%
%	M A T H T E C H . S T Y
%
% MATHEMATICAL THESIS TECHNICAL-STYLE option
%
%					     Version 1.4 released 14 Mar 1995
%					     Version 1.3 released 01 Mar 1995
%					     Version 1.2 released 06 Feb 1995
%					     Version 1.1 released 13 Sep 1994
%                                            Version 1.0 released 23 Jul 1993
%  for LaTeX /( AMS-LaTeX )
%
% Copyright (C) 1993 by Toshiyuki Imamura, imamura@kuamp.kyoto-u.ac.jp
%
%	This style option defines the mathematical technical macros,
%
%		numberwithin command
%
%		equation  and equation* environment
%		eqnarray and subeqnarray and sub equation environment
%
%		eqncases, subeqncases and cases environment
%
%		textin command
%		
%		newfunction, newoperator and newrelation command
%
%	and the slanted capital Greek, and resizable dots command.
%
%		Vdots, Hdots, Ddots, Qdots
%
%
%
\def\loadnewfont#1#2{%
  \def\tfm{#2}
  \f@ntcheck{\tfm5}\iffontexistence%
    \expandafter\font\csname#1v\endcsname=\tfm5\relax%
    \@addfontinfo\@vpt{%
      \expandafter\def\csname p#1\endcsname{\csname#1v\endcsname}}\fi%
  \f@ntcheck{\tfm7}\iffontexistence%
    \expandafter\font\csname#1vii\endcsname=\tfm7\relax%
    \@addfontinfo\@viipt{%
      \expandafter\def\csname p#1\endcsname{\csname#1vii\endcsname}}\fi%
  \f@ntcheck{\tfm10}\iffontexistence%
    \expandafter\font\csname#1x\endcsname=\tfm10\relax%
    \expandafter\font\csname#1xi\endcsname=\tfm10 scaled \magstephalf\relax%
    \expandafter\font\csname#1xii\endcsname=\tfm10 scaled \magstep1\relax%
    \expandafter\font\csname#1xiv\endcsname=\tfm10 scaled \magstep2\relax%
    \expandafter\font\csname#1xvii\endcsname=\tfm10 scaled \magstep3\relax%
   \@addfontinfo\@xpt{%
      \expandafter\def\csname p#1\endcsname{\csname#1x\endcsname}}%
    \@addfontinfo\@xipt{%
      \expandafter\def\csname p#1\endcsname{\csname#1xi\endcsname}}%
    \@addfontinfo\@xiipt{%
      \expandafter\def\csname p#1\endcsname{\csname#1xii\endcsname}}%
    \@addfontinfo\@xivpt{%
      \expandafter\def\csname p#1\endcsname{\csname#1xiv\endcsname}}%
    \@addfontinfo\@xviipt{%
      \expandafter\def\csname p#1\endcsname{\csname#1xvii\endcsname}}\fi%
  \expandafter\gdef\csname#1\endcsname{\protect\csname p#1\endcsname}}
%
%
\newif\iffontexistence \fontexistencefalse
\def\f@ntcheck#1{%
 \batchmode \font\fonts@mple=#1\relax \errorstopmode%
 \ifx\fonts@mple\nullfont \global\fontexistencefalse%
 \else \global\fontexistencetrue\fi}
%
%\loadnewfont{scr}{rsfs}		% scrpit type font
%\loadnewfont{Bbb}{msbm}		% blackboard bold face font
%\loadnewfont{frak}{eufm}		% german frake font
%
%
%
\def\numberwithin#1#2{%
\@addtoreset{#1}{#2}%
\expandafter\def\csname the#1\endcsname{\csname the#2\endcsname.\arabic{#1}}}
%
\numberwithin{equation}{section}
%
%
%
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}{Corollary}[section]
\newtheorem{lemma}{Lemma}[section]
\newtheorem{definition}{Definition}[section]
\newtheorem{algorithm}{Algorithm}[section]
%
%
% New equation, multilinable math with centering align.
% New subequation, numbering with subeqno.
%
\newcounter{subequation}[equation]
\def\thesubequation{\theequation\kern.8pt\hbox to1ex{\alph{subequation}\hss}}
%
\def\equation{\stepcounter{equation}%
 \def\@eqnstepcounter{\stepcounter{equation}}%
 \let\@@eqncr=\@@@eqncr%
 \let\@currentlabel=\theequation\@equation}
\def\endequation{%
 \@@@eqncr\egroup\global\advance\c@equation\m@ne$$\global\@ignoretrue}

