% fnspe 1.2a % This material is subject to the LaTeX Project Public License. % See https://www.latex-project.org/lppl/ for the details of that license. % % Useful commands for FNSPE students % % Created by Michal Zeman % Updated on September 20, 2017 % Uploaded on September 20, 2017 \documentclass{article} \usepackage[arrowtensor,oldcomplex]{fnspe} \usepackage{hyperref} \begin{document} \section*{Options} In this package there are four categories of options (examples and differences will be shown further) \begin{enumerate} \item for interval notation \begin{itemize} \item \texttt{isointerval} for using standardized format of interval described in \textbf{ISO 31-11} \item \texttt{isoointerval} for using standardized alternative format of interval described in \textbf{ISO 31-11} \item \texttt{fnspeinterval} for using special notation used at FNSPE CTU in Prague \end{itemize} \item for tensor notation (now for vectors and matrices) \begin{itemize} \item \texttt{isotensor} for using standardized format of tensor \item \texttt{undertensor} for using underline notation of tensor \item \texttt{arrowtensor} for using arrow notation of tensor \end{itemize} \item for complex notation (real and complex part) \begin{itemize} \item \texttt{isocomplex} for using standardized format of complex and real part \item \texttt{oldcomplex} for using old \LaTeX{} default format of complex and real part \end{itemize} \item for definition notation \begin{itemize} \item \texttt{deftext} for definition using \textit{def.} over the equal \item \texttt{defcolon} for definition using the colon with equal \end{itemize} \end{enumerate} \section*{Macros} \subsection*{Interval} Let $a$ and $b$ be real numbers. \subsubsection*{Closed interval} Using of macro \begin{lstlisting} \ci{a}{b} \end{lstlisting} as \textbf{c}losed \textbf{i}nterval. \begin{itemize} \item \texttt{isointerval} \begin{equation*} \left[ a , b \right] \end{equation*} \item \texttt{isoointerval} (same as for \texttt{isointerval}) \begin{equation*} \left[ a , b \right] \end{equation*} \item \texttt{fnspeinterval} \begin{equation*} \left< a , b \right> \end{equation*} \end{itemize} \subsubsection*{Opened interval} Using of macro \begin{lstlisting} \oi{a}{b} \end{lstlisting} as \textbf{o}pened \textbf{i}nterval. \begin{itemize} \item \texttt{isointerval} \begin{equation*} \left] a , b \right[ \end{equation*} \item \texttt{isoointerval} \begin{equation*} \left( a , b \right) \end{equation*} \item \texttt{fnspeinterval} (same as for \texttt{isoointerval}) \begin{equation*} \left( a , b \right) \end{equation*} \end{itemize} \subsubsection*{Right closed interval} Using of macro \begin{lstlisting} \rci{a}{b} \end{lstlisting} as \textbf{r}ight \textbf{c}losed \textbf{i}nterval. \begin{itemize} \item \texttt{isointerval} \begin{equation*} \left] a , b \right] \end{equation*} \item \texttt{isoointerval} \begin{equation*} \left( a , b \right] \end{equation*} \item \texttt{fnspeinterval} \begin{equation*} \left( a , b \right> \end{equation*} \end{itemize} \subsubsection*{Left closed interval} Using of macro \begin{lstlisting} \lci{a}{b} \end{lstlisting} as \textbf{l}eft \textbf{c}losed \textbf{i}nterval. \begin{itemize} \item \texttt{isointerval} \begin{equation*} \left[ a , b \right[ \end{equation*} \item \texttt{isoointerval} (same as for \texttt{isointerval}) \begin{equation*} \left[ a , b \right) \end{equation*} \item \texttt{fnspeinterval} \begin{equation*} \left< a , b \right) \end{equation*} \end{itemize} \subsubsection*{Using in text} All these macros can be used directly in text (thanks to the command \textit{ensuremath}). Therefore one can use this syntax \begin{lstlisting} Let $x$ be in \ci{a}{b} \end{lstlisting} which casts: Let $x$ be in \ci{a}{b}. \subsection*{Tensor} Let $x$ be vector and $A$ be matrix. \subsubsection*{Vector} Using of macro \begin{lstlisting} \vec{x} \end{lstlisting} as \textbf{vec}tor. \begin{itemize} \item \texttt{isotensor} - small letter with italic boldface \begin{equation*} \bm{\mathrm{x}} \end{equation*} \item \texttt{undertensor} \begin{equation*} \underline{x} \end{equation*} \item \texttt{arrowtensor} \begin{equation*} \vec x \end{equation*} \end{itemize} \subsubsection*{Matrix} Using of macro \begin{lstlisting} \mat{x} \end{lstlisting} as \textbf{mat}rix. \begin{itemize} \item \texttt{isotensor} - capital letter with italic boldface \begin{equation*} \bm{\mathrm{A}} \end{equation*} \item \texttt{undertensor} \begin{equation*} \underline{\underline{A}} \end{equation*} \item \texttt{arrowtensor} \begin{equation*} \mat{A} \end{equation*} \end{itemize} \subsubsection*{Using in text} All these macros can be used directly in text (thanks to the command \textit{ensuremath}). Therefore one can use this syntax \begin{lstlisting} Let \vec{x} be real. \end{lstlisting} which casts: Let \vec{x} be real. \subsection*{Macro for set} \subsubsection*{Set of natural numbers from 1 to $n$} Using of macro \begin{lstlisting} \allset{n} \end{lstlisting} as \textbf{all} natural number up to $n$ \textbf{set} leads to \begin{equation*} \allset{n}. \end{equation*} \subsubsection*{Set of natural numbers from 0 to $n$} Using of macro \begin{lstlisting} \allsetzero{n} \end{lstlisting} as \textbf{all} natural number up to $n$ \textbf{set} with \textbf{zero} leads to \begin{equation*} \allsetzero{n}. \end{equation*} \subsection*{Differentiability class} \subsubsection*{Just symbol} Using of macro \begin{lstlisting} \cclass \end{lstlisting} as \textbf{C} \textbf{class} leads to \begin{equation*} \cclass. \end{equation*} \subsubsection*{C infinity} Using of macro \begin{lstlisting} \ccinf \end{lstlisting} as \textbf{C} \textbf{class} of \textbf{inf}inity leads to \begin{equation*} \ccinf. \end{equation*} \subsubsection*{C of order $d$} Using of macro \begin{lstlisting} \ccof{d} \end{lstlisting} as \textbf{C} \textbf{class} \textbf{of} order leads to \begin{equation*} \ccof{d}. \end{equation*} \subsection*{Complex} Let $z \in \compn$. \subsubsection*{Real part} Using of macro \begin{lstlisting} \Re{x} \end{lstlisting} as \textbf{Re}al. \begin{itemize} \item \texttt{oldcomplex} \begin{equation*} \Re\left\{z\right\} \end{equation*} \item \texttt{isocomplex} \begin{equation*} \mathrm{Re}\; z \end{equation*} \end{itemize} \subsubsection*{Imaginary part} Using of macro \begin{lstlisting} \Im{x} \end{lstlisting} as \textbf{Im}aginary. \begin{itemize} \item \texttt{oldcomplex} \begin{equation*} \Im\left\{z\right\} \end{equation*} \item \texttt{isocomplex} \begin{equation*} \mathrm{Im}\; z \end{equation*} \end{itemize} \subsubsection*{Using in text} All these macros can be used directly in text (thanks to the command \textit{ensuremath}). Therefore one can use this syntax \begin{lstlisting} Let $x$ equal to \Re{z}. \end{lstlisting} which casts: Let $x$ equal to $\mathrm{Re}\;z$. \subsection*{Subscript} Subscript text with two or more characters should be written in roman style (not italic as default). One can use prefix ! which makes the word after it in roman style. Using of macro \begin{lstlisting} A_{!unique} \end{lstlisting} which leads to \begin{equation*} A_{!unigue} \end{equation*} instead of classic \begin{equation*} A_{unique} \end{equation*} \subsection*{Floor and ceiling functions} \subsubsection*{Floor function} Macro \begin{lstlisting} \floor{x} \end{lstlisting} as \textbf{floor} function leads to \begin{equation*} \floor{x} \end{equation*} \subsubsection*{Ceil function} Macro \begin{lstlisting} \ceil{x} \end{lstlisting} as \textbf{ceil} function leads to \begin{equation*} \ceil{x} \end{equation*} \subsection*{Definition operator} There are two ways to set a definition operator. First with \textit{text} and the second with \textit{colon}. \subsubsection*{Text definition} Macro \begin{lstlisting} x \df a \end{lstlisting} \begin{itemize} \item \texttt{deftext} \begin{equation*} x \stackrel{\mathclap{\normalfont{\mbox{\tiny def.}}}}{=} a \end{equation*} \item \texttt{defcolon} \begin{equation*} x \df a \end{equation*} \end{itemize} \subsection*{Special sets of numbers} \subsubsection*{Natural number} Macro \begin{lstlisting} \natun \end{lstlisting} as \textbf{natu}ral \textbf{n}umber leads to \begin{equation*} \natun \end{equation*} \subsubsection*{Natural number with zero included} Macro \begin{lstlisting} \nnzero \end{lstlisting} as \textbf{n}atural \textbf{n}umber \textbf{zero} leads to \begin{equation*} \nnzero \end{equation*} \subsubsection*{Integers} Macro \begin{lstlisting} \inte \end{lstlisting} as \textbf{inte}regers leads to \begin{equation*} \inte \end{equation*} \subsubsection*{Rational number} Macro \begin{lstlisting} \ratin \end{lstlisting} as \textbf{rati}onal \textbf{n}umber leads to \begin{equation*} \ratin \end{equation*} \subsubsection*{Real number} Macro \begin{lstlisting} \realn \end{lstlisting} as \textbf{real} \textbf{n}umber leads to \begin{equation*} \realn \end{equation*} \subsubsection*{Complex number} Macro \begin{lstlisting} \compn \end{lstlisting} as \textbf{comp}ex \textbf{n}umber leads to \begin{equation*} \compn \end{equation*} \subsubsection*{Using in text} All these macros can be used directly in text (thanks to the command \textit{ensuremath}). Therefore one can use this syntax \begin{lstlisting} Let $n$ be in \natun \end{lstlisting} which casts: Let $n$ be in \natun. \subsection*{Derivative} It is derived from \textit{physics} package. The manual is \href{http://mirrors.ctan.org/macros/latex/contrib/physics/physics.pdf}{here}. \subsection*{Operator} Partially derived from \textit{physics} package. \subsubsection*{Gradient} Macro \begin{lstlisting} \grad \end{lstlisting} as \textbf{grad}ient leads to \begin{equation*} \grad \end{equation*} \subsubsection*{Divergence} Macro \begin{lstlisting} \div \end{lstlisting} as \textbf{div}ergence leads to \begin{equation*} \div \end{equation*} \noindent Derived from \textit{physics} package, the original meaning of this command as a maths symbol for dividing has alias \begin{lstlisting} \divisionsymbol \end{lstlisting} which cast \begin{equation*} \divisionsymbol \end{equation*} \subsubsection*{Rotation} In English literature as \textbf{curl} operator has macro \begin{lstlisting} \rot \end{lstlisting} as \textbf{rot}ation and leads to \begin{equation*} \rot \end{equation*} \noindent One can also use \textit{physics} package command \begin{lstlisting} \curl \end{lstlisting} \subsubsection*{Laplacian} Macro \begin{lstlisting} \lapl \end{lstlisting} as \textbf{lapl}acian leads to \begin{equation*} \lapl \end{equation*} \noindent One can also use \textit{physics} package notation \begin{equation*} \laplacian \end{equation*} which is cast by macro \begin{lstlisting} \laplacian \end{lstlisting} \section*{Degree} Macro \begin{lstlisting} \degree \end{lstlisting} as \textbf{degree} leads to \degree. Can be used without math mode. \section*{Physics unit} \subsubsection*{Variable unit} Macro \begin{lstlisting} \varun{m}{kg} \end{lstlisting} as \textbf{var}iable \textbf{un}it leads to \begin{equation*} \varun{m}{kg} \end{equation*} \noindent This macro can be used directly in text (thanks to the \textit{ensure} function). Therefore one can use \begin{lstlisting} where \varun{m}{kg} is the mass. \end{lstlisting} which casts: where \varun{m}{kg} is the mass. \subsubsection*{Unit} Macro \begin{lstlisting} m\unit{kg} \end{lstlisting} as \textbf{unit} leads to \begin{equation*} m\unit{kg} \end{equation*} This macro looks as \begin{lstlisting} \;\mathrm{kg} \end{lstlisting} the space before the roman characters is very important in science publications. \subsection*{Expected value} Macro \begin{lstlisting} \expv{x} \end{lstlisting} as \textbf{exp}ected \textbf{v}alue leads to \begin{equation*} \expv{x} \end{equation*} \section*{Shortcuts} \subsubsection*{One half} Macro \begin{lstlisting} \hlf \end{lstlisting} as \textbf{h}a\textbf{lf} leads to \begin{equation*} \hlf \end{equation*} \subsubsection*{One over } Macro \begin{lstlisting} \oover{x} \end{lstlisting} as \textbf{o}ne \textbf{over} leads to \begin{equation*} \oover{x} \end{equation*} \section*{Spaces} \subsubsection*{Horizontal space} Macro \begin{lstlisting} \hem[width] \end{lstlisting} as \textbf{h}space\{\textbf{em}\} leads to horizontal space of specific width (multiples of em). Special case is 1em \begin{lstlisting} \mathrm{text}\hem\mathrm{text} \end{lstlisting} which leads to \begin{equation*} \mathrm{text}\hem\mathrm{text} \end{equation*} or shortcut form space with 2em width \begin{lstlisting} \mathrm{text}\htem\mathrm{text} \end{lstlisting} which casts \begin{equation*} \mathrm{text}\htem\mathrm{text} \end{equation*} \subsection*{Implies with em spaces} Macro \begin{lstlisting} \impem \end{lstlisting} as \textbf{implies} with \textbf{em} spaces leads to \begin{equation*} \mathrm{text}\impem\mathrm{text} \end{equation*} \end{document}