]> git.lyx.org Git - lyx.git/blobdiff - lib/doc/Math.lyx
Japanese Tutorial.lyx: update by Koji
[lyx.git] / lib / doc / Math.lyx
index 12046fd832e11d08b69f3148d37930902e4b2de4..674de2ea31d4aff24f0374771bb69f8c0d3471b7 100644 (file)
@@ -1,5 +1,5 @@
-#LyX 1.6.0svn created this file. For more info see http://www.lyx.org/
-\lyxformat 344
+#LyX 2.0.0svn created this file. For more info see http://www.lyx.org/
+\lyxformat 348
 \begin_document
 \begin_header
 \textclass scrartcl
@@ -13,7 +13,6 @@
 % the documentation team
 % email: lyx-docs@lists.lyx.org
 
-
 % if pdflatex is used
 \usepackage{ifpdf}
 \ifpdf
@@ -247,7 +246,7 @@ author: Uwe Stöhr
 
 
 \family sans
-Version 1.6svn
+Version 2.0.x
 \end_layout
 
 \begin_layout Standard
@@ -908,9 +907,11 @@ always
 
 \begin_layout Standard
 A protected space is inserted with 
-\family sans
-Ctrl+Space
-\family default
+\begin_inset Info
+type  "shortcut"
+arg   "space-insert protected"
+\end_inset
+
 .
 \end_layout
 
@@ -1013,7 +1014,7 @@ Available units
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="13" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -1521,7 +1522,7 @@ _
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="4" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -1805,7 +1806,7 @@ dfrac
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="4" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -2353,7 +2354,7 @@ root
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="3" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -2749,7 +2750,7 @@ brack
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="6" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -3023,7 +3024,7 @@ Case differentiations
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="3" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -3241,7 +3242,7 @@ not
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="4" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -3438,7 +3439,7 @@ When displaying e.
 \end_inset
 
 g.
-\begin_inset space ~
+\begin_inset space \space{}
 \end_inset
 
 isotopes
@@ -3465,7 +3466,7 @@ reference "sub:Chemical-Symbols-and"
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="2" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -3603,7 +3604,7 @@ phantom
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="4" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -4021,7 +4022,7 @@ Formula ! underlined
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="4" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -4242,7 +4243,10 @@ To double underline e.
 \end_inset
 
 g.
- results, one uses 
+\begin_inset space \space{}
+\end_inset
+
+results, one uses 
 \series bold
 
 \backslash
@@ -4438,7 +4442,7 @@ dots
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="8" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -5196,7 +5200,7 @@ reference "sub:Automatic-Bracket-Size"
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="4" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -5390,7 +5394,7 @@ matrix
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="4" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -5577,7 +5581,7 @@ When e.
 \end_inset
 
 g.
-\begin_inset space ~
+\begin_inset space \space{}
 \end_inset
 
 
@@ -5686,7 +5690,7 @@ arraystretch
 \end_inset
 
 g.
-\begin_inset space ~
+\begin_inset space \space{}
 \end_inset
 
 the row separation, use the factor 2.
@@ -5778,7 +5782,7 @@ Brackets ! vertical
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="9" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -6002,7 +6006,7 @@ lfloor
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="9" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -6378,7 +6382,7 @@ These commands are used to emphasize levels of brackets:
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="2" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -6633,7 +6637,7 @@ In the following table is a comparison of the variants:
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="5" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="middle" width="0">
 <column alignment="center" valignment="middle" width="0">
 <row>
@@ -7197,7 +7201,7 @@ middle
 \end_inset
 
 g.
-\begin_inset space ~
+\begin_inset space \space{}
 \end_inset
 
 needed for physical vectors:
@@ -7234,7 +7238,7 @@ Brackets ! horizontal
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="4" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -7896,7 +7900,7 @@ Arrows ! horizontal
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="8" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -8105,7 +8109,7 @@ hookleftarrow
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="8" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -8321,7 +8325,7 @@ hookrightarrow
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="6" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -8485,7 +8489,7 @@ rightleftharpoons
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="5" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -8628,7 +8632,7 @@ Arrows used as accent like e.
 \end_inset
 
 g.
-\begin_inset space ~
+\begin_inset space \space{}
 \end_inset
 
 vector arrows are listed in 
@@ -8714,7 +8718,7 @@ vspace{4mm}
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="3" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -8883,7 +8887,7 @@ Arrows ! vertical
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="7" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -9067,7 +9071,7 @@ downarrow
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="5" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -9356,7 +9360,7 @@ Accents ! for one character
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="8" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -9669,7 +9673,7 @@ A
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="7" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -9985,7 +9989,7 @@ real
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="3" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -10132,7 +10136,7 @@ in mathematical text
 \end_inset
 
