IndexMacro subentry
657 \begin_layout Plain Layout
664 \begin_inset IndexMacro subentry
667 \begin_layout Plain Layout
681 A new blue box will appear in which the desired formula part is inserted.
684 \begin_layout Standard
685 Only inline formulas are allowed inside tables.
688 \begin_layout Standard
690 \change_deleted 232239728 1610897673
695 can be turned on in the menu
697 View\SpecialChar menuseparator
701 When you click there on
702 \begin_inset Quotes eld
706 \begin_inset Quotes erd
709 the toolbar will be shown permanently at the bottom; this state is visualized
714 menu with a checkmark.
715 When you click in this state again on
716 \begin_inset Quotes eld
720 \begin_inset Quotes erd
731 is only shown when the cursor is within a formula; this state is visualized
732 by the renaming of the menu entry from
733 \begin_inset Quotes eld
737 \begin_inset Quotes erd
741 \begin_inset Quotes eld
749 \begin_inset Quotes erd
753 \change_inserted 232239728 1610897478
757 \begin_layout Standard
759 \change_inserted 232239728 1610918987
764 visibility is controlled in the menu
766 View\SpecialChar menuseparator
767 Toolbars\SpecialChar menuseparator
771 Three options will be presented, On, Off, and Automatic.
772 Selecting On will cause the toolbar to be shown permanently at the bottom
774 Selecting Off will disable the toolbar.
775 Selecting Automatic will cause the toolbar to automatically appear when
776 the cursor is located within a formula.
777 The active state of the toolbar is indicated by a checkmark next to the
778 current menu selection.
779 \begin_inset Note Note
782 \begin_layout Plain Layout
784 \change_inserted 232239728 1610897730
785 The menu functionality appears to have changed, I rewrote the paragraph
786 for the current functionality
798 \begin_layout Standard
801 \begin_inset Index idx
806 \begin_layout Plain Layout
807 \begin_inset IndexMacro sortkey
810 \begin_layout Plain Layout
822 is invoked by pressing the toolbar button
830 Insert\SpecialChar menuseparator
842 \begin_layout Standard
843 To change the \SpecialChar LaTeX
845 \begin_inset Index idx
850 \begin_layout Plain Layout
851 \begin_inset IndexMacro sortkey
854 \begin_layout Plain Layout
868 Document\SpecialChar menuseparator
869 Settings\SpecialChar menuseparator
879 \begin_layout Standard
880 To edit matrices, case differentiations and multiline formulas, use the
883 Edit\SpecialChar menuseparator
888 Edit\SpecialChar menuseparator
890 \begin_inset space \thinspace{}
894 \begin_inset space \thinspace{}
904 When lines and columns are swapped via the menu, the column or line where
905 the cursor is in is exchanged with the column to the right or the line
907 If the cursor is in the last column or row, the exchange is done with the
908 column to the left or the line above.
911 \begin_layout Standard
912 To write text in formulas
916 \begin_layout Plain Layout
917 For multiline formulas the command
924 \begin_inset CommandInset ref
926 reference "subsec:Text-in-multiline"
940 \begin_inset Index idx
945 \begin_layout Plain Layout
947 \begin_inset IndexMacro subentry
950 \begin_layout Plain Layout
962 \begin_inset Index idx
967 \begin_layout Plain Layout
974 This mode is invoked with the shortcut
980 or by the insertion of the command
987 \begin_inset Index idx
992 \begin_layout Plain Layout
994 \begin_inset IndexMacro subentry
997 \begin_layout Plain Layout
1004 \begin_inset IndexMacro subentry
1007 \begin_layout Plain Layout
1021 The text appears black in \SpecialChar LyX
1022 and can therefore be distinguished from the
1023 other formula parts which appear blue.
1024 In the output, mathematical text is set upright contrary to other formula
1028 \begin_layout Subsection*
1032 \begin_layout Standard
1033 Most \SpecialChar LaTeX
1034 -commands for math constructs have the following syntax:
1037 \begin_layout Standard
1042 commandname[optional
1053 \begin_layout Standard
1054 A command always starts with a backslash
1055 \begin_inset Quotes gld
1065 \begin_inset Quotes grd
1077 s, also omit the associated brackets.
1078 The braces around the
1086 are referred to in this document as \SpecialChar TeX
1088 \begin_inset Index idx
1093 \begin_layout Plain Layout
1094 \begin_inset IndexMacro sortkey
1097 \begin_layout Plain Layout
1110 If you append a left brace to a command name inside a formula, \SpecialChar LyX
1112 creates a right \SpecialChar TeX
1114 In all other cases standalone \SpecialChar TeX
1115 braces are created in formulas with the
1123 Normal braces are created by typing
1129 braces appear red in \SpecialChar LyX
1130 , normal braces appear blue.
1132 mode a command is not needed to get \SpecialChar TeX
1135 braces don't appear in the output while normal braces do.
1138 \begin_layout Standard
1139 When commands without arguments, like commands for symbols, are entered
1141 mode, a space character must
1145 be behind the command to end it.
1146 This space doesn't appear in the output.
1147 When the space should appear in the output, the space must be followed
1149 \change_deleted 177693 1654668848
1151 \change_inserted 177693 1654668851
1154 space in normal text.
1157 \begin_layout Standard
1159 \change_deleted 177693 1654668857
1161 \change_inserted 177693 1654668860
1164 space is inserted with
1165 \change_inserted 232239728 1610908934
1167 \change_deleted 5863208 1612729787
1169 \change_inserted 5863208 1612729774
1173 arg "command-alternatives math-space ; space-insert protected"
1177 \change_deleted 232239728 1610908788
1181 arg "command-alternatives space-insert protected; math-space"
1185 \change_inserted 5863208 1612729766
1186 or with the menu selection
1189 \change_inserted 232239728 1610908897
1190 Insert\SpecialChar menuseparator
1191 Formatting\SpecialChar menuseparator
1193 \change_deleted 177693 1654668863
1195 \change_inserted 177693 1654668975
1197 \change_inserted 232239728 1610908897
1201 \change_inserted 5863208 1612729638
1205 \change_deleted 5863208 1612729640
1213 \begin_layout Subsection*
1214 \begin_inset Newpage newpage
1218 \change_deleted 5863208 1612098922
1222 \change_inserted 5863208 1612100879
1223 of Syntax Used in this Manual
1228 \begin_layout Itemize
1230 \begin_inset space \textvisiblespace{}
1233 denotes a space character to be input
1234 \change_inserted 5863208 1612098935
1240 \begin_layout Itemize
1242 \begin_inset Formula $\to$
1245 denotes the usage of the corresponding arrow key on the keyboard.
1250 key can often be used instead of
1251 \begin_inset Formula $\to$
1255 \begin_inset Formula $\downarrow$
1263 \begin_inset Formula $\leftarrow$
1267 \begin_inset Formula $\uparrow$
1273 \begin_layout Subsection*
1277 \begin_layout Standard
1279 \begin_inset Float table
1286 \begin_layout Plain Layout
1288 \begin_inset Caption Standard
1290 \begin_layout Plain Layout
1291 \begin_inset CommandInset label
1293 name "tab:Available-units"
1305 \begin_layout Plain Layout
1307 \begin_inset Tabular
1308 <lyxtabular version="3" rows="13" columns="2">
1309 <features booktabs="true" tabularvalignment="middle">
1310 <column alignment="center" valignment="top">
1311 <column alignment="center" valignment="top" width="0pt">
1313 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1316 \begin_layout Plain Layout
1322 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1325 \begin_layout Plain Layout
1333 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1336 \begin_layout Plain Layout
1342 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1345 \begin_layout Plain Layout
1353 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1356 \begin_layout Plain Layout
1362 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1365 \begin_layout Plain Layout
1373 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1376 \begin_layout Plain Layout
1382 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1385 \begin_layout Plain Layout
1387 \begin_inset space \thinspace{}
1391 \change_deleted 232239728 1610909338
1393 \change_inserted 232239728 1610909338
1397 \begin_inset space \thinspace{}
1407 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1410 \begin_layout Plain Layout
1416 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1419 \begin_layout Plain Layout
1421 \begin_inset space \thinspace{}
1425 \begin_inset space \thinspace{}
1435 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1438 \begin_layout Plain Layout
1444 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1447 \begin_layout Plain Layout
1449 \begin_inset space \thinspace{}
1453 \begin_inset space \thinspace{}
1463 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1466 \begin_layout Plain Layout
1472 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1475 \begin_layout Plain Layout
1477 \begin_inset space \thinspace{}
1481 \begin_inset space \thinspace{}
1491 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1494 \begin_layout Plain Layout
1500 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1503 \begin_layout Plain Layout
1505 \begin_inset space \thinspace{}
1509 \begin_inset space \thinspace{}
1519 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1522 \begin_layout Plain Layout
1528 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1531 \begin_layout Plain Layout
1533 \begin_inset space \thinspace{}
1537 \begin_inset Formula $\approx$
1541 \begin_inset space \thinspace{}
1551 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1554 \begin_layout Plain Layout
1560 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1563 \begin_layout Plain Layout
1565 \begin_inset space \thinspace{}
1569 \begin_inset space \thinspace{}
1579 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1582 \begin_layout Plain Layout
1588 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1591 \begin_layout Plain Layout
1595 \begin_inset Quotes eld
1601 \begin_inset Quotes erd
1611 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1614 \begin_layout Plain Layout
1620 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1623 \begin_layout Plain Layout
1625 \begin_inset Quotes eld
1633 \begin_inset Quotes erd
1643 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1646 \begin_layout Plain Layout
1652 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1655 \begin_layout Plain Layout
1657 \begin_inset space \thinspace{}
1661 \begin_inset Formula $\nicefrac{1}{18}$
1665 \begin_inset space \thinspace{}
1686 \begin_layout Section
1690 \begin_layout Subsection
1692 \begin_inset Index idx
1697 \begin_layout Plain Layout
1704 \begin_inset Index idx
1709 \begin_layout Plain Layout
1716 \begin_inset Index idx
1721 \begin_layout Plain Layout
1723 \begin_inset IndexMacro see
1726 \begin_layout Plain Layout
1738 \begin_inset Index idx
1743 \begin_layout Plain Layout
1745 \begin_inset IndexMacro see
1748 \begin_layout Plain Layout
1762 \begin_layout Standard
1763 Indices are created with an underscore
1764 \begin_inset Quotes eld
1768 \begin_inset Quotes erd
1771 or via the math toolbar button
1774 arg "math-subscript"
1777 , exponents with a caret
1778 \begin_inset Quotes eld
1782 \begin_inset Quotes erd
1785 or via the math toolbar button
1788 arg "math-superscript"
1794 \begin_layout Standard
1796 \begin_inset Tabular
1797 <lyxtabular version="3" rows="4" columns="2">
1798 <features booktabs="true" tabularvalignment="middle">
1799 <column alignment="center" valignment="top" width="0pt">
1800 <column alignment="center" valignment="top" width="0pt">
1802 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1805 \begin_layout Plain Layout
1811 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1814 \begin_layout Plain Layout
1822 <cell alignment="center" valignment="top" usebox="none">
1825 \begin_layout Plain Layout
1831 <cell alignment="center" valignment="top" usebox="none">
1834 \begin_layout Plain Layout
1835 \begin_inset Formula $B_{V}$
1844 <row topspace="1.5mm">
1845 <cell alignment="center" valignment="top" usebox="none">
1848 \begin_layout Plain Layout
1854 <cell alignment="center" valignment="top" usebox="none">
1857 \begin_layout Plain Layout
1858 \begin_inset Formula $B^{V}$
1867 <row topspace="1.5mm">
1868 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1871 \begin_layout Plain Layout
1873 \begin_inset space \textvisiblespace{}
1881 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1884 \begin_layout Plain Layout
1885 \begin_inset Formula $B^{A}$
1901 \begin_layout Standard
1902 As the caret is in some languages an accent, vowels will be accentuated
1903 in this case and not set as exponents
1907 \begin_layout Plain Layout
1908 Depending on the keyboard settings used this can also happen for characters
1915 To get exponents in this case, press
1919 after the caret as in the last example.
1922 \begin_layout Subsection
1924 \begin_inset CommandInset label
1926 name "subsec:Fractions"
1931 \begin_inset Index idx
1936 \begin_layout Plain Layout
1945 \begin_layout Standard
1946 Fractions are generated with the command
1953 \begin_inset Index idx
1958 \begin_layout Plain Layout
1960 \begin_inset IndexMacro subentry
1963 \begin_layout Plain Layout
1970 \begin_inset IndexMacro subentry
1973 \begin_layout Plain Layout
1986 or via the math toolbar button
1989 arg "math-insert \\frac"
1993 The font size is adjusted automatically, depending on whether the fraction
1994 is in an inline or display style formula.
1995 With the math toolbar button
1998 arg "math-insert \\frac-square"
2001 you can select different fraction types.
2004 \begin_layout Standard
2012 \begin_inset Index idx
2017 \begin_layout Plain Layout
2019 \begin_inset IndexMacro subentry
2022 \begin_layout Plain Layout
2029 \begin_inset IndexMacro subentry
2032 \begin_layout Plain Layout
2045 a fraction can be created that always has the size of a display style formula.
2053 \begin_inset Index idx
2058 \begin_layout Plain Layout
2060 \begin_inset IndexMacro subentry
2063 \begin_layout Plain Layout
2070 \begin_inset IndexMacro subentry
2073 \begin_layout Plain Layout
2086 the fraction appears always with the size of an inline formula.
2090 \begin_layout Standard
2091 A line with the fraction
2092 \begin_inset Formula $\frac{1}{2}$
2095 that was created with the command
2104 \begin_layout Standard
2105 A line with the fraction
2106 \begin_inset Formula $\dfrac{1}{2}$
2109 that was created with the command
2118 \begin_layout Standard
2120 \begin_inset Tabular
2121 <lyxtabular version="3" rows="4" columns="2">
2122 <features booktabs="true" tabularvalignment="middle">
2123 <column alignment="center" valignment="top" width="0pt">
2124 <column alignment="center" valignment="top" width="0pt">
2126 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2129 \begin_layout Plain Layout
2135 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2138 \begin_layout Plain Layout
2145 <row topspace="1.5mm">
2146 <cell alignment="center" valignment="top" usebox="none">
2149 \begin_layout Plain Layout
2153 \begin_inset space \textvisiblespace{}
2157 \begin_inset Formula $\downarrow$
2165 <cell alignment="center" valignment="top" usebox="none">
2168 \begin_layout Plain Layout
2169 \begin_inset Formula $\frac{A}{B}$
2178 <row topspace="2mm">
2179 <cell alignment="center" valignment="top" usebox="none">
2182 \begin_layout Plain Layout
2186 \begin_inset space \textvisiblespace{}
2190 \begin_inset Formula $\downarrow$
2198 <cell alignment="center" valignment="top" usebox="none">
2201 \begin_layout Plain Layout
2202 \begin_inset Formula $\dfrac{A}{B}$
2211 <row topspace="2mm" bottomspace="1mm">
2212 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2215 \begin_layout Plain Layout
2219 \begin_inset space \textvisiblespace{}
2225 \begin_inset space \textvisiblespace{}
2229 \begin_inset Formula $\downarrow$
2233 \begin_inset Formula $\downarrow\downarrow$
2241 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2244 \begin_layout Plain Layout
2245 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
2261 \begin_layout Standard
2262 \begin_inset VSpace bigskip
2266 \begin_inset Newpage newpage
2269 For nested fractions the command
2276 \begin_inset Index idx
2281 \begin_layout Plain Layout
2283 \begin_inset IndexMacro subentry
2286 \begin_layout Plain Layout
2293 \begin_inset IndexMacro subentry
2296 \begin_layout Plain Layout
2311 \begin_inset VSpace -3mm
2317 \begin_layout Standard
2318 \begin_inset Formula
2320 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2321 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2329 \begin_layout Standard
2330 The command for the example above is:
2333 \begin_layout Standard
2339 \begin_inset space \textvisiblespace{}
2343 \begin_inset Formula $\downarrow$
2349 \begin_inset space \textvisiblespace{}
2355 \begin_inset space \textvisiblespace{}
2359 \begin_inset Formula $\downarrow$
2363 \begin_inset Formula $\downarrow$
2369 \begin_layout Standard
2370 \begin_inset VSpace medskip
2376 \begin_layout Standard
2383 always sets the fraction size to that of a displayed formula, even when
2384 it is part of another fraction.
2387 \begin_layout Standard
2388 It is possible to specify the alignment of the numerator.
2395 is used to left align it, the command
2408 centers the numerator.
2409 These fractions demonstrate the different alignments:
2412 \begin_layout Standard
2415 \begin_inset Formula
2417 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2425 \begin_layout Standard
2426 \begin_inset Note Greyedout
2429 \begin_layout Plain Layout
2446 are not real \SpecialChar LaTeX
2447 commands but represent the command
2451 cfrac[alignment]{numerator}{denominator}
2454 Therefore you cannot use them in \SpecialChar TeX
2463 \begin_layout Standard
2464 \begin_inset VSpace medskip
2467 It is often advantageous to combine
2480 \begin_inset Formula
2482 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2490 \begin_layout Standard
2491 For inline fractions with a sloped fraction stroke you can use the command
2499 \begin_inset Index idx
2504 \begin_layout Plain Layout
2506 \begin_inset IndexMacro subentry
2509 \begin_layout Plain Layout
2516 \begin_inset IndexMacro subentry
2519 \begin_layout Plain Layout
2533 \begin_inset Formula $\nicefrac{5}{31}$
2543 \begin_inset Index idx
2548 \begin_layout Plain Layout
2550 \begin_inset IndexMacro subentry
2553 \begin_layout Plain Layout
2560 \begin_inset IndexMacro subentry
2563 \begin_layout Plain Layout
2577 \begin_inset Formula $\unitfrac{5}{31}$
2580 There is also the command
2586 which allows you to write a fraction in combination with a number:
2587 \begin_inset Formula $\unitfrac[2]{1}{3}$
2593 \begin_layout Standard
2594 \begin_inset Note Greyedout
2597 \begin_layout Plain Layout
2608 is not a real \SpecialChar LaTeX
2609 command but the command
2610 \begin_inset Newline newline
2617 unitfrac[number]{numerator}{denominator}
2620 Therefore you cannot use it in \SpecialChar TeX
2629 \begin_layout Standard
2630 How to define your own fractions where the fraction stroke can be changed
2632 \begin_inset CommandInset ref
2634 reference "subsec:Self-defined-Fractions"
2641 \begin_layout Standard
2642 Multiline fractions are explained in
2643 \begin_inset CommandInset ref
2645 reference "subsec:Multiline-Fractions"
2652 \begin_layout Subsection
2654 \begin_inset Index idx
2659 \begin_layout Plain Layout
2668 \begin_layout Standard
2669 Square roots are created with
2676 \begin_inset Index idx
2681 \begin_layout Plain Layout
2683 \begin_inset IndexMacro subentry
2686 \begin_layout Plain Layout
2693 \begin_inset IndexMacro subentry
2696 \begin_layout Plain Layout
2709 or the math toolbar button
2712 arg "math-insert \\sqrt"
2715 , all other roots with the command
2722 \begin_inset Index idx
2727 \begin_layout Plain Layout
2729 \begin_inset IndexMacro subentry
2732 \begin_layout Plain Layout
2739 \begin_inset IndexMacro subentry
2742 \begin_layout Plain Layout
2755 or with the math toolbar button
2758 arg "math-insert \\root"
2764 \begin_layout Standard
2766 \begin_inset Tabular
2767 <lyxtabular version="3" rows="3" columns="2">
2768 <features booktabs="true" tabularvalignment="middle">
2769 <column alignment="center" valignment="top" width="0pt">
2770 <column alignment="center" valignment="top" width="0pt">
2772 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2775 \begin_layout Plain Layout
2781 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2784 \begin_layout Plain Layout
2791 <row topspace="1mm">
2792 <cell alignment="center" valignment="top" usebox="none">
2795 \begin_layout Plain Layout
2799 \begin_inset space \textvisiblespace{}
2807 <cell alignment="center" valignment="top" usebox="none">
2810 \begin_layout Plain Layout
2811 \begin_inset Formula $\sqrt{A-B}$
2820 <row topspace="1mm">
2821 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2824 \begin_layout Plain Layout
2828 \begin_inset space \textvisiblespace{}
2832 \begin_inset Formula $\downarrow$
2840 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2843 \begin_layout Plain Layout
2844 \begin_inset Formula $\sqrt[3]{A-B}$
2860 \begin_layout Standard
2861 A square root can also be created with
2867 when the root index field is left empty.
2870 \begin_layout Standard
2871 With certain indices the distance to the root is too small, like in this
2873 \begin_inset Formula $\sqrt[\beta]{B}$
2877 \begin_inset Newline newline
2881 \begin_inset Formula $\beta$
2885 To avoid this, the commands
2892 \begin_inset Index idx
2897 \begin_layout Plain Layout
2899 \begin_inset IndexMacro subentry
2902 \begin_layout Plain Layout
2909 \begin_inset IndexMacro subentry
2912 \begin_layout Plain Layout
2932 \begin_inset Index idx
2937 \begin_layout Plain Layout
2939 \begin_inset IndexMacro subentry
2942 \begin_layout Plain Layout
2949 \begin_inset IndexMacro subentry
2952 \begin_layout Plain Layout
2965 are used with the following scheme:
2968 \begin_layout Standard
2982 \begin_layout Standard
2983 Distance is the number of Big Points (unit bp;
2984 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2987 ), that the index should be moved to the left or up, resp..
2988 The commands are written to the index.
2989 This way the command
2990 \begin_inset Newline newline
3000 \begin_inset Formula $\to$
3006 \begin_inset Formula $\to$
3012 \begin_inset space \textvisiblespace{}
3016 \begin_inset Formula $\to$
3020 \begin_inset Newline newline
3025 produces a correct typeset formula:
3026 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
3032 \begin_layout Subsection
3033 Binomial Coefficients
3034 \begin_inset Index idx
3039 \begin_layout Plain Layout
3040 Binomial coefficients
3048 \begin_layout Standard
3049 Binomial coefficients are inserted with the command
3056 \begin_inset Index idx
3061 \begin_layout Plain Layout
3063 \begin_inset IndexMacro subentry
3066 \begin_layout Plain Layout
3073 \begin_inset IndexMacro subentry
3076 \begin_layout Plain Layout
3089 or with the submenu of the math toolbar button
3092 arg "math-insert \\frac-square"
3108 there are the commands
3115 \begin_inset Index idx
3120 \begin_layout Plain Layout
3122 \begin_inset IndexMacro subentry
3125 \begin_layout Plain Layout
3132 \begin_inset IndexMacro subentry
3135 \begin_layout Plain Layout
3155 \begin_inset Index idx
3160 \begin_layout Plain Layout
3162 \begin_inset IndexMacro subentry
3165 \begin_layout Plain Layout
3172 \begin_inset IndexMacro subentry
3175 \begin_layout Plain Layout
3189 For other brackets around binomial coefficients there are the commands
3197 \begin_inset Index idx
3202 \begin_layout Plain Layout
3204 \begin_inset IndexMacro subentry
3207 \begin_layout Plain Layout
3214 \begin_inset IndexMacro subentry
3217 \begin_layout Plain Layout
3237 \begin_inset Index idx
3242 \begin_layout Plain Layout
3244 \begin_inset IndexMacro subentry
3247 \begin_layout Plain Layout
3254 \begin_inset IndexMacro subentry
3257 \begin_layout Plain Layout
3273 \begin_layout Standard
3275 \begin_inset Tabular
3276 <lyxtabular version="3" rows="6" columns="2">
3277 <features booktabs="true" tabularvalignment="middle">
3278 <column alignment="center" valignment="top" width="0pt">
3279 <column alignment="center" valignment="top" width="0pt">
3281 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3284 \begin_layout Plain Layout
3290 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3293 \begin_layout Plain Layout
3300 <row topspace="1mm">
3301 <cell alignment="center" valignment="top" usebox="none">
3304 \begin_layout Plain Layout
3308 \begin_inset space \textvisiblespace{}
3312 \begin_inset Formula $\downarrow$
3320 <cell alignment="center" valignment="top" usebox="none">
3323 \begin_layout Plain Layout
3324 \begin_inset Formula $\binom{A}{B}$
3333 <row topspace="2mm">
3334 <cell alignment="center" valignment="top" usebox="none">
3337 \begin_layout Plain Layout
3341 \begin_inset space \textvisiblespace{}
3345 \begin_inset Formula $\downarrow$
3353 <cell alignment="center" valignment="top" usebox="none">
3356 \begin_layout Plain Layout
3357 \begin_inset Formula $\dbinom{A}{B}$
3366 <row topspace="2mm" bottomspace="0.5mm">
3367 <cell alignment="center" valignment="top" usebox="none">
3370 \begin_layout Plain Layout
3374 \begin_inset space \textvisiblespace{}
3378 \begin_inset Formula $\downarrow$
3386 <cell alignment="center" valignment="top" usebox="none">
3389 \begin_layout Plain Layout
3390 \begin_inset Formula $\tbinom{A}{B}$
3399 <row topspace="1mm">
3400 <cell alignment="center" valignment="top" topline="true" usebox="none">
3403 \begin_layout Plain Layout
3407 \begin_inset space \textvisiblespace{}
3411 \begin_inset Formula $\downarrow$
3419 <cell alignment="center" valignment="top" topline="true" usebox="none">
3422 \begin_layout Plain Layout
3423 \begin_inset Formula ${A \brack B}$
3432 <row topspace="2mm" bottomspace="0.5mm">
3433 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3436 \begin_layout Plain Layout
3440 \begin_inset space \textvisiblespace{}
3444 \begin_inset Formula $\downarrow$
3452 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3455 \begin_layout Plain Layout
3456 \begin_inset Formula ${A \brace B}$
3472 \begin_layout Subsection
3473 Case Differentiations
3474 \begin_inset Index idx
3479 \begin_layout Plain Layout
3480 Case differentiations
3488 \begin_layout Standard
3490 \begin_inset Tabular
3491 <lyxtabular version="3" rows="3" columns="2">
3492 <features booktabs="true" tabularvalignment="middle">
3493 <column alignment="center" valignment="top" width="0pt">
3494 <column alignment="center" valignment="top" width="0pt">
3496 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3499 \begin_layout Plain Layout
3505 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3508 \begin_layout Plain Layout
3516 <cell alignment="center" valignment="top" usebox="none">
3519 \begin_layout Plain Layout
3523 \begin_inset space \textvisiblespace{}
3527 \begin_inset Formula $\to$
3531 \begin_inset Index idx
3536 \begin_layout Plain Layout
3538 \begin_inset IndexMacro subentry
3541 \begin_layout Plain Layout
3548 \begin_inset IndexMacro subentry
3551 \begin_layout Plain Layout
3569 <cell alignment="center" valignment="top" usebox="none">
3572 \begin_layout Plain Layout
3573 \begin_inset Formula $\begin{cases}
3583 <row topspace="1.5mm">
3584 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3587 \begin_layout Plain Layout
3591 \begin_inset space \textvisiblespace{}
3597 arg "newline-insert newline"
3605 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
3608 \begin_layout Plain Layout
3609 \begin_inset Formula $\begin{cases}
3610 A & \textrm{for }x>0\\
3611 B & \textrm{for }x=0
3628 \begin_layout Standard
3635 or pressing the math toolbar button
3638 arg "math-insert \\cases"
3641 you can create new lines with the shortcut
3644 arg "newline-insert newline"
3647 or the table toolbar button
3650 arg "tabular-feature append-row"
3656 \begin_layout Standard
3663 is also available via the menu
3665 Insert\SpecialChar menuseparator
3666 Math\SpecialChar menuseparator
3672 \begin_layout Subsection
3674 \begin_inset Index idx
3679 \begin_layout Plain Layout
3688 \begin_layout Standard
3696 \begin_inset Index idx
3701 \begin_layout Plain Layout
3703 \begin_inset IndexMacro subentry
3706 \begin_layout Plain Layout
3713 \begin_inset IndexMacro subentry
3716 \begin_layout Plain Layout
3729 every character can be displayed canceled.
3730 The characters are quasi accentuated by a slash.
3733 \begin_layout Standard
3735 \begin_inset Tabular
3736 <lyxtabular version="3" rows="4" columns="2">
3737 <features booktabs="true" tabularvalignment="middle">
3738 <column alignment="center" valignment="top" width="0pt">
3739 <column alignment="center" valignment="top" width="0pt">
3741 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3744 \begin_layout Plain Layout
3750 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3753 \begin_layout Plain Layout
3761 <cell alignment="center" valignment="top" usebox="none">
3764 \begin_layout Plain Layout
3772 <cell alignment="center" valignment="top" usebox="none">
3775 \begin_layout Plain Layout
3776 \begin_inset Formula $\not=$
3786 <cell alignment="center" valignment="top" usebox="none">
3789 \begin_layout Plain Layout
3799 <cell alignment="center" valignment="top" usebox="none">
3802 \begin_layout Plain Layout
3803 \begin_inset Formula $\not\le$
3813 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3816 \begin_layout Plain Layout
3826 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3829 \begin_layout Plain Layout
3830 \begin_inset Formula $\not\parallel$
3846 \begin_layout Standard
3847 The last example shows that not all negations look good.
3848 Therefore there are special commands for some negations (see
3849 \begin_inset CommandInset ref
3851 reference "subsec:Mathematical-Symbols"
3856 \begin_inset CommandInset ref
3858 reference "sec:Relations"
3865 \begin_layout Subsection
3867 \begin_inset CommandInset label
3869 name "subsec:Placeholders"
3874 \begin_inset Index idx
3879 \begin_layout Plain Layout
3886 \begin_inset Index idx
3891 \begin_layout Plain Layout
3893 \begin_inset IndexMacro subentry
3896 \begin_layout Plain Layout
3908 \begin_inset Index idx
3913 \begin_layout Plain Layout
3915 \begin_inset IndexMacro see
3918 \begin_layout Plain Layout
3932 \begin_layout Standard
3934 \begin_inset space \thinspace{}
3938 \begin_inset space \space{}
3945 \begin_layout Plain Layout
3946 Typesetting isotopes and chemical symbols is described in
3947 \begin_inset CommandInset ref
3949 reference "subsec:Chemical-Symbols-and"
3958 the following problem occurs:
3961 \begin_layout Standard
3963 \begin_inset Tabular
3964 <lyxtabular version="3" rows="2" columns="2">
3965 <features booktabs="true" tabularvalignment="middle">
3966 <column alignment="center" valignment="top" width="0pt">
3967 <column alignment="center" valignment="top" width="0pt">
3969 <cell alignment="center" valignment="top" usebox="none">
3972 \begin_layout Plain Layout
3973 Indices created with sub- and superscripts:
3978 <cell alignment="center" valignment="top" usebox="none">
3981 \begin_layout Plain Layout
3982 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3991 <row topspace="1.5mm">
3992 <cell alignment="center" valignment="top" usebox="none">
3995 \begin_layout Plain Layout
4001 <cell alignment="center" valignment="top" usebox="none">
4004 \begin_layout Plain Layout
4005 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
4021 \begin_layout Standard
4022 The shorter index is placed by default below or above the first character
4023 of the longer index.
4024 This is corrected using the command
4031 \begin_inset Index idx
4036 \begin_layout Plain Layout
4038 \begin_inset IndexMacro subentry
4041 \begin_layout Plain Layout
4048 \begin_inset IndexMacro subentry
4051 \begin_layout Plain Layout
4064 or the math toolbar button
4065 \begin_inset space \thinspace{}
4072 \begin_layout Plain Layout
4073 Found in the submenu of the toolbar button
4076 arg "math-insert \\space"
4090 to create one or more phantom characters.
4091 When inserting phantom characters a small blue box appears that is superposed
4092 with two red arrows.
4093 The arrows indicate the width and height of the box to be created as a
4095 Phantom characters are placeholders with the same character size.
4098 \begin_layout Standard
4100 \begin_inset Tabular
4101 <lyxtabular version="3" rows="4" columns="2">
4102 <features booktabs="true" tabularvalignment="middle">
4103 <column alignment="center" valignment="top" width="0pt">
4104 <column alignment="center" valignment="top" width="0pt">
4106 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4109 \begin_layout Plain Layout
4115 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4118 \begin_layout Plain Layout
4125 <row topspace="1.5mm">
4126 <cell alignment="center" valignment="top" usebox="none">
4129 \begin_layout Plain Layout
4131 \begin_inset space \textvisiblespace{}
4137 \begin_inset space \textvisiblespace{}
4141 \begin_inset Formula $\to$
4145 \begin_inset space \textvisiblespace{}
4149 \change_inserted 5863208 1612176450
4153 \begin_inset space \textvisiblespace{}
4163 <cell alignment="center" valignment="top" usebox="none">
4166 \begin_layout Plain Layout
4167 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
4176 <row topspace="1.5mm" bottomspace="0.5mm">
4177 <cell alignment="center" valignment="top" usebox="none">
4180 \begin_layout Plain Layout
4182 \begin_inset space \textvisiblespace{}
4188 \begin_inset space \textvisiblespace{}
4192 \begin_inset Formula $\to$
4196 \begin_inset space \textvisiblespace{}
4200 \change_inserted 5863208 1612707447
4204 \begin_inset space \textvisiblespace{}
4214 <cell alignment="center" valignment="top" usebox="none">
4217 \begin_layout Plain Layout
4218 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
4227 <row topspace="1.5mm" bottomspace="0.5mm">
4228 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4231 \begin_layout Plain Layout
4235 \change_inserted 5863208 1612707546
4237 \begin_inset space \textvisiblespace{}
4243 \change_deleted 5863208 1612707563
4245 \begin_inset space \textvisiblespace{}
4253 \begin_inset space \textvisiblespace{}
4257 \begin_inset Formula $\to$
4261 \begin_inset space \textvisiblespace{}
4269 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4272 \begin_layout Plain Layout
4273 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
4289 \begin_layout Standard
4290 Furthermore there are the commands
4297 \begin_inset Index idx
4302 \begin_layout Plain Layout
4304 \begin_inset IndexMacro subentry
4307 \begin_layout Plain Layout
4314 \begin_inset IndexMacro subentry
4317 \begin_layout Plain Layout
4343 \begin_inset Index idx
4348 \begin_layout Plain Layout
4350 \begin_inset IndexMacro subentry
4353 \begin_layout Plain Layout
4360 \begin_inset IndexMacro subentry
4363 \begin_layout Plain Layout
4389 creates only space for the maximal height of the characters in the box
4390 but not for its width.
4397 creates only space for the width of the box content.
4398 Therefore the boxes of both commands have only one red arrow.
4401 \begin_layout Standard
4402 For example the command
4407 \begin_inset space \textvisiblespace{}
4414 creates space for the height of the integral sign,
4418 \begin_layout Plain Layout
4425 creates an integral sign, see
4426 \begin_inset CommandInset ref
4428 reference "subsec:Big-Operators"
4437 because this is the larger character.
4438 An example application is in
4439 \begin_inset CommandInset ref
4441 reference "subsec:Multiline-Brackets"
4448 \begin_layout Standard
4449 Placeholders can also be used for text when they are inserted via the menu
4452 Insert\SpecialChar menuseparator
4453 Formatting\SpecialChar menuseparator
4459 \begin_layout Standard
4461 \begin_inset Newline newline
4465 \begin_inset Phantom Phantom
4468 \begin_layout Plain Layout
4477 \begin_layout Subsection
4479 \begin_inset Index idx
4484 \begin_layout Plain Layout
4491 \begin_inset Index idx
4496 \begin_layout Plain Layout
4498 \begin_inset IndexMacro subentry
4501 \begin_layout Plain Layout
4515 \begin_layout Standard
4517 \begin_inset Tabular
4518 <lyxtabular version="3" rows="4" columns="2">
4519 <features booktabs="true" tabularvalignment="middle">
4520 <column alignment="center" valignment="top" width="0pt">
4521 <column alignment="center" valignment="top" width="0pt">
4523 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4526 \begin_layout Plain Layout
4532 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4535 \begin_layout Plain Layout
4542 <row topspace="2mm">
4543 <cell alignment="center" valignment="top" usebox="none">
4546 \begin_layout Plain Layout
4550 \begin_inset space \textvisiblespace{}
4554 \begin_inset Index idx
4559 \begin_layout Plain Layout
4561 \begin_inset IndexMacro subentry
4564 \begin_layout Plain Layout
4571 \begin_inset IndexMacro subentry
4574 \begin_layout Plain Layout
4592 <cell alignment="center" valignment="top" usebox="none">
4595 \begin_layout Plain Layout
4596 \begin_inset Formula $\overline{A+B}$
4605 <row bottomspace="1mm">
4606 <cell alignment="center" valignment="top" usebox="none">
4609 \begin_layout Plain Layout
4613 \begin_inset space \textvisiblespace{}
4617 \begin_inset Index idx
4622 \begin_layout Plain Layout
4624 \begin_inset IndexMacro subentry
4627 \begin_layout Plain Layout
4634 \begin_inset IndexMacro subentry
4637 \begin_layout Plain Layout
4655 <cell alignment="center" valignment="top" usebox="none">
4658 \begin_layout Plain Layout
4659 \begin_inset Formula $\underline{A+B}$
4668 <row topspace="2mm" bottomspace="1mm">
4669 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4672 \begin_layout Plain Layout
4676 \begin_inset space \textvisiblespace{}
4682 \begin_inset space \textvisiblespace{}
4690 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4693 \begin_layout Plain Layout
4694 \begin_inset Formula $\overline{\underline{A+B}}$
4710 \begin_layout Standard
4711 In the last example it doesn't matter if
4726 \begin_layout Standard
4727 To double underline use
4734 \change_deleted 5863208 1612707977
4736 \change_inserted 5863208 1612707993
4737 (or as many times you want).
4742 \begin_layout Standard
4744 \change_deleted 232239728 1610990247
4745 It is possible to place up to 6 lines above or below characters.
4746 \change_deleted 5863208 1612729848
4748 \begin_inset Note Note
4751 \begin_layout Plain Layout
4753 \change_inserted 232239728 1610990434
4754 I put 30 over and under lines in my test so I don't know what the actual
4755 maximum is, but it's greater than 6.
4765 \begin_layout Standard
4766 \begin_inset VSpace bigskip
4769 Custom lines can be created using the command
4776 \begin_inset Index idx
4781 \begin_layout Plain Layout
4783 \begin_inset IndexMacro subentry
4786 \begin_layout Plain Layout
4793 \begin_inset IndexMacro subentry
4796 \begin_layout Plain Layout
4809 which has the following scheme:
4812 \begin_layout Standard
4817 rule[vertical offset]{length}{thickness}
4820 \begin_layout Standard
4821 The optional vertical offset shifts the line upwards (or downwards, when
4822 the value is negative).
4824 \begin_inset CommandInset ref
4826 reference "tab:Available-units"
4830 can be used for the values.
4831 Here are two example lines created with the commands
4832 \begin_inset Newline newline
4839 rule[-2ex]{3cm}{2pt}
4850 \begin_layout Standard
4852 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4858 \begin_layout Standard
4865 can also be used for text when a line is inserted via the menu
4867 Insert\SpecialChar menuseparator
4868 Formatting\SpecialChar menuseparator
4870 \begin_inset space ~
4878 \begin_layout Standard
4880 \begin_inset CommandInset line
4891 \begin_layout Subsection
4893 \begin_inset CommandInset label
4895 name "subsec:Ellipses"
4900 \begin_inset Index idx
4905 \begin_layout Plain Layout
4914 \begin_layout Standard
4915 There are different types of ellipses available.
4919 \begin_layout Plain Layout
4920 In the math toolbar in the submenu of the button
4923 arg "math-insert \\ldots"
4931 For listings, dots at the baseline are used (
4938 \begin_inset Index idx
4943 \begin_layout Plain Layout
4945 \begin_inset IndexMacro subentry
4948 \begin_layout Plain Layout
4955 \begin_inset IndexMacro subentry
4958 \begin_layout Plain Layout
4971 ), while for operations, dots are needed that are on the same height as
4979 \begin_inset Index idx
4984 \begin_layout Plain Layout
4986 \begin_inset IndexMacro subentry
4989 \begin_layout Plain Layout
4996 \begin_inset IndexMacro subentry
4999 \begin_layout Plain Layout
5013 When using the command
5020 \begin_inset Index idx
5025 \begin_layout Plain Layout
5027 \begin_inset IndexMacro subentry
5030 \begin_layout Plain Layout
5037 \begin_inset IndexMacro subentry
5040 \begin_layout Plain Layout
5053 , \SpecialChar LaTeX
5054 decides on the basis of the next character what type is used.
5057 \begin_layout Standard
5059 \begin_inset Tabular
5060 <lyxtabular version="3" rows="9" columns="2">
5061 <features booktabs="true" tabularvalignment="middle">
5062 <column alignment="center" valignment="top" width="0pt">
5063 <column alignment="center" valignment="top" width="0pt">
5065 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5068 \begin_layout Plain Layout
5074 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5077 \begin_layout Plain Layout
5085 <cell alignment="center" valignment="top" usebox="none">
5088 \begin_layout Plain Layout
5090 \begin_inset space \textvisiblespace{}
5096 \begin_inset space \textvisiblespace{}
5104 <cell alignment="center" valignment="top" usebox="none">
5107 \begin_layout Plain Layout
5108 \begin_inset Formula $A_{1},\dots,A_{n}$
5118 <cell alignment="center" valignment="top" usebox="none">
5121 \begin_layout Plain Layout
5123 \begin_inset space \textvisiblespace{}
5129 \begin_inset space \textvisiblespace{}
5137 <cell alignment="center" valignment="top" usebox="none">
5140 \begin_layout Plain Layout
5141 \begin_inset Formula $A_{1}+\dots+A_{n}$
5151 <cell alignment="center" valignment="top" usebox="none">
5154 \begin_layout Plain Layout
5156 \begin_inset space \textvisiblespace{}
5162 \begin_inset space \textvisiblespace{}
5170 <cell alignment="center" valignment="top" usebox="none">
5173 \begin_layout Plain Layout
5174 \begin_inset Formula $A_{1},\ldots,A_{n}$
5184 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5187 \begin_layout Plain Layout
5189 \begin_inset space \textvisiblespace{}
5195 \begin_inset space \textvisiblespace{}
5203 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5206 \begin_layout Plain Layout
5207 \begin_inset Formula $A_{1}+\cdots+A_{n}$
5217 <cell alignment="center" valignment="top" usebox="none">
5220 \begin_layout Plain Layout
5228 <cell alignment="center" valignment="top" usebox="none">
5231 \begin_layout Plain Layout
5232 \begin_inset Formula $\vdots$
5242 <cell alignment="center" valignment="top" usebox="none">
5245 \begin_layout Plain Layout
5253 <cell alignment="center" valignment="top" usebox="none">
5256 \begin_layout Plain Layout
5257 \begin_inset Formula $\ddots$
5267 <cell alignment="center" valignment="top" usebox="none">
5270 \begin_layout Plain Layout
5278 <cell alignment="center" valignment="top" usebox="none">
5281 \begin_layout Plain Layout
5282 \begin_inset Formula $\iddots$
5292 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5295 \begin_layout Plain Layout
5297 \begin_inset space \thinspace{}
5300 matrix with the different dots
5305 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5308 \begin_layout Plain Layout
5309 \begin_inset Formula $\begin{array}{ccc}
5310 A_{11} & \cdots & A_{1m}\\
5311 \vdots & \ddots & \vdots\\
5312 A_{n1} & \cdots & A_{nm}
5329 \begin_layout Standard
5330 The ellipses available in menu
5332 Insert\SpecialChar menuseparator
5334 \begin_inset space ~
5348 \begin_layout Standard
5349 \begin_inset VSpace medskip
5360 Use mathdots package (automatically)
5362 must be set in the document settings under
5365 \begin_inset space ~
5371 \begin_inset Newline newline
5376 Use mathdots package
5378 will improve the appearance of all dots in the documents if their font
5379 style or size is not the default.
5382 \begin_layout Standard
5383 \begin_inset VSpace medskip
5386 Specially for matrices there are ellipses that span over several columns.
5387 They are created with the command
5394 \begin_inset Index idx
5399 \begin_layout Plain Layout
5401 \begin_inset IndexMacro subentry
5404 \begin_layout Plain Layout
5411 \begin_inset IndexMacro subentry
5414 \begin_layout Plain Layout
5427 and have the following scheme
5428 \change_inserted 5863208 1612709418
5440 \begin_inset space ~
5450 \begin_layout Standard
5455 hdotsfor[distance]{number of columns}
5458 \begin_layout Standard
5459 The number of columns specifies how many columns should be spanned.
5460 Distance is a factor for the distance between the dots.
5463 \begin_layout Standard
5464 In the following matrix the command
5470 was inserted in the first box of the second line to get an ellipsis with
5471 a dot distance twice as long as with the command
5478 \begin_inset Formula
5480 \left(\begin{array}{cccc}
5489 Note that the matrix fields that should be spanned must be empty, otherwise
5490 you get \SpecialChar LaTeX
5494 \begin_layout Standard
5495 \begin_inset VSpace bigskip
5498 Furthermore you can fill with the command
5505 \begin_inset Index idx
5510 \begin_layout Plain Layout
5512 \begin_inset IndexMacro subentry
5515 \begin_layout Plain Layout
5522 \begin_inset IndexMacro subentry
5525 \begin_layout Plain Layout
5538 the rest of a line with dots.
