% Style File: Math.Sty % % Updated Aug 18, 2018 % Y. Tokieda % This style file defines and provides LaTeX macro for % mathematical expressions complicated mathematical formulea. % To look up the specification of the style file, see the % attached documentation. % \makeatletter % <<<<<<<<<< Greek Alphabet for math >>>>>>>>>> \def\eps{\varepsilon} \def\mGamma{{\mit\Gamma}} \def\mDelta{{\mit\Delta}} \def\mTheta{{\mit\Theta}} \def\mXi{{\mit\Xi}} \def\mLambda{{\mit\Lambda}} \def\mSigma{{\mit\Sigma}} \def\mPhi{{\mit\Phi}} \def\mPsi{{\mit\Psi}} \def\mOmega{{\mit\Omega}} % <<<<<<<<<< Arithmetic >>>>>>>>>> \def\lowsqrt{\@ifnextchar[{\@lowsqrt}{\@lowsqrt[\empty]}} \def\@lowsqrt[#1]#2{% \setbox0\hbox{$#2$} \sqrt[#1]{\hbox to\wd0{\hss\vbox to1.7ex{\vss\null\vss}\hss}}% \null\hskip-\wd0{#2}} \def\frtsqrt{\@ifnextchar[{\@frtsqrt}{\@frtsqrt[\empty]}} \def\@frtsqrt[#1]#2{% \setbox0\hbox{$\displaystyle #2$} \null\kern0.32em\sqrt[#1]{% \raise-1.8ex\hbox to\wd0{\hss\vbox to5ex{\vss\null\vss}}}% \null\hskip-\wd0\hbox to\wd0{\hss$\displaystyle #2$\hss}} %% \def\lowsuffix@#1#2#3{#2_{\raise-0.2ex\hbox{% \kern-0.03em$#1 {#3}$}}} \def\lowsuffix#1#2{\mathchoice{\lowsuffix@{\scriptstyle}{#1}{#2}}% {\lowsuffix@{\scriptstyle}{#1}{#2}}% {\lowsuffix@{\scriptscriptstyle}{#1}{#2}}% {\lowsuffix@{\scriptscriptstyle}{#1}{#2}}} %%%% Fraction in displaystyle \def\frt@#1#2#3{#1\frac{% {}\mathstrut\hskip 0.2em #2 \hskip 0.2em{}}{% {}\mathstrut\hskip 0.2em #3 \hskip0.2em{}}} \def\frt#1#2{\mathchoice{\frt@{\displaystyle}{#1}{#2}}% {\frt@{\displaystyle}{#1}{#2}}{\frt@{\scriptstyle}{#1}{#2}}% {\frt@{\scriptscriptstyle}{#1}{#2}}} % Alternative command name \def\dfrac{\frt} %%%% Slanted parallel symbol \def\para@#1{#1/\kern-0.27em\raise-0.25ex\hbox{$#1/$}} \def\para{\mathchoice{\para@{\displaystyle}}{\para@{\displaystyle}} {\para@{\scriptstyle}}{\para@{\scriptscriptstyle}} } % <<<<<<<<<< Linear Algebra >>>>>>>>>> \def\transpose#1{{}\,^{\rm t}\hskip-0.1em#1} % <<<<<<<<<< Vector Algebra >>>>>>>>>> \def\vc@#1#2{\mbox{#1\boldmath$#2$}} \def\vc#1{\mathchoice{{\vc@{\normalsize}{#1}}}{{\vc@{\normalsize}{#1}}}% {{\vc@{\scriptsize}{#1}}}{{\vc@{\tiny}{#1}}}} \def\ftvc#1{\mathchoice{{\vc@{\footnotesize}{#1}}}{{\vc@{\footnotesize}{#1}}}% {{\vc@{\tiny}{#1}}}{{\vc@{\tiny}{#1}}}} \def\Div{\nabla\!\cdot\kern-0.07em{}} \def\Curl{\nabla\!\times\!{}} % <<<<<<<<<< Integrodifferentiation >>>>>>>>>> \def\dlt{{\rm d}} \def\odf{\@ifnextchar[{\@odf}{\@@odf}} \def\@odf[#1]#2#3{\frt{\dlt^{#1}\kern-0.08em#2}{\dlt #3^{#1}}} \def\@@odf#1#2{\frt{\dlt #1}{\dlt #2}} \def\odd#1#2{\frt{\dlt^2#1}{\dlt #2^2}} \def\pdf{\@ifnextchar[{\@pdf}{\@@pdf}} \def\@pdf[#1]#2#3{\frt{\partial^{#1}\kern-0.08em#2}{\partial #3^{#1}}} \def\@@pdf#1#2{\frt{\partial #1}{\partial #2}} \def\pdd#1#2{\frt{\partial{}^2\hskip-0.08em#1}{\partial #2{}^2}} \def\pdm#1#2#3{\frt{\partial{}^2\hskip-0.08em#1}{% \partial #2\kern0.07em\partial #3}} \def\todf{\@ifnextchar[{\@todf}{\@todf[\empty]}} \def\@todf[#1]#2#3{\dlt^{#1}\kern-0.08em#2/\dlt #3^{#1}} \def\todd#1#2{\dlt^2\kern-0.08em#1/\dlt #2^2} \def\tpdf{\@ifnextchar[{\@tpdf}{\@@tpdf}} \def\@tpdf[#1]#2#3{\partial^{#1}\kern-0.08em#2/\partial #3^{#1}} \def\@@tpdf#1#2{\partial #1/\partial #2} \def\tpdd#1#2{\partial^2\kern-0.08em#1/\partial #2^2} \def\tpdm#1#2#3{\partial^2\kern-0.08em#1/\partial#2\partial#3} % <<<<<<<<<< Differential Geometry >>>>>>>>>> \def\Chris#1#2{{\mit\Gamma}^{#1}\!