 g.
-\begin_inset space ~
+\begin_inset space \space{}
 \end_inset
 
 to italic or bold.
@@ -10394,7 +10398,7 @@ Accents ! for several characters
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="5" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -10596,7 +10600,7 @@ A=B
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="5" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -10925,16 +10929,17 @@ Space ! horizontal ! predefined
 \begin_layout Standard
 Sometimes it is necessary to insert horizontal space to a formula.
  This is done by inserting a protected space (shortcut 
-\family sans
-Ctrl+Space
-\family default
+\begin_inset Info
+type  "shortcut"
+arg   "space-insert protected"
+\end_inset
+
 ).
- A blue 
+ A 
 \begin_inset Quotes eld
 \end_inset
 
 
-\series bold
 \color blue
 
 \begin_inset ERT
@@ -10950,7 +10955,6 @@ spce
 \end_inset
 
 
-\series default
 \color inherit
 
 \begin_inset Quotes erd
@@ -10986,7 +10990,7 @@ Space
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="3" columns="7">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="middle" width="6.8cm">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
@@ -11241,7 +11245,7 @@ The last size seem to produce no space.
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="3" columns="3">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="middle" width="6.8cm">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
@@ -11360,7 +11364,7 @@ Negative spaces can lead to characters overlapping each other.
 \end_inset
 
 g.
-\begin_inset space ~
+\begin_inset space \space{}
 \end_inset
 
 useful for summation operators: 
@@ -11370,7 +11374,7 @@ useful for summation operators:
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="3" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -11508,7 +11512,7 @@ Relations like for example equal signs, are always surrounded by space.
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="2" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -11628,7 +11632,7 @@ An example to visualize the difference:
 \begin_layout Standard
 \begin_inset Tabular
 <lyxtabular version="3" rows="2" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="left" valignment="top" width="0">
 <column alignment="left" valignment="top" width="0">
 <row>
@@ -11778,15 +11782,11 @@ Space ! horizontal ! variable
 \end_layout
 
 \begin_layout Standard
-Space with a defined length can be inserted in LyX with the command
-\begin_inset Newline newline
-\end_inset
-
-
+Space with a defined length can be inserted with the command 
 \series bold
 
 \backslash
-hspace{length}
+hspace
 \series default
 
 \begin_inset Index
@@ -11801,18 +11801,54 @@ hspace
 \end_inset
 
 .
- For the length all units listed in 
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "tab:Available-units"
+ Then a long 
+\begin_inset Quotes eld
+\end_inset
+
+
+\color blue
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+spce 
+\end_layout
 
 \end_inset
 
- are allowed, except of the unit 
+
+\color inherit
+
+\begin_inset Quotes erd
+\end_inset
+
+ appears.
+ The length can be specified by left-clicking on the 
 \begin_inset Quotes eld
 \end_inset
 
-mu
+
+\color blue
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+spce 
+\end_layout
+
+\end_inset
+
+
+\color inherit
+
 \begin_inset Quotes erd
 \end_inset
 
@@ -11851,7 +11887,7 @@ hfill
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="4" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -11859,7 +11895,9 @@ hfill
 \begin_inset Text
 
 \begin_layout Plain Layout
-Command
+Command (
+\backslash
+hspace length)
 \end_layout
 
 \end_inset
@@ -11881,13 +11919,30 @@ Result
 \begin_layout Plain Layout
 A=B
 \backslash
-hspace{3cm
+hspace
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+spce 
+\end_layout
+
+\end_inset
+
+
 \begin_inset Formula $\to$
 \end_inset
 
 A
 \backslash
-not=C
+not=C (3
+\begin_inset space \thinspace{}
+\end_inset
+
+cm)
 \end_layout
 
 \end_inset
@@ -11912,13 +11967,30 @@ not=C
 \begin_layout Plain Layout
 A
 \backslash
-hspace{-1mm
+hspace
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+spce 
+\end_layout
+
+\end_inset
+
+
 \begin_inset Formula $\to$
 \end_inset
 
 A
 \backslash
-not=A
+not=A (-1
+\begin_inset space \thinspace{}
+\end_inset
+
+mm)
 \end_layout
 
 \end_inset
@@ -12054,7 +12126,7 @@ Horizontal
 
 Space
 \family default
-, what is not possible in formulas:
+:
 \end_layout
 
 \begin_layout Standard
@@ -12542,7 +12614,7 @@ status open
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="5" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -13113,7 +13185,7 @@ fbox
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="4" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -13533,7 +13605,7 @@ yellow
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="4" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -14797,7 +14869,7 @@ Options
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="11" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -14827,14 +14899,14 @@ Result
 \begin_layout Plain Layout
 
