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248 lines
9.9 KiB
Plaintext
248 lines
9.9 KiB
Plaintext
8 years ago
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% latex package with useful macros for scientific documents
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% Authors: Emanuel Regnath, Martin Zellner
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% Contact: info@latex4ei.de
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% Version: 1.0
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% License: TBD
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%
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% © 2011-2015, LaTeX4EI
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\NeedsTeXFormat{LaTeX2e}
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\ProvidesPackage{scientific}[2015/03/30 Scientific Macros for LaTeX4EI]
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% ======================================================================
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% Basic
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% ======================================================================
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% Identify Compiler
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\RequirePackage{ifxetex}
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\ifxetex%
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\relax
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\else%
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% load following packages if and only if compiler is pdflatex
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\fi
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% load packages, order matter
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\RequirePackage{amsmath} % math symbols and \DeclareMathOperator
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\RequirePackage{esint} % more integral symbols
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%\RequirePackage{accents} % accents such as \vec and \ddot
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% additional packages
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\RequirePackage{amssymb} % additional math
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% save old commands
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\let\oldvec = \vec
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\let\olddot = \dot
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\let\diameter = \O
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% formating indices
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\newcommand{\ir}[1]{\sf #1} % index roman
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% differential delta
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\newcommand{\diff}{\mathop{}\!\mathrm{\vphantom( d}}
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% ======================================================================
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% SI Units
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% ======================================================================
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\RequirePackage{siunitx} % SI package
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\sisetup{per-mode=reciprocal} % use ^-1 instead of fractals
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\sisetup{sticky-per=true} % every unit behind "per" is reciprocal
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\newcommand{\unitof}[1]{\ensuremath{\left[#1\right]}} % unit of
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% ======================================================================
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% Vectors and Matrices
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% ======================================================================
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% Define \utilde: from package undertilde.sty
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\newlength\knuthian@fdfive
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\def\mathpal@save#1{\let\was@math@style=#1\relax}
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\def\utilde#1{\mathpalette\mathpal@save
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{\setbox124=\hbox{$\was@math@style#1$}%
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\setbox125=\hbox{$\fam=3\global\knuthian@fdfive=\fontdimen5\font$}
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\setbox125=\hbox{$\widetilde{\vrule height 0pt depth 0pt width \wd124}$}%
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\baselineskip=1pt\relax
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\vtop{\copy124\copy125\vskip -\knuthian@fdfive}}}
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% vectors and matrices
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\newcommand{\ma}[1]{\ensuremath{\utilde{\boldsymbol {#1}}}} % Matrixsymbol
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\newcommand{\mat}[1]{\ensuremath{\arraycolsep=0.5em \begin{bmatrix} #1 \end{bmatrix}}} % Matrix
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\newcommand{\tma}[3]{\ensuremath{{}_{#1} \ma #2_#3 }} % Trafomatrix
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%\renewcommand{\vec}[1]{\ensuremath{\underline{\boldsymbol \begingroup#1\endgroup}}} % Vector bold and underlined
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\newcommand{\vect}[1]{\ensuremath{\begin{pmatrix} #1 \end{pmatrix}}} % Vector
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\newcommand{\mvect}[1]{\ensuremath{\left.\begin{matrix} #1 \end{matrix}\right]}}% Matrixvector
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\newcommand{\tensor}[1]{\ensuremath{\underline{\underline{\boldsymbol #1}}}} % Tensor
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\DeclareMathOperator{\diag}{diag} % diagonal matrix
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% vector operations
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\newcommand{\norm}[1]{\ensuremath{\left\|#1\right\|}} % Norm
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\DeclareMathOperator{\Sp}{Sp} % Spur (german for trace \tr)
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% ======================================================================
