Formelsammlungen/ELK2_FS/latex4ei/scientific.sty

%
% latex package with useful macros for scientific documents
%
% Authors: Emanuel Regnath, Martin Zellner
% Contact: info@latex4ei.de
% Version: 1.1
% License: TBD
%
% © 2011-2019, LaTeX4EI


\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{scientific}[2015/03/30 Scientific Macros for LaTeX4EI]

% ======================================================================
% Basic
% ======================================================================

	% Identify Compiler
	\RequirePackage{ifxetex}
	\ifxetex%
		\relax
	\else%
		% load following packages if and only if compiler is pdflatex



	\fi

	% load packages, order matter
	\RequirePackage{amsmath}				% math symbols and \DeclareMathOperator
	\RequirePackage{esint}					% more integral symbols
	%\RequirePackage{accents}				% accents such as \vec and \ddot
	% additional packages
	\RequirePackage{amssymb}				% additional math


	% save old commands
	\let\oldvec = \vec
	\let\olddot = \dot
	\let\diameter = \O

	% formating indices
	\newcommand{\ir}[1]{\sf #1}				% index roman

	% differential delta
	\newcommand{\diff}{\mathop{}\!\mathrm{\vphantom( d}}


% ======================================================================
% SI Units
% ======================================================================
\RequirePackage{siunitx}				% SI package
\sisetup{per-mode=reciprocal}			% use ^-1 instead of fractals
\sisetup{sticky-per=true}				% every unit behind "per" is reciprocal
\newcommand{\unitof}[1]{\ensuremath{\left[#1\right]}}		% unit of

\DeclareSIUnit{\degree}{deg}

% ======================================================================
% Vectors and Matrices
% ======================================================================

	% Define \utilde: from package undertilde.sty
	\newlength\knuthian@fdfive
	\def\mathpal@save#1{\let\was@math@style=#1\relax}
	\def\utilde#1{\mathpalette\mathpal@save
				  {\setbox124=\hbox{$\was@math@style#1$}%
	\setbox125=\hbox{$\fam=3\global\knuthian@fdfive=\fontdimen5\font$}
	\setbox125=\hbox{$\widetilde{\vrule height 0pt depth 0pt width \wd124}$}%
				   \baselineskip=1pt\relax
				   \vtop{\copy124\copy125\vskip -\knuthian@fdfive}}}

	% vectors and matrices
	\newcommand{\ma}[1]{\ensuremath{\utilde{\boldsymbol {#1}}}}						% Matrixsymbol
	\newcommand{\mat}[1]{\ensuremath{\arraycolsep=0.5em \begin{bmatrix} #1 \end{bmatrix}}}				% Matrix
	\newcommand{\tma}[3]{\ensuremath{{}_{#1} \ma #2_#3 }}							% Trafomatrix
	%\renewcommand{\vec}[1]{\ensuremath{\underline{\boldsymbol \begingroup#1\endgroup}}}				% Vector bold and underlined
	\newcommand{\vect}[1]{\ensuremath{\begin{pmatrix} #1 \end{pmatrix}}}			% Vector
	\newcommand{\mvect}[1]{\ensuremath{\left.\begin{matrix} #1 \end{matrix}\right]}}% Matrixvector
	\newcommand{\tensor}[1]{\ensuremath{\underline{\underline{\boldsymbol #1}}}}	% Tensor
	\DeclareMathOperator{\diag}{diag}												% diagonal matrix

	% vector operations
	\newcommand{\norm}[1]{\ensuremath{\left\|#1\right\|}}							% Norm
	\DeclareMathOperator{\Sp}{Sp}													% Spur (german for trace \tr)




% ======================================================================
% Misc
% ======================================================================

