%%%%%%%%%%%%%%% modification %%%%%%%%%%%%%%%%%

\def\defaultscriptratio{.66}
\def\defaultscriptscriptratio{.5}
\DeclareMathSizes{5}{5}{5}{5}
\DeclareMathSizes{6}{6}{5}{5}
\DeclareMathSizes{7}{7}{5}{5}
\DeclareMathSizes{8}{8}{6}{5}
\DeclareMathSizes{9}{9}{6.5}{5} 
\DeclareMathSizes{10}{10.5}{7}{5.5}
\DeclareMathSizes{11}{11.5}{7}{5.5}
\DeclareMathSizes{12}{12.5}{8}{6}
\DeclareMathSizes{14}{15}{9}{7}
\DeclareMathSizes{17}{18}{11}{8}
\DeclareMathSizes{20}{21}{14}{10}

\thinmuskip=3mu plus 0.5mu minus 0.5mu
\medmuskip=4mu plus 1mu minus 1mu
\thickmuskip=4mu plus 1mu minus 1mu

\renewcommand{\ttdefault}{txtt}
\newif\iftx@libertine

\SetSymbolFont{operators}{bold}{OT1}{ntxr}{b}{n}
\SetSymbolFont{letters}{bold}{OML}{ntxmi}{b}{it}
\DeclareFontSubstitution{OML}{ntxmi}{m}{it}

\DeclareSymbolFont{largesymbolsTXA}{U}{ntxexa}{m}{n}
\SetSymbolFont{largesymbolsTXA}{bold}{U}{ntxexa}{b}{n}
\DeclareFontSubstitution{U}{ntxexa}{m}{n}
\DeclareMathSymbol{\newintop}{\mathop}{largesymbolsTXA}{86}

\DeclareFontFamily{OMX}{mcmex}{}
\DeclareFontShape{OMX}{mcmex}{m}{n}
			{<-> s * [0.8] cmex8}{}
\DeclareSymbolFont{cmbitlargesymbols}{OMX}{mcmex}{m}{n}
\DeclareMathSymbol{\cmsumop}{\mathop}{cmbitlargesymbols}{'120}

\let\sum\cmsumop
\let\intop\newintop

\DeclareSymbolFont{txoperators}{OT1}{ntxr}{m}{n}
\DeclareMathSymbol{=}{\mathrel}{txoperators}{61}
\DeclareMathSymbol{+}{\mathbin}{txoperators}{43} %これがないと+がcmになる
\SetSymbolFont{txoperators}{bold}{OT1}{ntxr}{b}{n}

\DeclareSymbolFont{txsymbols}{OMS}{ntxsy}{m}{n}
\DeclareMathSymbol{-}{\mathbin}{txsymbols}{0}

\DeclareMathSymbol{\cdotp}{\mathpunct}{txsymbols}{1}
\DeclareMathSymbol{\cdot}{\mathbin}{txsymbols}{1}
\DeclareMathSymbol{\times}{\mathbin}{txsymbols}{2}
\DeclareMathSymbol{\ast}{\mathbin}{txsymbols}{3}
\DeclareMathSymbol{*}{\mathbin}{txsymbols}{3} 
\DeclareMathSymbol{\div}{\mathbin}{txsymbols}{4}
\DeclareMathSymbol{\diamond}{\mathbin}{txsymbols}{5}
\DeclareMathSymbol{\pm}{\mathbin}{txsymbols}{6}
\DeclareMathSymbol{\mp}{\mathbin}{txsymbols}{7}
\DeclareMathSymbol{\oplus}{\mathbin}{txsymbols}{8}

