# Why no metrics for left subscripts and superscripts?

The math typesetting system in TeX aims at perfect spacing between symbols, hence has metrics describing the correct position of (right) subscripts and superscripts for each math symbol (as far as I have understood). What has bothered me for a long time is why there are no corresponding metrics for left subscripts and superscripts. In fact, there is no build-in interface for them; Knuth himself suggests in the TeXbook that you use ad-hoc solutions like {}^t A and {}_M A. However, this method is unsatisfactory, since it often requires a lot of manual adjustment of the spacing and height to make it look just right. As an example, the below MWE was typeset using the tensor package as well as the manual solution.

My question is two-fold: Is there a good reason why no metrics were included for left subscripts and superscripts in TeX, and Have there been any attempts to add such metrics to the math engine? From what I gathered about the OpenType MATH Tables, not even these add such metrics, so unicode-math does not solve the problem.

\documentclass{article}

\usepackage{amsmath,tensor}

\begin{document}

$\tensor[^t]{M}{}$ and ${}^t M$ look more or less OK

$\tensor[^t]{A}{}$ does not; it should be ${}^t\! A$

\end{document}

• It might help if you were a bit more specific as to what exactly you mean by "metrics". (For all use cases of prefixed subscripts and superscripts I'm familiar with, the vertical positioning parameters are the same as for suffixed subscripts and superscripts. However, I may be missing something.) Separately, are you familiar with various chemistry packages and the tensor package, all of which make the use of left-prefix subscripts and superscripts quite easy? – Mico Aug 16 '15 at 7:36
• Yes I know it. To quote the manual, "A fairly robust (if somewhat crude) attempt is made to ensure the correct spacing and skew of the preposed indices with respect to the tensor object itself." To me, that does not sound like an actual solution, but a rather ad-hoc approach, which may or may not yield the expected results. – Gaussler Aug 16 '15 at 7:43
• Well, the parameters for suffixed subscripts and superscripts were never intended for left subscripts and superscripts and often yield unsatisfactory spacing, both vertical and horizontal. I have also seen approaches based on putting a \vphantom on the left; but that is usually not very pretty either. Left superscripts are often too high, for instance. – Gaussler Aug 16 '15 at 7:50
• @Mico, see the example above to see what I mean. – Gaussler Aug 16 '15 at 8:10
• Regarding the horizontal spacing between the prefixes and the main expression, I'd say that there's nothing special about prefixed subscripts and superscripts. This may be verified by considering the expressions \Gamma_x and r_D; both look much better if typeset as \Gamma_{\!x} and r^{}_{\!D}. When TeX is constructing the "math molecules", it arranges "boxes". TeX has no idea at that stage what's inside the boxes. There will thus always be cases where the spacing -- whether vertical or horizontal, or both -- can be improved by manual fine-tuning. – Mico Aug 16 '15 at 8:20