\@namedef{equation*}{\def\@eqncr{\nonumber\@seqncr}\equation}
\@namedef{endequation*}{\global\advance\c@equation\m@ne%
			\nonumber\endequation}

\def\subequation{%
 \def\@eqnstepcounter{\stepcounter{subequation}}%
 \stepcounter{equation}\global\c@subequation\@ne%%
 \let\@eqnnum=\sub@eqnnum%
 \let\@@eqncr=\@@@eqncr%
 \let\@currentlabel=\thesubequation\@equation}
 \def\endsubequation{%
 \@@@eqncr\egroup$$\global\@ignoretrue}

\def\@equation{%
%
% ref command bug fix
% Thanks to bear@hashi1.civil.tohoku.ac.jp
%
% \let\@currentlabel=\theequation
%
 \global\@eqnswtrue\let\\=\@eqncr%
 \tabskip\@centering$$\halign to \displaywidth\bgroup\@eqnsel%
 \let\@currentlabel=\theequation%
 \hfil$\displaystyle{##}$\hfil&\llap{##}\tabskip\z@\cr}
%
% New eqnarray, such that 2nd column's space are reduced.
% New subeqnarray, numbering with subeqno
%
\def\eqnarray{\stepcounter{equation}%
 \def\@eqnstepcounter{\stepcounter{equation}}%
 \let\@currentlabel=\theequation\@eqnarray}

\def\subeqnarray{%
 \def\@eqnstepcounter{\stepcounter{subequation}}%
 \stepcounter{equation}\global\c@subequation\@ne%
 \let\@eqnnum=\sub@eqnnum%
 \let\@currentlabel=\thesubequation\@eqnarray}
\def\endsubeqnarray{\@@eqncr\egroup$$\global\@ignoretrue}

\def\@eqnarray{%
%
% ref command bug fix
% Thanks to bear@hashi1.civil.tohoku.ac.jp
%
% \let\@currentlabel=\theequation% Thanks to bear@hashi1.civil.tohoku.ac.jp
%
 \global\@eqnswtrue%
 \global\@eqcnt\z@\tabskip\@centering\let\\=\@eqncr%
 $$\halign to \displaywidth\bgroup\@eqnsel\hskip\@centering%
 $\displaystyle\tabskip\z@%
 \let\@currentlabel=\theequation%
 {##}$&\global\@eqcnt\@ne%
 \hfil$\displaystyle{{}##{}}$\hfil%
 &\global\@eqcnt\tw@$\displaystyle\tabskip\z@{##}$\hfil%
 \tabskip\@centering&\llap{##}\tabskip\z@\cr}
%
%
\def\@@eqncr{\let\@tempa\relax%
 \ifcase\@eqcnt\def\@tempa{&&&}\or\def\@tempa{&&}\else\def\@tempa{&}\fi%
 \@tempa\if@eqnsw\@eqnnum\@eqnstepcounter\fi%
 \global\@eqnswtrue\global\@eqcnt\z@\cr}
\def\@@@eqncr{&\if@eqnsw\@eqnnum\@eqnstepcounter\fi%
 \global\@eqnswtrue\cr}
%
%
%\def\sub@eqnnum{\hbox to .01pt{}\rlap%		for left-eq-no.
%	{\rm\hskip-\displaywidth(\thesubequation)}}
%
%\def\sub@eqnnum{\rm(\thesubequation)}%		for right-eq-no.
%
%
%	If you wnat to change Right-eq-no <-> Left-eq-no,
%	you may use \lefteqno or \righteqno outside eq-env.
%
\def\lefteqno{\global\def\@eqnnummode{l}}
\def\righteqno{\global\def\@eqnnummode{r}}
\def\@eqnnum{%
 \if\@eqnnummode l%
  {\hbox to .01pt{}\rlap{\rm \hskip -\displaywidth(\theequation)}}%
 \else%
  {\rm(\theequation)}\fi}
\def\sub@eqnnum{%
 \if\@eqnnummode l%
  {\hbox to .01pt{}\rlap{\rm \hskip -\displaywidth(\thesubequation)}}%
 \else%
  {\rm(\thesubequation)}\fi}

