mailing-list for TeXmacs Users

[Chris Austin <address@hidden>]

On Tuesday 31 January 2012 14:39:00 François Poulain wrote:
> Hi,
> 
> I just started working with Joris on the TeX/LaTeX import/export 
> module, for a few weeks.

A very important point for working with tensors with both upper and lower 
indices, is to be able to preserve the relative *horizontal* positions of the 
indices.  For example the Riemann tensor, which is ubiquitous in work on 
Einstein gravity, has 4 indices, each of which, independently of the others, 
can be either upper or lower, and swapping either its first two indices or 
its last two indices is equivalent to multiplying it by -1.  So it is 
essential to maintain the gap above each lower index and the gap below each 
upper index: if indices get swept to the left to fill these gaps, the 
resulting expression is undefined.

Neither LaTeX nor TeXmacs has any built-in mechanism for dealing with this, 
(so far as I know), so work-arounds have to be used.  The standard 
work-around in LaTeX, used for example by the Cadabra program, seems to be to 
insert an empty pair of braces at each point where the index position has to 
switch from upper to lower, or vice versa.  For example, to write a Riemann 
tensor whose 1st and 3rd indices are lower, and whose 2nd and 4th indices are 
upper, we can write, in LaTeX: $ R_a{}^b{}_c{}^d $.  However this does not 
convert properly to TeXmacs, at least in 1.0.7.10 and earlier versions: the 
gaps needed to define the horizontal positions of the indices just vanish.

A work-around I have been using for about 4 years now is, in TeXmacs, to put 
\,\! at each point where the index position has to switch from upper to 
lower, or vice versa.  (\,\! is a space whose total length is 0.)  This is 
the simplest work-around which I found, after some experiments about 4 years 
ago, was maintained uncorrupted on both conversions TeXmacs -> LaTeX and 
LaTeX -> TeXmacs.  This work-around fortunately still works in 1.0.7.10, but 
while it is maintained uncorrupted in the TeXmacs -> LaTeX conversion, it now 
gets changed to \hspace{0.25em} \hspace{-0.25em} in the LaTeX -> TeXmacs 
conversion.  This does no harm apart from lengthening the source file, and it 
does not get altered any further on further conversions back to LaTeX then 
back to TeXmacs and so on.

However I would like to mention that I am a bit concerned that if the TeXmacs 
< - > LaTeX conversions were to become a bit more "intelligent", this very 
important zero-length space might simply get deleted.

In general I would like to say that I think TeXmacs is a really wonderful 
program that I use very heavily, and I very much appreciate the work of 
Joris, François, and the other TeXmacs developers.  I hope the forthcoming 
TeXmacs meeting is a great success.

Best regards,
Chris