5539 The effect of these commands is the same as with
5546 \begin_inset CommandInset ref
5548 reference "subsec:Variable-Space"
5555 \begin_layout Standard
5556 For example the command
5561 \begin_inset space \textvisiblespace{}
5569 \begin_layout Standard
5570 \begin_inset Formula $A\dotfill B$
5576 \begin_layout Standard
5583 there is for a line the command
5590 \begin_inset Index idx
5595 \begin_layout Plain Layout
5597 \begin_inset IndexMacro subentry
5600 \begin_layout Plain Layout
5607 \begin_inset IndexMacro subentry
5610 \begin_layout Plain Layout
5626 \begin_layout Standard
5627 \begin_inset Formula $A\hrulefill B$
5633 \begin_layout Standard
5634 To use the commands for text, they have to be inserted in \SpecialChar TeX
5638 \begin_layout Section
5640 \begin_inset CommandInset label
5647 \begin_inset Index idx
5652 \begin_layout Plain Layout
5661 \begin_layout Standard
5662 Matrices can be inserted via the math toolbar button
5665 arg "dialog-show mathmatrix"
5670 Insert\SpecialChar menuseparator
5671 Math\SpecialChar menuseparator
5675 In the matrix dialog you can specify the number of columns and rows, the
5676 alignment and the decoration.
5677 The vertical alignment is only of importance for matrices in inline formulas:
5680 \begin_layout Standard
5681 The first matrix is top
5682 \begin_inset Formula $\begin{array}[t]{cccc}
5690 \begin_inset Formula $\begin{array}{cccc}
5697 and the third bottom
5698 \begin_inset Formula $\begin{array}[b]{cccc}
5708 \begin_layout Standard
5709 The horizontal alignment specifies how the column entries should be aligned.
5710 It is set by entering a letter for every column.
5715 denotes left aligned,
5724 To create for example a 4
5729 \begin_inset space ~
5732 matrix where the first column is left aligned, the second and third are
5733 centered and the last one is right aligned, one enters for the horizontal
5739 Normally in a matrix all columns are centered, therefore the default for
5747 \begin_layout Standard
5748 Horizontal alignment:
5751 \begin_layout Standard
5757 \begin_inset Formula $\begin{array}{lll}
5769 \begin_inset Formula $\begin{array}{ccc}
5781 \begin_inset Formula $\begin{array}{rrr}
5791 \begin_layout Standard
5792 To subsequently add or delete rows and columns, the math toolbar buttons
5796 arg "tabular-feature append-row"
5802 arg "tabular-feature delete-row"
5806 \begin_inset space \thinspace{}
5811 Edit\SpecialChar menuseparator
5815 New rows can also be created with
5818 arg "newline-insert newline"
5824 \begin_layout Standard
5825 \begin_inset VSpace bigskip
5829 \change_deleted 47243155 1563226130
5831 \change_deleted -563046850 1563190969
5835 \change_inserted -563046850 1563190971
5841 \change_deleted -563046850 1563192602
5843 \change_inserted -563046850 1563192607
5846 parentheses in the selected style around the matrix
5847 \change_inserted -563046850 1563192780
5852 style, suitable for an inline matrix like this one
5853 \begin_inset Formula $\bigl(\begin{smallmatrix}0 & \textrm{-}\mathrm{i}\\
5855 \end{smallmatrix}\bigr)$
5862 \change_inserted -563046850 1563192943
5863 Here the parentheses have been added manually using commands
5876 \begin_layout Standard
5878 \change_deleted -563046850 1563192735
5881 Alternatively, parentheses can
5882 \change_deleted -563046850 1563192971
5885 be created with the commands
5892 \begin_inset Index idx
5897 \begin_layout Plain Layout
5899 \begin_inset IndexMacro subentry
5902 \begin_layout Plain Layout
5909 \begin_inset IndexMacro subentry
5912 \begin_layout Plain Layout
5932 \begin_inset Index idx
5937 \begin_layout Plain Layout
5939 \begin_inset IndexMacro subentry
5942 \begin_layout Plain Layout
5949 \begin_inset IndexMacro subentry
5952 \begin_layout Plain Layout
5968 \begin_inset space ~
5974 \begin_inset CommandInset ref
5976 reference "subsec:Automatic-Bracket-Size"
5980 , or by using the following commands:
5981 \begin_inset VSpace medskip
5987 \begin_layout Standard
5988 \begin_inset space \hfill{}
5992 \begin_inset Tabular
5993 <lyxtabular version="3" rows="4" columns="2">
5994 <features booktabs="true" tabularvalignment="middle">
5995 <column alignment="center" valignment="top" width="0pt">
5996 <column alignment="center" valignment="top">
5998 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6001 \begin_layout Plain Layout
6007 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6010 \begin_layout Plain Layout
6017 <row topspace="1.5mm">
6018 <cell alignment="center" valignment="top" usebox="none">
6021 \begin_layout Plain Layout
6025 \begin_inset space \textvisiblespace{}
6033 \begin_inset space \thinspace{}
6041 <cell alignment="center" valignment="top" usebox="none">
6044 \begin_layout Plain Layout
6045 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
6046 0 & \textrm{-}\mathrm{i}\\
6048 \end{array}\end{bmatrix}$
6057 <row topspace="1.5mm" bottomspace="0.5mm">
6058 <cell alignment="center" valignment="top" usebox="none">
6061 \begin_layout Plain Layout
6065 \begin_inset space \textvisiblespace{}
6073 \begin_inset space \thinspace{}
6081 <cell alignment="center" valignment="top" usebox="none">
6084 \begin_layout Plain Layout
6085 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
6086 0 & \textrm{-}\mathrm{i}\\
6088 \end{array}\end{Bmatrix}$
6098 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6101 \begin_layout Plain Layout
6105 \begin_inset space \textvisiblespace{}
6113 \begin_inset space \thinspace{}
6121 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6124 \begin_layout Plain Layout
6125 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
6126 0 & \textrm{-}\mathrm{i}\\
6128 \end{array}\end{pmatrix}$
6142 \begin_inset space \hfill{}
6146 \begin_inset Tabular
6147 <lyxtabular version="3" rows="4" columns="2">
6148 <features booktabs="true" tabularvalignment="middle">
6149 <column alignment="center" valignment="top" width="0pt">
6150 <column alignment="center" valignment="top">
6152 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6155 \begin_layout Plain Layout
6161 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6164 \begin_layout Plain Layout
6171 <row topspace="1.5mm">
6172 <cell alignment="center" valignment="top" usebox="none">
6175 \begin_layout Plain Layout
6179 \begin_inset space \textvisiblespace{}
6187 \begin_inset space \thinspace{}
6195 <cell alignment="center" valignment="top" usebox="none">
6198 \begin_layout Plain Layout
6199 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
6200 0 & \textrm{-}\mathrm{i}\\
6202 \end{array}\end{vmatrix}$
6211 <row topspace="1.5mm" bottomspace="0.5mm">
6212 <cell alignment="center" valignment="top" usebox="none">
6215 \begin_layout Plain Layout
6219 \begin_inset space \textvisiblespace{}
6227 \begin_inset space \thinspace{}
6235 <cell alignment="center" valignment="top" usebox="none">
6238 \begin_layout Plain Layout
6239 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
6240 0 & \textrm{-}\mathrm{i}\\
6242 \end{array}\end{Vmatrix}$
6252 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6255 \begin_layout Plain Layout
6259 \begin_inset space \textvisiblespace{}
6267 \begin_inset space \thinspace{}
6275 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6278 \begin_layout Plain Layout
6279 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
6280 0 & \textrm{-}\mathrm{i}\\
6282 \end{array}\end{matrix}$
6296 \begin_inset space \hfill{}
6302 \begin_layout Standard
6303 \begin_inset VSpace medskip
6307 \begin_inset space \thinspace{}
6311 \begin_inset space \space{}
6320 is inserted, a blue box appears between two vertical lines where the matrix
6322 \begin_inset Newline newline
6325 Note that decorated matrices ignore the vertical alignment.
6328 \begin_layout Standard
6329 \begin_inset VSpace bigskip
6332 As all multiline formulas are matrices, the length
6339 \begin_inset Index idx
6344 \begin_layout Plain Layout
6346 \begin_inset IndexMacro subentry
6349 \begin_layout Plain Layout
6356 \begin_inset IndexMacro subentry
6359 \begin_layout Plain Layout
6372 that is described in
6373 \begin_inset CommandInset ref
6375 reference "subsec:Column-Separation"
6379 can also be used to change the column separation of matrices.
6382 \begin_layout Standard
6383 To change the row separation, the command
6390 \begin_inset Index idx
6395 \begin_layout Plain Layout
6397 \begin_inset IndexMacro subentry
6400 \begin_layout Plain Layout
6407 \begin_inset IndexMacro subentry
6410 \begin_layout Plain Layout
6426 \begin_layout Standard
6433 arraystretch}{stretch factor}
6434 \begin_inset Index idx
6439 \begin_layout Plain Layout
6441 \begin_inset IndexMacro subentry
6444 \begin_layout Plain Layout
6451 \begin_inset IndexMacro subentry
6454 \begin_layout Plain Layout
6470 \begin_layout Standard
6477 assigns the stretch factor to the predefined command
6484 For example to double the row separation, use a stretch factor of 2.
6485 This is then used for all following matrices.
6486 To restore the original separation, assign a stretch factor of 1 to
6495 \begin_layout Standard
6497 \change_inserted 47243155 1563226178
6498 Small inline matrices can also be obtained using
6499 \change_deleted 47243155 1563226182
6500 To set matrices into a text line,
6509 \begin_inset Index idx
6514 \begin_layout Plain Layout
6516 \begin_inset IndexMacro subentry
6519 \begin_layout Plain Layout
6526 \begin_inset IndexMacro subentry
6529 \begin_layout Plain Layout
6543 \change_deleted 47243155 1563226186
6547 When it is inserted in a line a blue box with two dashed lines appears.
6548 Adjust the matrix rows and columns as desired.
6551 \begin_layout Standard
6553 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
6555 \end{smallmatrix}\right)$
6559 \change_inserted 47243155 1563226243
6560 with automatic delimiters around it
6565 \begin_layout Section
6566 Brackets and Delimiters
6567 \begin_inset Index idx
6572 \begin_layout Plain Layout
6579 \begin_inset Index idx
6584 \begin_layout Plain Layout
6593 \begin_layout Subsection
6594 Vertical Brackets and Delimiters
6595 \begin_inset Index idx
6600 \begin_layout Plain Layout
6602 \begin_inset IndexMacro subentry
6605 \begin_layout Plain Layout
6619 \begin_layout Standard
6620 \begin_inset space \hfill{}
6624 \begin_inset Tabular
6625 <lyxtabular version="3" rows="9" columns="2">
6626 <features booktabs="true" tabularvalignment="middle">
6627 <column alignment="center" valignment="top" width="0pt">
6628 <column alignment="center" valignment="top" width="0pt">
6630 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6633 \begin_layout Plain Layout
6639 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6642 \begin_layout Plain Layout
6650 <cell alignment="center" valignment="top" usebox="none">
6653 \begin_layout Plain Layout
6659 <cell alignment="center" valignment="top" usebox="none">
6662 \begin_layout Plain Layout
6663 \begin_inset Formula $($
6673 <cell alignment="center" valignment="top" usebox="none">
6676 \begin_layout Plain Layout
6682 <cell alignment="center" valignment="top" usebox="none">
6685 \begin_layout Plain Layout
6686 \begin_inset Formula $\{$
6696 <cell alignment="center" valignment="top" usebox="none">
6699 \begin_layout Plain Layout
6705 <cell alignment="center" valignment="top" usebox="none">
6708 \begin_layout Plain Layout
6709 \begin_inset Formula $[$
6719 <cell alignment="center" valignment="top" usebox="none">
6722 \begin_layout Plain Layout
6730 <cell alignment="center" valignment="top" usebox="none">
6733 \begin_layout Plain Layout
6734 \begin_inset Formula $\langle$
6744 <cell alignment="center" valignment="top" usebox="none">
6747 \begin_layout Plain Layout
6755 <cell alignment="center" valignment="top" usebox="none">
6758 \begin_layout Plain Layout
6759 \begin_inset Formula $\lceil$
6769 <cell alignment="center" valignment="top" usebox="none">
6772 \begin_layout Plain Layout
6780 <cell alignment="center" valignment="top" usebox="none">
6783 \begin_layout Plain Layout
6784 \begin_inset Formula $\lfloor$
6794 <cell alignment="center" valignment="top" usebox="none">
6797 \begin_layout Plain Layout
6803 <cell alignment="center" valignment="top" usebox="none">
6806 \begin_layout Plain Layout
6807 \begin_inset Formula $/$
6817 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6820 \begin_layout Plain Layout
6826 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
6829 \begin_layout Plain Layout
6830 \begin_inset Formula $|$
6844 \begin_inset space \hfill{}
6848 \begin_inset Tabular
6849 <lyxtabular version="3" rows="9" columns="2">
6850 <features booktabs="true" tabularvalignment="middle">
6851 <column alignment="center" valignment="top" width="0pt">
6852 <column alignment="center" valignment="top" width="0pt">
6854 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6857 \begin_layout Plain Layout
6863 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6866 \begin_layout Plain Layout
6874 <cell alignment="center" valignment="top" usebox="none">
6877 \begin_layout Plain Layout
6883 <cell alignment="center" valignment="top" usebox="none">
6886 \begin_layout Plain Layout
6887 \begin_inset Formula $)$
6897 <cell alignment="center" valignment="top" usebox="none">
6900 \begin_layout Plain Layout
6906 <cell alignment="center" valignment="top" usebox="none">
6909 \begin_layout Plain Layout
6910 \begin_inset Formula $\}$
6920 <cell alignment="center" valignment="top" usebox="none">
6923 \begin_layout Plain Layout
6929 <cell alignment="center" valignment="top" usebox="none">
6932 \begin_layout Plain Layout
6933 \begin_inset Formula $]$
6943 <cell alignment="center" valignment="top" usebox="none">
6946 \begin_layout Plain Layout
6954 <cell alignment="center" valignment="top" usebox="none">
6957 \begin_layout Plain Layout
6958 \begin_inset Formula $\rangle$
6968 <cell alignment="center" valignment="top" usebox="none">
6971 \begin_layout Plain Layout
6979 <cell alignment="center" valignment="top" usebox="none">
6982 \begin_layout Plain Layout
6983 \begin_inset Formula $\rceil$
6993 <cell alignment="center" valignment="top" usebox="none">
6996 \begin_layout Plain Layout
7004 <cell alignment="center" valignment="top" usebox="none">
7007 \begin_layout Plain Layout
7008 \begin_inset Formula $\rfloor$
7018 <cell alignment="center" valignment="top" usebox="none">
7021 \begin_layout Plain Layout
7031 <cell alignment="center" valignment="top" usebox="none">
7034 \begin_layout Plain Layout
7035 \begin_inset Formula $\backslash$
7045 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7048 \begin_layout Plain Layout
7056 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7059 \begin_layout Plain Layout
7060 \begin_inset Formula $\|$
7074 \begin_inset space \hfill{}
7080 \begin_layout Standard
7083 \begin_inset Note Greyedout
7086 \begin_layout Plain Layout
7099 \begin_inset Index idx
7104 \begin_layout Plain Layout
7106 \begin_inset IndexMacro subentry
7109 \begin_layout Plain Layout
7116 \begin_inset IndexMacro subentry
7119 \begin_layout Plain Layout
7132 must be used for the backslash, because the command
7140 produces a line break there.
7148 \begin_layout Standard
7149 For all characters listed above the size can be adjusted with the commands
7150 described in the following two subsections.
7151 When using these commands, the characters < and > can directly be used
7152 instead of the commands
7167 \begin_layout Subsubsection
7169 \begin_inset CommandInset label
7171 name "subsec:Manual-Bracket-Size"
7176 \begin_inset Index idx
7181 \begin_layout Plain Layout
7183 \begin_inset IndexMacro subentry
7186 \begin_layout Plain Layout
7200 \begin_layout Standard
7201 The bracket size can be specified manually by the \SpecialChar LaTeX
7209 \begin_inset Index idx
7214 \begin_layout Plain Layout
7216 \begin_inset IndexMacro subentry
7219 \begin_layout Plain Layout
7226 \begin_inset IndexMacro subentry
7229 \begin_layout Plain Layout
7267 denotes the smallest and
7273 the largest bracket size.
7276 \begin_layout Standard
7277 These commands are used to emphasize levels of brackets:
7280 \begin_layout Standard
7282 \begin_inset Tabular
7283 <lyxtabular version="3" rows="2" columns="2">
7284 <features booktabs="true" tabularvalignment="middle">
7285 <column alignment="center" valignment="top" width="0pt">
7286 <column alignment="center" valignment="top" width="0pt">
7288 <cell alignment="center" valignment="top" usebox="none">
7291 \begin_layout Plain Layout
7292 All brackets in the same size:
7297 <cell alignment="center" valignment="top" usebox="none">
7300 \begin_layout Plain Layout
7301 \begin_inset Formula $((A+B)(A-B))^{C}$
7310 <row topspace="2mm">
7311 <cell alignment="center" valignment="top" usebox="none">
7314 \begin_layout Plain Layout
7320 <cell alignment="center" valignment="top" usebox="none">
7323 \begin_layout Plain Layout
7324 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
7340 \begin_layout Standard
7341 For the second formula the command
7348 \begin_inset space \textvisiblespace{}
7356 \begin_layout Standard
7357 Here is an example containing all bracket sizes:
7360 \begin_layout Standard
7377 \begin_inset space \textvisiblespace{}
7385 \begin_inset space \textvisiblespace{}
7389 \begin_inset space \textvisiblespace{}
7399 \begin_layout Standard
7401 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
7407 \begin_layout Standard
7414 -commands there is a variant,
7421 \begin_inset Index idx
7426 \begin_layout Plain Layout
7428 \begin_inset IndexMacro subentry
7431 \begin_layout Plain Layout
7438 \begin_inset IndexMacro subentry
7441 \begin_layout Plain Layout
7454 , that adds a bit more space between the bracket and its content.
7468 \begin_inset Index idx
7473 \begin_layout Plain Layout
7475 \begin_inset IndexMacro subentry
7478 \begin_layout Plain Layout
7485 \begin_inset IndexMacro subentry
7488 \begin_layout Plain Layout
7503 , don't add additional space.
7508 at the end of the command
7514 is for a left bracket; for a right bracket this is replaced by an
7519 A left or right bracket can each be an opening or closing bracket.
7522 \begin_layout Standard
7523 The following table contains comparisons of the variants:
7526 \begin_layout Standard
7528 \begin_inset Tabular
7529 <lyxtabular version="3" rows="5" columns="2">
7530 <features booktabs="true" tabularvalignment="middle">
7531 <column alignment="center" valignment="top" width="0pt">
7532 <column alignment="center" valignment="middle">
7534 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7537 \begin_layout Plain Layout
7543 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7546 \begin_layout Plain Layout
7553 <row topspace="2mm">
7554 <cell alignment="center" valignment="top" usebox="none">
7557 \begin_layout Plain Layout
7567 \begin_inset space \textvisiblespace{}
7577 <cell alignment="center" valignment="top" usebox="none">
7580 \begin_layout Plain Layout
7581 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
7590 <row topspace="2mm">
7591 <cell alignment="center" valignment="top" usebox="none">
7594 \begin_layout Plain Layout
7604 \begin_inset space \textvisiblespace{}
7614 <cell alignment="center" valignment="top" usebox="none">
7617 \begin_layout Plain Layout
7618 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
7627 <row topspace="2mm" bottomspace="0.5mm">
7628 <cell alignment="center" valignment="top" usebox="none">
7631 \begin_layout Plain Layout
7641 \begin_inset space \textvisiblespace{}
7651 <cell alignment="center" valignment="top" usebox="none">
7654 \begin_layout Plain Layout
7655 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
7664 <row topspace="1.5mm" bottomspace="0.5mm">
7665 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7668 \begin_layout Plain Layout
7680 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7683 \begin_layout Plain Layout
7684 \begin_inset Formula $\bigl)\ln(3x)\bigr($
7700 \begin_layout Subsubsection
7701 Automatic Bracket Size
7702 \begin_inset CommandInset label
7704 name "subsec:Automatic-Bracket-Size"
7709 \begin_inset Index idx
7714 \begin_layout Plain Layout
7716 \begin_inset IndexMacro subentry
7719 \begin_layout Plain Layout
7733 \begin_layout Standard
7734 Variably sized brackets can be inserted with the commands
7741 \begin_inset Index idx
7746 \begin_layout Plain Layout
7748 \begin_inset IndexMacro subentry
7751 \begin_layout Plain Layout
7758 \begin_inset IndexMacro subentry
7761 \begin_layout Plain Layout
7781 \begin_inset Index idx
7786 \begin_layout Plain Layout
7788 \begin_inset IndexMacro subentry
7791 \begin_layout Plain Layout
7798 \begin_inset IndexMacro subentry
7801 \begin_layout Plain Layout
7814 or via the math toolbar button
7817 arg "dialog-show mathdelimiter"
7821 The desired bracket must be inserted directly behind the
7834 The bracket size will then automatically be calculated for the output.
7837 \begin_layout Standard
7839 normal bracket: The command
7846 \begin_inset space \textvisiblespace{}
7850 \begin_inset Formula $\downarrow$
7854 \begin_inset space \textvisiblespace{}
7860 \begin_inset Formula
7870 \begin_layout Standard
7872 multiline bracket: The command
7881 \begin_inset space \textvisiblespace{}
7885 \begin_inset Formula $\downarrow$
7889 \begin_inset space \textvisiblespace{}
7897 \begin_inset Formula
7899 \ln\left(\frac{A}{C}\right)
7907 \begin_layout Standard
7923 \begin_inset space ~
7929 This has the advantage that you can see in \SpecialChar LyX
7930 immediately the real bracket
7931 size and that the matching right bracket will be created too.
7932 \begin_inset Newline newline
7935 The command for the last example would then be:
7946 \begin_inset space \textvisiblespace{}
7950 \begin_inset Formula $\downarrow$
7956 \begin_layout Standard
7957 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7958 For example the command
7965 \begin_inset space \textvisiblespace{}
7969 \begin_inset Formula $\downarrow$
7973 \begin_inset space \textvisiblespace{}
7983 \begin_inset Formula
7985 \left.\frac{A}{B}\right\}
8004 will be converted by \SpecialChar LyX
8005 to brackets with the correct size when the document
8006 is reloaded and an omitted bracket will appear as dashed line.
8009 \begin_layout Standard
8010 \begin_inset VSpace bigskip
8013 Because all popular \SpecialChar LaTeX
8014 distributions use e\SpecialChar TeX
8015 , an extension to \SpecialChar LaTeX
8024 \begin_inset Index idx
8029 \begin_layout Plain Layout
8031 \begin_inset IndexMacro subentry
8034 \begin_layout Plain Layout
8041 \begin_inset IndexMacro subentry
8044 \begin_layout Plain Layout
8057 is available for all brackets and limits.
8058 With this command the height of the following character is adapted to the
8059 one of the surrounding brackets, for example in the case of physical vectors:
8060 \begin_inset Formula
8062 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
8067 For physical vectors there is a special \SpecialChar LaTeX
8068 -package, described in
8069 \begin_inset CommandInset ref
8071 reference "subsec:Physical-Vectors"
8078 \begin_layout Subsection
8080 \begin_inset Index idx
8085 \begin_layout Plain Layout
8087 \begin_inset IndexMacro subentry
8090 \begin_layout Plain Layout
8104 \begin_layout Standard
8106 \begin_inset Tabular
8107 <lyxtabular version="3" rows="4" columns="2">
8108 <features booktabs="true" tabularvalignment="middle">
8109 <column alignment="center" valignment="top" width="0pt">
8110 <column alignment="center" valignment="top" width="0pt">
8112 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8115 \begin_layout Plain Layout
8121 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8124 \begin_layout Plain Layout
8132 <cell alignment="center" valignment="top" usebox="none">
8135 \begin_layout Plain Layout
8139 \begin_inset space \textvisiblespace{}
8143 \begin_inset space \textvisiblespace{}
8147 \begin_inset Index idx
8152 \begin_layout Plain Layout
8154 \begin_inset IndexMacro subentry
8157 \begin_layout Plain Layout
8164 \begin_inset IndexMacro subentry
8167 \begin_layout Plain Layout
8185 <cell alignment="center" valignment="top" usebox="none">
8188 \begin_layout Plain Layout
8189 \begin_inset Formula $\overbrace{A+B}^{3}$
8198 <row topspace="2mm">
8199 <cell alignment="center" valignment="top" usebox="none">
8202 \begin_layout Plain Layout
8206 \begin_inset space \textvisiblespace{}
8210 \begin_inset space \textvisiblespace{}
8214 \begin_inset Index idx
8219 \begin_layout Plain Layout
8221 \begin_inset IndexMacro subentry
8224 \begin_layout Plain Layout
8231 \begin_inset IndexMacro subentry
8234 \begin_layout Plain Layout
8252 <cell alignment="center" valignment="top" usebox="none">
8255 \begin_layout Plain Layout
8256 \begin_inset Formula $\underbrace{A+B}_{5}$
8266 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8269 \begin_layout Plain Layout
8273 \begin_inset space \textvisiblespace{}
8279 \begin_inset space \textvisiblespace{}
8283 \begin_inset space \textvisiblespace{}
8287 \begin_inset space \textvisiblespace{}
8291 \begin_inset space \textvisiblespace{}
8295 \begin_inset space \textvisiblespace{}
8299 \begin_inset space \textvisiblespace{}
8307 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8310 \begin_layout Plain Layout
8311 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
8327 \begin_layout Standard
8328 In the last example it doesn't matter if
8343 \begin_layout Standard
8344 \begin_inset VSpace medskip
8350 \begin_layout Standard
8351 If in document settings under
8354 \begin_inset space ~
8359 the option for the package
8364 \begin_inset Index idx
8369 \begin_layout Plain Layout
8371 \begin_inset IndexMacro subentry
8374 \begin_layout Plain Layout
8388 \begin_inset space ~
8393 , you will also have access to square brackets:
8396 \begin_layout Standard
8398 \begin_inset Tabular
8399 <lyxtabular version="3" rows="4" columns="2">
8400 <features booktabs="true" tabularvalignment="middle">
8401 <column alignment="center" valignment="top" width="0pt">
8402 <column alignment="center" valignment="top" width="0pt">
8404 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8407 \begin_layout Plain Layout
8413 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8416 \begin_layout Plain Layout
8424 <cell alignment="center" valignment="top" usebox="none">
8427 \begin_layout Plain Layout
8455 \begin_inset space \textvisiblespace{}
8459 \begin_inset Index idx
8464 \begin_layout Plain Layout
8466 \begin_inset IndexMacro subentry
8469 \begin_layout Plain Layout
8476 \begin_inset IndexMacro subentry
8479 \begin_layout Plain Layout
8497 <cell alignment="center" valignment="top" usebox="none">
8500 \begin_layout Plain Layout
8501 \begin_inset Formula $\overbracket{A+B}^{3}$
8510 <row topspace="2mm">
8511 <cell alignment="center" valignment="top" usebox="none">
8514 \begin_layout Plain Layout
8542 \begin_inset space \textvisiblespace{}
8546 \begin_inset Index idx
8551 \begin_layout Plain Layout
8553 \begin_inset IndexMacro subentry
8556 \begin_layout Plain Layout
8563 \begin_inset IndexMacro subentry
8566 \begin_layout Plain Layout
8596 <cell alignment="center" valignment="top" usebox="none">
8599 \begin_layout Plain Layout
8600 \begin_inset Formula $\underbracket{A+B}_{5}$
8610 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8613 \begin_layout Plain Layout
8619 \begin_inset space \textvisiblespace{}
8623 \begin_inset space \textvisiblespace{}
8627 \begin_inset space \textvisiblespace{}
8631 \begin_inset space \textvisiblespace{}
8635 \change_deleted 5863208 1612711596
8637 \begin_inset space \textvisiblespace{}
8647 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8650 \begin_layout Plain Layout
8651 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
8667 \begin_layout Standard
8680 you can change the thickness of the bracket's stroke by specifying the
8681 desired thickness in square brackets behind the command:
8684 \begin_layout Standard
8686 \begin_inset Tabular
8687 <lyxtabular version="3" rows="3" columns="2">
8688 <features booktabs="true" tabularvalignment="middle">
8689 <column alignment="center" valignment="top" width="0pt">
8690 <column alignment="center" valignment="top" width="0pt">
8692 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8695 \begin_layout Plain Layout
8701 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8704 \begin_layout Plain Layout
8712 <cell alignment="center" valignment="top" usebox="none">
8715 \begin_layout Plain Layout
8745 \begin_inset space \textvisiblespace{}
8753 <cell alignment="center" valignment="top" usebox="none">
8756 \begin_layout Plain Layout
8757 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
8766 <row topspace="2mm">
8767 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8770 \begin_layout Plain Layout
8800 \begin_inset space \textvisiblespace{}
8808 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8811 \begin_layout Plain Layout
8812 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
8828 \begin_layout Standard
8829 \begin_inset VSpace bigskip
8832 When brackets overlap each other, multiline formulas as described in
8833 \begin_inset CommandInset ref
8835 reference "sec:Multiline-Formulas"
8840 \begin_inset Formula
8842 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
8843 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
8848 In the first row, the formula is inserted together with the first brace.
8849 It is important that the space command
8853 \begin_layout Plain Layout
8854 Space commands are explained in
8855 \begin_inset CommandInset ref
8857 reference "subsec:Predefined-Space"
8872 is inserted before the first
8873 \begin_inset Formula $d$
8876 because the brace that ends behind the
8877 \begin_inset Formula $q$
8880 prevents the following
8881 \begin_inset Quotes eld
8885 \begin_inset Quotes erd
8888 from being surrounded by spaces.
8892 \begin_layout Plain Layout
8893 Because a bracket is not handled as a character, see
8894 \begin_inset CommandInset ref
8896 reference "subsec:Binary-Operators"
8905 The second brace is inserted in the second row.
8906 As it should begin before the
8907 \begin_inset Formula $b$
8922 \begin_layout Plain Layout
8930 \begin_inset CommandInset ref
8932 reference "subsec:Placeholders"
8941 This space is needed because the
8942 \begin_inset Quotes eld
8946 \begin_inset Quotes erd
8949 is surrounded by spaces in the formula.
8950 The brace is placed under the command
8959 \begin_layout Standard
8960 It gets more complicated when brackets overlap each other above and under
8961 the formula as in the following example:
8965 \begin_layout Plain Layout
8977 \begin_inset Formula
8979 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
8980 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
8989 \begin_layout Plain Layout
9000 The first formula row is the same as the second row of the previous example,
9001 with the difference that the brace is above.
9002 The second row contains the formula together with the second brace.
9003 To avoid the space between the upper brace in the first row and the formula,
9004 the row spacing needs to be reduced.
9005 This is not easily done due to a bug in \SpecialChar LyX
9010 \begin_layout Plain Layout
9011 \begin_inset CommandInset href
9013 name "LyX-bug #1505"
9014 target "https://www.lyx.org/trac/ticket/1505"
9024 As a solution for the problem, the global formula row separation
9031 \begin_inset Index idx
9036 \begin_layout Plain Layout
9038 \begin_inset IndexMacro subentry
9041 \begin_layout Plain Layout
9048 \begin_inset IndexMacro subentry
9051 \begin_layout Plain Layout
9064 must be changed to -6
9065 \begin_inset space \thinspace{}
9068 pt before the formula with the command
9084 is set back after the formula to the standard value of 3
9085 \begin_inset space \thinspace{}
9088 pt using the same command.
9089 More about the row separation in formulas is explained in
9090 \begin_inset CommandInset ref
9092 reference "subsec:Line-Separation"
9099 \begin_layout Section
9101 \begin_inset Index idx
9106 \begin_layout Plain Layout
9115 \begin_layout Standard
9116 Arrows can be inserted via the math toolbar button
9119 arg "math-insert \\leftarrow"
9122 or the commands listed in the following subsections.
9125 \begin_layout Subsection
9127 \begin_inset Index idx
9132 \begin_layout Plain Layout
9134 \begin_inset IndexMacro subentry
9137 \begin_layout Plain Layout
9151 \begin_layout Standard
9152 \begin_inset space \hfill{}
9156 \begin_inset Tabular
9157 <lyxtabular version="3" rows="8" columns="2">
9158 <features booktabs="true" tabularvalignment="middle">
9159 <column alignment="center" valignment="top" width="0pt">
9160 <column alignment="center" valignment="top" width="0pt">
9162 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9165 \begin_layout Plain Layout
9171 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9174 \begin_layout Plain Layout
9182 <cell alignment="center" valignment="top" usebox="none">
9185 \begin_layout Plain Layout
9193 <cell alignment="center" valignment="top" usebox="none">
9196 \begin_layout Plain Layout
9197 \begin_inset Formula $\gets$
9207 <cell alignment="center" valignment="top" usebox="none">
9210 \begin_layout Plain Layout
9218 <cell alignment="center" valignment="top" usebox="none">
9221 \begin_layout Plain Layout
9222 \begin_inset Formula $\Leftarrow$
9232 <cell alignment="center" valignment="top" usebox="none">
9235 \begin_layout Plain Layout
9243 <cell alignment="center" valignment="top" usebox="none">
9246 \begin_layout Plain Layout
9247 \begin_inset Formula $\longleftarrow$
9257 <cell alignment="center" valignment="top" usebox="none">
9260 \begin_layout Plain Layout
9268 <cell alignment="center" valignment="top" usebox="none">
9271 \begin_layout Plain Layout
9272 \begin_inset Formula $\Longleftarrow$
9282 <cell alignment="center" valignment="top" usebox="none">
9285 \begin_layout Plain Layout
9293 <cell alignment="center" valignment="top" usebox="none">
9296 \begin_layout Plain Layout
9297 \begin_inset Formula $\leftharpoonup$
9307 <cell alignment="center" valignment="top" usebox="none">
9310 \begin_layout Plain Layout
9318 <cell alignment="center" valignment="top" usebox="none">
9321 \begin_layout Plain Layout
9322 \begin_inset Formula $\leftharpoondown$
9332 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9335 \begin_layout Plain Layout
9343 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9346 \begin_layout Plain Layout
9347 \begin_inset Formula $\hookleftarrow$
9361 \begin_inset space \hfill{}
9365 \begin_inset Tabular
9366 <lyxtabular version="3" rows="8" columns="2">
9367 <features booktabs="true" tabularvalignment="middle">
9368 <column alignment="center" valignment="top" width="0pt">
9369 <column alignment="center" valignment="top" width="0pt">
9371 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9374 \begin_layout Plain Layout
9380 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9383 \begin_layout Plain Layout
9391 <cell alignment="center" valignment="top" usebox="none">
9394 \begin_layout Plain Layout
9402 <cell alignment="center" valignment="top" usebox="none">
9405 \begin_layout Plain Layout
9406 \begin_inset Formula $\to$
9416 <cell alignment="center" valignment="top" usebox="none">
9419 \begin_layout Plain Layout
9427 <cell alignment="center" valignment="top" usebox="none">
9430 \begin_layout Plain Layout
9431 \begin_inset Formula $\Rightarrow$
9441 <cell alignment="center" valignment="top" usebox="none">
9444 \begin_layout Plain Layout
9452 <cell alignment="center" valignment="top" usebox="none">
9455 \begin_layout Plain Layout
9456 \begin_inset Formula $\longrightarrow$
9466 <cell alignment="center" valignment="top" usebox="none">
9469 \begin_layout Plain Layout
9477 <cell alignment="center" valignment="top" usebox="none">
9480 \begin_layout Plain Layout
9481 \begin_inset Formula $\Longrightarrow$
9491 <cell alignment="center" valignment="top" usebox="none">
9494 \begin_layout Plain Layout
9502 <cell alignment="center" valignment="top" usebox="none">
9505 \begin_layout Plain Layout
9506 \begin_inset Formula $\rightharpoonup$
9516 <cell alignment="center" valignment="top" usebox="none">
9519 \begin_layout Plain Layout
9527 <cell alignment="center" valignment="top" usebox="none">
9530 \begin_layout Plain Layout
9531 \begin_inset Formula $\rightharpoondown$
9541 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9544 \begin_layout Plain Layout
9552 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9555 \begin_layout Plain Layout
9556 \begin_inset Formula $\hookrightarrow$
9570 \begin_inset space \hfill{}
9576 \begin_layout Standard
9577 \begin_inset space \hfill{}
9581 \begin_inset Tabular
9582 <lyxtabular version="3" rows="6" columns="2">
9583 <features booktabs="true" tabularvalignment="middle">
9584 <column alignment="center" valignment="top" width="0pt">
9585 <column alignment="center" valignment="top" width="0pt">
9587 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9590 \begin_layout Plain Layout
9596 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9599 \begin_layout Plain Layout
9607 <cell alignment="center" valignment="top" usebox="none">
9610 \begin_layout Plain Layout
9618 <cell alignment="center" valignment="top" usebox="none">
9621 \begin_layout Plain Layout
9622 \begin_inset Formula $\leftrightarrow$
9632 <cell alignment="center" valignment="top" usebox="none">
9635 \begin_layout Plain Layout
9643 <cell alignment="center" valignment="top" usebox="none">
9646 \begin_layout Plain Layout
9647 \begin_inset Formula $\Leftrightarrow$
9657 <cell alignment="center" valignment="top" usebox="none">
9660 \begin_layout Plain Layout
9668 <cell alignment="center" valignment="top" usebox="none">
9671 \begin_layout Plain Layout
9672 \begin_inset Formula $\longleftrightarrow$
9682 <cell alignment="center" valignment="top" usebox="none">
9685 \begin_layout Plain Layout
9693 <cell alignment="center" valignment="top" usebox="none">
9696 \begin_layout Plain Layout
9697 \begin_inset Formula $\Longleftrightarrow$
9707 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9710 \begin_layout Plain Layout
9718 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9721 \begin_layout Plain Layout
9722 \begin_inset Formula $\rightleftharpoons$
9736 \begin_inset space \hspace{}
9741 \begin_inset space \hfill{}
9745 \begin_inset Tabular
9746 <lyxtabular version="3" rows="5" columns="2">
9747 <features booktabs="true" tabularvalignment="middle">
9748 <column alignment="center" valignment="top" width="0pt">
9749 <column alignment="center" valignment="top" width="0pt">
9751 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9754 \begin_layout Plain Layout
9760 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9763 \begin_layout Plain Layout
9771 <cell alignment="center" valignment="top" usebox="none">
9774 \begin_layout Plain Layout
9782 <cell alignment="center" valignment="top" usebox="none">
9785 \begin_layout Plain Layout
9786 \begin_inset Formula $\mapsto$
9796 <cell alignment="center" valignment="top" usebox="none">
9799 \begin_layout Plain Layout
9807 <cell alignment="center" valignment="top" usebox="none">
9810 \begin_layout Plain Layout
9811 \begin_inset Formula $\longmapsto$
9821 <cell alignment="center" valignment="top" usebox="none">
9824 \begin_layout Plain Layout
9832 <cell alignment="center" valignment="top" usebox="none">
9835 \begin_layout Plain Layout
9836 \begin_inset Formula $\leadsto$
9846 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9849 \begin_layout Plain Layout
9857 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9860 \begin_layout Plain Layout
9861 \begin_inset Formula $\dasharrow$
9875 \begin_inset space \hfill{}
9881 \begin_layout Standard
9882 \begin_inset VSpace medskip
9885 Arrows used as accents such as vector arrows are listed in
9886 \begin_inset CommandInset ref
9888 reference "sec:Accents"
9895 \begin_layout Standard
9896 \begin_inset VSpace bigskip
9900 \begin_inset Index idx
9905 \begin_layout Plain Layout
9907 \begin_inset IndexMacro subentry
9910 \begin_layout Plain Layout
9921 are also available using the commands
9928 \begin_inset Index idx
9933 \begin_layout Plain Layout
9935 \begin_inset IndexMacro subentry
9938 \begin_layout Plain Layout
9945 \begin_inset IndexMacro subentry
9948 \begin_layout Plain Layout
9968 \begin_inset Index idx
9973 \begin_layout Plain Layout
9975 \begin_inset IndexMacro subentry
9978 \begin_layout Plain Layout
9985 \begin_inset IndexMacro subentry
9988 \begin_layout Plain Layout
10002 When inserting one of these commands in a formula, an arrow with two blue
10003 boxes appears indicating where the labels can be inserted.
