From 2574c6e24468c1aa6d40fceb1ddf679ce9f74ba3 Mon Sep 17 00:00:00 2001 From: Henry Haustein Date: Sun, 5 Aug 2018 20:02:50 +0200 Subject: [PATCH] Issues abarbeiten --- .../LAAG_ueberarbeitet/Vorlesung LAAG.tex | 699 +---------------- .../Bilinearformen_und_Sesquilinearformen.tex | 2 +- .../TeX_files/Das_Lemma_von_Zorn.tex | 2 +- .../TeX_files/Das_Minimalpolynom.tex | 2 +- .../TeX_files/Die_Jordan_Normalform.tex | 4 +- .../TeX_files/Nilpotente_Endomorphismen.tex | 2 +- .../TeX_files/Orthogonalitaet.tex | 17 + .../LAAG 1+2 Semester/Vorlesung LAAG.pdf | Bin 1186567 -> 1166280 bytes .../LAAG 1+2 Semester/Vorlesung LAAG.tex | 697 +---------------- .../Bilinearformen_und_Sesquilinearformen.tex | 2 +- .../LAAG/TeX_files/Das_Lemma_von_Zorn.tex | 2 +- .../LAAG/TeX_files/Das_Minimalpolynom.tex | 2 +- .../LAAG/TeX_files/Die_Jordan_Normalform.tex | 4 +- .../TeX_files/Nilpotente_Endomorphismen.tex | 2 +- .../LAAG/TeX_files/Orthogonalitaet.tex | 17 + 2. Semester/LAAG/Vorlesung LAAG.pdf | Bin 983781 -> 802260 bytes 2. Semester/LAAG/Vorlesung LAAG.tex | 700 +----------------- .../tex/latex/mathoperators/mathoperators.sty | 110 +++ texmf/tex/latex/mathscript/mathscript.cls | 648 ++++++++++++++++ texmf/texmf.cnf | 1 + 20 files changed, 812 insertions(+), 2101 deletions(-) create mode 100644 texmf/tex/latex/mathoperators/mathoperators.sty create mode 100644 texmf/tex/latex/mathscript/mathscript.cls create mode 100644 texmf/texmf.cnf diff --git a/1. Semester/LAAG_ueberarbeitet/Vorlesung LAAG.tex b/1. Semester/LAAG_ueberarbeitet/Vorlesung LAAG.tex index 11d6bdc..0d7b3d1 100644 --- a/1. Semester/LAAG_ueberarbeitet/Vorlesung LAAG.tex +++ b/1. Semester/LAAG_ueberarbeitet/Vorlesung LAAG.tex @@ -1,648 +1,9 @@ -\RequirePackage{ifluatex,ifpdf} -\documentclass[ngerman,a4paper]{report} -\usepackage[left=2.1cm,right=3.1cm,bottom=3cm,footskip=0.75cm,headsep=0.5cm]{geometry} -\usepackage[ngerman]{babel} -\usepackage[onehalfspacing]{setspace} -\ifpdf -\usepackage[utf8]{inputenc} %not recommended with lualatex -%\usepackage[T1]{fontenc} -\usepackage{chngcntr} -\fi - -\usepackage{zref-base} -\usepackage{etoolbox} -\usepackage{xparse}%better macros -\usepackage{calc} -\usepackage{xstring} -\usepackage[bb=boondox]{mathalfa} %spezielle Null mit \mathbb{0}, sollte auch mit 1 klappen, aber dafür haben wir \mathbbm{1} - -\usepackage{scalerel,stackengine} -\usepackage{tocloft} - -\ifluatex -\usepackage{fontspec} -\usepackage{eufrac} -%awesome package for debugging spacing issues -%\usepackage{lua-visual-debug} -%\usepackage{luacode} -\fi - -\usepackage[texindy]{imakeidx} -\indexsetup{ - level=\chapter* -} -\makeindex[intoc] - -%\usepackage[xindy,acronym]{glossaries} -%\makeglossaries - -\usepackage[title,titletoc]{appendix} - -\usepackage{amsmath} -\usepackage{amssymb} -\usepackage{amsfonts} -\usepackage{mathtools} -\usepackage{latexsym} -\usepackage{marvosym} %lighning -\usepackage{bbm} %unitary matrix 1 -\usepackage{cancel} -\usepackage{xfrac}%sfrac -> fractions e.g. 3/4 - -\usepackage[table]{xcolor} -\usepackage{graphicx} -\usepackage{pgfplots} -\pgfplotsset{compat=1.10} -\usepgfplotslibrary{fillbetween} -\usepackage{pgf} -\usepackage{tikz} -\usetikzlibrary{patterns,arrows,calc,decorations.pathmorphing,backgrounds, positioning,fit,petri} -\usetikzlibrary{matrix} -\usetikzlibrary{arrows,cd} % for commutative diagrams -\usetikzlibrary{babel} -\usepackage{color} -\usepackage{wasysym} -\usepackage{tcolorbox} - -\usepackage{enumerate} -\usepackage{enumitem} %customize label -\usepackage{stmaryrd} % Lightning symbol - -\usepackage{tabularx} -\usepackage{multirow} -\usepackage{booktabs} - -\usepackage{ulem} %better underlines - -\usepackage{parskip}%split paragraphs by vspace instead of intendations -\usepackage{fancyhdr} -\usepackage{titlesec}%customize titles -\usepackage{marginnote} - -\usepackage[amsmath,amsthm,thmmarks,hyperref]{ntheorem}%customize theorem-environments more effectively -\usepackage[ntheorem,framemethod=TikZ]{mdframed} - -\usepackage[unicode,bookmarks=true]{hyperref} -\hypersetup{ - colorlinks, - citecolor=green, - filecolor=green, - linkcolor=blue, - urlcolor=blue -} -\usepackage{cleveref} -\usepackage{bookmark} - -\newcommand{\coloredRule}[3][black]{\textcolor{#1}{\rule{#2}{#3}}} -\newlength{\blacktrianglewidth} -\settowidth{\blacktrianglewidth}{$\blacktriangleright$} - -\definecolor{lightgrey}{gray}{0.91} -\definecolor{lightred}{rgb}{1,0.6,0.6} -\definecolor{darkgrey}{gray}{0.6} -\definecolor{darkgreen}{rgb}{0,0.6,0} - -%numbered theorems -\theoremstyle{break} -\theorembodyfont{} - -\mdfdefinestyle{boxedtheorem}{% - outerlinewidth=3pt,% - skipabove=5pt,% - skipbelow=10pt,% - frametitlefont=\normalfont\bfseries\color{black},% - nobreak,%enforce no pagebrakes in the whole frame -} - -\newmdtheoremenv[% - style=boxedtheorem,% - innertopmargin=\topskip,% - 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skipabove=5pt,% - skipbelow=10pt,% -]{conclusion}[theorem]{Folgerung} - -\newmdtheoremenv[% - hidealllines=true,% - frametitlefont=\normalfont\bfseries\color{black},% - innerleftmargin=0pt,% - skipabove=5pt,% - innerleftmargin=10pt,% -]{remark}[theorem]{\hspace*{-10pt}$\blacktriangleright$\hspace*{\dimexpr 10pt - \blacktrianglewidth\relax}Bemerkung} - -\newmdtheoremenv[% - hidealllines=true,% - frametitlefont=\normalfont\bfseries\color{black},% - innerleftmargin=10pt,% -]{example}[theorem]{\hspace*{-10pt}\rule{5pt}{5pt}\hspace*{5pt}Beispiel} - -%unnumbered theorems -\theoremstyle{nonumberbreak} -\theoremindent0cm -\newmdtheoremenv[% - style=boxedtheorem,% - linecolor=red,% - topline=false,% - rightline=false,% - bottomline=false,% - innertopmargin=1pt,% - innerbottommargin=1pt,% -]{*definition}{Definition} - -\newmdtheoremenv[% - hidealllines=true,% - frametitlefont=\normalfont\bfseries\color{black},% - skipabove=5pt,% - innerleftmargin=10pt,% -]{*remark}{\hspace*{-10pt}$\blacktriangleright$\hspace*{\dimexpr 10pt - 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-%for \cref: printed environment names -\crefname{theorem}{Theorem}{Theoreme} -\crefname{proposition}{Satz}{Sätze} -\crefname{lemma}{Lemma}{Lemmata} -\crefname{conclusion}{Folgerung}{Folgerungen} -\crefname{definition}{Definition}{Definitionen} -\crefname{remark}{Bemerkung}{Bemerkungen} -\crefname{example}{Beispiel}{Beispiele} -\crefname{*definition}{Definition}{Definitionen} -\crefname{*remark}{Bemerkung}{Bemerkungen} -\crefname{*example}{Beispiel}{Beispiele} - -\makeatletter -%output a number in upper roman letters -\newcommand*{\rom}[1]{\expandafter\@slowromancap\romannumeral #1@} -%declare a new label; store current chapter number -\newcommand*{\proplbl}[1]{% - \@bsphack - \begingroup - \label{#1}% - \zref@setcurrent{default}{\arabic{chapter}}% -% \zref@wrapper@immediate{% - \zref@labelbyprops{#1@chapter}{default} -% } - \endgroup - \@esphack -} - -%refer to a label set by proplbl. -%If the label is not defined (yet), question marks are output at the calling position. 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Arguments: border color (optional), background color (mandatory), content (mandatory) -%two lengths to get width / height of content (important for width / height of the circle) -\newlength{\@kringel@contentheight} -\newlength{\@kringel@contentwidth} -\newlength{\@kringel@depth} -\NewDocumentCommand{\kringel}{O{blue} m m}{% -%as the macro should work for both text and math mode, add some macros for later use to distinguish -%in text mode, nothing happens (except discarding the 1st argument for the raisebox, that is permantently given), in math mode, the content needs to be enbraced by \ensuremath, the tcolorbox-environment by a raisebox -%ATTENTION: when changing the height-factor of tcolorbox, the depth correction needs to be changed as well - \let\@kringel@inner\relax - \let\@kringel@outer\@secondoftwo - \ifmmode - \let\@kringel@inner\ensuremath - \let\@kringel@outer\raisebox - \fi -%set the width and height - \settoheight{\@kringel@contentheight}{\hbox{\@kringel@inner{#3}}} - \settowidth{\@kringel@contentwidth}{\@kringel@inner{#3}} - \settodepth{\@kringel@depth}{\@kringel@inner{#3}} -%change the depth correction dependend whethere there is a depth (e.g. y) or not (e.g. a) - \ifdim \@kringel@depth > 0pt% - \setlength{\@kringel@depth}{\dimexpr\@kringel@depth+0.5mm\relax} - \else - \settodepth{\@kringel@depth}{y} - \setlength{\@kringel@depth}{\dimexpr\@kringel@depth+0.3mm\relax} - \fi -%output the colorbox width given parameter: frame color, background color, computed width and height, and escaped content depending on math / text mode - \@kringel@outer{\dimexpr-\@kringel@contentheight/2-\@kringel@depth\relax}{\begin{tcolorbox}[colframe=#1,halign=center,valign=center,width=\dimexpr1.5\@kringel@contentwidth+1mm\relax,height=2.5\@kringel@contentheight,left=0pt,right=0pt,bottom=0pt,top=0pt,boxrule=0.8pt,colback=#2,boxsep=0pt,bean arc] - \@kringel@inner{#3} - \end{tcolorbox}} -} - -%switch numbering of equations (amsmath-environments) -\newcommand{\leqnos}{\tagsleft@true\let\veqno\@@leqno} -\newcommand{\reqnos}{\tagsleft@false\let\veqno\@@eqno} -\reqnos - -\pdfstringdefDisableCommands{% - \def\\{}% - \def\texttt#1{<#1>}% - \def\mathbb#1{<#1>}% -} -\makeatother - -%General newcommands! -\newcommand{\comp}{\mathbb{C}} % complex set C -\newcommand{\real}{\mathbb{R}} % real set R -\newcommand{\whole}{\mathbb{Z}} % whole number Symbol -\newcommand{\natur}{\mathbb{N}} % natural number Symbol -\newcommand{\ratio}{\mathbb{Q}} % rational number symbol -\newcommand{\field}{\mathbb{K}} % general field for the others above! -\newcommand{\diff}{\mathrm{d}} % differential d -\newcommand{\s}{\,\,} % space after the function in the intergral -\newcommand{\cont}{\mathcal{C}} % Contour C -\newcommand{\fuk}{f(z) \s\diff z} % f(z) dz -\newcommand{\diffz}{\s\diff z} -\newcommand{\subint}{\int\limits} % lower boundaries for the integral -\newcommand{\poly}{\mathcal{P}} % special P - polygon -\newcommand{\defi}{\mathcal{D}} % D for the domain of a function -\newcommand{\cover}{\mathcal{U}} % cover for a set -\newcommand{\setsys}{\mathcal{M}} % set system M -\newcommand{\setnys}{\mathcal{N}} % set system N -\newcommand{\zetafunk}{f(\zeta)\s\diff \zeta} %f(zeta) d zeta -\newcommand{\ztfunk}{f(\zeta)} % f(zeta) -\newcommand{\bocirc}{S_r(z)} -\newcommand{\prop}{\,|\,} -\newcommand*{\QEDA}{\hfill\ensuremath{\blacksquare}} %tombstone -\newcommand{\emptybra}{\{\varnothing\}} % empty set with set-bracket -\newcommand{\realpos}{\real_{>0}} -\newcommand{\realposr}{\real_{\geq0}} -\newcommand{\naturpos}{\natur_{>0}} -\newcommand{\Imag}{\operatorname{Im}} % Imaginary symbol -\newcommand{\Realz}{\operatorname{Re}} % Real symbol -\newcommand{\norm}{\Vert \cdot \Vert} -\newcommand{\metric}{\vert \cdot \vert} -\newcommand{\foralln}{\forall n} %all n -\newcommand{\forallnset}{\forall n \in \natur} %all n € |N -\newcommand{\forallnz}{\forall n \geq _0} % all n >= n_0 -\newcommand{\conjz}{\overline{z}} % conjugated z -\newcommand{\tildz}{\tilde{z}} % different z -\newcommand{\lproofar}{"`$ \Leftarrow $"'} % "`<="' -\newcommand{\rproofar}{"`$ \Rightarrow $"'} % "`=>"' -\newcommand{\beha}{\Rightarrow \text{ Behauptung}} -\newcommand{\powerset}{\mathcal{P}} -\newcommand{\person}[1]{\textsc{#1}} -\newcommand{\highlight}[1]{\emph{#1}} -\newcommand{\realz}{\mathfrak{Re}} -\newcommand{\imagz}{\mathfrak{Im}} -\renewcommand{\epsilon}{\varepsilon} -\renewcommand{\phi}{\varphi} -\newcommand{\lebesque}{\person{Lebesgue}} -\renewcommand{\Re}{\mathfrak{Re}} -\renewcommand{\Im}{\mathfrak{Im}} -\renewcommand*{\arraystretch}{1.4} -\newcommand{\skalar}[2]{\left\langle #1,#2\right\rangle} -\newcommand{\qraum}[2]{\sfrac{#1}{#2}} - -% Math Operators -\DeclareMathOperator{\inn}{int} % Set of inner points -\DeclareMathOperator{\ext}{ext} % Set of outer points -\DeclareMathOperator{\cl}{cl} % Closure -\DeclareMathOperator{\grad}{grad} -\DeclareMathOperator{\D}{d} -\DeclareMathOperator{\id}{id} -\DeclareMathOperator{\graph}{graph} -\DeclareMathOperator{\Int}{int} -\DeclareMathOperator{\Ext}{ext} -\DeclareMathOperator{\diam}{diam} - -\DeclareMathOperator{\End}{End} -\DeclareMathOperator{\Aff}{Aff} -\DeclareMathOperator{\Aut}{Aut} -\DeclareMathOperator{\Hom}{Hom} -\DeclareMathOperator{\Abb}{Abb} -\DeclareMathOperator{\Bil}{Bil} -\DeclareMathOperator{\Eig}{Eig} -\DeclareMathOperator{\Mat}{Mat} -\DeclareMathOperator{\Ker}{Ker} -\DeclareMathOperator{\diag}{diag} -\DeclareMathOperator{\GL}{GL} -\DeclareMathOperator{\tr}{tr} -\DeclareMathOperator{\rk}{rk} -\DeclareMathOperator{\ZR}{ZR} -\DeclareMathOperator{\SR}{SR} -\DeclareMathOperator{\sgn}{sgn} -\DeclareMathOperator{\Span}{span} -\DeclareMathOperator{\Image}{Im} -\DeclareMathOperator{\Sym}{Sym} -\DeclareMathOperator{\Hau}{Hau} -\DeclareMathOperator{\pr}{pr} -\DeclareMathOperator{\Orth}{O} -\DeclareMathOperator{\SO}{SO} -\DeclareMathOperator{\Uni}{U} -\DeclareMathOperator{\SU}{SU} -\DeclareMathOperator{\SL}{SL} -\DeclareMathOperator{\ggT}{ggT} -\DeclareMathOperator{\kgV}{kgV} - -%change headings: -\titlelabel{\thetitle.