   \let\circledplus\oplus
\DeclareMathSymbol{\ominus}{\mathbin}{txsymbols}{9}
   \let\circledminus\ominus
\DeclareMathSymbol{\otimes}{\mathbin}{txsymbols}{10}
   \let\circledtimes\otimes
\DeclareMathSymbol{\oslash}{\mathbin}{txsymbols}{11}
   \let\circledslash\oslash
\DeclareMathSymbol{\odot}{\mathbin}{txsymbols}{12}
   \let\circleddot\odot
\DeclareMathSymbol{\bigcirc}{\mathbin}{txsymbols}{13}
\DeclareMathSymbol{\circ}{\mathbin}{txsymbols}{14}
\DeclareMathSymbol{\bullet}{\mathbin}{txsymbols}{15}
\DeclareMathSymbol{\asymp}{\mathrel}{txsymbols}{16}
\DeclareMathSymbol{\equiv}{\mathrel}{txsymbols}{17}
\DeclareMathSymbol{\subseteq}{\mathrel}{txsymbols}{18}
\DeclareMathSymbol{\supseteq}{\mathrel}{txsymbols}{19}
\DeclareMathSymbol{\leq}{\mathrel}{txsymbols}{20}
   \let\le=\leq
\DeclareMathSymbol{\geq}{\mathrel}{txsymbols}{21}
   \let\ge=\geq
\DeclareMathSymbol{\preceq}{\mathrel}{txsymbols}{22}
\DeclareMathSymbol{\succeq}{\mathrel}{txsymbols}{23}
\DeclareMathSymbol{\sim}{\mathrel}{txsymbols}{24}
\DeclareMathSymbol{\approx}{\mathrel}{txsymbols}{25}
\DeclareMathSymbol{\subset}{\mathrel}{txsymbols}{26}
\DeclareMathSymbol{\supset}{\mathrel}{txsymbols}{27}
\DeclareMathSymbol{\ll}{\mathrel}{txsymbols}{28}
\DeclareMathSymbol{\gg}{\mathrel}{txsymbols}{29}
\DeclareMathSymbol{\prec}{\mathrel}{txsymbols}{30}
\DeclareMathSymbol{\succ}{\mathrel}{txsymbols}{31}

\DeclareMathSymbol{\leftarrow}{\mathrel}{txsymbols}{32}
   \let\gets=\leftarrow
\DeclareMathSymbol{\rightarrow}{\mathrel}{txsymbols}{33}
   \let\to=\rightarrow
\DeclareMathSymbol{\txleftrightarrow}{\mathrel}{txsymbols}{36}

\DeclareMathSymbol{\nearrow}{\mathrel}{txsymbols}{37}
\DeclareMathSymbol{\searrow}{\mathrel}{txsymbols}{38}
\DeclareMathSymbol{\simeq}{\mathrel}{txsymbols}{39}

\DeclareMathSymbol{\Leftarrow}{\mathrel}{txsymbols}{40}
\DeclareMathSymbol{\Rightarrow}{\mathrel}{txsymbols}{41}
\DeclareMathSymbol{\Leftrightarrow}{\mathrel}{txsymbols}{44}

