diff --git a/mymath.sty b/mymath.sty deleted file mode 100644 index e26a41d..0000000 --- a/mymath.sty +++ /dev/null @@ -1,320 +0,0 @@ -\NeedsTeXFormat{LaTeX2e} -\ProvidesPackage{mymath}[2021/03/31 - Math package by Maximilian Keßler (private use)] -%%%%%%Provides the basic math packages used for my lecture-note write-ups - -%The language to pass to babel -\newif\ifenglish\englishtrue -\DeclareOption{german}{\englishfalse} -\DeclareOption{english}{\englishtrue} -% When working with beamer some things have to be done differently -\newif\ifbeamer\beamerfalse -\DeclareOption{nobeamer}{\beamerfalse} -\DeclareOption{beamer}{\beamertrue} - -\newif\ifsubfig\subfigtrue -\DeclareOption{nosubfig}{\subfigfalse} - - -%Options for onehalf-spacing of lines -\newif\ifonehalfspacing\onehalfspacingfalse %default is normalspace -\DeclareOption{onehalfspacing}{\onehalfspacingtrue} -\DeclareOption{normalspacing}{\onehalfspacingfalse} - -%Options for utf8 or utf8x - encoding -\newif\ifutf\utftrue %by default, utf8 is not enabled -\DeclareOption{utf8x}{\utffalse} -\DeclareOption{utf8}{\utftrue} - -%Options for lukas -\newif\iflukas\lukasfalse -\DeclareOption{lukas}{\lukastrue} - -%Options for including theorem-environments or not. -\newif\iffancythm\fancythmfalse -\DeclareOption{fancythm}{\fancythmtrue} - - -\DeclareOption*{\PackageWarning{mymath}{Unknown '\CurrentOption'}} -\ProcessOptions\relax - - -\RequirePackage[\ifenglish english \else ngerman\fi]{babel} -\RequirePackage[T1]{fontenc} - -% When using utf8x, we have to load ucs and inputenc with utf8x option and must exclude bibtex -% When not using utf8x (plan utf8), we must NOT load ucs, and then load inputenc with utf8-option as well as bibtex -% also, when using plain utf8, we want to load the newunicodechar package -\ifutf -\RequirePackage{newunicodechar} -\newunicodechar{α}{\ensuremath\alpha} -\newunicodechar{β}{\ensuremath\beta} -\newunicodechar{γ}{\ensuremath\gamma} -\newunicodechar{δ}{\ensuremath\delta} -\newunicodechar{ε}{\ensuremath\epsilon} -\newunicodechar{ζ}{\ensuremath\zeta} -\newunicodechar{η}{\ensuremath\eta} -\newunicodechar{θ}{\ensuremath\theta} -\newunicodechar{ι}{\ensuremath\iota} -\newunicodechar{κ}{\ensuremath\kappa} -\newunicodechar{λ}{\ensuremath\lambda} -\newunicodechar{μ}{\ensuremath\mu} -\newunicodechar{ν}{\ensuremath\nu} -\newunicodechar{ξ}{\ensuremath\xi} -\newunicodechar{π}{\ensuremath\pi} -\newunicodechar{ρ}{\ensuremath\rho} -\newunicodechar{σ}{\ensuremath\sigma} -\newunicodechar{τ}{\ensuremath\tau} -\newunicodechar{υ}{\ensuremath\upsilon} -\newunicodechar{φ}{\ensuremath\phi} -\newunicodechar{χ}{\ensuremath\chi} -\newunicodechar{ψ}{\ensuremath\psi} -\newunicodechar{ω}{\ensuremath\omega} -\ifbeamer\else -\RequirePackage[backend=biber,style=alphabetic]{biblatex} -\fi -\else -\RequirePackage[mathletters]{ucs} -\fi -\RequirePackage[\ifutf utf8\else utf8x\fi]{inputenc} - -\RequirePackage{anyfontsize} -\RequirePackage{lmodern} -\RequirePackage{amsmath} -\RequirePackage{mathtools} -\RequirePackage{amsthm} -\RequirePackage{amssymb} -\ifbeamer\else -\RequirePackage{bm} % bold math symbols -\fi -\RequirePackage{comment} -\RequirePackage{soul} -\ifsubfig -\RequirePackage{subfig}\else\fi -\RequirePackage{mathrsfs} -\RequirePackage{bbm} -\ifbeamer -\else \RequirePackage[shortlabels]{enumitem}\fi -\ifbeamer\else -\RequirePackage[colorlinks=true]{hyperref} % Hyperlinks -\fi - -% TIKZ -\RequirePackage{tikz} -\usetikzlibrary{calc, intersections, through, quotes, angles, babel, positioning} -\RequirePackage{tkz-euclide} -\RequirePackage[export]{adjustbox} -%Commutative diagrams -\RequirePackage{tikz-cd} - -%%for small diagrams, similar to tikz-cd -\usepackage{xy} % for small diagrams, e.g. arrows -\xyoption{all} - -%%% AMSTHM -\iffancythm - \RequirePackage{mkessler-fancythm} -\else -\theoremstyle{plain} -\ifbeamer\else -\newtheorem{theorem}{\ifenglish Theorem\else Satz\fi} -\newtheorem{corollary}{\ifenglish Corollary\else Korollar\fi} -\newtheorem*{lemma}{Lemma} -\newtheorem{proposition}{Proposition} -\fi - - -\theoremstyle{definition} -\ifbeamer\else -\newtheorem{definition}{Definition} -\newtheorem{example}{\ifenglish Example\else Beispiel\fi} -\newtheorem*{remark}{\ifenglish Remark\else Bemerkung\fi} -\newtheorem*{notation}{Notation} -\fi - - - -%%Theorems needed in any case (fancy or not fancy theorems) - -\theoremstyle{plain} -\newtheorem{claim}{\ifenglish Claim\else Behauptung\fi} -\newtheorem{variant}{\ifenglish Variant\else Variante\fi} -\newtheorem{assumption}{\ifenglish Assumption\else Annahme\fi} - -\theoremstyle{definition} -\ifbeamer\else -\newtheorem*{fact}{\ifenglish Fact\else Fakt\fi} -\newtheorem*{note}{\ifenglish Note\else Anmerkung\fi} -\newtheorem*{problem}{Problem} -\fi -\newtheorem*{warning}{\color{red}\ifenglish Warning \else Warnung\fi} -\newtheorem*{goal}{\ifenglish Goal \else Ziel\fi} -\newtheorem*{question}{\ifenglish Question \else Frage \fi} -\newtheorem*{info}{Information} -\newtheorem*{moral}{Moral} -\newtheorem*{answer}{\ifenglish Answer\else Antwort\fi} -\newtheorem*{observe}{\ifenglish Observe\else Beobachte\fi} -\newtheorem*{property}{\ifenglish Property\else Eigenschaft\fi} -\newtheorem*{intuition}{Intuition} -\newtheorem*{recall}{\ifenglish Recall\else Erinnerung\fi} -\newtheorem*{idea}{\ifenglish Idea\else Idee\fi} -\newtheorem{exercise}{\ifenglish Exercise\else Aufgabe\fi} -\ifbeamer\else\newenvironment{solution}[1][]{\begin{proof}[\ifenglish{}Solution\else{}Lösung\fi{}#1]}{\end{proof}}\fi -\fi %end of theorem definitions - - - - -% Für Formeln -\RequirePackage{mathabx} -\RequirePackage{faktor} -\RequirePackage[mathscr]{eucal} - -\RequirePackage{blindtext} -\RequirePackage{tabto} -\ifbeamer\else -\RequirePackage{lastpage} %\pageref{LastPage} for reference on the last page -\fi - -% Für Tabulatoren - -\RequirePackage{pdfpages} % PDF-Dateien einbinden - -% Für Zeilenumbruch -\RequirePackage{microtype} -\RequirePackage{changepage} - - -%Für Zeilenabstand 1,5 -\ifonehalfspacing -\RequirePackage[onehalfspacing]{setspace} \else -\fi - -%For setting counters of itemns in \enemerate -\makeatletter -\newcommand\setItemnumber[1]{\setcounter{enum\romannumeral\@enumdepth}{\numexpr#1-1\relax}} -\makeatother - -%Make circled symbols -\newcommand*\circled[1]{\tikz[baseline=(char.base)]{ - \node[shape=circle,draw,inner sep=2pt] (char) {#1};}} - -%Print a warning sign -\newcommand\Warning{% - \makebox[1.4em][c]{% - \makebox[0pt][c]{\raisebox{.1em}{\small!