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% Misc
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% ======================================================================
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% basic math
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\providecommand{\hateq}{\ensuremath{\stackrel{\wedge}{=}}} % Entspricht
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\providecommand{\floor}[1]{\ensuremath{\left\lfloor#1\right\rfloor}} % Abrunden
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\providecommand{\ceil}[1]{\ensuremath{\left\lceil {#1} \right\rceil}} % Aufrunden
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\providecommand{\sprod}[2]{\ensuremath{\left\langle #1, #2 \right\rangle }} % scalar product
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\providecommand{\abs}[1]{\ensuremath{\left\vert#1\right\vert}} % absolute value)
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\DeclareMathOperator{\const}{const.} % constant
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\DeclareMathOperator{\sgn}{sgn} % signum
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\DeclareMathOperator{\ld}{ld} % log_2
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\DeclareMathOperator{\ggT}{ggT} % ggT (german for gcd)
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% chemistry
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\newcommand{\chem}[1]{\ensuremath{\displaystyle{\mathrm{#1}}}} % chemistry with \chem (simple)
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\RequirePackage[version=3]{mhchem} % chemistry with \ce (advanced)
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\newcommand{\rom}[1]{\ensuremath{\underline{\overline{\textsc{#1}}}}} % roman numbers
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% ======================================================================
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% Important Constants
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% ======================================================================
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% math
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\providecommand{\e}{\mathrm{e}}
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% physical
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\providecommand{\kB}{\ensuremath{\mathrm{k}_{\text{B}}}} % Boltzman
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\providecommand{\Rgas}{\ensuremath{\mathrm{R}}} % Allg. Gaskonstante
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\providecommand{\NA}{\ensuremath{\mathrm{N}_{\text{A}}}} % Avogadro
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% ======================================================================
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% Complex and Hyper-complex Numbers
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% ======================================================================
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\newcommand{\cx}[1]{\boldsymbol{#1}} % complex number
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\newcommand{\cxc}[1]{\ensuremath{\boldsymbol #1^*}} % Konjugiert complex number
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\newcommand{\hx}[1]{\ensuremath{\mathfrak #1}} % hyper-complex number
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\renewcommand{\i}{\ensuremath{\mathrm{i}}} % imaginary unit
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\renewcommand{\j}{\ensuremath{\mathrm{j}}} % imaginary unit
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\renewcommand{\k}{\ensuremath{\mathrm{k}}} % imaginary unit
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% real and imaginary part
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\renewcommand{\Re}[1]{\ensuremath{\operatorname{Re}\left\{#1\right\}}}
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\renewcommand{\Im}[1]{\ensuremath{\operatorname{Im}\left\{#1\right\}}}
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% ======================================================================
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% Sets
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% ======================================================================
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% define sets
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\newcommand{\iset}[2]{\ensuremath{\bigl\{ \bigl. #1 \, \bigr| \, #2 \bigr\}}} % intensional set
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\newcommand{\eset}[1]{\ensuremath{\bigl\{#1\bigr\}}} % extensional set
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% abbreviations for important sets
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\DeclareMathOperator{\N}{\mathbb N} % Natürliche Zahlen
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\DeclareMathOperator{\R}{\mathbb R} % Reele Zahlen
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\DeclareMathOperator{\C}{\mathbb C} % Komplexe Zahlen
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\DeclareMathOperator{\K}{\mathbb K} % Reele oder komplexe Zahlen
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\def\B{\operatorname{\mathbb B}} % Binäre Zahlen 1,0
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\def\O{\operatorname{\mathcal O}} % Landau
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% set operations
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\let\cupplus\uplus % Vereinigunsmenge bzw. OR
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\newlength{\caplength}
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\setlength{\caplength}{\widthof{$\cap$}}
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\DeclareMathOperator{\capdot}{\cap\hspace{-0.7\caplength}\text{\textperiodcentered}\hspace{0.4\caplength}} % Schnittmenge bzw. AND
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% topology
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\newcommand{\interior}[1]{\ensuremath{\overset{{}_\circ}{#1}}} % Das Innere
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% ======================================================================
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% Frequency Transformations (Fourier, Laplace, etc.)