 \backslash
-sum
+int
 \begin_inset Index
 status collapsed
 
 \begin_layout Plain Layout
-Commands ! S ! 
+Commands ! I ! 
 \backslash
-sum
+int
 \end_layout
 
 \end_inset
@@ -14848,7 +14920,7 @@ sum
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\sum$
+\begin_inset Formula $\int$
 \end_inset
 
 
@@ -14864,19 +14936,7 @@ sum
 \begin_layout Plain Layout
 
 \backslash
-int
-\begin_inset Index
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! I ! 
-\backslash
-int
-\end_layout
-
-\end_inset
-
-
+oint
 \end_layout
 
 \end_inset
@@ -14885,7 +14945,7 @@ int
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\int$
+\begin_inset Formula $\oint$
 \end_inset
 
 
@@ -14901,7 +14961,7 @@ int
 \begin_layout Plain Layout
 
 \backslash
-intop
+ointctrclockwise
 \end_layout
 
 \end_inset
@@ -14910,7 +14970,7 @@ intop
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\intop$
+\begin_inset Formula $\ointctrclockwise$
 \end_inset
 
 
@@ -14926,7 +14986,7 @@ intop
 \begin_layout Plain Layout
 
 \backslash
-oint
+ointclockwise
 \end_layout
 
 \end_inset
@@ -14935,7 +14995,7 @@ oint
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\oint$
+\begin_inset Formula $\ointclockwise$
 \end_inset
 
 
@@ -14951,7 +15011,7 @@ oint
 \begin_layout Plain Layout
 
 \backslash
-ointop
+sqint
 \end_layout
 
 \end_inset
@@ -14960,7 +15020,7 @@ ointop
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\ointop$
+\begin_inset Formula $\sqint$
 \end_inset
 
 
@@ -14976,7 +15036,7 @@ ointop
 \begin_layout Plain Layout
 
 \backslash
-ointctrclockwise
+fint
 \end_layout
 
 \end_inset
@@ -14985,7 +15045,8 @@ ointctrclockwise
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\ointctrclockwise$
+\begin_inset Formula $\fint$
 \end_inset
 
 
@@ -15001,7 +15062,7 @@ ointctrclockwise
 \begin_layout Plain Layout
 
 \backslash
-ointclockwise
+landupint
 \end_layout
 
 \end_inset
@@ -15010,7 +15071,8 @@ ointclockwise
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\ointclockwise$
+\begin_inset Formula $\landupint$
 \end_inset
 
 
@@ -15026,7 +15088,7 @@ ointclockwise
 \begin_layout Plain Layout
 
 \backslash
-sqint
+landdownint
 \end_layout
 
 \end_inset
@@ -15035,7 +15097,8 @@ sqint
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\sqint$
+\begin_inset Formula $\landdownint$
 \end_inset
 
 
@@ -15104,8 +15167,8 @@ bigcup
 
 
 \begin_inset Tabular
-<lyxtabular version="3" rows="10" columns="2">
-<features>
+<lyxtabular version="3" rows="11" columns="2">
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -15134,6 +15197,43 @@ Result
 
 \begin_layout Plain Layout
 
+\backslash
+sum
+\begin_inset Index
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! S ! 
+\backslash
+sum
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sum$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
 \backslash
 prod
 \begin_inset Index
@@ -15394,32 +15494,32 @@ The operators are called big because they are bigger than the sometimes
 \end_layout
 
 \begin_layout Standard
-The operators 
+For all integral operators there is a second version available, ending on
 \series bold
-
-\backslash
-intop
+op
 \series default
- and 
+: 
 \series bold
 
 \backslash
-ointop
+intop,
 \series default
- are different from 
 \series bold
 
 \backslash
-int
+ointop
 \series default
- and 
+ etc..
+ These operators are different from 
 \series bold
 
 \backslash
-oint
+int
 \series default
-, resp.
-\begin_inset space ~
+ etc.
+\begin_inset space \space{}
 \end_inset
 
 in the style the operator limits are displayed, see 
@@ -15527,7 +15627,7 @@ For multiple integrals there are the following commands:
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="4" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -15652,7 +15752,7 @@ sqiint
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="4" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -15790,7 +15890,7 @@ Limits are created by super- and subscripts:
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="2" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -15934,19 +16034,23 @@ Inline
 
 \end_inset
 
-For integrals, except of 
+For integrals, except those ending with 
+\series bold
+op
+\series default
+ like 
 \series bold
 
