Zobrazení zdroje stránky 01ALG:Header

\documentclass[12pt, a4paper]{article}

\usepackage[czech]{babel}
\usepackage[IL2]{fontenc}

\usepackage[mathscr]{eucal}
\usepackage{amsfonts, amssymb, amsmath}
%\usepackage[T1]{fontenc}
\usepackage{makeidx}
%\usepackage{showidx}


%VZOROVE SOUBORY

%%CSLATEX
%\documentclass[12pt]{article}
%\listfiles
%\usepackage[IL2]{czech}
%\usepackage{graphics}
%\pagestyle{plain}
%\title{N?ZEV}
%\author{AUTOR}
%%\date{18. b?ezna 2003}
%\input{u_text}
%\begin{document}
%
%
%\end{document}


\newcommand{\te}[2]{\begin{#1}#2\end{#1}} %prostredi

%Preambule
\newcommand{\setjot}[1][1.5ex]{\setlength{\jot}{#1}}
\newcounter{alphlistcounter}
\newlength{\itsmyownlength}
\setcounter{alphlistcounter}{0}

%Znaky
\newcommand{\ia}{\' a}
\newcommand{\ie}{\' e}
\newcommand{\ii}{\'\i}
\newcommand{\io}{\' o}
\newcommand{\iu}{\' u}
\newcommand{\iy}{\' y}
\newcommand{\uu}{\r u}
\newcommand{\vc}{\v c}
\newcommand{\vd}{\v d}
\newcommand{\ve}{\v e}
\newcommand{\vn}{\v n}
\newcommand{\vr}{\v r}
\newcommand{\vs}{\v s}
\newcommand{\vt}{\v t}
\newcommand{\vz}{\v z}
\newcommand{\IA}{\' A}
\newcommand{\IE}{\' E}
\newcommand{\II}{\' I}
\newcommand{\IO}{\' O}
\newcommand{\IU}{\' U}
\newcommand{\IY}{\' Y}
\newcommand{\UU}{\r U}
\newcommand{\VC}{\v C}
\newcommand{\VD}{\v D}
\newcommand{\VE}{\v E}
\newcommand{\VN}{\v N}
\newcommand{\VR}{\v R}
\newcommand{\VS}{\v S}
\newcommand{\VT}{\v T}
\newcommand{\VZ}{\v Z}
\newcommand{\ax}{a~}
\newcommand{\ix}{i~}
\newcommand{\kx}{k~}
\newcommand{\ox}{o~}
\newcommand{\sx}{s~}
\newcommand{\ux}{u~}
\newcommand{\vx}{v~}
\newcommand{\zx}{z~}
\newcommand{\bs}{\char47}
\newcommand{\x}{~}
\newcommand{\tilda}{\~ }
\newcommand{\xl}{\\*}
\newcommand{\xx}{\x\\ }
\newcommand{\puntik}{\textbullet }
\newcommand{\ctverecek}{{\rule[0.3ex]{1ex}{1ex}}}
\newcommand{\pom}{---\x }
\def\mathfunction#1{\mathop {\mathgroup \symoperators #1}\nolimits }
\newcommand{\asin}{\mathfunction{asin}}
\newcommand{\acos}{\mathfunction{acos}}
\newcommand{\atg}{\mathfunction{atg}}
\newcommand{\tgh}{\mathfunction{tgh}}
\newcommand{\cotgh}{\mathfunction{cotgh}}
\newcommand{\tg}{\mathfunction{tg}}
\newcommand{\cotg}{\mathfunction{cotg}}
\newcommand{\arctg}{\mathfunction{arctg}}
\newcommand{\arccotg}{\mathfunction{arccotg}}
\newcommand{\argtgh}{\mathfunction{argtgh}}
\newcommand{\argcotgh}{\mathfunction{argcotgh}}
\newcommand{\cosec}{\mathfunction{cosec}}
\newcommand{\arcsec}{\mathfunction{arcsec}}
\newcommand{\arccosec}{\mathfunction{arccosec}}
\newcommand{\sech}{\mathfunction{sech}}
\newcommand{\cosech}{\mathfunction{cosech}}
\newcommand{\argsech}{\mathfunction{argsech}}
\newcommand{\argcosech}{\mathfunction{argcosech}}
\newcommand{\arc}{\mathfunction{arc}}
\newcommand{\ROT}{\mathfunction{rot}}
\newcommand{\DIV}{\mathfunction{div}}
\newcommand{\md}{\mathrm{d}}
\newcommand{\mmd}{{\,\md}}
\newcommand{\mx}{\cdot}
\newcommand{\imathrm}{\symbol{16}}
\newcommand{\jmathrm}{\symbol{17}}
\newcommand{\convexangle}{\! <\!\!\! )\,}
\newcommand{\qk}[1][1]{{\; |\;}} %v mnozinach znak uvozujici vlastnosti
\newcommand{\prumer}{\not\kern-.12em\circ\kern.1em}
\newcommand{\hlinefill}{\noindent$\underline{}$\hrulefill $\underline{}$}
\newcommand{\msi}{\ensuremath{\,m\cdot s^{-1}}}
\newcommand{\msii}{\ensuremath{\,m\cdot s^{-2}}}
\newcommand{\specialfootnotemark}{\addtocounter{footnote}{1}\mui\thefootnote}
\def\nothing#1{{}}
%Prikazy prostredi