}}% - \makebox[0pt][c]{\color{red}\Large$\bigtriangleup$}}}% - -% Add \contra symbol to denote contradiction -\usepackage{stmaryrd} % for \lightning -\newcommand\contra{\scalebox{1.5}{$\lightning$}} - - -%Emphasize \vocabulary -\newcommand{\vocab}[1]{\textbf{\color{blue} #1}} - - - - -%%%%math operators -\usepackage{operators} - -%Short commands for \mathbb{} - -\newcommand{\C}{\ensuremath{\mathbb{C}}} -\newcommand{\F}{\ensuremath{\mathbb{F}}} -\newcommand{\K}{\ensuremath{\mathbb{K}}} -\newcommand{\N}{\ensuremath{\mathbb{N}}} -\newcommand{\Q}{\ensuremath{\mathbb{Q}}} -\newcommand{\R}{\ensuremath{\mathbb{R}}} -\newcommand{\Z}{\ensuremath{\mathbb{Z}}} - - -%Paired Delimiters -\DeclarePairedDelimiter\ceil{\lceil}{\rceil} -\DeclarePairedDelimiter\floor{\lfloor}{\rfloor} - -%Norm and absolute value -%Make them scaling by default and have \abs*{} as the non-scaling version of the command -\DeclarePairedDelimiter\abs{\lvert}{\rvert} -\makeatletter -\let\oldabs\abs -\def\abs{\@ifstar{\oldabs}{\oldabs*}} - -\DeclarePairedDelimiter\norm{\lVert}{\rVert} -\let\oldnorm\norm -\def\norm{\@ifstar{\oldnorm}{\oldnorm*}} -\makeatother - - -%Fixes of common misbehaviour -\renewcommand{\degree}{^\circ} - -%Used to start an exercise and resetting the equation number -\newcommand{\nr}[1]{\setcounter{equation}{0}\section*{\ifenglish Exercise \else Aufgabe \fi #1}~} - - -\ifbeamer\else\RequirePackage{esint}\fi - -\RequirePackage{IEEEtrantools} - -\RequirePackage[ngerman,ruled,vlined]{algorithm2e} - -\iflukas -\newcommand{\RrClA}{\begin{IEEEeqnarray*}{RrCl}} -\newcommand{\RrClZ}{\end{IEEEeqnarray*}} -\newcommand{\RrCla}{\begin{IEEEeqnarray}{RrCl}} -\newcommand{\RrClz}{\end{IEEEeqnarray}} -\newcommand{\ud}{\,\mathrm{d}} -\newcommand{\dLx}[1]{\;\ud\mathcal{L}^{#1}(x)} -\setenumerate[1]{label=(\alph*)} - -%%%%%%%%%%%%% INDUKTION %%%%%%%%%%%%%%%%% -\newcommand{\its}{Das gilt offentsichtlich.} -\newcommand\induktion[6][\its]{ - \def\n{#2} - \def\kn{#2} - Es sei $P(\n)$ die Aussage, dass: - \RrClA - P(\n) : \equiv \qquad \left(#5 \right) - \RrClZ - Diese soll nun per Induktion über $#3$ gezeigt werden. - \begin{enumerate} - \item [\underline{IA:}]Für den Induktionsanfang muss $P(#4)$ gezeigt werden, d.h.: - \def\n{#4} - \def\kn{#4} - \RrClA - P(#4) \equiv \qquad \left(#5\right) - \RrClZ - #1\ Also ist der Induktionsanfang gezeigt. - \def\n{#2} - \def\kn{#2} - \item [\underline{IV:}] Angenommen $P(\n)$ gilt für ein $\n \in #3$, d.h. es gilt: - \RrClA - P(\n) \equiv \qquad \left(#5\right) - \RrClZ - \item [\underline{IS:}] - Im Induktionsschritt von $\n$ auf $\n+1$ muss gezeigt werden, dass unter Annahme der Induktionsvoraussetzung auch die Induktionsbehauptung gilt: - \def\n{#2+1} - \def\kn{(#2+1)} -\RrClA - P(\n) \equiv \qquad \left(#5\right) -\RrClZ -#6 - -\def\n{#2} -\def\kn{#2} -Damit ist der Induktionsschritt erbracht und es gilt für alle $#2$ in $#3$: -\RrClA - \forall \n \in #3 : #5 -\RrClZ - \end{enumerate} -} -%[Begründung IA]{$Variablenname$}{$Ursprungsmenge$}{$Startwert$}{$Aussage (variable ist \n, \kn)$}{Begründung IS} -%\n ist n oder n+1, \kn ist n oder (n+1) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\else -\fi - - - - diff --git a/operators.sty b/operators.sty deleted file mode 100644 index 1337a23..0000000 --- a/operators.sty +++ /dev/null @@ -1,121 +0,0 @@ -\NeedsTeXFormat{LaTeX2e} -\ProvidesPackage{operators}[2021-04-27 - Operator Package] -%%%%%%%%%%%%%%%%%%mmmm -%Provides some commonly used Operators used in the