Define a \bigplus operator in plain TeX

Question

How to define a big plus operator that behaves exactly like bigsum but uses the plus symbol instead of a capital sigma?

I know that the best option (or at least the way Don would do it) is probably to design this symbol using metafont but scaling is good enough for me.

Answer 1

You can use \mathchoice to use a suitably scaled font in each math style.

\font \zzz = cmr10 at 14pt
\font\zzzb  cmr10 at 20pt
\font\zzzsy =cmsy10 at 14pt
\font\zzzsyb =cmsy10 at 20pt

\def\bigplus{\mathop{\mathchoice{\hbox{\zzzb+}}{\hbox{\zzz+}}{\scriptstyle+}{\scriptscriptstyle+}}}
\def\bigtimes{\mathop{\mathchoice{\hbox{\zzzsyb\char2}}{\hbox{\zzzsy\char2}}{\scriptstyle\times}{\scriptscriptstyle\times}}}

\def\test{\sum_{i=0}^nx^i \rightarrow \bigplus_{i=0}^nx^i \rightarrow \bigtimes_{i=0}^nx^i}
$$
\test
$$
or..

\bigskip

This $\test$

\bigskip

Or this $x^{\test}$
\bye

Or with vertical center for Barbara

\def\bigplus{\mathop{\mathchoice{\vcenter{\hbox{\zzzb+}}}{\vcenter{\hbox{\zzz+}}}{\scriptstyle+}{\scriptscriptstyle+}}}
\def\bigtimes{\mathop{\mathchoice{\vcenter{\hbox{\zzzsyb\char2}}}{\vcenter{\hbox{\zzzsy\char2}}}{\scriptstyle\times}{\scriptscriptstyle\times}}}