10004 The length of the arrow adapts to the label width.
10007 \begin_layout Standard
10009 \begin_inset Tabular
10010 <lyxtabular version="3" rows="3" columns="2">
10011 <features booktabs="true" tabularvalignment="middle">
10012 <column alignment="center" valignment="top" width="0pt">
10013 <column alignment="center" valignment="top" width="0pt">
10015 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10018 \begin_layout Plain Layout
10024 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10027 \begin_layout Plain Layout
10035 <cell alignment="center" valignment="top" usebox="none">
10038 \begin_layout Plain Layout
10042 \begin_inset space \textvisiblespace{}
10046 \begin_inset Formula $\downarrow$
10050 \begin_inset Formula $\to$
10058 <cell alignment="center" valignment="top" usebox="none">
10061 \begin_layout Plain Layout
10062 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
10071 <row topspace="2mm">
10072 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10075 \begin_layout Plain Layout
10079 \begin_inset space \textvisiblespace{}
10083 \begin_inset Formula $\downarrow$
10087 \begin_inset Formula $\to$
10095 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10098 \begin_layout Plain Layout
10099 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
10115 \begin_layout Standard
10116 \begin_inset VSpace medskip
10122 \begin_layout Standard
10123 If in the document settings under
10126 \begin_inset space ~
10136 \begin_inset Index idx
10141 \begin_layout Plain Layout
10143 \begin_inset IndexMacro subentry
10146 \begin_layout Plain Layout
10160 \begin_inset space ~
10165 is set, you will have access to the following labeled arrows:
10168 \begin_layout Standard
10169 \begin_inset Newpage newpage
10175 \begin_layout Standard
10177 \begin_inset space \hspace*{\fill}
10181 \begin_inset Tabular
10182 <lyxtabular version="3" rows="7" columns="2">
10183 <features booktabs="true" tabularvalignment="middle">
10184 <column alignment="center" valignment="top" width="0pt">
10185 <column alignment="center" valignment="top" width="0pt">
10187 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10190 \begin_layout Plain Layout
10196 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10199 \begin_layout Plain Layout
10207 <cell alignment="center" valignment="top" usebox="none">
10210 \begin_layout Plain Layout
10230 <cell alignment="center" valignment="top" usebox="none">
10233 \begin_layout Plain Layout
10234 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
10243 <row topspace="2mm">
10244 <cell alignment="center" valignment="top" usebox="none">
10247 \begin_layout Plain Layout
10267 <cell alignment="center" valignment="top" usebox="none">
10270 \begin_layout Plain Layout
10271 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
10280 <row topspace="2mm">
10281 <cell alignment="center" valignment="top" usebox="none">
10284 \begin_layout Plain Layout
10304 <cell alignment="center" valignment="top" usebox="none">
10307 \begin_layout Plain Layout
10308 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
10317 <row topspace="2mm">
10318 <cell alignment="center" valignment="top" usebox="none">
10321 \begin_layout Plain Layout
10341 <cell alignment="center" valignment="top" usebox="none">
10344 \begin_layout Plain Layout
10345 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
10354 <row topspace="2mm">
10355 <cell alignment="center" valignment="top" usebox="none">
10358 \begin_layout Plain Layout
10378 <cell alignment="center" valignment="top" usebox="none">
10381 \begin_layout Plain Layout
10382 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
10391 <row topspace="2mm">
10392 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10395 \begin_layout Plain Layout
10415 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10418 \begin_layout Plain Layout
10419 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
10433 \begin_inset space \hspace*{\fill}
10437 \begin_inset Tabular
10438 <lyxtabular version="3" rows="7" columns="2">
10439 <features booktabs="true" tabularvalignment="middle">
10440 <column alignment="center" valignment="top" width="0pt">
10441 <column alignment="center" valignment="top" width="0pt">
10443 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10446 \begin_layout Plain Layout
10452 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10455 \begin_layout Plain Layout
10463 <cell alignment="center" valignment="top" usebox="none">
10466 \begin_layout Plain Layout
10486 <cell alignment="center" valignment="top" usebox="none">
10489 \begin_layout Plain Layout
10490 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
10499 <row topspace="2mm">
10500 <cell alignment="center" valignment="top" usebox="none">
10503 \begin_layout Plain Layout
10523 <cell alignment="center" valignment="top" usebox="none">
10526 \begin_layout Plain Layout
10527 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
10536 <row topspace="2mm">
10537 <cell alignment="center" valignment="top" usebox="none">
10540 \begin_layout Plain Layout
10560 <cell alignment="center" valignment="top" usebox="none">
10563 \begin_layout Plain Layout
10564 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
10573 <row topspace="2mm">
10574 <cell alignment="center" valignment="top" usebox="none">
10577 \begin_layout Plain Layout
10597 <cell alignment="center" valignment="top" usebox="none">
10600 \begin_layout Plain Layout
10601 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
10610 <row topspace="2mm">
10611 <cell alignment="center" valignment="top" usebox="none">
10614 \begin_layout Plain Layout
10634 <cell alignment="center" valignment="top" usebox="none">
10637 \begin_layout Plain Layout
10638 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
10647 <row topspace="2mm">
10648 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10651 \begin_layout Plain Layout
10671 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10674 \begin_layout Plain Layout
10675 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
10689 \begin_inset space \hspace*{\fill}
10695 \begin_layout Standard
10696 The command scheme for all of these arrows is:
10699 \begin_layout Standard
10701 \begin_inset Tabular
10702 <lyxtabular version="3" rows="2" columns="2">
10703 <features booktabs="true" tabularvalignment="middle">
10704 <column alignment="center" valignment="top" width="0pt">
10705 <column alignment="center" valignment="top" width="0pt">
10707 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10710 \begin_layout Plain Layout
10716 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10719 \begin_layout Plain Layout
10726 <row bottomspace="0.5mm">
10727 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10730 \begin_layout Plain Layout
10733 xleftrightarrow[x=a]
10736 \begin_inset Formula $\to$
10744 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10747 \begin_layout Plain Layout
10748 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
10764 \begin_layout Subsection
10765 Vertical and Diagonal Arrows
10766 \begin_inset Index idx
10771 \begin_layout Plain Layout
10773 \begin_inset IndexMacro subentry
10776 \begin_layout Plain Layout
10788 \begin_inset Index idx
10793 \begin_layout Plain Layout
10795 \begin_inset IndexMacro subentry
10798 \begin_layout Plain Layout
10812 \begin_layout Standard
10813 \begin_inset space \hfill{}
10817 \begin_inset Tabular
10818 <lyxtabular version="3" rows="7" columns="2">
10819 <features booktabs="true" tabularvalignment="middle">
10820 <column alignment="center" valignment="top" width="0pt">
10821 <column alignment="center" valignment="top" width="0pt">
10823 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10826 \begin_layout Plain Layout
10832 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10835 \begin_layout Plain Layout
10843 <cell alignment="center" valignment="top" usebox="none">
10846 \begin_layout Plain Layout
10854 <cell alignment="center" valignment="top" usebox="none">
10857 \begin_layout Plain Layout
10858 \begin_inset Formula $\uparrow$
10868 <cell alignment="center" valignment="top" usebox="none">
10871 \begin_layout Plain Layout
10879 <cell alignment="center" valignment="top" usebox="none">
10882 \begin_layout Plain Layout
10883 \begin_inset Formula $\Uparrow$
10893 <cell alignment="center" valignment="top" usebox="none">
10896 \begin_layout Plain Layout
10904 <cell alignment="center" valignment="top" usebox="none">
10907 \begin_layout Plain Layout
10908 \begin_inset Formula $\updownarrow$
10918 <cell alignment="center" valignment="top" usebox="none">
10921 \begin_layout Plain Layout
10929 <cell alignment="center" valignment="top" usebox="none">
10932 \begin_layout Plain Layout
10933 \begin_inset Formula $\Updownarrow$
10943 <cell alignment="center" valignment="top" usebox="none">
10946 \begin_layout Plain Layout
10954 <cell alignment="center" valignment="top" usebox="none">
10957 \begin_layout Plain Layout
10958 \begin_inset Formula $\Downarrow$
10968 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10971 \begin_layout Plain Layout
10979 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10982 \begin_layout Plain Layout
10983 \begin_inset Formula $\downarrow$
10997 \begin_inset space \hfill{}
11001 \begin_inset Tabular
11002 <lyxtabular version="3" rows="5" columns="2">
11003 <features booktabs="true" tabularvalignment="middle">
11004 <column alignment="center" valignment="top" width="0pt">
11005 <column alignment="center" valignment="top" width="0pt">
11007 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11010 \begin_layout Plain Layout
11016 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11019 \begin_layout Plain Layout
11027 <cell alignment="center" valignment="top" usebox="none">
11030 \begin_layout Plain Layout
11038 <cell alignment="center" valignment="top" usebox="none">
11041 \begin_layout Plain Layout
11042 \begin_inset Formula $\nearrow$
11052 <cell alignment="center" valignment="top" usebox="none">
11055 \begin_layout Plain Layout
11063 <cell alignment="center" valignment="top" usebox="none">
11066 \begin_layout Plain Layout
11067 \begin_inset Formula $\searrow$
11077 <cell alignment="center" valignment="top" usebox="none">
11080 \begin_layout Plain Layout
11088 <cell alignment="center" valignment="top" usebox="none">
11091 \begin_layout Plain Layout
11092 \begin_inset Formula $\swarrow$
11102 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11105 \begin_layout Plain Layout
11113 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11116 \begin_layout Plain Layout
11117 \begin_inset Formula $\nwarrow$
11131 \begin_inset space \hfill{}
11137 \begin_layout Standard
11138 \begin_inset VSpace medskip
11141 Vertical arrows can also be used as delimiters together with the commands
11143 \begin_inset CommandInset ref
11145 reference "subsec:Manual-Bracket-Size"
11150 \begin_inset CommandInset ref
11152 reference "subsec:Automatic-Bracket-Size"
11159 \begin_layout Section
11161 \begin_inset CommandInset label
11168 \begin_inset Index idx
11173 \begin_layout Plain Layout
11182 \begin_layout Standard
11183 Accents can be inserted via the math toolbar button
11186 arg "math-insert \\hat"
11189 or the commands listed in the following subsections.
11192 \begin_layout Subsection
11193 Accents for One Character
11197 \begin_layout Plain Layout
11210 \begin_layout Plain Layout
11211 For accents in text see
11212 \begin_inset CommandInset ref
11214 reference "subsec:Accents-in-Text"
11227 \begin_layout Plain Layout
11235 \begin_inset Note Note
11238 \begin_layout Plain Layout
11245 is used to avoid that the footnote appears in the PDF-bookmark.
11248 \begin_layout Plain Layout
11256 \begin_inset CommandInset ref
11258 reference "subsec:Formulas-in-Section"
11268 \begin_inset CommandInset label
11270 name "subsec:Accents-for-one"
11275 \begin_inset Index idx
11280 \begin_layout Plain Layout
11282 \begin_inset IndexMacro subentry
11285 \begin_layout Plain Layout
11299 \begin_layout Standard
11300 \begin_inset space \hfill{}
11304 \begin_inset Tabular
11305 <lyxtabular version="3" rows="8" columns="2">
11306 <features booktabs="true" tabularvalignment="middle">
11307 <column alignment="center" valignment="top" width="0pt">
11308 <column alignment="center" valignment="top" width="0pt">
11310 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11313 \begin_layout Plain Layout
11319 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11322 \begin_layout Plain Layout
11329 <row topspace="1.5mm">
11330 <cell alignment="center" valignment="top" usebox="none">
11333 \begin_layout Plain Layout
11337 \begin_inset space \textvisiblespace{}
11345 <cell alignment="center" valignment="top" usebox="none">
11348 \begin_layout Plain Layout
11349 \begin_inset Formula $\dot{A}$
11358 <row topspace="1.5mm">
11359 <cell alignment="center" valignment="top" usebox="none">
11362 \begin_layout Plain Layout
11366 \begin_inset space \textvisiblespace{}
11374 <cell alignment="center" valignment="top" usebox="none">
11377 \begin_layout Plain Layout
11378 \begin_inset Formula $\ddot{A}$
11387 <row topspace="1.5mm">
11388 <cell alignment="center" valignment="top" usebox="none">
11391 \begin_layout Plain Layout
11395 \begin_inset space \textvisiblespace{}
11403 <cell alignment="center" valignment="top" usebox="none">
11406 \begin_layout Plain Layout
11407 \begin_inset Formula $\dddot{A}$
11416 <row topspace="1.5mm">
11417 <cell alignment="center" valignment="top" usebox="none">
11420 \begin_layout Plain Layout
11424 \begin_inset space \textvisiblespace{}
11432 <cell alignment="center" valignment="top" usebox="none">
11435 \begin_layout Plain Layout
11436 \begin_inset Formula $\ddddot{A}$
11445 <row topspace="1.5mm">
11446 <cell alignment="center" valignment="top" usebox="none">
11449 \begin_layout Plain Layout
11453 \begin_inset space \textvisiblespace{}
11457 \begin_inset Index idx
11462 \begin_layout Plain Layout
11473 <cell alignment="center" valignment="top" usebox="none">
11476 \begin_layout Plain Layout
11477 \begin_inset Formula $\vec{A}$
11486 <row topspace="1.5mm">
11487 <cell alignment="center" valignment="top" usebox="none">
11490 \begin_layout Plain Layout
11494 \begin_inset space \textvisiblespace{}
11502 <cell alignment="center" valignment="top" usebox="none">
11505 \begin_layout Plain Layout
11506 \begin_inset Formula $\bar{A}$
11515 <row topspace="1.5mm">
11516 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11519 \begin_layout Plain Layout
11523 \begin_inset space \textvisiblespace{}
11531 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11534 \begin_layout Plain Layout
11535 \begin_inset Formula $\mathring{A}$
11549 \begin_inset space \hfill{}
11553 \begin_inset Tabular
11554 <lyxtabular version="3" rows="7" columns="2">
11555 <features booktabs="true" tabularvalignment="middle">
11556 <column alignment="center" valignment="top" width="0pt">
11557 <column alignment="center" valignment="top" width="0pt">
11559 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11562 \begin_layout Plain Layout
11568 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11571 \begin_layout Plain Layout
11578 <row topspace="1.5mm">
11579 <cell alignment="center" valignment="top" usebox="none">
11582 \begin_layout Plain Layout
11586 \begin_inset space \textvisiblespace{}
11594 <cell alignment="center" valignment="top" usebox="none">
11597 \begin_layout Plain Layout
11598 \begin_inset Formula $\tilde{A}$
11607 <row topspace="1.5mm">
11608 <cell alignment="center" valignment="top" usebox="none">
11611 \begin_layout Plain Layout
11615 \begin_inset space \textvisiblespace{}
11623 <cell alignment="center" valignment="top" usebox="none">
11626 \begin_layout Plain Layout
11627 \begin_inset Formula $\hat{A}$
11636 <row topspace="1.5mm">
11637 <cell alignment="center" valignment="top" usebox="none">
11640 \begin_layout Plain Layout
11644 \begin_inset space \textvisiblespace{}
11652 <cell alignment="center" valignment="top" usebox="none">
11655 \begin_layout Plain Layout
11656 \begin_inset Formula $\check{A}$
11665 <row topspace="1.5mm">
11666 <cell alignment="center" valignment="top" usebox="none">
11669 \begin_layout Plain Layout
11673 \begin_inset space \textvisiblespace{}
11681 <cell alignment="center" valignment="top" usebox="none">
11684 \begin_layout Plain Layout
11685 \begin_inset Formula $\acute{A}$
11694 <row topspace="1.5mm">
11695 <cell alignment="center" valignment="top" usebox="none">
11698 \begin_layout Plain Layout
11702 \begin_inset space \textvisiblespace{}
11710 <cell alignment="center" valignment="top" usebox="none">
11713 \begin_layout Plain Layout
11714 \begin_inset Formula $\grave{A}$
11723 <row topspace="1.5mm">
11724 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11727 \begin_layout Plain Layout
11731 \begin_inset space \textvisiblespace{}
11739 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11742 \begin_layout Plain Layout
11743 \begin_inset Formula $\breve{A}$
11757 \begin_inset space \hfill{}
11763 \begin_layout Standard
11764 \begin_inset VSpace bigskip
11770 \begin_layout Standard
11771 You can directly insert accents such as é in formulas.
11773 will transform them to the corresponding accent command.
11775 \begin_inset Index idx
11780 \begin_layout Plain Layout
11786 however it is better to insert a quotation mark before the vowel.
11787 These two characters are then treated by \SpecialChar LaTeX
11792 character when the formula part with the umlaut is marked as German.
11800 \begin_inset Quotes eld
11804 \begin_inset Quotes erd
11807 umlauts are created as demonstrated in the following example:
11810 \begin_layout Standard
11811 \begin_inset VSpace -2mm
11817 \begin_layout Standard
11819 \begin_inset Tabular
11820 <lyxtabular version="3" rows="3" columns="2">
11821 <features booktabs="true" tabularvalignment="middle">
11822 <column alignment="center" valignment="top" width="0pt">
11823 <column alignment="center" valignment="top">
11825 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11828 \begin_layout Plain Layout
11834 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
11837 \begin_layout Plain Layout
11845 <cell alignment="center" valignment="top" usebox="none">
11848 \begin_layout Plain Layout
11849 \begin_inset Quotes grd
11857 <cell alignment="center" valignment="top" usebox="none">
11860 \begin_layout Plain Layout
11861 \begin_inset space \hspace{}
11868 \begin_inset Formula $"i$
11877 <row topspace="1.5mm">
11878 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11881 \begin_layout Plain Layout
11885 \begin_inset space \textvisiblespace{}
11893 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
11896 \begin_layout Plain Layout
11897 \begin_inset Formula $\ddot{i}$
11913 \begin_layout Standard
11920 is that umlauts can be directly converted to mathematical text because
11921 the accent commands above are
11927 in mathematical text
11930 To convert an accented character to mathematical text, only the character
11931 under the accent may be converted.
11932 This applies for all conversions, e.
11933 \begin_inset space \thinspace{}
11937 \begin_inset space \space{}
11943 \begin_layout Standard
11944 \begin_inset VSpace bigskip
11950 \begin_layout Standard
11952 also supports a tilde under the character if the \SpecialChar LaTeX
11958 \begin_inset Index idx
11963 \begin_layout Plain Layout
11965 \begin_inset IndexMacro subentry
11968 \begin_layout Plain Layout
11979 is installed on your system:
11982 \begin_layout Standard
11986 \begin_layout Plain Layout
11996 \begin_inset Note Note
11999 \begin_layout Plain Layout
12000 The following table will only be displayed when the \SpecialChar LaTeX
12013 \begin_layout Standard
12016 \begin_inset Tabular
12017 <lyxtabular version="3" rows="2" columns="2">
12018 <features booktabs="true" tabularvalignment="middle">
12019 <column alignment="center" valignment="top" width="0pt">
12020 <column alignment="center" valignment="top" width="0pt">
12022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12025 \begin_layout Plain Layout
12031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12034 \begin_layout Plain Layout
12042 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
12045 \begin_layout Plain Layout
12049 \begin_inset space \textvisiblespace{}
12057 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12060 \begin_layout Plain Layout
12061 \begin_inset Formula $\utilde{A}$
12077 \begin_layout Standard
12081 \begin_layout Plain Layout
12091 \begin_inset Note Note
12094 \begin_layout Plain Layout
12095 The following will be displayed when the \SpecialChar LaTeX
12108 \begin_layout Standard
12109 You need to install the \SpecialChar LaTeX
12114 to see the rest of this subsection in the output.
12117 \begin_layout Standard
12121 \begin_layout Plain Layout
12133 \begin_layout Subsection
12134 Accents for Several Characters
12135 \begin_inset Index idx
12140 \begin_layout Plain Layout
12142 \begin_inset IndexMacro subentry
12145 \begin_layout Plain Layout
12146 for several characters
12159 \begin_layout Standard
12160 \begin_inset space \hfill{}
12164 \begin_inset Tabular
12165 <lyxtabular version="3" rows="5" columns="2">
12166 <features booktabs="true" tabularvalignment="middle">
12167 <column alignment="center" valignment="top" width="0pt">
12168 <column alignment="center" valignment="top" width="0pt">
12170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12173 \begin_layout Plain Layout
12179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12182 \begin_layout Plain Layout
12189 <row topspace="1.5mm">
12190 <cell alignment="center" valignment="top" usebox="none">
12193 \begin_layout Plain Layout
12197 \begin_inset space \textvisiblespace{}
12205 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12208 \begin_layout Plain Layout
12209 \begin_inset Formula $\overleftarrow{A=B}$
12218 <row topspace="1.5mm">
12219 <cell alignment="center" valignment="top" usebox="none">
12222 \begin_layout Plain Layout
12226 \begin_inset space \textvisiblespace{}
12234 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12237 \begin_layout Plain Layout
12238 \begin_inset Formula $\underleftarrow{A=B}$
12247 <row topspace="1.5mm">
12248 <cell alignment="center" valignment="top" usebox="none">
12251 \begin_layout Plain Layout
12255 \begin_inset space \textvisiblespace{}
12263 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12266 \begin_layout Plain Layout
12267 \begin_inset Formula $\overleftrightarrow{A=B}$
12276 <row topspace="1.5mm" bottomspace="1mm">
12277 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12280 \begin_layout Plain Layout
12283 underleftrightarrow
12284 \begin_inset space \textvisiblespace{}
12292 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12295 \begin_layout Plain Layout
12296 \begin_inset Formula $\underleftrightarrow{A=B}$
12310 \begin_inset space \hfill{}
12314 \begin_inset Tabular
12315 <lyxtabular version="3" rows="5" columns="2">
12316 <features booktabs="true" tabularvalignment="middle">
12317 <column alignment="center" valignment="top" width="0pt">
12318 <column alignment="center" valignment="top" width="0pt">
12320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12323 \begin_layout Plain Layout
12329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12332 \begin_layout Plain Layout
12339 <row topspace="1.5mm">
12340 <cell alignment="center" valignment="top" usebox="none">
12343 \begin_layout Plain Layout
12347 \begin_inset space \textvisiblespace{}
12355 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12358 \begin_layout Plain Layout
12359 \begin_inset Formula $\overrightarrow{A=B}$
12368 <row topspace="1.5mm">
12369 <cell alignment="center" valignment="top" usebox="none">
12372 \begin_layout Plain Layout
12376 \begin_inset space \textvisiblespace{}
12384 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12387 \begin_layout Plain Layout
12388 \begin_inset Formula $\underrightarrow{A=B}$
12397 <row topspace="1.5mm">
12398 <cell alignment="center" valignment="top" usebox="none">
12401 \begin_layout Plain Layout
12405 \begin_inset space \textvisiblespace{}
12413 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12416 \begin_layout Plain Layout
12417 \begin_inset Formula $\widetilde{A=B}$
12426 <row topspace="1.5mm" bottomspace="1mm">
12427 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12430 \begin_layout Plain Layout
12434 \begin_inset space \textvisiblespace{}
12442 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12445 \begin_layout Plain Layout
12446 \begin_inset Formula $\widehat{A=B}$
12460 \begin_inset space \hfill{}
12466 \begin_layout Standard
12467 \begin_inset VSpace medskip
12470 Using these commands you can accent as many characters as you like.
12483 will only be set in the output with a length of three characters, as shown
12484 in the following example:
12485 \begin_inset Formula
12487 \widetilde{A+B=C-D}
12495 \begin_layout Standard
12496 It is also possible to accent several characters using the commands
12503 \begin_inset Index idx
12508 \begin_layout Plain Layout
12510 \begin_inset IndexMacro subentry
12513 \begin_layout Plain Layout
12520 \begin_inset IndexMacro subentry
12523 \begin_layout Plain Layout
12543 \begin_inset Index idx
12548 \begin_layout Plain Layout
12550 \begin_inset IndexMacro subentry
12553 \begin_layout Plain Layout
12560 \begin_inset IndexMacro subentry
12563 \begin_layout Plain Layout
12576 described in the previous subsection.
12582 \begin_inset space \textvisiblespace{}
12586 \begin_inset Formula $\downarrow$
12592 \begin_inset Formula
12594 \underset{***}{A=B}
12602 \begin_layout Section
12604 \begin_inset CommandInset label
12606 name "subsec:Space"
12611 \begin_inset Index idx
12616 \begin_layout Plain Layout
12618 \begin_inset IndexMacro subentry
12621 \begin_layout Plain Layout
12635 \begin_layout Subsection
12637 \begin_inset CommandInset label
12639 name "subsec:Predefined-Space"
12644 \begin_inset Index idx
12649 \begin_layout Plain Layout
12651 \begin_inset IndexMacro subentry
12654 \begin_layout Plain Layout
12661 \begin_inset IndexMacro subentry
12664 \begin_layout Plain Layout
12678 \begin_layout Standard
12679 Sometimes it is necessary to insert horizontal space into a formula.
12680 This is done by inserting a
12681 \change_deleted 177693 1654668870
12683 \change_inserted 177693 1654668872
12687 \change_inserted 5863208 1612729962
12691 arg "command-alternatives math-space ; space-insert protected"
12695 \change_deleted 5863208 1612729965
12699 arg "command-alternatives space-insert protected ; math-space"
12703 \begin_inset Note Note
12706 \begin_layout Plain Layout
12708 \change_inserted 232239728 1611160593
12709 What is intended here?
12720 \begin_inset Quotes eld
12726 \begin_inset space \textvisiblespace{}
12732 \begin_inset Quotes erd
12735 appears and by pressing
12739 several times one can select one of eight different space sizes.
12740 The spaces can also be inserted using the math toolbar button
12743 arg "math-insert \\space"
12746 or special commands.
12747 The size can be adjusted at any time by positioning the cursor on the
12750 arg "math-insert \\space"
12757 until the desired size is achieved.
12760 \begin_layout Standard
12763 \begin_inset Tabular
12764 <lyxtabular version="3" rows="6" columns="3">
12765 <features booktabs="true" tabularvalignment="middle">
12766 <column alignment="center" valignment="top">
12767 <column alignment="center" valignment="top" width="15col%">
12768 <column alignment="center" valignment="top">
12770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12773 \begin_layout Plain Layout
12779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12782 \begin_layout Plain Layout
12792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12795 \begin_layout Plain Layout
12803 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12806 \begin_layout Plain Layout
12814 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12817 \begin_layout Plain Layout
12823 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12826 \begin_layout Plain Layout
12827 \begin_inset Formula $A\,B$
12837 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12840 \begin_layout Plain Layout
12848 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12851 \begin_layout Plain Layout
12857 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12860 \begin_layout Plain Layout
12861 \begin_inset Formula $A\:B$
12871 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12874 \begin_layout Plain Layout
12882 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12885 \begin_layout Plain Layout
12891 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12894 \begin_layout Plain Layout
12895 \begin_inset Formula $A\;B$
12905 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12908 \begin_layout Plain Layout
12916 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12919 \begin_layout Plain Layout
12925 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12928 \begin_layout Plain Layout
12929 \begin_inset Formula $A\quad B$
12939 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
12942 \begin_layout Plain Layout
12950 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
12953 \begin_layout Plain Layout
12959 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12962 \begin_layout Plain Layout
12963 \begin_inset Formula $A\qquad B$
12977 \begin_inset space \hfill{}
12981 \begin_inset Tabular
12982 <lyxtabular version="3" rows="6" columns="3">
12983 <features booktabs="true" tabularvalignment="middle">
12984 <column alignment="center" valignment="top">
12985 <column alignment="center" valignment="top" width="15col%">
12986 <column alignment="center" valignment="top">
12988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12991 \begin_layout Plain Layout
12997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13000 \begin_layout Plain Layout
13010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13013 \begin_layout Plain Layout
13021 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13024 \begin_layout Plain Layout
13032 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13035 \begin_layout Plain Layout
13041 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13044 \begin_layout Plain Layout
13045 \begin_inset Formula $A\hfill B$
13055 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13058 \begin_layout Plain Layout
13066 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13069 \begin_layout Plain Layout
13075 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13078 \begin_layout Plain Layout
13079 \begin_inset Formula $A\hspace*{1em}B$
13089 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13092 \begin_layout Plain Layout
13100 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13103 \begin_layout Plain Layout
13109 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13112 \begin_layout Plain Layout
13113 \begin_inset Formula $A\hspace{1em}B$
13123 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13126 \begin_layout Plain Layout
13130 \begin_inset space \textvisiblespace{}
13138 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13141 \begin_layout Plain Layout
13147 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13150 \begin_layout Plain Layout
13151 \begin_inset Formula $A\ B$
13161 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13164 \begin_layout Plain Layout
13172 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13175 \begin_layout Plain Layout
13181 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13184 \begin_layout Plain Layout
13185 \begin_inset Formula $A\!B$
13201 \begin_layout Standard
13203 \begin_inset space ~
13207 \begin_inset space \thinspace{}
13211 \begin_inset space \thinspace{}
13214 7 are variable spaces which are explained in
13215 \begin_inset CommandInset ref
13217 reference "subsec:Variable-Space"
13223 \begin_inset space ~
13226 9 appears to produce no space.
13227 It is displayed red in \SpecialChar LyX
13228 contrary to the other sizes, because it is a negative
13230 There are two more negative spaces:
13233 \begin_layout Standard
13235 \begin_inset Tabular
13236 <lyxtabular version="3" rows="3" columns="3">
13237 <features booktabs="true" tabularvalignment="middle">
13238 <column alignment="center" valignment="middle" width="6.8cm">
13239 <column alignment="center" valignment="top" width="0pt">
13240 <column alignment="center" valignment="top" width="0pt">
13242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13245 \begin_layout Plain Layout
13251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13254 \begin_layout Plain Layout
13262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13265 \begin_layout Plain Layout
13275 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13278 \begin_layout Plain Layout
13283 keystrokes after inserting the
13284 \change_deleted 177693 1654668881
13286 \change_inserted 177693 1654668883
13294 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13297 \begin_layout Plain Layout
13303 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13306 \begin_layout Plain Layout
13314 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13317 \begin_layout Plain Layout
13323 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13326 \begin_layout Plain Layout
13327 \begin_inset Formula $A\negmedspace B$
13335 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13338 \begin_layout Plain Layout
13339 \begin_inset Formula $A\negthickspace B$
13355 \begin_layout Standard
13356 Negative spaces can lead to characters overlapping each other.
13357 Thus they can be used to enforce ligatures, which are useful for things
13358 such as summation operators:
13361 \begin_layout Standard
13363 \begin_inset Tabular
13364 <lyxtabular version="3" rows="3" columns="2">
13365 <features booktabs="true" tabularvalignment="middle">
13366 <column alignment="center" valignment="top" width="0pt">
13367 <column alignment="center" valignment="top">
13369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13372 \begin_layout Plain Layout
13378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13381 \begin_layout Plain Layout
13389 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13392 \begin_layout Plain Layout
13398 \begin_inset space \textvisiblespace{}
13406 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13409 \begin_layout Plain Layout
13410 \begin_inset Formula $\sum\sum f_{kl}$
13420 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
13423 \begin_layout Plain Layout
13431 \begin_inset space \textvisiblespace{}
13439 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13442 \begin_layout Plain Layout
13443 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
13459 \begin_layout Standard
13461 \begin_inset VSpace medskip
13467 \begin_layout Standard
13469 Relational operators, for example equal or less than signs, are always surrounde
13471 To suppress this, the operator is placed into a \SpecialChar TeX
13473 The following example demonstrates this:
13476 \begin_layout Standard
13478 \begin_inset Tabular
13479 <lyxtabular version="3" rows="2" columns="2">
13480 <features tabularvalignment="middle">
13481 <column alignment="center" valignment="top" width="0pt">
13482 <column alignment="center" valignment="top" width="0pt">
13484 <cell alignment="center" valignment="top" usebox="none">
13487 \begin_layout Plain Layout
13493 <cell alignment="center" valignment="top" usebox="none">
13496 \begin_layout Plain Layout
13497 \begin_inset Formula $A=B$
13507 <cell alignment="center" valignment="top" usebox="none">
13510 \begin_layout Plain Layout
13511 Equation without space
13516 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
13519 \begin_layout Plain Layout
13520 \begin_inset Formula $A{=}B$
13536 \begin_layout Standard
13538 The command for the last formula is:
13543 \begin_inset Formula $\to$
13549 \begin_layout Standard
13550 \begin_inset VSpace bigskip
13556 \begin_layout Standard
13557 Another example of controlled spaces is physical units.
13558 The space between a value and its unit is smaller than a normal space,
13559 typically a thin space is used.
13560 For units in text, the smaller space is inserted via the menu
13562 Insert\SpecialChar menuseparator
13563 Formatting\SpecialChar menuseparator
13565 \begin_inset space ~
13573 arg "space-insert thin"
13579 \begin_layout Standard
13580 An example to visualize the difference:
13583 \begin_layout Standard
13584 \begin_inset Tabular
13585 <lyxtabular version="3" rows="2" columns="2">
13586 <features tabularvalignment="middle">
13587 <column alignment="left" valignment="top">
13588 <column alignment="left" valignment="top">
13590 <cell alignment="center" valignment="top" usebox="none">
13593 \begin_layout Plain Layout
13595 \begin_inset Formula $\cdot$
13603 <cell alignment="center" valignment="top" usebox="none">
13606 \begin_layout Plain Layout
13607 Space between value and unit
13614 <cell alignment="center" valignment="top" usebox="none">
13617 \begin_layout Plain Layout
13619 \begin_inset space \thinspace{}
13623 \begin_inset Formula $\cdot$
13631 <cell alignment="center" valignment="top" usebox="none">
13634 \begin_layout Plain Layout
13635 Thin space between value and unit
13648 \begin_layout Subsection
13653 \begin_layout Plain Layout
13666 \begin_layout Plain Layout
13667 For vertical space in formulas see
13668 \begin_inset CommandInset ref
13670 reference "subsec:Line-Separation"
13683 \begin_layout Plain Layout
13691 \begin_inset Note Note
13694 \begin_layout Plain Layout
13697 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
13700 \begin_layout Plain Layout
13703 texorpdfstring is in section
13704 \begin_inset CommandInset ref
13706 reference "subsec:Formulas-in-Section"
13716 \begin_inset CommandInset label
13718 name "subsec:Variable-Space"
13723 \begin_inset Index idx
13728 \begin_layout Plain Layout
13730 \begin_inset IndexMacro subentry
13733 \begin_layout Plain Layout
13740 \begin_inset IndexMacro subentry
13743 \begin_layout Plain Layout
13757 \begin_layout Standard
13758 Space with a defined length can be inserted with the command
13765 \begin_inset Index idx
13770 \begin_layout Plain Layout
13772 \begin_inset IndexMacro subentry
13775 \begin_layout Plain Layout
13782 \begin_inset IndexMacro subentry
13785 \begin_layout Plain Layout
13800 \begin_inset Quotes eld
13806 \begin_inset space \textvisiblespace{}
13812 \begin_inset Quotes erd
13815 will appear, the length of which can be specified by left-clicking on the
13817 \begin_inset Quotes eld
13823 \begin_inset space \textvisiblespace{}
13829 \begin_inset Quotes erd
13833 The length may also be negative.
13834 If the space is the first character in a line, it will ordinarily be omitted.
13835 To force its output use the command
13847 or left-click on the
13848 \begin_inset Quotes eld
13854 \begin_inset space \textvisiblespace{}
13860 \begin_inset Quotes erd
13863 and check the option
13868 \begin_inset Newline newline
13871 To insert as much space as is available, the command
13878 \begin_inset Index idx
13883 \begin_layout Plain Layout
13885 \begin_inset IndexMacro subentry
13888 \begin_layout Plain Layout
13895 \begin_inset IndexMacro subentry
13898 \begin_layout Plain Layout
13914 \begin_layout Standard
13916 \begin_inset Tabular
13917 <lyxtabular version="3" rows="4" columns="2">
13918 <features booktabs="true" tabularvalignment="middle">
13919 <column alignment="center" valignment="top" width="0pt">
13920 <column alignment="center" valignment="top">
13922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13925 \begin_layout Plain Layout
13933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13936 \begin_layout Plain Layout
13944 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13947 \begin_layout Plain Layout
13951 \begin_inset space \textvisiblespace{}
13957 \begin_inset space \thinspace{}
13965 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13968 \begin_layout Plain Layout
13969 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
13979 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13982 \begin_layout Plain Layout
13986 \begin_inset space \textvisiblespace{}
13992 \begin_inset space \thinspace{}
14000 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14003 \begin_layout Plain Layout
14004 \begin_inset Formula $A\hspace{-1mm}A\not=A$
14014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14017 \begin_layout Plain Layout
14021 \begin_inset space \textvisiblespace{}
14029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14032 \begin_layout Plain Layout
14033 \begin_inset Formula $A=A\hfill B=B$
14049 \begin_layout Standard
14050 In the last example the available space is given by the longest column entry
14052 In an inline formula the space depends on the length of the line in which
14060 Thus, when the line uses the full width, no space will be created.
14067 only has an effect on displayed formulas when the formula style
14072 (Formula styles are explained in
14073 \begin_inset CommandInset ref
14075 reference "sec:Formula-Styles"
14082 \begin_layout Standard
14089 , there are also commands,
14101 that fill the space with a pattern.
14103 \begin_inset CommandInset ref
14105 reference "subsec:Ellipses"
14112 \begin_layout Standard
14113 For text, variable space can be inserted via the menu
14115 Insert\SpecialChar menuseparator
14116 Formatting\SpecialChar menuseparator
14118 \begin_inset space ~
14126 \begin_layout Standard
14127 This is a line with
14128 \begin_inset space \hspace{}
14133 \begin_inset space \thinspace{}
14139 \begin_layout Standard
14140 This is a line with
14141 \begin_inset space \hfill{}
14147 \begin_layout Subsection
14148 Space Besides Inline Formulas
14149 \begin_inset Index idx
14154 \begin_layout Plain Layout
14156 \begin_inset IndexMacro subentry
14159 \begin_layout Plain Layout
14160 besides inline formulas
14173 \begin_layout Standard
14174 The space that surrounds inline formulas can be adjusted with the length
14182 \begin_inset Index idx
14187 \begin_layout Plain Layout
14189 \begin_inset IndexMacro subentry
14192 \begin_layout Plain Layout
14199 \begin_inset IndexMacro subentry
14202 \begin_layout Plain Layout
14216 The value of a length is set with the command
14223 \begin_inset Index idx
14228 \begin_layout Plain Layout
14230 \begin_inset IndexMacro subentry
14233 \begin_layout Plain Layout
14240 \begin_inset IndexMacro subentry
14243 \begin_layout Plain Layout
14256 which has the following scheme:
14259 \begin_layout Standard
14264 setlength{length name}{value}
14267 \begin_layout Standard
14275 \begin_inset space \thinspace{}
14281 \begin_layout Standard
14291 \begin_layout Standard
14292 is inserted in \SpecialChar TeX
14295 \begin_inset space \thinspace{}
14298 mm space will now be set around all inline formulas:
14302 \begin_layout Plain Layout
14316 \begin_layout Standard
14317 This is a line with an inline formula
14318 \begin_inset Formula $A=B$
14322 \begin_inset space \thinspace{}
14325 mm surrounding space.
14329 \begin_layout Plain Layout
14343 \begin_layout Standard
14344 To return to the predefined value,
14350 is set to the value 0
14351 \begin_inset space \thinspace{}
14357 \begin_layout Section
14359 \begin_inset Index idx
14364 \begin_layout Plain Layout
14371 \begin_inset Index idx
14376 \begin_layout Plain Layout
14378 \begin_inset IndexMacro see
14381 \begin_layout Plain Layout
14395 \begin_layout Standard
14396 Boxes for text are described in chapter
14403 \begin_inset space ~
14411 \begin_layout Subsection
14413 \begin_inset CommandInset label
14415 name "subsec:Boxes-with-Frame"
14420 \begin_inset Index idx
14425 \begin_layout Plain Layout
14427 \begin_inset IndexMacro subentry
14430 \begin_layout Plain Layout
14444 \begin_layout Standard
14445 It is possible to frame a formula or part of one with the commands
14452 \begin_inset Index idx
14457 \begin_layout Plain Layout
14459 \begin_inset IndexMacro subentry
14462 \begin_layout Plain Layout
14469 \begin_inset IndexMacro subentry
14472 \begin_layout Plain Layout
14492 \begin_inset Index idx
14497 \begin_layout Plain Layout
14499 \begin_inset IndexMacro subentry
14502 \begin_layout Plain Layout
14509 \begin_inset IndexMacro subentry
14512 \begin_layout Plain Layout
14528 \begin_layout Standard
14529 When one of these commands is inserted in a formula, a blue box appears
14530 within a frame to enter formula parts.
14537 an additional formula has to be created by
14541 within this box, because the box content will otherwise be treated as mathemati
14549 is used, a new formula is automatically created inside the frame.
14552 \begin_layout Standard
14559 is not suitable to frame displayed formulas because the formula will always
14560 be set in the size of the documents text.
14567 is not suitable to frame inline formulas because the formula will always
14568 be set in the size of a displayed formula.
14571 \begin_layout Standard
14585 \begin_inset Index idx
14590 \begin_layout Plain Layout
14592 \begin_inset IndexMacro subentry
14595 \begin_layout Plain Layout
14602 \begin_inset IndexMacro subentry
14605 \begin_layout Plain Layout
14618 with which the frame width and the alignment can be specified.
14625 is used in the following scheme:
14628 \begin_layout Standard
14633 framebox[frame width][position]{box content}
14636 \begin_layout Standard
14637 The position can either be
14654 right aligns the formula in the box.
14655 If no position is given the formula will be centered.
14656 \begin_inset Newline newline
14659 If width is not given then position can not be given.
14660 In this case the frame width is adjusted to the box content like for
14669 \begin_layout Standard
14676 is inserted, a box appears containing three blue boxes.
14677 The first two boxes are surrounded by brackets and denote the two optional
14679 The third box is for formula parts like for
14688 \begin_layout Standard
14690 \begin_inset Tabular
14691 <lyxtabular version="3" rows="5" columns="2">
14692 <features booktabs="true" tabularvalignment="middle">
14693 <column alignment="center" valignment="top" width="0pt">
14694 <column alignment="center" valignment="top">
14696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14699 \begin_layout Plain Layout
14705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14708 \begin_layout Plain Layout
14715 <row topspace="1.5mm">
14716 <cell alignment="center" valignment="top" usebox="none">
14719 \begin_layout Plain Layout
14723 \begin_inset space \textvisiblespace{}
14733 \begin_inset space \textvisiblespace{}
14741 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14744 \begin_layout Plain Layout
14745 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
14754 <row topspace="1.5mm">
14755 <cell alignment="center" valignment="top" usebox="none">
14758 \begin_layout Plain Layout
14762 \begin_inset space \textvisiblespace{}
14768 \begin_inset space \textvisiblespace{}
14776 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14779 \begin_layout Plain Layout
14780 \begin_inset Formula $\boxed{\int A=B}$
14789 <row topspace="1.5mm">
14790 <cell alignment="center" valignment="top" usebox="none">
14793 \begin_layout Plain Layout
14797 \begin_inset space \textvisiblespace{}
14805 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14808 \begin_layout Plain Layout
14809 \begin_inset Formula $A+\fbox{B}$
14818 <row topspace="1.5mm" bottomspace="1mm">
14819 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
14822 \begin_layout Plain Layout
14826 \begin_inset space \textvisiblespace{}
14830 \begin_inset Formula $\to$
14834 \begin_inset Formula $\to$
14844 \begin_inset space \textvisiblespace{}
14848 \begin_inset Formula $\downarrow$
14856 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
14859 \begin_layout Plain Layout
14860 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
14876 \begin_layout Standard
14877 To adjust the frame thickness the following commands are inserted in \SpecialChar TeX
14879 before the formula:
14882 \begin_layout Standard
14892 \begin_inset Quotes eld
14896 \begin_inset Quotes erd
14910 \begin_inset Quotes eld
14914 \begin_inset Quotes erd
14920 \begin_layout Standard
14921 \begin_inset Quotes eld
14925 \begin_inset Quotes erd
14928 specifies the minimum distance between the frame and the first character
14930 An example of this is given in the following framed formula:
14934 \begin_layout Plain Layout
14946 \begin_inset Formula
14953 Before this formula the commands
14956 \begin_layout Standard
14978 \begin_layout Standard
14979 were inserted in \SpecialChar TeX
14981 These values are then used for all following boxes.
14984 \begin_layout Standard
14985 To return to the standard frame size, the command
14988 \begin_layout Standard
15013 \begin_layout Plain Layout
15027 \begin_layout Standard
15028 is inserted in \SpecialChar TeX
15029 mode before the next formula.
15032 \begin_layout Subsection
15033 Boxes Without Frame
15034 \begin_inset CommandInset label
15036 name "subsec:Boxes-without-Frame"
15041 \begin_inset Index idx
15046 \begin_layout Plain Layout
15048 \begin_inset IndexMacro subentry
15051 \begin_layout Plain Layout
15065 \begin_layout Standard
15066 For boxes without a frame the following box commands:
15073 \begin_inset Index idx
15078 \begin_layout Plain Layout
15080 \begin_inset IndexMacro subentry
15083 \begin_layout Plain Layout
15090 \begin_inset IndexMacro subentry
15093 \begin_layout Plain Layout
15113 \begin_inset Index idx
15118 \begin_layout Plain Layout
15120 \begin_inset IndexMacro subentry
15123 \begin_layout Plain Layout
15130 \begin_inset IndexMacro subentry
15133 \begin_layout Plain Layout
15153 \begin_inset Index idx
15158 \begin_layout Plain Layout
15160 \begin_inset IndexMacro subentry
15163 \begin_layout Plain Layout
15170 \begin_inset IndexMacro subentry
15173 \begin_layout Plain Layout
15189 \begin_layout Standard
15196 a box can be super- or subscripted.
15197 But in contrary to normal super- and subscripting, the characters in the
15198 box keep their font size.
15205 is used in the following scheme:
15208 \begin_layout Standard
15213 raisebox{height}{box content}
15216 \begin_layout Standard
15217 When the box contains a formula, an extra formula is needed like for
15226 \begin_layout Standard
15229 \begin_inset Note Greyedout
15232 \begin_layout Plain Layout
15243 this extra formula is created by pressing
15247 twice instead of once because \SpecialChar LyX
15248 doesn't yet support
15262 \begin_layout Standard
15264 \begin_inset Tabular
15265 <lyxtabular version="3" rows="4" columns="2">
15266 <features booktabs="true" tabularvalignment="middle">
15267 <column alignment="center" valignment="top" width="0pt">
15268 <column alignment="center" valignment="top">
15270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15273 \begin_layout Plain Layout
15279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15282 \begin_layout Plain Layout
15290 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15293 \begin_layout Plain Layout
15297 \begin_inset Formula $\to$
15303 \begin_inset Formula $\to$
15311 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15314 \begin_layout Plain Layout
15315 \begin_inset Formula $H\raisebox{2mm}{al}lo$
15325 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15328 \begin_layout Plain Layout
15332 \begin_inset Formula $\to$
15338 \begin_inset Formula $\to$
15346 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15349 \begin_layout Plain Layout
15350 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
15360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15363 \begin_layout Plain Layout
15367 \begin_inset Formula $\to$
15383 \begin_inset space \textvisiblespace{}
15391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15394 \begin_layout Plain Layout
15395 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
15411 \begin_layout Standard
15436 , except that there is no frame.
15439 \begin_layout Subsection
15441 \begin_inset CommandInset label
15443 name "subsec:Colored-Boxes"
15448 \begin_inset Index idx
15453 \begin_layout Plain Layout
15455 \begin_inset IndexMacro subentry
15458 \begin_layout Plain Layout
15472 \begin_layout Standard
15473 To be able to use all commands explained in this section, the \SpecialChar LaTeX
15482 \begin_layout Plain Layout
15483 The \SpecialChar LaTeX
15488 is part of every \SpecialChar LaTeX
15489 standard installation.
