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 αA
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 αA. 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=H1★HH2.
Here is how to do
this : construct a bipartite quiver with the left vertices corresponding
to the irreducible representations of H1, say S1,..,Sk of
dimensions (d1,..,dk) and the right vertices corresponding to the
irreducible representations of H2, T1,..,Tl of dimensions
(e1,..,el). The number of arrows from the i-th left vertex to
the j-th right vertex is given by the dimension of HomH(Si,Tj)
This is the quiver I call the Zariski quiver for G as the finite
dimensional G-representations correspond to θ-semistable
representations of this quiver for the stability structure θ=(d1,..,dk;−e1,..,−el). The one-quiver Q(G) has vertices
corresponding to the minimal θ-stable dimension vectors (say
α,β,..of the Zariski quiver and with the number of arrows
between two such vertices determined by δαβ−χ(α,β) where χ is the Euler form of the Zariski
quiver. In the old note I've included the example of the projective
modular group PSL2(Z)=Z2★Z3 (which can easily be
generalized to the modular group SL2(Z)=Z4★Z2Z6)
which turns out to be the double of the extended Dynkin quiver
~A5. In the rewrite I've also included an example of a
congruence subgroup Γ0(2)=Z4★HNNZ2 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 GL2(Z)=D8★Z2×Z2(S3×Z2)where D8 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.