+Formulas | see
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+{
+\end_layout
+
+\end_inset
+
+Math
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "chap:Mathematical-Formulas"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The issues of this chapter are described in detail in the
+\emph on
+Math
+\emph default
+ manual.
+ There you will also find tips and tricks for special cases.
+\end_layout
+
+\begin_layout Section
+Basic Math Editing
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Basics
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To create a math formula, you can just click on the toolbar icon
+\begin_inset Info
+type "icon"
+arg "math-mode on"
+\end_inset
+
+ (shortcut
+\begin_inset Info
+type "shortcut"
+arg "math-mode"
+\end_inset
+
+).
+ That will create a little blue rectangle, with purple markers around its
+ corners.
+ That blue rectangle is the formula itself; the purple markers indicate
+ what level of nesting within the formula you are at.
+ You can also choose a particular formula type to insert via the
+\family sans
+Insert\SpecialChar menuseparator
+Math
+\family default
+ menu.
+\end_layout
+
+\begin_layout Standard
+Editing the parameters of a formula and adding math constructs can be done
+ with the
+\family sans
+math
+\begin_inset space ~
+\end_inset
+
+toolbar
+\family default
+, that appears if the cursor is in a formula.
+\end_layout
+
+\begin_layout Standard
+There are two main types of formulas, inline formulas and display formulas.
+ Inline formulas appear within a text line, like this one:
+\end_layout
+
+\begin_layout Standard
+This is a line with an inline formula
+\begin_inset Formula $A=B$
+\end_inset
+
+ in it.
+\end_layout
+
+\begin_layout Standard
+Displayed formulas appear outside the text like if they were in a separate
+ paragraph, like this one:
+\begin_inset Formula
+\[
+A=B
+\]
+
+\end_inset
+
+You can only number and reference displayed formulas.
+\end_layout
+
+\begin_layout Standard
+\SpecialChar LyX
+ also supports many \SpecialChar LaTeX
+ math commands.
+ For example, typing
+\begin_inset Quotes eld
+\end_inset
+
+
+\series bold
+
+\backslash
+alpha
+\series default
+
+\begin_inset Quotes erd
+\end_inset
+
+, followed by a space, in a formula will create the Greek letter
+\begin_inset Formula $\alpha$
+\end_inset
+
+.
+ Typing commands might sometimes be faster than using the
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Panel
+\family default
+.
+\end_layout
+
+\begin_layout Subsection
+Navigating in Formulas
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Navigating
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The best control over the cursor position within an existing formula is
+ achieved with the arrow keys.
+ \SpecialChar LyX
+ uses small rectangles to indicate places where something can be inserted.
+ The arrow keys can be used to navigate between parts of a formula.
+ Pressing
+\family sans
+Space
+\family default
+ will leave a formula construct (a square root
+\begin_inset Formula $\sqrt{2}$
+\end_inset
+
+, or parentheses
+\begin_inset Formula $\left(f\right)$
+\end_inset
+
+, or a matrix
+\begin_inset Formula $\left[\begin{array}{cc}
+1 & 2\\
+3 & 4
+\end{array}\right]$
+\end_inset
+
+).
+ Pressing
+\family sans
+Escape
+\family default
+ will leave the formula, placing the cursor after the formula.
+
+\family sans
+Tab
+\family default
+ can be used to move horizontally in a formula; for example, through the
+ cells of a matrix or the positions in a multi-line equation.
+\end_layout
+
+\begin_layout Standard
+
+\family sans
+Space
+\family default
+, printed in this document as
+\begin_inset Quotes eld
+\end_inset
+
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset Quotes erd
+\end_inset
+
+, seems to do nothing in a formula, since it does not add a space between
+ characters, but it does exit a nested structure.
+ For this reason, you have to be careful about using
+\family sans
+Space
+\family default
+.
+ For example, if you want
+\begin_inset Formula $\sqrt{2x+1}$
+\end_inset
+
+, type
+\series bold
+
+\backslash
+sqrt
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2x+1
+\series default
+ and not
+\series bold
+
+\backslash
+sqrt
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+2x
+\begin_inset space \textvisiblespace{}
+\end_inset
+
++1
+\series default
+, since in the latter case only the
+\family typewriter
+
+\begin_inset Formula $2x$
+\end_inset
+
+
+\family default
+ will be under the square root sign:
+\begin_inset Formula $\sqrt{2x}+1$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+You can leave many parts of a formula, like this matrix, partially filled
+ in, such as:
+\begin_inset Formula
+\[
+\left(\begin{array}{ccc}
+\lambda_{1}\\
+ & \ddots\\
+ & & \lambda_{n}
+\end{array}\right)
+\]
+
+\end_inset
+
+If you leave a fraction only partially filled in, or a subscript with nothing
+ in it, the results will be unpredictable, but most constructs don't mind.
+\end_layout
+
+\begin_layout Subsection
+Selecting Text
+\end_layout
+
+\begin_layout Standard
+You can select text within a formula in two different ways.
