% Translation: p�elo�il: jaih
% Checking: 2006-11-10 zyka
\startcomponent ma-cb-cz-math
\project ma-cb
\product ma-cb-cz
\environment ma-cb-env-cz

%\chapter[formulas]{Typesetting math}
\chapter[formulas]{Sazba matematiky}

%\section{Introduction}
\section{�vod}

%\index {math}
\index {matematika}

%\TEX\ is {\em the} typesetting program for math. However,
%this is not the extensive chapter on typesetting math you
%might expect. We advise you to do some further reading on
%typesetting formulae in \TEX. See for example: \footnote{In
%this introduction on typesetting math we relied on the
%booklet {\em \TEX niques} by Arthur Samuel.}
%
%\TEX\ je {\em p�edev��m} s�zec� program pro matematiku. Nicm�n�
%toto nen� rozs�hl� kapitola t�kaj�c� se sazby matematiky, jak
%mo�n� o�ek�v�te. Pokud pot�ebujete v~ \TEX u s�zet vzorce,
\TEX\ je {\em p�edev��m} program pro sazbu matematiky. P�esto
tato kapitola t�kaj�c� se sazby matematiky nen� rozs�hl�, jak
byste mo�n� o�ek�vali. Pokud pot�ebujete v~\TEX u s�zet vzorce,
doporu�ujeme v�m ke studiu:\footnote{V~tomto
manu�lu se p�i sazb� matematiky op�r�me o~kn��ku
{\em \TEX niques}, kterou napsal Arthur Samuel.}

%\startitemize[packed]
%\item {\em The \TeX Book} by D.E. Knuth
%\item {\em The Beginners Book of \TeX} by S. Levy and R. Seroul
%\stopitemize
\startitemize[packed]
\item {\em The \TeX Book}, autor: D.\,E.~Knuth
\item {\em The Beginners Book of \TeX}, auto�i: S.~Levy a~R.~Seroul
\stopitemize

%Furthermore a \CONTEXT\ math module and its
%accompanying manual will be published in due time.
% VZ (2006-11-12):
Krom� toho o~sazb� matematick�ch rovnic pojedn�v� \CONTEXT ov� magaz�n
\quote{My Way: Using \type{\startalign} and friends} od Aditya
Mahajana, viz \in{p��lohu}[sec:info].

%\section{Typesetting math}
\section{Sazba matematiky}

%\index {math mode}
%\index {display mode}
%\index {text mode}
\index {matematick� m�d}
\index {display m�d}
\index {textov� m�d}

%Normally different conventions are applied for typesetting
%normal text and math text. These conventions are \quote{known}
%by \TEX\ and applied accordingly when generating a document.
%We can rely on \TEX\ for delivering high quality math output.
Zvyklosti pro sazbu b�n�ho a matematick�ho
textu se obvykle li��.
\TEX\ tyto zvyklosti \quote{zn�} a~b�hem vytv��en� dokumentu
je p�esn� aplikuje. Pokud je po�adov�na vysok� kvalita matematick� sazby,
m��eme se na \TEX\ pln� spolehnout.

%A number of conventions for math are:
N�kolik zvyklost� pro sazbu matematiky:

\startitemize[n,packed]
%\item Characters are typeset in $math\ italic$ (don't confuse
%this with the normal {\it italic characters} in a font).
\item Znaky jsou s�zeny v~$matematicke\ kurzive$ (nepl�st
      s~{\it b�nou kurz�vou} p�i pou�it� font�).

%\item Symbols like Greek characters ($\alpha$, $\chi$)
%      and math symbols ($\leq$, $\geq$, $\in$) are used.
\item U��vaj� se symboly jako �eck� znaky ($\alpha$, $\chi$)
      a~matematick� zna�ky ($\leq$, $\geq$, $\in$).

%\item Spacing will differ from normal spacing.
\item D�lky mezer jsou tak� jin� ne� v~b�n�m textu.

