Master Thesis, LaTeXML and Quantum Groups (part 1)
I wanted to wait for my oral defense before blogging about my master thesis and how I manage to publish Web and paper versions of it. However, I finally met my supervisor today and the oral defense is only likely to take place next Wednesday. I do not want to delay too much this blog post and thus decided to publish it today...
This year, I have taken the following approach to write my master thesis:
from LaTeX input files, I used XeLaTeX to generate a pdf document and LaTeXML
to generate HTML+MathML Web pages. I had to handle some small differences via
separate configuration files. However in general, these two tools are compatible
and accept more or less the same LaTeX input. I did not really have to make
graphics: I only used the
amscd package to draw simple commutative
diagrams and did not try to draw schemas for representations of quantum groups.
Hence I did not get the opportunity to test how LaTeXML can generate
MathML inside SVG, although I saw on July something interesting for Firefox on
the LaTeXML mailing list.
The pdf version provides a good print layout which allows to workaround some issues that I had two years ago when I printed my Master Thesis in Computer Science directly from Firefox. XeLaTeX also seems much faster and so more convenient to use when you only want to check that your LaTeX code is syntactically correct and get a quick preview. It seems that XeLaTeX uses a kind of cache: there are intermediary files that I guess are used again when you regenerate the document. In contrast, LaTeXML seems to always regenerate one big XML file in a first step and the Web pages in a second step. Perhaps LaTeXML has an option to avoid that behavior or perhaps the idea of a cache system does not work well in the case of Web pages.
The output of LaTeXML has the classical advantages of HTML+MathML for
publication on the Web and is much more comfortable to read on a screen.
Generally speaking, I think Firefox renders pretty well the LaTeXML output.
LaTeXML generates HTML rows to implement labelling and does not rely on
mathvariant, which allow to avoid issues with
<mlabeledtr> and token elements. However, I still note some
MathML's rendering imperfections which, not surprisingly, have already be
mentioned in the MathML
- Linebreaking: bad line breaks inside some equations, apparently those
generated by some environments like
gathered. Sometimes, I also see bad line breaks around equations for example when they are inside parenthesis.
- Spacing: the lack of support for
mtable@rowspacing/columnspacingseems to give wrong spacing inside binom-like notations. For some reason LaTeXML generates
<mpadded>elements of zero width in some places and they cause weird overlappings in some summations.
- Operator Stretching: commutative diagrams in the definition of Hopf algebras would look better if we support stretching operators in table cells.
This also gives me the opportunity to report various bugs and give some
suggestions to the LaTeXML team, including the use of MathJax (for
browsers without MathML support), the replacement of
<mfenced> by the equivalent
<mo> constructions (better rendering in Firefox),
improvement to the generation of headers in HTML5 and more.
The title of my master thesis is "Specialization of Quantum Groups at a Root of Unity and Finite Dimensional Representations". The concept of Quantum Groups is based on ideas from theoretical physics, but I studied these structures from a purely algebraic point of view. That is not likely to be interesting if you have never heard about Lie algebras or are not familiar with representation theory, so I will present my contribution in a separate blog post.