How do I adjust the height of a superscript?

Question

I have an operation that I call \conv, that I defined as follows:

\newcommand\conv{{}^{\scriptstyle\smile}}

Sometimes I use it in this situation:

$a\conv$

and sometimes I use it in this situation:

$$\big(\prod a\big)\conv$$

In both cases, the superscript \conv is at the same level. However, in the second case, the \sum is so big, that the \conv seems to hit it at mid-level. I want it to somehow adjust to the larger size of the \sum so that it is up at the top of the \big), not so far down.

Please let me know how I can clarify my question.

Answer 1

There may a be a beeter way to do this. Using

\newcommand\conv{^{\scriptstyle\smile}}

Should do the job. The empty {} is responsible for the constant height of smile.

\documentclass{article}
\newcommand\conv{^{\scriptstyle\smile}}
\begin{document}
\[\left(\prod a\right)\conv\]
\[a\conv\]
\end{document}

I suggest using \[ \] instead of $$ $$ and \( \) for $ $. Also instead of using static \big( and \big), it is better to use dynamic \left( and \right)

EDIT Different version:

\documentclass{article}
\newcommand{\conv}[1]{{#1}^{\scriptstyle\smile}}
% \newcommand\conv{^{\scriptstyle\smile}}
\begin{document}
\[\conv{\left(\prod a\right)}\]
\[\conv{a}\]
\(\conv{}\conv{}\)
\end{document}

Answer 2

A method for being able to use \conv\conv is the following

\makeatletter
\newcommand\conv{^\bgroup\scriptscriptstyle\@conv\conv}
\def\@conv#1{\smile\@ifnextchar\conv\@conv\egroup}
\makeatother

I've used \scriptscriptstyle, as \scriptstyle is redundant.

Here's an example:

\documentclass{article}
\makeatletter
\newcommand\conv{^\bgroup\scriptscriptstyle\@conv\conv}
\def\@conv#1{\smile\@ifnextchar\conv\@conv\egroup}
\makeatother

\begin{document}
$a\conv$

$a\conv\conv$

$\Bigl[a\Bigr]\conv$
\end{document}