15495 \begin_inset Index idx
15500 \begin_layout Plain Layout
15502 \begin_inset IndexMacro subentry
15505 \begin_layout Plain Layout
15516 must be loaded in the \SpecialChar LaTeX
15517 -preamble with the line
15521 \begin_layout Plain Layout
15522 When text is colored somewhere in the document with a predefined color,
15524 loads the \SpecialChar LaTeX
15530 Thus it is possible that the package is loaded twice, but this does not
15537 \begin_inset Note Note
15540 \begin_layout Plain Layout
15541 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
15550 \begin_layout Standard
15558 \begin_layout Standard
15559 \begin_inset VSpace medskip
15562 To create color boxes, the command
15569 \begin_inset Index idx
15574 \begin_layout Plain Layout
15576 \begin_inset IndexMacro subentry
15579 \begin_layout Plain Layout
15586 \begin_inset IndexMacro subentry
15589 \begin_layout Plain Layout
15602 is used in the following scheme:
15605 \begin_layout Standard
15610 colorbox{color}{box content}
15613 \begin_layout Standard
15614 The box content can also be a box and a
15620 can also be part of another box (see the 2nd and 3rd example).
15621 When the box should contain a formula, an extra formula has to be created,
15622 the same way as for
15632 \begin_layout Plain Layout
15633 This also applies for the command
15647 \begin_layout Standard
15648 One of the following predefined colors can be chosen:
15651 \begin_layout Standard
15683 \begin_inset VSpace smallskip
15689 \begin_layout Standard
15691 \begin_inset Tabular
15692 <lyxtabular version="3" rows="4" columns="2">
15693 <features booktabs="true" tabularvalignment="middle">
15694 <column alignment="center" valignment="top" width="0pt">
15695 <column alignment="center" valignment="top">
15697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15700 \begin_layout Plain Layout
15706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15709 \begin_layout Plain Layout
15717 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15720 \begin_layout Plain Layout
15724 \begin_inset Formula $\to$
15734 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15737 \begin_layout Plain Layout
15738 \begin_inset Formula $\colorbox{yellow}{A=B}$
15747 <row topspace="1.5mm">
15748 <cell alignment="center" valignment="top" usebox="none">
15751 \begin_layout Plain Layout
15755 \begin_inset Formula $\to$
15763 \begin_inset space \textvisiblespace{}
15767 \change_inserted 232239728 1611182042
15769 \begin_inset Formula $\gets\gets$
15779 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15782 \begin_layout Plain Layout
15783 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
15792 <row topspace="1.5mm" bottomspace="1mm">
15793 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15796 \begin_layout Plain Layout
15800 \begin_inset space \textvisiblespace{}
15804 \change_inserted 232239728 1611182036
15806 \begin_inset Formula $\gets\gets$
15814 \begin_inset Formula $\to$
15830 \begin_inset space \textvisiblespace{}
15838 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15841 \begin_layout Plain Layout
15842 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
15856 \begin_inset VSpace smallskip
15862 \begin_layout Standard
15869 only colors the box background, not the characters in the box.
15870 To color all characters, the whole formula is highlighted and the desired
15871 color is chosen in the
15874 \begin_inset space ~
15880 The dialog can be called with the toolbar button
15883 arg "dialog-show character"
15888 Edit\SpecialChar menuseparator
15890 \begin_inset space ~
15893 Properties\SpecialChar menuseparator
15897 The formula number will have the same color as the formula.
15898 If a different color for the formula number is desired, the color must
15899 be changed within the formula.
15902 \begin_layout Standard
15906 \begin_layout Standard
15909 \begin_inset Formula
15911 \int A=B\label{eq:red}
15919 \begin_inset Formula
15921 \textcolor{red}{\int A=B}\label{eq:redgreen}
15929 \begin_layout Standard
15931 \begin_inset CommandInset ref
15937 is completely colored red.
15938 \begin_inset Newline newline
15942 \begin_inset CommandInset ref
15944 reference "eq:redgreen"
15948 was first completely colored green to set the color for the formula number.
15949 Subsequently the formula characters were colored red.
15952 \begin_layout Standard
15953 \begin_inset VSpace bigskip
15956 To color the frame different than the rest of the box, the command
15963 \begin_inset Index idx
15968 \begin_layout Plain Layout
15970 \begin_inset IndexMacro subentry
15973 \begin_layout Plain Layout
15980 \begin_inset IndexMacro subentry
15983 \begin_layout Plain Layout
15996 is used in the following scheme:
15999 \begin_layout Standard
16004 fcolorbox{frame color}{color}{box content}
16007 \begin_layout Standard
16014 is an extension of the command
16021 The frame width is set, like for
16044 \begin_layout Plain Layout
16056 \begin_inset Formula
16058 \fcolorbox{cyan}{magenta}{A=B}
16067 \begin_layout Plain Layout
16081 \begin_layout Standard
16082 This formula was created with the command
16083 \begin_inset Newline newline
16091 \begin_inset Formula $\to$
16097 \begin_inset Formula $\to$
16107 \begin_layout Standard
16108 \begin_inset VSpace bigskip
16111 To use colors other than predefined ones, they must be defined first.
16114 \begin_layout Standard
16115 One can for example define the color
16116 \begin_inset Quotes eld
16124 \begin_inset Quotes erd
16127 with the \SpecialChar LaTeX
16131 \begin_layout Standard
16136 definecolor{darkgreen}{cmyk}{0.5,
16151 \begin_inset Index idx
16156 \begin_layout Plain Layout
16158 \begin_inset IndexMacro subentry
16161 \begin_layout Plain Layout
16168 \begin_inset IndexMacro subentry
16171 \begin_layout Plain Layout
16187 \begin_layout Standard
16192 is the color space denoting the colors
16209 The four comma separated numbers are the portion factors for the corresponding
16210 colors of the color space.
16211 The factors can be in the range of 0
16212 \begin_inset space \thinspace{}
16216 \begin_inset space \thinspace{}
16228 can also be used for definitions.
16245 , so there are three portion factors for the corresponding colors.
16246 Furthermore there is the color space
16250 with one portion factor for the gray value.
16253 \begin_layout Standard
16254 As an example here is a framed box with the newly defined color
16258 where the characters have been colored
16263 \begin_inset Formula
16265 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
16273 \begin_layout Standard
16274 Self-defined colors can also be used for text with the help of the command
16282 \begin_inset Index idx
16287 \begin_layout Plain Layout
16289 \begin_inset IndexMacro subentry
16292 \begin_layout Plain Layout
16306 \begin_layout Standard
16310 \begin_layout Plain Layout
16314 textcolor{darkgreen}{
16320 \begin_inset Quotes eld
16324 \begin_inset Quotes erd
16331 \begin_layout Plain Layout
16341 \begin_layout Standard
16349 \begin_inset Index idx
16354 \begin_layout Plain Layout
16356 \begin_inset IndexMacro subentry
16359 \begin_layout Plain Layout
16366 \begin_inset IndexMacro subentry
16369 \begin_layout Plain Layout
16382 is used in the scheme
16386 textcolor{color}{characters to color}
16391 \begin_layout Subsection
16393 \begin_inset CommandInset label
16395 name "subsec:Paragraph-Boxes"
16400 \begin_inset Index idx
16405 \begin_layout Plain Layout
16407 \begin_inset IndexMacro subentry
16410 \begin_layout Plain Layout
16424 \begin_layout Standard
16425 A box that can contain several lines and paragraphs, a so-called paragraph
16426 box (parbox), can be created with the menu
16428 Insert\SpecialChar menuseparator
16431 or the toolbar button
16440 \begin_layout Standard
16441 The following example shows a framed parbox in a line:
16444 \begin_layout Standard
16445 \begin_inset VSpace medskip
16449 \begin_inset Box Boxed
16459 height_special "totalheight"
16464 backgroundcolor "none"
16467 \begin_layout Plain Layout
16468 This is a paragraph box.
16470 \begin_inset space \thinspace{}
16473 cm long and can also contain formulas:
16474 \begin_inset Formula $\int A\,\mathrm{d}s=C$
16485 \begin_layout Standard
16486 \begin_inset VSpace medskip
16492 \begin_layout Standard
16493 Such a box is created by right-clicking on the gray box inset.
16494 A dialog pops up showing the box properties.
16508 \begin_inset space \thinspace{}
16513 Vertical Box Alignment
16518 \begin_layout Standard
16519 \begin_inset VSpace medskip
16522 In \SpecialChar LaTeX
16523 a parbox is created with the command
16530 \begin_inset Index idx
16535 \begin_layout Plain Layout
16537 \begin_inset IndexMacro subentry
16540 \begin_layout Plain Layout
16547 \begin_inset IndexMacro subentry
16550 \begin_layout Plain Layout
16563 which has the following scheme:
16566 \begin_layout Standard
16571 parbox[position]{width}{box content}
16574 \begin_layout Standard
16589 \begin_inset Quotes eld
16593 \begin_inset Quotes erd
16596 means that the box is aligned within the surrounding text with its last
16603 \begin_inset Quotes eld
16607 \begin_inset Quotes erd
16610 this is done with the first line.
16611 When no position is given, the box will be vertically centered, see section
16619 \begin_inset space ~
16624 manual for examples.
16627 \begin_layout Standard
16628 \begin_inset VSpace bigskip
16631 To frame formulas completely, including the formula number, the formula
16632 must be set into a parbox.
16633 To do this, the command
16647 is inserted in \SpecialChar TeX
16648 mode before the formula.
16656 \begin_inset Index idx
16661 \begin_layout Plain Layout
16663 \begin_inset IndexMacro subentry
16666 \begin_layout Plain Layout
16673 \begin_inset IndexMacro subentry
16676 \begin_layout Plain Layout
16689 is the line width set for the document.
16690 Because the frame is outside the parbox, two times the frame separation
16691 and the frame thickness must be subtracted from the line width.
16692 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
16701 \begin_layout Plain Layout
16706 is part of every \SpecialChar LaTeX
16707 standard installation.
16713 \begin_inset Index idx
16718 \begin_layout Plain Layout
16720 \begin_inset IndexMacro subentry
16723 \begin_layout Plain Layout
16734 must be loaded in the \SpecialChar LaTeX
16735 -preamble with the line
16738 \begin_layout Standard
16746 \begin_layout Standard
16747 Behind the formula both boxes are closed by entering
16751 in \SpecialChar TeX
16753 Here is an example:
16757 \begin_layout Plain Layout
16771 \begin_layout Standard
16775 \begin_layout Plain Layout
16793 \begin_inset Formula
16795 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
16804 \begin_layout Plain Layout
16815 \begin_layout Plain Layout
16829 \begin_layout Standard
16830 \begin_inset VSpace medskip
16833 As a parbox is used as the argument of
16839 , there is in this case no difference between
16854 \begin_layout Standard
16855 \begin_inset VSpace bigskip
16858 Paragraph boxes are very useful to comment formulas directly.
16865 is used in combination with the command
16879 \begin_inset CommandInset ref
16881 reference "subsec:User-defined-Numbering"
16888 \begin_layout Standard
16889 An example of a formula commented with
16898 \begin_layout Standard
16902 \begin_layout Plain Layout
16915 This is a description.
16916 It is distinctly separated from the formula and multiline.
16920 \begin_layout Plain Layout
16932 \begin_layout Standard
16933 Such a formula must be inserted completely in \SpecialChar TeX
16934 mode because \SpecialChar LyX
16936 support the command
16943 The formula is created with the following command sequence:
16946 \begin_layout Standard
16959 is inserted in \SpecialChar TeX
16964 \begin_layout Plain Layout
16965 When the formula style
16977 can also be replaced by
16984 (formula styles see
16985 \begin_inset CommandInset ref
16987 reference "sec:Formula-Styles"
16996 Then the description follows as normal text and finally
17002 is inserted in \SpecialChar TeX
17016 create a displayed formula.
17019 \begin_layout Standard
17026 can be seen in this example that was
17027 \begin_inset Quotes eld
17031 \begin_inset Quotes erd
17034 using the mathematical textmode:
17035 \begin_inset Formula
17037 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
17045 \begin_layout Section
17047 \begin_inset Index idx
17052 \begin_layout Plain Layout
17061 \begin_layout Subsection
17063 \begin_inset CommandInset label
17065 name "subsec:Big-Operators"
17070 \begin_inset Index idx
17075 \begin_layout Plain Layout
17077 \begin_inset IndexMacro subentry
17080 \begin_layout Plain Layout
17092 \begin_inset Index idx
17097 \begin_layout Plain Layout
17104 \begin_inset Index idx
17109 \begin_layout Plain Layout
17118 \begin_layout Standard
17119 To be able to use all of the integral operators listed here, the
17127 must be set in the document settings under
17130 \begin_inset space ~
17138 \begin_layout Standard
17139 \begin_inset space \hfill{}
17143 \begin_inset Tabular
17144 <lyxtabular version="3" rows="11" columns="2">
17145 <features booktabs="true" tabularvalignment="middle">
17146 <column alignment="center" valignment="top" width="0pt">
17147 <column alignment="center" valignment="top" width="0pt">
17149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17152 \begin_layout Plain Layout
17158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17161 \begin_layout Plain Layout
17169 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17172 \begin_layout Plain Layout
17176 \begin_inset Index idx
17181 \begin_layout Plain Layout
17183 \begin_inset IndexMacro subentry
17186 \begin_layout Plain Layout
17193 \begin_inset IndexMacro subentry
17196 \begin_layout Plain Layout
17214 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17217 \begin_layout Plain Layout
17218 \begin_inset Formula $\int$
17228 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17231 \begin_layout Plain Layout
17239 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17242 \begin_layout Plain Layout
17243 \begin_inset Formula $\oint$
17253 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17256 \begin_layout Plain Layout
17264 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17267 \begin_layout Plain Layout
17268 \begin_inset Formula $\ointctrclockwise$
17278 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17281 \begin_layout Plain Layout
17289 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17292 \begin_layout Plain Layout
17293 \begin_inset Formula $\ointclockwise$
17303 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17306 \begin_layout Plain Layout
17314 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17317 \begin_layout Plain Layout
17318 \begin_inset Formula $\sqint$
17328 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17331 \begin_layout Plain Layout
17339 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17342 \begin_layout Plain Layout
17344 \begin_inset Formula $\fint$
17354 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17357 \begin_layout Plain Layout
17365 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17368 \begin_layout Plain Layout
17370 \begin_inset Formula $\landupint$
17380 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17383 \begin_layout Plain Layout
17391 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17394 \begin_layout Plain Layout
17396 \begin_inset Formula $\landdownint$
17406 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17409 \begin_layout Plain Layout
17417 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17420 \begin_layout Plain Layout
17421 \begin_inset Formula $\bigcap$
17431 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17434 \begin_layout Plain Layout
17442 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17445 \begin_layout Plain Layout
17446 \begin_inset Formula $\bigcup$
17460 \begin_inset space \hfill{}
17464 \begin_inset Tabular
17465 <lyxtabular version="3" rows="11" columns="2">
17466 <features booktabs="true" tabularvalignment="middle">
17467 <column alignment="center" valignment="top" width="0pt">
17468 <column alignment="center" valignment="top" width="0pt">
17470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17473 \begin_layout Plain Layout
17479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17482 \begin_layout Plain Layout
17490 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17493 \begin_layout Plain Layout
17497 \begin_inset Index idx
17502 \begin_layout Plain Layout
17504 \begin_inset IndexMacro subentry
17507 \begin_layout Plain Layout
17514 \begin_inset IndexMacro subentry
17517 \begin_layout Plain Layout
17535 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17538 \begin_layout Plain Layout
17539 \begin_inset Formula $\sum$
17549 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17552 \begin_layout Plain Layout
17556 \begin_inset Index idx
17561 \begin_layout Plain Layout
17563 \begin_inset IndexMacro subentry
17566 \begin_layout Plain Layout
17573 \begin_inset IndexMacro subentry
17576 \begin_layout Plain Layout
17594 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17597 \begin_layout Plain Layout
17598 \begin_inset Formula $\prod$
17608 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17611 \begin_layout Plain Layout
17619 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17622 \begin_layout Plain Layout
17623 \begin_inset Formula $\coprod$
17633 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17636 \begin_layout Plain Layout
17644 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17647 \begin_layout Plain Layout
17648 \begin_inset Formula $\bigodot$
17658 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17661 \begin_layout Plain Layout
17669 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17672 \begin_layout Plain Layout
17673 \begin_inset Formula $\bigotimes$
17683 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17686 \begin_layout Plain Layout
17694 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17697 \begin_layout Plain Layout
17698 \begin_inset Formula $\bigoplus$
17708 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17711 \begin_layout Plain Layout
17719 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17722 \begin_layout Plain Layout
17723 \begin_inset Formula $\bigwedge$
17733 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17736 \begin_layout Plain Layout
17744 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17747 \begin_layout Plain Layout
17748 \begin_inset Formula $\bigvee$
17758 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17761 \begin_layout Plain Layout
17769 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17772 \begin_layout Plain Layout
17773 \begin_inset Formula $\bigsqcup$
17783 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17786 \begin_layout Plain Layout
17794 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17797 \begin_layout Plain Layout
17798 \begin_inset Formula $\biguplus$
17812 \begin_inset space \hfill{}
17818 \begin_layout Standard
17819 All big operators can also be inserted via the math toolbar button
17822 arg "math-insert \\intop"
17828 \begin_layout Standard
17829 The operators are called big because they are bigger than the sometimes
17830 equal looking binary operators.
17831 All big operators can have limits as described in the next subsection.
17834 \begin_layout Standard
17835 For all integral operators there is a second version available, ending in
17853 These operators differ in the style the operator limits are displayed,
17855 \begin_inset CommandInset ref
17857 reference "subsec:Operator-Limits"
17864 \begin_layout Subsubsection*
17865 Advice for Integrals
17868 \begin_layout Standard
17873 in an integral is an operator that has to be set upright.
17874 This is done by highlighting the
17878 and using the keyboard shortcut
17888 \begin_layout Plain Layout
17894 \begin_inset CommandInset ref
17896 reference "subsec:Font-Styles"
17906 Also the smallest space is inserted before the
17910 , as this is usual for operators.
17914 \begin_layout Standard
17916 \begin_inset Formula $\int A(x)dx$
17920 \begin_inset Newline newline
17924 \begin_inset Phantom HPhantom
17927 \begin_layout Plain Layout
17934 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
17940 \begin_layout Standard
17941 The following commands exist for multiple integrals:
17942 \begin_inset VSpace medskip
17948 \begin_layout Standard
17949 \begin_inset space \hfill{}
17953 \begin_inset Tabular
17954 <lyxtabular version="3" rows="4" columns="2">
17955 <features booktabs="true" tabularvalignment="middle">
17956 <column alignment="center" valignment="top" width="0pt">
17957 <column alignment="center" valignment="top" width="0pt">
17959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17962 \begin_layout Plain Layout
17968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17971 \begin_layout Plain Layout
17978 <row bottomspace="1mm">
17979 <cell alignment="center" valignment="top" usebox="none">
17982 \begin_layout Plain Layout
17990 <cell alignment="center" valignment="top" usebox="none">
17993 \begin_layout Plain Layout
17994 \begin_inset Formula $\iint$
18003 <row bottomspace="1mm">
18004 <cell alignment="center" valignment="top" usebox="none">
18007 \begin_layout Plain Layout
18015 <cell alignment="center" valignment="top" usebox="none">
18018 \begin_layout Plain Layout
18019 \begin_inset Formula $\oiint$
18028 <row bottomspace="1mm">
18029 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18032 \begin_layout Plain Layout
18040 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18043 \begin_layout Plain Layout
18044 \begin_inset Formula $\sqiint$
18058 \begin_inset space \hfill{}
18062 \begin_inset Tabular
18063 <lyxtabular version="3" rows="4" columns="2">
18064 <features booktabs="true" tabularvalignment="middle">
18065 <column alignment="center" valignment="top" width="0pt">
18066 <column alignment="center" valignment="top" width="0pt">
18068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18071 \begin_layout Plain Layout
18077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18080 \begin_layout Plain Layout
18087 <row bottomspace="1mm">
18088 <cell alignment="center" valignment="top" usebox="none">
18091 \begin_layout Plain Layout
18099 <cell alignment="center" valignment="top" usebox="none">
18102 \begin_layout Plain Layout
18103 \begin_inset Formula $\iiint$
18112 <row bottomspace="1mm">
18113 <cell alignment="center" valignment="top" usebox="none">
18116 \begin_layout Plain Layout
18124 <cell alignment="center" valignment="top" usebox="none">
18127 \begin_layout Plain Layout
18128 \begin_inset Formula $\iiiint$
18137 <row bottomspace="1mm">
18138 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18141 \begin_layout Plain Layout
18149 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18152 \begin_layout Plain Layout
18153 \begin_inset Formula $\dotsint$
18167 \begin_inset space \hfill{}
18173 \begin_layout Subsection
18175 \begin_inset CommandInset label
18177 name "subsec:Operator-Limits"
18182 \begin_inset Index idx
18187 \begin_layout Plain Layout
18189 \begin_inset IndexMacro subentry
18192 \begin_layout Plain Layout
18206 \begin_layout Standard
18207 Limits are created by super- and subscripts:
18210 \begin_layout Standard
18212 \begin_inset Tabular
18213 <lyxtabular version="3" rows="2" columns="2">
18214 <features booktabs="true" tabularvalignment="middle">
18215 <column alignment="center" valignment="top" width="0pt">
18216 <column alignment="center" valignment="top" width="0pt">
18218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18221 \begin_layout Plain Layout
18227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18230 \begin_layout Plain Layout
18238 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18241 \begin_layout Plain Layout
18247 \begin_inset space \textvisiblespace{}
18251 \begin_inset Formula $\to$
18255 \begin_inset Formula $\to$
18263 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18266 \begin_layout Plain Layout
18267 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
18283 \begin_layout Standard
18284 Limits of inline formulas are set on the right side of the operator.
18285 Limits in displayed formulas are set above or below the operator, except
18286 for integral limits.
18289 \begin_layout Standard
18290 To force the limits to be set beside the operator, the cursor is placed
18291 directly behind the operator and the limits type is changed with the menu
18294 Edit\SpecialChar menuseparator
18295 Math\SpecialChar menuseparator
18314 \begin_layout Standard
18315 The default displayed formulas limits type is this:
18316 \begin_inset Formula
18318 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
18323 This is how it looks when the limits type is changed to
18330 \begin_inset Formula
18332 \sum\nolimits_{x=0}^{\infty}\frac{1}{x^{2}}
18337 For integrals, except those ending with
18353 etc., the limits by default are set beside the operator.
18354 But for multiple integrals the limits are often set below the operator.
18355 In the following example the limits type was set to
18359 and so set below the integrals:
18360 \begin_inset Formula
18362 \iiint\limits_{V}X\,\mathrm{d}V=U\label{eq:VolInt}
18368 \change_deleted 5863208 1612725771
18370 \begin_inset Note Note
18373 \begin_layout Plain Layout
18375 \change_inserted 232239728 1611193306
18376 This integral did not have its limits set to Display in the original document
18388 \begin_layout Standard
18389 \begin_inset VSpace medskip
18392 To specify conditions for limits, the commands
18399 \begin_inset Index idx
18404 \begin_layout Plain Layout
18406 \begin_inset IndexMacro subentry
18409 \begin_layout Plain Layout
18416 \begin_inset IndexMacro subentry
18419 \begin_layout Plain Layout
18439 \begin_inset Index idx
18444 \begin_layout Plain Layout
18446 \begin_inset IndexMacro subentry
18449 \begin_layout Plain Layout
18456 \begin_inset IndexMacro subentry
18459 \begin_layout Plain Layout
18473 To create this expression
18474 \begin_inset Formula
18476 \sum_{\begin{subarray}{c}
18478 \\k\,\in\,\mathbb{N}
18479 \end{subarray}}^{n}k^{-2}\label{eq:substack}
18487 \begin_layout Standard
18488 the following must be done:
18489 \begin_inset Newline newline
18501 \begin_inset space \textvisiblespace{}
18507 The cursor is now in a blue box under the summation operator.
18513 \begin_inset space \textvisiblespace{}
18519 The blue box is now within a purple box and now multiple limit lines can
18521 A new line is created by inserting a line break (
18524 arg "newline-insert newline"
18529 \begin_inset Newline newline
18534 0<k<1000 Ctrl+Return
18535 \begin_inset Newline newline
18540 is typed in, a new box appears below for the new limit line.
18543 \begin_layout Standard
18544 The alignment of the lines can be changed to left aligned with the
18554 Edit\SpecialChar menuseparator
18558 To get right alignment,
18563 \begin_inset space \textvisiblespace{}
18568 is inserted at the beginning of the line.
18571 \begin_layout Standard
18584 with the difference that the lines are always centered.
18587 \begin_layout Standard
18588 \begin_inset VSpace bigskip
18592 \begin_inset CommandInset ref
18594 reference "eq:substack"
18598 there can be too much space beside an operator.
18599 This occurs because the characters following the operator are set beside
18601 To avoid this the command
18608 \begin_inset Index idx
18613 \begin_layout Plain Layout
18615 \begin_inset IndexMacro subentry
18618 \begin_layout Plain Layout
18625 \begin_inset IndexMacro subentry
18628 \begin_layout Plain Layout
18642 To use it, set the package
18647 \begin_inset Index idx
18652 \begin_layout Plain Layout
18654 \begin_inset IndexMacro subentry
18657 \begin_layout Plain Layout
18668 in the document settings under
18671 \begin_inset space ~
18679 \begin_inset space ~
18691 sets the space besides the operator to 0
18692 \begin_inset space \thinspace{}
18696 \begin_inset Newline newline
18700 \begin_inset CommandInset ref
18702 reference "eq:substack"
18706 , one uses the command
18709 \begin_layout Standard
18717 \begin_layout Standard
18718 and inserts the operator with its limits into the braces.
18719 Behind the brace one continues the formula:
18720 \begin_inset Formula
18722 \smashoperator{\sum_{\begin{subarray}{c}
18724 \\k\,\in\,\mathbb{N}
18725 \end{subarray}}^{n}}k^{-2}
18733 \begin_layout Standard
18734 It is possible to set the space of only one side of the operator to 0
18735 \begin_inset space \thinspace{}
18739 To do this write either
18758 stands for the left and
18762 for the right side of the operator.
18763 Here is an example of the possible
18772 \begin_layout Standard
18773 \begin_inset Formula
18775 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}
18783 \begin_layout Standard
18784 \begin_inset VSpace bigskip
18790 \begin_layout Standard
18791 When several consecutive operators have limits the typesetting of the limits
18792 looks often imperfect in the output, for example:
18793 \begin_inset Formula
18795 \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}
18800 To improve the typesetting, in the document settings under
18803 \begin_inset space ~
18813 \begin_inset Index idx
18818 \begin_layout Plain Layout
18820 \begin_inset IndexMacro subentry
18823 \begin_layout Plain Layout
18834 , set the option to
18837 \begin_inset space ~
18843 Then insert the command
18850 \begin_inset Index idx
18855 \begin_layout Plain Layout
18857 \begin_inset IndexMacro subentry
18860 \begin_layout Plain Layout
18867 \begin_inset IndexMacro subentry
18870 \begin_layout Plain Layout
18883 directly before the first operator.
18884 The example will then look like this:
18885 \begin_inset Formula
18887 \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}
18895 \begin_layout Standard
18896 \begin_inset VSpace bigskip
18899 How to use one limit for several operators is described in
18900 \begin_inset CommandInset ref
18902 reference "subsec:Self-defined-Operators"
18909 \begin_layout Subsection
18910 Decoration for Operators
18911 \begin_inset Index idx
18916 \begin_layout Plain Layout
18918 \begin_inset IndexMacro subentry
18921 \begin_layout Plain Layout
18935 \begin_layout Standard
18943 \begin_inset Index idx
18948 \begin_layout Plain Layout
18950 \begin_inset IndexMacro subentry
18953 \begin_layout Plain Layout
18960 \begin_inset IndexMacro subentry
18963 \begin_layout Plain Layout
18983 \begin_inset Index idx
18988 \begin_layout Plain Layout
18990 \begin_inset IndexMacro subentry
18993 \begin_layout Plain Layout
19000 \begin_inset IndexMacro subentry
19003 \begin_layout Plain Layout
19016 characters can be placed above or below an operator respectively.
19024 \begin_inset Index idx
19029 \begin_layout Plain Layout
19031 \begin_inset IndexMacro subentry
19034 \begin_layout Plain Layout
19041 \begin_inset IndexMacro subentry
19044 \begin_layout Plain Layout
19057 characters can be set before and behind a big operator.
19060 \begin_layout Standard
19062 \begin_inset space ~
19074 \begin_layout Itemize
19081 is used to set characters at the corners of the operator
19084 \begin_layout Itemize
19091 is used to set characters before and/or behind the operator (this variant
19092 represents \SpecialChar LaTeX
19102 \begin_layout Itemize
19109 is used to set characters at the left corners and/or behind the operator
19112 \begin_layout Itemize
19119 is used to set characters at the right corners and/or before the operator
19122 \begin_layout Standard
19123 For example the command
19128 \begin_inset space \textvisiblespace{}
19134 \begin_inset space \textvisiblespace{}
19138 \begin_inset Formula $\to$
19142 \begin_inset Formula $\to$
19146 \begin_inset space \textvisiblespace{}
19156 \begin_inset Formula
19158 \sideset{}{'}\sum_{k=1}^{n}
19166 \begin_layout Standard
19167 \begin_inset Note Greyedout
19170 \begin_layout Plain Layout
19177 can only be used to decorate big operators, binary operators are not allowed.
19185 \begin_layout Standard
19198 can also be used to decorate symbols and characters.
19199 For example, the command
19204 \begin_inset space \textvisiblespace{}
19210 \begin_inset space \textvisiblespace{}
19216 \begin_inset Formula $\uparrow$
19224 \begin_inset Formula
19226 \overset{a}{\maltese}
19234 \begin_layout Subsection
19236 \begin_inset CommandInset label
19238 name "subsec:Binary-Operators"
19243 \begin_inset Index idx
19248 \begin_layout Plain Layout
19250 \begin_inset IndexMacro subentry
19253 \begin_layout Plain Layout
19267 \begin_layout Standard
19268 Binary operators are surrounded by space when there is a character before
19270 \begin_inset VSpace medskip
19276 \begin_layout Standard
19277 \begin_inset Tabular
19278 <lyxtabular version="3" rows="13" columns="2">
19279 <features booktabs="true" tabularvalignment="middle">
19280 <column alignment="center" valignment="top" width="0pt">
19281 <column alignment="center" valignment="top" width="0pt">
19283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19286 \begin_layout Plain Layout
19288 \begin_inset Note Note
19291 \begin_layout Plain Layout
19298 is only used as spacer.
19308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19311 \begin_layout Plain Layout
19319 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19322 \begin_layout Plain Layout
19328 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19331 \begin_layout Plain Layout
19332 \begin_inset Formula $+$
19342 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19345 \begin_layout Plain Layout
19351 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19354 \begin_layout Plain Layout
19355 \begin_inset Formula $-$
19365 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19368 \begin_layout Plain Layout
19376 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19379 \begin_layout Plain Layout
19380 \begin_inset Formula $\pm$
19390 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19393 \begin_layout Plain Layout
19401 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19404 \begin_layout Plain Layout
19405 \begin_inset Formula $\mp$
19415 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19418 \begin_layout Plain Layout
19426 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19429 \begin_layout Plain Layout
19430 \begin_inset Formula $\cdot$
19440 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19443 \begin_layout Plain Layout
19451 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19454 \begin_layout Plain Layout
19455 \begin_inset Formula $\times$
19465 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19468 \begin_layout Plain Layout
19476 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19479 \begin_layout Plain Layout
19480 \begin_inset Formula $\div$
19490 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19493 \begin_layout Plain Layout
19497 \begin_layout Plain Layout
19510 \begin_layout Plain Layout
19522 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19525 \begin_layout Plain Layout
19526 \begin_inset Formula $*$
19536 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19539 \begin_layout Plain Layout
19547 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19550 \begin_layout Plain Layout
19551 \begin_inset Formula $\star$
19561 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19564 \begin_layout Plain Layout
19572 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19575 \begin_layout Plain Layout
19576 \begin_inset Formula $\circ$
19586 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19589 \begin_layout Plain Layout
19597 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19600 \begin_layout Plain Layout
19601 \begin_inset Formula $\diamond$
19611 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19614 \begin_layout Plain Layout
19622 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19625 \begin_layout Plain Layout
19626 \begin_inset Formula $\bullet$
19640 \begin_inset space \hfill{}
19644 \begin_inset Tabular
19645 <lyxtabular version="3" rows="13" columns="2">
19646 <features booktabs="true" tabularvalignment="middle">
19647 <column alignment="center" valignment="top" width="0pt">
19648 <column alignment="center" valignment="top" width="0pt">
19650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19653 \begin_layout Plain Layout
19659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19662 \begin_layout Plain Layout
19670 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19673 \begin_layout Plain Layout
19681 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19684 \begin_layout Plain Layout
19685 \begin_inset Formula $\nabla$
19695 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19698 \begin_layout Plain Layout
19706 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19709 \begin_layout Plain Layout
19710 \begin_inset Formula $\bigtriangledown$
19720 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19723 \begin_layout Plain Layout
19731 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19734 \begin_layout Plain Layout
19735 \begin_inset Formula $\bigtriangleup$
19745 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19748 \begin_layout Plain Layout
19756 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19759 \begin_layout Plain Layout
19760 \begin_inset Formula $\Box$
19770 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19773 \begin_layout Plain Layout
19781 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19784 \begin_layout Plain Layout
19785 \begin_inset Formula $\cap$
19795 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19798 \begin_layout Plain Layout
19806 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19809 \begin_layout Plain Layout
19810 \begin_inset Formula $\cup$
19820 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19823 \begin_layout Plain Layout
19831 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19834 \begin_layout Plain Layout
19835 \begin_inset Formula $\dagger$
19845 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19848 \begin_layout Plain Layout
19856 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19859 \begin_layout Plain Layout
19860 \begin_inset Formula $\ddagger$
19870 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19873 \begin_layout Plain Layout
19881 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19884 \begin_layout Plain Layout
19885 \begin_inset Formula $\wr$
19895 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19898 \begin_layout Plain Layout
19906 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19909 \begin_layout Plain Layout
19910 \begin_inset Formula $\bigcirc$
19920 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19923 \begin_layout Plain Layout
19931 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19934 \begin_layout Plain Layout
19935 \begin_inset Formula $\wedge$
19945 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19948 \begin_layout Plain Layout
19956 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19959 \begin_layout Plain Layout
19960 \begin_inset Formula $\vee$
19974 \begin_inset space \hfill{}
19978 \begin_inset Tabular
19979 <lyxtabular version="3" rows="13" columns="2">
19980 <features booktabs="true" tabularvalignment="middle">
19981 <column alignment="center" valignment="top" width="0pt">
19982 <column alignment="center" valignment="top" width="0pt">
19984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19987 \begin_layout Plain Layout
19993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19996 \begin_layout Plain Layout
20004 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20007 \begin_layout Plain Layout
20015 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20018 \begin_layout Plain Layout
20019 \begin_inset Formula $\oplus$
20029 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20032 \begin_layout Plain Layout
20040 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20043 \begin_layout Plain Layout
20044 \begin_inset Formula $\ominus$
20054 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20057 \begin_layout Plain Layout
20065 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20068 \begin_layout Plain Layout
20069 \begin_inset Formula $\otimes$
20079 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20082 \begin_layout Plain Layout
20090 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20093 \begin_layout Plain Layout
20094 \begin_inset Formula $\oslash$
20104 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20107 \begin_layout Plain Layout
20115 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20118 \begin_layout Plain Layout
20119 \begin_inset Formula $\odot$
20129 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20132 \begin_layout Plain Layout
20140 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20143 \begin_layout Plain Layout
20144 \begin_inset Formula $\amalg$
20154 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20157 \begin_layout Plain Layout
20165 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20168 \begin_layout Plain Layout
20169 \begin_inset Formula $\uplus$
20179 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20182 \begin_layout Plain Layout
20190 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20193 \begin_layout Plain Layout
20194 \begin_inset Formula $\setminus$
20204 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20207 \begin_layout Plain Layout
20215 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20218 \begin_layout Plain Layout
20219 \begin_inset Formula $\sqcap$
20229 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20232 \begin_layout Plain Layout
20240 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20243 \begin_layout Plain Layout
20244 \begin_inset Formula $\sqcup$
20254 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20257 \begin_layout Plain Layout
20265 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20268 \begin_layout Plain Layout
20269 \begin_inset Formula $\triangleleft$
20279 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20282 \begin_layout Plain Layout
20290 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20293 \begin_layout Plain Layout
20294 \begin_inset Formula $\triangleright$
20310 \begin_layout Standard
20311 All binary operators can also be inserted via the math toolbar button
20314 arg "math-insert \\pm"
20320 \begin_layout Standard
20321 To typeset the Laplace operator,
20338 \begin_inset Formula $\nabla^{2}$
20341 ) can also be used instead of
20350 \begin_layout Standard
20357 Insert\SpecialChar menuseparator
20369 \begin_layout Subsection
20370 Self-defined Operators
20371 \begin_inset CommandInset label
20373 name "subsec:Self-defined-Operators"
20378 \begin_inset Index idx
20383 \begin_layout Plain Layout
20385 \begin_inset IndexMacro subentry
20388 \begin_layout Plain Layout
20402 \begin_layout Standard
20403 With the help of the command
20407 DeclareMathOperator
20410 \begin_inset Index idx
20415 \begin_layout Plain Layout
20417 \begin_inset IndexMacro subentry
20420 \begin_layout Plain Layout
20427 \begin_inset IndexMacro subentry
20430 \begin_layout Plain Layout
20431 \begin_inset IndexMacro sortkey
20434 \begin_layout Plain Layout
20444 DeclareMathOperator
20454 , custom operators can be defined in the \SpecialChar LaTeX
20456 Its command scheme is:
20459 \begin_layout Standard
20464 DeclareMathOperator{new command}{display}
20467 \begin_layout Standard
20468 Display can be characters or symbols that define how the operator looks
20470 To define a big operator a * is set behind the command.
20471 All self-defined big operators can have limits as described in
20472 \begin_inset CommandInset ref
20474 reference "subsec:Operator-Limits"
20481 \begin_layout Standard
20482 For example the \SpecialChar LaTeX
20486 \begin_layout Standard
20491 DeclareMathOperator*{
20498 \begin_layout Standard
20499 defines the command
20505 , that inserts a big operator consisting of the black lozenge symbol from
20507 \begin_inset CommandInset ref
20509 reference "subsec:Miscellaneous-Symbols"
20514 \begin_inset Formula
20516 \Lozenge_{n=1}^{\infty}
20521 The command for this formula is:
20532 \begin_inset Formula $\to$
20538 \begin_layout Standard
20539 \begin_inset VSpace bigskip
20542 When self-defined operators are not used several times in the document,
20543 they can also be defined with the commands
20550 \begin_inset Index idx
20555 \begin_layout Plain Layout
20557 \begin_inset IndexMacro subentry
20560 \begin_layout Plain Layout
20567 \begin_inset IndexMacro subentry
20570 \begin_layout Plain Layout
20590 \begin_inset Index idx
20595 \begin_layout Plain Layout
20597 \begin_inset IndexMacro subentry
20600 \begin_layout Plain Layout
20607 \begin_inset IndexMacro subentry
20610 \begin_layout Plain Layout
20623 , which have the following scheme:
20626 \begin_layout Standard
20640 \begin_layout Standard
20647 defines big operators,
20656 \begin_layout Standard
20663 can be used to use one limit for several operators:
20666 \begin_layout Standard
20667 \begin_inset Formula
20669 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
20677 \begin_layout Standard
20678 The command for the formula above is:
20679 \begin_inset Newline newline
20695 \begin_inset space \textvisiblespace{}
20701 \begin_inset Formula $\to$
20707 \begin_inset space \textvisiblespace{}
20715 \begin_layout Section
20717 \begin_inset Index idx
20722 \begin_layout Plain Layout
20731 \begin_layout Subsection
20733 \begin_inset CommandInset label
20735 name "subsec:Font-Styles"
20740 \begin_inset Index idx
20745 \begin_layout Plain Layout
20747 \begin_inset IndexMacro subentry
20750 \begin_layout Plain Layout
20764 \begin_layout Standard
20765 Latin letters in formulas can be set in one of the following font styles:
20768 \begin_layout Standard
20770 \begin_inset Tabular
20771 <lyxtabular version="3" rows="6" columns="3">
20772 <features booktabs="true" tabularvalignment="middle">
20773 <column alignment="center" valignment="top" width="0pt">
20774 <column alignment="center" valignment="top">
20775 <column alignment="center" valignment="top">
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
20795 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
20798 \begin_layout Plain Layout
20806 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20809 \begin_layout Plain Layout
20815 \begin_inset space \textvisiblespace{}
20825 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20828 \begin_layout Plain Layout
20829 \begin_inset Formula $\mathbb{ABC}$
20837 <cell alignment="center" valignment="top" usebox="none">
20840 \begin_layout Plain Layout
20848 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20851 \begin_layout Plain Layout
20857 \begin_inset space \textvisiblespace{}
20867 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20870 \begin_layout Plain Layout
20871 \begin_inset Formula $\mathbf{AbC}$
20879 <cell alignment="center" valignment="top" usebox="none">
20882 \begin_layout Plain Layout
20895 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20898 \begin_layout Plain Layout
20904 \begin_inset space \textvisiblespace{}
20914 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20917 \begin_layout Plain Layout
20918 \begin_inset Formula $\boldsymbol{AbC}$
20926 <cell alignment="center" valignment="top" usebox="none">
20929 \begin_layout Plain Layout
20932 arg "font-boldsymbol"
20942 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20945 \begin_layout Plain Layout
20951 \begin_inset space \textvisiblespace{}
20961 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20964 \begin_layout Plain Layout
20965 \begin_inset Formula $\mathcal{ABC}$
20973 <cell alignment="center" valignment="top" usebox="none">
20976 \begin_layout Plain Layout
20984 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20987 \begin_layout Plain Layout
20993 \begin_inset space \textvisiblespace{}
21003 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21006 \begin_layout Plain Layout
21007 \begin_inset Formula $\mathfrak{AbC}$
21015 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
21018 \begin_layout Plain Layout
21032 \begin_layout Standard
21034 \begin_inset Tabular
21035 <lyxtabular version="3" rows="6" columns="3">
21036 <features booktabs="true" tabularvalignment="middle">
21037 <column alignment="center" valignment="top" width="0pt">
21038 <column alignment="center" valignment="top">
21039 <column alignment="center" valignment="top">
21041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21044 \begin_layout Plain Layout
21050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21053 \begin_layout Plain Layout
21059 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
21062 \begin_layout Plain Layout
21070 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21073 \begin_layout Plain Layout
21079 \begin_inset space \textvisiblespace{}
21089 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21092 \begin_layout Plain Layout
21093 \begin_inset Formula $\mathit{AbC}$
21101 <cell alignment="center" valignment="top" usebox="none">
21104 \begin_layout Plain Layout
21112 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21115 \begin_layout Plain Layout
21121 \begin_inset space \textvisiblespace{}
21131 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21134 \begin_layout Plain Layout
21135 \begin_inset Formula $\mathrm{AbC}$
21143 <cell alignment="center" valignment="top" usebox="none">
21146 \begin_layout Plain Layout
21159 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21162 \begin_layout Plain Layout
21168 \begin_inset space \textvisiblespace{}
21178 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21181 \begin_layout Plain Layout
21182 \begin_inset Formula $\mathsf{AbC}$
21190 <cell alignment="center" valignment="top" usebox="none">
21193 \begin_layout Plain Layout
21206 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21209 \begin_layout Plain Layout
21215 \begin_inset space \textvisiblespace{}
21225 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21228 \begin_layout Plain Layout
21229 \begin_inset Formula $\mathtt{AbC}$
21237 <cell alignment="center" valignment="top" usebox="none">
21240 \begin_layout Plain Layout
21243 arg "font-typewriter"
21253 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21256 \begin_layout Plain Layout
21262 \begin_inset space \textvisiblespace{}
21272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21275 \begin_layout Plain Layout
21276 \begin_inset Formula $\mathscr{ABC}$
21284 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
21287 \begin_layout Plain Layout
21301 \begin_layout Standard
21302 \begin_inset Note Greyedout
21305 \begin_layout Plain Layout
21328 can only be used for big letters.
21336 \begin_layout Standard
21346 \begin_layout Standard
21347 The style commands also work for letters in mathematical constructs:
21348 \begin_inset Formula
21350 \mathfrak{A=\frac{b}{C}}
21358 \begin_layout Standard
21359 Characters in mathematical text don't appear in a math font style but in
21360 the text font style
21367 Note that their style can't be set correctly via the text style dialog.
21368 This is a known bug in \SpecialChar LyX
21373 \begin_layout Plain Layout
21374 \begin_inset CommandInset href
21376 name "LyX-bug #4629"
21377 target "https://www.lyx.org/trac/ticket/4629"
21390 \begin_layout Standard
21391 Instead of the style commands,
21393 Edit\SpecialChar menuseparator
21394 Math\SpecialChar menuseparator
21397 dialog, or the toolbar button,
21400 arg "math-insert \\font"
21406 \begin_layout Subsection
21408 \begin_inset CommandInset label
21410 name "subsec:Bold-Formulas"
21415 \begin_inset Index idx
21420 \begin_layout Plain Layout
21422 \begin_inset IndexMacro subentry
21425 \begin_layout Plain Layout
21439 \begin_layout Standard
21440 To make a complete formula bold, the command
21446 from the previous subsection cannot be used because it doesn't work for
21447 small Greek letters.