\DeclareMathSymbol{\nwarrow}{\mathrel}{txsymbols}{45}
\DeclareMathSymbol{\swarrow}{\mathrel}{txsymbols}{46}
\DeclareMathSymbol{\propto}{\mathrel}{txsymbols}{47}
\DeclareMathSymbol{\prime}{\mathord}{txsymbols}{48}
\DeclareMathSymbol{\infty}{\mathord}{txsymbols}{49}
\DeclareMathSymbol{\in}{\mathrel}{txsymbols}{50}
\DeclareMathSymbol{\ni}{\mathrel}{txsymbols}{51}
    \let\owns=\ni
\DeclareMathSymbol{\triangle}{\mathord}{txsymbols}{52}
\DeclareMathSymbol{\bigtriangleup}{\mathbin}{txsymbols}{52}
\DeclareMathSymbol{\bigtriangledown}{\mathbin}{txsymbols}{53}
\DeclareMathSymbol{\not}{\mathrel}{txsymbols}{54}
\DeclareMathSymbol{\mapstochar}{\mathrel}{txsymbols}{55}
   \def\mapsto{\mapstochar\rightarrow}
\DeclareMathSymbol{\forall}{\mathord}{txsymbols}{56}
\DeclareMathSymbol{\exists}{\mathord}{txsymbols}{57}
\DeclareMathSymbol{\neg}{\mathord}{txsymbols}{58}
    \let\lnot=\neg
\DeclareMathSymbol{\emptyset}{\mathord}{txsymbols}{59}
\DeclareMathSymbol{\Re}{\mathord}{txsymbols}{60}
\DeclareMathSymbol{\Im}{\mathord}{txsymbols}{61}
\DeclareMathSymbol{\top}{\mathord}{txsymbols}{62}
\DeclareMathSymbol{\bot}{\mathord}{txsymbols}{63}
\DeclareMathSymbol{\perp}{\mathrel}{txsymbols}{63}
\DeclareMathSymbol{\aleph}{\mathord}{txsymbols}{64}
% "41-"5A: \mathcal{A-Z}
\DeclareMathSymbol{\cup}{\mathbin}{txsymbols}{91}
\DeclareMathSymbol{\cap}{\mathbin}{txsymbols}{92}
\DeclareMathSymbol{\uplus}{\mathbin}{txsymbols}{93}
\DeclareMathSymbol{\wedge}{\mathbin}{txsymbols}{94}
   \let\land=\wedge
\DeclareMathSymbol{\vee}{\mathbin}{txsymbols}{95}
   \let\lor=\vee
\DeclareMathSymbol{\vdash}{\mathrel}{txsymbols}{96}
\DeclareMathSymbol{\dashv}{\mathrel}{txsymbols}{97}

\SetSymbolFont{txsymbols}{bold}{OMS}{ntxsy}{b}{n}



\DeclareSymbolFont{txletters}{OML}{ntxmi}{m}{it}

\DeclareMathSymbol{\alpha}{\mathord}{txletters}{11}
\DeclareMathSymbol{\beta}{\mathord}{txletters}{12}
\DeclareMathSymbol{\gamma}{\mathord}{txletters}{13}
\DeclareMathSymbol{\delta}{\mathord}{txletters}{14}
\DeclareMathSymbol{\epsilon}{\mathord}{txletters}{15}
\DeclareMathSymbol{\zeta}{\mathord}{txletters}{16}
\DeclareMathSymbol{\eta}{\mathord}{txletters}{17}
\DeclareMathSymbol{\theta}{\mathord}{txletters}{18}
\DeclareMathSymbol{\iota}{\mathord}{txletters}{19}
\DeclareMathSymbol{\kappa}{\mathord}{txletters}{20}
\DeclareMathSymbol{\lambda}{\mathord}{txletters}{21}
\DeclareMathSymbol{\mu}{\mathord}{txletters}{22}
\DeclareMathSymbol{\nu}{\mathord}{txletters}{23}
\DeclareMathSymbol{\xi}{\mathord}{txletters}{24}
\DeclareMathSymbol{\pi}{\mathord}{txletters}{25}
\DeclareMathSymbol{\rho}{\mathord}{txletters}{26}
\DeclareMathSymbol{\sigma}{\mathord}{txletters}{27}
\DeclareMathSymbol{\tau}{\mathord}{txletters}{28}
\DeclareMathSymbol{\upsilon}{\mathord}{txletters}{29}
\DeclareMathSymbol{\phi}{\mathord}{txletters}{30}
\DeclareMathSymbol{\chi}{\mathord}{txletters}{31}
\DeclareMathSymbol{\psi}{\mathord}{txletters}{32}
\DeclareMathSymbol{\omega}{\mathord}{txletters}{33}
\DeclareMathSymbol{\varepsilon}{\mathord}{txletters}{34}
\DeclareMathSymbol{\vartheta}{\mathord}{txletters}{35}
\DeclareMathSymbol{\varpi}{\mathord}{txletters}{36}
\DeclareMathSymbol{\varrho}{\mathord}{txletters}{37}
\DeclareMathSymbol{\varsigma}{\mathord}{txletters}{38}
\DeclareMathSymbol{\varphi}{\mathord}{txletters}{39}