 \backslash
 intop
 \series default
- and 
+, 
 \series bold
 
 \backslash
 ointop
 \series default
-, the limits are by default set beside the operator.
+ etc., the limits are by default set beside the operator.
  But for multiple integrals the limits are often set below the operator.
  In the following example the limits type was therefore set to 
 \series bold
@@ -16345,7 +16449,7 @@ Binary operators are surrounded by space when there is a character before
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="13" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -16712,7 +16816,7 @@ bullet
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="13" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -17046,7 +17150,7 @@ vee
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="13" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -17647,7 +17751,7 @@ mathop
 \end_inset
 
 g.
-\begin_inset space ~
+\begin_inset space \space{}
 \end_inset
 
 be used to use one limit for several operators:
@@ -17765,7 +17869,7 @@ Latin letters in formulas can be set in one of the following font styles:
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="6" columns="3">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
@@ -18084,7 +18188,7 @@ AbC
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="5" columns="3">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
@@ -18992,7 +19096,7 @@ Alt+M
 \series default
  
 \series bold
-m 
+M 
 \backslash
 tiny
 \begin_inset ERT
@@ -19091,7 +19195,7 @@ Greek letters ! small
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="11" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -19375,7 +19479,7 @@ vartheta
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="12" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -19682,7 +19786,7 @@ rho
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="11" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -20005,7 +20109,7 @@ Greek letters ! big
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="7" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -20189,7 +20293,7 @@ Pi
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="6" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -20413,7 +20517,7 @@ boldsymbol
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="3" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -20628,7 +20732,7 @@ Symbols ! mathematical
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="10" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -20887,7 +20991,7 @@ jmath
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="10" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -21186,7 +21290,7 @@ Bbbk
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="10" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -21471,7 +21575,7 @@ Symbols ! miscellaneous
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="10" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="10" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -21977,7 +22081,7 @@ bullet
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="10" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -22421,7 +22525,7 @@ An overview about the different Euro symbols:
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="4" columns="3">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
@@ -22695,7 +22799,7 @@ All relations can also be inserted via the toolbar button
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="17" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -23127,7 +23231,7 @@ nmid
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="17" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -23559,7 +23663,7 @@ widehat=
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="17" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -24052,7 +24156,7 @@ stackrel
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="2" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -24233,7 +24337,7 @@ italic
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="2" columns="4">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
@@ -24344,7 +24448,7 @@ The following functions are predefined:
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="9" columns="4">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
@@ -24899,7 +25003,7 @@ In LyX self-defined functions are displayed red, predefined ones black.
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="3" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -24955,7 +25059,7 @@ sgn(x)+B
 A
 \backslash
 ,
-\begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
+\begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
 \end_inset
 
 (x)+B
@@ -25040,7 +25144,7 @@ limsup
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="5" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -25202,7 +25306,7 @@ The limit is created by inserting a subscript.
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="2" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -25387,7 +25491,7 @@ The following commands can only be used in mathematical text or in TeX-mode:
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="8" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="block" valignment="top" width="0">
 <column alignment="block" valignment="top" width="0">
 <row>
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="8" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="block" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -25955,7 +26059,7 @@ With the following commands all letters can be accented.
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="8" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="block" valignment="top" width="0">
 <column alignment="block" valignment="top" width="0">
 <row>
@@ -26283,7 +26387,7 @@ t ee
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="8" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="block" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -26793,7 +26897,7 @@ textcircled
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="3" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -27072,7 +27176,7 @@ The following characters can only be inserted to formulas by using commands:
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="4" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -27964,43 +28068,13 @@ Long formulas can be typeset using these methods:
 \begin_layout Itemize
 When one side of the equation is much shorther than the line width, this
  one is chosen for the left side and the right side is typeset over two
- lines:
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-medskip
-\end_layout
-
-\end_inset
-
+ lines: 
 \begin_inset Formula \begin{eqnarray}
 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 \\
- &  & -\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:kurzlang}\end{eqnarray}
-
-\end_inset
-
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-smallskip
-\end_layout
+ &  & -\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}\end{eqnarray}
 
 \end_inset
 
-
-\begin_inset Newline newline
-\end_inset
-
 The minus sign at the beginning of the second line does normally not appear
  as operator because it is the first character of the line.
  Thus it would not be surrounded by space and could not be distinguished
@@ -28072,19 +28146,6 @@ lefteqn
  is used.
  It is inserted to the first column of the first line and effects that all
  further insertions overwrite the following columns:
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-medskip
-\end_layout
-
-\end_inset
-
-
 \begin_inset Formula \begin{eqnarray}
 \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 \\
  &  & -\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 \\
@@ -28092,23 +28153,6 @@ medskip
 
 \end_inset
 
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-smallskip
-\end_layout
-
-\end_inset
-
-
-\begin_inset Newline newline
-\end_inset
-
 After the insertion of 
 \series bold
 