\newcommand{\minimizeleftrightborders}{\setlength{\itsmyownlength}{\oddsidemargin}\setlength{\oddsidemargin}{-.5in}\addtolength{\textwidth}{3\itsmyownlength}}

\newcommand{\minimizeupdownborders}{\addtolength{\topmargin}{-1in}\addtolength{\textheight}{1.5in}}

\newcommand{\minimizeborders}{\minimizeleftrightborders\minimizeupdownborders}

\newcommand{\tpicture}[8][thbp]{\te{figure}{[#1] \setlength{\unitlength}{1mm}\center{\te{picture}{(#2,#3)(#4,#5){#8}}}\caption{#6}\label{#7}}}
%plovouci obrazek. Parametry:
%#1 umisteni
%#2,#3 rozmery
%#4,#5 levy dolni roh
%#6 nazev
%#7 label
%#8 aktivni prikazy obrazku

\newcommand{\qlq}[1]{\qquad\ldots\qquad} %navazani definice
\newcommand{\qlr}[3]{\ensuremath{\left#1{#3}\right#2}} %velka ohraniceni vyrazu
\newcommand{\qlb}[1]{\ensuremath{\left({#1}\right)}} %velka ohraniceni vyrazu
\newcommand{\qz}[1]{\par {\footnotesize\sf #1}\x\\ } %odstavec malym pismem
\newcommand{\qe}[2]{\te{equation}{\label{#1}#2}} %vysazeny vzorec
\newcommand{\qq}[1]{$${#1}$$} %vysazeny vzorec s implicitnim navestim
\newcommand{\qu}[1]{\qquad\left| #1\right.} %prikaz v mat. protredi pro upravu rovnice
\newcommand{\mo}[1][]{\raisebox{1ex}{\scriptsize o}#1} %stupne ...
\newcommand{\ttitle}[1]{\te{center}{\LARGE\sf {#1}}}
\newcommand{\ttab}[1]{\te{tabbing}{{#1}}} %tabulka
\newcommand{\tcal}[1]{$\mathcal{#1}$} %caligraficke pismo v textu
\newcommand{\tbf}[1]{{\bf #1}} %tucne
\newcommand{\tit}[1]{{\it #1}} %kurziva
\newcommand{\trm}[1]{{\rm #1}} %normalne
\newcommand{\tulsl}[1]{\tul{\sl{#1}}} %podtrzena kurziva
\newcommand{\tul}[1]{\underline{#1}} %podtrzene
\newcommand{\tuul}[1]{\tul{\tul{#1}}} %dvojte podtryene
\newcommand{\tsc}[1]{{\sc #1}} %kapitalky
\newcommand{\tsf}[1]{{\sf #1}} %grotesk
\newcommand{\tsl}[1]{{\sl #1}\/} %sklonene
\newcommand{\tam}[2][]{\te{tabular}{[#1]{l}{#2}}} %textove pole
\newcommand{\tram}[2][]{\te{tabular}{[#1]{|l|}\hline {#2} \\\hline}} %ramecek
\newcommand{\trram}[2][]{\te{tabular}{[#1]{||l||}\hline\hline {#2} \\\hline\hline}} %dvojity ramecek
\newcommand{\ttram}[2][]{\te{tabular}{[#1]{|p{.98\textwidth}|}\hline {#2} \\\hline}} %ramecek na sirku strany
\newcommand{\ttrram}[2][]{\te{tabular}{[#1]{||p{.98\textwidth}||}\hline\hline #2 \\\hline\hline}} %dvojity ramacek na sirku strany
\newcommand{\mb}[1]{$\displaystyle {#1}$}
\newcommand{\mab}[1]{\tam{$\displaystyle {#1}$}}
\newcommand{\mrab}[1]{\fbox{$\displaystyle {#1}$}}