%\item Math expression have a different alignment than that of
%      the running text.
\item V~matematick�ch v�razech se tak� u��v� jin� zp�sob 
      zarovn�n� textu.

%\item  The sub and superscripts are downsized automatically,
%      like in $a^{b}_{c}$.
\item  Horn� a doln� indexy jsou um�st�ny automaticky.
       Nap��klad: $a^{b}_{c}$.

%\item Certain symbols have different appearances in the
%      inline and display mode.
\item Ur�it� symboly maj� r�zn� vzhled podle toho, zda jsou uvedeny
  ve vnit�n�m nebo v~display matematick�m m�du.

\stopitemize

%When typesetting math you have to work in the so called math
%mode in which math expressions can be defined by means of
%plain \TEX||commands.
P�i sazb� matematiky mus�te pracovat v~tak zvan�m matematick�m
m�du, ve kter�m jsou v�razy definov�ny pomoc� p��kaz�
plain \TEX u.

%Math mode has two alternatives: text mode and display mode.
%Math mode in text mode is activated by \type{$} and
%\type{$}, while display mode is activated by \type{$$} and
%\type{$$}.
Matematick� m�d m� dv� alternativy: vnit�n� matematick� m�d
a~display matematick� m�d. Vnit�n� matematick� m�d je ohrani�en znaky
\type{$} a~\type{$}, zat�mco display m�d je aktivov�n pomoc�
\type{$$} a~\type{$$}.

%\startbuffer
%The Hasselt community covers an area of 42,05 \Square \Kilo \Meter.
%Now if you consider a circular area of this size with the market
%place of Hasselt as the center point $M$ you can calculate its
%diameter with ${{1}\over{4}} \pi r^2$.
%\stopbuffer
\startbuffer
M�sto Hasselt pokr�v� plochu 42,05 \Square \Kilo \Meter.
Pokud budeme uva�ovat kruhovou oblast t�to velikosti
s~hasseltsk�m tr�i�t�m v~geometrick�m st�edu $T$, m��eme 
spo��tat pr�m�r t�to oblasti pomoc� vzorce ${{1}\over{4}} \pi d^2$.
\stopbuffer
\typebuffer

%This will become:
Tento text bude vypadat po vys�zen� takto:

\getbuffer

%The many \type{{}} (grouping) in ${{1}\over{4}} \pi r^2$ are
%essential for separating operations in the expression. If
%you omit the outer curly braces like this:
%\type{${1}\over{4} \pi r^2$}, you would get a non desired
%result: ${1}\over{4} \pi r^2$.
V�t�� mno�stv� \type{{}} (slo�en�ch z�vorek) ve v�razu
${{1}\over{4}} \pi d^2$ je pot�eba pro ur�en� priority
jednotliv�ch operac�. Pokud zapomeneme na vn�j�� z�vorky
a zap��eme: \type{${1}\over{4} \pi d^2$}, dostaneme ne��douc�
v�sledek: ${1}\over{4} \pi d^2$.

%The letters and numbers are typeset in three different
%sizes: text size $a+b$, script size $\scriptstyle a+b$ and
%scriptscript size $\scriptscriptstyle a+b$. These can be
%influenced by the commands \type{\scriptstyle} and
%\type{\scriptscriptstyle}.
P�smena a ��slice jsou s�zena ve t�ech velikostech (stylech):
velikost textu $a+b$, velikost indexu (script): $\scriptstyle a+b$
a~velikost indexu v~indexu (scriptscript) $\scriptscriptstyle a+b$.
Velikost lze ovlivnit p��kazy
\type{\scriptstyle} a \type{\scriptscriptstyle}.