\SetSymbolFont{txletters}{bold}{OML}{ntxmi}{b}{it}


\DeclareSymbolFont{AMSa}{U}{ntxsya}{m}{n}
\SetSymbolFont{AMSa}{bold}{U}{ntxsya}{b}{n}
\DeclareFontSubstitution{U}{txsya}{m}{n}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Math Symbol A Definitions % AMSa
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\DeclareMathSymbol{\boxdot}{\mathbin}{AMSa}{0}
\DeclareMathSymbol{\boxplus}{\mathbin}{AMSa}{1}
\DeclareMathSymbol{\boxtimes}{\mathbin}{AMSa}{2}
\DeclareMathSymbol{\square}{\mathord}{AMSa}{3}
\DeclareMathSymbol{\blacksquare}{\mathord}{AMSa}{4}
\DeclareMathSymbol{\centerdot}{\mathbin}{AMSa}{5}
\DeclareMathSymbol{\lozenge}{\mathord}{AMSa}{6}
\DeclareMathSymbol{\blacklozenge}{\mathord}{AMSa}{7}
\DeclareMathSymbol{\circlearrowright}{\mathrel}{AMSa}{8}
\DeclareMathSymbol{\circlearrowleft}{\mathrel}{AMSa}{9}
\DeclareMathSymbol{\rightleftharpoons}{\mathrel}{AMSa}{10}
\DeclareMathSymbol{\leftrightharpoons}{\mathrel}{AMSa}{11}
\DeclareMathSymbol{\boxminus}{\mathbin}{AMSa}{12}
\DeclareMathSymbol{\Vdash}{\mathrel}{AMSa}{13}
\DeclareMathSymbol{\Vvdash}{\mathrel}{AMSa}{14}
\DeclareMathSymbol{\vDash}{\mathrel}{AMSa}{15}
\DeclareMathSymbol{\twoheadrightarrow}{\mathrel}{AMSa}{16}
\DeclareMathSymbol{\twoheadleftarrow}{\mathrel}{AMSa}{17}
\DeclareMathSymbol{\leftleftarrows}{\mathrel}{AMSa}{18}
\DeclareMathSymbol{\rightrightarrows}{\mathrel}{AMSa}{19}
\DeclareMathSymbol{\upuparrows}{\mathrel}{AMSa}{20}
\DeclareMathSymbol{\downdownarrows}{\mathrel}{AMSa}{21}
\DeclareMathSymbol{\upharpoonright}{\mathrel}{AMSa}{22}
   \let\restriction\upharpoonright
\DeclareMathSymbol{\downharpoonright}{\mathrel}{AMSa}{23}
\DeclareMathSymbol{\upharpoonleft}{\mathrel}{AMSa}{24}
\DeclareMathSymbol{\downharpoonleft}{\mathrel}{AMSa}{25}
\DeclareMathSymbol{\rightarrowtail}{\mathrel}{AMSa}{26}
\DeclareMathSymbol{\leftarrowtail}{\mathrel}{AMSa}{27}
\DeclareMathSymbol{\leftrightarrows}{\mathrel}{AMSa}{28}
\DeclareMathSymbol{\rightleftarrows}{\mathrel}{AMSa}{29}
\DeclareMathSymbol{\Lsh}{\mathrel}{AMSa}{30}
\DeclareMathSymbol{\Rsh}{\mathrel}{AMSa}{31}
\DeclareMathSymbol{\rightsquigarrow}{\mathrel}{AMSa}{32}
\DeclareMathSymbol{\leftrightsquigarrow}{\mathrel}{AMSa}{33}
\DeclareMathSymbol{\looparrowleft}{\mathrel}{AMSa}{34}
\DeclareMathSymbol{\looparrowright}{\mathrel}{AMSa}{35}
\DeclareMathSymbol{\circeq}{\mathrel}{AMSa}{36}
\DeclareMathSymbol{\succsim}{\mathrel}{AMSa}{37}