@@ -28118,35 +28162,13 @@ lefteqn
 , the cursor is in a purple box that is a bit shifted to the left from the
  blue one.
  In this the formula is inserted.
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-medskip
-\end_layout
-
-\end_inset
-
-
 \begin_inset Newline newline
 \end_inset
 
 The content of the further lines is inserted to the second or another formula
  column.
  The greater the column number where it was inserted, the larger the indentation.
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-medskip
-\end_layout
-
+\begin_inset VSpace medskip
 \end_inset
 
 
@@ -28174,7 +28196,7 @@ The formula doesn't use the full page width.
 \end_inset
 
 g.
-\begin_inset space ~
+\begin_inset space \space{}
 \end_inset
 
 the term 
@@ -29084,7 +29106,7 @@ The aligned environment is also suitable for long formulas whose lines are
  As example formula 
 \begin_inset CommandInset ref
 LatexCommand eqref
-reference "eq:kurzlang"
+reference "eq:shortlong"
 
 \end_inset
 
@@ -29445,7 +29467,7 @@ equation
 \end_inset
 
 g.
-\begin_inset space ~
+\begin_inset space \space{}
 \end_inset
 
 section labels.
@@ -30434,7 +30456,7 @@ To number e.
 \end_inset
 
 g.
-\begin_inset space ~
+\begin_inset space \space{}
 \end_inset
 
 tables so that the number of the part is the sectioning,
@@ -30635,7 +30657,7 @@ theequation
 \backslash
 roman{equation}
 \series default
-
+.
 \begin_inset Foot
 status collapsed
 
@@ -30655,7 +30677,7 @@ newcommand
  that is described in 
 \begin_inset CommandInset ref
 LatexCommand ref
-reference "sec:User-defined-Commands"
+reference "sub:The-Command-newcommand"
 
 \end_inset
 
@@ -30664,7 +30686,6 @@ reference "sec:User-defined-Commands"
 
 \end_inset
 
-.
  
 \series bold
 equation
@@ -30991,13 +31012,6 @@ target "Formula-numbering.lyx"
 
 \begin_layout Section
 User-defined Commands
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:User-defined-Commands"
-
-\end_inset
-
-
 \begin_inset Index
 status collapsed
 
@@ -31011,13 +31025,45 @@ User-defined commands
 \end_layout
 
 \begin_layout Standard
-Many LaTeX-commands are too long to be used frequently.
- But it is possible to define with the command 
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
 \series bold
+Note:
+\series default
+ The names of user-defined commands and macros may only consist of Latin
+ letters.
+\end_layout
+
+\end_inset
 
+
+\end_layout
+
+\begin_layout Subsection
+The Command 
 \backslash
 newcommand
-\series default
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:The-Command-newcommand"
+
+\end_inset
+
+
+\begin_inset Index
+status collapsed
+
+\begin_layout Plain Layout
+User-defined commands ! 
+\backslash
+newcommand
+\end_layout
+
+\end_inset
+
 
 \begin_inset Index
 status collapsed
@@ -31030,6 +31076,17 @@ newcommand
 
 \end_inset
 
+
+\end_layout
+
+\begin_layout Standard
+Many LaTeX-commands are too long to be used frequently.
+ But it is possible to define with the command 
+\series bold
+
+\backslash
+newcommand
+\series default
  new shorter commands.
 \end_layout
 
 \end_inset
 
 
-\end_layout
-
-\begin_layout Standard
-\begin_inset Note Greyedout
-status open
-
-\begin_layout Plain Layout
-
-\series bold
-Note:
-\series default
- The names of user-defined commands may only consist of Latin letters.
-\end_layout
-
-\end_inset
-
-
 \end_layout
 
 \begin_layout Standard
 Longrightarrow
 \series default
 , the LaTeX-preamble line is:
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-medskip
-\end_layout
-
+\begin_inset VSpace medskip
 \end_inset
 
 
-\series bold
-
 \begin_inset Newline newline
 \end_inset
 
 
+\series bold
+
 \backslash
 newcommand{
 \backslash
@@ -31233,25 +31264,16 @@ underline
 \series default
 , the argument (that should be underlined) must be taken into account.
  For this the preamble line is:
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-medskip
-\end_layout
-
+\begin_inset VSpace medskip
 \end_inset
 
 
-\series bold
-
 \begin_inset Newline newline
 \end_inset
 
 
+\series bold
+
 \backslash
 newcommand{
 \backslash
@@ -31260,26 +31282,13 @@ us}[1]{
 underline{#1}}
 \series default
 
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-medskip
-\end_layout
-
+\begin_inset VSpace medskip
 \end_inset
 