%Symbols like $\int$ and $\sum$ will have a different form in
%text and display mode. If we type \type {$\sum_{n=1}^{m}$}
%or \type {$\int_{-\infty}^{+\infty}$} we will get
%{$\sum_{n=1}^{m}$} and {$\int_{-\infty}^{+\infty}$}. But
%when you type \type {$$\sum_{n=1}^{m}$$} \type
%{$$\int_{-\infty}^{+\infty}$$} to activate display mode you
%will get:
Symboly jako $\int$ a $\sum$ vypadaj� jinak ve vnit�n�m a jinak
v~display matematick�m m�du. Pokud nap��eme \type {$\sum_{n=1}^{m}$}
nebo \type {$\int_{-\infty}^{+\infty}$}, dostaneme 
{$\sum_{n=1}^{m}$} a {$\int_{-\infty}^{+\infty}$}. To sam�
v~display m�du: \type {$$\sum_{n=1}^{m}$$} a
\type {$$\int_{-\infty}^{+\infty}$$} v�ak bude vypadat takto:

\startformula
\sum_{n=1}^{m} \quad {\rm a} \quad \int_{-\infty}^{+\infty}
\stopformula

%With the commands \type {\nolimits} and \type{\limits} you
%can influence the appearances of \type{\sum} and \type{\int}:
Pomoc� p��kaz� \type {\nolimits} a~\type{\limits} m��eme
ovlivnit vzhled symbol� \type{\sum} a~\type{\int}: 

\startformula
\sum_{n=1}^{m}\nolimits \quad {\rm a} \quad \int_{-\infty}^{+\infty}\limits
\stopformula

%For typesetting fractions there is the command \type
%{\over}. In \CONTEXT\ you can use the alternative
%\type {\frac}. For ${\frac{a}{1+b}}+c$ we type for instance
%\type {${\frac{a}{1+b}}+c$}.
Pro sazbu zlomk� m��eme pou��t p��kaz \type{\over}.
V~\CONTEXT{}u m��eme pou��vat tak� alternativu
\type{\frac}. Nap��klad pro vys�zen� $\frac{a}{1+b}+c$
sta�� zapsat: \type{$\frac{a}{1+b}+c$}.

%Other commands to put one thing above the other, are:
Dal�� p��kazy pro um�st�n� r�zn�ch ��st� v�razu nad sebe:

\startbuffer[atop]
${a} \atop {b}$
\stopbuffer
\startbuffer[choose]
${n+1} \choose {k}$
\stopbuffer
\startbuffer[brack]
${m} \brack {n}$
\stopbuffer
\startbuffer[brace]
${m} \brace {n-1}$
\stopbuffer

\starttabulate[|l|l|l|l|]
\NC \type {\atop}
\NC \typebuffer[atop]
\NC \mathstrut\getbuffer[atop]
\NC
\NC\NR
\NC \type {\choose}
\NC \typebuffer[choose]
\NC
\NC \mathstrut\getbuffer[choose]
\NC\NR
\NC \type {\brack}
\NC \typebuffer[brack]
\NC \mathstrut\getbuffer[brack]
\NC
\NC\NR
\NC \type {\brace}
\NC \typebuffer[brace]
\NC
\NC \mathstrut\getbuffer[brace]
\NC\NR
\stoptabulate

%\TEX\ can enlarge delimiters like (~) and $\{~\}$
%automatically if the left and right delimiter is preceeded
%by the commands \type {\left} and \type {\right}
%respectively. If we type \type
%{$$1+\left(\frac{1}{1-x^{x-2}}\right)^3$$} we get:
\TEX\ m��e p�izp�sobit velikost z�vorek jako (~) a $\{~\}$
automaticky, pokud levou z�vorku p�edch�z� p��kaz \type {\left}
a podobn� pravou \type {\right}. Nap��klad z�pis 
\type{$$1+\left(\frac{1}{1-x^{x-2}}\right)^3$$} bude vypadat:

\startformula
1+\left(\frac{1}{1-x^{x-2}}\right)^3
\stopformula

%Sub and superscripts are invoked by \quote {\type{_}} and
%\quote {\type{^}}. They have effect on the next first
%character so grouping with $\{$~$\}$ is necessary in case of
%multi character sub and superscripts.
Sazby horn�ho a doln�ho indexu dos�hneme pomoc� \quote {\type{_}}
a \quote {\type{^}}. Tyto zna�ky maj� vliv pouze na prvn� 
n�sleduj�c� znak, tak�e v�ceznakov� indexy je nutn� ohrani�ovat
slo�en�ma z�vorkama $\{$~$\}$.

