Having
latexrender available, one can edit the _class.latexrender.php_ file
to include additional LaTeX-packages. For example adding the lines
string .= '\usepackage{xy}\n';
string .= '\xyoption{all}\n';
string .= '\newcommand{\vtx}[1]{*+[o][F-]{\scriptscriptstyle #1}}\n';
makes it possible to include quiver-pictures in this weblog.
Observe the double blackslash before newcommand, a single backslash
would produce a new-line and fail to define something.
After
three days of desperate trial-and-error I seem to have managed to get latexrender working for
wordpress under Mac
OS X.
First things first : if you only want to include some
symbols in your blog-posts the easiest way to do so is to use mimetex and the
corresponding
wordpress-plugin written by Steve Mayer. Follow the
instructions and you will be able to include a limited subset of LaTeX
in your blog within 10 minutes.
If you want more, you have to
work a lot harder. The starting point is to follow Steve’s
blog-entries on latexrender
.
But then under Mac OS X you will probably get error messages
when you activate the plugin. The reason seems to be that most versions
of imagemagick available for
OS X require X-terminal support and PHP gets confused between the two
shells. A typical error message is
Warning:
copy(70afbabac176169545d01f4bd91f3055.gif): failed to open
stream:
No such file or directory in
/Users/lieven/Sites/wordpress/latexrender/class.latexrender.php on
line
269
[Unparseable or potentially dangerous latex
formula. Error 6 ]
As suggested by Steve Mayer there are
two roads to obtain more information on what goes wrong. The first is to
uncomment the _unlink commands _ at the end of the
_class.latexrender.php_ file and look in the _wordpress/latexrender/tmp_
directory for which conversions were done and which failed. The normal
latexrender-procedure is : tex->dvi->ps->gif. Probably you will
get all files but the gifs!
Another (and more useful) source of
informations is to look in the _error-log_ of the Apache-WebServer and
see whether you get things like
This is dvips(k) 5.94a
Copyright 2003 Radical Eye Software (www.radicaleye.com)
\\’
TeX output 2004.08.30:1433\\’ ->
0d48700a5dde6d746813733d26dd8df8.ps
. [1]
sh: line 1:
gs: command not found
convert: no decode delegate for this image
format
/Users/lieven/Sites/weblog/latexrender/tmp/
0d48700a5dde6d746813733d26dd8df8.ps\\’.
convert: missing an image
filename/Users/lieven/Sites/weblog/latexrender/tmp/
0d48700a5dde6d746813733d26dd8df8.gif\\’.
identify: unable to
open image 0d48700a5dde6d746813733d26dd8df8.gif\\': No such file0d48700a5dde6d746813733d26dd8df8.gif\\’.
or directory.
identify: missing an image
filename
`
Here the essential point is that the webserver doesn’t
seem to be able to find GhostScript (even if you have several versions
installed).
To bypass these problems I did two essential
things : (1) in the _class.latexrender.php_ file I rewrote the
conversions so as to use _pdflatex_ instead of tex (to get
immediately a pdf-file rather than the tex->dvi->ps process) and then
use _convert_ to translate this pdf-file into a gif-file. (2) the
version of _convert_ and _include_ (both part of the
ImageMagick package) are those provided by Fink but you should be extremely
careful to install the imagemagick-nox package and not
the imagemagick package! After the command
sudo fink
install imagemagick-nox
you are presented with several
configuration choices. Do _not_ choose on auto-pilot the default
choices but look for options specifying that there is no X-support!
After this, everything should work. If you want to have a look at how
I changed the PHP files, mail
me.
Before the vacation I finished a rewrite of the One quiver to rule them
all note. The main point of that note was to associate to any qurve
$A$ (formerly known as a quasi-free algebra in the terminology of
Cuntz-Quillen or a formally smooth algebra in the terminology of
Kontsevich-Rosenberg) a quiver $Q(A)$ and a dimension vector $\alpha_A$
such that $A$ is etale isomorphic (in a yet to be defined
non-commutative etale toplogy) to a ring Morita equivalent to the path
algebra $lQ(A)$ where the Morita setting is determined by the dimension
vector $\alpha_A$. These “one-quiver settings” are easy to
work out for a group algebra $lG$ if $G$ is the amalgamated free product
of finite groups $G = H_1 \bigstar_H H_2$.
Here is how to do
this : construct a bipartite quiver with the left vertices corresponding
to the irreducible representations of $H_1$, say ${ S_1, .. ,S_k }$ of
dimensions $(d_1, .. ,d_k)$ and the right vertices corresponding to the
irreducible representations of $H_2$, ${ T_1, .. ,T_l }$ of dimensions
$(e_1, .. ,e_l)$. The number of arrows from the $i$-th left vertex to
the $j$-th right vertex is given by the dimension of $Hom_H(S_i,T_j)$
This is the quiver I call the Zariski quiver for $G$ as the finite
dimensional $G$-representations correspond to $\theta$-semistable
representations of this quiver for the stability structure $\theta=(d_1,
.. ,d_k ; -e_1, .. ,-e_l)$. The one-quiver $Q(G)$ has vertices
corresponding to the minimal $\theta$-stable dimension vectors (say
$\alpha,\beta, .. $of the Zariski quiver and with the number of arrows
between two such vertices determined by $\delta_{\alpha
\beta}-\chi(\alpha,\beta)$ where $\chi$ is the Euler form of the Zariski
quiver. In the old note I've included the example of the projective
modular group $PSL_2(Z) = Z_2 \bigstar Z_3$ (which can easily be
generalized to the modular group $SL_2(Z) = Z_4 \bigstar_{Z_2} Z_6$)
which turns out to be the double of the extended Dynkin quiver
$\tilde{A_5}$. In the rewrite I've also included an example of a
congruence subgroup $\Gamma_0(2) = Z_4 \bigstar_{Z_2}^{HNN}$ which is an
HNN-extension. These are somehow the classical examples of interesting
amalgamated (HNN) groups and one would like to have plenty of other
interesting examples. Yesterday I read a paper by Karen Vogtmann called
Automorphisms of free groups and outer space in which I encountered
an amalgamated product decomposition for $GL_2(Z) = D_8 \bigstar_{Z_2
\times Z_2} (S_3 \times Z_2)$where $D_8$ is the diheder group of 8
elements. When I got back from vacation I found a reference to this
result in my mail-box from Warren Dicks. Theorem 23.1, p. 82, in Heiner
Zieschang, Finite Groups of Mapping Classes of Surfaces, LNM 875,
Springer, Berlin, 1981.
I worked out the one-quiver and it has
the somewhat strange form depicted above. It is perfectly possible that
I made mistakes so if you find another result, please let me know.
added material (febr 2007) : mistakes were made and
the correct one quiver can be found elsewhere on this blog.