_{#2}} \def\Chrisi#1#2{{\mit\Gamma}\!_{#1,#2}} \def\chris#1#2{\{\!\!\vbox to1ex{\vss% \hbox{$\begin{array}{c}{\scriptstyle#1}\\[-10pt]% {\scriptstyle#2}\\[-2.6ex]{}\end{array}$}\vss}\!\!\}} \def\chrisi#1#2{[\raisebox{0.5ex}{% ${}_{#1,\,#2}$}]} % <<<<<<<<<< Integers >>>>>>>>>> \def\floor#1{\left\lfloor#1\right\rfloor} \def\ceil#1{\left\lceil#1\right\rceil} % <<<<<<<<<< Quantum Mechanics >>>>>>>>>> \def\avrg#1{\left\langle #1 \right\rangle} \def\bra#1{\left\langle #1 \right|} \def\ket#1{\left| #1 \right\rangle} \def\braket#1#2{\left\langle #1 \left|\right. #2 \right\rangle} \def\Braket#1#2#3{\left\langle #1 \left| #2 \right| #3 \right\rangle} \def\tavrg#1{\langle #1 \rangle} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % eqnarray environment % \def\eqnarray{\stepcounter{equation}\let\@currentlabel\theequation \global\@eqnswtrue\m@th \global\@eqcnt\z@\tabskip\@centering\let\\\@eqncr $$\halign to\displaywidth\bgroup\@eqnsel\hskip\@centering $\displaystyle\tabskip\z@{##}$&\global\@eqcnt\@ne \hskip .57\arraycolsep \hfil${##}$\hfil &\global\@eqcnt\tw@ \hskip .57\arraycolsep $\displaystyle\tabskip\z@{##}$\hfil \tabskip\@centering&\llap{##}\tabskip\z@\cr} \def\endeqnarray{\@@eqncr\egroup \global\advance\c@equation\m@ne$$\global\@ignoretrue} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % eqnarraya environment % \def\eqnarraya{\eqn@rraya \eqnarray} \newif\ifnakaguro \nakagurotrue \def\niten{\mbox{.}} %\def\niten{\mbox{$\cdot$}} %\def\niten{\hbox to .5zw{\hfil\raise.5ex\hbox{.}\hfil}} \def\eqn@rraya{\c@enumi=\c@equation \advance\c@enumi by1\relax \c@equation=0\relax \@ifundefined{chapter}% {\def\theequation{\theenumi\alph{equation}}}% {\def\theequation{\ifnakaguro \thechapter\niten\theenumi\alph{equation}% \else\thechapter.\theenumi\alph{equation}\fi}}} \def\endeqnarraya{\endeqnarray \global\c@equation=\c@enumi} %%%%%%% delta in mathematics style \newdimen\th@line \th@line=0.06pt % for 1200 dpi printers \newdimen\th@majline \th@majline=0.065em \newdimen\th@minline \th@minline=0.025em \newdimen\xa@kern % \newdimen\len@xa % \newdimen\len@max % \newdimen\cur@yy % \def\mdelt@{% \cur@yy=1.6ex% \th@majline=0.065em% \th@minline=0.025em% \leavevmode\raise\z@%\cur@yy% \vbox{\offinterlineskip% \xa@kern=0.7\cur@yy \len@xa=\z@ % 0.5\th@majline%\z@ \len@max=\th@majline % \advance\len@max\th@minline \loop\hbox{\kern\xa@kern\vbox to\th@line{% \hrule width\len@xa height\th@line}} \advance\len@xa0.6\th@line \advance\xa@kern-0.7\th@line \advance\cur@yy-\th@line \ifdim\len@xa<\len@max\relax% \repeat % \len@xa=-\th@minline%\z@ \loop\hbox{\kern\xa@kern\vbox to\th@line{% \hrule width\th@minline height\th@line}\kern\len@xa% \vbox to\th@line{\hrule width\th@majline height\th@line}} \advance\len@xa0.6\th@line \advance\xa@kern-0.7\th@line \advance\cur@yy-\th@line \ifdim\cur@yy>\th@majline\relax% \repeat% \advance\len@xa\th@majline %\advance\len@xa-\th@minline \advance\len@xa\th@minline %\advance\len@xa-\th@minline \loop\hbox{\kern\xa@kern\vbox to\th@line{% \hrule width\len@xa height\th@line}} \advance\cur@yy-\th@line% \advance\xa@kern-0.7\th@line \advance\len@xa0.6\th@line \ifdim\cur@yy>\z@\relax% \repeat %end while }\kern0.07em\relax} \def\mdelta{\mathchoice{{\mdelt@}}{{\mdelt@}}% {{\mbox{\scriptsize$\mdelt@$}}}{{\mbox{\tiny$\mdelt@$}}}} %% \makeatother