21448 Additionally it always prints Latin letters upright, as in the following
21452 \begin_layout Standard
21453 \begin_inset Formula
21455 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
21463 \begin_layout Standard
21464 To display the formula correctly, the command
21471 \begin_inset Formula
21473 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
21478 It is also possible to set the formula in a
21480 boldmath environment
21483 This environment is created by inserting the command
21490 \begin_inset Index idx
21495 \begin_layout Plain Layout
21497 \begin_inset IndexMacro subentry
21500 \begin_layout Plain Layout
21507 \begin_inset IndexMacro subentry
21510 \begin_layout Plain Layout
21523 in \SpecialChar TeX
21525 To end the environment, the command
21532 \begin_inset Index idx
21537 \begin_layout Plain Layout
21539 \begin_inset IndexMacro subentry
21542 \begin_layout Plain Layout
21549 \begin_inset IndexMacro subentry
21552 \begin_layout Plain Layout
21565 is inserted in \SpecialChar TeX
21570 \begin_layout Plain Layout
21580 \begin_inset Formula
21582 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
21591 \begin_layout Plain Layout
21603 \begin_layout Subsection
21605 \begin_inset Index idx
21610 \begin_layout Plain Layout
21612 \begin_inset IndexMacro subentry
21615 \begin_layout Plain Layout
21629 \begin_layout Standard
21630 Formulas can be colored like normal text: Highlight a formula or a formula
21636 Here is a formula in magenta:
21637 \begin_inset Formula
21639 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
21647 \begin_layout Standard
21648 You can also define your own colors as described in
21649 \begin_inset CommandInset ref
21651 reference "subsec:Colored-Boxes"
21656 They can be used with the \SpecialChar TeX
21664 \begin_inset Index idx
21669 \begin_layout Plain Layout
21671 \begin_inset IndexMacro subentry
21674 \begin_layout Plain Layout
21681 \begin_inset IndexMacro subentry
21684 \begin_layout Plain Layout
21700 \begin_layout Standard
21705 textcolor{color}{characters or formula}
21708 \begin_layout Standard
21709 The following example was colored completely dark green and partly red:
21712 \begin_layout Standard
21716 \begin_layout Plain Layout
21720 textcolor{darkgreen}{
21726 \begin_inset Formula
21728 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
21737 \begin_layout Plain Layout
21747 \begin_layout Standard
21748 Due to a bug in \SpecialChar LyX
21749 only complete formulas can be colored with self-defined
21754 \begin_layout Plain Layout
21755 \begin_inset CommandInset href
21757 name "LyX-bug #5269"
21758 target "https://www.lyx.org/trac/ticket/5269"
21771 \begin_layout Subsection
21773 \begin_inset CommandInset label
21775 name "subsec:Font-Sizes"
21780 \begin_inset Index idx
21785 \begin_layout Plain Layout
21787 \begin_inset IndexMacro subentry
21790 \begin_layout Plain Layout
21804 \begin_layout Standard
21805 As with characters in text, the following size commands are available for
21806 formula characters:
21809 \begin_layout Standard
21853 \begin_inset Newline newline
21875 \begin_layout Standard
21876 The font size produced by the commands depends on the document's original
21877 font size, which corresponds to the command
21884 The other commands produce character sizes smaller or larger than
21891 There are however limits to how small or large the font size can be changed.
21892 If for example the document font size is 12
21893 \begin_inset space \thinspace{}
21902 switches to the same size as
21911 \begin_layout Standard
21912 A size command is inserted in \SpecialChar TeX
21913 mode before a formula and sets the size for
21914 all of the following formulas and text characters.
21915 To switch back to the initial size, the command
21921 is inserted behind the formula, again in \SpecialChar TeX
21925 \begin_layout Standard
21926 Size can also be changed within a formula using the following size commands
21927 or the toolbar button
21930 arg "math-insert \\style"
21936 \begin_layout Standard
21939 \begin_inset Tabular
21940 <lyxtabular version="3" rows="5" columns="2">
21941 <features booktabs="true" tabularvalignment="middle">
21942 <column alignment="center" valignment="top" width="0pt">
21943 <column alignment="center" valignment="top">
21945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21948 \begin_layout Plain Layout
21954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21957 \begin_layout Plain Layout
21965 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21968 \begin_layout Plain Layout
21972 \begin_inset Index idx
21977 \begin_layout Plain Layout
21979 \begin_inset IndexMacro subentry
21982 \begin_layout Plain Layout
21989 \begin_inset IndexMacro subentry
21992 \begin_layout Plain Layout
22010 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22013 \begin_layout Plain Layout
22014 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
22023 <row topspace="1mm">
22024 <cell alignment="center" valignment="top" usebox="none">
22027 \begin_layout Plain Layout
22035 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22038 \begin_layout Plain Layout
22039 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
22049 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22052 \begin_layout Plain Layout
22060 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22063 \begin_layout Plain Layout
22064 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
22074 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22077 \begin_layout Plain Layout
22085 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22088 \begin_layout Plain Layout
22089 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
22105 \begin_layout Standard
22106 After entering these commands, a blue box appears in which the formula parts
22110 \begin_layout Standard
22111 There is another method for changing the font size, although it only works
22112 for symbols or letters in mathematical text.
22113 To use it, one of the above text size commands is inserted into mathematical
22115 All characters until the end of the mathematical text or until another
22116 size command will have the selected size.
22118 \begin_inset VSpace -2mm
22124 \begin_layout Standard
22128 \begin_layout Plain Layout
22138 \begin_inset Formula
22140 A=\frac{B}{c}\cdot\maltese
22146 \begin_inset Formula
22148 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
22157 \begin_layout Plain Layout
22167 \begin_inset VSpace medskip
22170 Before the first formula the command
22177 The command for the second formula is:
22178 \begin_inset Newline newline
22186 \begin_inset space \textvisiblespace{}
22192 \begin_inset space \textvisiblespace{}
22198 \begin_inset space \textvisiblespace{}
22204 \begin_inset space \textvisiblespace{}
22208 \begin_inset Formula $\to$
22212 \begin_inset Formula $\to$
22216 \begin_inset Newline newline
22220 \begin_inset space \hspace*{}
22231 \begin_inset space \textvisiblespace{}
22237 \begin_inset space \textvisiblespace{}
22243 \begin_inset space \textvisiblespace{}
22249 \begin_layout Standard
22250 If a symbol cannot be displayed in different sizes, it will always be displayed
22251 in the default size.
22254 \begin_layout Section
22256 \begin_inset Index idx
22261 \begin_layout Plain Layout
22270 \begin_layout Standard
22271 Greek letters can be inserted via the toolbar button
22274 arg "math-insert \\alpha"
22277 as well as by command.
22278 All international typesetting norms purport that Greek letters in math
22279 have to be typeset italic/slanted.
22280 In some languages, like French or Russian, they are nevertheless sometimes
22284 \begin_layout Subsection
22286 \begin_inset Index idx
22291 \begin_layout Plain Layout
22293 \begin_inset IndexMacro subentry
22296 \begin_layout Plain Layout
22310 \begin_layout Standard
22311 \begin_inset space \hfill{}
22315 \begin_inset Tabular
22316 <lyxtabular version="3" rows="11" columns="2">
22317 <features booktabs="true" tabularvalignment="middle">
22318 <column alignment="center" valignment="top" width="0pt">
22319 <column alignment="center" valignment="top" width="0pt">
22321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22324 \begin_layout Plain Layout
22330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22333 \begin_layout Plain Layout
22341 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22344 \begin_layout Plain Layout
22352 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22355 \begin_layout Plain Layout
22356 \begin_inset Formula $\alpha$
22366 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22369 \begin_layout Plain Layout
22377 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22380 \begin_layout Plain Layout
22381 \begin_inset Formula $\beta$
22391 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22394 \begin_layout Plain Layout
22402 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22405 \begin_layout Plain Layout
22406 \begin_inset Formula $\gamma$
22416 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22419 \begin_layout Plain Layout
22427 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22430 \begin_layout Plain Layout
22431 \begin_inset Formula $\delta$
22441 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22444 \begin_layout Plain Layout
22452 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22455 \begin_layout Plain Layout
22456 \begin_inset Formula $\epsilon$
22466 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22469 \begin_layout Plain Layout
22477 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22480 \begin_layout Plain Layout
22481 \begin_inset Formula $\varepsilon$
22491 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22494 \begin_layout Plain Layout
22502 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22505 \begin_layout Plain Layout
22506 \begin_inset Formula $\zeta$
22516 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22519 \begin_layout Plain Layout
22527 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22530 \begin_layout Plain Layout
22531 \begin_inset Formula $\eta$
22541 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22544 \begin_layout Plain Layout
22552 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22555 \begin_layout Plain Layout
22556 \begin_inset Formula $\theta$
22566 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22569 \begin_layout Plain Layout
22577 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22580 \begin_layout Plain Layout
22581 \begin_inset Formula $\vartheta$
22595 \begin_inset space \hfill{}
22599 \begin_inset Tabular
22600 <lyxtabular version="3" rows="12" columns="2">
22601 <features booktabs="true" tabularvalignment="middle">
22602 <column alignment="center" valignment="top" width="0pt">
22603 <column alignment="center" valignment="top" width="0pt">
22605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22608 \begin_layout Plain Layout
22614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22617 \begin_layout Plain Layout
22625 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22628 \begin_layout Plain Layout
22636 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22639 \begin_layout Plain Layout
22640 \begin_inset Formula $\iota$
22650 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22653 \begin_layout Plain Layout
22661 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22664 \begin_layout Plain Layout
22665 \begin_inset Formula $\kappa$
22675 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22678 \begin_layout Plain Layout
22686 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22689 \begin_layout Plain Layout
22690 \begin_inset Formula $\varkappa$
22700 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22703 \begin_layout Plain Layout
22711 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22714 \begin_layout Plain Layout
22715 \begin_inset Formula $\lambda$
22725 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22728 \begin_layout Plain Layout
22736 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22739 \begin_layout Plain Layout
22740 \begin_inset Formula $\mu$
22750 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22753 \begin_layout Plain Layout
22761 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22764 \begin_layout Plain Layout
22765 \begin_inset Formula $\nu$
22775 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22778 \begin_layout Plain Layout
22786 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22789 \begin_layout Plain Layout
22790 \begin_inset Formula $\xi$
22800 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22803 \begin_layout Plain Layout
22809 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22812 \begin_layout Plain Layout
22813 \begin_inset Formula $o$
22823 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22826 \begin_layout Plain Layout
22834 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22837 \begin_layout Plain Layout
22838 \begin_inset Formula $\pi$
22848 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22851 \begin_layout Plain Layout
22859 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22862 \begin_layout Plain Layout
22863 \begin_inset Formula $\varpi$
22873 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22876 \begin_layout Plain Layout
22884 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22887 \begin_layout Plain Layout
22888 \begin_inset Formula $\rho$
22902 \begin_inset space \hfill{}
22906 \begin_inset Tabular
22907 <lyxtabular version="3" rows="11" columns="2">
22908 <features booktabs="true" tabularvalignment="middle">
22909 <column alignment="center" valignment="top" width="0pt">
22910 <column alignment="center" valignment="top" width="0pt">
22912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22915 \begin_layout Plain Layout
22921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22924 \begin_layout Plain Layout
22932 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22935 \begin_layout Plain Layout
22943 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22946 \begin_layout Plain Layout
22947 \begin_inset Formula $\varrho$
22957 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22960 \begin_layout Plain Layout
22968 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22971 \begin_layout Plain Layout
22972 \begin_inset Formula $\sigma$
22982 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22985 \begin_layout Plain Layout
22993 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22996 \begin_layout Plain Layout
22997 \begin_inset Formula $\varsigma$
23007 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23010 \begin_layout Plain Layout
23018 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23021 \begin_layout Plain Layout
23022 \begin_inset Formula $\tau$
23032 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23035 \begin_layout Plain Layout
23043 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23046 \begin_layout Plain Layout
23047 \begin_inset Formula $\upsilon$
23057 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23060 \begin_layout Plain Layout
23068 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23071 \begin_layout Plain Layout
23072 \begin_inset Formula $\phi$
23082 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23085 \begin_layout Plain Layout
23093 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23096 \begin_layout Plain Layout
23097 \begin_inset Formula $\varphi$
23107 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23110 \begin_layout Plain Layout
23118 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23121 \begin_layout Plain Layout
23122 \begin_inset Formula $\chi$
23132 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23135 \begin_layout Plain Layout
23143 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23146 \begin_layout Plain Layout
23147 \begin_inset Formula $\psi$
23157 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23160 \begin_layout Plain Layout
23168 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23171 \begin_layout Plain Layout
23172 \begin_inset Formula $\omega$
23186 \begin_inset space \hfill{}
23192 \begin_layout Standard
23193 \begin_inset VSpace medskip
23199 \begin_layout Standard
23200 Creating upright Greek letters is explained in
23201 \begin_inset CommandInset ref
23203 reference "subsec:Upright-small-Greek"
23210 \begin_layout Subsection
23212 \begin_inset Index idx
23217 \begin_layout Plain Layout
23219 \begin_inset IndexMacro subentry
23222 \begin_layout Plain Layout
23236 \begin_layout Standard
23237 \begin_inset space \hfill{}
23241 \begin_inset Tabular
23242 <lyxtabular version="3" rows="7" columns="2">
23243 <features booktabs="true" tabularvalignment="middle">
23244 <column alignment="center" valignment="top" width="0pt">
23245 <column alignment="center" valignment="top" width="0pt">
23247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23250 \begin_layout Plain Layout
23256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23259 \begin_layout Plain Layout
23267 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23270 \begin_layout Plain Layout
23278 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23281 \begin_layout Plain Layout
23282 \begin_inset Formula $\Gamma$
23292 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23295 \begin_layout Plain Layout
23303 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23306 \begin_layout Plain Layout
23307 \begin_inset Formula $\Delta$
23317 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23320 \begin_layout Plain Layout
23328 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23331 \begin_layout Plain Layout
23332 \begin_inset Formula $\Theta$
23342 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23345 \begin_layout Plain Layout
23353 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23356 \begin_layout Plain Layout
23357 \begin_inset Formula $\Lambda$
23367 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23370 \begin_layout Plain Layout
23378 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23381 \begin_layout Plain Layout
23382 \begin_inset Formula $\Xi$
23392 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23395 \begin_layout Plain Layout
23403 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23406 \begin_layout Plain Layout
23407 \begin_inset Formula $\Pi$
23421 \begin_inset space \hfill{}
23425 \begin_inset Tabular
23426 <lyxtabular version="3" rows="6" columns="2">
23427 <features booktabs="true" tabularvalignment="middle">
23428 <column alignment="center" valignment="top" width="0pt">
23429 <column alignment="center" valignment="top" width="0pt">
23431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23434 \begin_layout Plain Layout
23440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23443 \begin_layout Plain Layout
23451 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23454 \begin_layout Plain Layout
23462 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23465 \begin_layout Plain Layout
23466 \begin_inset Formula $\Sigma$
23476 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23479 \begin_layout Plain Layout
23487 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23490 \begin_layout Plain Layout
23491 \begin_inset Formula $\Upsilon$
23501 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23504 \begin_layout Plain Layout
23512 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23515 \begin_layout Plain Layout
23516 \begin_inset Formula $\Phi$
23526 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23529 \begin_layout Plain Layout
23537 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23540 \begin_layout Plain Layout
23541 \begin_inset Formula $\Psi$
23551 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23554 \begin_layout Plain Layout
23562 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23565 \begin_layout Plain Layout
23566 \begin_inset Formula $\Omega$
23580 \begin_inset space \hfill{}
23586 \begin_layout Standard
23587 \begin_inset VSpace medskip
23590 The big Greek letters appearing upright is caused by a design bug in \SpecialChar TeX
23592 To create correct italic big letters, begin every command with
23597 For example the command
23604 \begin_inset Formula $\varGamma$
23608 Another way is to load the package
23616 \begin_layout Plain Layout
23621 is part of the \SpecialChar LaTeX
23627 \begin_inset Index idx
23632 \begin_layout Plain Layout
23634 \begin_inset IndexMacro subentry
23637 \begin_layout Plain Layout
23654 \begin_inset Index idx
23659 \begin_layout Plain Layout
23661 \begin_inset IndexMacro subentry
23664 \begin_layout Plain Layout
23675 with the \SpecialChar LaTeX
23679 \begin_layout Standard
23684 usepackage{fixmath}
23687 \begin_layout Standard
23688 Then all big Greek letters in a document will automatically be typeset italic.
23691 \begin_layout Subsection
23693 \begin_inset Index idx
23698 \begin_layout Plain Layout
23700 \begin_inset IndexMacro subentry
23703 \begin_layout Plain Layout
23717 \begin_layout Standard
23718 Greek letters cannot be set with different font styles like Latin letters.
23719 They can only be made bold with the command
23726 \begin_inset Index idx
23731 \begin_layout Plain Layout
23733 \begin_inset IndexMacro subentry
23736 \begin_layout Plain Layout
23743 \begin_inset IndexMacro subentry
23746 \begin_layout Plain Layout
23762 \begin_layout Standard
23764 \begin_inset Tabular
23765 <lyxtabular version="3" rows="3" columns="2">
23766 <features booktabs="true" tabularvalignment="middle">
23767 <column alignment="center" valignment="top" width="0pt">
23768 <column alignment="center" valignment="top">
23770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23773 \begin_layout Plain Layout
23779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23782 \begin_layout Plain Layout
23790 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23793 \begin_layout Plain Layout
23805 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23808 \begin_layout Plain Layout
23809 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
23819 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23822 \begin_layout Plain Layout
23834 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23837 \begin_layout Plain Layout
23838 \begin_inset Formula $\theta\boldsymbol{\theta}$
23854 \begin_layout Section
23859 \begin_layout Plain Layout
23872 \begin_layout Plain Layout
23873 A list with all symbols of most of the \SpecialChar LaTeX
23874 -packages can be found in
23875 \begin_inset CommandInset citation
23891 \begin_layout Plain Layout
23899 \begin_inset Note Note
23902 \begin_layout Plain Layout
23905 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
23908 \begin_layout Plain Layout
23911 texorpdfstring is in section
23912 \begin_inset CommandInset ref
23914 reference "subsec:Formulas-in-Section"
23924 \begin_inset Index idx
23929 \begin_layout Plain Layout
23938 \begin_layout Standard
23939 Many of the symbols listed in this section can also be inserted via the
23943 arg "math-insert \\nabla"
23949 arg "math-insert \\digamma"
23955 \begin_layout Subsection
23956 Mathematical Symbols
23957 \begin_inset CommandInset label
23959 name "subsec:Mathematical-Symbols"
23964 \begin_inset Index idx
23969 \begin_layout Plain Layout
23971 \begin_inset IndexMacro subentry
23974 \begin_layout Plain Layout
23988 \begin_layout Standard
23989 \begin_inset Tabular
23990 <lyxtabular version="3" rows="10" columns="2">
23991 <features booktabs="true" tabularvalignment="middle">
23992 <column alignment="center" valignment="top" width="0pt">
23993 <column alignment="center" valignment="top" width="0pt">
23995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23998 \begin_layout Plain Layout
24004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24007 \begin_layout Plain Layout
24015 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24018 \begin_layout Plain Layout
24026 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24029 \begin_layout Plain Layout
24030 \begin_inset Formula $\neg$
24040 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24043 \begin_layout Plain Layout
24051 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24054 \begin_layout Plain Layout
24055 \begin_inset Formula $\Im$
24065 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24068 \begin_layout Plain Layout
24076 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24079 \begin_layout Plain Layout
24080 \begin_inset Formula $\Re$
24090 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24093 \begin_layout Plain Layout
24101 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24104 \begin_layout Plain Layout
24105 \begin_inset Formula $\aleph$
24115 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24118 \begin_layout Plain Layout
24126 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24129 \begin_layout Plain Layout
24130 \begin_inset Formula $\partial$
24140 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24143 \begin_layout Plain Layout
24151 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24154 \begin_layout Plain Layout
24155 \begin_inset Formula $\infty$
24165 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24168 \begin_layout Plain Layout
24176 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24179 \begin_layout Plain Layout
24180 \begin_inset Formula $\wp$
24190 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24193 \begin_layout Plain Layout
24201 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24204 \begin_layout Plain Layout
24205 \begin_inset Formula $\imath$
24215 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24218 \begin_layout Plain Layout
24226 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24229 \begin_layout Plain Layout
24230 \begin_inset Formula $\jmath$
24244 \begin_inset space \hfill{}
24248 \begin_inset Tabular
24249 <lyxtabular version="3" rows="10" columns="2">
24250 <features booktabs="true" tabularvalignment="middle">
24251 <column alignment="center" valignment="top" width="0pt">
24252 <column alignment="center" valignment="top" width="0pt">
24254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24257 \begin_layout Plain Layout
24263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24266 \begin_layout Plain Layout
24268 \begin_inset Note Note
24271 \begin_layout Plain Layout
24278 is only used as spacer.
24290 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24293 \begin_layout Plain Layout
24301 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24304 \begin_layout Plain Layout
24305 \begin_inset Formula $\forall$
24315 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24318 \begin_layout Plain Layout
24326 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24329 \begin_layout Plain Layout
24330 \begin_inset Formula $\exists$
24340 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24343 \begin_layout Plain Layout
24351 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24354 \begin_layout Plain Layout
24355 \begin_inset Formula $\nexists$
24365 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24368 \begin_layout Plain Layout
24376 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24379 \begin_layout Plain Layout
24380 \begin_inset Formula $\emptyset$
24390 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24393 \begin_layout Plain Layout
24401 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24404 \begin_layout Plain Layout
24405 \begin_inset Formula $\varnothing$
24415 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24418 \begin_layout Plain Layout
24426 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24429 \begin_layout Plain Layout
24430 \begin_inset Formula $\dag$
24440 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24443 \begin_layout Plain Layout
24451 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24454 \begin_layout Plain Layout
24455 \begin_inset Formula $\ddag$
24465 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24468 \begin_layout Plain Layout
24476 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24479 \begin_layout Plain Layout
24483 \begin_layout Plain Layout
24493 \begin_inset Formula $\complement$
24500 \begin_layout Plain Layout
24514 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24517 \begin_layout Plain Layout
24525 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24528 \begin_layout Plain Layout
24529 \begin_inset Formula $\Bbbk$
24543 \begin_inset space \hfill{}
24547 \begin_inset Tabular
24548 <lyxtabular version="3" rows="10" columns="2">
24549 <features booktabs="true" tabularvalignment="middle">
24550 <column alignment="center" valignment="top" width="0pt">
24551 <column alignment="center" valignment="top" width="0pt">
24553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24556 \begin_layout Plain Layout
24562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24565 \begin_layout Plain Layout
24573 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24576 \begin_layout Plain Layout
24584 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24587 \begin_layout Plain Layout
24588 \begin_inset Formula $\prime$
24598 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24601 \begin_layout Plain Layout
24609 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24612 \begin_layout Plain Layout
24613 \begin_inset Formula $\backprime$
24623 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24626 \begin_layout Plain Layout
24634 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24637 \begin_layout Plain Layout
24638 \begin_inset Formula $\mho$
24648 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24651 \begin_layout Plain Layout
24659 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24662 \begin_layout Plain Layout
24663 \begin_inset Formula $\triangle$
24673 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24676 \begin_layout Plain Layout
24684 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24687 \begin_layout Plain Layout
24688 \begin_inset Formula $\angle$
24698 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24701 \begin_layout Plain Layout
24709 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24712 \begin_layout Plain Layout
24713 \begin_inset Formula $\measuredangle$
24723 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24726 \begin_layout Plain Layout
24734 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24737 \begin_layout Plain Layout
24738 \begin_inset Formula $\sphericalangle$
24748 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24751 \begin_layout Plain Layout
24759 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24762 \begin_layout Plain Layout
24763 \begin_inset Formula $\top$
24773 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24776 \begin_layout Plain Layout
24784 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24787 \begin_layout Plain Layout
24788 \begin_inset Formula $\bot$
24804 \begin_layout Subsection
24805 Miscellaneous Symbols
24806 \begin_inset CommandInset label
24808 name "subsec:Miscellaneous-Symbols"
24813 \begin_inset Index idx
24818 \begin_layout Plain Layout
24820 \begin_inset IndexMacro subentry
24823 \begin_layout Plain Layout
24837 \begin_layout Standard
24840 \begin_inset Tabular
24841 <lyxtabular version="3" rows="10" columns="2">
24842 <features booktabs="true" tabularvalignment="middle">
24843 <column alignment="center" valignment="top" width="0pt">
24844 <column alignment="center" valignment="top" width="0pt">
24846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24849 \begin_layout Plain Layout
24855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24858 \begin_layout Plain Layout
24866 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24869 \begin_layout Plain Layout
24877 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24880 \begin_layout Plain Layout
24881 \begin_inset Formula $\flat$
24891 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24894 \begin_layout Plain Layout
24902 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24905 \begin_layout Plain Layout
24906 \begin_inset Formula $\natural$
24916 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24919 \begin_layout Plain Layout
24927 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24930 \begin_layout Plain Layout
24931 \begin_inset Formula $\sharp$
24941 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24944 \begin_layout Plain Layout
24952 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24955 \begin_layout Plain Layout
24956 \begin_inset Formula $\surd$
24966 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24969 \begin_layout Plain Layout
24977 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24980 \begin_layout Plain Layout
24981 \begin_inset Formula $\checkmark$
24991 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24994 \begin_layout Plain Layout
25002 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25005 \begin_layout Plain Layout
25006 \begin_inset Formula $\yen$
25016 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25019 \begin_layout Plain Layout
25027 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25030 \begin_layout Plain Layout
25031 \begin_inset Formula $\pounds$
25041 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25044 \begin_layout Plain Layout
25050 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25053 \begin_layout Plain Layout
25054 \begin_inset Formula $\$$
25064 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25067 \begin_layout Plain Layout
25073 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25076 \begin_layout Plain Layout
25077 \begin_inset Formula $§$
25091 \begin_inset space \hfill{}
25095 \begin_inset Tabular
25096 <lyxtabular version="3" rows="10" columns="2">
25097 <features booktabs="true" tabularvalignment="middle">
25098 <column alignment="center" valignment="top" width="0pt">
25099 <column alignment="center" valignment="top">
25101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25104 \begin_layout Plain Layout
25110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25113 \begin_layout Plain Layout
25121 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25124 \begin_layout Plain Layout
25132 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25135 \begin_layout Plain Layout
25136 \begin_inset Formula $\hbar$
25146 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25149 \begin_layout Plain Layout
25157 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25160 \begin_layout Plain Layout
25161 \begin_inset Formula $\hslash$
25171 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25174 \begin_layout Plain Layout
25182 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25185 \begin_layout Plain Layout
25186 \begin_inset Formula $\clubsuit$
25196 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25199 \begin_layout Plain Layout
25207 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25210 \begin_layout Plain Layout
25211 \begin_inset Formula $\spadesuit$
25221 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25224 \begin_layout Plain Layout
25232 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25235 \begin_layout Plain Layout
25236 \begin_inset Formula $\bigstar$
25246 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25249 \begin_layout Plain Layout
25257 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25260 \begin_layout Plain Layout
25261 \begin_inset Formula $\blacklozenge$
25271 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25274 \begin_layout Plain Layout
25282 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25285 \begin_layout Plain Layout
25286 \begin_inset Formula $\blacktriangle$
25296 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25299 \begin_layout Plain Layout
25307 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25310 \begin_layout Plain Layout
25311 \begin_inset Formula $\blacktriangledown$
25321 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25324 \begin_layout Plain Layout
25332 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25335 \begin_layout Plain Layout
25336 \begin_inset Formula $\bullet$
25350 \begin_inset space \hfill{}
25354 \begin_inset Tabular
25355 <lyxtabular version="3" rows="10" columns="2">
25356 <features booktabs="true" tabularvalignment="middle">
25357 <column alignment="center" valignment="top" width="0pt">
25358 <column alignment="center" valignment="top" width="0pt">
25360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25363 \begin_layout Plain Layout
25369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25372 \begin_layout Plain Layout
25380 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25383 \begin_layout Plain Layout
25391 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25394 \begin_layout Plain Layout
25395 \begin_inset Formula $\diamondsuit$
25405 <cell alignment="center" valignment="top" rightline="true" usebox="none">
25408 \begin_layout Plain Layout
25416 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25419 \begin_layout Plain Layout
25420 \begin_inset Formula $\Diamond$
25430 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25433 \begin_layout Plain Layout
25441 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25444 \begin_layout Plain Layout
25445 \begin_inset Formula $\heartsuit$
25455 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25458 \begin_layout Plain Layout
25466 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25469 \begin_layout Plain Layout
25470 \begin_inset Formula $\P$
25480 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25483 \begin_layout Plain Layout
25491 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25494 \begin_layout Plain Layout
25495 \begin_inset Formula $\copyright$
25505 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25508 \begin_layout Plain Layout
25516 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25519 \begin_layout Plain Layout
25520 \begin_inset Formula $\circledR$
25530 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25533 \begin_layout Plain Layout
25541 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25544 \begin_layout Plain Layout
25545 \begin_inset Formula $\maltese$
25555 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25558 \begin_layout Plain Layout
25566 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25569 \begin_layout Plain Layout
25570 \begin_inset Formula $\diagup$
25580 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25583 \begin_layout Plain Layout
25591 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25594 \begin_layout Plain Layout
25595 \begin_inset Formula $\diagdown$
25611 \begin_layout Standard
25612 \begin_inset VSpace medskip
25618 \begin_layout Standard
25619 Some symbols can be displayed in different sizes, see
25620 \begin_inset CommandInset ref
25622 reference "subsec:Font-Sizes"
25629 \begin_layout Subsection
25631 \begin_inset Index idx
25636 \begin_layout Plain Layout
25638 \begin_inset IndexMacro subentry
25641 \begin_layout Plain Layout
25653 \begin_inset Index idx
25658 \begin_layout Plain Layout
25659 \begin_inset IndexMacro sortkey
25662 \begin_layout Plain Layout
25674 \begin_layout Plain Layout
25691 \begin_layout Standard
25692 To use the Euro symbol in formulas, the \SpecialChar LaTeX
25698 \begin_inset Index idx
25703 \begin_layout Plain Layout
25705 \begin_inset IndexMacro subentry
25708 \begin_layout Plain Layout
25719 must be installed and loaded with the \SpecialChar LaTeX
25723 \begin_layout Standard
25728 usepackage[gennarrow]{eurosym}
25731 \begin_layout Standard
25732 The Euro symbol can now be inserted with the command
25739 \begin_inset Index idx
25744 \begin_layout Plain Layout
25746 \begin_inset IndexMacro subentry
25749 \begin_layout Plain Layout
25756 \begin_inset IndexMacro subentry
25759 \begin_layout Plain Layout
25775 \begin_layout Standard
25776 The Euro symbol can directly be inserted with the € key in mathematical
25777 text, without having
25792 can also be inserted in \SpecialChar TeX
25794 The official currency symbol can then be inserted with the command
25801 \begin_inset Index idx
25806 \begin_layout Plain Layout
25808 \begin_inset IndexMacro subentry
25811 \begin_layout Plain Layout
25818 \begin_inset IndexMacro subentry
25821 \begin_layout Plain Layout
25834 , which is also only available in \SpecialChar TeX
25838 \begin_layout Standard
25842 \begin_layout Plain Layout
25852 \begin_inset Note Note
25855 \begin_layout Plain Layout
25856 The following table will only be displayed when the \SpecialChar LaTeX
25869 \begin_layout Standard
25870 An overview about the different Euro symbols:
25873 \begin_layout Standard
25875 \begin_inset Tabular
25876 <lyxtabular version="3" rows="4" columns="3">
25877 <features booktabs="true" tabularvalignment="middle">
25878 <column alignment="center" valignment="top" width="0pt">
25879 <column alignment="center" valignment="top" width="0pt">
25880 <column alignment="center" valignment="top" width="0pt">
25882 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25885 \begin_layout Plain Layout
25889 \begin_layout Plain Layout
25893 cmidrule[0.08em]{2-3}
25903 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25906 \begin_layout Plain Layout
25912 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25915 \begin_layout Plain Layout
25923 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25926 \begin_layout Plain Layout
25932 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25935 \begin_layout Plain Layout
25943 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25946 \begin_layout Plain Layout
25947 \begin_inset Formula $\euro$
25957 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25960 \begin_layout Plain Layout
25966 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25969 \begin_layout Plain Layout
25975 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25978 \begin_layout Plain Layout
25979 \begin_inset Formula $\mbox{€}$
25989 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25992 \begin_layout Plain Layout
25999 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26002 \begin_layout Plain Layout
26010 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26013 \begin_layout Plain Layout
26017 \begin_layout Plain Layout
26037 \begin_inset Note Note
26040 \begin_layout Plain Layout
26047 is used here only for table borders.
26057 manual for details.
26065 \begin_layout Standard
26069 \begin_layout Plain Layout
26079 \begin_inset Note Note
26082 \begin_layout Plain Layout
26083 The following will be displayed when the \SpecialChar LaTeX
26096 \begin_layout Standard
26097 You need to install the \SpecialChar LaTeX
26102 to see the rest of this subsection in the output.
26105 \begin_layout Standard
26109 \begin_layout Plain Layout
26121 \begin_layout Section
26123 \begin_inset CommandInset label
26125 name "sec:Relations"
26130 \begin_inset Index idx
26135 \begin_layout Plain Layout
26142 \begin_inset Index idx
26147 \begin_layout Plain Layout
26149 \begin_inset IndexMacro see
26152 \begin_layout Plain Layout
26166 \begin_layout Standard
26167 All of the following relations can also be inserted via the toolbar button
26171 arg "math-insert \\leq"
26177 \begin_layout Standard
26178 \begin_inset Tabular
26179 <lyxtabular version="3" rows="17" columns="2">
26180 <features booktabs="true" tabularvalignment="middle">
26181 <column alignment="center" valignment="top" width="0pt">
26182 <column alignment="center" valignment="top" width="0pt">
26184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26187 \begin_layout Plain Layout
26193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26196 \begin_layout Plain Layout
26204 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26207 \begin_layout Plain Layout
26213 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26216 \begin_layout Plain Layout
26217 \begin_inset Formula $<$
26227 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26230 \begin_layout Plain Layout
26238 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26241 \begin_layout Plain Layout
26242 \begin_inset Formula $\le$
26252 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26255 \begin_layout Plain Layout
26263 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26266 \begin_layout Plain Layout
26267 \begin_inset Formula $\ll$
26277 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26280 \begin_layout Plain Layout
26288 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26291 \begin_layout Plain Layout
26292 \begin_inset Formula $\prec$
26302 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26305 \begin_layout Plain Layout
26313 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26316 \begin_layout Plain Layout
26317 \begin_inset Formula $\preceq$
26327 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26330 \begin_layout Plain Layout
26338 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26341 \begin_layout Plain Layout
26342 \begin_inset Formula $\subset$
26352 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26355 \begin_layout Plain Layout
26363 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26366 \begin_layout Plain Layout
26367 \begin_inset Formula $\subseteq$
26377 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26380 \begin_layout Plain Layout
26388 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26391 \begin_layout Plain Layout
26392 \begin_inset Formula $\sqsubseteq$
26402 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26405 \begin_layout Plain Layout
26413 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26416 \begin_layout Plain Layout
26417 \begin_inset Formula $\in$
26427 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26430 \begin_layout Plain Layout
26438 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26441 \begin_layout Plain Layout
26442 \begin_inset Formula $\vdash$
26452 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26455 \begin_layout Plain Layout
26463 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26466 \begin_layout Plain Layout
26467 \begin_inset Formula $\smile$
26477 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26480 \begin_layout Plain Layout
26488 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26491 \begin_layout Plain Layout
26492 \begin_inset Formula $\lhd$
26502 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26505 \begin_layout Plain Layout
26513 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26516 \begin_layout Plain Layout
26517 \begin_inset Formula $\unlhd$
26527 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26530 \begin_layout Plain Layout
26538 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26541 \begin_layout Plain Layout
26542 \begin_inset Formula $\gtrless$
26552 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26555 \begin_layout Plain Layout
26563 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26566 \begin_layout Plain Layout
26567 \begin_inset Formula $\mid$
26577 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26580 \begin_layout Plain Layout
26588 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26591 \begin_layout Plain Layout
26592 \begin_inset Formula $\nmid$
26606 \begin_inset space \hfill{}
26610 \begin_inset Tabular
26611 <lyxtabular version="3" rows="17" columns="2">
26612 <features booktabs="true" tabularvalignment="middle">
26613 <column alignment="center" valignment="top" width="0pt">
26614 <column alignment="center" valignment="top" width="0pt">
26616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26619 \begin_layout Plain Layout
26625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26628 \begin_layout Plain Layout
26636 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26639 \begin_layout Plain Layout
26645 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26648 \begin_layout Plain Layout
26649 \begin_inset Formula $=$
26659 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26662 \begin_layout Plain Layout
26670 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26673 \begin_layout Plain Layout
26674 \begin_inset Formula $\not=$
26684 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26687 \begin_layout Plain Layout
26695 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26698 \begin_layout Plain Layout
26699 \begin_inset Formula $\equiv$
26709 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26712 \begin_layout Plain Layout
26720 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26723 \begin_layout Plain Layout
26724 \begin_inset Formula $\sim$
26734 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26737 \begin_layout Plain Layout
26745 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26748 \begin_layout Plain Layout
26749 \begin_inset Formula $\simeq$
26759 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26762 \begin_layout Plain Layout
26770 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26773 \begin_layout Plain Layout
26774 \begin_inset Formula $\approx$
26784 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26787 \begin_layout Plain Layout
26795 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26798 \begin_layout Plain Layout
26799 \begin_inset Formula $\cong$
26809 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26812 \begin_layout Plain Layout
26820 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26823 \begin_layout Plain Layout
26824 \begin_inset Formula $\bowtie$
26834 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26837 \begin_layout Plain Layout
26845 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26848 \begin_layout Plain Layout
26849 \begin_inset Formula $\notin$
26859 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26862 \begin_layout Plain Layout
26870 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26873 \begin_layout Plain Layout
26874 \begin_inset Formula $\perp$
26884 <cell alignment="center" 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
26899 \begin_inset Formula $\propto$
26909 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26912 \begin_layout Plain Layout
26920 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26923 \begin_layout Plain Layout
26924 \begin_inset Formula $\asymp$
26934 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26937 \begin_layout Plain Layout
26945 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26948 \begin_layout Plain Layout
26949 \begin_inset Formula $\doteq$
26959 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26962 \begin_layout Plain Layout
26970 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26973 \begin_layout Plain Layout
26974 \begin_inset Formula $\circeq$
26984 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26987 \begin_layout Plain Layout
26995 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26998 \begin_layout Plain Layout
26999 \begin_inset Formula $\models$
27009 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27012 \begin_layout Plain Layout
27020 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27023 \begin_layout Plain Layout
27024 \begin_inset Formula $\widehat{=}$
27038 \begin_inset space \hfill{}
27042 \begin_inset Tabular
27043 <lyxtabular version="3" rows="17" columns="2">
27044 <features booktabs="true" tabularvalignment="middle">
27045 <column alignment="center" valignment="top" width="0pt">
27046 <column alignment="center" valignment="top" width="0pt">
27048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27051 \begin_layout Plain Layout
27057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27060 \begin_layout Plain Layout
27068 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27071 \begin_layout Plain Layout
27077 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27080 \begin_layout Plain Layout
27081 \begin_inset Formula $>$
27091 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27094 \begin_layout Plain Layout
27102 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27105 \begin_layout Plain Layout
27106 \begin_inset Formula $\ge$
27116 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27119 \begin_layout Plain Layout
27127 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27130 \begin_layout Plain Layout
27131 \begin_inset Formula $\gg$
27141 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27144 \begin_layout Plain Layout
27152 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27155 \begin_layout Plain Layout
27156 \begin_inset Formula $\succ$
27166 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27169 \begin_layout Plain Layout
27177 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27180 \begin_layout Plain Layout
27181 \begin_inset Formula $\succeq$
27191 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27194 \begin_layout Plain Layout
27202 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27205 \begin_layout Plain Layout
27206 \begin_inset Formula $\supset$
27216 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27219 \begin_layout Plain Layout
27227 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27230 \begin_layout Plain Layout
27231 \begin_inset Formula $\supseteq$
27241 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27244 \begin_layout Plain Layout
27252 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27255 \begin_layout Plain Layout
27256 \begin_inset Formula $\sqsupseteq$
27266 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27269 \begin_layout Plain Layout
27277 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27280 \begin_layout Plain Layout
27281 \begin_inset Formula $\ni$
27291 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27294 \begin_layout Plain Layout
27302 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27305 \begin_layout Plain Layout
27306 \begin_inset Formula $\dashv$
27316 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27319 \begin_layout Plain Layout
27327 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27330 \begin_layout Plain Layout
27331 \begin_inset Formula $\frown$
27341 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27344 \begin_layout Plain Layout
27352 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27355 \begin_layout Plain Layout
27356 \begin_inset Formula $\rhd$
27366 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27369 \begin_layout Plain Layout
27377 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27380 \begin_layout Plain Layout
27381 \begin_inset Formula $\unrhd$
27391 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27394 \begin_layout Plain Layout
27402 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27405 \begin_layout Plain Layout
27406 \begin_inset Formula $\lessgtr$
27416 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27419 \begin_layout Plain Layout
27427 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27430 \begin_layout Plain Layout
27431 \begin_inset Formula $\parallel$
27441 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27444 \begin_layout Plain Layout
27452 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27455 \begin_layout Plain Layout
27456 \begin_inset Formula $\nparallel$
27472 \begin_layout Standard
27473 \begin_inset VSpace medskip
27488 are bigger than the equal looking operators
27503 \begin_layout Standard
27505 supports also many special relations.
27506 Use the toolbar button
27509 arg "math-insert \\leqq"
27512 to see a list of these relations.