\quad}%. behind section/sub... (3. instead of 3) -\counterwithout{section}{chapter} -\renewcommand{\thechapter}{\Roman{chapter}} -\renewcommand{\thepart}{\Alph{part}} -%italic chapters (due to titlesec package some more stuff) -%\titleformat{command}[shape]{format}{label}{sep}{before-code}[after-code] -\titleformat{\chapter}[display]{\bfseries}{\Large\chaptername\;\thechapter}{-5pt}{\huge\bfseries\itshape} -\titlespacing{\chapter}{0pt}{0pt}{10pt} -\titleformat{\section}[hang]{\bfseries\Large}{\thesection.}{8pt}{\Large\bfseries} -%\titlespacing{command}{left}{before-sep}{after-sep} -\titlespacing{\subsection}{0pt}{0pt}{5pt} - -%change appearence of heading of toc: 0 space above, bold, italic huge toc-heading -\renewcommand{\cftbeforetoctitleskip}{0pt} -\renewcommand{\cfttoctitlefont}{\itshape\Huge\bfseries} -%change indentations due to width of capital roman numbers -\renewcommand{\cftchapnumwidth}{2.5em} -\renewcommand{\cftsecindent}{2.5em} -%\renewcommand{\cftsecnumwidth}{3.3em} -\renewcommand{\cftsubsecindent}{4.8em} -%\renewcommand{\cftsubsecnumwidth}{4.2em} - -%change header: -\renewcommand{\headrulewidth}{0.75pt} -\renewcommand{\footrulewidth}{0.3pt} -\lhead{\rightmark}%left: section-number. section-title -\rhead{\leftmark}%right: chapter chapternumber: chapter-title - -% Add new page-style (just footer), patch \chapter command to use this page style -\fancypagestyle{plainChapter}{% - \fancyhf{}% - \fancyfoot[C]{\thepage}% - \renewcommand{\headrulewidth}{0pt}% Line at the header invisible - \renewcommand{\footrulewidth}{0.4pt}% Line at the footer visible -} -%changes pagestyle; instead of empty page the normal footer is printed -\patchcmd{\chapter}{\thispagestyle{plain}}{\thispagestyle{plainChapter}}{}{} -%usually, after a new chapter the section counter needs to be reset manually. Instead, automatic reset -\pretocmd{\chapter}{\setcounter{section}{0}}{}{} - -\pagestyle{fancy} -\pagenumbering{arabic} -%remember chapter-title in \leftmark and \rightmark -\renewcommand{\chaptermark}[1]{% - \markboth{\chaptername - \ \thechapter:\ #1}{}} -%remember section title in \leftmark -\renewcommand{\sectionmark}[1]{% - \markright{\thesection.\ #1}{}} - -%change numbering of equations to be section by section -\counterwithout{equation}{section} +\documentclass[ngerman,a4paper,order=firstname]{../../texmf/tex/latex/mathscript/mathscript} +\usepackage{../../texmf/tex/latex/mathoperators/mathoperators} \title{\textbf{Lineare Algebra WS2017/18}} \author{Dozent: Prof. Dr. Arno Fehm} -%remove page number from part{}-pages -\makeatletter -\let\sv@endpart\@endpart -\def\@endpart{\thispagestyle{empty}\sv@endpart} -\makeatother - \begin{document} \pagenumbering{roman} \pagestyle{plain} @@ -654,7 +15,6 @@ backgroundcolor=lightgrey,% \bookmark[dest=tocpage,level=1]{Inhaltsverzeichnis} \pagebreak -\pagestyle{fancy} \pagenumbering{arabic} \pagestyle{fancy} @@ -695,61 +55,6 @@ backgroundcolor=lightgrey,% \part*{Anhang} \addcontentsline{toc}{part}{Anhang} \appendix -\patchcmd{\chapter}{\thispagestyle{plainChapter}}{\thispagestyle{fancy}}{}{} -%\titleformat{command}[shape]{format}{label}{sep}{before-code}[after-code] -%\titlespacing{command}{left}{before-sep}{after-sep} -\renewcommand{\chaptername}{Anhang} -\renewcommand{\thechapter}{\Alph{chapter}} -\titleformat{\chapter}[hang]{\bfseries}{\LARGE\chaptername\ \thechapter:}{0.5em}{\LARGE\bfseries} -\titlespacing{\chapter}{0pt}{-0.75cm}{0pt} -\renewcommand{\thesection}{\Alph{chapter}.\arabic{section}} - -%from ntheorem.sty -%\def\thm@@thmline@name#1#2#3#4#5{% -% \ifx\\#5\\% -% \@dottedtocline{-2}{0em}{2.3em}% -% {#1 \protect\numberline{#2}#3}% -% {#4} -% \else -% \ifHy@linktocpage\relax\relax -% \@dottedtocline{-2}{0em}{2.3em}% -% {#1 \protect\numberline{#2}#3}% -% {\hyper@linkstart{link}{#5}{#4}\hyper@linkend}% -% \else -% \@dottedtocline{-2}{0em}{2.3em}% -% {\hyper@linkstart{link}{#5}% -% {#1 \protect\numberline{#2}#3}\hyper@linkend}% -% {#4}% -% \fi -% \fi -%} - -\makeatletter -%update ntheorem macro to provide space between theorem numbers and any optional comment -\renewcommand{\thm@@thmline@name}[5]{%- - \def\thm@@thmline@name@tmp{% - \if\relax\detokenize{#3}\relax\else% - {\hspace*{2.2ex}#3}% - \fi% - } - \StrBetween[1,2]{#5}{.}{.}[\thm@@thmline@name@chap@num]%get the chapter number for roman transliteration - \ifx\\#5\\% - \@dottedtocline{-2}{0em}{2.4em}% - {#1 \protect\numberline{#2\thm@@thmline@name@tmp}{}}% - {#4} - \else - \ifHy@linktocpage\relax\relax - \@dottedtocline{-2}{0em}{1.3em}% - {#1 \protect\numberline{#2:}\thm@@thmline@name@tmp}% - {\hyper@linkstart{link}{#5}{#4}\hyper@linkend}% - \else - \@dottedtocline{-2}{0em}{2.4em}% - {#1 \protect\numberline{\rom{\thm@@thmline@name@chap@num}.#2:}\thm@@thmline@name@tmp}% - {\hyper@linkstart{link}{#5}{#4}\hyper@linkend}% - \fi - \fi -} -\makeatother \chapter{Listen} \section{Liste der Theoreme} diff --git a/2. Semester/LAAG 1+2 Semester/TeX_files/Bilinearformen_und_Sesquilinearformen.tex b/2. Semester/LAAG 1+2 Semester/TeX_files/Bilinearformen_und_Sesquilinearformen.tex index 5a04d62..49a1aae 100644 --- a/2. Semester/LAAG 1+2 Semester/TeX_files/Bilinearformen_und_Sesquilinearformen.tex +++ b/2. Semester/LAAG 1+2 Semester/TeX_files/Bilinearformen_und_Sesquilinearformen.tex @@ -48,7 +48,7 @@ Sei $K=\real$ oder $K=\comp$. \end{proof} \begin{proposition} - ISei $B$ eine Basis von $V$. Die Abbildung $s\mapsto M_B(s)$ ist eine Bijektion zwischen den Sesquilinearformen auf $V$ und $\Mat_n(K)$. + Sei $B$ eine Basis von $V$. Die Abbildung $s\mapsto M_B(s)$ ist eine Bijektion zwischen den Sesquilinearformen auf $V$ und $\Mat_n(K)$. \end{proposition} \begin{proof} \begin{itemize} diff --git a/2. Semester/LAAG 1+2 Semester/TeX_files/Das_Lemma_von_Zorn.tex b/2. Semester/LAAG 1+2 Semester/TeX_files/Das_Lemma_von_Zorn.tex index 55d4e61..4fc31e1 100644 --- a/2. Semester/LAAG 1+2 Semester/TeX_files/Das_Lemma_von_Zorn.tex +++ b/2. Semester/LAAG 1+2 Semester/TeX_files/Das_Lemma_von_Zorn.tex @@ -27,7 +27,7 @@ Sei $K$ ein Körper und $U,V,W$ seien $K$-Vektorräume. Zudem sei $X$ eine Menge Totalordnung. \item Teilbarkeit $\vert$ ist eine Halbordnung auf $\natur$, aber Teilbarkeit ist keine Halbordnung auf $\whole$, da $1\vert -1$ und $-1\vert 1$, aber $1\neq -1$! \item $\mathcal{P}(X)$ ist die Potenzmenge. ``$\subseteq$'' ist eine Halbordnung auf $\mathcal{P}$, aber für $\vert X\vert>1$ ist ``$\subseteq$'' keine Totalordnung. - \item Sei $(X,\le)$ eine Halbordnung, sei $Y\subseteq X$, so ist $(Y,\subseteq\vert_Y)$ eine Halbordnung. + \item Sei $(X,\le)$ eine Halbordnung, sei $Y\subseteq X$, so ist $(Y,\le\vert_Y)$ eine Halbordnung. \end{enumerate} \end{example} diff --git a/2. Semester/LAAG 1+2 Semester/TeX_files/Das_Minimalpolynom.tex b/2. Semester/LAAG 1+2 Semester/TeX_files/Das_Minimalpolynom.tex index bc15e3e..905eba6 100644 --- a/2. Semester/LAAG 1+2 Semester/TeX_files/Das_Minimalpolynom.tex +++ b/2. Semester/LAAG 1+2 Semester/TeX_files/Das_Minimalpolynom.tex @@ -67,7 +67,7 @@ \begin{lemma} \proplbl{lemma_5_8} - Sei $x\in V$ und $x_i=f(x)$. Es gibt ein kleinstes $k$ mit $x_k\in\Span_K(x_0,x_1,...,x_{k-1})$, und $W=\Span_K(x_0,...,x_{k-1})$ ein $f$-zyklischer UVR von $V$ mit Basis $B=(x_0,...,x_{k-1})$ und $M_B(f\vert_W)=M_{\chi_{f\vert_W}}$. + Sei $x\in V$ und $x_i=f^i(x)$. Es gibt ein kleinstes $k$ mit $x_k\in\Span_K(x_0,x_1,...,x_{k-1})$, und $W=\Span_K(x_0,...,x_{k-1})$ ein $f$-zyklischer UVR von $V$ mit Basis $B=(x_0,...,x_{k-1})$ und $M_B(f\vert_W)=M_{\chi_{f\vert_W}}$. \end{lemma} \begin{proof} Da $\dim_K(V)=n$ ist $(x_0,...,x_n)$ linear abhängig, es gibt also ein kleinstes $k$ mit $(x_0,...,x_{k-1})$ linear unabhängig, aber $(x_0,...,x_k)$ linear abhängig, folglich $x_k\in\Span_K(x_0,...,x_{k-1})$. Mit $x_k=f(x_{k-1})=\sum_{i=0}^{k-1}-c_ix_i$ ist dann diff --git a/2. Semester/LAAG 1+2 Semester/TeX_files/Die_Jordan_Normalform.tex b/2. Semester/LAAG 1+2 Semester/TeX_files/Die_Jordan_Normalform.tex index 5b96ab3..415eaf6 100644 --- a/2. Semester/LAAG 1+2 Semester/TeX_files/Die_Jordan_Normalform.tex +++ b/2. Semester/LAAG 1+2 Semester/TeX_files/Die_Jordan_Normalform.tex @@ -90,7 +90,7 @@ Genau dann ist $f$ diagonalisierbar, wenn \begin{align} \chi_f(t)&=\prod_{i=1}^m (t-^\lambda_i)^{r_i}\quad \lambda_1,...,\lambda_m\in K\text{ paarweise verscheiden und} \notag \\ - P_f(t) &= \prod_{i=1}^mm (t-\lambda_i)\notag + P_f(t) &= \prod_{i=1}^m (t-\lambda_i)\notag \end{align} \end{conclusion} \begin{proof} @@ -98,7 +98,7 @@ \end{proof} \begin{remark} - Wider definiert man die \person{Jordan}-Invarianten, etc. von einer Matrix $A\in\Mat_n(K)$ als die \person{Jordan}-Invarianten von $f_A\in\End_K(K^n)$. + Wieder definiert man die \person{Jordan}-Invarianten, etc. von einer Matrix $A\in\Mat_n(K)$ als die \person{Jordan}-Invarianten von $f_A\in\End_K(K^n)$. \end{remark} \begin{conclusion} diff --git a/2. Semester/LAAG 1+2 Semester/TeX_files/Nilpotente_Endomorphismen.tex b/2. Semester/LAAG 1+2 Semester/TeX_files/Nilpotente_Endomorphismen.tex index 4e06040..3960cc0 100644 --- a/2. Semester/LAAG 1+2 Semester/TeX_files/Nilpotente_Endomorphismen.tex +++ b/2. Semester/LAAG 1+2 Semester/TeX_files/Nilpotente_Endomorphismen.tex @@ -17,7 +17,7 @@ Da $\dim_K(V)=n<\infty$ gibt es ein $d$ mit $\Ker(f^d)=\Ker(f^{d+i})$ und $\Imag $f=f_A$, $A\in\Mat_2(K)$. \begin{itemize} \item $A=\begin{henrysmatrix}1&0\\0&1\end{henrysmatrix}$: $\{0\}=\Ker(f^0)=\Ker(f^1)=...$ - \item $A=\begin{henrysmatrix}1&0\\0&0\end{henrysmatrix}$: $\{0\}=\Ker(f^0)\subset\Ker(f^1)=\Ker(f^2)=...=\Span_K(e_2)$ + \item $A=\begin{henrysmatrix}1&0\\0&0\end{henrysmatrix}$: $\{0\}=\Ker(f^0)\subset\Ker(f^1)\subsetneq\Ker(f^2)=...=\Span_K(e_2)$ \item $A=\begin{henrysmatrix}0&1\\0&0\end{henrysmatrix}$: $\{0\}=\Ker(f^0)\subset\underbrace{\Ker(f^1)}_{=\Span_K(e_1)}\subset \Ker(f^2)=... = K^2$ \item $A=\begin{henrysmatrix}0&0\\0&0\end{henrysmatrix}$: $\{0\}=\Ker(f^0)\subset\Ker(f^1)=\Ker(f^2)=...