+ Place the cursor at one end of the string of text you want, and press
+\family sans
+Shift
+\family default
+ and a cursor movement key to select text.
+ It will be highlighted as with regular text selection.
+ Alternatively, you can select text with the mouse in the usual way.
+ That text can then be cut or copied, and then pasted within any formula,
+ but not in a normal text region in \SpecialChar LyX
+.
+\end_layout
+
+\begin_layout Subsection
+Exponents and Subscripts
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Exponents
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Subscripts
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You can use the math panel to add super- or subscripts (buttons
+\begin_inset Info
+type "icon"
+arg "math-superscript"
+\end_inset
+
+ and
+\begin_inset Info
+type "icon"
+arg "math-subscript"
+\end_inset
+
+), but it is often much easier to use a command.
+ To get
+\begin_inset Formula $x^{2}$
+\end_inset
+
+, type in a formula
+\series bold
+x^2
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+.
+ The final
+\family sans
+Space
+\family default
+ puts the cursor back down on the base line of the expression.
+ If you type
+\series bold
+x^2y
+\series default
+, you will get
+\begin_inset Formula $x^{2y}$
+\end_inset
+
+, to get
+\begin_inset Formula $x^{2}y$
+\end_inset
+
+, type
+\series bold
+x^2
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+y
+\series default
+.
+ If you use characters in the superscript, that could be accented with the
+ circumflex
+\begin_inset Quotes eld
+\end_inset
+
+^
+\begin_inset Quotes erd
+\end_inset
+
+, you have to use an extra
+\family sans
+Space
+\family default
+ to separate the circumflex and the character.
+ For example, if you want
+\begin_inset Formula $x^{a}$
+\end_inset
+
+, type
+\series bold
+x^
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+a
+\series default
+.
+ Subscripts are similar: To get
+\begin_inset Formula $a_{1}$
+\end_inset
+
+, type
+\series bold
+a_1
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\series default
+.
+\end_layout
+
+\begin_layout Subsection
+Fractions
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Fractions
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Create a fraction either with the command
+\series bold
+
+\backslash
+frac
+\series default
+ or by using the icon
+\begin_inset Info
+type "icon"
+arg "math-insert \\frac"
+\end_inset
+
+ in the
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Panel
+\family default
+.
+ You will be presented with an empty fraction.
+ The cursor is above the fraction line.
+ To move it to the bottom, simply press
+\family sans
+Down
+\family default
+.
+ To move back up, press
+\family sans
+Up
+\family default
+.
+ Any math structure can be placed in a fraction, as this example shows:
+\begin_inset Formula
+\[
+\left[\frac{1}{\left(\begin{array}{cc}
+2 & 3\\
+4 & 5
+\end{array}\right)}\right]
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Roots
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Roots
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Roots can be created using the
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Panel
+\family default
+ buttons
+\begin_inset Info
+type "icon"
+arg "math-insert \\sqrt"
+\end_inset
+
+ or
+\begin_inset Info
+type "icon"
+arg "math-insert \\root"
+\end_inset
+
+ or the commands
+\series bold
+
+\backslash
+sqrt
+\series default
+ or
+\series bold
+
+\backslash
+root
+\series default
+.
+ With the command
+\series bold
+
+\backslash
+root
+\series default
+ you can produce roots of higher orders, like cube roots, while
+\series bold
+
+\backslash
+sqrt
+\series default
+ always produces a square root.
+\end_layout
+
+\begin_layout Subsection
+Operators with Limits
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Sums
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Integrals
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Operators-with-Limits"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Sum (
+\begin_inset Formula $\sum$
+\end_inset
+
+) and integral (
+\begin_inset Formula $\int$
+\end_inset
+
+) operators are very often decorated with limits.
+ These limits can be entered in \SpecialChar LyX
+ by entering them as you would enter a super-
+ or subscript, directly after the symbol.
+ The sum operator will automatically place its
+\begin_inset Quotes eld
+\end_inset
+
+limits
+\begin_inset Quotes erd
+\end_inset
+
+ over and under the symbol in displayed formulas, and to the side in inline
+ formulas, as in
+\begin_inset Formula $\sum_{n=0}^{\infty}\frac{1}{n!}=e$
+\end_inset
+
+, versus
+\begin_inset Formula
+\[
+\sum_{n=0}^{\infty}\frac{1}{n!}=e
+\]
+
+\end_inset
+
+Integral signs, however, will place the limits to the side in both formula
+ types.
+\end_layout
+
+\begin_layout Standard
+All operators with limits will be automatically re-sized when placed in
+ display mode.
+ The placement of the limits can be changed by placing the cursor directly
+ behind the operator and using the menu
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Change
+\begin_inset space ~
+\end_inset
+
+Limits
+\begin_inset space ~
+\end_inset
+
+Type
+\family default
+ or entering
+\begin_inset Info
+type "shortcut"
+arg "math-limits"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Certain other mathematical expressions also have this
+\begin_inset Quotes eld
+\end_inset
+
+moving limits
+\begin_inset Quotes erd
+\end_inset
+
+ feature, such as
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Limits
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\[
+\lim_{x\rightarrow\infty}f(x),
+\]
+
+\end_inset
+
+which will place the
+\begin_inset Formula $x\rightarrow\infty$
+\end_inset
+
+ underneath the
+\begin_inset Quotes eld
+\end_inset
+
+lim
+\begin_inset Quotes erd
+\end_inset
+
+ in display mode.
