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Diffstat (limited to 'tex/presentation/thomas/defs.tex')
| -rw-r--r-- | tex/presentation/thomas/defs.tex | 250 |
1 files changed, 250 insertions, 0 deletions
diff --git a/tex/presentation/thomas/defs.tex b/tex/presentation/thomas/defs.tex new file mode 100644 index 0000000..0f1ebfe --- /dev/null +++ b/tex/presentation/thomas/defs.tex @@ -0,0 +1,250 @@ +\usepackage{stmaryrd} + +% \usepackage{pala} +\definecolor{yellow}{rgb}{1,1,0.85} +\definecolor{orange}{rgb}{1.0,0.3759,0.0} +\definecolor{orange3}{rgb}{1.0,0.2538,0.1681} +\definecolor{green2}{rgb}{0,0.8125,0} +\definecolor{green3}{rgb}{0,0.55,0} +\definecolor{brown}{rgb}{0.7,0.1,0.1} +\definecolor{pink}{rgb}{0.8,0.0,0.8} +\definecolor{cyan1}{rgb}{0,.90,.90} +\definecolor{cyan3}{rgb}{0,.59,.59} +\definecolor{grey}{rgb}{.7,.7,.7} +% \definecolor{blau}{rgb}{0,.48627,0.78431} +\definecolor{blau}{rgb}{0,.39608,0.74118} +\definecolor{rot}{rgb}{0.79216,.12941,0.24706} +\newcommand\Color[2]{\textcolor{#1}{#2}} +\newcommand\Blue[1]{\Color{blue}{#1}} +\newcommand\Blau[1]{\Color{blau}{#1}} +\newcommand\Red[1]{\Color{red}{#1}} +\newcommand\Rot[1]{\Color{rot}{#1}} +\newcommand\Green[1]{\Color{green3}{#1}} +\newcommand\White[1]{\Color{white}{#1}} +\newcommand\Black[1]{\Color{black}{#1}} +\newcommand\Yellow[1]{\Color{yellow}{#1}} +\newcommand\Orange[1]{\Color{orange3}{#1}} +\newcommand\Brown[1]{\Color{brown}{#1}} +\newcommand\Pink[1]{\Color{pink}{#1}} +\newcommand\Cyan[1]{\Color{cyan3}{#1}} +\newcommand\Cyann[1]{\Color{cyan1}{#1}} +\newcommand\Grey[1]{\Color{grey}{#1}} +% \newcommand\Section[1]{\Color{red}{\section{ #1 }}} +% \newcommand\Subsection[1]{\Color{\red}{\subsection{ #1 }}} +\newcommand\Section[1]{\Red{{\Large\bf #1 }\\[2ex]}} +\newcommand\Subsection[1]{\Red{{\large\bf #1 }\\[2ex]}} +\newcommand\cinput[1]{\begin{center}\input{ #1 }\end{center}} +\newcommand\cpage[2]{\begin{center}\begin{minipage}{ #1 } #2 \end{minipage}\end{center}} +\newcommand\RR{=\!=\!\Rightarrow} +\newcommand\redRR{\Color{red}{$=\!=\!\Rightarrow$}} +\newcommand{\is}{\Blue{::\!{=}}} +\newcommand\Or{\quad\Blue{|}\quad} +\renewcommand\implies{\Rightarrow} +\newcommand{\T}[2]{\Blue{{\cal T}_\rho[\![} #1 \Blue{]\!]}\; #2 } +% \newcommand{\C}[2]{\Blue{{\cal C}_\rho[\![} #1 \Blue{]\!]}\; #2 } +\newcommand{\CC}[2]{\Blue{{\cal C}_\rho^\bullet[\![} #1 \Blue{]\!]