=K^2$ \end{itemize} diff --git a/2. Semester/LAAG 1+2 Semester/TeX_files/Orthogonalitaet.tex b/2. Semester/LAAG 1+2 Semester/TeX_files/Orthogonalitaet.tex index a9b782d..c3c23f8 100644 --- a/2. Semester/LAAG 1+2 Semester/TeX_files/Orthogonalitaet.tex +++ b/2. Semester/LAAG 1+2 Semester/TeX_files/Orthogonalitaet.tex @@ -10,6 +10,23 @@ Sei $V$ ein euklidischer bzw. unitärer Vektorraum. U^{\perp}=\{x\in V\mid x\perp u\text{ für alle } u\in U\}\notag \end{align} das \begriff{orthogonale Komplement} zu $U$. + \begin{center} + \begin{tikzpicture} + \draw[blue] (2.75,-2) -- (2.75,3); + \node[blue] at (3.2,3) (Komp) {$U^\perp$}; + + \draw[thick] (0,0) -- (4,0); + \draw[thick] (0,0) -- (1.5,1.5); + \draw[thick] (4,0) -- (5.5,1.5); + \draw[thick] (1.5,1.5) -- (5.5,1.5); + \node at (3.5,0.4) (U) {$U$}; + \node at (0,2.5) (R) {$\mathbb{R}^3$}; + + \coordinate (c2) at (2.75,0.75); + \draw ($(c2) + (0:0.4)$) arc (0:90:0.4); % radius=4mm, initial=0, final=90 + \draw[thick] (2.90,0.90) circle (0.01); + \end{tikzpicture} + \end{center} \end{definition} \begin{lemma} diff --git a/2. Semester/LAAG 1+2 Semester/Vorlesung LAAG.pdf b/2. 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-\theoremseparator{.} -\theorempreskip{5pt} -\theorempostskip{5pt} -\theoremsymbol{$\square$} -\renewtheorem{proof}{Beweis} - -%for \cref: printed environment names -\crefname{theorem}{Theorem}{Theoreme} -\crefname{proposition}{Satz}{Sätze} -\crefname{lemma}{Lemma}{Lemmata} -\crefname{conclusion}{Folgerung}{Folgerungen} -\crefname{definition}{Definition}{Definitionen} -\crefname{remark}{Bemerkung}{Bemerkungen} -\crefname{example}{Beispiel}{Beispiele} -\crefname{*definition}{Definition}{Definitionen} -\crefname{*remark}{Bemerkung}{Bemerkungen} -\crefname{*example}{Beispiel}{Beispiele} - -\makeatletter -%output a number in upper roman letters -\newcommand*{\rom}[1]{\expandafter\@slowromancap\romannumeral #1@} -%declare a new label; store current chapter number -\newcommand*{\proplbl}[1]{% - \@bsphack - \begingroup - \label{#1}% - \zref@setcurrent{default}{\arabic{chapter}}% -% \zref@wrapper@immediate{% - \zref@labelbyprops{#1@chapter}{default} -% } - \endgroup - \@esphack -} - -%refer to 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Arguments: border color (optional), background color (mandatory), content (mandatory) -%two lengths to get width / height of content (important for width / height of the circle) -\newlength{\@kringel@contentheight} -\newlength{\@kringel@contentwidth} -\newlength{\@kringel@depth} -\NewDocumentCommand{\kringel}{O{blue} m m}{% -%as the macro should work for both text and math mode, add some macros for later use to distinguish -%in text mode, nothing happens (except discarding the 1st argument for the raisebox, that is permantently given), in math mode, the content needs to be enbraced by \ensuremath, the tcolorbox-environment by a raisebox -%ATTENTION: when changing the height-factor of tcolorbox, the depth correction needs to be changed as well - \let\@kringel@inner\relax - \let\@kringel@outer\@secondoftwo - \ifmmode - \let\@kringel@inner\ensuremath - \let\@kringel@outer\raisebox - \fi -%set the width and height - \settoheight{\@kringel@contentheight}{\hbox{\@kringel@inner{#3}}} - \settowidth{\@kringel@contentwidth}{\@kringel@inner{#3}} - \settodepth{\@kringel@depth}{\@kringel@inner{#3}} -%change the depth correction dependend whethere there is a depth (e.g. y) or not (e.g. a) - \ifdim \@kringel@depth > 0pt% - \setlength{\@kringel@depth}{\dimexpr\@kringel@depth+0.5mm\relax} - \else - \settodepth{\@kringel@depth}{y} - \setlength{\@kringel@depth}{\dimexpr\@kringel@depth+0.3mm\relax} - \fi -%output the colorbox width given parameter: frame color, background color, computed width and height, and escaped content depending on math / text mode - \@kringel@outer{\dimexpr-\@kringel@contentheight/2-\@kringel@depth\relax}{\begin{tcolorbox}[colframe=#1,halign=center,valign=center,width=\dimexpr1.5\@kringel@contentwidth+1mm\relax,height=2.5\@kringel@contentheight,left=0pt,right=0pt,bottom=0pt,top=0pt,boxrule=0.8pt,colback=#2,boxsep=0pt,bean arc] - \@kringel@inner{#3} - \end{tcolorbox}} -} - -%switch numbering of equations (amsmath-environments) -\newcommand{\leqnos}{\tagsleft@true\let\veqno\@@leqno} -\newcommand{\reqnos}{\tagsleft@false\let\veqno\@@eqno} -\reqnos - -\pdfstringdefDisableCommands{% - \def\\{}% - \def\texttt#1{<#1>}% - \def\mathbb#1{<#1>}% -} -\makeatother - -%General newcommands! -\newcommand{\comp}{\mathbb{C}} % complex set C -\newcommand{\real}{\mathbb{R}} % real set R -\newcommand{\whole}{\mathbb{Z}} % whole number Symbol -\newcommand{\natur}{\mathbb{N}} % natural number Symbol -\newcommand{\ratio}{\mathbb{Q}} % rational number symbol -\newcommand{\field}{\mathbb{K}} % general field for the others above! -\newcommand{\diff}{\mathrm{d}} % differential d -\newcommand{\s}{\,\,} % space after the function in the intergral -\newcommand{\cont}{\mathcal{C}} % Contour C -\newcommand{\fuk}{f(z) \s\diff z} % f(z) dz -\newcommand{\diffz}{\s\diff z} -\newcommand{\subint}{\int\limits} % lower boundaries for the integral -\newcommand{\poly}{\mathcal{P}} % special P - polygon -\newcommand{\defi}{\mathcal{D}} % D for the domain of a function -\newcommand{\cover}{\mathcal{U}} % cover for a set -\newcommand{\setsys}{\mathcal{M}} % set system M -\newcommand{\setnys}{\mathcal{N}} % set system N -\newcommand{\zetafunk}{f(\zeta)\s\diff \zeta} %f(zeta) d zeta -\newcommand{\ztfunk}{f(\zeta)} % f(zeta) -\newcommand{\bocirc}{S_r(z)} -\newcommand{\prop}{\,|\,} -\newcommand*{\QEDA}{\hfill\ensuremath{\blacksquare}} %tombstone -\newcommand{\emptybra}{\{\varnothing\}} % empty set with set-bracket -\newcommand{\realpos}{\real_{>0}} -\newcommand{\realposr}{\real_{\geq0}} -\newcommand{\naturpos}{\natur_{>0}} -\newcommand{\Imag}{\operatorname{Im}} % Imaginary symbol -\newcommand{\Realz}{\operatorname{Re}} % Real symbol -\newcommand{\norm}{\Vert \cdot \Vert} -\newcommand{\metric}{\vert \cdot \vert} -\newcommand{\foralln}{\forall n} %all n -\newcommand{\forallnset}{\forall n \in \natur} %all n € |N -\newcommand{\forallnz}{\forall n \geq _0} % all n >= n_0 -\newcommand{\conjz}{\overline{z}} % conjugated z -\newcommand{\tildz}{\tilde{z}} % different z -\newcommand{\lproofar}{"`$ \Leftarrow $"'} % "`<="' -\newcommand{\rproofar}{"`$ \Rightarrow $"'} % "`=>"' -\newcommand{\beha}{\Rightarrow \text{ Behauptung}} -\newcommand{\powerset}{\mathcal{P}} -\newcommand{\person}[1]{\textsc{#1}} -\newcommand{\highlight}[1]{\emph{#1}} -\newcommand{\realz}{\mathfrak{Re}} -\newcommand{\imagz}{\mathfrak{Im}} -\renewcommand{\epsilon}{\varepsilon} -\renewcommand{\phi}{\varphi} -\newcommand{\lebesque}{\person{Lebesgue}} -\renewcommand{\Re}{\mathfrak{Re}} -\renewcommand{\Im}{\mathfrak{Im}} -\renewcommand*{\arraystretch}{1.4} -\newcommand{\skalar}[2]{\left\langle #1,#2\right\rangle} -\newcommand{\qraum}[2]{\sfrac{#1}{#2}} - -% Math Operators -\DeclareMathOperator{\inn}{int} % Set of inner points -\DeclareMathOperator{\ext}{ext} % Set of outer points -\DeclareMathOperator{\cl}{cl} % Closure -\DeclareMathOperator{\grad}{grad} -\DeclareMathOperator{\D}{d} -\DeclareMathOperator{\id}{id} -\DeclareMathOperator{\graph}{graph} -\DeclareMathOperator{\Int}{int} -\DeclareMathOperator{\Ext}{ext} -\DeclareMathOperator{\diam}{diam} - -\DeclareMathOperator{\End}{End} -\DeclareMathOperator{\Aff}{Aff} -\DeclareMathOperator{\Aut}{Aut} -\DeclareMathOperator{\Hom}{Hom} -\DeclareMathOperator{\Abb}{Abb} -\DeclareMathOperator{\Bil}{Bil} -\DeclareMathOperator{\Eig}{Eig} -\DeclareMathOperator{\Mat}{Mat} -\DeclareMathOperator{\Ker}{Ker} -\DeclareMathOperator{\diag}{diag} -\DeclareMathOperator{\GL}{GL} -\DeclareMathOperator{\tr}{tr} -\DeclareMathOperator{\rk}{rk} -\DeclareMathOperator{\ZR}{ZR} -\DeclareMathOperator{\SR}{SR} -\DeclareMathOperator{\sgn}{sgn} -\DeclareMathOperator{\Span}{span} -\DeclareMathOperator{\Image}{Im} -\DeclareMathOperator{\Sym}{Sym} -\DeclareMathOperator{\Hau}{Hau} -\DeclareMathOperator{\pr}{pr} -\DeclareMathOperator{\Orth}{O} -\DeclareMathOperator{\SO}{SO} -\DeclareMathOperator{\Uni}{U} -\DeclareMathOperator{\SU}{SU} -\DeclareMathOperator{\SL}{SL} -\DeclareMathOperator{\ggT}{ggT} -\DeclareMathOperator{\kgV}{kgV} - -%change headings: -\titlelabel{\thetitle.\quad}%. behind section/sub... (3. instead of 3) -\counterwithout{section}{chapter} -\renewcommand{\thechapter}{\Roman{chapter}} -\renewcommand{\thepart}{\Alph{part}} -%italic chapters (due to titlesec package some more stuff) -%\titleformat{command}[shape]{format}{label}{sep}{before-code}[after-code] -\titleformat{\chapter}[display]{\bfseries}{\Large\chaptername\;\thechapter}{-5pt}{\huge\bfseries\itshape} -\titlespacing{\chapter}{0pt}{0pt}{10pt} -\titleformat{\section}[hang]{\bfseries\Large}{\thesection.}{8pt}{\Large\bfseries} -%\titlespacing{command}{left}{before-sep}{after-sep} -\titlespacing{\subsection}{0pt}{0pt}{5pt} - -%change appearence of heading of toc: 0 space above, bold, italic huge toc-heading -\renewcommand{\cftbeforetoctitleskip}{0pt} -\renewcommand{\cfttoctitlefont}{\itshape\Huge\bfseries} -%change indentations due to width of capital roman numbers -\renewcommand{\cftchapnumwidth}{2.5em} -\renewcommand{\cftsecindent}{2.5em} -%\renewcommand{\cftsecnumwidth}{3.3em} -\renewcommand{\cftsubsecindent}{4.8em} -%\renewcommand{\cftsubsecnumwidth}{4.2em} - -%change header: -\renewcommand{\headrulewidth}{0.75pt} -\renewcommand{\footrulewidth}{0.3pt} -\lhead{\rightmark}%left: section-number. section-title -\rhead{\leftmark}%right: chapter chapternumber: chapter-title - -% Add new page-style (just footer), patch \chapter command to use this page style -\fancypagestyle{plainChapter}{% - \fancyhf{}% - \fancyfoot[C]{\thepage}% - \renewcommand{\headrulewidth}{0pt}% Line at the header invisible - \renewcommand{\footrulewidth}{0.4pt}% Line at the footer visible -} -%changes pagestyle; instead of empty page the normal footer is printed -\patchcmd{\chapter}{\thispagestyle{plain}}{\thispagestyle{plainChapter}}{}{} -%usually, after a new chapter the section counter needs to be reset manually. Instead, automatic reset -\pretocmd{\chapter}{\setcounter{section}{0}}{}{} - -\pagestyle{fancy} -\pagenumbering{arabic} -%remember chapter-title in \leftmark and \rightmark -\renewcommand{\chaptermark}[1]{% - \markboth{\chaptername - \ \thechapter:\ #1}{}} -%remember section title in \leftmark -\renewcommand{\sectionmark}[1]{% - \markright{\thesection.\ #1}{}} - -%change numbering of equations to be section by section -\counterwithout{equation}{section} \title{\textbf{Lineare Algebra WS2017/18 + SS2018}} \author{Dozent: Prof. Dr. Arno Fehm} -%remove page number from part{}-pages -\makeatletter -\let\sv@endpart\@endpart -\def\@endpart{\thispagestyle{empty}\sv@endpart} -\makeatother - \begin{document} \pagenumbering{roman} \pagestyle{plain} @@ -646,7 +16,6 @@ backgroundcolor=lightgrey,% \bookmark[dest=tocpage,level=1]{Inhaltsverzeichnis} \pagebreak -\pagestyle{fancy} \pagenumbering{arabic} \pagestyle{fancy} @@ -724,68 +93,6 @@ backgroundcolor=lightgrey,% \part*{Anhang} \addcontentsline{toc}{part}{Anhang} \appendix -\patchcmd{\chapter}{\thispagestyle{plainChapter}}{\thispagestyle{fancy}}{}{} -%\titleformat{command}[shape]{format}{label}{sep}{before-code}[after-code] -%\titlespacing{command}{left}{before-sep}{after-sep} -\renewcommand{\chaptername}{Anhang} -\renewcommand{\thechapter}{\Alph{chapter}} -\titleformat{\chapter}[hang]{\bfseries}{\LARGE\chaptername\ \thechapter:}{0.5em}{\LARGE\bfseries} -\titlespacing{\chapter}{0pt}{-0.75cm}{0pt} -\renewcommand{\thesection}{\Alph{chapter}.\arabic{section}} - -%from ntheorem.sty -%\def\thm@@thmline@name#1#2#3#4#5{% -% \ifx\\#5\\% -% \@dottedtocline{-2}{0em}{2.3em}% -% {#1 \protect\numberline{#2}#3}% -% {#4} -% \else -% \ifHy@linktocpage\relax\relax -% \@dottedtocline{-2}{0em}{2.3em}% -% {#1 \protect\numberline{#2}#3}% -% {\hyper@linkstart{link}{#5}{#4}\hyper@linkend}% -% \else -% \@dottedtocline{-2}{0em}{2.3em}% -% {\hyper@linkstart{link}{#5}% -% {#1 \protect\numberline{#2}#3}\hyper@linkend}% -% {#4}% -% \fi -% \fi -%} - -\makeatletter -%update ntheorem macro to provide space between theorem numbers and any optional comment, adds in upper roman letters the chapter number. removes any numbering for theorem environments with just one counter -\renewcommand{\thm@@thmline@name}[5]{%- - \def\thm@@thmline@name@tmp{% - \if\relax\detokenize{#3}\relax\else% - {\hspace*{2.2ex}#3}% - \fi% - } - \let\thm@@thmline@name@numbering\relax - \StrCount{#5}{.