\newcommand{\tvers}[1]{\te{verse}{#1}} %vers
\newcommand{\tenum}[1][1]{\addtocounter{tenumcounter}{#1} \arabic{tenumcounter}} %+radova cislovka
\newcommand{\tenumset}[1][0]{\setcounter{tenumcounter}{#1} \arabic{tenumcounter}} %radova cislovka
\newcommand{\tuv}[1]{\uv{{#1}}} %ceske uvozovky
\newcommand{\tnR}[1]{\setcounter{myowncounter}{#1}\Roman{myowncounter}} %velka rimska cislovka
\newcommand{\tna}[1]{\setcounter{myowncounter}{#1}\arabic{myowncounter}} %radova cislovka
\def\tc#1{{\Large\sf #1}}
\newcommand{\mm}[1]{\mathrm{#1}} %text ve vzorci
\newcommand{\mder}[2]{\frac{\md #1}{\md #2}} %derivace
\newcommand{\mint}[2]{\int#1\,\md#2} %integral
\newcommand{\overfrown}[1]{\stackrel{\frown}{{#1}}}
\newcommand{\mintu}[4]{\int\limits_{#1}^{#2}#3\,\md#4} %urcity integral
\newcommand{\sbod}[1]{{\x ---\x{#1}}\\}
\newcommand{\mui}[1]{\ensuremath{^\mathrm{#1}}}
\newcommand{\mdi}[1]{\ensuremath{_\mathrm{#1}}}
\newcommand{\alphitem}[1]{\addtocounter{alphlistcounter}{1}\alph{alphlistcounter} & \te{minipage}{[t]{.95\textwidth}{#1}} \\[1ex]}
\newcommand{\alphlist}[1]{\setcounter{alphlistcounter}{0}\te{tabular}{{r@{)\kern1em}l} #1 }}
\newcommand{\tss}{\kern0.3em}
\newcommand{\tsm}{\kern0.6em}
\newcommand{\tsb}{\kern0.9em}
\newcommand{\tabl}{\\\hline}
\newcommand{\parag}[1]{\paragraph{{#1}}\setlength{\itsmyownlength}{\parindent}\addtolength{\itsmyownlength}{-0.8ex}\x\\\rule{\itsmyownlength}{0ex}}


%Fyzikalni olympiada
\newcommand{\hlavicka}[9]{\te{tabular}{{ll}Jm?no a p??jmen? : {\bf #1} & Ro?n?k: {\bf #6} \\ ?kola: {\bf #2} & ?loha: {\bf {#7}-{#8}-{#9}} \\ {\bf #3} & Posudek:\\
T??da: {\bf #4}\\ Vyu?uj?c? fyziky: {\bf #5} & Posuzoval:}\\[1ex]\hlinefill\\[1ex]}
\newcommand{\zadani}[2]{{\it \sc #1}\\ {\footnotesize #2}\\\\ }
\newcommand{\zadanii}[1]{{\footnotesize #1}\\\\ }
\newcommand{\odpoved}[3]{\large {\sc #1}\ {\bf $#2$}\ {\sc #3}.\\ }





\newcommand{\tqdl}{\textquotedblleft}
\newcommand{\tqdr}{\textquotedblright}
\newcommand{\tqdb}{\quotedblbase}
\newcommand{\FyGyZ}{FyGyZ}
\newcommand{\TuF}{{\v T\kern-0.1em\lower0.05em\hbox{\sc u}\kern-0.19em F}}
\newcommand{\TuuF}{{\v T\kern-0.09em\lower0.21em\hbox{U}\kern-0.21em F}}
\newcommand{\sazba}{\vfill\te{parbox}{{.9\textwidth}{\x\\Sazba:\x\LaTeX}}}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%\input{u_text}
\minimizeborders
\addtolength{\oddsidemargin}{.4in}
\def\stdunitlength{0.5ex}