}\; #2 } +\newcommand{\gT}{\Green{{\cal T}_{\rho^\sharp}^\sharp}} +\newcommand{\gC}{\Green{{\cal C}_{\rho^\sharp}^\sharp}} +\newcommand{\gCC}{\Green{({\cal C}_{\rho^\sharp}^\bullet)^\sharp}} +\newcommand{\oC}{\Orange{{\cal C}_{\rho^{\sharp\sharp}}^{\sharp\sharp}}} +\newcommand{\oCC}{\Orange{({\cal C}_{\rho^{\sharp\sharp}}^\bullet)^{\sharp\sharp}}} +\newcommand{\size}[1]{\Green{|} #1 \Green{|}} +\newcommand{\Min}{\Green{\sf min}} +\newcommand{\Max}{\Green{\sf max}} +\newcommand{\gplus}{\;\Green{+}\;} +\newcommand{\gdot}{\;\Green{\cdot}\;} +\newcommand{\sem}[1]{\left\llbracket #1 \right\rrbracket} +\newcommand{\asem}[1]{\sem{#1}^\sharp} +\newcommand{\eval}[1]{\sem{ #1 }_{\Red{r}}} +\newcommand{\E}{{\cal E}} +% \newcommand{\U}{{\cal U}} +\newcommand{\M}{{\mathbb M}_k(N)} +\newcommand{\D}{{\mathbb D}_{\Red{r}}} +\newcommand{\MM}{{\mathbb M}_3(N)} +% \newcommand{\Theorem}[1]{\Red{\large \bf Theorem}\\[1ex] #1 \\[2ex]} + + +\newcommand{\N}{{\mathbb N}} +\newcommand{\nz}{\mathrm{I\!N}} +% \newcommand{\F}{\mathrm{I\!F}} +\newcommand{\nf}{{\colon\nz\Total\nz}} +\newcommand{\rz}{\mathrm{I\!R}} +\newcommand{\BB}{\mathbf{I\!B}} +\newcommand{\gz}{\mathrm{Z\!\!Z}} +%\newcommand{\qz}{{\rmfamily Q \hspace{-.6em}\prime\hspace{.4em}}} +%\newcommand{\cz}{{\rmfamily C \hspace{-.6em}\prime\hspace{.4em}}} +\newcommand{\qz}{\mathrm{Q \!\!\!\prime\;}} +\newcommand{\cz}{\mathrm{C \!\!\!\prime\;}} +\newcommand{\minus}{\stackrel{\bullet}{\raisebox{0pt}[.3ex]{$-$}}} +\newcommand{\head}{\mathit{head\/}} +\newcommand{\tail}{\mathit{tail\/}} +\newtheorem{DeFsAtZ}{\hspace{-.3em}}[section] +% \newenvironment{definition}{\begin{DeFsAtZ} +% \Red{Definition}\quad\rmfamily}{\end{DeFsAtZ}} +% \newenvironment{theorem}{\begin{DeFsAtZ} +% \Red{Theorem}\quad\rmfamily}{\end{DeFsAtZ}} +% \newenvironment{corollary}{\begin{DeFsAtZ} +% \Pink{Corollary}\quad\rmfamily}{\end{DeFsAtZ}} +% \newenvironment{lemma}{\begin{DeFsAtZ} +% \Pink{Lemma}\quad\rmfamily}{\end{DeFsAtZ}} +% \newenvironment{example}{\begin{DeFsAtZ} +% \Green{Example}\rmfamily}{\end{DeFsAtZ}} +% \newcommand{\proof}{\noindent\brown{Proof:}} +\newcommand{\blitz}{\mbox{$\begin{array}{cc}\angle\\[-1ex]\swarrow\end{array}$}} +\newcommand{\existsone}{\exists!\hspace{.2em}} +\newcommand{\almev}{\mbox{\raisebox{-.4ex}{$\forall$} + \hspace{-.95em}\raisebox{.3ex}{$^\infty$}}} +\newcommand{\QED}{\mbox{}\hfill$\Box$\vspace{1ex}\linebreak\mbox{}} +\newcommand{\GLA}{\begin{eqnarray*}} +\newcommand{\GLE}{\end{eqnarray*}} +\newcommand{\Def}{{\rmfamily Def}} +\newcommand{\Bild}{{\rmfamily Bild}} +\newcommand{\ABS}[1]{\left|#1\right|} +\newcommand{\OO}[1]{{\cal O}(\Orange{ #1 } )} +\newcommand\va{{\bf a}} +\newcommand\vb{{\bf b}} +\newcommand\vx{{\bf x}} +\newcommand\vy{{\bf y}} +\newcommand\vz{{\bf z}} +\newcommand\vX{{\bf X}} +\newcommand\vY{{\bf Y}} +\newcommand\Main{\sf Main} +\renewcommand{\binom}[2]{(\!