}[\thm@@thmline@name@dot@number] - \ifnum\thm@@thmline@name@dot@number < 3% - \def\thm@@thmline@name@tmp{\hspace*{-1em}#3} - \else% - \StrBetween[1,2]{#5}{.}{.}[\thm@@thmline@name@chap@num]%get the chapter number for roman transliteration - \def\thm@@thmline@name@numbering{\rom{\thm@@thmline@name@chap@num}.#2} - \fi - \ifx\\#5\\% - \@dottedtocline{-2}{0em}{4.4em}% - {#1 \protect\numberline{\thm@@thmline@name@numbering:}{}}% - {#4} - \else - \ifHy@linktocpage\relax\relax - \@dottedtocline{-2}{0em}{1.3em}% - {#1 \protect\numberline{\thm@@thmline@name@numbering:}\thm@@thmline@name@tmp}% - {\hyper@linkstart{link}{#5}{#4}\hyper@linkend}% - \else - \@dottedtocline{-2}{0em}{4.em}% - {#1 \protect\numberline{\thm@@thmline@name@numbering:}\thm@@thmline@name@tmp}% - {\hyper@linkstart{link}{#5}{#4}\hyper@linkend}% - \fi - \fi -} -\makeatother \chapter{Listen} \section{Liste der Theoreme} diff --git a/2. Semester/LAAG/TeX_files/Bilinearformen_und_Sesquilinearformen.tex b/2. Semester/LAAG/TeX_files/Bilinearformen_und_Sesquilinearformen.tex index 7528322..fbf9ba1 100644 --- a/2. Semester/LAAG/TeX_files/Bilinearformen_und_Sesquilinearformen.tex +++ b/2. Semester/LAAG/TeX_files/Bilinearformen_und_Sesquilinearformen.tex @@ -48,7 +48,7 @@ Sei $K=\real$ oder $K=\comp$. \end{proof} \begin{proposition} - ISei $B$ eine Basis von $V$. Die Abbildung $s\mapsto M_B(s)$ ist eine Bijektion zwischen den Sesquilinearformen auf $V$ und $\Mat_n(K)$. + Sei $B$ eine Basis von $V$. Die Abbildung $s\mapsto M_B(s)$ ist eine Bijektion zwischen den Sesquilinearformen auf $V$ und $\Mat_n(K)$. \end{proposition} \begin{proof} \begin{itemize} diff --git a/2. Semester/LAAG/TeX_files/Das_Lemma_von_Zorn.tex b/2. Semester/LAAG/TeX_files/Das_Lemma_von_Zorn.tex index baea5d9..2cdbe2e 100644 --- a/2. Semester/LAAG/TeX_files/Das_Lemma_von_Zorn.tex +++ b/2. Semester/LAAG/TeX_files/Das_Lemma_von_Zorn.tex @@ -27,7 +27,7 @@ Sei $K$ ein Körper und $U,V,W$ seien $K$-Vektorräume. Zudem sei $X$ eine Menge Totalordnung. \item Teilbarkeit $\vert$ ist eine Halbordnung auf $\natur$, aber Teilbarkeit ist keine Halbordnung auf $\whole$, da $1\vert -1$ und $-1\vert 1$, aber $1\neq -1$! \item $\mathcal{P}(X)$ ist die Potenzmenge. ``$\subseteq$'' ist eine Halbordnung auf $\mathcal{P}$, aber für $\vert X\vert>1$ ist ``$\subseteq$'' keine Totalordnung. - \item Sei $(X,\le)$ eine Halbordnung, sei $Y\subseteq X$, so ist $(Y,\subseteq\vert_Y)$ eine Halbordnung. + \item Sei $(X,\le)$ eine Halbordnung, sei $Y\subseteq X$, so ist $(Y,\le\vert_Y)$ eine Halbordnung. \end{enumerate} \end{example} diff --git a/2. Semester/LAAG/TeX_files/Das_Minimalpolynom.tex b/2. Semester/LAAG/TeX_files/Das_Minimalpolynom.tex index bf03df7..85398ce 100644 --- a/2. Semester/LAAG/TeX_files/Das_Minimalpolynom.tex +++ b/2. Semester/LAAG/TeX_files/Das_Minimalpolynom.tex @@ -66,7 +66,7 @@ \begin{lemma} \proplbl{lemma_5_8} - Sei $x\in V$ und $x_i=f(x)$. Es gibt ein kleinstes $k$ mit $x_k\in\Span_K(x_0,x_1,...,x_{k-1})$, und $W=\Span_K(x_0,...,x_{k-1})$ ein $f$-zyklischer UVR von $V$ mit Basis $B=(x_0,...,x_{k-1})$ und $M_B(f\vert_W)=M_{\chi_{f\vert_W}}$. + Sei $x\in V$ und $x_i=f^i(x)$. Es gibt ein kleinstes $k$ mit $x_k\in\Span_K(x_0,x_1,...,x_{k-1})$, und $W=\Span_K(x_0,...,x_{k-1})$ ein $f$-zyklischer UVR von $V$ mit Basis $B=(x_0,...,x_{k-1})$ und $M_B(f\vert_W)=M_{\chi_{f\vert_W}}$. \end{lemma} \begin{proof} Da $\dim_K(V)=n$ ist $(x_0,...,x_n)$ linear abhängig, es gibt also ein kleinstes $k$ mit $(x_0,...,x_{k-1})$ linear unabhängig, aber $(x_0,...,x_k)$ linear abhängig, folglich $x_k\in\Span_K(x_0,...,x_{k-1})$. Mit $x_k=f(x_{k-1})=\sum_{i=0}^{k-1}-c_ix_i$ ist dann diff --git a/2. Semester/LAAG/TeX_files/Die_Jordan_Normalform.tex b/2. Semester/LAAG/TeX_files/Die_Jordan_Normalform.tex index 5b96ab3..415eaf6 100644 --- a/2. Semester/LAAG/TeX_files/Die_Jordan_Normalform.tex +++ b/2. Semester/LAAG/TeX_files/Die_Jordan_Normalform.tex @@ -90,7 +90,7 @@ Genau dann ist $f$ diagonalisierbar, wenn \begin{align} \chi_f(t)&=\prod_{i=1}^m (t-^\lambda_i)^{r_i}\quad \lambda_1,...,\lambda_m\in K\text{ paarweise verscheiden und} \notag \\ - P_f(t) &= \prod_{i=1}^mm (t-\lambda_i)\notag + P_f(t) &= \prod_{i=1}^m (t-\lambda_i)\notag \end{align} \end{conclusion} \begin{proof} @@ -98,7 +98,7 @@ \end{proof} \begin{remark} - Wider definiert man die \person{Jordan}-Invarianten, etc. von einer Matrix $A\in\Mat_n(K)$ als die \person{Jordan}-Invarianten von $f_A\in\End_K(K^n)$. + Wieder definiert man die \person{Jordan}-Invarianten, etc. von einer Matrix $A\in\Mat_n(K)$ als die \person{Jordan}-Invarianten von $f_A\in\End_K(K^n)$. \end{remark} \begin{conclusion} diff --git a/2. Semester/LAAG/TeX_files/Nilpotente_Endomorphismen.tex b/2. Semester/LAAG/TeX_files/Nilpotente_Endomorphismen.tex index 6ded566..7b06afe 100644 --- a/2. Semester/LAAG/TeX_files/Nilpotente_Endomorphismen.tex +++ b/2. Semester/LAAG/TeX_files/Nilpotente_Endomorphismen.tex @@ -17,7 +17,7 @@ Da $\dim_K(V)=n<\infty$ gibt es ein $d$ mit $\Ker(f^d)=\Ker(f^{d+i})$ und $\Imag $f=f_A$, $A\in\Mat_2(K)$. \begin{itemize} \item $A=\begin{henrysmatrix}1&0\\0&1\end{henrysmatrix}$: $\{0\}=\Ker(f^0)=\Ker(f^1)=...$ - \item $A=\begin{henrysmatrix}1&0\\0&0\end{henrysmatrix}$: $\{0\}=\Ker(f^0)\subset\Ker(f^1)=\Ker(f^2)=...=\Span_K(e_2)$ + \item $A=\begin{henrysmatrix}1&0\\0&0\end{henrysmatrix}$: $\{0\}=\Ker(f^0)\subset\Ker(f^1)\subsetneq\Ker(f^2)=...=\Span_K(e_2)$ \item $A=\begin{henrysmatrix}0&1\\0&0\end{henrysmatrix}$: $\{0\}=\Ker(f^0)\subset\underbrace{\Ker(f^1)}_{=\Span_K(e_1)}\subset \Ker(f^2)=... = K^2$ \item $A=\begin{henrysmatrix}0&0\\0&0\end{henrysmatrix}$: $\{0\}=\Ker(f^0)\subset\Ker(f^1)=\Ker(f^2)=...=K^2$ \end{itemize} diff --git a/2. Semester/LAAG/TeX_files/Orthogonalitaet.tex b/2. Semester/LAAG/TeX_files/Orthogonalitaet.tex index a9b782d..c3c23f8 100644 --- a/2. Semester/LAAG/TeX_files/Orthogonalitaet.tex +++ b/2. Semester/LAAG/TeX_files/Orthogonalitaet.tex @@ -10,6 +10,23 @@ Sei $V$ ein euklidischer bzw. unitärer Vektorraum. U^{\perp}=\{x\in V\mid x\perp u\text{ für alle } u\in U\}\notag \end{align} das \begriff{orthogonale Komplement} zu $U$. + \begin{center} + \begin{tikzpicture} + \draw[blue] (2.75,-2) -- (2.75,3); + \node[blue] at (3.2,3) (Komp) {$U^\perp$}; + + \draw[thick] (0,0) -- (4,0); + \draw[thick] (0,0) -- (1.5,1.5); + \draw[thick] (4,0) -- (5.5,1.5); + \draw[thick] (1.5,1.5) -- (5.5,1.5); + \node at (3.5,0.4) (U) {$U$}; + \node at (0,2.5) (R) {$\mathbb{R}^3$}; + + \coordinate (c2) at (2.75,0.75); + \draw ($(c2) + (0:0.4)$) arc (0:90:0.4); % radius=4mm, initial=0, final=90 + \draw[thick] (2.90,0.90) circle (0.01); + \end{tikzpicture} + \end{center} \end{definition} \begin{lemma} diff --git a/2. Semester/LAAG/Vorlesung LAAG.pdf b/2. 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Semester/LAAG/Vorlesung LAAG.tex b/2. Semester/LAAG/Vorlesung LAAG.tex index ba4532b..ec5e1e9 100644 --- a/2. Semester/LAAG/Vorlesung LAAG.tex +++ b/2. Semester/LAAG/Vorlesung LAAG.tex @@ -1,640 +1,9 @@ -\RequirePackage{ifluatex,ifpdf} -\documentclass[ngerman,a4paper]{report} -\usepackage[left=2.1cm,right=3.1cm,bottom=3cm,footskip=0.75cm,headsep=0.5cm]{geometry} -\usepackage[ngerman]{babel} -\usepackage[onehalfspacing]{setspace} -\ifpdf -\usepackage[utf8]{inputenc} %not recommended with lualatex -%\usepackage[T1]{fontenc} -\usepackage{chngcntr} -\fi - -\usepackage{zref-base} -\usepackage{etoolbox} -\usepackage{xparse}%better macros -\usepackage{calc} -\usepackage{xstring} -\usepackage[bb=boondox]{mathalfa} %spezielle Null mit \mathbb{0}, sollte auch mit 1 klappen, aber dafür haben wir \mathbbm{1} -\usepackage{bigdelim} -\newcommand\undermat[2]{% - \makebox[0pt][l]{$\smash{\underbrace{\phantom{% - \begin{matrix}#2\end{matrix}}}_{\text{$#1$}}}$}#2} - -\usepackage{scalerel,stackengine} -\usepackage{tocloft} - -\ifluatex -\usepackage{fontspec} -\usepackage{eufrac} -%awesome package for debugging spacing issues -%\usepackage{lua-visual-debug} -%\usepackage{luacode} -\fi - -\usepackage[texindy]{imakeidx} -\indexsetup{ - level=\chapter* -} -\makeindex[intoc] - -%\usepackage[xindy,acronym]{glossaries} -%\makeglossaries - -\usepackage[title,titletoc]{appendix} - -\usepackage{amsmath} -\usepackage{amssymb} -\usepackage{amsfonts} -\usepackage{mathtools} -\usepackage{latexsym} -\usepackage{marvosym} %lighning -\usepackage{bbm} %unitary matrix 1 -\usepackage{cancel} -\usepackage{xfrac}%sfrac -> fractions e.g. 3/4 - -\usepackage[table]{xcolor} -\usepackage{graphicx} -\usepackage{pgfplots} -\pgfplotsset{compat=1.10} -\usepgfplotslibrary{fillbetween} -\usepackage{pgf} -\usepackage{tikz} -\usetikzlibrary{patterns,arrows,calc,decorations.pathmorphing,backgrounds, positioning,fit,petri} -\usetikzlibrary{matrix} -\usepackage{color} -\usepackage{wasysym} -\usepackage{tcolorbox} - -\usepackage{enumerate} -\usepackage{enumitem} %customize label -\usepackage{stmaryrd} % Lightning symbol - -\usepackage{tabularx} -\usepackage{multirow} -\usepackage{booktabs} - -\usepackage{ulem} %better underlines - -\usepackage{parskip}%split paragraphs by vspace instead of intendations -\usepackage{fancyhdr} -\usepackage{titlesec}%customize titles -\usepackage{marginnote} - -\usepackage[amsmath,amsthm,thmmarks,hyperref]{ntheorem}%customize theorem-environments more effectively -\usepackage[ntheorem,framemethod=TikZ]{mdframed} - -\usepackage{tikz} %diagrams -\usetikzlibrary{arrows,cd} % for commutative diagrams -\usetikzlibrary{babel} - -\usepackage[unicode,bookmarks=true]{hyperref} -\hypersetup{ - colorlinks, - citecolor=green, - filecolor=green, - linkcolor=blue, - urlcolor=blue -} -\usepackage{cleveref} -\usepackage{bookmark} - -\newcommand{\coloredRule}[3][black]{\textcolor{#1}{\rule{#2}{#3}}} -\newlength{\blacktrianglewidth} -\settowidth{\blacktrianglewidth}{$\blacktriangleright$} - -\definecolor{lightgrey}{gray}{0.91} -\definecolor{lightred}{rgb}{1,0.6,0.6} -\definecolor{darkgrey}{gray}{0.6} -\definecolor{darkgreen}{rgb}{0,0.6,0} - -%numbered theorems -\theoremstyle{break} -\theorembodyfont{} - -\mdfdefinestyle{boxedtheorem}{% - outerlinewidth=3pt,% - skipabove=5pt,% - skipbelow=10pt,% - frametitlefont=\normalfont\bfseries\color{black},% - nobreak,%enforce no pagebrakes in the whole frame -} - -\newmdtheoremenv[% - style=boxedtheorem,% - innertopmargin=\topskip,% - innerbottommargin=\topskip,% - linecolor=darkgrey,% - backgroundcolor=lightgrey,% -]{theorem}{Theorem}[section] - -\newmdtheoremenv[% - style=boxedtheorem,% - linecolor=darkgrey,% - topline=false,% - rightline=false,% - bottomline=false,% - innertopmargin=\topskip,% - innerbottommargin=\topskip,% - backgroundcolor=lightgrey,% -]{proposition}[theorem]{Satz} - -\newmdtheoremenv[% - style=boxedtheorem,% - linecolor=darkgrey,% - topline=false,% - rightline=false,% - bottomline=false,% - backgroundcolor=lightgrey,% - innertopmargin=\topskip,% - innerbottommargin=\topskip,% -]{lemma}[theorem]{Lemma} - -\newmdtheoremenv[% - style=boxedtheorem,% - linecolor=red,% - topline=false,% - rightline=false,% - bottomline=false,% - innertopmargin=0,% - innerbottommargin=-3pt,% -]{definition}[theorem]{Definition} - -\newmdtheoremenv[% - outerlinewidth=3pt,% - linecolor=black,% - topline=false,% - rightline=false,% - bottomline=false,% - innertopmargin=0pt,% - innerbottommargin=-0pt,% - frametitlefont=\normalfont\bfseries\color{black},% - skipabove=5pt,% - skipbelow=10pt,% -]{conclusion}[theorem]{Folgerung} - -\newmdtheoremenv[% - hidealllines=true,% - frametitlefont=\normalfont\bfseries\color{black},% - innerleftmargin=0pt,% - skipabove=5pt,% - innerleftmargin=10pt,% -]{remark}[theorem]{\hspace*{-10pt}$\blacktriangleright$\hspace*{\dimexpr 