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% ======================================================================
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% Define symbol for Transformations. Source: trfsigns.sty
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\newcommand{\ftsymbol}{\mbox{\setlength{\unitlength}{0.1em}
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\begin{picture}(25,4)
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\put(3,3){\circle{4}} % empty
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\put(5,3){\line(1,0){13}}
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\put(19,3){\circle*{4}} % filled
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\end{picture}}}
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% Define Transformations
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\DeclareMathOperator{\FT}{\overset{\scriptscriptstyle\mathcal{F}}{\ftsymbol}} % Fourier Transform
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\DeclareMathOperator{\LT}{\overset{\scriptscriptstyle\mathcal{L}}{\ftsymbol}} % Laplace Transform
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\DeclareMathOperator{\DFT}{\overset{\scriptscriptstyle\mathcal{DF}}{\ftsymbol}} % Discrete Fourier Transform
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\DeclareMathOperator{\DTFT}{\overset{\scriptscriptstyle\mathcal{DTF}}{\ftsymbol}} % Discrete Time Fourier Transform
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\DeclareMathOperator{\ZT}{\overset{\scriptscriptstyle\mathcal{Z}}{\ftsymbol}} % Z-Transform
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% ======================================================================
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% Differential Geometry
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% ======================================================================
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\DeclareMathOperator{\grad}{grad} % Gradient
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\def\div{\operatorname{div}} % Divergence
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\DeclareMathOperator{\rot}{rot} % rotation
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\DeclareMathOperator{\lpo}{\Delta} % laplace operator
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\DeclareMathOperator{\laplace}{\Delta} % laplace operator
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\DeclareMathOperator{\waveop}{\square} % wave operator
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% ======================================================================
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% Signals
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% ======================================================================
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\DeclareMathOperator{\dirac}{\ensuremath{\delta}} % Dirac Distribution
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\DeclareMathOperator{\heavi}{\ensuremath{\theta}} % Heaviside Step Function
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\DeclareMathOperator{\sinc}{sinc} % Sinus Cardinalis
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\DeclareMathOperator{\rect}{rect} % Rectangular
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\DeclareMathOperator{\tri}{tri} % Triangular
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\DeclareMathOperator{\erf}{erf} % Error Function
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\DeclareMathOperator{\erfc}{erfc} % Error Function
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\providecommand{\SNR}{\mathrm{SNR}} % Signal Noise Ratio
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\providecommand{\ACF}{\ensuremath{\varphi}} % autocorrelation function
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\providecommand{\PSD}{\ensuremath{\Phi}} % Power-Spectral-Density
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% ======================================================================
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% Stochastic
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% ======================================================================
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\renewcommand{\P}{\operatorname{\textsf{P}}} % Wahrscheinlichkeitsmaß
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\DeclareMathOperator{\F}{\mathbb F} % Ereignisalgebra
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\DeclareMathOperator{\X}{\textsf{\textit{X}}} % Zufallsvariable X
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\DeclareMathOperator{\Y}{\textsf{\textit{Y}}} % Zufallsvariable Y
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\DeclareMathOperator{\Z}{\textsf{\textit{Z}}} % Zufallsvariable Z
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\DeclareMathOperator{\E}{\textsf{E}} % Erwartungswert
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\newcommand{\ew}[1]{\textit{E} \left[ #1 \right]} % Erwartungswert (mit Parameter)
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\DeclareMathOperator{\Var}{\textsf{Var}} % Varianz
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\DeclareMathOperator{\Cov}{\textsf{Cov}} % Kovarianz
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% ======================================================================
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% Logic
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% ======================================================================
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\renewcommand{\implies}{\ensuremath{\rightarrow}} % →
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\let\limplies\implies
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\providecommand{\lequiv}{\ensuremath{\leftrightarrow}} % ↔
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\providecommand{\lnand}{\ensuremath{|}}
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\providecommand{\lxor}{\ensuremath{\downarrow}}
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\providecommand{\ltrue}{w}
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\providecommand{\lfalse}{f}
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% Ende von \input
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\endinput
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