27515 \begin_layout Standard
27516 Contrary to symbols, relations are always surrounded by space.
27519 \begin_layout Standard
27520 Relations with labels can be created with the command
27527 \begin_inset Index idx
27532 \begin_layout Plain Layout
27534 \begin_inset IndexMacro subentry
27537 \begin_layout Plain Layout
27544 \begin_inset IndexMacro subentry
27547 \begin_layout Plain Layout
27563 \begin_layout Standard
27565 \begin_inset Tabular
27566 <lyxtabular version="3" rows="2" columns="2">
27567 <features booktabs="true" tabularvalignment="middle">
27568 <column alignment="center" valignment="top" width="0pt">
27569 <column alignment="center" valignment="top">
27571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27574 \begin_layout Plain Layout
27580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27583 \begin_layout Plain Layout
27590 <row topspace="1.5mm">
27591 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27594 \begin_layout Plain Layout
27598 \begin_inset space \textvisiblespace{}
27606 \begin_inset space \textvisiblespace{}
27610 \begin_inset Formula $\downarrow$
27616 \begin_inset space \textvisiblespace{}
27620 \begin_inset space \textvisiblespace{}
27628 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27631 \begin_layout Plain Layout
27632 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
27648 \begin_layout Section
27652 \begin_layout Subsection
27653 Predefined Functions
27654 \begin_inset CommandInset label
27656 name "subsec:Predefined-Functions"
27661 \begin_inset Index idx
27666 \begin_layout Plain Layout
27668 \begin_inset IndexMacro subentry
27671 \begin_layout Plain Layout
27685 \begin_layout Standard
27686 In general, variables are set
27690 in mathematical expressions, but not function names, because
27691 \begin_inset Formula $sin$
27694 could be misunderstood as
27695 \begin_inset Formula $s\cdot i\cdot n$
27699 Also predefined functions are separated a bit from the character in front
27701 They are inserted as commands starting with a backslash before their name.
27704 \begin_layout Standard
27706 \begin_inset Tabular
27707 <lyxtabular version="3" rows="2" columns="2">
27708 <features booktabs="true" tabularvalignment="middle">
27709 <column alignment="center" valignment="top" width="0pt">
27710 <column alignment="center" valignment="top" width="0pt">
27712 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
27715 \begin_layout Plain Layout
27721 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
27724 \begin_layout Plain Layout
27732 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27735 \begin_layout Plain Layout
27741 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
27744 \begin_layout Plain Layout
27745 \begin_inset Formula $Asin(x)+B$
27759 \begin_inset space \quad{}
27763 \begin_inset Tabular
27764 <lyxtabular version="3" rows="2" columns="2">
27765 <features booktabs="true" tabularvalignment="middle">
27766 <column alignment="center" valignment="top" width="0pt">
27767 <column alignment="center" valignment="top" width="0pt">
27769 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
27772 \begin_layout Plain Layout
27778 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
27781 \begin_layout Plain Layout
27789 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27792 \begin_layout Plain Layout
27800 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27803 \begin_layout Plain Layout
27804 \begin_inset Formula $A\sin(x)+B$
27820 \begin_layout Standard
27821 The following functions are predefined:
27824 \begin_layout Standard
27825 \begin_inset VSpace -2mm
27831 \begin_layout Standard
27833 \begin_inset Tabular
27834 <lyxtabular version="3" rows="9" columns="4">
27835 <features booktabs="true" tabularvalignment="middle">
27836 <column alignment="center" valignment="top" width="0pt">
27837 <column alignment="center" valignment="top" width="0pt">
27838 <column alignment="center" valignment="top" width="0pt">
27839 <column alignment="center" valignment="top" width="0pt">
27841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27844 \begin_layout Plain Layout
27850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27853 \begin_layout Plain Layout
27859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27862 \begin_layout Plain Layout
27868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27871 \begin_layout Plain Layout
27879 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27882 \begin_layout Plain Layout
27890 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27893 \begin_layout Plain Layout
27901 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27904 \begin_layout Plain Layout
27912 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27915 \begin_layout Plain Layout
27925 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27928 \begin_layout Plain Layout
27936 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27939 \begin_layout Plain Layout
27947 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27950 \begin_layout Plain Layout
27958 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27961 \begin_layout Plain Layout
27971 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27974 \begin_layout Plain Layout
27982 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27985 \begin_layout Plain Layout
27993 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27996 \begin_layout Plain Layout
28004 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28007 \begin_layout Plain Layout
28017 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28020 \begin_layout Plain Layout
28028 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28031 \begin_layout Plain Layout
28039 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28042 \begin_layout Plain Layout
28050 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28053 \begin_layout Plain Layout
28063 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28066 \begin_layout Plain Layout
28074 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28077 \begin_layout Plain Layout
28085 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28088 \begin_layout Plain Layout
28096 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28099 \begin_layout Plain Layout
28109 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28112 \begin_layout Plain Layout
28120 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28123 \begin_layout Plain Layout
28131 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28134 \begin_layout Plain Layout
28142 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28145 \begin_layout Plain Layout
28155 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28158 \begin_layout Plain Layout
28166 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28169 \begin_layout Plain Layout
28177 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28180 \begin_layout Plain Layout
28188 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28191 \begin_layout Plain Layout
28201 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
28204 \begin_layout Plain Layout
28212 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
28215 \begin_layout Plain Layout
28223 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
28226 \begin_layout Plain Layout
28234 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
28237 \begin_layout Plain Layout
28253 \begin_layout Standard
28254 They can also be inserted with the math toolbar button
28257 arg "math-insert \\functions"
28263 \begin_layout Subsection
28264 Self-defined Functions
28265 \begin_inset Index idx
28270 \begin_layout Plain Layout
28272 \begin_inset IndexMacro subentry
28275 \begin_layout Plain Layout
28289 \begin_layout Standard
28290 To use a function that is not predefined, for instance the sign function
28291 sgn(x), there are two possibilities:
28294 \begin_layout Itemize
28295 Define the function by inserting the following line in the \SpecialChar LaTeX
28300 \begin_layout Plain Layout
28305 DeclareMathOperator
28308 \begin_inset CommandInset ref
28310 reference "subsec:Self-defined-Operators"
28320 \begin_inset Newline newline
28324 \begin_inset VSpace -3mm
28328 \begin_inset Newline newline
28335 DeclareMathOperator{
28340 \begin_inset Index idx
28345 \begin_layout Plain Layout
28347 \begin_inset IndexMacro subentry
28350 \begin_layout Plain Layout
28357 \begin_inset IndexMacro subentry
28360 \begin_layout Plain Layout
28361 \begin_inset IndexMacro sortkey
28364 \begin_layout Plain Layout
28374 DeclareMathOperator
28385 \begin_inset Newline newline
28389 \begin_inset VSpace -2mm
28393 \begin_inset Newline newline
28396 Now the newly defined function can be called with the command
28405 \begin_layout Itemize
28406 Write the formula as usual, mark the formula name, in our example the letters
28411 , and change it to mathematical text.
28412 Finally, insert a space between the prefactor and function.
28415 \begin_layout Standard
28416 The result is the same with both methods as with a predefined function
28420 \begin_layout Plain Layout
28421 In \SpecialChar LyX
28422 self-defined functions are displayed red, predefined ones black.
28430 \begin_layout Standard
28432 \begin_inset Tabular
28433 <lyxtabular version="3" rows="3" columns="2">
28434 <features booktabs="true" tabularvalignment="middle">
28435 <column alignment="center" valignment="top" width="0pt">
28436 <column alignment="center" valignment="top" width="0pt">
28438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28441 \begin_layout Plain Layout
28447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
28450 \begin_layout Plain Layout
28458 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28461 \begin_layout Plain Layout
28469 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28472 \begin_layout Plain Layout
28473 \begin_inset Formula $A\sgn(x)+B$
28483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28486 \begin_layout Plain Layout
28490 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
28498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
28501 \begin_layout Plain Layout
28502 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
28518 \begin_layout Standard
28519 The first method is more suitable when the self-defined function will be
28520 used several times.
28523 \begin_layout Subsection
28525 \begin_inset Index idx
28530 \begin_layout Plain Layout
28539 \begin_layout Standard
28540 For limits, in addition to the commands
28547 \begin_inset Index idx
28552 \begin_layout Plain Layout
28554 \begin_inset IndexMacro subentry
28557 \begin_layout Plain Layout
28564 \begin_inset IndexMacro subentry
28567 \begin_layout Plain Layout
28592 the following functions are defined:
28595 \begin_layout Standard
28597 \begin_inset Tabular
28598 <lyxtabular version="3" rows="5" columns="2">
28599 <features booktabs="true" tabularvalignment="middle">
28600 <column alignment="center" valignment="top" width="0pt">
28601 <column alignment="center" valignment="top" width="0pt">
28603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28606 \begin_layout Plain Layout
28612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
28615 \begin_layout Plain Layout
28623 <cell alignment="center" valignment="top" leftline="true" usebox="none">
28626 \begin_layout Plain Layout
28634 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28637 \begin_layout Plain Layout
28638 \begin_inset Formula $\varliminf$
28647 <row topspace="1.5mm">
28648 <cell alignment="center" valignment="top" usebox="none">
28651 \begin_layout Plain Layout
28659 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28662 \begin_layout Plain Layout
28663 \begin_inset Formula $\varlimsup$
28672 <row topspace="1.5mm">
28673 <cell alignment="center" valignment="top" usebox="none">
28676 \begin_layout Plain Layout
28684 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28687 \begin_layout Plain Layout
28688 \begin_inset Formula $\varprojlim$
28697 <row topspace="1.5mm" bottomspace="1mm">
28698 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
28701 \begin_layout Plain Layout
28709 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
28712 \begin_layout Plain Layout
28713 \begin_inset Formula $\varinjlim$
28729 \begin_layout Standard
28730 \begin_inset VSpace medskip
28733 The limit is created by inserting a subscript.
28734 It is set right beside the function in an inline formula:
28737 \begin_layout Standard
28739 \begin_inset Tabular
28740 <lyxtabular version="3" rows="2" columns="2">
28741 <features booktabs="true" tabularvalignment="middle">
28742 <column alignment="center" valignment="top" width="0pt">
28743 <column alignment="center" valignment="top" width="0pt">
28745 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
28748 \begin_layout Plain Layout
28754 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
28757 \begin_layout Plain Layout
28765 <cell alignment="center" valignment="top" usebox="none">
28768 \begin_layout Plain Layout
28774 \begin_inset space \textvisiblespace{}
28778 \begin_inset space \textvisiblespace{}
28786 <cell alignment="center" valignment="top" usebox="none">
28789 \begin_layout Plain Layout
28790 \begin_inset Formula $\lim_{x\to A}x=B$
28806 \begin_layout Standard
28807 In a displayed formula the limit is set below the formula, as usual:
28808 \begin_inset Formula
28818 \begin_layout Standard
28819 \begin_inset VSpace medskip
28825 \begin_layout Standard
28826 How to adjust the typesetting of the limits see
28827 \begin_inset CommandInset ref
28829 reference "subsec:Operator-Limits"
28836 \begin_layout Subsection
28838 \begin_inset Index idx
28843 \begin_layout Plain Layout
28845 \begin_inset IndexMacro subentry
28848 \begin_layout Plain Layout
28862 \begin_layout Standard
28863 The modulo-function is special, because it exists in four variants.
28864 The variants in a displayed formula are:
28865 \begin_inset Formula
28867 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
28868 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
28869 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
28870 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
28871 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
28879 \begin_layout Standard
28880 In an inline formula less space is set before the function names for all
28882 By default the modulo-functions take only the first character following
28883 the command into account.
28884 To use more than one character, put them in \SpecialChar TeX
28886 \begin_inset Formula
28888 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
28889 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
28890 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
28898 \begin_layout Section
28900 \begin_inset Index idx
28905 \begin_layout Plain Layout
28914 \begin_layout Standard
28915 The characters ^ and _ would normally create a superscript and subscript,
28917 To get these characters you have to insert them with a leading
28922 \begin_layout Standard
28925 \begin_inset Tabular
28926 <lyxtabular version="3" rows="3" columns="2">
28927 <features booktabs="true" tabularvalignment="middle">
28928 <column alignment="left" valignment="top" width="0pt">
28929 <column alignment="block" valignment="top">
28931 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
28934 \begin_layout Plain Layout
28940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
28943 \begin_layout Plain Layout
28951 <cell alignment="left" valignment="top" leftline="true" usebox="none">
28954 \begin_layout Plain Layout
28958 \begin_inset space \textvisiblespace{}
28966 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
28969 \begin_layout Plain Layout
28970 \begin_inset Formula $\mathcircumflex$
28980 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
28983 \begin_layout Plain Layout
28991 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
28994 \begin_layout Plain Layout
28995 \begin_inset Formula $\_$
29011 \begin_layout Subsection
29012 Special Characters in Mathematical Text
29015 \begin_layout Standard
29016 The following commands can only be used in mathematical text or in \SpecialChar TeX
29020 \begin_layout Standard
29021 \begin_inset space \hfill{}
29025 \begin_inset Tabular
29026 <lyxtabular version="3" rows="8" columns="2">
29027 <features booktabs="true" tabularvalignment="middle">
29028 <column alignment="left" valignment="top" width="0pt">
29029 <column alignment="block" valignment="top">
29031 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
29034 \begin_layout Plain Layout
29040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
29043 \begin_layout Plain Layout
29051 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29054 \begin_layout Plain Layout
29062 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29065 \begin_layout Plain Layout
29066 \begin_inset Formula $\textrm{œ}$
29076 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29079 \begin_layout Plain Layout
29087 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29090 \begin_layout Plain Layout
29091 \begin_inset Formula $\textrm{Œ}$
29101 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29104 \begin_layout Plain Layout
29112 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29115 \begin_layout Plain Layout
29116 \begin_inset Formula $\textrm{æ}$
29126 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29129 \begin_layout Plain Layout
29137 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29140 \begin_layout Plain Layout
29141 \begin_inset Formula $\textrm{Æ}$
29151 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29154 \begin_layout Plain Layout
29162 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29165 \begin_layout Plain Layout
29166 \begin_inset Formula $\textrm{å}$
29176 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29179 \begin_layout Plain Layout
29187 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29190 \begin_layout Plain Layout
29191 \begin_inset Formula $\textrm{Å}$
29201 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
29204 \begin_layout Plain Layout
29212 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
29215 \begin_layout Plain Layout
29216 \begin_inset Formula $\textrm{ı}$
29230 \begin_inset space \hfill{}
29234 \begin_inset Tabular
29235 <lyxtabular version="3" rows="8" columns="2">
29236 <features booktabs="true" tabularvalignment="middle">
29237 <column alignment="left" valignment="top" width="0pt">
29238 <column alignment="center" valignment="top">
29240 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
29243 \begin_layout Plain Layout
29245 \begin_inset Note Note
29248 \begin_layout Plain Layout
29250 \begin_inset space \thinspace{}
29253 mm is used for separation, because otherwise the output will be ¡ and ¿
29264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
29267 \begin_layout Plain Layout
29275 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29278 \begin_layout Plain Layout
29286 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29289 \begin_layout Plain Layout
29290 \begin_inset Formula $\textrm{ø}$
29300 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29303 \begin_layout Plain Layout
29311 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29314 \begin_layout Plain Layout
29315 \begin_inset Formula $\textrm{Ø}$
29325 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29328 \begin_layout Plain Layout
29336 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29339 \begin_layout Plain Layout
29340 \begin_inset Formula $\textrm{ł}$
29350 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29353 \begin_layout Plain Layout
29361 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29364 \begin_layout Plain Layout
29365 \begin_inset Formula $\textrm{Ł}$
29375 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29378 \begin_layout Plain Layout
29380 \begin_inset space \hspace{}
29385 \begin_inset space \textvisiblespace{}
29393 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29396 \begin_layout Plain Layout
29397 \begin_inset Formula $\textrm{!`}$
29407 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29410 \begin_layout Plain Layout
29412 \begin_inset space \hspace{}
29417 \begin_inset space \textvisiblespace{}
29425 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29428 \begin_layout Plain Layout
29429 \begin_inset Formula $\textrm{?`}$
29439 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
29442 \begin_layout Plain Layout
29450 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
29453 \begin_layout Plain Layout
29454 \begin_inset Formula $\textrm{ȷ}$
29468 \begin_inset space \hfill{}
29474 \begin_layout Standard
29476 \begin_inset Formula $\textrm{Å}$
29480 \begin_inset Formula $\textrm{Ø}$
29483 can also be inserted via the math toolbar button
29486 arg "math-insert \\digamma"
29492 \begin_layout Standard
29496 \begin_inset space \hspace{}
29505 \begin_inset space \hspace{}
29511 are exceptions because they can be inserted in \SpecialChar LyX
29515 \begin_layout Subsection
29517 \begin_inset CommandInset label
29519 name "subsec:Accents-in-Text"
29524 \begin_inset Index idx
29529 \begin_layout Plain Layout
29531 \begin_inset IndexMacro subentry
29534 \begin_layout Plain Layout
29548 \begin_layout Standard
29549 Any letter can be accented with the following commands.
29550 The commands must be inserted in \SpecialChar TeX
29554 \begin_layout Standard
29555 \begin_inset space \hfill{}
29559 \begin_inset Tabular
29560 <lyxtabular version="3" rows="8" columns="2">
29561 <features booktabs="true" tabularvalignment="middle">
29562 <column alignment="left" valignment="top" width="0pt">
29563 <column alignment="block" valignment="top">
29565 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
29568 \begin_layout Plain Layout
29574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
29577 \begin_layout Plain Layout
29585 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29588 \begin_layout Plain Layout
29592 \begin_inset Quotes grd
29600 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29603 \begin_layout Plain Layout
29607 \begin_layout Plain Layout
29623 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29626 \begin_layout Plain Layout
29634 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29637 \begin_layout Plain Layout
29641 \begin_layout Plain Layout
29657 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29660 \begin_layout Plain Layout
29664 \begin_inset space \textvisiblespace{}
29672 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29675 \begin_layout Plain Layout
29679 \begin_layout Plain Layout
29695 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29698 \begin_layout Plain Layout
29706 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29709 \begin_layout Plain Layout
29713 \begin_layout Plain Layout
29729 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29732 \begin_layout Plain Layout
29736 \begin_inset space \textvisiblespace{}
29744 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29747 \begin_layout Plain Layout
29751 \begin_layout Plain Layout
29767 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29770 \begin_layout Plain Layout
29774 \begin_inset space \textvisiblespace{}
29782 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29785 \begin_layout Plain Layout
29789 \begin_layout Plain Layout
29805 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
29808 \begin_layout Plain Layout
29812 \begin_inset space \textvisiblespace{}
29820 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
29823 \begin_layout Plain Layout
29827 \begin_layout Plain Layout
29847 \begin_inset space \hfill{}
29851 \begin_inset Tabular
29852 <lyxtabular version="3" rows="8" columns="2">
29853 <features booktabs="true" tabularvalignment="middle">
29854 <column alignment="left" valignment="top" width="0pt">
29855 <column alignment="center" valignment="top">
29857 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
29860 \begin_layout Plain Layout
29866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
29869 \begin_layout Plain Layout
29877 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29880 \begin_layout Plain Layout
29884 \begin_inset space \textvisiblespace{}
29892 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29895 \begin_layout Plain Layout
29899 \begin_layout Plain Layout
29915 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29918 \begin_layout Plain Layout
29926 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29929 \begin_layout Plain Layout
29933 \begin_layout Plain Layout
29949 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29952 \begin_layout Plain Layout
29956 \begin_inset Index idx
29961 \begin_layout Plain Layout
29972 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
29975 \begin_layout Plain Layout
29979 \begin_layout Plain Layout
29995 <cell alignment="left" valignment="top" leftline="true" usebox="none">
29998 \begin_layout Plain Layout
30006 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30009 \begin_layout Plain Layout
30013 \begin_layout Plain Layout
30029 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30032 \begin_layout Plain Layout
30036 \begin_inset space \textvisiblespace{}
30044 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30047 \begin_layout Plain Layout
30051 \begin_layout Plain Layout
30067 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30070 \begin_layout Plain Layout
30074 \begin_inset space \textvisiblespace{}
30082 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30085 \begin_layout Plain Layout
30089 \begin_layout Plain Layout
30105 <cell alignment="left" valignment="top" leftline="true" usebox="none">
30108 \begin_layout Plain Layout
30112 \begin_inset space \textvisiblespace{}
30120 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30123 \begin_layout Plain Layout
30127 \begin_layout Plain Layout
30147 \begin_inset space \hfill{}
30153 \begin_layout Standard
30154 \begin_inset VSpace medskip
30163 also two different characters can be accented.
30169 \begin_inset space \textvisiblespace{}
30178 \begin_layout Plain Layout
30190 \begin_layout Standard
30203 can in combination with vowels be directly inserted with the keyboard without
30204 using \SpecialChar TeX
30206 The same applies for the tilde
30210 \begin_layout Plain Layout
30211 This only applies for keyboards where the tilde is defined as accent.
30220 in combination with
30235 \begin_layout Standard
30278 and accents that are inserted directly with the keyboard are also available
30279 in mathematical text.
30280 For the other accents there are special math commands used in formulas,
30282 \begin_inset CommandInset ref
30284 reference "subsec:Accents-for-one"
30291 \begin_layout Standard
30292 \begin_inset VSpace bigskip
30302 \begin_inset Index idx
30307 \begin_layout Plain Layout
30309 \begin_inset IndexMacro subentry
30312 \begin_layout Plain Layout
30319 \begin_inset IndexMacro subentry
30322 \begin_layout Plain Layout
30335 any number or letter can be set into a circle, quasi accented with a circle,
30336 similar to the copyright symbol.
30339 \begin_layout Standard
30341 \begin_inset Tabular
30342 <lyxtabular version="3" rows="3" columns="2">
30343 <features booktabs="true" tabularvalignment="middle">
30344 <column alignment="center" valignment="top" width="0pt">
30345 <column alignment="center" valignment="top">
30347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30350 \begin_layout Plain Layout
30356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30359 \begin_layout Plain Layout
30367 <cell alignment="center" valignment="top" leftline="true" usebox="none">
30370 \begin_layout Plain Layout
30378 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
30381 \begin_layout Plain Layout
30385 \begin_layout Plain Layout
30400 <row topspace="1mm">
30401 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
30404 \begin_layout Plain Layout
30415 raisebox{-1.5pt}{W}}
30420 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
30423 \begin_layout Plain Layout
30427 \begin_layout Plain Layout
30457 \begin_layout Standard
30458 One has to take care that the character fits into the circle.
30469 \begin_layout Plain Layout
30471 \begin_inset CommandInset ref
30473 reference "subsec:Font-Sizes"
30482 specifies the size of the circle.
30493 \begin_layout Plain Layout
30495 \begin_inset CommandInset ref
30497 reference "subsec:Boxes-without-Frame"
30506 the character can be centered.
30509 \begin_layout Subsection
30511 \begin_inset Index idx
30516 \begin_layout Plain Layout
30525 \begin_layout Standard
30526 Old-style figures (also known as old-style numerals) are created with the
30534 \begin_inset Index idx
30539 \begin_layout Plain Layout
30541 \begin_inset IndexMacro subentry
30544 \begin_layout Plain Layout
30551 \begin_inset IndexMacro subentry
30554 \begin_layout Plain Layout
30568 The command can be used in formulas and in \SpecialChar TeX
30570 The command scheme is:
30573 \begin_layout Standard
30578 oldstylenums{number}
30581 \begin_layout Standard
30586 oldstylenums{0123456789}
30589 \begin_inset Formula $\oldstylenums{0123456789}$
30595 \begin_layout Section
30597 \begin_inset CommandInset label
30599 name "sec:Formula-Styles"
30604 \begin_inset Index idx
30609 \begin_layout Plain Layout
30611 \begin_inset IndexMacro subentry
30614 \begin_layout Plain Layout
30628 \begin_layout Itemize
30629 There are two different alignment styles:
30633 \begin_layout Description
30634 Centered is the predefined standard.
30637 \begin_layout Description
30638 Indented can be set using the menu
30640 Document\SpecialChar menuseparator
30646 \begin_inset space ~
30652 \begin_layout Standard
30657 is used, the indentation can be adjusted.
30658 The default value depends on the document class.
30662 \begin_layout Itemize
30663 Two different numbering styles are available in the menu
30665 Document\SpecialChar menuseparator
30671 \begin_inset space ~
30680 \begin_layout Description
30681 Right is in most cases the default.
30684 \begin_layout Description
30689 \begin_layout Standard
30690 The chosen styles are used for all displayed formulas of the document.
30691 When both, centered and indented formulas should be created in a document,
30697 The indented formulas are then set in a flalign environment, see
30698 \begin_inset CommandInset ref
30700 reference "subsec:Flalign-Environment"
30707 \begin_layout Section
30709 \begin_inset CommandInset label
30711 name "sec:Multiline-Formulas"
30716 \begin_inset Index idx
30721 \begin_layout Plain Layout
30723 \begin_inset IndexMacro subentry
30726 \begin_layout Plain Layout
30740 \begin_layout Subsection
30744 \begin_layout Standard
30745 In \SpecialChar LyX
30746 , multiline formulas are created by pressing
30749 arg "newline-insert newline"
30753 This creates either an
30757 that is described in
30758 \begin_inset CommandInset ref
30760 reference "subsec:Standard-align-Environment"
30764 or, when automatically loading of the package
30768 is disabled in the document settings, an
30770 eqnarray environment
30772 that is described in
30773 \begin_inset CommandInset ref
30775 reference "subsec:Eqnarray-Environment"
30780 The align environment is recommended as it provides a typographically correct
30781 output in all cases.
30784 \begin_layout Standard
30785 There are other multiline formula environments that can be created via the
30788 Insert\SpecialChar menuseparator
30792 These environments are described in the following sections.
30795 \begin_layout Standard
30796 In all multiline formula environments a new line is created by pressing
30800 arg "newline-insert newline"
30804 To add or delete lines, use the math toolbar buttons
30807 arg "tabular-feature append-row"
30813 arg "tabular-feature delete-row"
30816 respectively, or the menu option
30818 Edit\SpecialChar menuseparator
30824 \begin_layout Subsubsection
30826 \begin_inset CommandInset label
30828 name "subsec:Line-Separation"
30833 \begin_inset Index idx
30838 \begin_layout Plain Layout
30840 \begin_inset IndexMacro subentry
30843 \begin_layout Plain Layout
30850 \begin_inset IndexMacro subentry
30853 \begin_layout Plain Layout
30867 \begin_layout Standard
30868 Sometimes there is not enough space in multiline formulas between the lines:
30869 \begin_inset Formula
30871 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}\\
30872 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
30880 \begin_layout Standard
30881 In \SpecialChar LaTeX
30882 additional line space is specified as an optional argument of the new
30884 This is not yet possible in \SpecialChar LyX
30889 \begin_layout Plain Layout
30891 \begin_inset CommandInset href
30893 name "LyX-bug #1505"
30894 target "https://www.lyx.org/trac/ticket/1505"
30904 , therefore the whole formula must be inserted in \SpecialChar TeX
30906 To add in our example space, the command
30914 is inserted at the end of the first line.
30919 \begin_layout Plain Layout
30926 \begin_layout Plain Layout
30928 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
30931 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
30938 \begin_layout Plain Layout
30942 left(B^{2}+x_{0}^{2}
30950 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
30955 \begin_layout Plain Layout
30967 \begin_layout Standard
30968 \begin_inset VSpace bigskip
30971 To set the line separation for all lines in a formula, the length of
30978 \begin_inset Index idx
30983 \begin_layout Plain Layout
30985 \begin_inset IndexMacro subentry
30988 \begin_layout Plain Layout
30995 \begin_inset IndexMacro subentry
30998 \begin_layout Plain Layout
31013 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
31024 \begin_inset space \thinspace{}
31029 \begin_inset space \thinspace{}
31032 mm of additional line separation as in the previous example, the command
31035 \begin_layout Standard
31045 \begin_layout Standard
31046 is inserted in \SpecialChar TeX
31047 mode before the formula.
31048 This requires that the \SpecialChar LaTeX
31057 \begin_layout Plain Layout
31062 is part of every \SpecialChar LaTeX
31063 standard installation.
31069 \begin_inset Index idx
31074 \begin_layout Plain Layout
31076 \begin_inset IndexMacro subentry
31079 \begin_layout Plain Layout
31090 was loaded in \SpecialChar LaTeX
31091 -preamble with the line
31094 \begin_layout Standard
31102 \begin_layout Standard
31107 \begin_layout Plain Layout
31119 \begin_inset Formula
31121 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}\\
31122 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
31130 \begin_layout Standard
31134 \begin_layout Plain Layout
31151 to its original value,
31157 is set to the value 3
31158 \begin_inset space \thinspace{}
31164 \begin_layout Subsubsection
31166 \begin_inset CommandInset label
31168 name "subsec:Column-Separation"
31173 \begin_inset Index idx
31178 \begin_layout Plain Layout
31180 \begin_inset IndexMacro subentry
31183 \begin_layout Plain Layout
31190 \begin_inset IndexMacro subentry
31193 \begin_layout Plain Layout
31207 \begin_layout Standard
31208 Multiline formulas form a matrix.
31209 A formula in the eqnarray environment for example is a matrix with three
31211 By changing the column separation in this environment, the space beside
31212 the relation sign can be changed.
31215 \begin_layout Standard
31216 The column separation is specified with the length
31223 \begin_inset Index idx
31228 \begin_layout Plain Layout
31230 \begin_inset IndexMacro subentry
31233 \begin_layout Plain Layout
31240 \begin_inset IndexMacro subentry
31243 \begin_layout Plain Layout
31256 according to the formula: column separation = 2
31257 \begin_inset space \thinspace{}
31265 \change_deleted 5863208 1612730022
31269 \begin_inset Note Note
31272 \begin_layout Plain Layout
31274 \change_inserted 232239728 1611406079
31275 How does units play into this? (cm/in/pt) Is the 2 unitless and the result
31276 takes on the units of the input value?
31286 \begin_inset Newline newline
31292 \begin_layout Standard
31302 \begin_layout Standard
31303 inserted in \SpecialChar TeX
31304 mode, sets all following formula column separations to 2
31305 \begin_inset space \thinspace{}
31309 To return to the predefined distance,
31316 \begin_inset space \thinspace{}
31322 \begin_layout Standard
31324 \begin_inset space \thinspace{}
31327 cm column separation:
31331 \begin_layout Plain Layout
31343 \begin_inset Formula
31351 A formula with the predefined column separation for matrices of 10
31352 \begin_inset space \thinspace{}
31359 \begin_layout Plain Layout
31371 \begin_inset Formula
31382 \begin_layout Standard
31383 \begin_inset Newpage newpage
31389 \begin_layout Subsubsection
31391 \begin_inset Index idx
31396 \begin_layout Plain Layout
31398 \begin_inset IndexMacro subentry
31401 \begin_layout Plain Layout
31415 \begin_layout Standard
31416 Long formulas can be typeset using these methods:
31419 \begin_layout Itemize
31420 If one side of an equation is much shorter than the line width, this is
31421 chosen for the left side and the right side is typeset over two lines:
31422 \begin_inset Formula
31424 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 \\
31425 & & -\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}
31430 The minus sign at the beginning of the second line does normally not appear
31431 as an operator because it is the first character of the line.
31432 Thus it would not be surrounded by space and could not be distinguished
31433 from the fraction bar.
31435 \begin_inset space \thinspace{}
31438 pt space was inserted behind the minus sign with the command
31448 \begin_layout Plain Layout
31456 \begin_inset CommandInset ref
31458 reference "subsec:Variable-Space"
31468 \begin_inset Index idx
31473 \begin_layout Plain Layout
31475 \begin_inset IndexMacro subentry
31478 \begin_layout Plain Layout
31485 \begin_inset IndexMacro subentry
31488 \begin_layout Plain Layout
31504 \begin_layout Itemize
31505 When both sides of the equation are long, the command
31512 \begin_inset Index idx
31517 \begin_layout Plain Layout
31519 \begin_inset IndexMacro subentry
31522 \begin_layout Plain Layout
31529 \begin_inset IndexMacro subentry
31532 \begin_layout Plain Layout
31546 It is inserted in the first column of the first line and causes all further
31547 insertions to overwrite the following columns:
31548 \begin_inset Formula
31550 \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 \\
31551 & & -\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 \\
31552 & & =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}
31557 After the insertion of
31563 , the cursor is in a purple box that is shifted a bit to the left from the
31565 The formula is inserted there.
31566 \begin_inset Newline newline
31569 The content of additional lines is inserted in the second or another formula
31571 The greater the insertion column number , the larger the indentation.
31572 \begin_inset VSpace medskip
31576 \begin_inset Newline newline
31580 \begin_inset Note Greyedout
31583 \begin_layout Plain Layout
31584 Note the following when using
31593 \begin_layout Itemize
31594 The formula doesn't use the full page width.
31596 \begin_inset space \thinspace{}
31600 \begin_inset space \space{}
31604 \begin_inset Formula $-B^{2}$
31607 is added to the first line in the above example, it would have been outside
31609 To better use the width, negative space can be inserted at the beginning
31613 \begin_layout Itemize
31614 Due to a bug in \SpecialChar LyX
31615 the cursor cannot be set with the mouse in the first line.
31619 \begin_layout Plain Layout
31620 \begin_inset CommandInset href
31622 name "LyX-bug #1429"
31623 target "https://www.lyx.org/trac/ticket/1429"
31633 One can only set the cursor at the beginning of the line and move it with
31642 \begin_layout Itemize
31643 Other methods to set long formulas are offered by the environments described
31645 \begin_inset CommandInset ref
31647 reference "subsec:Multline-Environment"
31652 \begin_inset CommandInset ref
31654 reference "subsec:Multiline-Formula-Parts"
31661 \begin_layout Subsubsection
31662 Multiline Fractions
31663 \begin_inset CommandInset label
31665 name "subsec:Multiline-Fractions"
31670 \begin_inset Index idx
31675 \begin_layout Plain Layout
31677 \begin_inset IndexMacro subentry
31680 \begin_layout Plain Layout
31694 \begin_layout Standard
31695 There are cases where the denominator and/or the numerator of a fraction
31696 is so long that the fraction does not fit on one line.
31697 It is then necessary to add a line break within the fraction.
31698 This can be done using the command
31705 \begin_inset Index idx
31710 \begin_layout Plain Layout
31712 \begin_inset IndexMacro subentry
31715 \begin_layout Plain Layout
31722 \begin_inset IndexMacro subentry
31725 \begin_layout Plain Layout
31739 To activate it, go to the document settings under
31742 \begin_inset space ~
31752 \begin_inset Index idx
31757 \begin_layout Plain Layout
31759 \begin_inset IndexMacro subentry
31762 \begin_layout Plain Layout
31773 and set its option to
31776 \begin_inset space ~
31791 \begin_layout Standard
31796 splitfrac{first line}{second line}
31799 \begin_layout Standard
31800 and is used for either the denominator or numerator:
31803 \begin_layout Standard
31804 \begin_inset Formula
31806 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}
31811 The command for the first numerator above is:
31814 \begin_layout Standard
31819 splitfrac{xy+xy+xy+xy+xy
31820 \begin_inset space \textvisiblespace{}
31828 \begin_layout Subsubsection
31830 \begin_inset CommandInset label
31832 name "subsec:Multiline-Brackets"
31837 \begin_inset Index idx
31842 \begin_layout Plain Layout
31844 \begin_inset IndexMacro subentry
31847 \begin_layout Plain Layout
31848 for multiline expressions
31861 \begin_layout Standard
31862 For brackets spanning multiple lines the following problem occurs:
31863 \begin_inset Formula
31865 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
31866 & & \left.\cdots+B-D\right]
31874 \begin_layout Standard
31875 The closing bracket is smaller than the opening bracket because brackets
31876 with variable size may not span multiple lines.
31879 \begin_layout Standard
31880 To set the bracket size for the second line correctly, the first line is
31888 \begin_inset Index idx
31893 \begin_layout Plain Layout
31895 \begin_inset IndexMacro subentry
31898 \begin_layout Plain Layout
31905 \begin_inset IndexMacro subentry
31908 \begin_layout Plain Layout
31921 and the second line with
31929 \begin_layout Plain Layout
31943 \begin_inset CommandInset ref
31945 reference "subsec:Automatic-Bracket-Size"
31957 \begin_inset Index idx
31962 \begin_layout Plain Layout
31964 \begin_inset IndexMacro subentry
31967 \begin_layout Plain Layout
31974 \begin_inset IndexMacro subentry
31977 \begin_layout Plain Layout
32005 \begin_inset space \textvisiblespace{}
32015 \begin_inset space \textvisiblespace{}
32025 \begin_inset space \textvisiblespace{}
32031 \begin_inset Formula $\downarrow$
32037 \begin_inset Index idx
32042 \begin_layout Plain Layout
32044 \begin_inset IndexMacro subentry
32047 \begin_layout Plain Layout
32054 \begin_inset IndexMacro subentry
32057 \begin_layout Plain Layout
32070 is inserted, because the multiplication operator with its limits is the
32071 largest symbol in the first line and this should be the size for the bracket
32072 in the second line.
32075 \begin_layout Standard
32076 The result is this:
32077 \begin_inset Formula
32079 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
32080 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
32088 \begin_layout Subsection
32092 \begin_layout Standard
32093 Align environments can be used for every kind of multiline formulas.
32094 They are especially useful to set several formulas side by side.
32097 \begin_layout Standard
32098 Align environments consist of columns.
32099 The odd columns are right aligned, the even ones left aligned.
32100 Every line in an Align environment can be numbered.
32103 \begin_layout Standard
32104 Align environments are created via the menu
32106 Insert\SpecialChar menuseparator
32112 Edit\SpecialChar menuseparator
32113 Math\SpecialChar menuseparator
32114 Change Formula Type
32116 pre-existing formulas can be converted to Align environments.
32119 \begin_layout Standard
32120 To add or delete columns, use the math toolbar buttons
32123 arg "tabular-feature append-column"
32129 arg "tabular-feature delete-column"
32132 respectively, or the menu option
32134 Edit\SpecialChar menuseparator
32140 \begin_layout Subsubsection
32141 Standard Align Environment
32142 \begin_inset CommandInset label
32144 name "subsec:Standard-align-Environment"
32149 \begin_inset Index idx
32154 \begin_layout Plain Layout
32156 \begin_inset IndexMacro subentry
32159 \begin_layout Plain Layout
32166 \begin_inset IndexMacro subentry
32169 \begin_layout Plain Layout
32183 \begin_layout Standard
32184 This align environment is created by pressing
32187 arg "newline-insert newline"
32190 in a formula or by the menu
32192 Insert\SpecialChar menuseparator
32193 Math\SpecialChar menuseparator
32194 AMS align Environment
32199 \begin_layout Standard
32200 An example for two formulas set side by side, that are created with a four
32201 column align environment:
32202 \begin_inset Formula
32204 A & =\sin(B) & C & =D\\
32205 C & \ne A & B & \ne D
32210 As it can be seen, the formulas in this environment are placed so as if
32219 \begin_layout Plain Layout
32227 \begin_inset CommandInset ref
32229 reference "subsec:Variable-Space"
32240 before the first and after every even column.
32241 When the formula style
32247 \begin_layout Plain Layout
32248 For formula styles see
32249 \begin_inset CommandInset ref
32251 reference "sec:Formula-Styles"
32262 is used, the formula is set without the
32268 before the first column.
32271 \begin_layout Subsubsection
32272 Alignat Environment
32273 \begin_inset Index idx
32278 \begin_layout Plain Layout
32280 \begin_inset IndexMacro subentry
32283 \begin_layout Plain Layout
32290 \begin_inset IndexMacro subentry
32293 \begin_layout Plain Layout
32294 alignat environment
32307 \begin_layout Standard
32308 The alignat environment has no predefined column separation.
32309 It can be inserted manually with the spaces that are described in
32310 \begin_inset CommandInset ref
32312 reference "subsec:Space"
32319 \begin_layout Standard
32320 The above example is shown in the alignat environment where 1
32321 \begin_inset space \thinspace{}
32324 cm space was inserted at the beginning of the second formula:
32325 \begin_inset Formula
32326 \begin{alignat*}{2}
32327 A & =\sin(B) & \hspace{1cm}C & =D\\
32328 C & \ne A & B & \ne D
32333 Because the column separation can be set separately for every column, this
32334 environment is especially suitable to set three or more formulas side by
32338 \begin_layout Subsubsection
32339 Flalign Environment
32340 \begin_inset CommandInset label
32342 name "subsec:Flalign-Environment"
32347 \begin_inset Index idx
32352 \begin_layout Plain Layout
32354 \begin_inset IndexMacro subentry
32357 \begin_layout Plain Layout
32364 \begin_inset IndexMacro subentry
32367 \begin_layout Plain Layout
32368 flalign environment
32381 \begin_layout Standard
32382 In this environment the first column is always set to the left as much as
32383 possible and the last one to the right.
32385 \begin_inset Formula
32387 A & =1 & B & =2 & C & =3\\
32388 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
32396 \begin_layout Standard
32397 By creating a flalign environment with an odd number of columns where an
32398 empty \SpecialChar TeX
32399 brace is inserted in the last column, several formulas in a document
32400 can be set to the left, although the formula style
32405 As example the indented formula
32406 \begin_inset CommandInset ref
32408 reference "eq:VolInt"
32413 \begin_inset Formula
32415 \hspace{30pt}\iiint_{V}X\,\mathrm{d}V & =U & {}
32420 The first two columns contain the formula.
32421 To indent it as with the formula style
32426 \begin_inset space \thinspace{}
32429 pt space was inserted at the beginning of the first column.
32432 \begin_layout Subsection
32433 Eqnarray Environment
32434 \begin_inset CommandInset label
32436 name "subsec:Eqnarray-Environment"
32441 \begin_inset Index idx
32446 \begin_layout Plain Layout
32448 \begin_inset IndexMacro subentry
32451 \begin_layout Plain Layout
32458 \begin_inset IndexMacro subentry
32461 \begin_layout Plain Layout
32462 eqnarray environment
32475 \begin_layout Standard
32476 When this environment is created, three blue boxes appear.
32477 The content of the first box is right aligned, the content of the last
32479 The content of the middle box appears centered and a bit smaller because
32480 it is intended for relational characters only.
32481 \begin_inset Formula
32483 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
32493 \begin_layout Subsection
32495 \begin_inset Index idx
32500 \begin_layout Plain Layout
32502 \begin_inset IndexMacro subentry
32505 \begin_layout Plain Layout
32512 \begin_inset IndexMacro subentry
32515 \begin_layout Plain Layout
32529 \begin_layout Standard
32530 This environment consists of one centered column.
32531 Every line can be numbered.
32532 \begin_inset Formula
32543 \begin_layout Subsection
32544 Multline Environment
32545 \begin_inset CommandInset label
32547 name "subsec:Multline-Environment"
32552 \begin_inset Index idx
32557 \begin_layout Plain Layout
32559 \begin_inset IndexMacro subentry
32562 \begin_layout Plain Layout
32569 \begin_inset IndexMacro subentry
32572 \begin_layout Plain Layout
32573 multline environment
32586 \begin_layout Standard
32587 The multline environment consists, like the gather environment, of one column.
32588 But the first line is left aligned, the last one right aligned.
32589 All other lines are centered.
32590 Therefore this environment is suitable for long formulas.
32591 Using example formula
32592 \begin_inset CommandInset ref
32594 reference "eq:lefteqn"
32598 in the multline environment:
32599 \begin_inset Formula
32601 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}\\
32602 -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}\\
32603 =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}}
32611 \begin_layout Standard
32612 In the output, only the last line of a multline environment appears numbered
32613 when the document numbering is on the right .
32614 If the document numbering is on the left then only the first line will
32619 \begin_layout Plain Layout
32620 For numbering styles see
32621 \begin_inset CommandInset ref
32623 reference "sec:Formula-Styles"
32635 \begin_layout Standard
32643 \begin_inset Index idx
32648 \begin_layout Plain Layout
32650 \begin_inset IndexMacro subentry
32653 \begin_layout Plain Layout
32660 \begin_inset IndexMacro subentry
32663 \begin_layout Plain Layout
32683 \begin_inset Index idx
32688 \begin_layout Plain Layout
32690 \begin_inset IndexMacro subentry
32693 \begin_layout Plain Layout
32700 \begin_inset IndexMacro subentry
32703 \begin_layout Plain Layout
32716 a centered line can be right or left aligned, respectively.
32717 The commands are used as follows:
32720 \begin_layout Standard
32725 shoveright{line content}
32731 shoveleft{line content}
32734 \begin_layout Standard
32735 \begin_inset VSpace medskip
32745 \begin_inset Index idx
32750 \begin_layout Plain Layout
32752 \begin_inset IndexMacro subentry
32755 \begin_layout Plain Layout
32762 \begin_inset IndexMacro subentry
32765 \begin_layout Plain Layout
32778 specifies the distance of the first line from the left page margin.
32779 Predefined is the length 0
32780 \begin_inset space \thinspace{}
32786 \begin_layout Standard
32787 As example the above formula where the command
32790 \begin_layout Standard
32800 \begin_layout Standard
32801 was inserted in \SpecialChar TeX
32806 \begin_layout Plain Layout
32818 \begin_inset Formula
32820 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}\\
32821 \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}}\\
32822 =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}}
32831 \begin_layout Plain Layout
32842 The second line was left aligned using
32851 \begin_layout Subsection
32852 Multiline Formula Parts
32853 \begin_inset CommandInset label
32855 name "subsec:Multiline-Formula-Parts"
32860 \begin_inset Index idx
32865 \begin_layout Plain Layout
32867 \begin_inset IndexMacro subentry
32870 \begin_layout Plain Layout
32877 \begin_inset IndexMacro subentry
32880 \begin_layout Plain Layout
32894 \begin_layout Standard
32895 To display only parts of a formula with multiple lines, one of the following
32896 environments is used:
32913 They can be inserted via the menu
32915 Insert\SpecialChar menuseparator
32918 or by using the commands described in this section.
32921 \begin_layout Standard
32922 The first three have the same properties as the corresponding multiline
32923 formula environments, but it is possible to set additional formula parts
32926 \begin_inset Formula
32928 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
32929 \Delta E\Delta t & \ge\frac{\hbar}{2}
32931 \right\} \textrm{Uncertainty relations}
32939 \begin_layout Standard
32940 To get this formula, a displayed formula is created where the command
32947 \begin_inset Index idx
32952 \begin_layout Plain Layout
32954 \begin_inset IndexMacro subentry
32957 \begin_layout Plain Layout
32964 \begin_inset IndexMacro subentry
32967 \begin_layout Plain Layout
32981 A purple box appears around the blue formula box where now columns and
32982 lines can be added.
32983 Outside the multiline environment other formula parts can be set, like
32987 \begin_layout Standard
32988 The aligned environment is also suitable for long formulas whose lines are
32989 horizontally aligned.
32990 Using aligned in a displayed formula has the advantage that the formula
32991 number is vertically centered behind the lines.