\DeclareMathSymbol{\gtrsim}{\mathrel}{AMSa}{38}
\DeclareMathSymbol{\gtrapprox}{\mathrel}{AMSa}{39}
\DeclareMathSymbol{\multimap}{\mathrel}{AMSa}{40}
\DeclareMathSymbol{\therefore}{\mathrel}{AMSa}{41}
\DeclareMathSymbol{\because}{\mathrel}{AMSa}{42}
\DeclareMathSymbol{\doteqdot}{\mathrel}{AMSa}{43}
   \let\Doteq\doteqdot
\DeclareMathSymbol{\triangleq}{\mathrel}{AMSa}{44}
\DeclareMathSymbol{\precsim}{\mathrel}{AMSa}{45}
\DeclareMathSymbol{\lesssim}{\mathrel}{AMSa}{46}
\DeclareMathSymbol{\lessapprox}{\mathrel}{AMSa}{47}
\DeclareMathSymbol{\eqslantless}{\mathrel}{AMSa}{48}
\DeclareMathSymbol{\eqslantgtr}{\mathrel}{AMSa}{49}
\DeclareMathSymbol{\curlyeqprec}{\mathrel}{AMSa}{50}
\DeclareMathSymbol{\curlyeqsucc}{\mathrel}{AMSa}{51}
\DeclareMathSymbol{\preccurlyeq}{\mathrel}{AMSa}{52}
\DeclareMathSymbol{\leqq}{\mathrel}{AMSa}{53}
\DeclareMathSymbol{\leqslant}{\mathrel}{AMSa}{54}
\DeclareMathSymbol{\lessgtr}{\mathrel}{AMSa}{55}
\DeclareMathSymbol{\backprime}{\mathord}{AMSa}{56}
\DeclareMathSymbol{\risingdotseq}{\mathrel}{AMSa}{58}
\DeclareMathSymbol{\fallingdotseq}{\mathrel}{AMSa}{59}
\DeclareMathSymbol{\succcurlyeq}{\mathrel}{AMSa}{60}
\DeclareMathSymbol{\geqq}{\mathrel}{AMSa}{61}
\DeclareMathSymbol{\geqslant}{\mathrel}{AMSa}{62}
\DeclareMathSymbol{\gtrless}{\mathrel}{AMSa}{63}
\DeclareMathSymbol{\sqsubset}{\mathrel}{AMSa}{64}
\DeclareMathSymbol{\sqsupset}{\mathrel}{AMSa}{65}
\DeclareMathSymbol{\vartriangleright}{\mathrel}{AMSa}{66}
\DeclareMathSymbol{\vartriangleleft}{\mathrel}{AMSa}{67}
\DeclareMathSymbol{\trianglerighteq}{\mathrel}{AMSa}{68}
\DeclareMathSymbol{\trianglelefteq}{\mathrel}{AMSa}{69}
\DeclareMathSymbol{\bigstar}{\mathord}{AMSa}{70}
\DeclareMathSymbol{\between}{\mathrel}{AMSa}{71}
\DeclareMathSymbol{\blacktriangledown}{\mathord}{AMSa}{72}
\DeclareMathSymbol{\blacktriangleright}{\mathrel}{AMSa}{73}
\DeclareMathSymbol{\blacktriangleleft}{\mathrel}{AMSa}{74}
\DeclareMathSymbol{\vartriangle}{\mathrel}{AMSa}{77}
\DeclareMathSymbol{\blacktriangle}{\mathord}{AMSa}{78}
\DeclareMathSymbol{\triangledown}{\mathord}{AMSa}{79}
\DeclareMathSymbol{\eqcirc}{\mathrel}{AMSa}{80}
\DeclareMathSymbol{\lesseqgtr}{\mathrel}{AMSa}{81}
\DeclareMathSymbol{\gtreqless}{\mathrel}{AMSa}{82}
\DeclareMathSymbol{\lesseqqgtr}{\mathrel}{AMSa}{83}
\DeclareMathSymbol{\gtreqqless}{\mathrel}{AMSa}{84}
\DeclareMathSymbol{\Rrightarrow}{\mathrel}{AMSa}{86}