+ In inline formulas it looks like this:
+\begin_inset Formula $\lim_{x\rightarrow\infty}f(x)$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Note that the lim-function was entered as the function macro
+\series bold
+
+\backslash
+lim
+\series default
+.
+ Have a look at section
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Functions"
+
+\end_inset
+
+ for an explanation of function macros.
+\end_layout
+
+\begin_layout Subsection
+Math Symbols
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Symbols
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Most math symbols can be found in the
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Panel
+\family default
+ under one of several categories; including
+\family sans
+Greek
+\family default
+,
+\family sans
+Operators
+\family default
+,
+\family sans
+Relations
+\family default
+,
+\family sans
+Arrows
+\family default
+.
+ There are also the additional symbols provided by the American Mathematical
+ Society (AMS).
+\end_layout
+
+\begin_layout Standard
+If you know the \SpecialChar LaTeX
+-command for a construct or symbol you wish to use, you
+ don't have to use the
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Panel
+\family default
+; you can type the command directly into the formula.
+ \SpecialChar LyX
+ will convert it to the corresponding symbol or construct.
+\end_layout
+
+\begin_layout Subsection
+Altering Spacing
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Spaces
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You may want to create spaces that differ from the standard spacing that
+ \SpecialChar LaTeX
+ provides.
+ To do this, press
+\begin_inset Info
+type "shortcut"
+arg "command-alternatives math-space ; space-insert protected"
+\end_inset
+
+ or use the
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Panel
+\family default
+ button
+\begin_inset Info
+type "icon"
+arg "math-insert \\space"
+\end_inset
+
+.
+ This generates a small space, and shows a small marker on the screen.
+ For example, the sequence
+\series bold
+a Ctrl+Space b
+\series default
+:
+\begin_inset Formula $a\,b$
+\end_inset
+
+ appears in \SpecialChar LyX
+ as
+\begin_inset Graphics
+ filename clipart/SpaceMarker.png
+
+\end_inset
+
+.
+ You can change the space to different sizes when you set the cursor behind
+ the space marker and enter space again several times.
+ With every space enter the size will be changed.
+ Some markers for the space size appear red in \SpecialChar LyX
+, because they are negative
+ spaces.
+ Here are two examples:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+a Ctrl+Space b
+\series default
+ and 3×
+\family sans
+Space
+\family default
+:
+\begin_inset Formula $a\quad b$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+a Ctrl+Space b
+\series default
+ and 5×
+\family sans
+Space
+\family default
+:
+\begin_inset Formula $a\!b$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Functions
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Functions
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Functions"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Panel
+\family default
+ contains under the button
+\begin_inset Info
+type "icon"
+arg "math-insert \\functions"
+\end_inset
+
+ a number of function macros, such as
+\begin_inset Formula $\sin$
+\end_inset
+
+,
+\begin_inset Formula $\lim$
+\end_inset
+
+,
+\emph on
+etc
+\emph default
+.
+ (you can also insert them in a formula by typing
+\series bold
+
+\backslash
+sin
+\series default
+ etc.).
+ Standard mathematical practice is that functions are printed upright to
+ avoid confusions, because
+\begin_inset Formula $sin$
+\end_inset
+
+ does normally mean
+\begin_inset Formula $s\cdot i\cdot n$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Using the function macros will also produce correct spacing around the function:
+
+\begin_inset Formula $a\sin x$
+\end_inset
+
+ is different from
+\begin_inset Formula $asinx$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+For some mathematical objects, like limits, the macro changes where subscripts
+ are placed, as described in section
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Operators-with-Limits"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Accents
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Accents
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In a formula you can insert accented characters in the same way as in text
+ mode.
+ This may depend on your keyboard, or the bindings file you use.
+ You can also use \SpecialChar LaTeX
+ commands, for example, to enter
+\begin_inset Formula $\hat{a}$
+\end_inset
+
+ even if your keyboard doesn't have the circumflex enabled.
+ Our example is entered by typing
+\series bold
+
+\backslash
+hat
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+a
+\series default
+ in a formula.
+ Table
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "tab:Accent-names-and"
+
+\end_inset
+
+ shows the equivalences between the accent names and the commands.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float table
+placement document
+alignment document
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "tab:Accent-names-and"
+
+\end_inset
+
+Accent names and the corresponding commands.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="11" columns="3">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Name
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\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
+E
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+xample
+\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
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+circumflex
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+hat
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+\begin_inset Formula $\hat{a}$
+\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
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+grave
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+grave
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+\begin_inset Formula $\grave{a}$
+\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
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+acute
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+acute
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
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