 
-\series bold
-
 \begin_inset Newline newline
 \end_inset
 
-
-\series default
 The character 
 \series bold
 #
@@ -31303,7 +31312,7 @@ framebox
 \end_inset
 
 g.
-\begin_inset space ~
+\begin_inset space \space{}
 \end_inset
 
 define the command 
@@ -31313,25 +31322,16 @@ define the command
 fb
 \series default
 :
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-medskip
-\end_layout
-
+\begin_inset VSpace medskip
 \end_inset
 
 
-\series bold
-
 \begin_inset Newline newline
 \end_inset
 
 
+\series bold
+
 \backslash
 newcommand{
 \backslash
@@ -31340,26 +31340,13 @@ fb}[3]{
 framebox#1#2{$#3$}}
 \series default
 
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-medskip
-\end_layout
-
+\begin_inset VSpace medskip
 \end_inset
 
 
-\series bold
-
 \begin_inset Newline newline
 \end_inset
 
-
-\series default
 The two Dollar signs creates the extra formula needed for 
 \series bold
 
@@ -31385,25 +31372,16 @@ fcolorbox
 \series default
  where the color for the box needn't to be specified, the argument for the
  color is defined optional:
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-medskip
-\end_layout
-
+\begin_inset VSpace medskip
 \end_inset
 
 
-\series bold
-
 \begin_inset Newline newline
 \end_inset
 
 
+\series bold
+
 \backslash
 newcommand{
 \backslash
@@ -31412,16 +31390,7 @@ cb}[3][white]{
 fcolorbox{#2}{#1}{$#3$}}
 \series default
 
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-medskip
-\end_layout
-
+\begin_inset VSpace medskip
 \end_inset
 
 
@@ -31449,7 +31418,7 @@ A test of the new defined commands:
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="6" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
 \end_inset
 