%In certain situations the delimiters can be preceeded by
%\type{\bigl}, \type{\Bigl}, \type{\biggl} and \type{\Biggl}
%and their right counterparts. Even bigger delimiters can be
%produced by placing \type{\left} and \type{\right} in a
%\type{\vbox} construction. When we type a senseless
%expression like \type{$$\left(\vbox to
%16pt{}x^{2^{2^{2^{2}}}}\right)$$} we get:
V~ur�it�ch situac�ch mohou b�t z�vorky zv�t�eny pomoc�
p��kaz� \type{\bigl}, \type{\Bigl}, \type{\biggl},
\type{\Biggl} a jejich pravostrann�ch ekvivalent�. Pokud to 
nesta��, tak je�t� v�t��ch z�vorek m��eme dos�hnout
spoluprac� p��kaz� \type{\left} a \type{\right} s~konstrukc�
\type{\vbox}. V�ce ne� popis to objasn� p��klad, by� pon�kud
m�n� �iteln�: 
\type{$$\left(\vbox to 16pt{}x^{2^{2^{2^{2}}}}\right)$$}

\startformula
\left(\vbox to 16pt{}x^{2^{2^{2^{2}}}}\right)
\stopformula

%In display mode the following delimiters will work in the
%automatic enlargement mechanism:
V~display matematick�m m�du podl�haj� automatick�mu p�izp�soben�
velikosti n�sleduj�c� symboly:

\starttabulate[|l|l|l|l|l|l|l|l|]
\NC \type{\lfloor}      \NC $\lfloor$
\NC \type{\langle}      \NC $\langle$
\NC \type{\vert}        \NC $\vert$
\NC \type{\downarrow}   \NC $\downarrow$
\NC\NR
\NC \type{\rfloor}      \NC $\rfloor$
\NC \type{\rangle}      \NC $\rangle$
\NC \type{\Vert}        \NC $\Vert$
\NC \type{\Downarrow}   \NC $\Downarrow$
\NC\NR
\NC \type{\lceil}       \NC $\lceil$
\NC \type{/}            \NC $/$
\NC \type{\uparrow}     \NC $\uparrow$
\NC \type{\updownarrow} \NC $\updownarrow$
\NC\NR
\NC \type{\rceil}       \NC $\rceil$
\NC \type{\backslash}   \NC $\backslash$
\NC \type{\Uparrow}     \NC $\Uparrow$
\NC \type{\Updownarrow} \NC $\Updownarrow$
\NC\NR
\stoptabulate
 
%In display mode we should typeset only one fraction and
%otherwise switch to the \type{a/b} notation. To get:
Pokud v~display m�du chceme pou��t slo�en� zlomky,
pak bychom m�li zapsat b�n�m zp�sobem pouze ten vn�j��
a~pro ostatn� by se m�la zvolit forma \type{a/b}. Pro 
vys�zen�:

\startformula
a_0 + {\frac{a}{a_1 + \frac{1}{a_2}}}
\stopformula

%we will not type
bychom nem�li ps�t
\type{$$a_0 + {\frac{a}{a_1 + \frac{1}{a_2}}}$$}
%but prefer
ale sp��e
\type{$$a_0 + {\frac{a}{a_1 + 1/a_2}}$$},
%to obtain:
abychom dostali p�ehledn�j��

