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+\documentclass[a4paper]{article}
+\usepackage{shortvrb}
+\MakeShortVerb{\|}
+\def\meta#1{$\langle${\normalfont\itshape#1}$\rangle$}
+
+\DeclareFontFamily{U}{tf}{\skewchar\font=42}
+\DeclareFontShape{U}{tf}{m}{n}{<5> tf5 <7> tf7 <10> tf10}{}
+\DeclareSymbolFont{newsym}{U}{tf}{m}{n}
+
+\begin{document}
+
+\paragraph*{Accents} This demonstrates the extended semantics of
+|\mathaccent|. The first row uses an accent whose |charlist| ends with
+an |extensible recipe|, the second uses a traditional |charlist|.
+
+\def\acca{\mathaccent"410 }
+\def\accb{\mathaccent"418 }
+
+\[\acca{a}\ \acca{ab}\ \acca{abc}\ \acca{abcd}\ \acca{abcde}\]
+\[\accb{a}\ \accb{ab}\ \accb{abc}\ \accb{abcd}\ \accb{abcde}\]
+
+Nested accents and under accents with |\nesting|\-|math|\-|accent|,
+|\math|\-|under|\-|accent| and |\nesting|\-|math|\-|under|\-|accent|. The
+positioning information for the under accents is taken from the
+\meta{skewchar}-\meta{accentee} kerning and the \meta{accent}-\meta{accent}
+kerning.
+
+\def\hat{\mathaccent"0428 }
+\def\uhat{\mathunderaccent"0428 }
+\def\Hat{\nestingmathaccent"0428 }
+\def\uHat{\nestingmathunderaccent"0428 }
+\mathcode`A="0429
+
+\[
+\hat A\ \uhat A\ \Hat{\Hat A}\ \uHat{\uHat A}\ \Hat{\uHat{\Hat{\uHat A}}}
+\quad
+\Hat{\hat {\Hat A}}\ \hat{\Hat {\Hat A}}\ \uHat{\hat{\uHat{\hat A}}}\
+\]
+
+\paragraph*{Radicals} Generalized radicals with |\genradical|.
+\def\radl{\genradical"400401 "4FF4FF }
+\def\radlx{\genradical"400401 "40F40F }
+\def\radr{\genradical"4FF4FF "408409 }
+\def\radrx{\genradical"407407 "408409 }
+\def\radlr{\genradical"400401 "408409 }
+
+\[\radl{a^{a^a}bc}\ \radlx{a^{a^a}bc}\ \radr{a^{a^a}bc}\ \radrx{a^{a^a}bc}\]
+\[\radlr{\radr{\radl{a}}}\]
+
+\paragraph*{Math style} This sample shows that |\mathstyle| keeps track of the
+math style while scanning the formula.
+
+\def\sh{%
+ \ifnum\the\mathstyle<0 X\else
+ \ifcase\the\mathstyle D\or D'\or T\or T'\or S\or S'\or SS\or SS'
+ \else !!\the\mathstyle!!\fi
+ \fi}
+
+\[
+\sh\fraction{\sh\over\sh}\sh\overline{\sh}\underline{\sh}\sqrt{\sh}\sh
+{}^{{\sh}^{\sh}}_{{\sh}_{\sh}}\hat{\sh}\sh\quad\textstyle\sh\hbox{\sh$\sh$}\sh
+\]
+
+And here is the list of all math styles, activated via
+|\displaystyle|, |\cramped|\-|display|\-|style|, \dots,
+|\script|\-|script|\-|style|, |\cramped|\-|script|\-|script|\-|style|.
+
+\[
+\displaystyle\sh\,
+\crampeddisplaystyle\sh\,
+\textstyle\sh\,
+\crampedtextstyle\sh\,
+\scriptstyle\sh\,
+\crampedscriptstyle\sh\,
+\scriptscriptstyle\sh\,
+\crampedscriptscriptstyle\sh
+\]
+
+The following display shows that |\fraction| has no influence on the
+typesetting.
+
+\[\hbox{|\fraction{a+b\over c-d}={a+b\over c-d}|}\]
+
+\[\fraction{a+b\over c-d}={a+b\over c-d}\]
+
+
+\paragraph*{Extensible operators} These have not been implemented in \TeX{}
+the program, since this turned out to be a bit complicated (the limits of a
+|mathop| are positioned in the first pass over the |mlist|, but the size of
+big delimiters is not determined until the second pass). But I have done some
+macro hackery to show how this would look like. The input for the middle
+integral was (after a suitable redefinition of |\left|)
+\[\hbox{|\left\int\limits^{\infty}_{-\infty}...\right.dx|}\]
+
+\def\int{\mathchar"1420 }
+\let\ooleft\left
+\def\left{\futurelet\next\oint}
+\def\oint{%
+ \ifx\next\int
+ \let\next\ooint
+ \else
+ \let\next\ooleft
+ \fi
+ \next}
+\def\ooint\int{\def\isb{}\def\isp{}\let\li\limits\futurelet\next\oooint}
+\def\oooint{%
+ \ifx_\next
+ \let\next\getsb
+ \else
+ \ifx^\next
+ \let\next\getsp
+ \else
+ \ifx\next\limits
+ \let\next\eatlimits
+ \else
+ \ifx\next\nolimits
+ \let\next\eatlimits
+ \else
+ \let\next\ooooint
+ \fi
+ \fi
+ \fi
+ \fi
+ \next}
+\def\getsb_#1{\def\isb{#1}\futurelet\next\oooint}
+\def\getsp^#1{\def\isp{#1}\futurelet\next\oooint}
+\def\eatlimits#1{\let\li#1\futurelet\next\oooint}
+\def\ooooint#1\right.{%
+ \mathop{\nulldelimiterspace=0pt\ooleft\delimiter"4420420\vphantom{#1}\right.}%
+ \li_{\isb}^{\isp}#1}
+
+\[
+\int_{-\infty}^{\infty}abc^{a^{b^{d^e}}}dx\
+\left\int^{\infty}_{-\infty}
+\left(\begin{array}{llll}
+a&b&c&d\\
+e&f&g&h\\
+i&j&k&l\\
+m&n&o&p\\\end{array}\right)\right.dx\
+\left\int\nolimits_{-\infty}^{\infty}abc^{a^{b^{d^e}}}\right.dx
+\]
+
+\end{document}
+
+
+
+
+