 
+\end_layout
+
+\begin_layout Subsection
+Math Macros
+\begin_inset Index
+status collapsed
+
+\begin_layout Plain Layout
+User-defined commands! Math macros
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index
+status collapsed
+
+\begin_layout Plain Layout
+Macros
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+User-defined commands are especially convenient for complex expressions.
+ When you are for example dealing in a document with quadratic equations,
+ the same solution type occurs several times.
+ The general form of a quadratic equation is
+\begin_inset Formula \[
+0=\lambda^{2}+p\lambda+q\]
+
+\end_inset
+
+The general form of the solution is
+\begin_inset Formula \[
+\lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To define a command for the solution formula where only the three parameters
+\begin_inset Formula $\lambda$
+\end_inset
+
+, 
+\begin_inset Formula $p$
+\end_inset
+
+, and 
+\begin_inset Formula $q$
+\end_inset
+
+ need to be specified and the index of 
+\begin_inset Formula $\lambda$
+\end_inset
+
+ can be given optionally, the LaTeX-preamble line is
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+qG}[4][1,
+\backslash
+,2]{#2_{#1}=-
+\backslash
+frac{#3}{2}
+\backslash
+pm
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+hphantom{
+\end_layout
+
+\end_inset
+
+
+\backslash
+newcommand
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+
+\backslash
+sqrt{
+\backslash
+frac{#3^{2}}{4}-#4}}
+\end_layout
+
+\begin_layout Standard
+To create with this the solution formula, the command
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+
+\backslash
+qG{
+\backslash
+lambda
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{p
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{q
+\series default
+ is inserted to a formula
+\series bold
+.
+\end_layout
+
+\begin_layout Standard
+The definition of the new command is unintuitive because one has to know
+ the schemes of all used LaTeX commands, e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+that a fraction is inserted in LaTeX as 
+\series bold
+
+\backslash
+frac{numerator}{denominator}
+\series default
+.
+ Furthermore one can easily forget a brace in the definition and cannot
+ see in LyX what the new command is doing.
+ To avoid these problems LyX offers the possibility to use math macros instead
+ of the command 
+\series bold
+
+\backslash
+newcommand
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+A math macro is created by using the menu 
+\family sans
+Insert\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\family default
+ or the toolbar button 
+\begin_inset Graphics
+       filename ../images/math-macro_newmacroname_newcommand.png
+       scale 85
+
+\end_inset
+
+.
+ The math macro toolbar appears together with the following box where the
+ macro is defined:
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset space \hspace*{\fill}
+\end_inset
+
+
+\begin_inset Graphics
+       filename clipart/macrobox.png
+       lyxscale 90
+       scale 90
+
+\end_inset
+
+
+\begin_inset space \hspace*{\fill}
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset FormulaMacro
+\newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
+\end_inset
+
+
+\backslash
+newmacroname is the default name of the macro that should be changed to
+ something sensible.
+ The wanted formula is inserted in the first blue box.
+ An argument placeholder is inserted with the command 
+\series bold
+
+\backslash
+#argumentnumber
+\series default
+, e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g
+\begin_inset space \space{}
+\end_inset
+
+
+\series bold
+
+\backslash
+#1
+\series default
+ or by using the macro toolbar button 
+\begin_inset Graphics
+       filename ../images/math-macro-add-param.png
+       scale 85
+
+\end_inset
+
+.
+ Argument placeholders are displayed red.
+ Maximum 9 arguments are possible.
+ Optional arguments are created with the toolbar button 
+\begin_inset Graphics
+       filename ../images/math-macro-add-optional-param.png
+       scale 85
+
+\end_inset
+
+.
+ The first non-optional argument can be transformed to an optional one with
+ the toolbar button 
+\begin_inset Graphics
+       filename ../images/math-macro-make-optional.png
+       scale 85
+
+\end_inset
+
+.
+ In the second blue box the appearance of the macro in LyX can be defined.
+ Normally you want to see it as it is defined, so the box is kept empty.
+ But when you have created a macro that needs lot of space on the screen,
+ you can insert in the box for example
+\begin_inset Newline newline
+\end_inset
+
+
+\series bold
+qG: 
+\backslash
+#1
+\series default
+\series bold
+,
+\series default
+\series bold
+
+\backslash
+#2
+\series default
+\series bold
+,
+\series default
+\series bold
+
+\backslash
+#3, 
+\backslash
+#4
+\begin_inset Newline newline
+\end_inset
+
+
+\series default
+For the macro only the arguments with the macro name in front of them will
+ then be displayed in LyX, leading to a better overview.
+ The formula appears in the output as defined in the first box.
+\begin_inset Newline newline
+\end_inset
+
+The appearance of macros in formulas can furthermore be changed for single
+ macros by setting the cursor in the macro and using the menu 
+\family sans
+View\SpecialChar \menuseparator
+(Un)fold
+\begin_inset space ~
+\end_inset
+
+Math
+\begin_inset space ~
+\end_inset
+
+Macro
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+To use a macro, the macro name is inserted as command to a formula, in our
+ case 
+\series bold
+
+\backslash
+qG
+\series default
+.
+ Our macro looks in LyX like this:
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset space \hspace*{\fill}
+\end_inset
+
+
+\begin_inset Graphics
+       filename clipart/macrouse.png
+       lyxscale 75
+       scale 75
+
+\end_inset
+
+
+\begin_inset space \hspace*{\fill}
+\end_inset
+
+
+\begin_inset Newline newline
+\end_inset
+
+Here is our macro example with the arguments 
+\begin_inset Formula $x$
+\end_inset
+
+, 
+\begin_inset Formula $\ln(x)$
+\end_inset
+
+, and 
+\begin_inset Formula $B$
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+\qG x{\ln(x)}B\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+A math macro is transformed internally to a 
+\series bold
+
+\backslash
+newcommand
+\series default
+ command when exporting the document.
+ The created 
+\series bold
+
+\backslash
+newcommand
+\series default
+ command is not placed in the LaTeX-preamble, therefore macros can only
+ be used in formulas that are in the document below the macro definition
+ box.
+\end_layout
+
+\begin_layout Standard
+Math macros can also be directly be created from a 
+\series bold
+
+\backslash
+newcommand
+\series default
+ command.
+ When writing for example the command
+\series bold
+
+\begin_inset Newline newline
+\end_inset
+
+
+\backslash
+newcommand{
+\backslash
+larrow}[2]{
+\backslash
+xleftarrow[#2]{#1}}
+\begin_inset Newline newline
+\end_inset
+
+
+\series default
+in LyX as normal text, highlighting it completely and using then the shortcut
+\family sans
+Ctrl+M
+\family default
+, the command will be transformed to a math macro.
+ Using this method you need to be careful that the 
+\series bold
+
+\backslash
+newcommand
+\series default
+ command is typed correctly, otherwise you get a faulty macro leading to
+ LaTeX errors.
+\end_layout
+
+\begin_layout Standard
+Math macros currently yet have the problem that further formulas in macro
+ definitions are handled wrongly.
+ Therefore the example 
+\series bold
+
+\backslash
+fb
+\series default
+ from 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:The-Command-newcommand"
+
+\end_inset
+
+ cannot be created as macro.
+\end_layout
+
+\begin_layout Standard
+When the cursor is in a macro definition box, you will see the macro toolbar
+ in LyX:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace defskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Graphics
+       filename clipart/MacroToolbar.png
+
+\end_inset
+
+
+\begin_inset Index
+status collapsed
+
+\begin_layout Plain Layout
+Macros ! Toolbar
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace defskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The macro toolbar contains from left to right the following buttons:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace defskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="9" columns="2">
+<features islongtable="true" tabularvalignment="middle">
+<column alignment="left" valignment="top" width="0">
+<column alignment="left" valignment="top" width="85col%">
+<row interlinespace="2.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+       filename ../images/math-macro-remove-param.png
+       BoundingBox 0bp 5bp 20bp 25bp
+       rotateOrigin center
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+Remove Argument
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row interlinespace="2.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+       filename ../images/math-macro-add-param.png
+       BoundingBox 0bp 5bp 20bp 25bp
+       rotateOrigin center
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+Append Last Argument
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row interlinespace="2.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+       filename ../images/math-macro-make-optional.png
+       BoundingBox 0bp 5bp 20bp 25bp
+       rotateOrigin center
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+Make First Non-Optional into
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+hphantom{
+\end_layout
+
+\end_inset
+
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+Optional Argument
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row interlinespace="2.5mm">
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+       filename ../images/math-macro-make-nonoptional.png
+       BoundingBox 0bp 5bp 20bp 25bp
+       rotateOrigin center
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
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+
+Definition\SpecialChar \menuseparator
+Make Last Optional into
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+
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+
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+
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+
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+\begin_inset space ~
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+
+Definition\SpecialChar \menuseparator
+
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+status collapsed
+
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+}
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+
+\end_inset
+
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+
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+
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+
+Definition\SpecialChar \menuseparator
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+\end_layout
+
+\end_inset
+</cell>
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+<cell alignment="center" valignment="top" usebox="none">
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+       filename ../images/math-macro-add-optional-param.png
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+       rotateOrigin center
+
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+
+
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+
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+<cell alignment="center" valignment="top" usebox="none">
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+
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+
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+<cell alignment="center" valignment="top" usebox="none">
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+
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+
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+
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+Spitting Out To The Right
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+
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+       filename ../images/math-macro-append-greedy-param.png
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+
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+
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+\begin_inset space ~
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+
+Definition\SpecialChar \menuseparator
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+
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+\begin_layout Plain Layout
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+Edit\SpecialChar \menuseparator
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+Eating From The Right
+\end_layout
+
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+
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+
+
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+
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+</cell>
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+
+\begin_layout Plain Layout
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Macro
+\begin_inset space ~
+\end_inset
+
+Definition\SpecialChar \menuseparator
+Append Optional Argument
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
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+
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+
+Edit\SpecialChar \menuseparator
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+
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+\begin_inset ERT
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+
+}
+\end_layout
+
+\end_inset
+
+Eating From The Right
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
 \end_layout
 