\startformula
a_0 + {\frac{a}{a_1 + 1/a_2}}
\stopformula

%In addition we could also use the command
%\type{\displaystyle}. If we would type \type {$$a_0 +
%{\frac{a}{a_1 + \frac{1}{\strut \displaystyle a_2}}}$$} we
%will get:
Mimoto lze pou��t p��kaz 
\type{\displaystyle}. Pokud zap��eme \type {$$a_0 +
{\frac{a}{a_1 + \frac{1}{\strut \displaystyle a_2}}}$$}
, tak dostaneme:

\startformula
a_0 + {\frac{a}{a_1 + \frac{1}{\displaystyle a_2}}}
\stopformula

%Below we demonstrate the commands \type{\matrix},
%\type{\pmatrix}, \type{\ldots}, \type{\cdots} and
%\type{\cases} without any further explanation.
N��e uk�eme pou�it� p��kaz� \type{\matrix},
\type{\pmatrix}, \type{\ldots}, \type{\cdots} 
a \type{\cases} bez dal��ho vysv�tlov�n�.

\startbuffer[b]
$$
\stopbuffer

\startbuffer[a]
A=\left(\matrix{x-\lambda & 1         & 0         \cr
                0         & x-\lambda & 1         \cr
                0         & 0         & x-\lambda \cr}\right)
\stopbuffer

\typebuffer[b,a,b] \startformula\getbuffer[a]\stopformula

\startbuffer[a]
A=\left|\matrix{x-\mu& 1     & 0     \cr
                0    & x-\mu & 1     \cr
                0    & 0     & x-\mu \cr}\right|
\stopbuffer

\typebuffer[b,a,b] \startformula\getbuffer[a]\stopformula

%\startbuffer[a]
%A=\pmatrix{a_{11} & a_{12} & \ldots & a_{1n} \cr
%           a_{21} & a_{22} & \ldots & a_{2n} \cr
%           \vdots & \vdots & \ddots & \vdots \cr
%           a_{m1} & a_{m2} & \ldots & a_{mn} \cr}
%\stopbuffer
%
%\typebuffer[b,a,b] \startformula\getbuffer[a]\stopformula
\startbuffer[a]
A=\pmatrix{a_{11} & a_{12} & \ldots & a_{1n} \cr
           a_{21} & a_{22} & \ldots & a_{2n} \cr
           \vdots & \vdots & \ddots & \vdots \cr
           a_{m1} & a_{m2} & \ldots & a_{mn} \cr}
\stopbuffer

\typebuffer[b,a,b] \startformula\getbuffer[a]\stopformula

%% \startbuffer[a]
%% |x|=\cases{ x, & als $x\geq0$; \cr
%%            -x, & anders        \cr}
%% \stopbuffer
\startbuffer[a]
|x|=\cases{\hphantom{-}x, & pokud $x\geq0$; \cr
                      -x, & jinak.          \cr}
\stopbuffer

\typebuffer[b,a,b]  \startformula\getbuffer[a]\stopformula

%To typeset normal text in a math expression we have to
%consider the following. First a space is not typeset in math
%mode so we have to enforce one with \type{ \ } (backslash).
%Second we have to indicate a font switch, because the text
%should not appear in $math\ italic$ but in the actual font.
%So in \CONTEXT\ we have to type \type{$$x^3+{\tf lower\
%order\ terms}$$} to get:
Pokud chceme vys�zet v~matematick�m v�razu b�n� text,
mus�me uv�it dv� v�ci. Za prv�, mezera se
v~matematick�m m�du se nevys�z� b�n�m zp�sobem 
a je t�eba ji vynutit pomoc� \type{ \ } (obr�cen�ho lom�tka).
Za druh�, je nutn� zm�nit font, proto�e b�n� text
by se nem�l s�zet $matematickou\ kurzivou$, ale aktu�ln�m
fontem.

