Horizontally misalligned sub-/superscripts in fractions when using 'minus' sign

Question

I am combining sub- and superscripts in the denominator of a fraction. I get ill behaviour when the exponent is preceded with a minus sign:

I would expect the sub- and superscript of the first two elements be aligned. I do understand the different alignment of the third element, when the superscript is absent. However, the misalignment cannot be rescued by the usage of \vphantom.

Here's the minimal example:

\documentclass{minimal}
\usepackage{amsmath}

\begin{document}

\begin{equation*}
  \frac{1}{l_e^{1} l_e^{-1} l_e l_e^{\vphantom{3}-1}}
\end{equation*}

\end{document}

Any help is highly appreciated. Thank you very much for your time.

Answer 1

The minus sign has the same height and depth of the +, which has depth, so this pushes down the subscript a bit more than if only 1 is in it. For this reason, your \vphantom{3} does nothing.

Solution: use proper phantoms or smash the minus.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{equation*}
  \frac{1}{l_e^{\vphantom{-}1} l_e^{-1} l_e^{\vphantom{-}} l_e^{-1}}
\quad
  \frac{1}{l_e^{1} l_e^{\smash{-}1} l_e^{} l_e^{\smash{-}1}}
\quad
  \frac{1}{l_e^{1\mathstrut} l_e^{-1\mathstrut} l_e^{\mathstrut} l_e^{-1\mathstrut}}
\end{equation*}

\end{document}

As you see, the \mathstrut device has its drawbacks.

Answer 2

One possibility is

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{equation*}
  \frac{1}{l_e^{\mathstrut{1}} l_e^{\mathstrut{-1}} l_e l_e^{\mathstrut{1}}}
\end{equation*}

\end{document}

Answer 3

This is an old question, but I figured I'd add an alternative. As @egreg mentions in the comments, the rules for subscript and superscript placement are complicated. To bypass the "cramped" style in the denominator, you can add \textstyle, even though intuition tells us the denominator should already be in \textstyle. To even out the subscripts, add an empty exponent.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{equation*}
  \frac{1}{\textstyle l_e^{1} l_e^{-1} l^{}_e l_e^{-1}}
\end{equation*}

\end{document}