>> I found another, important issue:
>>
>> you are using \usepackage{subscript} but subscript is not a real
>> LaTeX-package (the author calls it a fragment) and therefore not
>> installable via the package managers of TeXLive and MiKTeX:
>> http://www.ctan.org/tex-archive/help/Catalogue/entries/subscript.html
>
> This is not true. This file is included in the "fragments" package in
> TeXLive, and I believe also in MikTeX. Also the file contains the lines
> % the fragment may be used as a package in its own right, if so
> % needed.
>
> What is the problem with using that package?

That it is not included in MiKTeX, also not via the fragments or fixltx2e package. Therefore all LyX on Windows would be forced to install the file manually which is not acceptable.

I provide LyX for Windows as one-click instalation. So you start the installer and at the end of the installation process, you have a full-equipped LyX, LaTeX environment and all necessary third-party programs. All LaTeX-packages needed by LyX are automatically installed when LyX is started the first time. This mechanism only works for packages available in MiKTeX.
I can ask the MiKTeX maintainer to include subfigure but I can understand if he 
denies this.

With your current implementation I'm forced to ship the subfigure.sty with the installer and install it using installer code. This is a lot of extra work and becomes complicated for fresh installation (where MiKTeX is installed together with LyX). That's why I shout.

>> So we must insert these lines instead of using subscript.sty.
>
> This is wrong IMO. There is a package for this purpose, so we should use it.
> The less LaTeX hardcoding in LyX, the better. I added a note about the
> "fragments" package to LaTeXConfig.lyx, so that users will find it more
> easily.

In principle yes. As these lines are also used by other packages like KOMA-script and have not been touched at CTAN for 11 years we can assume them being stable to insert them directly via LyX.

regards Uwe

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