%% \startformula
%% x^3+{\tf lower\ order\ terms}
%% \stopformula
\startformula
x^3+\hbox{termy ni���ch ��d�}
\stopformula

%The math functions like $\sin$ and $\tan$ that have to be
%typeset in the actual font are predefined functions in
%\TEX:
Matematick� funkce jako $\sin$ a $\tan$, kter� se mus�
vys�zet aktu�ln�m fontem, jsou v~\TEX u p�eddefinovan�:

\starttabulate[|l|l|l|l|l|l|l|l|]
\NC \type{\arccos} \NC \type{\cos} \NC \type{\csc} \NC \type{\exp} \NC \type{\ker} \NC \type{\limsup} \NC \type{\min} \NC \type{\sinh} \NC\NR
\NC \type{\arcsin} \NC \type{\cosh} \NC \type{\deg} \NC \type{\gcd} \NC \type{\lg} \NC \type{\ln} \NC \type{\Pr} \NC \type{\sup} \NC\NR
\NC \type{\arctan} \NC \type{\cot} \NC \type{\det} \NC \type{\hom} \NC \type{\lim} \NC \type{\log} \NC \type{\sec} \NC \type{\tan} \NC\NR
\NC \type{\arg} \NC \type{\coth} \NC \type{\dim} \NC \type{\inf} \NC \type{\liminf} \NC \type{\max} \NC \type{\sin} \NC \type{\tanh} \NC\NR
\stoptabulate

%If we type the  sinus function
Pokud zap��eme funkci sinus
\type {$$\sin 2\theta=2\sin\theta\cos\theta$$}
%or type the limit function
nebo limitu
\type {$$\lim_{x\to0}{\frac{\sin x}{x}}=1$$}
%we will get:
dostaneme:

\startformula
\sin 2\theta=2\sin\theta\cos\theta
%\quad {\tf or} \quad
\quad \hbox{nebo} \quad
\lim_{x\to0}{\frac{\sin x}{x}}=1
\stopformula

%Alignment in math expressions may need special attention. In
%multi line expressions we sometimes need alignment at the
%\quote {$=$} sign. This is done by the command
%\type{\eqalign}. If we type:
Zarovn�n� v~matematick�ch v�razech si zaslou�� zvl�tn� pozornost.
Ve v�ce��dkov�ch v�razech n�kdy pot�ebujeme zarovn�n� podle
znam�nka \quote {$=$}. To se d�l� pomoc� p��kazu \type{\eqalign}.
Pokud zap��eme:

\startbuffer
$$\eqalign{
      ax^2+bx+c &= 0                                \cr
      x         &= \frac{-b \pm \sqrt{b^2-4ac}}{2a} \cr}$$
\stopbuffer

\typebuffer

vys�z� se:

\startformula
\eqalign{
      ax^2+bx+c &= 0                                \cr
      x         &= \frac{-b \pm \sqrt{b^2-4ac}}{2a} \cr}
\stopformula

%Sometimes alignment at more than one location is wanted.
%Watch the second line in the next example and see how it is
%defined:
N�kdy je pot�eba zarovn�vat podle v�ce r�zn�ch m�st.
Jak lze tento po�adavek uskute�nit, je vid�t na druh�m
��dku n�sleduj�c�ho p��kladu:

\startbuffer
$$\eqalign{
      ax+bx+\cdots+yx+zx &         = x(a +b+ \cdots \cr
                         &\phantom{= x(a~}+y+z)     \cr
                         &         = y              \cr}$$
\stopbuffer

\typebuffer

%This results in:
V�sledkem pak je:

\startformula
\eqalign{
      ax+bx+\cdots+yx+zx &         = x(a +b+ \cdots \cr
                         &\phantom{= x(a~}+y+z)     \cr
                         &         = y              \cr}
\stopformula

%Next to the command \type{\phantom} there are
%\type{\hphantom} without height and depth and
%\type{\vphantom} without width.
Vedle p��kazu \type{\phantom} je zde je�t� 
\type{\hphantom} bez v��ky a hloubky a 
\type{\vphantom} bez ���ky.