\tracingmacros=0

%%\usepackage[IL2]{czech}
\makeindex
%\parindent=0pt
\parskip=0ex

\catcode`\@=11

\newtheorem{parnum}{\unaccessible}[subsection]
%\@newctr{parnum}[subsection]

%\newcounter{parnum}
\def\NUMBEREDPAR{\refstepcounter{parnum}\paragraph{\mdseries\scshape\raise .2ex \hbox to 0pt{\kern-3ex $\blacktriangleright$}\theparnum. \PARNAME.}\IFLABEL}
\def\NUMBEREDPARBRACKET(#1){\refstepcounter{parnum}\paragraph{\mdseries\scshape\raise .2ex \hbox to 0pt{\kern-3ex $\blacktriangleright$}\theparnum. \PARNAME{} (#1).}\IFLABEL}
\def\numberedpar#1{\edef\PARNAME{{#1}}\@ifnextchar(\NUMBEREDPARBRACKET\NUMBEREDPAR}
\def\PARLABEL[#1]{\@bsphack\protected@write\@auxout{}{\string\newlabel{#1}{{\theparnum}{\thepage}}}\@esphack }
\def\IFLABEL{\@ifnextchar[\PARLABEL\relax}

\def\axiom(#1)#2.#3\par{\paragraph{Axiom #1. #2.}#3\par}
\def\axiom(#1)#2.{\numberedpar{Axiom}(#1. #2)}
%\def\example#1\par{\paragraph{\newparnum{} Příklad.}#1\par}
\def\define{\numberedpar{Definice}}
\def\example{\numberedpar{Příklad}}
\def\theorem{\numberedpar{Věta}}
\def\observation{\numberedpar{Pozorování}}
\def\lemma{\numberedpar{Lemma}}
\def\remark{\numberedpar{Poznámka}}
\def\consequence{\numberedpar{Důsledek}}
\def\proof{\paragraph{\raise .2ex \hbox to 0pt{\kern-3ex $\circ$}\it Důkaz.}}

\def\removepar#1\par{\relax}

\def\DEFINEDINDEX[#1]#2{\underline{\smash{#2}}\index{#1}}
\def\DEFINED#1{\underline{\smash{#1}}}
\def\defined{\@ifnextchar[\DEFINEDINDEX\DEFINED}

\long\def\nothing#1{\relax}

\def\xy#1#2{\relax}

\def\xxy#1#2{
\refstepcounter{subsection}
\refstepcounter{section}
\addcontentsline{toc}{section}{\numberline{\thesection.} #2}
\subsection*{
\hglue -1ex
\hbox to 0pt{\rule[3ex]{\textwidth}{1pt}}
\hfil
{{\rm\large\bfseries\thesection.} {\rm\large\scshape #1}}
\hfil}
}

\def\xxxy#1#2{
\refstepcounter{subsection}
\addcontentsline{toc}{subsection}{\numberline{\thesubsection.} #2}
\subsubsection*{
\hglue -1ex
\hbox to 0pt{\kern-3.7ex$\bullet$}
\hfil
{{\rm\normalsize\bfseries\thesubsection.} {\rm\normalsize\scshape #1}}
\hfil}
}