10pt - \blacktrianglewidth\relax}Bemerkung} - -\newmdtheoremenv[% - hidealllines=true,% - frametitlefont=\normalfont\bfseries\color{black},% - innerleftmargin=10pt,% -]{example}[theorem]{\hspace*{-10pt}\rule{5pt}{5pt}\hspace*{5pt}Beispiel} - -%unnumbered theorems -\theoremstyle{nonumberbreak} -\theoremindent0cm -\newmdtheoremenv[% - style=boxedtheorem,% - linecolor=red,% - topline=false,% - rightline=false,% - bottomline=false,% - innertopmargin=1pt,% - innerbottommargin=1pt,% -]{*definition}{Definition} - -\newmdtheoremenv[% - hidealllines=true,% - frametitlefont=\normalfont\bfseries\color{black},% - skipabove=5pt,% - innerleftmargin=10pt,% -]{*remark}{\hspace*{-10pt}$\blacktriangleright$\hspace*{\dimexpr 10pt - \blacktrianglewidth\relax}Bemerkung} - -\newmdtheoremenv[% - hidealllines=true,% - innerleftmargin=10pt,% -]{*example}{\hspace*{-10pt}\rule{5pt}{5pt}\hspace*{5pt}Beispiel} -\newtheorem{overview}[theorem]{Überblick} - -\newmdtheoremenv[% - style=boxedtheorem,% - topline=false,% - rightline=false,% - leftline=false, - bottomline=false,% - innertopmargin=\topskip,% - innerbottommargin=\topskip,% - backgroundcolor=lightgrey,% -]{*anmerkung}{Anmerkung} - -\newmdtheoremenv[% -style=boxedtheorem,% -topline=false,% -rightline=false,% -leftline=false, -bottomline=false,% -innertopmargin=\topskip,% -innerbottommargin=\topskip,% -backgroundcolor=lightgrey,% -]{mathematica}{Mathematica/WolframAlpha-Befehle} - -%Hinweis-Theoremstyle and environment -%To get rid of the parentheses, a new theorem style is neccessary (definition of nonumberbreak from ntheorem.sty) -%to achieve the underlining, this needed to put in the theoremstyle definition -\theoremheaderfont{\mdseries} -\theoremseparator{:} -\theorempostskip{0pt} -\makeatletter -\newtheoremstyle{noparentheses}% - {\item[\rlap{\vbox{\hbox{\hskip\labelsep \theorem@headerfont - \underline{##1}\theorem@separator}\hbox{\strut}}}]}% - {\item[\rlap{\vbox{\hbox{\hskip\labelsep \theorem@headerfont - \underline{##1\ ##3\theorem@separator}}\hbox{\strut}}}]} -\newtheoremstyle{underlinedPlain}% - {\item[\hskip\labelsep \uline{\theorem@headerfont ##1\theorem@separator}]}% - {\item[\hskip\labelsep \uline{\theorem@headerfont ##1\ \theorem@headerfont(##3)\theorem@separator}]} -\newtheoremstyle{underlinedEnvironment}{}% -{\item[\hskip\labelsep \uline{##1\theorem@headerfont ##3\theorem@separator}]} -\newtheoremstyle{boldEnvironment}{}% -{\item[\hskip\labelsep \textbf{##1\theorem@headerfont ##3\theorem@separator}]} -\newtheoremstyle{proofstyle}% -{\item[\hskip\labelsep {\theorem@headerfont ##1}\theorem@separator]}% -{\item[\hskip\labelsep {\theorem@headerfont ##1}\ (##3)\theorem@separator]} -\makeatother - -\theoremstyle{noparentheses} -\newmdtheoremenv[% - hidealllines=true,% - innerleftmargin=1em,% - innerbottommargin=0pt,% - innerrightmargin=0,% - skipbelow=0pt,% -]{interpretation}{\hspace*{\dimexpr - \mdflength{innerleftmargin}\relax}Interpretation} -\theoremstyle{underlinedPlain} -\newmdtheoremenv[% - hidealllines=true,% - innerleftmargin=1em,% - innerrightmargin=0,% - skipbelow=0pt,% -]{hint}{\hspace*{\dimexpr - \mdflength{innerleftmargin}\relax}Hinweis} - -\theoremstyle{underlinedEnvironment} -\newmdtheoremenv[% - hidealllines=true,% - innerleftmargin=1em,% - innerrightmargin=0,% - skipbelow=0pt,% -]{underlinedenvironment}{\hspace*{\dimexpr -\mdflength{innerleftmargin}\relax}} -\theoremheaderfont{\bfseries} -\theoremstyle{boldEnvironment} -\newmdtheoremenv[% - hidealllines=true,% - innerleftmargin=1em,% - innerrightmargin=0,% - skipbelow=0pt,% -]{boldenvironment}{\hspace*{\dimexpr -\mdflength{innerleftmargin}\relax}} - -\theoremstyle{proofstyle} -\theoremheaderfont{\normalfont\normalsize\itshape} -\theorembodyfont{\normalfont\small} -\theoremseparator{.} -\theorempreskip{5pt} -\theorempostskip{5pt} -\theoremsymbol{$\square$} -\renewtheorem{proof}{Beweis} - -%for \cref: printed environment names -\crefname{theorem}{Theorem}{Theoreme} -\crefname{proposition}{Satz}{Sätze} -\crefname{lemma}{Lemma}{Lemmata} -\crefname{conclusion}{Folgerung}{Folgerungen} -\crefname{definition}{Definition}{Definitionen} -\crefname{remark}{Bemerkung}{Bemerkungen} -\crefname{example}{Beispiel}{Beispiele} -\crefname{*definition}{Definition}{Definitionen} -\crefname{*remark}{Bemerkung}{Bemerkungen} -\crefname{*example}{Beispiel}{Beispiele} - -\makeatletter -%output a number in upper roman letters -\newcommand*{\rom}[1]{\expandafter\@slowromancap\romannumeral #1@} -%declare a new label; store current chapter number -\newcommand*{\proplbl}[1]{% - \@bsphack - \begingroup - \label{#1}% - \zref@setcurrent{default}{\arabic{chapter}}% -% \zref@wrapper@immediate{% - \zref@labelbyprops{#1@chapter}{default} -% } - \endgroup - \@esphack -} - -%refer to a label set by proplbl. -%If the label is not defined (yet), question marks are output at the calling position. If the label is defined, the chapter number is prepended to the link output by \cref if the current chapter number and the one set when calling \proplbl differ. -%the macro handels both text and math mode. mbox is needed due to a feature concerning ulem / cleveref -\newcommand*{\propref}[1]{% - \ifcsdef{r@#1}%in first compilation the label may not be defined yet - {% - \zref@refused{#1@chapter}% - \cref@gettype{#1}{\propositionref@current@type}%get the environment's name - \ifnumcomp{\value{chapter}}{=}{\zref@extractdefault{#1@chapter}{default}{0}}% - {%same chapter - \ifmmode - \ref{#1}% - \else - \mbox{\cref{#1}}% - \fi - }% - {%otherwise - %example for following line: - %\crefformat{truetheorem}{\cref@truetheorem@name~##2\rom{\zref@extractdefault{#1}{#1chapter}{1}}.##1##3} - %this changes the format used by \cref to .. - \crefformat{\propositionref@current@type}{% - \csname cref@\propositionref@current@type @name\endcsname ~##2\rom{\zref@extractdefault{#1@chapter}{default}{1}}.##1##3% - }% - \ifmmode - \ref{#1}% - \else - \mbox{\cref{#1}}% - \fi - \crefformat{\propositionref@current@type}{% - \csname cref@\propositionref@current@type @name\endcsname~##2##1##3% - }% - }% - }% - {??}%similar to \ref\cref: question marks in case of undefined labels -} -\makeatother - -%declare new term to the index, output if no star is given to call position -\NewDocumentCommand{\begriff}{s O{} m O{}}{% - \IfBooleanTF{#1}% - {\index{#2#3#4}}% - {% - \uline{#3} % - \index{#2#3#4}% - }% -} - -%append a new mathsymbol to the index, output if no star is given at the call position -\NewDocumentCommand{\mathsymbol}{s O{} m m O{}}{% - \IfBooleanTF{#1}% - {\index[symbols]{#2#3@\detokenize{#4}#5}}% - {#4\index[symbols]{#2#3@\detokenize{#4}#5}}% -} - -%remove skip before / after amsmath-environments: default to 0pt. 1star: just before the environment, 2stars: just after the environment, no star: both -\NewDocumentCommand{\zeroAmsmathAlignVSpaces}{s s O{0 pt} O{0 pt}}{% - \IfBooleanTF{#1}% - {% - \IfBooleanTF{#2}% - {\setlength{\belowdisplayskip}{#4}}% - {\setlength{\abovedisplayskip}{#3}}% - }% - {% - \setlength{\abovedisplayskip}{#3}% - \setlength{\belowdisplayskip}{#4}% - }% -} - -%general transpose-makro -\NewDocumentCommand{\transpose}{m}{\ensuremath{#1^\mathsf{T}}} - -%unused -\NewDocumentCommand{\itemEq}{s m}{% - \begingroup% - \setlength{\abovedisplayskip}{\dimexpr -\parskip + 1pt\relax}% - \setlength{\belowdisplayskip}{0pt}% - \IfBooleanTF{#1}% - {\parbox[c]{\linewidth}{\begin{flalign*}#2&&\end{flalign*}}}%} - {\parbox[c]{\linewidth}{\begin{flalign}#2&&\end{flalign}}}%} - \endgroup% -} - -%new macro for "equals" ^= -\newcommand\equalhat{\mathrel{\stackon[1.5pt]{=}{\stretchto{% - \scalerel*[\widthof{=}]{\wedge}{\rule{1ex}{3ex}}}{0.5ex}}}} - -%macro that defines the spacing between bracket and content of a matrix -\NewDocumentCommand{\matrixBracketSpacing}{}{\mspace{4.0mu plus 3.0mu minus 1.0mu}} -%macro width customized spacing between bracktes / content, lineheight and columnwidth -\newenvironment{henrysmatrix}{% - \renewcommand*{\arraystretch}{1.2} - \setlength\arraycolsep{5pt} - \left(\matrixBracketSpacing - \begin{matrix} -}{% - \end{matrix} - \matrixBracketSpacing\right) -} - -\makeatletter -%redefine \overline to customize the space between text / line (currently 0.4mm + height of the content) -%ATTENTION: when changing the 0.4mm unfortunately, in \kringel the 0.4mm need to be changed accordingly -\let\@old@overline\overline -\renewcommand*{\overline}[1]{% - \@old@overline{\raisebox{0pt}[\dimexpr\height+0.4mm\relax]{$#1$}}% -} - -%encircle some content. Arguments: border color (optional), background color (mandatory), content (mandatory) -%two lengths to get width / height of content (important for width / height of the circle) -\newlength{\@kringel@contentheight} -\newlength{\@kringel@contentwidth} -\newlength{\@kringel@depth} -\NewDocumentCommand{\kringel}{O{blue} m m}{% -%as the macro should work for both text and math mode, add some macros for later use to distinguish -%in text mode, nothing happens (except discarding the 1st argument for the raisebox, that is permantently given), in math mode, the content needs to be enbraced by \ensuremath, the tcolorbox-environment by a raisebox -%ATTENTION: when changing the height-factor of tcolorbox, the depth correction needs to be changed as well - \let\@kringel@inner\relax - \let\@kringel@outer\@secondoftwo - \ifmmode - \let\@kringel@inner\ensuremath - \let\@kringel@outer\raisebox - \fi -%set the width and height - \settoheight{\@kringel@contentheight}{\hbox{\@kringel@inner{#3}}} - \settowidth{\@kringel@contentwidth}{\@kringel@inner{#3}} - \settodepth{\@kringel@depth}{\@kringel@inner{#3}} -%change the depth correction dependend whethere there is a depth (e.g. y) or not (e.g. a) - \ifdim \@kringel@depth > 0pt% - \setlength{\@kringel@depth}{\dimexpr\@kringel@depth+0.5mm\relax} - \else - \settodepth{\@kringel@depth}{y} - \setlength{\@kringel@depth}{\dimexpr\@kringel@depth+0.3mm\relax} - \fi -%output the colorbox width given parameter: frame color, background color, computed width and height, and escaped content depending on math / text mode - \@kringel@outer{\dimexpr-\@kringel@contentheight/2-\@kringel@depth\relax}{\begin{tcolorbox}[colframe=#1,halign=center,valign=center,width=\dimexpr1.5\@kringel@contentwidth+1mm\relax,height=2.5\@kringel@contentheight,left=0pt,right=0pt,bottom=0pt,top=0pt,boxrule=0.8pt,colback=#2,boxsep=0pt,bean arc] - \@kringel@inner{#3} - \end{tcolorbox}} -} - -%switch numbering of equations (amsmath-environments) -\newcommand{\leqnos}{\tagsleft@true\let\veqno\@@leqno} -\newcommand{\reqnos}{\tagsleft@false\let\veqno\@@eqno} -\reqnos - -\pdfstringdefDisableCommands{% - \def\\{}% - \def\texttt#1{<#1>}% - \def\mathbb#1{<#1>}% -} -\makeatother - -%General newcommands! -\newcommand{\comp}{\mathbb{C}} % complex set C -\newcommand{\real}{\mathbb{R}} % real set R -\newcommand{\whole}{\mathbb{Z}} % whole number Symbol -\newcommand{\natur}{\mathbb{N}} % natural number Symbol -\newcommand{\ratio}{\mathbb{Q}} % rational number symbol -\newcommand{\field}{\mathbb{K}} % general field for the others above! -\newcommand{\diff}{\mathrm{d}} % differential d -\newcommand{\s}{\,\,} % space after the function in the intergral -\newcommand{\cont}{\mathcal{C}} % Contour C -\newcommand{\fuk}{f(z) \s\diff z} % f(z) dz -\newcommand{\diffz}{\s\diff z} -\newcommand{\subint}{\int\limits} % lower boundaries for the integral -\newcommand{\poly}{\mathcal{P}} % special P - polygon -\newcommand{\defi}{\mathcal{D}} % D