%You can rely on \TEX\ for spacing within a math expression.
%In some situations, however you may want to influence
%spacing. This is done by:
Na velikosti mezer v~matematick�m v�razu
se v�t�inou m��eme na \TEX\ pln� spolehnout. Nicm�n� v~n�kter�ch
situac�ch se n�m m��e hodit jejich velikost ovliv�ovat.
To se d�l� pomoc�:

\starttabulate[|l|r|]
\NC \type{\!} \NC $-\frac{1}{6}$\type{\quad} \NC\NR
\NC \type{\,} \NC $\frac{1}{6}$\type{\quad}  \NC\NR
\NC \type{\>} \NC $\frac{2}{9}$\type{\quad}  \NC\NR
\NC \type{\;} \NC $\frac{5}{18}$\type{\quad} \NC\NR
\stoptabulate

%These \quote {spaces} are related to \type {\quad} that stands
%for the width of the capital \quote{M}.
Velikost t�chto \quote {mezer} je ur�ena relativn� k~meze�e,
kterou lze vyvolat p��kazem \type {\quad} a kter� m� ���ku 
velk�ho p�smene \quote{M}.

%The use of the command \type{\prime} speaks for itself. For
%example if would want $y_1^\prime+y_2^{\prime\prime}$ you
%should type \type{$y_1^\prime+y_2^{\prime\prime}$}.
U�it� p��kazu \type{\prime} \footnote{\quote{prime}
je anglick� v�raz pro ��rku v~indexu. Pozn. p�ekl.} hovo�� sama za sebe. 
Pokud bychom nap��klad cht�li vys�zet $y_1^\prime+y_2^{\prime\prime}$, 
m�li bychom zapsat \type{$y_1^\prime+y_2^{\prime\prime}$}.

%An expression like $\root 3 \of {x^2+y^2}$ is obtained by
%\type{$\root 3 \of {x^2+y^2}$}.
V�raz jako $\root 3 \of {x^2+y^2}$ lze z�skat pomoc�
z�pisu \type{$\root 3 \of {x^2+y^2}$}.

%At the end of this section we point to the command
%\type{\mathstrut} which we can use to enforce
%consistency, for example within the root symbol.
%With \type{$\sqrt{\mathstrut a}+\sqrt{\mathstrut d}+\sqrt{\mathstrut y}$}
%we will get $\sqrt{\mathstrut a}+\sqrt{\mathstrut d}+\sqrt{\mathstrut y}$
%in stead of $\sqrt{a}+\sqrt{d}+\sqrt{y}$.
Na konci t�to sekce si uk�eme pou�it� p��kazu
\type{\mathstrut}, kter�m m��eme dos�hnout vyrovn�n� 
velikost�, nap��klad symbol� odmocnin.
Pomoc� \type{$\sqrt{\mathstrut a}+\sqrt{\mathstrut d}+\sqrt{\mathstrut y}$}
dostaneme $\sqrt{\mathstrut a}+\sqrt{\mathstrut d}+\sqrt{\mathstrut y}$. Bez
p��kazu \type{\mathstrut} bychom dostali $\sqrt{a}+\sqrt{d}+\sqrt{y}$.

%See \in{appendix}[overviews] for a complete overview
%of math commands.
% VZ: (2006-11-12)
%Na kompletn� v�pis matematick�ch p��kaz� se m��ete 
%pod�vat na \in{appendix}[overviews].

