stdmath.sty

% vim: set spelllang=de,en:
% ----------------------------------------------
% this package should provide a standard set of packages
% and commands that are usually useful when writing
% mathematical texts

% options
% -------
% \renewcommand{\bibfile}{<your bibliography file>}
% standard is bibliography.bib

% tikz
% also loads tikz

% graphicx OR pictures
% also loads package graphicx (for picture handling)

% pdflatex
% defines everything necessary to use neo2 possibilities with pdflatex

% german
% makes the names of environments german
% otherwise they are in english

% scriptLetters
% loads the package mathrsfs that enables you to write curly letters as Sigma-Algebras
% this is done via the command \scr
% ----------------------------------------------

\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{stdmath}[2017/10/17 stdmath package]

% optional:
\newif\ifopt@german
\opt@germanfalse % Standard
\DeclareOption{german}{\opt@germantrue}

\newif\ifopt@pics
\opt@picsfalse
\DeclareOption{graphicx}{\opt@picstrue}
\DeclareOption{pictures}{\opt@picstrue}

\newif\ifopt@tikz
\opt@tikzfalse
\DeclareOption{tikz}{\opt@tikztrue}

\newif\ifopt@script
\opt@scriptfalse
\DeclareOption{scriptLetters}{\opt@scripttrue}

\ProcessOptions\relax

\ifopt@pics\RequirePackage{graphicx}\fi
\ifopt@tikz\RequirePackage{tikz}\RequirePackage{tikz-cd}\fi
\ifopt@script\RequirePackage{mathrsfs}\newcommand{\scr}[1]{\mathscr{#1}}\fi % for script A (sigma-Algebra-A)

% ---------
% Packages
% ---------

% ---------------------------------------------------
%  this is a UTF8-symbol to LaTeX-formula-converting
% ---------------------------------------------------
\RequirePackage{.maindir/tex/header/specialChars}

% maybe that works one day:
% \RequirePackage{polyglossia}
% \ifopt@german{\setdefaultlanguage{german}}\else{\setdefaultlanguage{english}}\fi
\RequirePackage[\ifopt@german ngerman \else english \fi]{babel}
\RequirePackage{amsmath, amsfonts} 
\RequirePackage{aligned-overset}  % for nicely aligned text over relation symbols
% with \overset{\text{Definition}}&{=} instead of &\stackrel{\text{Definition}}=
\RequirePackage{mathtools}    % for := (defined as)
\RequirePackage{amsthm}                   % for theorems environments
\RequirePackage{enumerate}                  % for different kind of numbering in enumerations

% bibliography
\newcommand{\bibfile}{.maindir/tex/bibliography.bib}
\RequirePackage{csquotes}
\RequirePackage[backend=biber,
  style=alphabetic,
  backref=true,
  autocite=inline,
  sortlocale=de_DE.UTF-8,
  % sortlocale=en_GB,
  sorting=nty]{biblatex}
\addbibresource{\bibfile}
\AtEndDocument{\printbibliography}

% to allow links to break over lines at hyphens
% must be loaded before hyperref because hyperref loads package url
\PassOptionsToPackage{hyphens}{url}
\RequirePackage
  [
%   colorlinks=true,
%   linkcolor=black,
%   citecolor=black,
%   filecolor=black,
%   %pagecolor=black,
%   urlcolor=black,
%   bookmarks=true,
%   bookmarksopen=true,
%   bookmarksopenlevel=3,
%   plainpages=false,
%   pdfpagelabels=true
   pdfencoding=auto
  ]{hyperref}
%\parindent0.0em % = Einrueckungsweite des ersten Satzes eines Absatzes

% ---------------------------------------------------------------
% Custom commands, rougly grouped
% ---------------------------------------------------------------

% ----------------
%  math operators
% ----------------
\DeclareMathOperator{\id}{id}               % identity map
\DeclareMathOperator{\Id}{I}                % identity operator/ matrix
\DeclareMathOperator{\Lin}{Lin}             % Linear span
\DeclareMathOperator{\supp}{supp}           % support
\DeclareMathOperator{\GL}{GL}               % general linear group
%TODO: bin ir unsicher, ob das nicht kursiv geschriebn werden soll
\DeclareMathOperator{\dom}{D}               % domain
\DeclareMathOperator{\grad}{grad}           % gradient
\DeclareMathOperator{\Rang}{Rang}             % Rang einer Matrix
\DeclareMathOperator{\sign}{sign}           % signum (einer Permutation)
% \newcommand{\card}[1]{\abs{#1}}             % cardinality
\DeclareMathOperator{\gr}{gr}               % graph of a function f:A ⟶ B as a subset of A × B