32992 For example here is formula
32993 \begin_inset CommandInset ref
32995 reference "eq:shortlong"
32999 in the aligned environment:
33000 \begin_inset Formula
33002 \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}|}\\
33003 & -\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}|}
33012 \begin_layout Standard
33013 To use the environments
33032 \begin_inset Index idx
33037 \begin_layout Plain Layout
33039 \begin_inset IndexMacro subentry
33042 \begin_layout Plain Layout
33049 \begin_inset IndexMacro subentry
33052 \begin_layout Plain Layout
33072 \begin_inset Index idx
33077 \begin_layout Plain Layout
33079 \begin_inset IndexMacro subentry
33082 \begin_layout Plain Layout
33089 \begin_inset IndexMacro subentry
33092 \begin_layout Plain Layout
33112 \begin_inset Index idx
33117 \begin_layout Plain Layout
33119 \begin_inset IndexMacro subentry
33122 \begin_layout Plain Layout
33129 \begin_inset IndexMacro subentry
33132 \begin_layout Plain Layout
33145 are inserted, respectively.
33146 The split environment has the same properties as the aligned environment
33147 but it can only have two columns.
33150 \begin_layout Subsection
33151 Text in Multiline Formulas
33152 \begin_inset CommandInset label
33154 name "subsec:Text-in-multiline"
33159 \begin_inset Index idx
33164 \begin_layout Plain Layout
33166 \begin_inset IndexMacro subentry
33169 \begin_layout Plain Layout
33181 \begin_inset Index idx
33186 \begin_layout Plain Layout
33188 \begin_inset IndexMacro subentry
33191 \begin_layout Plain Layout
33198 \begin_inset IndexMacro subentry
33201 \begin_layout Plain Layout
33215 \begin_layout Standard
33216 In the align environments as well as the multline and gather environment,
33217 text can be inserted that will appear in a separate line and doesn't affect
33218 the column alignment.
33219 To do this, the command
33226 \begin_inset Index idx
33231 \begin_layout Plain Layout
33233 \begin_inset IndexMacro subentry
33236 \begin_layout Plain Layout
33243 \begin_inset IndexMacro subentry
33246 \begin_layout Plain Layout
33259 is used in the following scheme:
33262 \begin_layout Standard
33270 \begin_layout Standard
33271 The text should not be longer than a line because it cannot be hyphenated.
33272 As \SpecialChar LyX
33273 doesn't yet support
33279 directly, the text is written as mathematical text.
33286 must be at the beginning of a line and will appear in the output above
33288 An example where the text was inserted at the beginning of the second line:
33289 \begin_inset Formula
33291 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
33292 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
33300 \begin_layout Standard
33307 always creates some vertical space between the text and the formula lines.
33308 To avoid this space, in the document settings under
33311 \begin_inset space ~
33321 \begin_inset Index idx
33326 \begin_layout Plain Layout
33328 \begin_inset IndexMacro subentry
33331 \begin_layout Plain Layout
33345 \begin_inset space ~
33351 Then you can use the command
33358 \begin_inset Index idx
33363 \begin_layout Plain Layout
33365 \begin_inset IndexMacro subentry
33368 \begin_layout Plain Layout
33375 \begin_inset IndexMacro subentry
33378 \begin_layout Plain Layout
33400 \begin_layout Standard
33401 \begin_inset Formula
33403 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
33404 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
33412 \begin_layout Section
33414 \begin_inset Index idx
33419 \begin_layout Plain Layout
33426 \begin_inset Index idx
33431 \begin_layout Plain Layout
33433 \begin_inset IndexMacro subentry
33436 \begin_layout Plain Layout
33443 \begin_inset IndexMacro see
33446 \begin_layout Plain Layout
33460 \begin_layout Subsection
33464 \begin_layout Standard
33465 Numbered formulas can be created with the menu
33467 Insert\SpecialChar menuseparator
33468 Math\SpecialChar menuseparator
33470 \begin_inset space ~
33478 arg "command-sequence math-display; math-number-toggle;"
33482 Existing formulas can be numbered with the menu
33484 Edit\SpecialChar menuseparator
33485 Math\SpecialChar menuseparator
33487 \begin_inset space ~
33491 \begin_inset space ~
33499 arg "math-number-toggle"
33503 The formula number is displayed in \SpecialChar LyX
33504 behind the formula as a number in parenthes
33507 \change_deleted 232239728 1611410645
33508 The number sign is replaced in the output by the formula number.
33509 \change_deleted 5863208 1612727075
33511 \begin_inset Note Note
33514 \begin_layout Plain Layout
33516 \change_inserted 232239728 1611410697
33517 LyX appears to put the actual formula number in the raw file now
33529 \begin_layout Standard
33530 When numbering is turned on in multiline formulas, all formulas will be
33532 But the numbering can be controlled with the menu
33534 Edit\SpecialChar menuseparator
33535 Math\SpecialChar menuseparator
33537 \begin_inset space ~
33541 \begin_inset space ~
33549 arg "math-number-line-toggle"
33552 ) for every formula.
33555 \begin_layout Standard
33556 Except for inline formulas, all formulas can be numbered with two different
33558 \begin_inset CommandInset ref
33560 reference "sec:Formula-Styles"
33567 \begin_layout Subsection
33569 \begin_inset Index idx
33574 \begin_layout Plain Layout
33576 \begin_inset IndexMacro subentry
33579 \begin_layout Plain Layout
33593 \begin_layout Standard
33594 All labeled formulas can be cross-referenced.
33595 A label is added with the menu
33597 Insert\SpecialChar menuseparator
33600 or the toolbar button
33607 The cursor must be inside a displayed formula.
33608 Alternatively you can right-click on the formula and choose
33613 A dialog pops up displaying the prefix
33618 The label is inserted behind the prefix.
33619 The predefined prefix means
33620 \begin_inset Quotes eld
33624 \begin_inset Quotes erd
33627 and makes it easier to find labels in large documents because it marks
33628 it as a formula label to distinguish it from e.
33629 \begin_inset space \thinspace{}
33633 \begin_inset space \space{}
33637 To change a label, the menu
33639 Insert\SpecialChar menuseparator
33642 is used again or you can right-click on a formula and then on
33649 \begin_layout Standard
33650 The name of the label is displayed in \SpecialChar LyX
33651 within parentheses behind the formula
33653 A formula with a label is always numbered.
33656 \begin_layout Standard
33657 Cross-references are inserted via the menu
33659 Insert\SpecialChar menuseparator
33662 or with the toolbar button
33665 arg "dialog-show-new-inset ref"
33669 A formula cross-reference appears in the output as formula number.
33670 When in the cross-reference dialog window the format
33674 is chosen, the cross-reference appears in the output as formula number
33676 \begin_inset Newline newline
33679 By right-clicking on a cross-reference in \SpecialChar LyX
33680 , one jumps to the formula that
33684 \begin_layout Standard
33685 Here are as examples cross-references to formulas of the following subsections:
33686 \begin_inset Note Note
33689 \begin_layout Plain Layout
33690 Note the different cross-reference types.
33698 \begin_layout Standard
33700 \begin_inset CommandInset ref
33707 \begin_inset CommandInset ref
33715 \begin_inset CommandInset ref
33721 ) big Latin letters are used for the numbering in contrary to (
33722 \begin_inset CommandInset ref
33731 \begin_layout Standard
33732 \begin_inset VSpace medskip
33735 When the argument of
33743 \begin_layout Plain Layout
33751 \begin_inset CommandInset ref
33753 reference "subsec:User-defined-Numbering"
33764 contains a box like in
33765 \begin_inset CommandInset ref
33767 reference "subsec:Paragraph-Boxes"
33771 , the formula cannot be referenced.
33774 \begin_layout Subsection
33776 \begin_inset Index idx
33781 \begin_layout Plain Layout
33783 \begin_inset IndexMacro subentry
33786 \begin_layout Plain Layout
33800 \begin_layout Standard
33801 Formulas can be numbered as subequations.
33802 To activate this feature, add the module
33806 to the document in the menu
33808 Document\SpecialChar menuseparator
33809 Settings\SpecialChar menuseparator
33813 To insert subequations use the menu
33815 Insert\SpecialChar menuseparator
33816 Custom Insets\SpecialChar menuseparator
33822 \begin_layout Standard
33823 The equations to be subnumbered are put into the
33829 \begin_inset Formula
33837 \begin_inset VSpace -5mm
33841 \begin_inset Flex Subequations
33844 \begin_layout Plain Layout
33845 \begin_inset Formula
33853 \begin_inset Formula
33868 \begin_layout Standard
33869 Every formula in the
33873 inset will be subnumbered with a, b, c, \SpecialChar ldots
33875 For multiline formulas every line will be subnumbered.
33878 \begin_layout Standard
33879 Referencing subequations works like normal equations:
33880 \begin_inset CommandInset ref
33887 \begin_inset CommandInset ref
33894 If you want to reference the subequations collectively, insert a label
33895 as first thing in the
33901 \begin_inset CommandInset ref
33903 reference "eq:Here-is-an"
33913 \begin_layout Standard
33914 When inserting subequations, vertical space is added before the equation.
33915 To remove this, insert -5
33916 \begin_inset space \thinspace{}
33919 mm vertical space right before the
33924 If the formula style
33930 \begin_layout Plain Layout
33931 For formula styles see
33932 \begin_inset CommandInset ref
33934 reference "sec:Formula-Styles"
33946 \begin_inset space \thinspace{}
33952 \begin_layout Standard
33953 To get another subnumber instead of small Latin letters, insert this command
33954 as \SpecialChar TeX
33955 code before the equations in the
33962 \begin_layout Standard
33971 theparentequation -
33976 \begin_layout Standard
33983 creates the parent number and
33989 adds a small Roman number as subnumber.
33990 For more information about the customization of the numbering, see
33991 \begin_inset CommandInset ref
33993 reference "subsec:Numbering-with-Roman"
34000 \begin_layout Standard
34001 Here is an example of a multiline formula where the numbering is customized
34002 and turned off for the second line:
34003 \begin_inset Flex Subequations
34006 \begin_layout Plain Layout
34007 \begin_inset CommandInset label
34009 name "eq:Here-is-an"
34017 \begin_layout Plain Layout
34025 theparentequation -
34033 \begin_inset Formula
34035 A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
34036 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
34037 & = & B^{2}-2BZ+Z^{2}
34050 \begin_layout Subsection
34051 Numbering with Roman Numbers and Letters
34052 \begin_inset CommandInset label
34054 name "subsec:Numbering-with-Roman"
34059 \begin_inset Index idx
34064 \begin_layout Plain Layout
34066 \begin_inset IndexMacro subentry
34069 \begin_layout Plain Layout
34081 \begin_inset Index idx
34086 \begin_layout Plain Layout
34088 \begin_inset IndexMacro subentry
34091 \begin_layout Plain Layout
34105 \begin_layout Standard
34106 Formulas can also be numbered with Roman numbers and Latin letters.
34107 To number with small Roman numbers, the command
34110 \begin_layout Standard
34122 \begin_layout Standard
34123 is inserted before the formula in \SpecialChar TeX
34132 \begin_inset Index idx
34137 \begin_layout Plain Layout
34139 \begin_inset IndexMacro subentry
34142 \begin_layout Plain Layout
34149 \begin_inset IndexMacro subentry
34152 \begin_layout Plain Layout
34165 redefines the predefined command
34181 \begin_layout Plain Layout
34188 has the same scheme as the command
34195 \begin_inset CommandInset ref
34197 reference "subsec:The-Command-newcommand"
34210 is the formula counter.
34217 is used as prefix for a counter, the value of the counter is output as
34219 When a formula is numbered, \SpecialChar LaTeX
34220 sets internally the command
34226 behind the formula.
34232 \begin_inset Index idx
34237 \begin_layout Plain Layout
34239 \begin_inset IndexMacro subentry
34242 \begin_layout Plain Layout
34249 \begin_inset IndexMacro subentry
34252 \begin_layout Plain Layout
34267 outputs the counter as small Roman number.
34270 \begin_layout Standard
34271 All formulas behind the command
34281 are now numbered Roman.
34282 To switch to numbering with big Roman numbers, the command is inserted
34296 \begin_inset Index idx
34301 \begin_layout Plain Layout
34303 \begin_inset IndexMacro subentry
34306 \begin_layout Plain Layout
34313 \begin_inset IndexMacro subentry
34316 \begin_layout Plain Layout
34317 \begin_inset IndexMacro sortkey
34320 \begin_layout Plain Layout
34342 \begin_inset Quotes eld
34346 \begin_inset Quotes erd
34349 with small Latin letters there is the command
34356 \begin_inset Index idx
34361 \begin_layout Plain Layout
34363 \begin_inset IndexMacro subentry
34366 \begin_layout Plain Layout
34373 \begin_inset IndexMacro subentry
34376 \begin_layout Plain Layout
34389 , for big ones there is the command
34396 \begin_inset Index idx
34401 \begin_layout Plain Layout
34403 \begin_inset IndexMacro subentry
34406 \begin_layout Plain Layout
34413 \begin_inset IndexMacro subentry
34416 \begin_layout Plain Layout
34417 \begin_inset IndexMacro sortkey
34420 \begin_layout Plain Layout
34443 \begin_layout Standard
34444 \begin_inset Note Greyedout
34447 \begin_layout Plain Layout
34452 Only a maximum of 26
34453 \begin_inset space ~
34456 formulas can be numbered with Latin letters in one document.
34464 \begin_layout Standard
34468 \begin_layout Plain Layout
34484 \begin_layout Standard
34485 \begin_inset Formula
34487 A=\textrm{small roman}
34496 \begin_layout Plain Layout
34510 \begin_inset Formula
34512 B=\textrm{big Roman}\label{eq:Rom}
34521 \begin_layout Plain Layout
34535 \begin_inset Formula
34537 C=\textrm{small Latin}
34546 \begin_layout Plain Layout
34560 \begin_inset Formula
34562 D=\textrm{big Latin}\label{eq:Lat}
34570 \begin_layout Standard
34571 To switch back to the default numbering, insert the command:
34574 \begin_layout Standard
34584 \begin_inset Index idx
34589 \begin_layout Plain Layout
34591 \begin_inset IndexMacro subentry
34594 \begin_layout Plain Layout
34601 \begin_inset IndexMacro subentry
34604 \begin_layout Plain Layout
34620 \begin_layout Standard
34624 \begin_layout Plain Layout
34638 \begin_inset Formula
34648 \begin_layout Standard
34649 \begin_inset VSpace medskip
34652 As you see, formulas are numbered serially independent from the numbering
34654 When then numbering should start with
34655 \begin_inset Quotes eld
34659 \begin_inset Quotes erd
34662 when the style is changed, new equation counters have to be defined.
34663 A description of this can be found in the file
34664 \begin_inset CommandInset href
34666 name "Formula-numbering.lyx"
34667 target "run:Formula-numbering.lyx"
34675 \begin_layout Subsection
34676 User-defined Numbering
34677 \begin_inset CommandInset label
34679 name "subsec:User-defined-Numbering"
34684 \begin_inset Index idx
34689 \begin_layout Plain Layout
34691 \begin_inset IndexMacro subentry
34694 \begin_layout Plain Layout
34708 \begin_layout Standard
34709 \begin_inset Note Greyedout
34712 \begin_layout Plain Layout
34717 If the document language is a right-to-left language such as Arabic, you
34718 must add this to the to the \SpecialChar LaTeX
34719 -preamble to be able to use the commands described
34721 \begin_inset Newline newline
34729 \begin_inset Newline newline
34733 \begin_inset Phantom HPhantom
34736 \begin_layout Plain Layout
34739 \begin_inset space ~
34765 \begin_layout Standard
34766 \begin_inset Index idx
34771 \begin_layout Plain Layout
34773 \begin_inset IndexMacro subentry
34776 \begin_layout Plain Layout
34777 self-defined delimiters
34787 With standard numbering, parentheses are set around a formula number.
34788 To replace the parentheses for example with vertical bars, the following
34789 line is added to the \SpecialChar LaTeX
34793 \begin_layout Standard
34799 \begin_inset Newline newline
34803 \begin_inset Phantom HPhantom
34806 \begin_layout Plain Layout
34809 \begin_inset space ~
34823 maketag@@@{|#1|}} }
34826 \begin_inset Note Note
34829 \begin_layout Plain Layout
34830 This macro is already declared in the \SpecialChar LaTeX
34831 -preamble for testing.
34832 To activate it, remove the percent signs at the beginning.
34840 \begin_layout Standard
34841 To use other characters, the vertical bars besides the
34845 are replaced by one or more characters.
34846 To display only the formula number the vertical bars are omitted.
34849 \begin_layout Standard
34850 \begin_inset VSpace bigskip
34853 When there should be an expression of your choice instead of the consecutive
34854 formula number in parentheses behind the formula, the command
34861 \begin_inset Index idx
34866 \begin_layout Plain Layout
34868 \begin_inset IndexMacro subentry
34871 \begin_layout Plain Layout
34878 \begin_inset IndexMacro subentry
34881 \begin_layout Plain Layout
34895 \begin_inset Formula
34897 A+B=C\tag{something}\label{eq:tag}
34902 In this example the command
34907 \begin_inset space \textvisiblespace{}
34912 was inserted in the formula.
34915 \begin_layout Standard
34921 \begin_inset space \textvisiblespace{}
34926 is inserted instead, the parentheses are removed:
34927 \begin_inset Formula
34929 A+B=C\tag*{something}
34937 \begin_layout Standard
34938 \begin_inset VSpace bigskip
34941 To restart the formula numbering with new document parts or sections, the
34942 following command is used:
34945 \begin_layout Standard
34950 @addtoreset{equation}{part}
34953 \begin_inset Index idx
34958 \begin_layout Plain Layout
34960 \begin_inset IndexMacro subentry
34963 \begin_layout Plain Layout
34967 \begin_layout Plain Layout
34980 \begin_inset IndexMacro subentry
34983 \begin_layout Plain Layout
34990 \begin_layout Plain Layout
35008 \begin_inset Newline newline
35012 \begin_inset Newline newline
35019 @addtoreset{equation}{section}
35022 \begin_layout Standard
35023 To be able to use these commands in \SpecialChar TeX
35025 \begin_inset Quotes eld
35029 \begin_inset Quotes erd
35032 character has to be made
35033 \begin_inset Quotes eld
35037 \begin_inset Quotes erd
35040 for \SpecialChar LaTeX
35055 So the command sequence in \SpecialChar TeX
35059 \begin_layout Standard
35065 \begin_inset Newline newline
35070 @addtoreset{equation}{section}
35071 \begin_inset Newline newline
35079 \begin_layout Standard
35080 In the \SpecialChar LaTeX
35093 can be omitted as they are automatically internally inserted by \SpecialChar LyX
35097 \begin_layout Standard
35112 \begin_layout Plain Layout
35117 is part of the \SpecialChar LaTeX
35123 \begin_inset Index idx
35128 \begin_layout Plain Layout
35130 \begin_inset IndexMacro subentry
35133 \begin_layout Plain Layout
35144 that is part of every \SpecialChar LaTeX
35145 standard installation.
35151 \begin_inset Index idx
35156 \begin_layout Plain Layout
35158 \begin_inset IndexMacro subentry
35161 \begin_layout Plain Layout
35172 has to be loaded in the \SpecialChar LaTeX
35173 -preamble with the line
35176 \begin_layout Standard
35181 usepackage{remreset}
35184 \begin_layout Standard
35192 \begin_inset Index idx
35197 \begin_layout Plain Layout
35199 \begin_inset IndexMacro subentry
35202 \begin_layout Plain Layout
35206 \begin_layout Plain Layout
35219 \begin_inset IndexMacro subentry
35222 \begin_layout Plain Layout
35229 \begin_layout Plain Layout
35246 can be used with the same scheme as
35255 \begin_layout Standard
35256 \begin_inset VSpace bigskip
35259 Sometimes formulas should be numbered in the following form:
35262 \begin_layout Standard
35265 (section number.formula number)
35268 \begin_layout Standard
35269 The formula number should start with every section with
35270 \begin_inset Quotes eld
35274 \begin_inset Quotes erd
35280 \begin_layout Standard
35281 For this case there is the command
35288 \begin_inset Index idx
35293 \begin_layout Plain Layout
35295 \begin_inset IndexMacro subentry
35298 \begin_layout Plain Layout
35305 \begin_inset IndexMacro subentry
35308 \begin_layout Plain Layout
35321 , which is used with the following scheme:
35324 \begin_layout Standard
35329 numberwithin{counter}{sectioning}
35332 \begin_layout Standard
35333 Counter denotes what kind of numbering is affected, sectioning denotes what
35334 the number before the dot is.
35337 \begin_layout Standard
35338 Thus in our case the following \SpecialChar LaTeX
35339 preamble or \SpecialChar TeX
35343 \begin_layout Standard
35348 numberwithin{equation}{section}
35351 \begin_layout Standard
35352 This is the result:
35356 \begin_layout Plain Layout
35360 numberwithin{equation}{section}
35366 \begin_inset Formula
35376 \begin_layout Standard
35378 \begin_inset space \thinspace{}
35382 \begin_inset space \space{}
35385 tables so that the number of the part is the sectioning,
35386 \begin_inset Newline newline
35393 numberwithin{table}{part}
35398 \begin_layout Standard
35399 To go back to the standard numbering or to prevent this kind of numbering
35400 when it is defined by the document class, the following command is inserted
35401 as \SpecialChar TeX
35402 code or to the \SpecialChar LaTeX
35406 \begin_layout Standard
35416 \begin_inset Index idx
35421 \begin_layout Plain Layout
35423 \begin_inset IndexMacro subentry
35426 \begin_layout Plain Layout
35433 \begin_inset IndexMacro subentry
35436 \begin_layout Plain Layout
35455 \begin_layout Plain Layout
35471 \begin_inset Newline newline
35479 \begin_inset Newline newline
35491 \begin_layout Standard
35498 internally uses the command
35504 , described above, and would also need to be reverted.
35508 \begin_layout Plain Layout
35515 \begin_layout Plain Layout
35519 @removefromreset{equation}{section}
35522 \begin_layout Plain Layout
35534 \begin_layout Section
35535 Chemical Symbols and Equations
35536 \begin_inset CommandInset label
35538 name "subsec:Chemical-Symbols-and"
35543 \begin_inset Index idx
35548 \begin_layout Plain Layout
35549 Chemical characters
35550 \begin_inset IndexMacro subentry
35553 \begin_layout Plain Layout
35565 \begin_inset Index idx
35570 \begin_layout Plain Layout
35577 \begin_inset Index idx
35582 \begin_layout Plain Layout
35584 \begin_inset IndexMacro subentry
35587 \begin_layout Plain Layout
35601 \begin_layout Standard
35602 An example text from chemistry:
35605 \begin_layout Quote
35607 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
35610 -ion reacts with two
35611 \begin_inset Formula $\mathrm{Na^{+}}$
35614 -ions to sodium sulfate
35615 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
35619 The chemical equation for this is:
35620 \begin_inset Formula
35622 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
35630 \begin_layout Standard
35631 Chemical equations can be created as formulas.
35632 To avoid the symbols appearing in italic, everything is highlighted and
35633 changed by the shortcut
35639 to the upright font style.
35643 \begin_layout Plain Layout
35649 \begin_inset CommandInset ref
35651 reference "subsec:Font-Styles"
35663 \begin_layout Standard
35664 A more convenient way to typeset chemical formulas is to use the command
35672 \begin_inset Index idx
35677 \begin_layout Plain Layout
35679 \begin_inset IndexMacro subentry
35682 \begin_layout Plain Layout
35689 \begin_inset IndexMacro subentry
35692 \begin_layout Plain Layout
35705 which is available when the \SpecialChar LaTeX
35711 \begin_inset Index idx
35716 \begin_layout Plain Layout
35718 \begin_inset IndexMacro subentry
35721 \begin_layout Plain Layout
35739 in a formula a new blue box appears where chemical formulas can be inserted
35740 in an intuitive way.
35743 \begin_layout Standard
35745 \begin_inset Tabular
35746 <lyxtabular version="3" rows="10" columns="2">
35747 <features booktabs="true" tabularvalignment="middle">
35748 <column alignment="center" valignment="top" width="0pt">
35749 <column alignment="center" valignment="top">
35751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35754 \begin_layout Plain Layout
35760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35763 \begin_layout Plain Layout
35771 <cell alignment="center" valignment="top" leftline="true" usebox="none">
35774 \begin_layout Plain Layout
35778 \begin_inset space \textvisiblespace{}
35786 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
35789 \begin_layout Plain Layout
35790 \begin_inset Formula $\ce{H2CO3}$
35799 <row topspace="1.5mm">
35800 <cell alignment="center" valignment="top" usebox="none">
35803 \begin_layout Plain Layout
35807 \begin_inset space \textvisiblespace{}
35815 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
35818 \begin_layout Plain Layout
35819 \begin_inset Formula $\ce{SO4^{2-}}$
35828 <row topspace="1.5mm">
35829 <cell alignment="center" valignment="top" usebox="none">
35832 \begin_layout Plain Layout
35836 \begin_inset space \textvisiblespace{}
35844 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
35847 \begin_layout Plain Layout
35848 \begin_inset Formula $\ce{(NH4)2S}$
35857 <row topspace="1.5mm">
35858 <cell alignment="center" valignment="top" usebox="none">
35861 \begin_layout Plain Layout
35865 \begin_inset space \textvisiblespace{}
35873 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
35876 \begin_layout Plain Layout
35877 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
35886 <row topspace="1.5mm">
35887 <cell alignment="center" valignment="top" usebox="none">
35890 \begin_layout Plain Layout
35894 \begin_inset space \textvisiblespace{}
35900 \begin_inset space \textvisiblespace{}
35906 \begin_inset space \textvisiblespace{}
35914 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
35917 \begin_layout Plain Layout
35918 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
35927 <row topspace="1.5mm">
35928 <cell alignment="center" valignment="top" usebox="none">
35931 \begin_layout Plain Layout
35935 \begin_inset space \textvisiblespace{}
35939 \begin_inset Formula $\downarrow$
35943 \begin_inset Formula $\to$
35951 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
35954 \begin_layout Plain Layout
35955 \begin_inset Formula $\ce{_{90}^{227}Th+}$
35965 <cell alignment="center" valignment="top" leftline="true" usebox="none">
35968 \begin_layout Plain Layout
35972 \begin_inset space \textvisiblespace{}
35978 \begin_inset space \textvisiblespace{}
35984 \begin_inset space \textvisiblespace{}
35992 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
35995 \begin_layout Plain Layout
35996 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
36006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36009 \begin_layout Plain Layout
36013 \begin_inset space \textvisiblespace{}
36017 \begin_inset space \textvisiblespace{}
36021 \begin_inset space \textvisiblespace{}
36025 \begin_inset space \textvisiblespace{}
36029 \begin_inset space \textvisiblespace{}
36037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36040 \begin_layout Plain Layout
36041 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
36050 <row topspace="1.5mm">
36051 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
36054 \begin_layout Plain Layout
36058 \begin_inset space \textvisiblespace{}
36062 \begin_inset space \textvisiblespace{}
36066 \begin_inset space \textvisiblespace{}
36070 \begin_inset space \textvisiblespace{}
36078 \begin_inset space \textvisiblespace{}
36086 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
36089 \begin_layout Plain Layout
36090 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
36106 \begin_layout Standard
36107 \begin_inset Note Greyedout
36110 \begin_layout Plain Layout
36115 It is not possible in \SpecialChar LyX
36116 to use the character ^ to get an up-arrow as described
36122 One instead uses a negative thin space followed by the command
36129 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
36140 \begin_layout Standard
36147 the command for equation
36148 \begin_inset space ~
36152 \begin_inset CommandInset ref
36154 reference "eq:chem-reaction"
36159 \begin_inset Newline newline
36167 \begin_inset space \textvisiblespace{}
36171 \begin_inset space \textvisiblespace{}
36175 \begin_inset space \textvisiblespace{}
36179 \begin_inset space \textvisiblespace{}
36183 \begin_inset space \textvisiblespace{}
36187 \begin_inset space \textvisiblespace{}
36193 \begin_layout Standard
36194 To create multiline chemical equations first a multiline formula is created
36196 \begin_inset CommandInset ref
36198 reference "sec:Multiline-Formulas"
36203 Afterwards the command
36209 is used in every small blue box of the formula.
36211 \begin_inset CommandInset ref
36213 reference "eq:TEOS-reaction-1"
36218 \begin_inset CommandInset ref
36220 reference "eq:TEOS-reaction-2"
36224 are an example of a multi-stage chemical reaction where every equation
36225 has its own number.
36226 \begin_inset Formula
36228 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
36229 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
36237 \begin_layout Standard
36248 package provides the command
36255 \begin_inset Index idx
36260 \begin_layout Plain Layout
36262 \begin_inset IndexMacro subentry
36265 \begin_layout Plain Layout
36272 \begin_inset IndexMacro subentry
36275 \begin_layout Plain Layout
36288 that is used for special cases.
36289 For more information about
36295 and more examples have a look at the documentation of
36300 \begin_inset CommandInset citation
36310 \begin_layout Section
36314 \begin_layout Standard
36316 supports two types of commutative diagrams:
36324 and are explained below.
36327 \begin_layout Subsection
36329 \begin_inset Index idx
36334 \begin_layout Plain Layout
36336 \begin_inset IndexMacro subentry
36339 \begin_layout Plain Layout
36353 \begin_layout Standard
36354 Diagrams of this type visualize relations by vertical and horizontal lines
36356 \begin_inset Formula
36358 \begin{CD}A@>>>B@>>>C\\
36369 \begin_layout Standard
36370 To create them, the command
36375 \begin_inset Index idx
36380 \begin_layout Plain Layout
36382 \begin_inset IndexMacro subentry
36385 \begin_layout Plain Layout
36392 \begin_inset IndexMacro subentry
36395 \begin_layout Plain Layout
36410 is inserted to a formula.
36411 A blue box appears with two dashed lines where additional commands can
36416 arg "newline-insert newline"
36419 a new line is created.
36420 Horizontal relations are inserted in odd formula lines, vertical in even
36424 \begin_layout Standard
36425 To create the relations use the following commands:
36428 \begin_layout Itemize
36433 creates a left arrow,
36444 \begin_layout Itemize
36449 creates an up arrow,
36457 a vertical equal sign
36460 \begin_layout Itemize
36466 is a placeholder for non-existent relations
36469 \begin_layout Standard
36470 All arrows can be labeled as follows:
36473 \begin_layout Itemize
36474 If text inserted between the first and second < or >, resp., it is placed
36476 When it is inserted between the second and third one, it appears under
36480 \begin_layout Itemize
36481 When text for vertical arrows is inserted between the first and second A
36482 or V, resp., it is placed left beside the arrow.
36483 When it is inserted between the second and third one, it appears right
36485 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
36489 \begin_layout Standard
36490 As example a diagram with all possible relations:
36493 \begin_layout Standard
36494 \begin_inset Formula
36496 \begin{CD}A@>j>>B@>>k>C@=F\\
36507 \begin_layout Standard
36508 The command for this is:
36509 \begin_inset Newline newline
36517 \begin_inset space \textvisiblespace{}
36520 A@>j>>B@>>k>C@=F Ctrl+Return
36521 \begin_inset Newline newline
36525 \begin_inset Phantom HPhantom
36528 \begin_layout Plain Layout
36534 \begin_inset space \textvisiblespace{}
36547 \begin_inset Formula $\to$
36553 \begin_inset Newline newline
36557 \begin_inset Phantom HPhantom
36560 \begin_layout Plain Layout
36566 \begin_inset space \textvisiblespace{}
36577 \begin_layout Subsection
36579 \begin_inset Index idx
36584 \begin_layout Plain Layout
36586 \begin_inset IndexMacro subentry
36589 \begin_layout Plain Layout
36603 \begin_layout Standard
36604 To be able to use xymatrices, the \SpecialChar LaTeX
36610 A xymatrix is created by inserting the command
36617 Then you are able to add new matrix columns and rows like for normal matrices,
36619 \begin_inset CommandInset ref
36621 reference "sec:Matrices"
36628 \begin_layout Standard
36629 Contrary to amscd diagrams, xymatrices support diagonal and curved arrows,
36631 The commands used to create commutative diagrams and decorations are explained
36638 Help\SpecialChar menuseparator
36640 \begin_inset space ~
36648 \begin_layout Subsection
36654 \begin_inset Index idx
36659 \begin_layout Plain Layout
36661 \begin_inset IndexMacro subentry
36664 \begin_layout Plain Layout
36678 \begin_layout Standard
36683 -diagrams, the \SpecialChar LaTeX
36693 -diagram is created by inserting the command
36700 Then you will be able to add new matrix columns and rows like for normal
36702 \begin_inset CommandInset ref
36704 reference "sec:Matrices"
36711 \begin_layout Standard
36712 Examples of how to create
36716 diagrams in \SpecialChar LyX
36721 manual that you find in the menu
36723 Help\SpecialChar menuseparator
36725 \begin_inset space ~
36733 \begin_layout Section
36734 User-defined Commands
36735 \begin_inset Index idx
36740 \begin_layout Plain Layout
36741 User-defined commands
36749 \begin_layout Standard
36750 \begin_inset Note Greyedout
36753 \begin_layout Plain Layout
36758 The names of user-defined commands and macros may only consist of Latin
36767 \begin_layout Subsection
36771 \begin_inset CommandInset label
36773 name "subsec:The-Command-newcommand"
36778 \begin_inset Index idx
36783 \begin_layout Plain Layout
36784 User-defined commands
36785 \begin_inset IndexMacro subentry
36788 \begin_layout Plain Layout
36802 \begin_inset Index idx
36807 \begin_layout Plain Layout
36809 \begin_inset IndexMacro subentry
36812 \begin_layout Plain Layout
36819 \begin_inset IndexMacro subentry
36822 \begin_layout Plain Layout
36838 \begin_layout Standard
36839 Many \SpecialChar LaTeX
36840 -commands are too long to be used frequently.
36841 But it is possible to define with the command
36847 new shorter commands.
36850 \begin_layout Standard
36851 The command scheme of
36860 \begin_layout Standard
36865 newcommand{new command name}[number of arguments][optional
36870 \begin_inset Newline newline
36874 \begin_inset Phantom HPhantom
36877 \begin_layout Plain Layout
36887 {command definition}
36890 \begin_layout Standard
36891 \begin_inset Note Greyedout
36894 \begin_layout Plain Layout
36899 Verify that the name of the new command is not already used in your document
36900 or by the \SpecialChar LaTeX
36901 -packages that you use.
36902 If you for example define the command
36914 , you will get an error message because
36920 is already defined as command for
36921 \begin_inset Quotes eld
36925 \begin_inset Formula $\le$
36929 \begin_inset Quotes erd
36940 \begin_layout Standard
36941 The number of arguments is an integer in the range 0
36942 \begin_inset space \thinspace{}
36946 \begin_inset space \thinspace{}
36949 9 and specifies how many arguments the new command should have.
36950 With the optional value a value for an optional argument can be predefined.
36951 When this is done, the
36959 rgument of the new command is automatically an optional one.
36962 \begin_layout Standard
36963 Here are some examples:
36966 \begin_layout Itemize
36967 To define the command
36979 , the \SpecialChar LaTeX
36981 \begin_inset VSpace medskip
36985 \begin_inset Newline newline
36999 \begin_layout Itemize
37000 To define the command
37012 , the argument (that should be underlined) must be taken into account.
37013 For this the preamble line is:
37014 \begin_inset VSpace medskip
37018 \begin_inset Newline newline
37032 \begin_inset VSpace medskip
37036 \begin_inset Newline newline
37043 acts as argument placeholder, the
37047 behind it denotes that it is the placeholder for the first argument.
37050 \begin_layout Itemize
37058 \begin_inset space \thinspace{}
37062 \begin_inset space \space{}
37072 \begin_inset VSpace medskip
37076 \begin_inset Newline newline
37087 framebox#1#2{$#3$}}
37090 \begin_inset VSpace medskip
37094 \begin_inset Newline newline
37097 The two Dollar signs creates the extra formula needed for
37104 \begin_inset CommandInset ref
37106 reference "subsec:Boxes-with-Frame"
37113 \begin_layout Itemize
37114 To create a new command for
37120 where the color for the box need not be specified, the argument for the
37121 color is defined optional:
37122 \begin_inset VSpace medskip
37126 \begin_inset Newline newline
37137 fcolorbox{#2}{#1}{$#3$}}
37140 \begin_inset VSpace medskip
37144 \begin_inset Newline newline
37147 When the color is not specified when using
37153 , the predefined color
37160 \begin_layout Standard
37161 A test of the new defined commands:
37164 \begin_layout Standard
37166 \begin_inset Tabular
37167 <lyxtabular version="3" rows="6" columns="2">
37168 <features booktabs="true" tabularvalignment="middle">
37169 <column alignment="center" valignment="top" width="0pt">
37170 <column alignment="center" valignment="top">
37172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37175 \begin_layout Plain Layout
37181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37184 \begin_layout Plain Layout
37192 <cell alignment="center" valignment="top" leftline="true" usebox="none">
37195 \begin_layout Plain Layout
37199 \begin_inset space \textvisiblespace{}
37207 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
37210 \begin_layout Plain Layout
37211 \begin_inset Formula $A\gr B$
37221 <cell alignment="center" valignment="top" leftline="true" usebox="none">
37224 \begin_layout Plain Layout
37232 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
37235 \begin_layout Plain Layout
37236 \begin_inset Formula $\us{ABcd}$
37245 <row topspace="1mm">
37246 <cell alignment="center" valignment="top" usebox="none">
37249 \begin_layout Plain Layout
37253 \begin_inset Formula $\to$
37259 \begin_inset Formula $\to$
37267 \begin_inset space \textvisiblespace{}
37275 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
37278 \begin_layout Plain Layout
37279 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
37288 <row topspace="1.5mm">
37289 <cell alignment="center" valignment="top" usebox="none">
37292 \begin_layout Plain Layout
37296 \begin_inset Formula $\to$
37304 \begin_inset space \textvisiblespace{}
37312 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
37315 \begin_layout Plain Layout
37316 \begin_inset Formula $\cb{red}{\int A=B}$
37325 <row topspace="1.5mm" bottomspace="1mm">
37326 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37329 \begin_layout Plain Layout
37335 \begin_inset Formula $\to$
37343 \begin_inset space \textvisiblespace{}
37351 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
37354 \begin_layout Plain Layout
37355 \begin_inset Formula $\cb[green]{red}{\int A=B}$
37371 \begin_layout Subsection
37373 \begin_inset Index idx
37378 \begin_layout Plain Layout
37379 User-defined commands! Math macros
37385 \begin_inset Index idx
37390 \begin_layout Plain Layout
37399 \begin_layout Standard
37400 User-defined commands are especially convenient for complex expressions.
37401 For example if you are dealing with a document that has quadratic equations,
37402 the same solution type occurs several times.
37403 The general form of a quadratic equation is
37404 \begin_inset Formula
37406 0=\lambda^{2}+p\lambda+q
37411 The general form of the solution is
37412 \begin_inset Formula
37414 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
37422 \begin_layout Standard
37423 To define a command for the solution formula where only the three parameters
37425 \begin_inset Formula $\lambda$
37429 \begin_inset Formula $p$
37433 \begin_inset Formula $q$
37436 need to be specified and the index of
37437 \begin_inset Formula $\lambda$
37440 can be given optionally, the \SpecialChar LaTeX
37442 \begin_inset Newline newline
37458 \begin_inset Newline newline
37462 \begin_inset Phantom HPhantom
37465 \begin_layout Plain Layout
37479 frac{#3^{2}}{4}-#4}}
37482 \begin_layout Standard
37483 To create with this the solution formula, the command
37484 \begin_inset Newline newline
37494 \begin_inset Formula $\to$
37500 \begin_inset Formula $\to$
37507 is inserted to a formula
37512 \begin_layout Standard
37513 The definition of the new command is unintuitive because one has to know
37514 the schemes of all used \SpecialChar LaTeX
37516 \begin_inset space \thinspace{}
37520 \begin_inset space \space{}
37523 that a fraction is inserted in \SpecialChar LaTeX
37528 frac{numerator}{denominator}
37531 Furthermore one can easily forget a brace in the definition and cannot
37532 see in \SpecialChar LyX
37533 what the new command is doing.
37534 To avoid these problems \SpecialChar LyX
37535 offers the possibility to use math macros instead
37545 \begin_layout Standard
37546 A math macro is created by using the menu
37548 Insert\SpecialChar menuseparator
37549 Math\SpecialChar menuseparator
37552 or the toolbar button
37555 arg "math-macro newmacroname_newcommand"
37559 The math macro toolbar appears together with the following box where the
37561 \begin_inset Newline newline
37565 \begin_inset space \hspace*{\fill}
37569 \begin_inset Graphics
37570 filename clipart/macrobox.png
37576 \begin_inset space \hspace*{\fill}
37580 \begin_inset Newline newline
37584 \begin_inset FormulaMacro
37585 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
37590 newmacroname is the default name of the macro that should be changed to
37591 something sensible.
37592 The wanted formula is inserted in the first blue box.
37593 An argument placeholder is inserted with the command
37600 \begin_inset space \thinspace{}
37604 \begin_inset space \space{}
37613 or by using the macro toolbar button
37616 arg "math-macro-add-param"
37620 Argument placeholders are displayed red.
37622 \begin_inset space ~
37625 arguments are possible.
37626 Optional arguments are created with the toolbar button
37629 arg "math-macro-add-optional-param"
37633 The first non-optional argument can be transformed to an optional one with
37637 arg "math-macro-make-optional"
37641 In the second blue box the appearance of the macro in \SpecialChar LyX
37643 Normally you want to see it as it is defined, so the box is kept empty.
37644 But when you have created a macro that needs lot of space on the screen,
37645 you can insert in the box for example
37646 \begin_inset Newline newline
37676 \begin_inset Newline newline
37681 For the macro only the arguments with the macro name in front of them will
37682 then be displayed in \SpecialChar LyX
37683 , leading to a better overview.
37684 The formula appears in the output as defined in the first box.
37685 \begin_inset Newline newline
37688 The appearance of macros in formulas can furthermore be changed for single
37689 macros by setting the cursor in the macro and using the menu
37691 View\SpecialChar menuseparator
37693 \begin_inset space ~
37697 \begin_inset space ~
37705 \begin_layout Standard
37706 To use a macro, the macro name is inserted as command to a formula, in our
37714 Our macro looks in \SpecialChar LyX
37716 \begin_inset Newline newline
37720 \begin_inset space \hspace*{\fill}
37724 \begin_inset Graphics
37725 filename clipart/macrouse.png
37731 \begin_inset space \hspace*{\fill}
37735 \begin_inset Newline newline
37738 Here is our macro example with the arguments
37739 \begin_inset Formula $x$
37743 \begin_inset Formula $\ln(x)$
37747 \begin_inset Formula $B$
37753 \begin_layout Standard
37754 \begin_inset Formula
37764 \begin_layout Standard
37768 Tools\SpecialChar menuseparator
37769 Preferences\SpecialChar menuseparator
37770 Editing\SpecialChar menuseparator
37773 different styles to edit macros.
37774 To find the style that suits you best, choose a style and set the cursor
37775 in a macro formula to see the difference.
37778 \begin_layout Standard
37779 A math macro is transformed internally to a
37785 command when exporting the document.
37792 command is not placed in the \SpecialChar LaTeX
37793 -preamble, therefore macros can only be used
37794 in formulas that are in the document below the macro definition box.
37797 \begin_layout Standard
37798 Math macros can also be directly created from a
37805 When writing for example the command
37808 \begin_inset Newline newline
37817 xleftarrow[#2]{#1}}
37818 \begin_inset Newline newline
37823 in \SpecialChar LyX
37824 as normal text, highlighting it completely and using the shortcut
37828 , the command will be transformed to a math macro.
37829 Using this method you need to be careful that the
37835 command is typed correctly, otherwise you get a faulty macro leading to
37840 \begin_layout Standard
37841 Math macros currently have the problem that further formulas in macro definition
37842 s are handled wrong.
37843 Therefore the example
37850 \begin_inset CommandInset ref
37852 reference "subsec:The-Command-newcommand"
37856 cannot be created as macro.
