% Version 2.21 (February 25, 2026)

\define\Abs{\opname{Abs}}
\define\acosh{\opname{cosh}^{-1}}
\define\acos{\opname{cos}^{-1}}
\define\actn{\opname{cotan}^{-1}}
\redefine\arccos{\acos}
\define\arcctg{\actn}
\define\arch{\acosh}
\redefine\arcsin{\asin}
\define\arctg{\atn}
\define\arcth{\atnh}
\define\arsh{\asinh}
\define\asinh{\opname{sinh}^{-1}}
\define\asin{\opname{sin}^{-1}}
\define\atanh{\atnh}
\define\atnh{\opname{tanh}^{-1}}
\define\atn{\opname{tan}^{-1}}
\define\Aut{\opname{Aut}}
\let\biggg\Bigg
\let\bigggl\Biggl
\let\bigggr\Biggr
\def\biglangle{\bigl\langle} \def\Biglangle{\Bigl\langle} \def\bigglangle{\biggl\langle} \def\Bigglangle{\Biggl\langle} \def\biggglangle{\Biggl\langle}
\def\bigrangle{\bigr\rangle} \def\Bigrangle{\Bigr\rangle} \def\biggrangle{\biggr\rangle} \def\Biggrangle{\Biggr\rangle} \def\bigggrangle{\Biggr\rangle}
\define\card{\opname{card}}
\define\ccap{\opname{cap}}
\define\ch{\opname{ch}}
\define\Cl{\opname{Cl}}
\define\cl{\opname{cl}}
\define\codim{\opname{codim}}
\define\coim{\opname{coim}}
\define\Coker{\opname{Coker}}
\define\coker{\opname{coker}}
\let\oldcolon\colon
\let\colon:
\define\const{\opname{const}}
\define\con{\opname{con}}
\define\core{\opname{core}}
\define\co{\opname{co}}
\define\ctg{\cot}
\define\cth{\coth}
\define\diag{\opname{diag}}
\define\diam{\opname{diam}}
\define\dist{\opname{dist}}
\define\diverg{\opname{div}}
\define\divtrg{\diverg}
\define\divv{\diverg}
\define\dom{\opname{dom}}
\redefine\emptyset{\varnothing}
\define\epi{\opname{epi}}
\define\essinf{\opnamewithlimits{ess\,inf}}
\define\esssup{\opnamewithlimits{ess\,sup}}
\define\ext{\opname{ext}}
\define\form{\opname{form}}
\define\fraction#1/#2{\leavevmode\kern.1em\raise.5ex\hbox{\the\scriptfont0 #1}\kern-.1em/\kern-.15em\lower.25ex\hbox{\the\scriptfont0 #2}}
\define\fr{\opname{fr}}
\define\grad{\opname{grad}}
\define\gr{\opname{gr}}
\define\Hom{\opname{Hom}}
\define\Id{\opname{Id}}
\define\id{\opname{id}}
\define\Image{\opname{Im}}
\define\imm{\opname{im}}
\define\inter{\opname{int}}
\define\intr{\inter}
\define\Intt{\opname{Int}}
\define\Ker{\opname{Ker}}
\define\leftbbrr{\mathopen{\kern1pt\vrule height10pt depth3pt width1pt\kern1.5pt}}
\define\leftbbr{\mathopen{\kern1pt \vrule height8pt depth2pt width1pt\kern1.5pt}}
\define\leftbrr{\mathopen{\kern1pt \vrule height8pt depth2pt width1pt\kern2.5pt}}
\define\Lip{\opname{Lip}}
\define\lip{\opname{lip}}
\redefine\ln{\opname{ln}}
\define\loc{\opname{loc}}
\define\mathit#1{{\text{\it#1}\mskip1mu}}
\define\mes{\opname{mes}}
\define\modulo{\opname{mod}}
\define\nol#1{\overset{\textstyle\circ}\to{#1}}
\define\olim{\mathop{o\mskip1mu\hbox{-}\!\lim}}
\define\Op{\opname{Op}}
\define\osum{\mathop{o\mskip1mu\hbox{-}\!\sum}}
\redefine\pmod#1{\ (\roman{mod}\ #1)}
\define\rank{\opname{rank}}
\define\Real{\opname{Re}}
\define\Repa{\opname{Re}}
\define\res{\opnamewithlimits{res}}
\define\Ric{\opname{Ric}}
\define\rightbbrr{\mathclose{\kern1.5pt \vrule height10pt depth3pt width1pt\kern1pt}}
\define\rightbbr{\mathclose{\kern1.5pt \vrule height8pt depth2pt width1pt\kern1pt}}
\define\rightbrr{\mathclose{\kern.5pt \vrule height8pt depth2pt width1pt\kern1pt}}
\define\rint{{\opname{rint}}}
\define\rlim{\mathop{r\mskip1mu\hbox{-}\!\lim}}
\define\rng{\opname{rng}}
\define\rot{\opname{curl}}
\define\seg{\opname{seg}}
\define\sgn{\opname{sgn}}
\define\sh{\sinh}
\define\sign{\opname{sign}}
\define\smallbullet{\raise1pt\hbox{$\scriptstyle\bullet$}}
\define\Spec{\opname{Sp}}
\define\st{\opname{st}}
\define\supp{\opname{supp}}
\define\tg{\opname{tan}}
\define\th{\tanh}
\define\trace{\opname{trace}}
\define\tr{\opname{tr}}
\define\var{\opname{var}}
\define\vraimax{\opnamewithlimits{vrai\,max}}
\define\vraisup{\opnamewithlimits{vrai\,sup}}
\define\widebar{\overline}