% -----------
%  constants
% -----------
% Zahlmengen
\newcommand{\Z}{\mathbb{Z}}             % integers
\newcommand{\N}{\mathbb{N}}             % natural numbers
\newcommand{\Q}{\mathbb{Q}}             % rationals
\newcommand{\R}{\mathbb{R}}             % reals
% \newcommand{\C}{\mathbb{C}}             % complex numbers  % does not work, is already defined
\newcommand{\K}{\mathbb{K}}             % a field

\newcommand{\im}{\ensuremath{\mathrm{i}}}       % imaginary number sqrt(-1)

\newcommand{\chFct}{χ}                  % characteristic function of a set
\newcommand{\kro}{\delta}                 % Kronecker-Symbol

% ---------
%  Symbols
% ---------

\newcommand{\definedas}{\coloneqq}    % left of this is defined to be the thing on the right
\newcommand{\define}{\eqqcolon}       % same other way around

% ---------------------
%  analysis & topology
% ---------------------

\newcommand{\abs}[1]{\left\lvert#1\right\rvert}     % absolute value
\newcommand{\norm}[1]{\left\lVert#1\right\rVert}    % norm
\newcommand{\normiii}[1]{{\left\vert\kern-0.25ex\left\vert\kern-0.25ex\left\vert #1 
    \right\vert\kern-0.25ex\right\vert\kern-0.25ex\right\vert}}
    % from http://tex.stackexchange.com/questions/54385/spacing-between-triple-vertical-lines       % norm with 3 lines

\newcommand{\rest}[2]{\left. #1 \right\vert_{#2}}   % restriction of a map #1 to the domain #2
\newcommand{\scaProd}[1]{\left\langle #1 \right\rangle} % scalar product
\newcommand{\conj}[1]{#1^{*}}             % (complex) conjugation

\newcommand{\D}{\ensuremath{d}}             % d in \D x \D z ... at integrals
% \newcommand{\D}{\ensuremath{\mathrm{d}}} %

\newcommand{\cl}[1]{\overline{#1}}            % closure

% ------------
%  set theory
% ------------

\newcommand{\setDef}[2]{\left\{#1 
\,\middle\vert\, #2\right\}}            % a typical set definition: #1 is the thing in the set #2 the condition on the variables {#1 | #2}
\newcommand{\Union}{\bigcup}              % Summation-like set union
\newcommand{\Disunion}{\bigsqcup}           % Summation-like disjoint set union
\newcommand{\Isect}{\bigcap}              % Summation-like set intersection
\newcommand{\Dsum}{\bigoplus}             % Summation-like direct sum

% ---------
%  algebra
% ---------

\newcommand{\Tens}{\bigotimes}              % Summation-like tensor product
\newcommand{\normal}{\vartriangleleft}          % normal subgroup

% ----------------
%  Typografisches
% ----------------

\newcommand{\TODO}[1]{\marginpar{TODO (#1)}}      % TODOs
\newcommand{\imp}[1]{\emph{#1}}             % important
\newcommand{\newTerm}[1]{\emph{#1}}         % newly introduced
% alternative: do nothing or \ul (underline)

% ----------------------------------------------------
% (Theorem) environments
% ----------------------------------------------------

\newtheorem {theorem} {\ifopt@german Satz \else Theorem \fi} [section]
% \newtheorem {theorem} {Satz} [section]

% das "`[theorem] "` bewirkt, dass es eine durchgehende
% Nummerierung dieser environments gibt und nicht jede
% Art seine eigene Nummerierung hat

% Für Lemmas dieses environment:
\newtheorem {lemma} [theorem] {Lemma}
% Für Folgerungen/ Korollare dieses environment 
\newtheorem {corollary} [theorem] {\ifopt@german Korollar \else Corollary \fi}

% Definitionen sehen dann anders aus, siehe 
% http://tex.stackexchange.com/questions/38260/non-italic-text-in-theorems-definitions-examples
\theoremstyle {definition}
% Für Definitionen dieses environment
\newtheorem {definition} [theorem] {Definition}

% Für Bemerkungen dieses environment
\theoremstyle {remark}
\newtheorem* {note} {\ifopt@german Bemerkung \else Remark \fi}

% Beispiele kriegen eine andere Formatierung %ohne Nummerierung falls mit *:
\newtheorem{example} [theorem] {\ifopt@german Beispiel \else Example \fi}

% environment without any meaning
% just text that can be folded in editor
% the optional argument is ignored and can be used to give a summery of the folded content
\newenvironment{textfold}[1][]{}{}

\endinput