\righteqno%		default is right-eq-no.
%
%
\long\def\textin#1{\noalign{\noindent%
 \vskip\topsep\hbox{\vbox{\hsize\textwidth%
 \let\\=\newline%
 \noindent#1\hss}}\vskip\topsep}}
%
%
\let\ds=\displaystyle%
\let\ss=\scriptstyle%
\let\sss=\scriptscriptstyle%
\let\ts=\textstyle%
\def\math@style{\mathchoice{\ds}{\ts}{\ss}{\sss}}
\def\math@style@down{\mathchoice{\ts}{\ss}{\sss}{\sss}}
%
\def\FRAC{\@ifnextchar[{\@FRAC}{\@FRAC[.4pt]}}
\def\@FRAC[#1]#2#3{%
 \edef\m@style{\math@style}%
 \setbox\@tempboxa=\hbox{$\m@style#2$}\@tempdima\wd\@tempboxa%
 \setbox\@tempboxa=\hbox{$\m@style#3$}\@tempdimb\ht\@tempboxa%
 \ifdim\@tempdima<\wd\@tempboxa\@tempdima\wd\@tempboxa\fi%
 \ifdim\@tempdima<1.6ex\@tempdima1.6ex\fi%
 \setbox\@tempboxa=\hbox{$\mathstrut$}%
 \advance\@tempdimb-\ht\@tempboxa\ifdim\@tempdimb>\z@\@tempdimb\z@\fi%
 {{\mathchoice{\lower1.6pt\hbox to\@tempdima{\hss$\m@style#2$\hss}}%
              {\lower1.6pt\hbox to\@tempdima{\hss$\m@style#2$\hss}}%
              {\hbox to\@tempdima{\hss$\m@style#2$\hss}}%
              {\hbox to\@tempdima{\hss$\m@style#2$\hss}}%
 }%
 \above#1\relax%
 {\mathchoice{\lower.5\@tempdimb\hbox{$\m@style#3$}}%
             {\lower.5\@tempdimb\hbox{$\m@style#3$}}%
             {\hbox{$\m@style#3$}}%
             {\hbox{$\m@style#3$}}%
 }%
}}
\def\pfrac{\@ifnextchar[{\@pfrac}{\@@pfrac}}
\def\@pfrac[#1]#2#3{\FRAC{\partial^{#1}#2}{\partial#3^{#1}}}
\def\@@pfrac#1#2{\FRAC{\partial#1}{\partial#2}}
\def\slfrac#1#2{\leavevmode%
 \ifmmode%
 \raise.5ex\hbox{$#1$}\kern-.1em/\kern-.1em\lower.25ex\hbox{$#2$}%
 \else%
 \raise.5ex\hbox{#1}\kern-.1em/\kern-.1em\lower.25ex\hbox{#2}%
 \fi}
%
%
\def\newfunction#1{%
 \expandafter\def\csname#1\endcsname{\mathop{\rm#1}\nolimits}}
\def\newoperator#1#2{%
 \expandafter\def\csname#1\endcsname{\mathop{#2}\limits}}
\def\newrelation#1#2{%
 \expandafter\def\csname#1\endcsname{\mathrel{#2}\limits}}
%
\def\@iint@kern{\mathchoice{\!\!\!}{\!\!}{\!\!}{\!\!}}
\def\@iiint@kern{\mathchoice{\!\!\!\!}{\!\!}{\!\!}{\!\!}}
%
\newoperator{Ker}{\rm Ker}
\newoperator{Im}{\rm Im}
\newoperator{sumsum}{\sum\!\sum}
\newoperator{iint}{\int\@iint@kern\int}
\newoperator{iiint}{\int\@iiint@kern\int\@iiint@kern\int}
\newoperator{span}{\it span}
%
\newfunction{cond}
\newfunction{diag}
\newfunction{det}
\newfunction{trace}
\newfunction{sign}
\newfunction{const}
\newfunction{Arcsin}
\newfunction{Arccos}
\newfunction{Arctan}
\newfunction{cosec}
%
\newfunction{Arcsec}		\newfunction{arcsec}
\newfunction{Arccosec}		\newfunction{arccosec}
\newfunction{Arccsc}		\newfunction{arccsc}
\newfunction{Arccot}		\newfunction{arccot}
%
\def\@addCapitalGreek#1{%
 \expandafter\def\csname var#1\endcsname{{\mit\csname#1\endcsname}}}
%
\@addCapitalGreek{Gamma}	\@addCapitalGreek{Delta}
\@addCapitalGreek{Theta}	\@addCapitalGreek{Lambda}
\@addCapitalGreek{Xi}		\@addCapitalGreek{Pi}
\@addCapitalGreek{Sigma}	\@addCapitalGreek{Upsilon}
\@addCapitalGreek{Phi}		\@addCapitalGreek{Psi}
\@addCapitalGreek{Omega}
%
%	(See RakuRaku LaTeX edited by Dr.Nodera)
%
\def\fillBox{{\rule[-2pt]{5pt}{6pt}}}
\newfont{\b@g}{cmr10 scaled\magstep4}
\def\bigzerol{\smash{\hbox{\b@g0}}}
\def\bigzerou{\smash{\lower1.7ex\hbox{\b@g0}}}
\def\bigzero{\smash{\lower.85ex\hbox{\b@g0}}}
%
%		  (     )	    (  .  )
%		  (. . .)	    (  .  )
% resizable Hdots (     ) and Vdots (  .  )
%
%		  (.    )	    (    .)
%		  (  .  )	    (  .  )
% resizable ddots (    .) and qdots (.    ).
%	    Ddots             Qdots
\def\Hdots[#1]{%
 \@tempdima=#1%
 \mathinner{\hbox to \@tempdima{\hss\raise.35\@tempdima\hbox{%
    .\kern.4\@tempdima.\kern.4\@tempdima.}\hss}}}
\def\Vdots[#1]{%
 \@tempdima=#1%
 \mathinner{\hbox to\@tempdima{\hss\hbox to0pt{.}%
     \raise.35\@tempdima\hbox to0pt{.}\raise.7\@tempdima\hbox to0pt{.}\hss}}}
\def\Ddots[#1]{%
 \@tempdima=#1\def\b@x{\hbox to\@tempdima{\hss}}
 \let\cdots=\b@x \let\vdots=\b@x \ddots}
\def\Qdots[#1]{%
 \@tempdima=#1\def\b@x{\hbox to\@tempdima{\hss}}
 \let\cdots=\b@x \let\vdots=\b@x \qdots}
\def\ddots{%
 \setbox\@tempboxa=\hbox{$\cdots$}\@tempdima\wd\@tempboxa
 \mathinner{\hbox to\@tempdima{\hss\raise.7\@tempdima\hbox{.}%
    \kern.2\@tempdima\raise.35\@tempdima\hbox{.}%
    \kern.2\@tempdima\hbox{.}\hss}}}
\def\qdots{%
 \setbox\@tempboxa=\hbox{$\cdots$}\@tempdima\wd\@tempboxa
 \mathinner{\hbox to\@tempdima{\hss\hbox{.}%
    \kern.2\@tempdima\raise.35\@tempdima\hbox{.}%
    \kern.2\@tempdima\raise.7\@tempdima\hbox{.}\hss}}}
\def\hdots{\cdots}
%
%
%	NEW (sub)eqncases environment
%
%
\newcount\@eqnccnt