 \begin_layout Section
@@ -32021,13 +33027,24 @@ reference "sec:Matrices"
 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
  and much more.
  All possibilities to create commutative diagrams and decorations are explained
- in detail in this manual: 
-\begin_inset CommandInset href
-LatexCommand href
-target "http://wiki.lyx.org/LyX/XY-pic#xy-manual"
+ in detail in the 
+\emph on
+XY-pic manual
+\emph default
+ that you find in the menu 
+\family sans
+Help\SpecialChar \menuseparator
+Specific
+\begin_inset space ~
+\end_inset
 
+Manuals\SpecialChar \menuseparator
+XY-pic
+\begin_inset space ~
 \end_inset
 
+Manual
+\family default
 .
 \end_layout
 
@@ -32285,7 +33302,7 @@ An example to visualize the problem:
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="3" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="right" valignment="top" width="0">
 <column alignment="left" valignment="top" width="0">
 <row>
@@ -32555,7 +33572,7 @@ The following commands are defined:
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="4" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -32863,7 +33880,7 @@ The style is a number in the range of 0
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="5" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -33140,7 +34157,7 @@ There are four ways to cancel formulas:
 \align center
 \begin_inset Tabular
 <lyxtabular version="3" rows="5" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
 <row>
@@ -33830,7 +34847,7 @@ end{multicols}
 
 
 \begin_inset Formula \begin{equation}
-S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
+S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
 
 \end_inset
 
@@ -33951,7 +34968,7 @@ reference "sec:Matrices"
 \end_inset
 
 g.
-\begin_inset space ~
+\begin_inset space \space{}
 \end_inset
 
 the command 
@@ -34693,7 +35710,7 @@ Some characters and symbols can be created with several commands.
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="12" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>
@@ -35020,7 +36037,7 @@ vert
 
 \begin_inset Tabular
 <lyxtabular version="3" rows="12" columns="2">
-<features>
+<features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
 <row>