37859 \begin_layout Standard
37860 When the cursor is in a macro definition box, you will see the macro toolbar
37861 in \SpecialChar LyX
37865 \begin_layout Standard
37866 \begin_inset VSpace defskip
37872 \begin_layout Standard
37873 \begin_inset Graphics
37874 filename clipart/MacroToolbar.png
37879 \begin_inset Index idx
37884 \begin_layout Plain Layout
37886 \begin_inset IndexMacro subentry
37889 \begin_layout Plain Layout
37903 \begin_layout Standard
37904 \begin_inset VSpace defskip
37910 \begin_layout Standard
37911 The macro toolbar contains from left to right the following buttons:
37914 \begin_layout Standard
37915 \begin_inset VSpace defskip
37921 \begin_layout Standard
37922 \begin_inset Tabular
37923 <lyxtabular version="3" rows="9" columns="2">
37924 <features islongtable="true" longtabularalignment="center">
37925 <column alignment="left" valignment="top">
37926 <column alignment="left" valignment="top" width="85col%">
37927 <row interlinespace="2.5mm">
37928 <cell alignment="center" valignment="top" usebox="none">
37931 \begin_layout Plain Layout
37934 arg "math-macro-remove-param"
37942 <cell alignment="center" valignment="top" usebox="none">
37945 \begin_layout Plain Layout
37948 Edit\SpecialChar menuseparator
37949 Math\SpecialChar menuseparator
37951 \begin_inset space ~
37954 Definition\SpecialChar menuseparator
37955 Remove Last Argument
37961 <row interlinespace="2.5mm">
37962 <cell alignment="center" valignment="top" usebox="none">
37965 \begin_layout Plain Layout
37968 arg "math-macro-add-param"
37976 <cell alignment="center" valignment="top" usebox="none">
37979 \begin_layout Plain Layout
37982 Edit\SpecialChar menuseparator
37983 Math\SpecialChar menuseparator
37985 \begin_inset space ~
37988 Definition\SpecialChar menuseparator
37995 <row interlinespace="2.5mm">
37996 <cell alignment="center" valignment="top" usebox="none">
37999 \begin_layout Plain Layout
38002 arg "math-macro-make-optional"
38010 <cell alignment="center" valignment="top" usebox="none">
38013 \begin_layout Plain Layout
38016 Edit\SpecialChar menuseparator
38017 Math\SpecialChar menuseparator
38019 \begin_inset space ~
38022 Definition\SpecialChar menuseparator
38023 Transform First Non-Optional to
38024 \begin_inset Newline newline
38028 \begin_inset Phantom HPhantom
38031 \begin_layout Plain Layout
38034 Edit\SpecialChar menuseparator
38035 Math\SpecialChar menuseparator
38037 \begin_inset space ~
38040 Definition\SpecialChar menuseparator
38052 <row interlinespace="2.5mm">
38053 <cell alignment="center" valignment="top" usebox="none">
38056 \begin_layout Plain Layout
38059 arg "math-macro-make-nonoptional"
38067 <cell alignment="center" valignment="top" usebox="none">
38070 \begin_layout Plain Layout
38073 Edit\SpecialChar menuseparator
38074 Math\SpecialChar menuseparator
38076 \begin_inset space ~
38079 Definition\SpecialChar menuseparator
38080 Transform Last Optional to
38081 \begin_inset Newline newline
38085 \begin_inset Phantom HPhantom
38088 \begin_layout Plain Layout
38091 Edit\SpecialChar menuseparator
38092 Math\SpecialChar menuseparator
38094 \begin_inset space ~
38097 Definition\SpecialChar menuseparator
38103 Non-Optional Argument
38109 <row interlinespace="2.5mm">
38110 <cell alignment="center" valignment="top" usebox="none">
38113 \begin_layout Plain Layout
38116 arg "math-macro-remove-optional-param"
38124 <cell alignment="center" valignment="top" usebox="none">
38127 \begin_layout Plain Layout
38130 Edit\SpecialChar menuseparator
38131 Math\SpecialChar menuseparator
38133 \begin_inset space ~
38136 Definition\SpecialChar menuseparator
38137 Remove Optional Argument
38143 <row interlinespace="2.5mm">
38144 <cell alignment="center" valignment="top" usebox="none">
38147 \begin_layout Plain Layout
38150 arg "math-macro-add-optional-param"
38158 <cell alignment="center" valignment="top" usebox="none">
38161 \begin_layout Plain Layout
38164 Edit\SpecialChar menuseparator
38165 Math\SpecialChar menuseparator
38167 \begin_inset space ~
38170 Definition\SpecialChar menuseparator
38171 Insert Optional Argument
38177 <row interlinespace="2.5mm">
38178 <cell alignment="center" valignment="top" usebox="none">
38181 \begin_layout Plain Layout
38184 arg "math-macro-remove-greedy-param"
38192 <cell alignment="center" valignment="top" usebox="none">
38195 \begin_layout Plain Layout
38198 Edit\SpecialChar menuseparator
38199 Math\SpecialChar menuseparator
38201 \begin_inset space ~
38204 Definition\SpecialChar menuseparator
38205 Remove Last Argument
38206 \begin_inset Newline newline
38210 \begin_inset Phantom HPhantom
38213 \begin_layout Plain Layout
38216 Edit\SpecialChar menuseparator
38217 Math\SpecialChar menuseparator
38219 \begin_inset space ~
38222 Definition\SpecialChar menuseparator
38228 Spitting Out To The Right
38234 <row interlinespace="2.5mm">
38235 <cell alignment="center" valignment="top" usebox="none">
38238 \begin_layout Plain Layout
38241 arg "math-macro-append-greedy-param"
38249 <cell alignment="center" valignment="top" usebox="none">
38252 \begin_layout Plain Layout
38255 Edit\SpecialChar menuseparator
38256 Math\SpecialChar menuseparator
38258 \begin_inset space ~
38261 Definition\SpecialChar menuseparator
38263 \begin_inset Newline newline
38267 \begin_inset Phantom HPhantom
38270 \begin_layout Plain Layout
38273 Edit\SpecialChar menuseparator
38274 Math\SpecialChar menuseparator
38276 \begin_inset space ~
38279 Definition\SpecialChar menuseparator
38285 Eating From The Right
38291 <row interlinespace="2.5mm">
38292 <cell alignment="center" valignment="top" usebox="none">
38295 \begin_layout Plain Layout
38298 arg "math-macro-add-greedy-optional-param"
38306 <cell alignment="center" valignment="top" usebox="none">
38309 \begin_layout Plain Layout
38312 Edit\SpecialChar menuseparator
38313 Math\SpecialChar menuseparator
38315 \begin_inset space ~
38318 Definition\SpecialChar menuseparator
38319 Append Optional Argument
38320 \begin_inset Newline newline
38324 \begin_inset Phantom HPhantom
38327 \begin_layout Plain Layout
38330 Edit\SpecialChar menuseparator
38331 Math\SpecialChar menuseparator
38333 \begin_inset space ~
38336 Definition\SpecialChar menuseparator
38342 Eating From The Right
38355 \begin_layout Section
38356 Computer Algebra Systems
38359 \begin_layout Standard
38361 offers the exchange between mathematical expressions written in \SpecialChar LyX
38363 editor and external applications or user defined scripts.
38364 Currently supported applications are
38381 Note that the set of supported mathematical constructs is limited only
38382 to very simple cases.
38385 \begin_layout Subsection
38389 \begin_layout Standard
38390 Write some expression in a formula, go to the
38392 Edit\SpecialChar menuseparator
38393 Math\SpecialChar menuseparator
38394 Use Computer Algebra System
38396 menu and choose the application you have installed on the computer.
38397 After that the result of computation should show on the right side of the
38398 expression together with the
38399 \begin_inset Quotes eld
38403 \begin_inset Quotes erd
38409 \begin_layout Standard
38410 Here are few simple examples (with results from
38414 ) to show what kind of computations can be performed:
38417 \begin_layout Itemize
38418 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
38424 \begin_layout Itemize
38425 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
38431 \begin_layout Itemize
38432 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
38438 \begin_layout Itemize
38439 \begin_inset Formula $\int\left(\frac{1}{1+x^{3}}\right)dx=-\frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\,x-1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log\left(x+1\right)}{3}$
38443 \begin_inset Newline newline
38447 \begin_inset Note Greyedout
38450 \begin_layout Plain Layout
38455 One needs to use proper delimiter insets
38456 \begin_inset Formula $\left(\right)$
38459 instead of simple '(' ')' characters.
38467 \begin_layout Itemize
38468 \begin_inset Formula $\det\left[\begin{array}{ccc}
38472 \end{array}\right]=-56$
38478 \begin_layout Itemize
38479 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
38485 \begin_layout Itemize
38486 \begin_inset Formula $powerseries\left(-\log\left(5-x\right),x,1\right)=\sum_{{\mathit{i}_{2}}=0}^{\infty}{\frac{4^{-{\mathit{i}_{2}}-1}\,\left(x-1\right)^{{\mathit{i}_{2}}+1}}{{\mathit{i}_{2}}+1}}-\log4$
38492 \begin_layout Itemize
38493 \begin_inset Formula $solve\left(x_{1}+y_{1}^{3}=y_{1}+x_{1}^{2},x_{1}\right)=\left[x_{1}=-\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}-1}{2},x_{1}=\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}+1}{2}\right]$
38499 \begin_layout Subsection
38503 \begin_layout Standard
38504 Currently there is no keyboard shortcut for calling the algebra applications.
38505 One can easily bind a shortcut to the
38519 \begin_inset space \thinspace{}
38523 \begin_inset space \space{}
38530 key inside the math editor.
38535 one would use this shortcut definition command:
38538 \begin_layout Standard
38541 command-alternatives paragraph-break;math-extern maxima
38544 \begin_layout Section
38546 \begin_inset Index idx
38551 \begin_layout Plain Layout
38560 \begin_layout Subsection
38562 \begin_inset Index idx
38567 \begin_layout Plain Layout
38569 \begin_inset IndexMacro subentry
38572 \begin_layout Plain Layout
38586 \begin_layout Standard
38587 Negative numbers often look ugly in formulas because the minus sign before
38588 the number is set with the same length as the minus operator sign.
38589 When writing the negative number in normal text, the minus sign appears
38593 \begin_layout Standard
38594 Thus, the problem disappears when converting the minus sign to mathematical
38598 \begin_layout Standard
38599 An example to visualize the problem:
38602 \begin_layout Standard
38604 \begin_inset Tabular
38605 <lyxtabular version="3" rows="3" columns="2">
38606 <features booktabs="true" tabularvalignment="middle">
38607 <column alignment="right" valignment="top" width="0pt">
38608 <column alignment="left" valignment="top">
38610 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
38613 \begin_layout Plain Layout
38619 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
38622 \begin_layout Plain Layout
38630 <cell alignment="right" valignment="top" leftline="true" usebox="none">
38633 \begin_layout Plain Layout
38639 <cell alignment="center" valignment="top" rightline="true" usebox="none">
38642 \begin_layout Plain Layout
38643 \begin_inset Formula $x=-2$
38653 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
38656 \begin_layout Plain Layout
38662 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
38665 \begin_layout Plain Layout
38666 \begin_inset Formula $x=\textrm{-}2$
38682 \begin_layout Subsection
38683 Comma as decimal Separator
38684 \begin_inset Index idx
38689 \begin_layout Plain Layout
38698 \begin_layout Standard
38699 In \SpecialChar LaTeX
38700 a comma inside a formula is used, according to the English convention,
38701 as number group separator.
38702 So there will be space added behind all commas in formulas.
38705 \begin_layout Standard
38706 To avoid this, the comma is highlighted and changed to mathematical text
38716 \begin_layout Standard
38717 To use all formula commas in the document as decimal separator, the file
38726 \begin_layout Plain Layout
38731 is part of the \SpecialChar LaTeX
38737 \begin_inset Index idx
38742 \begin_layout Plain Layout
38744 \begin_inset IndexMacro subentry
38747 \begin_layout Plain Layout
38764 \begin_inset Index idx
38769 \begin_layout Plain Layout
38771 \begin_inset IndexMacro subentry
38774 \begin_layout Plain Layout
38785 is loaded with the \SpecialChar LaTeX
38789 \begin_layout Standard
38797 \begin_layout Subsection
38799 \begin_inset CommandInset label
38801 name "subsec:Physical-Vectors"
38806 \begin_inset Index idx
38811 \begin_layout Plain Layout
38813 \begin_inset IndexMacro subentry
38816 \begin_layout Plain Layout
38830 \begin_layout Standard
38831 Predefined vectors are offered by the \SpecialChar LaTeX
38837 \begin_inset Index idx
38842 \begin_layout Plain Layout
38844 \begin_inset IndexMacro subentry
38847 \begin_layout Plain Layout
38858 that is loaded with the \SpecialChar LaTeX
38862 \begin_layout Standard
38870 \begin_layout Standard
38874 \begin_layout Plain Layout
38884 \begin_inset Note Note
38887 \begin_layout Plain Layout
38888 The following table will only be displayed when the \SpecialChar LaTeX
38901 \begin_layout Standard
38902 The following commands are defined:
38905 \begin_layout Standard
38907 \begin_inset Tabular
38908 <lyxtabular version="3" rows="4" columns="2">
38909 <features booktabs="true" tabularvalignment="middle">
38910 <column alignment="center" valignment="top" width="0pt">
38911 <column alignment="center" valignment="top">
38913 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
38916 \begin_layout Plain Layout
38922 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
38925 \begin_layout Plain Layout
38933 <cell alignment="center" valignment="top" usebox="none">
38936 \begin_layout Plain Layout
38946 <cell alignment="center" valignment="top" usebox="none">
38949 \begin_layout Plain Layout
38950 \begin_inset Formula $\Bra{\psi}$
38960 <cell alignment="center" valignment="top" usebox="none">
38963 \begin_layout Plain Layout
38973 <cell alignment="center" valignment="top" usebox="none">
38976 \begin_layout Plain Layout
38977 \begin_inset Formula $\Ket{\psi}$
38987 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
38990 \begin_layout Plain Layout
39002 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
39005 \begin_layout Plain Layout
39006 \begin_inset Formula $\Braket{\psi|\phi}$
39022 \begin_layout Standard
39029 assures that all vertical bars are set in the size of the surrounding brackets:
39030 \begin_inset Formula
39032 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
39041 \begin_layout Plain Layout
39051 \begin_inset Note Note
39054 \begin_layout Plain Layout
39055 The following will be displayed when the \SpecialChar LaTeX
39068 \begin_layout Standard
39069 You need to install the \SpecialChar LaTeX
39074 to see the rest of this subsection in the output.
39077 \begin_layout Standard
39081 \begin_layout Plain Layout
39093 \begin_layout Standard
39100 can also be achieved using the command
39106 , that is described in
39107 \begin_inset CommandInset ref
39109 reference "subsec:Automatic-Bracket-Size"
39116 \begin_layout Subsection
39117 Self-defined Fractions
39118 \begin_inset CommandInset label
39120 name "subsec:Self-defined-Fractions"
39125 \begin_inset Index idx
39130 \begin_layout Plain Layout
39132 \begin_inset IndexMacro subentry
39135 \begin_layout Plain Layout
39149 \begin_layout Standard
39150 To define custom commands for fractions, the command
39157 \begin_inset Index idx
39162 \begin_layout Plain Layout
39164 \begin_inset IndexMacro subentry
39167 \begin_layout Plain Layout
39174 \begin_inset IndexMacro subentry
39177 \begin_layout Plain Layout
39190 is used in the following scheme:
39193 \begin_layout Standard
39206 bracket}{fraction bar thickness}{style}
39207 \begin_inset Newline newline
39211 \begin_inset Phantom HPhantom
39214 \begin_layout Plain Layout
39224 {numerator}{denominator}
39227 \begin_layout Standard
39228 The style is a number in the range of 0
39229 \begin_inset space \thinspace{}
39233 \begin_inset space \thinspace{}
39239 \begin_layout Standard
39241 \begin_inset Tabular
39242 <lyxtabular version="3" rows="5" columns="2">
39243 <features booktabs="true" tabularvalignment="middle">
39244 <column alignment="center" valignment="top" width="0pt">
39245 <column alignment="center" valignment="top">
39247 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
39250 \begin_layout Plain Layout
39256 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
39259 \begin_layout Plain Layout
39267 <cell alignment="center" valignment="top" usebox="none">
39270 \begin_layout Plain Layout
39276 <cell alignment="center" valignment="top" usebox="none">
39279 \begin_layout Plain Layout
39280 display style formula
39287 <cell alignment="center" valignment="top" usebox="none">
39290 \begin_layout Plain Layout
39296 <cell alignment="center" valignment="top" usebox="none">
39299 \begin_layout Plain Layout
39307 <cell alignment="center" valignment="top" usebox="none">
39310 \begin_layout Plain Layout
39316 <cell alignment="center" valignment="top" usebox="none">
39319 \begin_layout Plain Layout
39327 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
39330 \begin_layout Plain Layout
39336 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
39339 \begin_layout Plain Layout
39353 \begin_layout Standard
39354 When no style is given, the size is adjusted to the surrounding environment
39355 like for the command
39364 \begin_layout Standard
39365 When no fraction bar thickness is given, the predefined value of 0.4
39366 \begin_inset space \thinspace{}
39372 \begin_layout Standard
39373 \begin_inset VSpace medskip
39376 For example, the commands
39389 \begin_inset CommandInset ref
39391 reference "subsec:Fractions"
39395 are defined with the commands
39398 \begin_layout Standard
39407 genfrac{}{}{}{0}{#1}{#2}}
39410 \begin_layout Standard
39414 \begin_layout Standard
39423 genfrac{(}{)}{0pt}{1}{#1}{#2}}
39426 \begin_layout Standard
39427 \begin_inset VSpace medskip
39430 To define a fraction where the fraction bar thickness can be given as optional
39431 argument, the following line is inserted to the \SpecialChar LaTeX
39435 \begin_layout Standard
39444 genfrac{}{}{#1}{}{#2}{#3}}
39447 \begin_layout Standard
39449 \begin_inset Formula
39451 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
39452 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
39457 As one can see, the distance of the numerator and the denominator to the
39458 fraction bar is round about three times the bar thickness.
39461 \begin_layout Subsection
39463 \begin_inset Index idx
39468 \begin_layout Plain Layout
39470 \begin_inset IndexMacro subentry
39473 \begin_layout Plain Layout
39487 \begin_layout Standard
39488 There are four ways to cancel formulas or parts of formulas:
39491 \begin_layout Standard
39495 \begin_layout Plain Layout
39505 \begin_inset Note Note
39508 \begin_layout Plain Layout
39509 The following table will only be displayed when the \SpecialChar LaTeX
39522 \begin_layout Standard
39524 \begin_inset Tabular
39525 <lyxtabular version="3" rows="5" columns="2">
39526 <features booktabs="true" tabularvalignment="middle">
39527 <column alignment="center" valignment="top" width="0pt">
39528 <column alignment="center" valignment="top">
39530 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
39533 \begin_layout Plain Layout
39539 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
39542 \begin_layout Plain Layout
39550 <cell alignment="center" valignment="top" usebox="none">
39553 \begin_layout Plain Layout
39557 \begin_inset space \textvisiblespace{}
39563 \begin_inset space \textvisiblespace{}
39571 <cell alignment="center" valignment="top" usebox="none">
39574 \begin_layout Plain Layout
39575 \begin_inset Formula $\cancel{\int A=B}$
39584 <row topspace="1.5mm">
39585 <cell alignment="center" valignment="top" usebox="none">
39588 \begin_layout Plain Layout
39592 \begin_inset space \textvisiblespace{}
39598 \begin_inset space \textvisiblespace{}
39606 <cell alignment="center" valignment="top" usebox="none">
39609 \begin_layout Plain Layout
39610 \begin_inset Formula $\bcancel{\int A=B}$
39619 <row topspace="1.5mm">
39620 <cell alignment="center" valignment="top" usebox="none">
39623 \begin_layout Plain Layout
39627 \begin_inset space \textvisiblespace{}
39633 \begin_inset space \textvisiblespace{}
39641 <cell alignment="center" valignment="top" usebox="none">
39644 \begin_layout Plain Layout
39645 \begin_inset Formula $\xcancel{\int A=B}$
39655 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
39658 \begin_layout Plain Layout
39662 \begin_inset space \textvisiblespace{}
39668 \begin_inset space \textvisiblespace{}
39672 \begin_inset Formula $\to$
39680 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
39683 \begin_layout Plain Layout
39684 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
39700 \begin_layout Standard
39707 is especially suitable to visualize the reduction of fractions within formulas:
39708 \begin_inset Formula
39710 \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}}}
39718 \begin_layout Standard
39719 To change the size of
39726 \begin_inset Quotes eld
39730 \begin_inset Quotes erd
39733 value one can add the \SpecialChar LaTeX
39737 \begin_layout Standard
39742 PassOptionsToPackage{option}{cancel}
39745 \begin_layout Standard
39754 which leads to the same size as for the canceled value, or
39758 which makes is it a bit smaller than normal.
39761 \begin_layout Standard
39762 To color the cancellation bar one adds this command as \SpecialChar TeX
39766 \begin_layout Standard
39778 \begin_layout Standard
39783 can be replaced by a color of your choice.
39786 \begin_layout Standard
39790 \begin_layout Plain Layout
39806 \begin_layout Standard
39807 \begin_inset Formula
39809 \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}}}
39817 \begin_layout Standard
39821 \begin_layout Plain Layout
39835 \begin_inset Note Note
39838 \begin_layout Plain Layout
39847 \begin_layout Standard
39848 For further customizations, see the documentation of the package
39853 \begin_inset CommandInset citation
39861 \begin_inset Index idx
39866 \begin_layout Plain Layout
39868 \begin_inset IndexMacro subentry
39871 \begin_layout Plain Layout
39885 \begin_layout Standard
39889 \begin_layout Plain Layout
39899 \begin_inset Note Note
39902 \begin_layout Plain Layout
39903 The following will be displayed when the \SpecialChar LaTeX
39916 \begin_layout Standard
39917 You need to install the \SpecialChar LaTeX
39922 to see the rest of this subsection in the output.
39925 \begin_layout Standard
39929 \begin_layout Plain Layout
39941 \begin_layout Subsection
39942 Formulas in Section Headings
39943 \begin_inset CommandInset label
39945 name "subsec:Formulas-in-Section"
39950 \begin_inset Index idx
39955 \begin_layout Plain Layout
39957 \begin_inset IndexMacro subentry
39960 \begin_layout Plain Layout
39961 in section headings
39974 \begin_layout Standard
39975 When formulas are used in section headings, the following has to be taken
39979 \begin_layout Standard
39980 \begin_inset Note Greyedout
39983 \begin_layout Plain Layout
39989 \begin_inset Index idx
39994 \begin_layout Plain Layout
39996 \begin_inset IndexMacro subentry
39999 \begin_layout Plain Layout
40010 support is enabled in the document settings dialog under
40013 \begin_inset space ~
40018 , PDF-bookmarks are created for every section heading in the table of contents.
40019 If a section heading contains formulas, they are incorrectly displayed
40020 in the bookmark text, because formulas in bookmarks infringe the PDF convention
40029 \begin_layout Standard
40030 Both problems can be solved by inserting at the end of the section heading
40031 a short title with the menu
40033 Insert\SpecialChar menuseparator
40035 \begin_inset space ~
40041 Short titles are used as alternative for multiline section headings to
40042 keep the table of contents clearly arranged.
40043 Only the short title appears in the table of contents and therefore also
40044 in the PDF-bookmark.
40047 \begin_layout Standard
40048 When formulas should be used in the table of contents but
40052 is used, one can use the following command in \SpecialChar TeX
40056 \begin_layout Standard
40061 texorpdfstring{part}{alternative}
40062 \begin_inset Index idx
40067 \begin_layout Plain Layout
40069 \begin_inset IndexMacro subentry
40072 \begin_layout Plain Layout
40079 \begin_inset IndexMacro subentry
40082 \begin_layout Plain Layout
40098 \begin_layout Standard
40099 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
40100 This can be characters, formulas, footnotes, but also cross-references.
40101 The alternative is used instead of the part for the bookmark.
40104 \begin_layout Standard
40105 Here are two example headings:
40106 \begin_inset VSpace -3mm
40113 \begin_layout Plain Layout
40125 \begin_layout Subsubsection
40126 Heading without formula in table of contents
40127 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
40131 \begin_inset Argument 1
40134 \begin_layout Plain Layout
40135 Heading without formula in table of contents
40143 \begin_layout Subsubsection
40144 Heading with formula in table of contents
40148 \begin_layout Plain Layout
40158 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
40165 \begin_layout Plain Layout
40175 \begin_layout Standard
40179 \begin_layout Plain Layout
40188 In the first heading a short title was used, in the second one
40197 \begin_layout Standard
40198 To get the same formatting as for the other headings, the complete heading
40207 \begin_layout Plain Layout
40209 \begin_inset CommandInset ref
40211 reference "subsec:Bold-Formulas"
40223 \begin_layout Subsection
40224 Formulas in multi-column Text
40225 \begin_inset Index idx
40230 \begin_layout Plain Layout
40232 \begin_inset IndexMacro subentry
40235 \begin_layout Plain Layout
40236 in multi-column text
40249 \begin_layout Standard
40250 Formulas in multi-column text are often too wide to fit into a column and
40251 thus need to be set over the whole page width.
40252 This is done by using the \SpecialChar LaTeX
40261 \begin_layout Plain Layout
40266 is part of every \SpecialChar LaTeX
40267 standard installation.
40273 \begin_inset Index idx
40278 \begin_layout Plain Layout
40280 \begin_inset IndexMacro subentry
40283 \begin_layout Plain Layout
40294 , that is loaded with the \SpecialChar LaTeX
40298 \begin_layout Standard
40303 usepackage{multicol}
40306 \begin_layout Standard
40307 \begin_inset Note Greyedout
40310 \begin_layout Plain Layout
40311 Note that in this case the setting
40314 \begin_inset space ~
40321 Document\SpecialChar menuseparator
40327 \begin_inset space ~
40347 \begin_layout Standard
40348 Before the multi-column text the command
40351 \begin_layout Standard
40356 begin{multicols}{column number}
40359 \begin_layout Standard
40360 is written in \SpecialChar TeX
40362 The column number is a number in the range of 2
40363 \begin_inset space \thinspace{}
40367 \begin_inset space \thinspace{}
40371 Before the formula the multi-column text is ended by inserting the command
40374 \begin_layout Standard
40382 \begin_layout Standard
40383 in \SpecialChar TeX
40387 \begin_layout Standard
40388 Due to the command some space is automatically added before the formula.
40389 To correct this, -6
40390 \begin_inset space \thinspace{}
40393 mm vertical space is inserted before the formula.
40394 When the formula style
40400 \begin_layout Plain Layout
40401 For formula styles see
40402 \begin_inset CommandInset ref
40404 reference "sec:Formula-Styles"
40416 \begin_inset space \thinspace{}
40419 mm space is inserted instead.
40422 \begin_layout Standard
40423 As example a multi-column text with a displayed formula:
40426 \begin_layout Standard
40432 \begin_layout Plain Layout
40436 begin{multicols}{2}
40441 Das Spektrum wird fouriertransformiert.
40442 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
40443 , Lösungsmittel) zu trennen.
40444 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
40445 nun das Aussehen des Ausgangssignals.
40446 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
40447 über alle Phasen integrieren muss.
40449 \begin_inset Formula $S$
40452 unser normiertes Ausgangssignal und
40453 \begin_inset Formula $P$
40456 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
40460 \begin_layout Plain Layout
40470 \begin_inset VSpace -6mm
40474 \begin_inset Formula
40476 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
40485 \begin_layout Plain Layout
40489 begin{multicols}{2}
40495 \begin_inset Formula $S_{0}$
40498 das Signal ohne Gradient ist und die Normierungsbedingung
40499 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
40503 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
40505 \begin_inset Formula $\nicefrac{\pi}{2}$
40509 \begin_inset space \thinspace{}
40512 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
40513 das Signal zusätzlich abschwächt.
40514 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
40516 \begin_inset Formula $T_{2}$
40522 \begin_layout Standard
40528 \begin_layout Plain Layout
40540 \begin_layout Subsection
40541 Formulas with Description of Variables
40542 \begin_inset Index idx
40547 \begin_layout Plain Layout
40549 \begin_inset IndexMacro subentry
40552 \begin_layout Plain Layout
40553 with description of variables
40566 \begin_layout Standard
40567 To describe variables within a formula, like in formula
40568 \begin_inset CommandInset ref
40570 reference "eq:within"
40579 \begin_inset Formula $n$
40583 \begin_inset space ~
40586 matrix is used with left aligned columns for the
40587 \begin_inset Formula $n$
40594 \begin_layout Plain Layout
40596 \begin_inset CommandInset ref
40598 reference "sec:Matrices"
40607 To set the description in a smaller size, before the matrix e.
40608 \begin_inset space \thinspace{}
40612 \begin_inset space \space{}
40625 \begin_layout Plain Layout
40627 \begin_inset CommandInset ref
40629 reference "subsec:Font-Sizes"
40641 \begin_layout Standard
40642 When the formula style
40648 \begin_layout Plain Layout
40649 For formula styles see
40650 \begin_inset CommandInset ref
40652 reference "sec:Formula-Styles"
40673 \begin_layout Plain Layout
40680 only works in formulas with the style
40685 \begin_inset CommandInset ref
40687 reference "subsec:Variable-Space"
40696 is inserted before and after the matrix to have the same separation of
40697 the matrix from the equation and the side margin.
40700 \begin_layout Standard
40701 When the formula style
40705 is used, the method described in
40706 \begin_inset CommandInset ref
40708 reference "subsec:Flalign-Environment"
40712 is used to indent formulas.
40714 \begin_inset CommandInset ref
40716 reference "eq:within"
40720 consists of five columns where in the first two columns contain the equation,
40721 the third the matrix and the last one an empty \SpecialChar TeX
40723 \begin_inset Formula
40725 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
40726 \rho & \textrm{density}\\
40727 V & \textrm{volume}\\
40728 g & \textrm{gravitational acceleration}
40729 \end{array} & & {}\label{eq:within}
40737 \begin_layout Subsection
40738 Upright small Greek Letters
40739 \begin_inset CommandInset label
40741 name "subsec:Upright-small-Greek"
40746 \begin_inset Index idx
40751 \begin_layout Plain Layout
40753 \begin_inset IndexMacro subentry
40756 \begin_layout Plain Layout
40770 \begin_layout Standard
40771 Most of the math fonts only provide italic small Greek letters.
40772 But for symbols of elementary particles like pions and neutrinos, upright
40773 Greek letters are needed.
40782 \begin_layout Plain Layout
40787 is part of the \SpecialChar LaTeX
40793 \begin_inset Index idx
40798 \begin_layout Plain Layout
40800 \begin_inset IndexMacro subentry
40803 \begin_layout Plain Layout
40820 \begin_inset Index idx
40825 \begin_layout Plain Layout
40827 \begin_inset IndexMacro subentry
40830 \begin_layout Plain Layout
40841 that is loaded with the \SpecialChar LaTeX
40845 \begin_layout Standard
40850 usepackage{upgreek}
40853 \begin_layout Standard
40859 \begin_layout Plain Layout
40869 \begin_inset Note Note
40872 \begin_layout Plain Layout
40873 The following table will only be displayed when the \SpecialChar LaTeX
40883 They are created when the command for a small Greek letter is started with
40889 For example the command
40896 \begin_inset Formula $\uptau$
40902 \begin_layout Standard
40903 With these commands reactions of elementary particles can be typeset:
40904 \begin_inset Formula
40906 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
40914 \begin_layout Standard
40915 The upright letters are more bold and wider than the italic ones.
40916 They should therefore not be used for units like
40917 \begin_inset Quotes eld
40921 \begin_inset Quotes erd
40927 \begin_layout Standard
40931 \begin_layout Plain Layout
40941 \begin_inset Note Note
40944 \begin_layout Plain Layout
40945 The following will be displayed when the \SpecialChar LaTeX
40958 \begin_layout Standard
40959 You need to install the \SpecialChar LaTeX
40964 to see the rest of this subsection in the output.
40967 \begin_layout Standard
40971 \begin_layout Plain Layout
40983 \begin_layout Subsection
40984 Text Characters in Formulas
40985 \begin_inset Index idx
40990 \begin_layout Plain Layout
40992 \begin_inset IndexMacro subentry
40995 \begin_layout Plain Layout
41009 \begin_layout Standard
41010 In some cases you might want to insert text characters directly into formulas.
41011 For example the centered dot · is often used in formulas like
41012 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
41016 One would have to insert the command
41026 \begin_layout Plain Layout
41028 \begin_inset CommandInset ref
41030 reference "subsec:Binary-Operators"
41039 all the time, because this character is defined in all encodings as a text
41041 But the encoding can be changed by this \SpecialChar LaTeX
41045 \begin_layout Standard
41050 Declare Inputtext{183}{
41060 f\SpecialChar ligaturebreak
41064 \begin_layout Standard
41065 The character encoding (menu
41067 Document\SpecialChar menuseparator
41068 Settings\SpecialChar menuseparator
41071 ) specifies what character appears when a keyboard key is pressed.
41072 When the key for the character '·' is pressed, internally the command
41079 But this command is not available in a formula so that you would get \SpecialChar LaTeX
41081 With the changed encoding the correct command is chosen automatically,
41082 depending on if the character was inserted into a formula or not.
41085 \begin_layout Standard
41086 The encoding of several characters is saved in definition files.
41087 For example the encoding
41091 is defined in the file
41095 which is in the installation folder of \SpecialChar LaTeX
41097 Encodings should only be changed via the \SpecialChar LaTeX
41098 -preamble and not in the definition
41100 Otherwise documents could not be edited by other \SpecialChar LyX
41101 users working on other
41105 \begin_layout Standard
41106 \begin_inset VSpace medskip
41109 Besides the centered dot, in this document the degree sign ° is defined
41110 with the following \SpecialChar LaTeX
41111 -preamble line so that it can be directly inserted into
41115 \begin_layout Standard
41120 DeclareInputtext{176}{
41130 f\SpecialChar ligaturebreak
41134 \begin_layout Subsection
41136 -comments in formulas
41137 \begin_inset Index idx
41142 \begin_layout Plain Layout
41152 \begin_layout Standard
41153 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
41155 code of your file with the menu
41157 Insert\SpecialChar menuseparator
41158 Note\SpecialChar menuseparator
41162 This is not possible in a formula but you can insert \SpecialChar LaTeX
41167 \begin_layout Standard
41175 \begin_layout Standard
41176 This creates a box in which you can write your comment.
41177 Due to a bug in \SpecialChar LyX
41182 \begin_layout Plain Layout
41183 \begin_inset CommandInset href
41185 name "LyX-bug #9002"
41186 target "https://www.lyx.org/trac/ticket/9002"
41196 you cannot write normal text inside the comment, even when you use mathematical
41197 text, you will see its \SpecialChar LaTeX
41198 -commands in the \SpecialChar LaTeX
41200 \begin_inset Newline newline
41203 This a formula with a \SpecialChar LaTeX
41205 \begin_inset Formula
41207 A=B%\text{This is the comment}
41215 \begin_layout Standard
41216 \begin_inset Newpage newpage
41222 \begin_layout Section
41225 \begin_inset Index idx
41230 \begin_layout Plain Layout
41239 \begin_layout Standard
41240 This section is a summary of the most important typographic rules, listed
41245 \begin_layout Plain Layout
41246 This collection was partly taken from the German semi-official dictionary
41248 \begin_inset Quotes eld
41252 \begin_inset Quotes erd
41256 \begin_inset CommandInset citation
41263 that lists some of the ISO rules.
41264 More rules are listed in
41265 \begin_inset CommandInset citation
41280 \begin_layout Itemize
41289 \begin_layout Plain Layout
41290 Done with font styles, see
41291 \begin_inset CommandInset ref
41293 reference "subsec:Font-Styles"
41302 , no matter if they appear in italic text: 30
41303 \begin_inset space \thinspace{}
41307 \begin_inset Newline newline
41310 Between the value and the unit is the smallest space, see
41311 \begin_inset CommandInset ref
41313 reference "subsec:Predefined-Space"
41318 \begin_inset Newline newline
41321 This convention is automatically fulfilled when the command
41328 When it is entered in a formula, two boxes appear.
41329 In the first one the value is inserted, in the second one the unit, and
41330 the result is as above:
41331 \begin_inset Formula $\unit[30]{km/h}$
41335 \begin_inset space \thinspace{}
41345 is not a real \SpecialChar LaTeX
41346 command but the command
41352 , therefore you cannot use it in \SpecialChar TeX
41356 \begin_layout Itemize
41357 Percent and perthousand signs are set like physical units:
41358 \begin_inset Newline newline
41362 \begin_inset space \thinspace{}
41368 \begin_layout Itemize
41369 The degree sign follows the value directly: 15°, except when it is used
41371 \begin_inset space \thinspace{}
41377 \begin_layout Itemize
41378 In numbers with more than four digits the smallest space is inserted before
41379 every third digit to group them:
41389 \begin_inset space \thinspace{}
41393 \begin_inset space \thinspace{}
41399 \begin_layout Itemize
41400 For dimensions like 120×90×40
41401 \begin_inset space \thinspace{}
41404 cm the multiplication sign
41405 \begin_inset Quotes eld
41409 \begin_inset Quotes erd
41413 It is available either via the command
41421 Insert\SpecialChar menuseparator
41422 Special Character\SpecialChar menuseparator
41428 \begin_layout Itemize
41429 Functions with names consisting of several letters are set upright to avoid
41431 \begin_inset CommandInset ref
41433 reference "subsec:Predefined-Functions"
41440 \begin_layout Itemize
41441 Indices consisting of several letters, are set upright:
41442 \begin_inset Formula $E_{\mathrm{kin}}$
41446 \begin_inset Newline newline
41449 Components of matrices are set italic:
41450 \begin_inset Formula $\hat{H}_{kl}$
41456 \begin_layout Itemize
41457 The differentiation/integration operator 'd', the Euler's number 'e' and
41458 the imaginary unit 'i' should be set upright, to avoid mixing them up with
41462 \begin_layout Itemize
41463 The character that denotes a
41467 transformation is inserted either by the command
41472 \begin_inset space \textvisiblespace{}
41479 Insert\SpecialChar menuseparator
41480 Special Character\SpecialChar menuseparator
41481 Symbols\SpecialChar menuseparator
41483 \begin_inset space ~
41489 \begin_inset Formula $\mathscr{F}$
41495 \begin_layout Standard
41496 \begin_inset Newpage newpage
41502 \begin_layout Section
41504 \begin_inset Index idx
41509 \begin_layout Plain Layout
41518 \begin_layout Standard
41519 Some characters and symbols can be created with several commands.
41520 Here is a list of the synonym commands:
41523 \begin_layout Standard
41524 \begin_inset VSpace bigskip
41528 \begin_inset space \hfill{}
41532 \begin_inset Tabular
41533 <lyxtabular version="3" rows="12" columns="2">
41534 <features booktabs="true" tabularvalignment="middle">
41535 <column alignment="center" valignment="top" width="0pt">
41536 <column alignment="center" valignment="top" width="0pt">
41538 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
41541 \begin_layout Plain Layout
41547 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
41550 \begin_layout Plain Layout
41558 <cell alignment="center" valignment="top" usebox="none">
41561 \begin_layout Plain Layout
41569 <cell alignment="center" valignment="top" usebox="none">
41572 \begin_layout Plain Layout
41580 <cell alignment="center" valignment="top" usebox="none">
41583 \begin_layout Plain Layout
41591 <cell alignment="center" valignment="top" usebox="none">
41594 \begin_layout Plain Layout
41604 <cell alignment="center" valignment="top" usebox="none">
41607 \begin_layout Plain Layout
41615 <cell alignment="center" valignment="top" usebox="none">
41618 \begin_layout Plain Layout
41628 <cell alignment="center" valignment="top" usebox="none">
41631 \begin_layout Plain Layout
41639 <cell alignment="center" valignment="top" usebox="none">
41642 \begin_layout Plain Layout
41650 <cell alignment="center" valignment="top" usebox="none">
41653 \begin_layout Plain Layout
41661 <cell alignment="center" valignment="top" usebox="none">
41664 \begin_layout Plain Layout
41672 <cell alignment="center" valignment="top" usebox="none">
41675 \begin_layout Plain Layout
41683 <cell alignment="center" valignment="top" usebox="none">
41686 \begin_layout Plain Layout
41696 <cell alignment="center" valignment="top" usebox="none">
41699 \begin_layout Plain Layout
41707 <cell alignment="center" valignment="top" usebox="none">
41710 \begin_layout Plain Layout
41720 <cell alignment="center" valignment="top" usebox="none">
41723 \begin_layout Plain Layout
41731 <cell alignment="center" valignment="top" usebox="none">
41734 \begin_layout Plain Layout
41744 <cell alignment="center" valignment="top" usebox="none">
41747 \begin_layout Plain Layout
41755 <cell alignment="center" valignment="top" usebox="none">
41758 \begin_layout Plain Layout
41768 <cell alignment="center" valignment="top" usebox="none">
41771 \begin_layout Plain Layout
41779 <cell alignment="center" valignment="top" usebox="none">
41782 \begin_layout Plain Layout
41790 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
41793 \begin_layout Plain Layout
41801 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
41804 \begin_layout Plain Layout
41816 \begin_inset space \hfill{}
41820 \begin_inset Tabular
41821 <lyxtabular version="3" rows="12" columns="2">
41822 <features booktabs="true" tabularvalignment="middle">
41823 <column alignment="center" valignment="top" width="0pt">
41824 <column alignment="center" valignment="top" width="0pt">
41826 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
41829 \begin_layout Plain Layout
41835 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
41838 \begin_layout Plain Layout
41846 <cell alignment="center" valignment="top" usebox="none">
41849 \begin_layout Plain Layout
41857 <cell alignment="center" valignment="top" usebox="none">
41860 \begin_layout Plain Layout
41872 <cell alignment="center" valignment="top" usebox="none">
41875 \begin_layout Plain Layout
41883 <cell alignment="center" valignment="top" usebox="none">
41886 \begin_layout Plain Layout
41896 <cell alignment="center" valignment="top" usebox="none">
41899 \begin_layout Plain Layout
41907 <cell alignment="center" valignment="top" usebox="none">
41910 \begin_layout Plain Layout
41920 <cell alignment="center" valignment="top" usebox="none">
41923 \begin_layout Plain Layout
41931 <cell alignment="center" valignment="top" usebox="none">
41934 \begin_layout Plain Layout
41942 <cell alignment="center" valignment="top" usebox="none">
41945 \begin_layout Plain Layout
41953 <cell alignment="center" valignment="top" usebox="none">
41956 \begin_layout Plain Layout
41964 <cell alignment="center" valignment="top" usebox="none">
41967 \begin_layout Plain Layout
41975 <cell alignment="center" valignment="top" usebox="none">
41978 \begin_layout Plain Layout
41988 <cell alignment="center" valignment="top" usebox="none">
41991 \begin_layout Plain Layout
41999 <cell alignment="center" valignment="top" usebox="none">
42002 \begin_layout Plain Layout
42012 <cell alignment="center" valignment="top" usebox="none">
42015 \begin_layout Plain Layout
42023 <cell alignment="center" valignment="top" usebox="none">
42026 \begin_layout Plain Layout
42036 <cell alignment="center" valignment="top" usebox="none">
42039 \begin_layout Plain Layout
42047 <cell alignment="center" valignment="top" usebox="none">
42050 \begin_layout Plain Layout
42060 <cell alignment="center" valignment="top" usebox="none">
42063 \begin_layout Plain Layout
42071 <cell alignment="center" valignment="top" usebox="none">
42074 \begin_layout Plain Layout
42084 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
42087 \begin_layout Plain Layout
42095 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
42098 \begin_layout Plain Layout
42112 \begin_inset space \hfill{}
42116 \begin_inset CommandInset href
42119 target "https://ctan.org/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
42127 \begin_layout Standard
42128 \begin_inset Newpage newpage
42134 \begin_layout Bibliography
42135 \begin_inset CommandInset bibitem
42136 LatexCommand bibitem
42150 The \SpecialChar LaTeX
42154 Addison Wesley, 2004
42157 \begin_layout Bibliography
42158 \begin_inset CommandInset bibitem
42159 LatexCommand bibitem
42166 \change_inserted 5863208 1612728717
42168 \begin_inset CommandInset href
42171 target "http://mirrors.ctan.org/obsolete/info/math/voss/mathmode/Mathmode.pdf"
42177 \change_deleted 5863208 1612728717
42179 \begin_inset CommandInset href
42182 target "https://www.tug.org/~hvoss/PDF/mathmode.pdf"
42189 of \SpecialChar LaTeX
42191 \change_deleted 5863208 1612728849
42193 \begin_inset Note Note
42196 \begin_layout Plain Layout
42198 \change_inserted 232239728 1611367909
42211 \begin_layout Bibliography
42212 \begin_inset CommandInset bibitem
42213 LatexCommand bibitem
42220 \change_inserted 5863208 1612728836
42222 \begin_inset CommandInset href
42225 target "http://tug.ctan.org/info/amslatex/english/amsldoc.pdf"
42231 \change_deleted 5863208 1612728836
42233 \begin_inset CommandInset href
42236 target "https://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/amsldoc.pdf"
42247 \begin_layout Plain Layout
42256 -\SpecialChar LaTeX
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