for the domain of a function -\newcommand{\cover}{\mathcal{U}} % cover for a set -\newcommand{\setsys}{\mathcal{M}} % set system M -\newcommand{\setnys}{\mathcal{N}} % set system N -\newcommand{\zetafunk}{f(\zeta)\s\diff \zeta} %f(zeta) d zeta -\newcommand{\ztfunk}{f(\zeta)} % f(zeta) -\newcommand{\bocirc}{S_r(z)} -\newcommand{\prop}{\,|\,} -\newcommand*{\QEDA}{\hfill\ensuremath{\blacksquare}} %tombstone -\newcommand{\emptybra}{\{\varnothing\}} % empty set with set-bracket -\newcommand{\realpos}{\real_{>0}} -\newcommand{\realposr}{\real_{\geq0}} -\newcommand{\naturpos}{\natur_{>0}} -\newcommand{\Imag}{\operatorname{Im}} % Imaginary symbol -\newcommand{\Realz}{\operatorname{Re}} % Real symbol -\newcommand{\norm}{\Vert \cdot \Vert} -\newcommand{\metric}{\vert \cdot \vert} -\newcommand{\foralln}{\forall n} %all n -\newcommand{\forallnset}{\forall n \in \natur} %all n € |N -\newcommand{\forallnz}{\forall n \geq _0} % all n >= n_0 -\newcommand{\conjz}{\overline{z}} % conjugated z -\newcommand{\tildz}{\tilde{z}} % different z -\newcommand{\lproofar}{"`$ \Leftarrow $"'} % "`<="' -\newcommand{\rproofar}{"`$ \Rightarrow $"'} % "`=>"' -\newcommand{\beha}{\Rightarrow \text{ Behauptung}} -\newcommand{\powerset}{\mathcal{P}} -\newcommand{\person}[1]{\textsc{#1}} -\newcommand{\highlight}[1]{\emph{#1}} -\newcommand{\realz}{\mathfrak{Re}} -\newcommand{\imagz}{\mathfrak{Im}} -\renewcommand{\epsilon}{\varepsilon} -\renewcommand{\phi}{\varphi} -\newcommand{\lebesque}{\person{Lebesgue}} -\renewcommand{\Re}{\mathfrak{Re}} -\renewcommand{\Im}{\mathfrak{Im}} -\renewcommand*{\arraystretch}{1.4} -\newcommand{\skalar}[2]{\left\langle #1,#2\right\rangle} -\newcommand{\qraum}[2]{\sfrac{#1}{#2}} - -% Math Operators -\DeclareMathOperator{\inn}{int} % Set of inner points -\DeclareMathOperator{\ext}{ext} % Set of outer points -\DeclareMathOperator{\cl}{cl} % Closure -\DeclareMathOperator{\grad}{grad} -\DeclareMathOperator{\D}{d} -\DeclareMathOperator{\id}{id} -\DeclareMathOperator{\graph}{graph} -\DeclareMathOperator{\Int}{int} -\DeclareMathOperator{\Ext}{ext} -\DeclareMathOperator{\diam}{diam} - -\DeclareMathOperator{\End}{End} -\DeclareMathOperator{\Aff}{Aff} -\DeclareMathOperator{\Aut}{Aut} -\DeclareMathOperator{\Hom}{Hom} -\DeclareMathOperator{\Abb}{Abb} -\DeclareMathOperator{\Bil}{Bil} -\DeclareMathOperator{\Eig}{Eig} -\DeclareMathOperator{\Mat}{Mat} -\DeclareMathOperator{\Ker}{Ker} -\DeclareMathOperator{\diag}{diag} -\DeclareMathOperator{\GL}{GL} -\DeclareMathOperator{\tr}{tr} -\DeclareMathOperator{\rk}{rk} -\DeclareMathOperator{\ZR}{ZR} -\DeclareMathOperator{\SR}{SR} -\DeclareMathOperator{\sgn}{sgn} -\DeclareMathOperator{\Span}{span} -\DeclareMathOperator{\Image}{Im} -\DeclareMathOperator{\Sym}{Sym} -\DeclareMathOperator{\Hau}{Hau} -\DeclareMathOperator{\pr}{pr} -\DeclareMathOperator{\Orth}{O} -\DeclareMathOperator{\SO}{SO} -\DeclareMathOperator{\Uni}{U} -\DeclareMathOperator{\SU}{SU} -\DeclareMathOperator{\SL}{SL} -\DeclareMathOperator{\ggT}{ggT} -\DeclareMathOperator{\kgV}{kgV} - -%change headings: -\titlelabel{\thetitle.\quad}%. behind section/sub... (3. instead of 3) -\counterwithout{section}{chapter} -\renewcommand{\thechapter}{\Roman{chapter}} -\renewcommand{\thepart}{\Alph{part}} -%italic chapters (due to titlesec package some more stuff) -%\titleformat{command}[shape]{format}{label}{sep}{before-code}[after-code] -\titleformat{\chapter}[display]{\bfseries}{\Large\chaptername\;\thechapter}{-5pt}{\huge\bfseries\itshape} -\titlespacing{\chapter}{0pt}{0pt}{10pt} -\titleformat{\section}[hang]{\bfseries\Large}{\thesection.}{8pt}{\Large\bfseries} -%\titlespacing{command}{left}{before-sep}{after-sep} -\titlespacing{\subsection}{0pt}{0pt}{5pt} - -%change appearence of heading of toc: 0 space above, bold, italic huge toc-heading -\renewcommand{\cftbeforetoctitleskip}{0pt} -\renewcommand{\cfttoctitlefont}{\itshape\Huge\bfseries} -%change indentations due to width of capital roman numbers -\renewcommand{\cftchapnumwidth}{2.5em} -\renewcommand{\cftsecindent}{2.5em} -%\renewcommand{\cftsecnumwidth}{3.3em} -\renewcommand{\cftsubsecindent}{4.8em} -%\renewcommand{\cftsubsecnumwidth}{4.2em} - -%change header: -\renewcommand{\headrulewidth}{0.75pt} -\renewcommand{\footrulewidth}{0.3pt} -\lhead{\rightmark}%left: section-number. section-title -\rhead{\leftmark}%right: chapter chapternumber: chapter-title - -% Add new page-style (just footer), patch \chapter command to use this page style -\fancypagestyle{plainChapter}{% - \fancyhf{}% - \fancyfoot[C]{\thepage}% - \renewcommand{\headrulewidth}{0pt}% Line at the header invisible - \renewcommand{\footrulewidth}{0.4pt}% Line at the footer visible -} -%changes pagestyle; instead of empty page the normal footer is printed -\patchcmd{\chapter}{\thispagestyle{plain}}{\thispagestyle{plainChapter}}{}{} -%usually, after a new chapter the section counter needs to be reset manually. Instead, automatic reset -\pretocmd{\chapter}{\setcounter{section}{0}}{}{} - -\pagestyle{fancy} -\pagenumbering{arabic} -%remember chapter-title in \leftmark and \rightmark -\renewcommand{\chaptermark}[1]{% - \markboth{\chaptername - \ \thechapter:\ #1}{}} -%remember section title in \leftmark -\renewcommand{\sectionmark}[1]{% - \markright{\thesection.\ #1}{}} - -%change numbering of equations to be section by section -\counterwithout{equation}{section} +\documentclass[ngerman,a4paper,order=firstname]{../../texmf/tex/latex/mathscript/mathscript} +\usepackage{../../texmf/tex/latex/mathoperators/mathoperators} \title{\textbf{Lineare Algebra SS2018}} \author{Dozent: Prof. Dr. Arno Fehm} -%remove page number from part{}-pages -\makeatletter -\let\sv@endpart\@endpart -\def\@endpart{\thispagestyle{empty}\sv@endpart} -\makeatother - \begin{document} \pagenumbering{roman} \pagestyle{plain} @@ -646,7 +15,6 @@ backgroundcolor=lightgrey,% \bookmark[dest=tocpage,level=1]{Inhaltsverzeichnis} \pagebreak -\pagestyle{fancy} \pagenumbering{arabic} \pagestyle{fancy} @@ -691,68 +59,6 @@ backgroundcolor=lightgrey,% \part*{Anhang} \addcontentsline{toc}{part}{Anhang} \appendix -\patchcmd{\chapter}{\thispagestyle{plainChapter}}{\thispagestyle{fancy}}{}{} -%\titleformat{command}[shape]{format}{label}{sep}{before-code}[after-code] -%\titlespacing{command}{left}{before-sep}{after-sep} -\renewcommand{\chaptername}{Anhang} -\renewcommand{\thechapter}{\Alph{chapter}} -\titleformat{\chapter}[hang]{\bfseries}{\LARGE\chaptername\ \thechapter:}{0.5em}{\LARGE\bfseries} -\titlespacing{\chapter}{0pt}{-0.75cm}{0pt} -\renewcommand{\thesection}{\Alph{chapter}.\arabic{section}} - -%from ntheorem.sty -%\def\thm@@thmline@name#1#2#3#4#5{% -% \ifx\\#5\\% -% \@dottedtocline{-2}{0em}{2.3em}% -% {#1 \protect\numberline{#2}#3}% -% {#4} -% \else -% \ifHy@linktocpage\relax\relax -% \@dottedtocline{-2}{0em}{2.3em}% -% {#1 \protect\numberline{#2}#3}% -% {\hyper@linkstart{link}{#5}{#4}\hyper@linkend}% -% \else -% \@dottedtocline{-2}{0em}{2.3em}% -% {\hyper@linkstart{link}{#5}% -% {#1 \protect\numberline{#2}#3}\hyper@linkend}% -% {#4}% -% \fi -% \fi -%} - -\makeatletter -%update ntheorem macro to provide space between theorem numbers and any optional comment, adds in upper roman letters the chapter number. removes any numbering for theorem environments with just one counter -\renewcommand{\thm@@thmline@name}[5]{%- - \def\thm@@thmline@name@tmp{% - \if\relax\detokenize{#3}\relax\else% - {\hspace*{2.2ex}#3}% - \fi% - } - \let\thm@@thmline@name@numbering\relax - \StrCount{#5}{.}[\thm@@thmline@name@dot@number] - \ifnum\thm@@thmline@name@dot@number < 3% - \def\thm@@thmline@name@tmp{\hspace*{-1em}#3} - \else% - \StrBetween[1,2]{#5}{.}{.}[\thm@@thmline@name@chap@num]%get the chapter number for roman transliteration - \def\thm@@thmline@name@numbering{\rom{\thm@@thmline@name@chap@num}.#2} - \fi - \ifx\\#5\\% - \@dottedtocline{-2}{0em}{4.4em}% - {#1 \protect\numberline{\thm@@thmline@name@numbering:}{}}% - {#4} - \else - \ifHy@linktocpage\relax\relax - \@dottedtocline{-2}{0em}{1.3em}% - {#1 \protect\numberline{\thm@@thmline@name@numbering:}\thm@@thmline@name@tmp}% - {\hyper@linkstart{link}{#5}{#4}\hyper@linkend}% - \else - \@dottedtocline{-2}{0em}{4.em}% - {#1 \protect\numberline{\thm@@thmline@name@numbering:}\thm@@thmline@name@tmp}% - {\hyper@linkstart{link}{#5}{#4}\hyper@linkend}% - \fi - \fi -} -\makeatother \chapter{Listen} \section{Liste der Theoreme} @@ -774,4 +80,4 @@ backgroundcolor=lightgrey,% \printindex -\end{document} +\end{document} \ No newline at end of file diff --git a/texmf/tex/latex/mathoperators/mathoperators.sty b/texmf/tex/latex/mathoperators/mathoperators.sty new file mode 100644 index 0000000..29db786 --- /dev/null +++ b/texmf/tex/latex/mathoperators/mathoperators.sty @@ -0,0 +1,110 @@ +\ProvidesPackage{mathoperators} + +%Provides some common math related commands and operators +\RequirePackage{amsmath} +\RequirePackage{amssymb} +\RequirePackage{amsfonts} +\RequirePackage{scalerel,stackengine} +\RequirePackage{calc} + +%transpose +\newcommand\transpose[1]{\ensuremath{#1^\mathsf{T}}} +%new macro for "equals" ^= +\newcommand\equalhat{\mathrel{\stackon[1.5pt]{=}{\stretchto{% + \scalerel*[\widthof{=}]{\wedge}{\rule{1ex}{3ex}}}{0.5ex}}}} + +%General newcommands! +\newcommand{\comp}{\mathbb{C}} % complex set C +\newcommand{\real}{\mathbb{R}} % real set R +\newcommand{\whole}{\mathbb{Z}} % whole number Symbol +\newcommand{\natur}{\mathbb{N}} % natural number Symbol +\newcommand{\ratio}{\mathbb{Q}} % rational number symbol +\newcommand{\field}{\mathbb{K}} % general field for the others above! +\newcommand{\diff}{\mathrm{d}} % differential d +\newcommand{\s}{\,\,} % space after the function in the intergral +\newcommand{\cont}{\mathcal{C}} % Contour C +\newcommand{\fuk}{f(z) \s\diff z} % f(z) dz +\newcommand{\diffz}{\s\diff z} +\newcommand{\subint}{\int\limits} % lower boundaries for the integral +\newcommand{\poly}{\mathcal{P}} % special P - polygon +\newcommand{\defi}{\mathcal{D}} % D for the domain of a function +\newcommand{\cover}{\mathcal{U}} % cover for a set +\newcommand{\setsys}{\mathcal{M}} % set system M +\newcommand{\setnys}{\mathcal{N}} % set system N +\newcommand{\zetafunk}{f(\zeta)\s\diff \zeta} %f(zeta) d zeta +\newcommand{\ztfunk}{f(\zeta)} % f(zeta) +\newcommand{\bocirc}{S_r(z)} +\newcommand{\prop}{\,|\,} +\newcommand*{\QEDA}{\hfill\ensuremath{\blacksquare}} %tombstone +\newcommand{\emptybra}{\{\varnothing\}} % empty set with set-bracket +\newcommand{\realpos}{\real_{>0}} +\newcommand{\realposr}{\real_{\geq0}} +\newcommand{\naturpos}{\natur_{>0}} +\newcommand{\Imag}{\operatorname{Im}} % Imaginary symbol +\newcommand{\Realz}{\operatorname{Re}} % Real symbol +\newcommand{\norm}{\Vert \cdot \Vert} +\newcommand{\metric}{\vert \cdot \vert} +\newcommand{\foralln}{\forall n} %all n +\newcommand{\forallnset}{\forall n \in \natur} %all n € |N +\newcommand{\forallnz}{\forall n \geq _0} % all n >= n_0 +\newcommand{\conjz}{\overline{z}} % conjugated z +\newcommand{\tildz}{\tilde{z}} % different z +\newcommand{\lproofar}{"`$ \Leftarrow $"'} % "`<="' +\newcommand{\rproofar}{"`$ \Rightarrow $"'} % "`=>"' +\newcommand{\beha}{\Rightarrow \text{ Behauptung}} +\newcommand{\powerset}{\mathcal{P}} +\newcommand{\person}[1]{\textsc{#1}} +\newcommand{\highlight}[1]{\emph{#1}} +\newcommand{\realz}{\mathfrak{Re}} +\newcommand{\imagz}{\mathfrak{Im}} +\renewcommand{\epsilon}{\varepsilon} +\renewcommand{\phi}{\varphi} +\newcommand{\lebesque}{\textsc{Lebesgue}} +\renewcommand{\Re}{\mathfrak{Re}} +\renewcommand{\Im}{\mathfrak{Im}} +\renewcommand*{\arraystretch}{1.4} +\newcommand{\skalar}[2]{\left\langle #1,#2\right\rangle} +\newcommand{\qraum}[2]{\sfrac{#1}{#2}} + +% Math Operators +\DeclareMathOperator{\inn}{int} % Set