%\section{Placing formulaes}
\section{Um�st�n� matematick�ch formul�}

%\index{formula}
\index{vzorce}

\Command{\tex{placeformula}}
\Command{\tex{startformula}}
\Command{\tex{setupformulae}}

%You can typeset numbered formulaes with:
Jednotliv� matematick� vzorce m��eme ��slovat pomoc�:

\shortsetup{placeformula}
\shortsetup{startformula}

%Two examples:
Dva p��klady:

\startbuffer
\placeformula[formula:aformula]
\startformula
   y=x^2
\stopformula

\placeformula
\startformula
  \int_0^1 x^2 dx
\stopformula
\stopbuffer

\typebuffer

\getbuffer

%The \CONTEXT\ commands \type {\startformula} $\cdots$
%\type{\stopformula} replace the begin and end \type{$$}. So
%if you type:
\CONTEXT ov� p��kazy \type {\startformula} $\cdots$
\type{\stopformula} nahrazuj� po��te�n� a koncov� \type{$$}.
Kdy� toti� nap��eme:

\startbuffer
$$
\int_0^1 x^2 dx
$$
\stopbuffer

\typebuffer

%you will get an expression that is {\em displayed} in the
%middle of a page, but that is not as well aligned as the
%previous examples.
dostaneme v�raz, kter� je sice {\em zobrazen} ve st�edu str�nky,
ale nen� tak dob�e zarovn�n jako v~p�edch�zej�c�ch p��kladech.

\getbuffer

%The command \type{\placeformula} handles spacing around the
%formulae and the numbering of the formula. The bracket pair
%is optional and is used for cross-references and to switch
%numbering on and off.
P��kaz \type{\placeformula} zajist� mezeru okolo matematick�ho 
vzorce a~tak� jej� ozna�en� ��slem. Hranat� z�vorky nejsou 
povinn� a~slou�� pro uveden� referen�n�ho jm�na pro odkazy, a~tak� pro
zapnut� a~vypnut� ��slov�n�.

\startbuffer
\placeformula[first one]
\startformula
  y=x^2
\stopformula

\placeformula[middle one]
\startformula
  y=x^3
\stopformula

\placeformula[last one]
\startformula
  y=x^4
\stopformula
\stopbuffer

\getbuffer

%\in{Formula}[middle one] was typed like this:
\in{Rovnice}[middle one] byla vys�zena takto:

\startbuffer
\placeformula[rovnice:prostredni]
  \startformula
     y=x^3
  \stopformula
\stopbuffer

\typebuffer

%The label \type{[middle one]} is used for refering to this
%formula. Such a reference is made with
%\type{\in{formula}[middle one]}.
N�pis v~hranat� z�vorce \type{[rovnice:prostredni]} slou��
pro odvol�n� se na tuto rovnici v~textu. Tuto referenci jsme provedli
p��kazem \type{\in{Rovnice}[rovnice:prostredni]}.

%If no numbering is required you type:
Jestli�e nevy�adujeme ��slov�n�, zap��eme:

\type{\placeformula[-]}

%Numbering of formulae is set up with \type{\setupnumbering}.
%In this manual numbering is set up with
%\type{\setupnumbering[way=bychapter]}. This means that
%the chapter number preceeds the formula number and numbering
%is reset with each new chapter. For reasons of consistency
%the tables, figures, intermezzi etc. are numbered in
%the same way. Therefore you use \type{\setupnumbering} in
%the set up area of your input file.
��slov�n� rovnic se nastavuje pomoc� \type{\setupnumbering}. 
V~tomto manu�lu je ��slov�n� nastaveno
p��kazem \type{\setupnumbering[way=bychapter]}. To znamen�,
�e p�ed ��slem rovnice je uvedeno ��slo kapitoly a v~ka�d�
dal�� kapitole je ��slov�n� op�t vynulov�no. Pro zachov�n�
jednotnosti jsou tabulky, obr�zky apod. ��slov�ny stejn�m 
zp�sobem. Proto se \type{\setupnumbering} pou��v� v~deklara�n� 
oblasti vstupn�ho souboru.

%Formulae can be set up with:
Rovnice mohou b�t nastaveny pomoc� p��kazu:

\shortsetup{setupformulae}

\stopcomponent
