Math symbols in plain TeX

Question

1. I would be much obliged if you cold tell me how can I make an arc over a letter (or a group of letters) in TeX. The command in LaTeX is

   \stackrel{\frown}{AB}
   

   but in TeX it proves to be useless.

2. How can I write in $\cases{ ...}$ math symbols to look like in $$...$$? For example, $\sum_a^b$ as compared to $$\sum_a^b$$. Thank you.

Answer 1

You can use the yhcmex10 font that provides an extensible arc accent:

\font\yhcmex=yhcmex10
\newfam\yhfam
\textfont\yhfam=\yhcmex
\def\hexdigit#1{\ifcase#1
  0\or 1\or 2\or 3\or 4\or 5\or 6\or 7\or
  8\or 9\or A\or B\or C\or D\or E\or F\fi}
\edef\wideparen{\mathaccent"0\hexdigit\yhfam F3}

\catcode`@=11
\def\dcases#1{%
  \left \{\,\vcenter{\normalbaselines\m@th\ialign
    {$\displaystyle##\hfil$&\quad##\hfil\crcr#1\crcr}}\right.}
\catcode`@=12

$\wideparen{AB}$

$$
f(x)=
\dcases{{x+1\over 2} & if $x<0$\cr\noalign{\vskip3pt}
       x^2 & if $x\ge 0$\cr}
$$

\bye