\let\@eqnnum@old=\relax

\def\eqncases{%
 \let\the@eqnc=\@eqnnum%
 \@eqncases}
\def\subeqncases{%
 \ifx\@currentlabel\theequation%
 \global\c@subequation\@ne\let\@currentlabel=\thesubequation%
 \let\the@eqnc=\sub@eqnnum\def\@eqnstepcounter{\stepcounter{subequation}}\fi%
 \@eqncases}

\def\@eqncases{%
 \global\setbox\z@=\vbox\bgroup\normalbaselines\m@th%
 \let\\=\@eqnccr\ialign\bgroup\global\@eqnccnt\z@$##\hfil$&%
 \global\@eqnccnt\@ne\quad\strut##\hfil\crcr}

\def\endeqncases{\@@eqnccr\egroup\egroup\mk@eqncnum}
\def\endsubeqncases{\@@eqnccr\egroup\egroup\mk@eqncnum}

\def\@eqnccr{\@@eqnccr\noalign{\vskip.5\jot}}
\def\@@eqnccr{\let\@tempa\relax%
 \ifcase\@eqnccnt\def\@tempa{&}\or\def\@tempa{}\fi%
 \if@eqnsw\global\setbox\@ne=\vbox{\unvbox\@ne\hbox{\the@eqnc}}%
 \@eqnstepcounter\else\global\setbox\@ne=\vbox{\unvbox\@ne\hbox{}}\fi%
 \global\@eqnswtrue\@tempa\cr}