\def\pp#1{\paragraph{#1.}}

\def\xx#1{\xy{#1}{#1}}
\def\xxx#1{\xxy{#1}{#1}}
\def\xxxx#1{\xxxy{#1}{#1}}

\def\QED{~\\\rightline{$\Box$}}
\newlength{\PARSKIP}
\def\QED{\setlength{\PARSKIP}{\parskip}\setlength{\parskip}{-2ex}
\hbox{}\allowbreak\hfill
%\hbox{}\allowbreak\hfill
{$\Box$}\par
 \setlength{\parskip}{\PARSKIP}}
\def\cldc{,\ldots,} %comma \ldots coma
\def\PP#1{\mathfunction{\mathscr P}\left({#1}\right)} %potence set
\def\UU{{\mathcal{U}}} %universum
\let\AA=\forall %forall
\let\EE=\exists %exists
\def\abs#1{\left|{#1}\right|} %absolute value
\def\Limpl{\Rightarrow} % short implication
\def\Lequiv{\Leftrightarrow} % short logical equivalence
\def\equivs{\;\;\Longleftrightarrow\;\;} % short logical equivalence
\def\Land{\wedge} % logical and
\def\Lor{\vee} % logical or
\def\TEXTREL#1{\mathrel{\text{#1}}}
\def\Tor{\TEXTREL{vel}}
\def\Tand{\TEXTREL{et}}
\def\Tnot{\TEXTREL{non}}
\def\SET#1#2{\left\{{#1}\divides{#2}\right\}}
\def\set#1#2{\left\{#1\left.\vphantom{#2}\vphantom{#1}\right|#2\right\}}
\def\anglevector#1{\left\langle{#1}\right\rangle}
\def\anglecouple#1#2{\anglevector{#1,#2}}
\def\map#1#2#3{#1:#2\rightarrow#3}
\def\maptype#1#2#3#4{#1:#2\stackrel{\text{#3.}}{\longrightarrow}#4}
\def\matrixtwo#1#2#3#4{\left({#1\atop#3}{#2\atop#4}\right)}
\def\1{{-1}}
\let\sse=\subseteq
\let\ssn=\varsubsetneq
\def\C{\mathbb{C}}
\def\N{\mathbb{N}}
\def\Q{\mathbb{Q}}
\def\R{\mathbb{R}}
\def\Z{\mathbb{Z}}
\def\bbA{\mathbb{A}}
\def\Nz{\mathbb{N}_0}
\def\bbP{\mathbb{P}}
\def\calU{\mathcal{U}}
\def\calR{\mathcal{R}}
\def\calF{\mathscr{F}}
\def\calS{\mathcal{S}}
\def\calB{\mathcal{B}}
\def\calA{\mathcal{A}}
\def\divides{\mathop{\mid}}
\def\pS#1{\mathscr{S}_{#1}} % permutation group
\def\pA#1{\mathscr{A}_{#1}} % even permutation group
\def\pp#1#2{\mathscr{#1}_{#2}}
\def\ord{\mathfunction{ord}}
\def\mathdef{\mathfunction{def}}
\let\sm=\smallsetminus % set minus
\let\pce=\preccurlyeq % subvalention
\let\pna=\precnapprox % sharp subvalention
\let\nsg=\vartriangleleft % normal sup-group
\let\sg=\Subset % normal sup-group
\def\supdot{^\bullet}
%\def\sublin{_{\mathrm{lin}}}
\def\sublin{_\lambda}
\def\subnat{_{\text{nat}}}
\def\hatn#1{\widehat{#1}}
\def\factorset#1{\mathop{/}{#1}}
\def\intpart#1{\left\lfloor#1\right\rfloor}
\def\sgn{\mathfunction{sgn}}
\def\ditem#1{\item[{\small\bfseries(#1)}]}
\def\ch{\mathfunction{ch}}
\def\ker{\mathfunction{ker}}
\let\rarr=\rightarrow
\def\AM#1{\mathscr{A}_{#1}}
\def\LM#1{\mathscr{L}_{#1}}
\def\KM#1{\mathscr{K}_{#1}}
\def\IM#1{\mathcal{I}_{#1}}
\def\UM#1{\mathcal{U}_{#1}}
\def\EM#1{\mathcal{E}_{#1}}
\def\FM#1{\mathscr{F}_{#1}}
\def\NM#1{\mathscr{N}_{#1}}
\def\MM#1{\mathscr{M}_{#1}}
\def\Nf{{\NM5}}
\def\Mf{{\MM5}}
\def\AL#1{\alpha_{#1}}
\def\EK{{\EH H}}
\def\id{\mathfunction{id}}
\def\lcm{\mathop{\nu}}
\def\gcd{\mathop{\delta}}
\def\HE#1{\mathrel{_{#1}\mathord\equiv}}
\def\EH#1{\mathrel{\mathord\equiv_{#1}}}
\def\subplus{_+}
\def\subdot{_\bullet}
\def\subast{_*}
\def\Pzero{{\rm\theta}}
\let\Pz=\Pzero
\let\SV=\lor
\let\SA=\land
\let\CO=\complement
\def\st{\mathfunction{st}}
\let\ol=\overline
\def\RE{\mathfunction{Re}}
\def\GF{\mathfunction{\mathrm{GF}}}
%\long\def\proof#1\QED{\relax}

\def\labelenumi{{\small \bfseries{(\theenumi)}}}

\title{Zápisky z~Algebry}
\author{Tomáš Hejda}