	% basic math
	\providecommand{\hateq}{\ensuremath{\stackrel{\wedge}{=}}} 				% Entspricht
	\providecommand{\floor}[1]{\ensuremath{\left\lfloor#1\right\rfloor}} 				% Abrunden
	\providecommand{\ceil}[1]{\ensuremath{\left\lceil {#1} \right\rceil}}				% Aufrunden
	\providecommand{\sprod}[2]{\ensuremath{\left\langle #1, #2 \right\rangle }}			% scalar product
	\providecommand{\abs}[1]{\ensuremath{\left\vert#1\right\vert}} 						% absolute value)
	\DeclareMathOperator{\const}{const.}											% constant
	\DeclareMathOperator{\sgn}{sgn}													% signum
	\DeclareMathOperator{\ld}{ld}													% log_2
	\DeclareMathOperator{\ggT}{ggT}													% ggT (german for gcd)

	% chemistry
	\newcommand{\chem}[1]{\ensuremath{\displaystyle{\mathrm{#1}}}}				% chemistry with \chem (simple)
	\RequirePackage[version=3]{mhchem}											% chemistry with \ce (advanced)


	\newcommand{\rom}[1]{\ensuremath{\underline{\overline{\textsc{#1}}}}} 			% roman numbers


% ======================================================================
% Important Constants
% ======================================================================

	% math
	\providecommand{\e}{\mathrm{e}}

	% physical
	\providecommand{\kB}{\ensuremath{\mathrm{k}_{\text{B}}}}		% Boltzman
	\providecommand{\Rgas}{\ensuremath{\mathrm{R}}}					% Allg. Gaskonstante
	\providecommand{\NA}{\ensuremath{\mathrm{N}_{\text{A}}}}		% Avogadro



% ======================================================================
% Complex and Hyper-complex Numbers
% ======================================================================

	\newcommand{\cx}[1]{\boldsymbol{#1}}											% complex number
	\newcommand{\cxc}[1]{\ensuremath{\boldsymbol #1^*}}								% Konjugiert complex number
	\newcommand{\hx}[1]{\ensuremath{\mathfrak #1}}									% hyper-complex number
	\renewcommand{\i}{\ensuremath{\mathrm{i}}}										% imaginary unit
	\renewcommand{\j}{\ensuremath{\mathrm{j}}}										% imaginary unit
	\renewcommand{\k}{\ensuremath{\mathrm{k}}}										% imaginary unit

	% real and imaginary part
	\renewcommand{\Re}[1]{\ensuremath{\operatorname{Re}\left\{#1\right\}}}
	\renewcommand{\Im}[1]{\ensuremath{\operatorname{Im}\left\{#1\right\}}}


% ======================================================================
% Sets
% ======================================================================

	% define sets
	\newcommand{\iset}[2]{\ensuremath{\bigl\{ \bigl. #1 \, \bigr| \, #2 \bigr\}}}	% intensional set
	\newcommand{\eset}[1]{\ensuremath{\bigl\{#1\bigr\}}}							% extensional set

	% abbreviations for important sets
	\DeclareMathOperator{\N}{\mathbb N}						% Natürliche Zahlen
	\DeclareMathOperator{\R}{\mathbb R}						% Reele Zahlen
	\DeclareMathOperator{\C}{\mathbb C}						% Komplexe Zahlen
	\DeclareMathOperator{\K}{\mathbb K}						% Reele oder komplexe Zahlen
	\def\B{\operatorname{\mathbb B}}						% Binäre Zahlen 1,0
	\def\O{\operatorname{\mathcal O}}						% Landau

	% set operations
	\let\cupplus\uplus														% Vereinigunsmenge bzw. OR
	\newlength{\caplength}
	\setlength{\caplength}{\widthof{$\cap$}}
	\DeclareMathOperator{\capdot}{\cap\hspace{-0.7\caplength}\text{\textperiodcentered}\hspace{0.4\caplength}}			% Schnittmenge bzw. AND

	% topology
	\newcommand{\interior}[1]{\ensuremath{\overset{{}_\circ}{#1}}}					% Das Innere


% ======================================================================
% Frequency Transformations (Fourier, Laplace, etc.)
% ======================================================================