write-ups of my lecture notes - -\newif\ifenglish\englishtrue -\DeclareOption{german}{\englishfalse} -\DeclareOption{english}{\englishtrue} -\DeclareOption*{\PackageWarning{operators}{Unknown '\CurrentOption'}} -\ProcessOptions\relax - -%Packages -\RequirePackage{amsmath} - -%%%%%%%%%%% Operators -%Basic commands -\renewcommand\subset\subseteq -\renewcommand\supset\supseteq -\DeclareMathOperator{\id}{id} -\DeclareMathOperator{\im}{im} -\DeclareMathOperator{\Bild}{Bild} -\DeclareMathOperator{\Span}{Span} -\let\ggT\relax\DeclareMathOperator{\ggT}{\ifenglish gcd \else ggT\fi} -\let\kgV\relax\DeclareMathOperator{\kgV}{\ifenglish lcm \elese kgV\fi} -\DeclareMathOperator{\rhs}{RHS} %Right hand side -\DeclareMathOperator{\lhs}{LHS} %Left hand side - -%Complex numbers -\DeclareMathOperator{\Impart}{Im} -\renewcommand\Im\Impart -\DeclareMathOperator{\Repart}{Re} -\renewcommand\Re\Repart - -%Linear Algebra -\DeclareMathOperator{\Sym}{Sym} -\DeclareMathOperator{\supp}{supp} -\DeclareMathOperator{\sgn}{sgn} -\DeclareMathOperator{\coker}{coker} -\DeclareMathOperator{\rank}{rank} -\DeclareMathOperator{\Mat}{Mat} -\DeclareMathOperator{\ev}{ev} - -%Algebra -\DeclareMathOperator{\Gal}{Gal} -\DeclareMathOperator{\Ext}{Ext} -\DeclareMathOperator{\Tor}{Tor} -\DeclareMathOperator{\Mspec}{MaxSpec} -\DeclareMathOperator{\Sh}{Sh} -\DeclareMathOperator{\Proj}{Proj} -\DeclareMathOperator{\QCoh}{QCoh} -\DeclareMathOperator{\MaxSpec}{MaxSpec} -\DeclareMathOperator{\Presh}{Pre-Sh} -\DeclareMathOperator{\Fun}{Fun} -\newcommand{\tensor}{\otimes} - -%Analysis -\DeclareMathOperator{\dx}{dx} -\DeclareMathOperator{\dy}{dy} -\DeclareMathOperator{\dz}{dz} -\DeclareMathOperator{\dt}{dt} - -%Sets -\DeclareMathOperator{\conv}{conv} -\DeclareMathOperator{\dist}{dist} -\DeclareMathOperator{\diam}{diam} - -%%Stochastic (Algorithmische Mathematik II) -\newcommand\distribution[1]{\operatorname{#1}} -\newcommand\DeclareDistribution[1]{\expandafter\def\csname #1\endcsname{\distribution{#1}}} -\DeclareDistribution{Bin} -\DeclareDistribution{Ber} -\DeclareDistribution{Geo} -\DeclareDistribution{Poi} -\DeclareDistribution{Unif} -\DeclareMathOperator{\Var}{Var} -\DeclareMathOperator{\Cov}{Cov} - -%Topology -\DeclareMathOperator\pr{pr} -\def\twedge{\vee} -\def\tsmash{\wedge} - -%Category Theory -\DeclareMathOperator{\Ob}{Ob} -\newcommand{\cat}[1]{ \mathscr{#1} } -\DeclareMathOperator{\Hom}{Hom} -\DeclareMathOperator{\Mor}{Mor} -\DeclareMathOperator{\End}{End} -\DeclareMathOperator{\opposite}{\textbf{opp}} -\newcommand\opp{^{\opposite}} -\newcommand\op{^{\opposite}} - -%Categories -\newcommand\category[1]{\operatorname{\textbf{#1}}} -\newcommand\DeclareCategory[1]{\expandafter\def\csname #1\endcsname{\category{#1}}} -\DeclareCategory{Top} -\DeclareCategory{hTop} -\DeclareCategory{Set} -\DeclareCategory{CHaus} -\DeclareCategory{Grp} -\DeclareCategory{Ab} -\DeclareCategory{CRing} -\DeclareCategory{Vect} -\DeclareCategory{Fin} -\DeclareCategory{Ab} -\DeclareCategory{Cat} -\DeclareMathOperator{\colim}{colim} - - - -% Characteristic function -\newcommand*{\cfun}{\ensuremath{\mathbbm{1}}} -\newcommand*{\One}{\ensuremath{\mathbbm{1}}} - - -%Set theory -\DeclareMathOperator\card{card} -\DeclareMathOperator\Cd{Cd} -\DeclareMathOperator\Ord{Ord} -\DeclareMathOperator\otp{otp} -\DeclareMathOperator\Card{Card}