\define\repeat@two#1{#1#1}
\define\make@double#1#2#3#4{\mathopen{#1\mkern-#3mu#1}#4\mathclose{#2\mkern-#3mu#2}}
\define\make@auto@double#1#2#3#4{\left#1\mkern-#3mu\left#1#4\right#2\mkern-#3mu\right#2}
\define\make@triple#1#2#3{\mathopen{#1\repeat@two{\mkern-#2mu#1}}#3\mathclose{#1\repeat@two{\mkern-#2mu#1}}}
\define\make@triple@choice#1#2#3#4#5#6{\mathopen{#1\repeat@two{\mathchoice{\mkern-#2mu}{\mkern-#3mu}{\mkern-#4mu}{\mkern-#5mu}#1}}#6\mathclose{#1\repeat@two{\mathchoice{\mkern-#2mu}{\mkern-#3mu}{\mkern-#4mu}{\mkern-#5mu}#1}}}
\define\make@auto@triple#1#2#3{\left#1\repeat@two{\mkern-#2mu\left#1}#3\right#1\repeat@two{\mkern-#2mu\right#1}}

\define\brbr#1{\make@double{[}{]}{3}{#1}}
\define\bigbrbr#1{\make@double{\big[}{\big]}{5.5}{#1}}
\define\Bigbrbr#1{\make@double{\Big[}{\Big]}{6.3}{#1}}
\define\biggbrbr#1{\make@double{\bigg[}{\bigg]}{7}{#1}}
\define\Biggbrbr#1{\make@double{\Bigg[}{\Bigg]}{8}{#1}}
\define\autobrbr#1{\make@auto@double{[}{]}{9.4}{#1}}

\define\boldnorm#1{\make@triple@choice|{4.3}{4.3}{4.3}{4.8}{#1}}
\define\bigboldnorm#1{\make@triple{\big|}{5.3}{#1}}
\define\Bigboldnorm#1{\make@triple{\Big|}{5.3}{#1}}
\define\biggboldnorm#1{\make@triple{\bigg|}{5.3}{#1}}
\define\Biggboldnorm#1{\make@triple{\Bigg|}{5.3}{#1}}
\define\autoboldnorm#1{\make@auto@triple|{5.3}{#1}}

\define\triplenorm#1{\make@triple@choice|{3}{3}{3}{3.5}{#1}}
\define\bigtriplenorm#1{\make@triple{\big|}{4}{#1}}
\define\Bigtriplenorm#1{\make@triple{\Big|}{4}{#1}}
\define\biggtriplenorm#1{\make@triple{\bigg|}{4}{#1}}
\define\Biggtriplenorm#1{\make@triple{\Bigg|}{4}{#1}}
\define\autotriplenorm#1{\make@auto@triple|{4}{#1}}

\def\={\hbox{\kern.7pt-}\nobreak\hskip0pt\relax}
\def\re#1{\,{#1}\,}
\newdimen\spaceamount\long\def\spacing#1#2{{\spaceamount=\fontdimen2\font\fontdimen2\font=#1\spaceamount\relax#2\fontdimen2\font=\spaceamount\relax}}
\def\todo{\vskip-6pt\relax\noindent\hbox{}\leaders\hbox to 6pt{\hss\vrule height 2pt width 3pt\hss}\hfill\hbox{}\vskip-2pt\relax}

\def\m@trix{\null\vcenter\bgroup\vspace@\Let@
  \baselineskip11\ex@\lineskip\ex@
  \ialign\bgroup\hfil$\m@th{##}$\hfil&&\thickspace\hfil
  $\m@th{##}$\hfil\crcr
}
\def\endm@trix{\crcr\egroup\egroup}
\def\midmatrix{\m@trix\vrule width 0pt height 6pt depth 0pt\relax}
\def\endmidmatrix{\vrule width 0pt height 0pt depth 3pt\relax\endm@trix}

\def\itemitemitem{\par\indent\indent \hangindent3\parindent \textindent}

\catcode`’=\active\let’'
\catcode`‘=\active\let‘`
\catcode`“=\active\def“{``}
\catcode`”=\active\def”{''}