\def\mk@eqncnum{%
 \left\{\;\vcenter{\copy\z@}\right.%
 \def\@num{\hbox{\vrule height\ht\tw@ depth\dp\tw@ width\z@}}
 \def\@last{\setbox\z@=\vbox{\unvbox\z@\unskip\global\setbox\tw@=\lastbox}}%
 \@last\setbox3=\vbox{\@num}\@last\@last%
 \loop\setbox3=\vbox{\@num\unvbox3}\@last\@last\ifhbox\tw@\repeat%
 \def\@num{\hbox{\box\z@\box\tw@}}%
 \def\@last{\setbox\@ne=\vbox{\unvbox\@ne\unskip\global\setbox\tw@=\lastbox}%
 \setbox3=\vbox{\unvbox3\unskip\global\setbox\z@=\lastbox}}
 \@last\setbox4=\vbox{\@num}\@last%
 \loop\setbox4=\vbox{\@num\kern.5\jot\unvbox4}\@last\ifhbox\tw@\repeat%
 \global\setbox\z@=\box4%
 \global\let\@eqnnum@old=\@eqnnum%
 \gdef\@eqnnum{\@eqncnum\global\let\@eqnnum=\@eqnnum@old}}

\def\@eqncnum{$\vcenter{\box\z@}$}

%
%	CASES environment
%
\def\cases{\left\{\;\vcenter\bgroup\normalbaselines\m@th%
 \def\@cr{\cr\noalign{\vskip.5\jot}}\let\\=\@cr%
 \ialign\bgroup$##\hfil$&\quad\strut##\hfil\crcr}
\def\endcases{\crcr\egroup\egroup\right.}

\endinput
%
%	Tiny document
%
mathematical envirnment

i) equation environment ( centering multi-eq-lines )
   No numbering can be done with '*'
	
	\begin{equation}
		f(x) = .... \\
		g(x) = ....
	\end{equation}

ii) subequation environment ( centering multi-eq-lines with sub-eq no.)
    No numbering can be done but it is nonsense.

	\begin{subequation}
		f(x) = .... \\
		g(x) = ....
	\end{subequation}

iii) eqnarray environment ( aligning ,at '&', multi-eq-lines )
     No numbering can be done with '*'

	\begin{eqnarray}
		f(x)&=&.... \\
		g(x)&=&....
	\end{eqnarray}

iv) subeqnarray environment ( aligning ,at '&', multi-eq-lines with sub-eq no. )
    No numbering can be done but it is nonsense.

	\begin{subeqnarray}
		f(x)&=&.... \\
		g(x)&=&....
	\end{subeqnarray}

\thesubequation is used in sub(equation|eqnarray) environment.
\ref command is also applied in sub* envirnment.


v) eqncases environment is the case environment with equation numbering
   with every items, and also subeqncases is with subeqation numbering.
   For each column, nonumber can be done. And after endsubeqncases nonumber
   means usual nonumber command of eqnarray.
  (in subeqnarray env, numbering is forced to subequation.)

	\begin{eqnarray}
		f(x) &=& \begin{subeqncases}
			   1 & if $x>0$\\
			  -1 & if $x\le0$
			 \end{subeqncases}\\
		g(x) &=& \tan x
	\end{eqnarray}

If only one numbering for cases, it is available with cases environment and
no numbering is able to use both cases and nonumber;

	\begin{eqnarray}
		f(x) &=& \begin{cases}
			   1 & if $x>0$\\
			  -1 & if $x\le0$
			 \end{cases}\\
		g(x) &=& \tan x
	\end{eqnarray}

vi) In multiline-eqs, \textin command can be very useful.
    This line can be forced not to be aligned.

	\begin{eqnarray}
		f(x)&=&.....\\
	\textin{where, x is in ...}
		g(x)&=&.....
	\end{eqnarray}

    Compiling image is,

		f(x)=......

	where, x is in ...

		g(x)=.....

    In \textin \par and \\ (breakline) is available, but some command,
    for example \verb, is not available.

vii) Some mathematical fonts can be loaded easily.

	\loadnewfont{frak}{eufm}

    Above commmad make us use to eufm(German frak font) as '\frak' command,
    and font-size changing is automatically applied.

viii) Slanted Greek Capital font can be used.

	\varXXXX means slanted Greek capital font in math-mode.

ix) re-sizable triple-dot commands(\cdot,\vdots,\ddots,and \qdots).

	normalsize is \hdots, \vdots, \ddots, \qdots
	(size of \ddots and \qdots is automatically changed with font-size)

	re-sizable  is \Hdots[#1], \Vdots[#1], \Ddots[#1], \Qdots[#1]
	(#1 is size of width)

ix) AMS-like command is also supported.

	\numberwithin
	\ds,\ss,\sss
	\newfunction,\newoperator,\newrelation ... etc.