of inner points +\DeclareMathOperator{\ext}{ext} % Set of outer points +\DeclareMathOperator{\cl}{cl} % Closure +\DeclareMathOperator{\grad}{grad} +\DeclareMathOperator{\D}{d} +\DeclareMathOperator{\id}{id} +\DeclareMathOperator{\graph}{graph} +\DeclareMathOperator{\Int}{int} +\DeclareMathOperator{\Ext}{ext} +\DeclareMathOperator{\diam}{diam} + +\DeclareMathOperator{\End}{End} +\DeclareMathOperator{\Aff}{Aff} +\DeclareMathOperator{\Aut}{Aut} +\DeclareMathOperator{\Hom}{Hom} +\DeclareMathOperator{\Abb}{Abb} +\DeclareMathOperator{\Bil}{Bil} +\DeclareMathOperator{\Eig}{Eig} +\DeclareMathOperator{\Mat}{Mat} +\DeclareMathOperator{\Ker}{Ker} +\DeclareMathOperator{\diag}{diag} +\DeclareMathOperator{\GL}{GL} +\DeclareMathOperator{\tr}{tr} +\DeclareMathOperator{\rk}{rk} +\DeclareMathOperator{\ZR}{ZR} +\DeclareMathOperator{\SR}{SR} +\DeclareMathOperator{\sgn}{sgn} +\DeclareMathOperator{\Span}{span} +\DeclareMathOperator{\Image}{Im} +\DeclareMathOperator{\Sym}{Sym} +\DeclareMathOperator{\Hau}{Hau} +\DeclareMathOperator{\pr}{pr} +\DeclareMathOperator{\Orth}{O} +\DeclareMathOperator{\SO}{SO} +\DeclareMathOperator{\Uni}{U} +\DeclareMathOperator{\SU}{SU} +\DeclareMathOperator{\SL}{SL} +\DeclareMathOperator{\ggT}{ggT} +\DeclareMathOperator{\kgV}{kgV} + +\endinput \ No newline at end of file diff --git a/texmf/tex/latex/mathscript/mathscript.cls b/texmf/tex/latex/mathscript/mathscript.cls new file mode 100644 index 0000000..778367c --- /dev/null +++ b/texmf/tex/latex/mathscript/mathscript.cls @@ -0,0 +1,648 @@ +\NeedsTeXFormat{LaTeX2e}[1995/12/01] +\ProvidesClass{mathscript}[2018/08/05 mathscript] + +%programming related packages +\RequirePackage{zref-base} +\RequirePackage{etoolbox} +\RequirePackage{xparse}%better macros +\RequirePackage{calc} +\RequirePackage{xstring} +\RequirePackage{xkeyval} + +%possible values: firstnumber, firstname +\def\theoremheader@order@val{firstnumber} +\DeclareOptionX{order}{% + %sets accordingly the required ntheoremoptions + \let\tempa\@empty + \IfEq{#1}{firstnumber}{\def\tempa{changebreak}}{% + \IfEq{#1}{firstname}{\def\tempa{break}}{% + \PackageWarning{mathscript}{Unknown Value} + } + } + \edef\theoremheader@order@val{\tempa} +} + +%possible values: all you can imagine. usefull values: in this class predefined theorem-environment-names +\listadd{\theorem@disable}{\@empty} +\DeclareOptionX{disable}{% + \listadd{\theorem@disable}{#1} +} + +\DeclareOptionX*{\PassOptionsToClass{\CurrentOption}{report}} +\ProcessOptionsX +\LoadClass[ngerman,a4paper]{report} + +\RequirePackage{ifpdf,ifluatex} + +%decent space; change explicitly the space between header and content and footer and content +\RequirePackage[left=2.1cm,right=3.1cm,bottom=3cm,footskip=0.75cm,headsep=0.5cm]{geometry} +\RequirePackage{babel} + + +\ifpdf + \ifluatex + %new lualatex needs explicit fontspec to draw properly e.g. german umlauts + \RequirePackage{fontspec} + \else + %old pdflatex needs explicitly utf-8-support + \RequirePackage[utf8]{inputenc} + \RequirePackage{chngcntr} + \RequirePackage{eufrac} + \fi +\fi + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%Layout related packages +\RequirePackage{parskip} %split paragraphs by vspace instead of intendations +\RequirePackage{fancyhdr} %customize header / footer +\RequirePackage{titlesec} %customize titles +\RequirePackage{tocloft} + +%tabulars +\RequirePackage{tabularx} %tabularx-environment (explicitly set width of columns) +\RequirePackage{multirow} +\RequirePackage{booktabs} %improved rules + +\RequirePackage[title,titletoc]{appendix} + +\RequirePackage{environ} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%Math related packages +%basic ams-math and enhancments +\RequirePackage{amsmath,amssymb,amsfonts,mathtools} + +%add some font-related stuff +\RequirePackage{latexsym} +\RequirePackage{marvosym} %lightning (contradiction) +\RequirePackage{stmaryrd} %Lightning symbol +\RequirePackage{bbm} %unitary matrix +\RequirePackage{wasysym} %add some symbols +\RequirePackage[bb=boondox]{mathalfa} %special zero using \mathbb{0} + +%further support for different equation setting +\RequirePackage{cancel} +\RequirePackage{xfrac} %sfrac -> fractions e.g. 3/4 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%Graphics-related packages +\RequirePackage[table]{xcolor} +\RequirePackage{graphicx} +\RequirePackage{tcolorbox} + +\RequirePackage{pgfplots} +\pgfplotsset{compat=1.10} +\usepgfplotslibrary{fillbetween} +\RequirePackage{pgf} +\RequirePackage{tikz} +\usetikzlibrary{patterns,arrows,calc,decorations.pathmorphing,backgrounds, positioning,fit,petri} +\usetikzlibrary{matrix} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%Text-related packages +%increase line spacing +\RequirePackage[onehalfspacing]{setspace} %increase row-space +\RequirePackage{parskip} %split paragraphs by vspace instead of intendations +\RequirePackage{ulem} %better underlines +\RequirePackage{marginnote} + +%enumeration +\RequirePackage{enumerate} +\RequirePackage{enumitem} %customize label + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%Index related packages +\RequirePackage[texindy]{imakeidx} +\indexsetup{ + level=\chapter* +} +\makeindex[intoc] + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%Theorem-related packages +\RequirePackage[amsmath,amsthm,thmmarks,hyperref]{ntheorem} +\RequirePackage[ntheorem,framemethod=TikZ]{mdframed} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\RequirePackage[unicode,bookmarks=true]{hyperref} +\hypersetup{ + colorlinks, + citecolor=green, + filecolor=green, + linkcolor=blue, + urlcolor=blue +} +\RequirePackage{cleveref} +\RequirePackage{bookmark} %pdf-bookmarks + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% End Packages % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\RenewDocumentCommand{\newmdtheoremenv}{O{} m o m o}{% + \ifinlist{#2}{\theorem@disable}{% + \IfStrEq{#2}{theorem}{\newtheorem{#2}{}[section]}{\newtheorem{#2}{}[theorem]} + \RenewEnviron{#2}{\stepcounter{theorem}}{} + }{% + %from mdframed.sty, definition of \newmdtheoremenv + \ifboolexpr{ test {\IfNoValueTF {#3}} and test {\IfNoValueTF {#5}} }% + {\newtheorem{#2}{#4}}{% + \IfValueTF{#3}{\newtheorem{#2}[#3]{#4}}{}% + \IfValueTF{#5}{\newtheorem{#2}{#4}[#5]}{}% + }% + \BeforeBeginEnvironment{#2}{% + \begin{mdframed}[#1]}% + \AfterEndEnvironment{#2}{% + \end{mdframed}}% + } +} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%Setup theorem environments + +%triangle symbol + length +\newlength{\blacktrianglewidth} +\settowidth{\blacktrianglewidth}{$\blacktriangleright$} + +%colors +\definecolor{lightgrey}{gray}{0.91} +\definecolor{lightred}{rgb}{1,0.6,0.6} +\definecolor{darkgrey}{gray}{0.6} +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\mdfdefinestyle{boxedtheorem}{% + outerlinewidth=3pt,% + skipabove=5pt,% + skipbelow=10pt,% + frametitlefont=\normalfont\bfseries\color{black},% + nobreak,%enforce no pagebrakes in the whole frame +} + +%numbered environments +\theoremstyle{\theoremheader@order@val} %set by pacakge options above +\theorembodyfont{} + +%including background +\newmdtheoremenv[% + style=boxedtheorem,% + innertopmargin=\topskip,% + innerbottommargin=\topskip,% + linecolor=darkgrey,% + backgroundcolor=lightgrey,% +]{theorem}{Theorem}[section] + +\newmdtheoremenv[% + style=boxedtheorem,% + linecolor=darkgrey,% + topline=false,% + rightline=false,% + bottomline=false,% + innertopmargin=\topskip,% + innerbottommargin=\topskip,% + backgroundcolor=lightgrey,% +]{proposition}[theorem]{Satz} + +\newmdtheoremenv[% + style=boxedtheorem,% + linecolor=darkgrey,% + topline=false,% + rightline=false,% + bottomline=false,% + backgroundcolor=lightgrey,% + innertopmargin=\topskip,% + innerbottommargin=\topskip,% +]{lemma}[theorem]{Lemma} + +%excluding background +\newmdtheoremenv[% + style=boxedtheorem,% + linecolor=red,% + topline=false,% + rightline=false,% + bottomline=false,% + innertopmargin=0,% + innerbottommargin=-3pt,% +]{definition}[theorem]{Definition} + +\newmdtheoremenv[% + outerlinewidth=3pt,% + linecolor=black,% + topline=false,% + rightline=false,% + bottomline=false,% + innertopmargin=0pt,% + innerbottommargin=-0pt,% + frametitlefont=\normalfont\bfseries\color{black},% + skipabove=5pt,% + skipbelow=10pt,% +]{conclusion}[theorem]{Folgerung} + +\newmdtheoremenv[% + hidealllines=true,% + frametitlefont=\normalfont\bfseries\color{black},% + innerleftmargin=0pt,% + skipabove=5pt,% + innerleftmargin=10pt,% +]{remark}[theorem]{\hspace*{-10pt}$\blacktriangleright$\hspace*{\dimexpr 10pt - \blacktrianglewidth\relax}Bemerkung} + +\newmdtheoremenv[% + hidealllines=true,% + frametitlefont=\normalfont\bfseries\color{black},% + innerleftmargin=10pt,% +]{example}[theorem]{\hspace*{-10pt}\rule{5pt}{5pt}\hspace*{5pt}Beispiel} + +%unnumbered theorems +\theoremstyle{nonumberbreak} +\theoremindent0cm + +\newmdtheoremenv[% + style=boxedtheorem,% + linecolor=red,% + topline=false,% + rightline=false,% + bottomline=false,% + innertopmargin=1pt,% + innerbottommargin=1pt,% +]{*definition}{Definition} + +\newmdtheoremenv[% + hidealllines=true,% + frametitlefont=\normalfont\bfseries\color{black},% + skipabove=5pt,% + innerleftmargin=10pt,% +]{*remark}{\hspace*{-10pt}$\blacktriangleright$\hspace*{\dimexpr 10pt - \blacktrianglewidth\relax}Bemerkung} + +\newmdtheoremenv[% + hidealllines=true,% + innerleftmargin=10pt,% +]{*example}{\hspace*{-10pt}\rule{5pt}{5pt}\hspace*{5pt}Beispiel} + +\newmdtheoremenv[% + style=boxedtheorem,% + hidealllines=true,% + innertopmargin=\topskip,% + innerbottommargin=\topskip,% + backgroundcolor=lightgrey,% +]{*anmerkung}{Anmerkung} + +\newmdtheoremenv[% + style=boxedtheorem,% + hidealllines=true,% + innertopmargin=\topskip,% + innerbottommargin=\topskip,% + backgroundcolor=lightgrey,% +]{mathematica}{Mathematica/WolframAlpha-Befehle} + +\newtheorem{overview}[theorem]{Überblick} + +%various unnumbered thereoms and environment (usually included in theorems like above) +%To get rid of the parentheses, a new theorem style is neccessary (definition of nonumberbreak from ntheorem.sty) +%to achieve the underlining, this needed to put in the theoremstyle definition +\theoremheaderfont{\mdseries} +\theoremseparator{:} +\theorempostskip{0pt} + +%define new theorem-styles +\newtheoremstyle{noparentheses}% +{\item[\rlap{\vbox{\hbox{\hskip\labelsep \theorem@headerfont + \underline{##1}\theorem@separator}\hbox{\strut}}}]}% +{\item[\rlap{\vbox{\hbox{\hskip\labelsep \theorem@headerfont + \underline{##1\ ##3\theorem@separator}}\hbox{\strut}}}]} + +\newtheoremstyle{underlinedPlain}% +{\item[\hskip\labelsep \uline{\theorem@headerfont ##1\theorem@separator}]}% +{\item[\hskip\labelsep \uline{\theorem@headerfont ##1\ \theorem@headerfont(##3)\theorem@separator}]} + +\newtheoremstyle{underlinedEnvironment}{}% +{\item[\hskip\labelsep \uline{##1\theorem@headerfont ##3\theorem@separator}]} + +\newtheoremstyle{boldEnvironment}{}% +{\item[\hskip\labelsep \textbf{##1\theorem@headerfont ##3\theorem@separator}]} + +%theorems +\theoremstyle{noparentheses} +\newmdtheoremenv[% + hidealllines=true,% + innerleftmargin=1em,% + innerbottommargin=0pt,% + innerrightmargin=0,% + skipbelow=0pt,% +]{interpretation}{\hspace*{\dimexpr - \mdflength{innerleftmargin}\relax}Interpretation} + +\theoremstyle{underlinedPlain} +\newmdtheoremenv[% + hidealllines=true,% + innerleftmargin=1em,% + innerrightmargin=0,% + skipbelow=0pt,% +]{hint}{\hspace*{\dimexpr - \mdflength{innerleftmargin}\relax}Hinweis} + +\theoremstyle{underlinedEnvironment} +\newmdtheoremenv[% + hidealllines=true,% + innerleftmargin=1em,% + innerrightmargin=0,% + skipbelow=0pt,% +]{underlinedenvironment}{\hspace*{\dimexpr -\mdflength{innerleftmargin}\relax}} + +\theoremheaderfont{\bfseries} +\theoremstyle{boldEnvironment} +\newmdtheoremenv[% + hidealllines=true,% + innerleftmargin=1em,% + innerrightmargin=0,% + skipbelow=0pt,% +]{boldenvironment}{\hspace*{\dimexpr -\mdflength{innerleftmargin}\relax}} + +%proofs +\newtheoremstyle{proofstyle}% +{\item[\hskip\labelsep {\theorem@headerfont ##1}\theorem@separator]}% +{\item[\hskip\labelsep {\theorem@headerfont ##1}\ (##3)\theorem@separator]} + +\theoremstyle{proofstyle} +\theoremheaderfont{\normalfont\normalsize\itshape} +\theorembodyfont{\normalfont\small} +\theoremseparator{.