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\catcode`\@=11
\def\alignedat#1{\null\,\vcenter\bgroup\doat@{#1}\vspace@\Let@
\ifinany@\else\openup\jot\fi\ialign\bgroup\span\preamble@@\crcr}
\def\doat@#1{\toks@{\hfil\strut@$\m@th
\displaystyle{\the\hashtoks@}$&$\m@th\displaystyle
{{}\the\hashtoks@}$\hfil}%
\atcount@#1\relax\advance\atcount@\m@ne
\loop\ifnum\atcount@>\z@\toks@=\expandafter{\the\toks@&\hfil$\m@th
\displaystyle{\the\hashtoks@}$&$\m@th
\displaystyle{{}\the\hashtoks@}$\hfil}\advance\atcount@\m@ne\repeat
\edef\preamble@{\the\toks@}\edef\preamble@@{\preamble@}}
\let\endalignedat\endaligned
\def\alignat{\RIfMIfI@\DN@{\onlydmatherr@\alignat}\else
\DN@{\csname alignat \endcsname}\fi\else
\DN@{\onlydmatherr@\alignat}\fi\next@}
\expandafter\def\csname alignat \endcsname#1#2\endalignat
{\inany@true\xat@false
\def\tag{\global\tag@true
\count@#1\relax\multiply\count@\tw@\advance\count@\m@ne
\gdef\tag@{&}%
\loop\ifnum\count@>\and@\xdef\tag@{&\omit\tag@}%
\advance\count@\m@ne\repeat
\tag@\relax}%
\vspace@\allowdisplaybreak@\displaybreak@\intertext@
\displ@y@\measuring@true\tag@CC\tag@C
\setbox\savealignat@\hbox{\noset@\unlabel@$\m@th\displaystyle\Let@
\attag@{#1}\vbox{\halign{\span\preamble@@\crcr#2\crcr}}$}%
\measuring@false
\Let@\attag@{#1}\tag@C\tag@CC
\tabskip\centering@\halign to\displaywidth
{\span\preamble@@\crcr#2\crcr\black@{\wd\savealignat@}}}
\Invalid@\endalignat
\def\xalignat{\RIfMIfI@
\DN@{\onlydmatherr@\xalignat}\else
\DN@{\csname xalignat \endcsname}\fi\else
\DN@{\onlydmatherr@\xalignat}\fi\next@}
\expandafter\def\csname xalignat \endcsname#1#2\endxalignat
{\inany@true\xat@true
\def\tag{\global\tag@true
\count@#1\relax\multiply\count@\tw@\advance\count@\m@ne
\gdef\tag@{&}%
\loop\ifnum\count@>\and@\xdef\tag@{&\omit\tag@}%
\advance\count@\m@ne\repeat
\tag@\relax}%
\vspace@\allowdisplaybreak@\displaybreak@\intertext@
\displ@y@\measuring@true\tag@CC\tag@C
\setbox\savealignat@\hbox{\noset@\unlabel@$\m@th\displaystyle\Let@
\attag@{#1}\vbox{\halign{\span\preamble@@\crcr#2\crcr}}$}%
\measuring@false\Let@\attag@{#1}\tag@C\tag@CC
\tabskip\centering@\halign to\displaywidth
{\span\preamble@@\crcr#2\crcr\black@{\wd\savealignat@}}}
\def\attag@#1{\let\Maketag@\maketag@\let\TAG@\Tag@
\let\Prepost@\prepost@\let\Reprepost@\reprepost@
\let\Tag@\relax\let\maketag@\relax
\let\prepost@\relax\let\reprepost@\relax
\ifmeasuring@
\def\llap@##1{\setboxz@h{##1}\hbox to\tw@\wdz@{}}%
\def\rlap@##1{\setboxz@h{##1}\hbox to\tw@\wdz@{}}%
\else\let\llap@\llap\let\rlap@\rlap\fi
\toks@{\hfil\strut@
$\m@th\displaystyle{\@lign\the\hashtoks@\prepost@}$%
\tabskip\z@skip\global\advance\and@\@ne&
$\m@th\displaystyle{{}\@lign\the\hashtoks@\prepost@}$\hfil
\ifxat@\tabskip\centering@\fi\global\advance\and@\@ne}%
\iftagsleft@
\toks@@{\tabskip\centering@&\Tag@\kern-\displaywidth
\rlap@{\@lign\reprepost@\maketag@\the\hashtoks@\maketag@}%
\global\advance\and@\@ne\tabskip\displaywidth}\else
\toks@@{\tabskip\centering@&\Tag@\llap@{\@lign\reprepost@\maketag@
\the\hashtoks@\maketag@}\global\advance\and@\@ne\tabskip\z@skip}\fi
\atcount@#1\relax\advance\atcount@\m@ne
\loop\ifnum\atcount@>\z@
\toks@\expandafter{\the\toks@&\hfil$\m@th\displaystyle{\@lign
\the\hashtoks@\prepost@}$\global\advance\and@\@ne
\tabskip\z@skip
&$\m@th\displaystyle{{}\@lign\the\hashtoks@\prepost@}$\hfil\ifxat@
\tabskip\centering@\fi\global\advance\and@\@ne}\advance\atcount@\m@ne
\repeat
\edef\preamble@{\the\toks@\the\toks@@}%
\edef\preamble@@{\preamble@}%
\let\maketag@\Maketag@\let\Tag@\TAG@
\let\prepost@\Prepost@\let\reprepost@\Reprepost@}
\Invalid@\endxalignat
\def\xxalignat{\RIfMIfI@
\DN@{\onlydmatherr@\xxalignat}\else\DN@{\csname xxalignat
\endcsname}\fi\else
\DN@{\onlydmatherr@\xxalignat}\fi\next@}
\expandafter\def\csname xxalignat \endcsname#1#2\endxxalignat{\inany@true
\vspace@\allowdisplaybreak@\displaybreak@\intertext@
\displ@y\setbox\savealignat@\hbox{$\m@th\displaystyle\Let@
\xxattag@{#1}\vbox{\halign{\span\preamble@@\crcr#2\crcr}}$}%
\Let@\xxattag@{#1}\tabskip\z@skip\halign to\displaywidth
{\span\preamble@@\crcr#2\crcr\black@{\wd\savealignat@}}}
\def\xxattag@#1{\toks@{\tabskip\z@skip\hfil\strut@
$\m@th\displaystyle{\the\hashtoks@}$&%
$\m@th\displaystyle{{}\the\hashtoks@}$\hfil\tabskip\centering@&}%
\atcount@#1\relax\advance\atcount@\m@ne\loop\ifnum\atcount@>\z@
\toks@=\expandafter{\the\toks@&\hfil$\m@th\displaystyle{\the\hashtoks@}$%
\tabskip\z@skip&$\m@th\displaystyle{{}\the\hashtoks@}$\hfil
\tabskip\centering@}\advance\atcount@\m@ne\repeat
\edef\preamble@{\the\toks@\tabskip\z@skip}\edef\preamble@@{\preamble@}}
\Invalid@\endxxalignat
\catcode`\@=\active
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