\DeclareMathSymbol{\Lleftarrow}{\mathrel}{AMSa}{87}
\DeclareMathSymbol{\veebar}{\mathbin}{AMSa}{89}
\DeclareMathSymbol{\barwedge}{\mathbin}{AMSa}{90}
\DeclareMathSymbol{\doublebarwedge}{\mathbin}{AMSa}{91}
\DeclareMathSymbol{\angle}{\mathord}{AMSa}{92}
\DeclareMathSymbol{\measuredangle}{\mathord}{AMSa}{93}
\DeclareMathSymbol{\sphericalangle}{\mathord}{AMSa}{94}
\DeclareMathSymbol{\varpropto}{\mathrel}{AMSa}{95}
\DeclareMathSymbol{\smallsmile}{\mathrel}{AMSa}{96}
\DeclareMathSymbol{\smallfrown}{\mathrel}{AMSa}{97}
\DeclareMathSymbol{\Subset}{\mathrel}{AMSa}{98}
\DeclareMathSymbol{\Supset}{\mathrel}{AMSa}{99}
\DeclareMathSymbol{\Cup}{\mathbin}{AMSa}{100}
   \let\doublecup\Cup
\DeclareMathSymbol{\Cap}{\mathbin}{AMSa}{101}
   \let\doublecap\Cap
\DeclareMathSymbol{\curlywedge}{\mathbin}{AMSa}{102}
\DeclareMathSymbol{\curlyvee}{\mathbin}{AMSa}{103}
\DeclareMathSymbol{\leftthreetimes}{\mathbin}{AMSa}{104}
\DeclareMathSymbol{\rightthreetimes}{\mathbin}{AMSa}{105}
\DeclareMathSymbol{\subseteqq}{\mathrel}{AMSa}{106}
\DeclareMathSymbol{\supseteqq}{\mathrel}{AMSa}{107}
\DeclareMathSymbol{\bumpeq}{\mathrel}{AMSa}{108}
\DeclareMathSymbol{\Bumpeq}{\mathrel}{AMSa}{109}
\DeclareMathSymbol{\lll}{\mathrel}{AMSa}{110}
   \let\llless\lll
\DeclareMathSymbol{\ggg}{\mathrel}{AMSa}{111}
   \let\gggtr\ggg
\DeclareMathDelimiter\ulcorner{\mathopen}{AMSa}{112}{AMSa}{112}
\DeclareMathDelimiter\urcorner{\mathclose}{AMSa}{113}{AMSa}{113}
\DeclareMathSymbol{\circledS}{\mathord}{AMSa}{115}
\DeclareMathSymbol{\pitchfork}{\mathrel}{AMSa}{116}
\DeclareMathSymbol{\dotplus}{\mathbin}{AMSa}{117}
\DeclareMathSymbol{\backsim}{\mathrel}{AMSa}{118}
\DeclareMathSymbol{\backsimeq}{\mathrel}{AMSa}{119}
\DeclareMathDelimiter\llcorner{\mathopen}{AMSa}{120}{AMSa}{120}
\DeclareMathDelimiter\lrcorner{\mathclose}{AMSa}{121}{AMSa}{121}
\DeclareMathSymbol{\complement}{\mathord}{AMSa}{123}
\DeclareMathSymbol{\intercal}{\mathbin}{AMSa}{124}
\DeclareMathSymbol{\circledcirc}{\mathbin}{AMSa}{125}
\DeclareMathSymbol{\circledast}{\mathbin}{AMSa}{126}
\DeclareMathSymbol{\circleddash}{\mathbin}{AMSa}{127}

%\let\Box=\square % LaTeX symbol
\DeclareMathSymbol{\rhd}{\mathbin}{AMSa}{66} % LaTeX symbol
\DeclareMathSymbol{\lhd}{\mathbin}{AMSa}{67} % LaTeX symbol
\DeclareMathSymbol{\unrhd}{\mathbin}{AMSa}{68} % LaTeX symbol
\DeclareMathSymbol{\unlhd}{\mathbin}{AMSa}{69} % LaTeX symbol


%%% nequiv

\newcommand{\nequiv}{\not\equiv}