} +\theorempreskip{5pt} +\theorempostskip{5pt} +\theoremsymbol{$\square$} + +\ifinlist{proof}{\theorem@disable}{\RenewEnviron{proof}{}{}}{\renewtheorem{proof}{Beweis}} + +%cref: print correct translation +\crefname{theorem}{Theorem}{Theoreme} +\crefname{proposition}{Satz}{Sätze} +\crefname{lemma}{Lemma}{Lemmata} +\crefname{conclusion}{Folgerung}{Folgerungen} +\crefname{definition}{Definition}{Definitionen} +\crefname{remark}{Bemerkung}{Bemerkungen} +\crefname{example}{Beispiel}{Beispiele} +\crefname{*definition}{Definition}{Definitionen} +\crefname{*remark}{Bemerkung}{Bemerkungen} +\crefname{*example}{Beispiel}{Beispiele} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%Additional features + +%some minor commands +\newcommand*{\rom}[1]{\expandafter\@slowromancap\romannumeral #1@} %print integer in capital roman letters +\newcommand{\leqnos}{\tagsleft@true\let\veqno\@@leqno} %set equation numbering left / right +\newcommand{\reqnos}{\tagsleft@false\let\veqno\@@eqno} + +%declare a new label; store current chapter number +\newcommand*{\proplbl}[1]{% + \@bsphack + \begingroup + \label{#1}% + \zref@setcurrent{default}{\c@chapter}% + \zref@wrapper@immediate{% + \zref@labelbyprops{#1@chapter}{default}% + } + \endgroup + \@esphack +} + +%refer to a label set by proplbl. +%If the label is not defined (yet), question marks are output at the calling position. If the label is defined, the chapter number is prepended to the link output by \cref if the current chapter number and the one set when calling \proplbl differ. +%the macro handels both text and math mode. mbox is needed due to a feature concerning ulem / cleveref +\newcommand*{\propref}[1]{% + \ifcsdef{r@#1}%in first compilation the label may not be defined yet + {% + \zref@refused{#1@chapter}% + \cref@gettype{#1}{\propositionref@current@type}%get the environment's name + \ifnumcomp{\c@chapter}{=}{\zref@extractdefault{#1@chapter}{default}{\z@}}% + {%same chapter + \ifmmode + \ref{#1}% + \else + \mbox{\cref{#1}}% + \fi + }% + {%otherwise + %example for following line: + %\crefformat{truetheorem}{\cref@truetheorem@name~##2\rom{\zref@extractdefault{#1}{#1chapter}{1}}.##1##3} + %this changes the format used by \cref to .. + \crefformat{\propositionref@current@type}{% + \csname cref@\propositionref@current@type @name\endcsname ~##2\rom{\zref@extractdefault{#1@chapter}{default}{\@ne}}.##1##3% + }% + \ifmmode + \ref{#1}% + \else + \mbox{\cref{#1}}% + \fi + \crefformat{\propositionref@current@type}{% + \csname cref@\propositionref@current@type @name\endcsname~##2##1##3% + }% + }% + }% + {???}%similar to \ref\cref: question marks in case of undefined labels +} + +%declare new term to the index, output if no star is given to call position +\NewDocumentCommand{\begriff}{s O{} m O{}}{% + \IfBooleanTF{#1}% + {\index{#2#3#4}}% + {% + \uline{#3} % + \index{#2#3#4}% + }% +} + +%append a new mathsymbol to the index, output if no star is given at the call position +\NewDocumentCommand{\mathsymbol}{s O{} m m O{}}{% + \IfBooleanTF{#1}% + {\index[symbols]{#2#3@\detokenize{#4}#5}}% + {#4\index[symbols]{#2#3@\detokenize{#4}#5}}% +} + +%remove skip before / after amsmath-environments: default to 0pt. 1star: just before the environment, 2stars: just after the environment, no star: both +\NewDocumentCommand{\zeroAmsmathAlignVSpaces}{s s O{0 pt} O{0 pt}}{% + \IfBooleanTF{#1}% + {% + \IfBooleanTF{#2}% + {\setlength{\belowdisplayskip}{#4}}% + {\setlength{\abovedisplayskip}{#3}}% + }% + {% + \setlength{\abovedisplayskip}{#3}% + \setlength{\belowdisplayskip}{#4}% + }% +} + +\NewDocumentCommand{\itemEq}{s m}{% + \begingroup% + \setlength{\abovedisplayskip}{\dimexpr -\parskip + 1pt\relax}% + \setlength{\belowdisplayskip}{0pt}% + \IfBooleanTF{#1}% + {\parbox[c]{\linewidth}{\begin{flalign*}#2&&\end{flalign*}}}%} + {\parbox[c]{\linewidth}{\begin{flalign}#2&&\end{flalign}}}%} + \endgroup% +} + +%macro that defines the spacing between bracket and content of a matrix +\NewDocumentCommand{\matrixBracketSpacing}{}{\mspace{4.0mu plus 3.0mu minus 1.0mu}} +%macro width customized spacing between bracktes / content, lineheight and columnwidth +\newenvironment{henrysmatrix}{% + \renewcommand*{\arraystretch}{1.2} + \setlength\arraycolsep{5pt} + \left(\matrixBracketSpacing + \begin{matrix} + }{% + \end{matrix} + \matrixBracketSpacing\right) +} + +%redefine \overline to customize the space between text / line (currently 0.4mm + height of the content) +%ATTENTION: when changing the 0.4mm unfortunately, in \kringel the 0.4mm need to be changed accordingly +\let\@old@overline\overline +\renewcommand*{\overline}[1]{% + \ifmmode + \@old@overline{\raisebox{0pt}[\dimexpr\height+0.4mm\relax]{$#1$}}% + \else + \bar{#1} + \fi +} + +%encircle some content. Arguments: border color (optional), background color (mandatory), content (mandatory) +%two lengths to get width / height of content (important for width / height of the circle) +\newlength{\@kringel@contentheight} +\newlength{\@kringel@contentwidth} +\newlength{\@kringel@depth} +\NewDocumentCommand{\kringel}{O{blue} m m}{% + %as the macro should work for both text and math mode, add some macros for later use to distinguish + %in text mode, nothing happens (except discarding the 1st argument for the raisebox, that is permantently given), in math mode, the content needs to be enbraced by \ensuremath, the tcolorbox-environment by a raisebox + %ATTENTION: when changing the height-factor of tcolorbox, the depth correction needs to be changed as well + \let\@kringel@inner\relax + \let\@kringel@outer\@secondoftwo + \ifmmode + \let\@kringel@inner\ensuremath + \let\@kringel@outer\raisebox + \fi + %set the width and height + \settoheight{\@kringel@contentheight}{\hbox{\@kringel@inner{#3}}} + \settowidth{\@kringel@contentwidth}{\@kringel@inner{#3}} + \settodepth{\@kringel@depth}{\@kringel@inner{#3}} + %change the depth correction dependend whethere there is a depth (e.g. y) or not (e.g. a) + \ifdim \@kringel@depth > 0pt% + \setlength{\@kringel@depth}{\dimexpr\@kringel@depth+0.5mm\relax} + \else + \settodepth{\@kringel@depth}{y} + \setlength{\@kringel@depth}{\dimexpr\@kringel@depth+0.3mm\relax} + \fi + %output the colorbox width given parameter: frame color, background color, computed width and height, and escaped content depending on math / text mode + \@kringel@outer{\dimexpr-\@kringel@contentheight/2-\@kringel@depth\relax}{\begin{tcolorbox}[colframe=#1,halign=center,valign=center,width=\dimexpr1.5\@kringel@contentwidth+1mm\relax,height=2.5\@kringel@contentheight,left=0pt,right=0pt,bottom=0pt,top=0pt,boxrule=0.8pt,colback=#2,boxsep=0pt,bean arc] + \@kringel@inner{#3} + \end{tcolorbox}} +} + +%update ntheorem macro to provide space between theorem numbers and any optional comment, adds in upper roman letters the chapter number. removes any numbering for theorem environments with just one counter +\renewcommand{\thm@@thmline@name}[5]{%- + \def\thm@@thmline@name@tmp{% + \if\relax\detokenize{#3}\relax\else% + {\hspace*{2.2ex}#3}% + \fi% + } + \let\thm@@thmline@name@numbering\relax + \StrCount{#5}{.}[\thm@@thmline@name@dot@number] + \ifnum\thm@@thmline@name@dot@number < 3% + \def\thm@@thmline@name@tmp{\hspace*{-1em}#3} + \else% + \StrBetween[1,2]{#5}{.}{.}[\thm@@thmline@name@chap@num]%get the chapter number for roman transliteration + \def\thm@@thmline@name@numbering{\rom{\thm@@thmline@name@chap@num}.#2} + \fi + \ifx\\#5\\% + \@dottedtocline{-2}{0em}{4.4em}% + {#1 \protect\numberline{\thm@@thmline@name@numbering:}{}}% + {#4} + \else + \ifHy@linktocpage\relax\relax + \@dottedtocline{-2}{0em}{1.3em}% + {#1 \protect\numberline{\thm@@thmline@name@numbering:}\thm@@thmline@name@tmp}% + {\hyper@linkstart{link}{#5}{#4}\hyper@linkend}% + \else + \@dottedtocline{-2}{0em}{4.em}% + {#1 \protect\numberline{\thm@@thmline@name@numbering:}\thm@@thmline@name@tmp}% + {\hyper@linkstart{link}{#5}{#4}\hyper@linkend}% + \fi + \fi +} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 +%Settings + +\pdfstringdefDisableCommands{% + \def\\{}% + \def\texttt#1{<#1>}% + \def\mathbb#1{<#1>}% +} +\reqnos + +%Headings +\titlelabel{\thetitle.\quad}%. behind section/sub... (3. instead of 3) +\counterwithout{section}{chapter} +\renewcommand{\thechapter}{\Roman{chapter}} +\renewcommand{\thepart}{\Alph{part}} +%italic chapters (due to titlesec package some more stuff) +%\titleformat{command}[shape]{format}{label}{sep}{before-code}[after-code] +\titleformat{\chapter}[display]{\bfseries}{\Large\chaptername\;\thechapter}{-5pt}{\huge\bfseries\itshape} +\titlespacing{\chapter}{0pt}{0pt}{10pt} +\titleformat{\section}[hang]{\bfseries\Large}{\thesection.}{8pt}{\Large\bfseries} +%\titlespacing{command}{left}{before-sep}{after-sep} +\titlespacing{\subsection}{0pt}{0pt}{5pt} + +%change appearence of heading of toc: 0 space above, bold, italic huge toc-heading +\renewcommand{\cftbeforetoctitleskip}{0pt} +\renewcommand{\cfttoctitlefont}{\itshape\Huge\bfseries} +%change indentations due to width of capital roman numbers +\renewcommand{\cftchapnumwidth}{2.5em} +\renewcommand{\cftsecindent}{2.5em} +\renewcommand{\cftsubsecindent}{4.8em} + +% Add new page-style (just footer), patch \chapter command to use this page style +\fancypagestyle{plainChapter}{% + \fancyhf{}% + \fancyfoot[C]{\thepage}% + \renewcommand{\headrulewidth}{0pt}% Line at the header invisible + \renewcommand{\footrulewidth}{0.4pt}% Line at the footer visible +} +%changes pagestyle; instead of empty page the normal footer is printed +\patchcmd{\chapter}{\thispagestyle{plain}}{\thispagestyle{plainChapter}}{}{} +%usually, after a new chapter the section counter needs to be reset manually. Instead, automatic reset +\pretocmd{\chapter}{\setcounter{section}{0}}{}{} + +\pagestyle{fancy} +\pagenumbering{arabic} +%remember chapter-title in \leftmark and \rightmark +\renewcommand{\chaptermark}[1]{% + \markboth{\chaptername + \ \thechapter:\ #1}{}} +%remember section title in \leftmark +\renewcommand{\sectionmark}[1]{% + \markright{\thesection.\ #1}{}} + +%remove page number from part{}-pages +\let\sv@endpart\@endpart +\def\@endpart{\thispagestyle{empty}\sv@endpart} + +%change header: +\renewcommand{\headrulewidth}{0.75pt} +\renewcommand{\footrulewidth}{0.3pt} +\lhead{\rightmark}%left: section-number. section-title +\rhead{\leftmark}%right: chapter chapternumber: chapter-title + +%change numbering of equations to be section by section +\counterwithout{equation}{section} + +%appendix: +\let\old@appendix\appendix +\def\appendix{% + \old@appendix% + \patchcmd{\chapter}{\thispagestyle{plainChapter}}{\thispagestyle{fancy}}{}{}% + \renewcommand{\chaptername}{Anhang}% + \renewcommand{\thesection}{\Alph{chapter}.\arabic{section}}% + \titleformat{\chapter}[hang]{\bfseries}{\LARGE\chaptername\ \thechapter:}{0.5em}{\LARGE\bfseries}% + \titlespacing{\chapter}{0pt}{-0.75cm}{0pt}% +} + +\endinput \ No newline at end of file diff --git a/texmf/texmf.cnf b/texmf/texmf.cnf new file mode 100644 index 0000000..523e0df --- /dev/null +++ b/texmf/texmf.cnf @@ -0,0 +1 @@ +TEXMFHOME= {/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,{/home/dani/git/TUD_MATH_BA/texmf,~/texmf}}}}}}}}}}}}}}}}}}}}}}