\begin{array}{c}#1 \\[-.3ex] + #2 \end{array}\!)} +\newcommand{\unter}[2]{\begin{array}{c}\scriptstyle #1 \\[-.3ex] + \scriptstyle #2 \end{array}} +\newcommand{\stackrelsub}[2]{\raisebox{0pt}[0pt][0pt]{$ + \begin{array}{c}\scriptstyle\mbox{}\\[-1.8ex]#1\\[-1.8ex] + \scriptstyle#2\end{array}$}} +\newcommand{\plusminus}{\begin{array}{c}+\\[-1.5ex]-\end{array}} +\newcommand{\stackrelall}[3]{\raisebox{0pt}[0pt][0pt]{$ + \begin{array}{@{}c@{}}\scriptstyle#1\\[-1.8ex]#2\\[-1.8ex] + \scriptstyle#3\end{array}$}} +\newcommand{\Einschub}[1]{\mbox{}\\\mbox{}\begin{center} + Einschub:\\\bfseries\large #1 + \end{center}\mbox{}\\[1ex]\mbox{}} +\newcommand{\angl}[1]{\langle #1\rangle} +\newcommand{\BNF}[1]{$\langle${\sl #1}\/$\rangle$} +\renewcommand{\sqsubset}{{\setlength{\unitlength}{1pt}\begin{picture}(10,10) +\put(2,0){\line(0,1){5}} +\put(2,0){\line(1,0){5}} +\put(2,5){\line(1,0){5}} +\end{picture}}} +\renewcommand{\sqsupset}{{\setlength{\unitlength}{1pt}\begin{picture}(9,9) +\put(7,0){\line(0,1){5}} +\put(2,0){\line(1,0){5}} +\put(2,5){\line(1,0){5}} +\end{picture}}} +\newcommand{\brl}{[\![} +\newcommand{\brr}{]\!]} + +\newcommand{\Vw}{$\uparrow$} +\newcommand{\id}{\hspace*{1em}} +\newcommand{\idx}[1]{#1} +\newcommand{\idxem}[1]{{\em #1}} +\renewcommand{\H}[1]{${\cal H}${\it #1\/}} + +\newlength\breite +\newenvironment{xlist}{% + \settowidth\breite{--}\begin{list}{--}{% + \setlength\itemsep{0pt}\setlength\topsep{.7ex}\setlength\parsep{.7ex}% + \setlength\itemindent{0mm}\setlength\listparindent{0mm}\setlength\labelsep{1ex}% + \setlength\labelwidth{\breite}% + \addtolength\breite{1ex}\addtolength\breite{.7ex}\setlength\leftmargin{\breite}% + }}{\end{list}} +\newenvironment{ylist}[1]{% + \settowidth\breite{#1}\begin{list}{#1}{% + \setlength\itemsep{0pt}\setlength\topsep{.7ex}\setlength\parsep{.7ex}% + \setlength\itemindent{0mm}\setlength\listparindent{0mm}\setlength\labelsep{1ex}% + \setlength\labelwidth{\breite}% + \addtolength\breite{1ex}\addtolength\breite{.7ex}\setlength\leftmargin{\breite}% + }}{\end{list}} +\setcounter{section}{-1} + +\newcommand{\MBlau}[1]{\Blau{\ {#1}\ }} +\newcommand{\MRot}[1]{\Rot{\ {#1}\ }} + +\newcommand{\neginfty}{{-\infty}} + +\newcommand{\I}{\mathcal{I}} + +\renewcommand{\L}{\mathbf{L}} +\newcommand{\var}[1]{\Rot{\left<#1\right>}} + + +\newcommand\BackgroundPicture[1]{% +\setbeamertemplate{background}{% +\parbox[c][\paperheight]{\paperwidth}{% +\vfill \hfill +\includegraphics[width=1\paperwidth,height=1\paperheight]{#1} +\hfill \vfill +}}} + +\newcommand\NoBackgroundPicture{\setbeamertemplate{background}{}} + +\newcommand{\pos}[2]{\textblockcolor{}\begin{textblock}{30}(#1)#2\end{textblock}} + +\newcommand{\speechbubble}[4]{% + {%\textblockcolor{orange} + %\TPMargin{3pt} + \begin{textblock}{10}(#1) + \begin{tikzpicture}[fill=orange] + \pgfpathmoveto{\pgfpointorigin} + \pgfpathlineto{\pgfpoint{0cm}{#3cm-0.2cm}} + \pgfpathlineto{\pgfpoint{-0.4cm}{#3cm+0.2cm}} + \pgfpathlineto{\pgfpoint{0.2cm}{#3cm}} + \pgfpathlineto{\pgfpoint{#2cm}{#3cm}} + \pgfpathlineto{\pgfpoint{#2cm}{0cm}} + \pgfusepath{fill} + {\color{black} + \pgftext[at=\pgfpoint{#2cm / 2}{#3cm / 2 - 0.15cm},center,base]{#4} + } + \end{tikzpicture} + \end{textblock} + }% +} + +\renewcommand{\emph}[1]{\Rot{\bf #1}} + +\newcommand{\Cite}[1]{\Rot{\cite{#1}}} + +\newcommand{\bvec}[1]{\mathbf{#1}} + +\newcommand{\R}{{\mathbb R}} +\newcommand{\CR}{\overline{\R}} +\newcommand{\Q}{{\mathbb Q}} +\newcommand{\CQ}{\overline{\Q}} + +\newcommand{\omu}{\Orange{\mu}} +\newcommand{\onu}{\Orange{\nu}} + +\newcommand{\handr}[1]{% + \pos{#1}{\includegraphics[width=10mm]{logos/hand_rechts.pdf}}% +} + +\newcommand{\marker}[4]{\pos{#3}{% + \begin{tikzpicture}[fill=#1,opacity=#2]% + \pgfsetstrokeopacity{#2} + \pgfsetstrokecolor{#1} + \pgfsetlinewidth{0pt} + \filldraw (0,0) rectangle (#4); + \end{tikzpicture} +}} + +\newcounter{cnt} +% +\newcommand\schachbrett{{% + \forloop[2]{cnt}{0}{\value{cnt} < 13}{\marker{orange}{0.2}{\value{cnt},0}{1,1}} + \forloop[2]{cnt}{1}{\value{cnt} < 12}{\marker{orange}{0.2}{\value{cnt},1}{1,1}} + \forloop[2]{cnt}{0}{\value{cnt} < 13}{\marker{orange}{0.2}{\value{cnt},2}{1,1}} + \forloop[2]{cnt}{1}{\value{cnt} < 12}{\marker{orange}{0.2}{\value{cnt},3}{1,1}} + \forloop[2]{cnt}{0}{\value{cnt} < 13}{\marker{orange}{0.2}{\value{cnt},4}{1,1}} + \forloop[2]{cnt}{1}{\value{cnt} < 12}{\marker{orange}{0.2}{\value{cnt},5}{1,1}} + \forloop[2]{cnt}{0}{\value{cnt} < 13}{\marker{orange}{0.2}{\value{cnt},6}{1,1}} + \forloop[2]{cnt}{1}{\value{cnt} < 12}{\marker{orange}{0.2}{\value{cnt},7}{1,1}} + \forloop[2]{cnt}{0}{\value{cnt} < 13}{\marker{orange}{0.2}{\value{cnt},8}{1,1}} + \forloop[2]{cnt}{1}{\value{cnt} < 12}{\marker{orange}{0.2}{\value{cnt},9}{1,1}} +}} + +\newcommand\Z{\mathbb{Z}} +\newcommand\CZ{\overline\Z}
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