	% Define symbol for Transformations. Source: trfsigns.sty
	\newcommand{\ftsymbol}{\mbox{\setlength{\unitlength}{0.1em}
								\begin{picture}(25,4)
								  \put(3,3){\circle{4}}				% empty
								  \put(5,3){\line(1,0){13}}
								  \put(19,3){\circle*{4}}			% filled
								\end{picture}}}

	% Define Transformations
	\DeclareMathOperator{\T}{\overset{\scriptscriptstyle\mathcal{}}{\ftsymbol}}  					% General Transformation
	\DeclareMathOperator{\FT}{\overset{\scriptscriptstyle\mathcal{F}}{\ftsymbol}}					% Fourier Transform
	\DeclareMathOperator{\LT}{\overset{\scriptscriptstyle\mathcal{L}}{\ftsymbol}}					% Laplace Transform
	\DeclareMathOperator{\DFT}{\overset{\scriptscriptstyle\mathcal{DF}}{\ftsymbol}}					% Discrete Fourier Transform
	\DeclareMathOperator{\DTFT}{\overset{\scriptscriptstyle\mathcal{DTF}}{\ftsymbol}}				% Discrete Time Fourier Transform
	\DeclareMathOperator{\ZT}{\overset{\scriptscriptstyle\mathcal{Z}}{\ftsymbol}}					% Z-Transform

% ======================================================================
% Differential Geometry
% ======================================================================

	\DeclareMathOperator{\grad}{grad}							% Gradient
	\def\div{\operatorname{div}}								% Divergence
	\DeclareMathOperator{\rot}{rot}								% rotation
	\DeclareMathOperator{\lpo}{\Delta}							% laplace operator
	\DeclareMathOperator{\laplace}{\Delta}						% laplace operator
	\DeclareMathOperator{\waveop}{\square}						% wave operator


% ======================================================================
% Signals
% ======================================================================

	\DeclareMathOperator{\dirac}{\ensuremath{\delta}}			% Dirac Distribution
	\DeclareMathOperator{\heavi}{\ensuremath{\theta}}			% Heaviside Step Function
	\DeclareMathOperator{\sinc}{sinc}							% Sinus Cardinalis
	\DeclareMathOperator{\rect}{rect}							% Rectangular
	\DeclareMathOperator{\tri}{tri}								% Triangular
	\DeclareMathOperator{\erf}{erf}								% Error Function
	\DeclareMathOperator{\erfc}{erfc}							% Error Function

	\providecommand{\SNR}{\mathrm{SNR}}							% Signal Noise Ratio
	\providecommand{\ACF}{\ensuremath{\varphi}}					% autocorrelation function
	\providecommand{\PSD}{\ensuremath{\Phi}}					% Power-Spectral-Density


% ======================================================================
% Stochastic
% ======================================================================

	\renewcommand{\P}{\operatorname{\textsf{P}}}		% Wahrscheinlichkeitsmaß
	\DeclareMathOperator{\F}{\mathbb F}					% Ereignisalgebra
	\DeclareMathOperator{\X}{\textsf{\textit{X}}}		% Zufallsvariable X
	\DeclareMathOperator{\Y}{\textsf{\textit{Y}}}		% Zufallsvariable Y
	\DeclareMathOperator{\Z}{\textsf{\textit{Z}}}		% Zufallsvariable Z
	\DeclareMathOperator{\E}{\textsf{E}}				% Erwartungswert
	\newcommand{\ew}[1]{\textit{E} \left[ #1 \right]}	% Erwartungswert (mit Parameter)
	\DeclareMathOperator{\Var}{\textsf{Var}}			% Varianz
	\DeclareMathOperator{\Cov}{\textsf{Cov}}			% Kovarianz


% ======================================================================
% Logic
% ======================================================================

	\renewcommand{\implies}{\ensuremath{\rightarrow}}			% →
	\let\limplies\implies
	\providecommand{\lequiv}{\ensuremath{\leftrightarrow}}		% ↔
	\providecommand{\lnand}{\ensuremath{|}}
	\providecommand{\lxor}{\ensuremath{\downarrow}}
	\providecommand{\ltrue}{w}
	\providecommand{\lfalse}{f}


% Ende von \input
\endinput