Skip to content →

neverendingbooks Posts

now I see you, now I don’t

someone as clumsy as me, it is no real surprise to loose one in three
hard disks, but what happened yesterday was a bit puzzling at first. I
tried to replace the original 4 Gb hard disk of an original iMac (a tray
loading iMac) following the instructions of the MacWorld : how to upgrade an iMac-page I used last
time together with Jan to replace two hard disks in slot-loading iMacs.
The whole process is a bit scary : unplug 4 connections, remove the
motherboard, remove the CD-driver in order to get at the hard disk, but
to my own surprise I managed to do all this fairly quickly and replaced
the hard disk by a 120 Gb Seagate Barracuda hard disk. I
put the iMac back together and started up from the OS 9 CD (last time I
forgot this and it is becoming fairly impossible to get a working
System9 defacto on 10.3). I opened DiskUtility and to my surprise the
utility found the new disk, so I managed to install everything properly.
I could even initialize and partition the disk (to run OS X on a first
generation iMac one needs to install it on a partition which is no
larger than 8 Gb) in two partitions (one 8Gb, the other the rest) and
installed System9 on the first partition. So far, so good but when I
restarted the iMac, a blinking question-mark appeared on the screen
indicating that it could not find the installed System9! Then I tried to
start-up from the 10.3-installation disk, started up the DiskUtility and
this time it found no hard disk at all. So I started up again from the
System9 CD and the two partitions appeared on my Desktop, seemingly in
perfect order. What was going on? There was an hard disk, I put System9
on one of its partitions but somehow it refused to find it, and starting
from the 10.3 CD it looked as if there was no hard disk whatsoever. If
you are knowledgeable, you know already where the problem was situated
but as I am more a software than a hardware guy I looked for similar
problems on the net and found an entry in which the solution was
obtained by installing System9 on the larger partition. So I tried this,
but again met the same problems.

So it must be a
hardware problem and I downloaded the product manual and began browsing through it until
I found one of these marvelous computer-terms : the master-slave
jumper settings
. Who invents this kind of terminology? The
master-slave jumper… Anyway, here are the possibilities for a
admit I didn’t look at the jumper-setting when I inserted the hard
disk. The previous two times it was not necessary and I assumed that the
default position would be the master-setting but wasn’t certain. Hence,
there was only one way to find out and that was redoing the whole
replacement-process… So, this morning I did this and found out that
the jumper-settings were set at Cable select which according to
Geert is the best setting for Windows-computers as
they then automatically decide whether to use the disk as master or
slave, so perhaps for Seagate there is some marketing logic in choosing
this as their default setting. Hence, I changed the setting to
master, quickly put back the iMac and in the end discovered that
I was left with two screws… As they must have been the screws
connecting the hard-disk cage to the motherboard I had little choice but
to redo the whole process a third time. Surprisingly, I began to like
the whole procedure, one should be forced as a computer-user to take
your computer apart a couple of time before working on it. Finally, I
tried to install OS X again, the DiskUtility recognized the two
partitions without any problem and the installation went smoothly.
Probably System9 can find a Cable-select connected hard disk, whereas OS
X cannot…

Leave a Comment

Singular via GAP on OSX

GAP-package is very good in working with finite
fields or Abelian extensions of the Rational numbers, but sooner or
later we will need to use the coordinate ring or function field of an
affine variety for which it is hopeless. On the other hand, there is an
excellent free package to do these calculations : Singular.
So, the ideal situation for us would be to be able to access Singular
from within GAP. Fortunately, Marco Costantini and Willem de
Graaf have written such an interface. Here is how to get in working
under OS X : One has to download two files from the Singular Mac OS X download page :
Singular-2-0-4-share.tar.gz. Once they are on your desktop you
can follow the instructions on the INSTALL.html file in the 2-0-4
Folder of the expanded Singular-2-0-4-ppcMac-darwin. Keep the
tarred version and open the INSTALL-file in your browser (to be
able to copy and paste) and open up the Terminal. Do the analog
thing to

cd /usr/local sudo tar -pxf
/Users/lieven/Desktop/Singular-2-0-4-ppcMac-darwin.tar sudo tar -pxf

follow the instructions making the symbolic links and you have Singular
working. The next step is to go to the GAP Packages page and go to the
package Singular for full documentation.
To use Singular in a GAP-session, here is an example

The GAP interface to Singular 
gap> StartSingular();
I  Started Singular (version 2004) 
gap> SetInfoLevel( InfoSingular, 2 ); 
gap> G:= SymmetricGroup( 3 );; 
gap> R:= PolynomialRing( GF(2), 3 );; 
gap> GeneratorsOfInvariantRing( R, G ); 
[ x_1 x_2 x_3, x_1*x_2 x_1*x_3 x_2*x_3, x_1*x_2*x_3 ] 
gap> I:= Ideal( R, last );; 
gap>GroebnerBasis( I );
I  running GroebnerBasis... I  done
GroebnerBasis. [ x_1 x_2 x_3, x_2^2 x_2*x_3 x_3^2, x_3^3 ] 
Leave a Comment


GAP the Groups, Algorithms, and Programming-tool
(developed by two groups, one in St. Andrews, the other in Aachen) is
the package if you want to work with (finite or finitely
presented) groups, but it has also some routines for algebras, fields,
division algebras, Lie algebras and the like. For years now it is
available on MacClassic but since the last clean install of my
computer I removed it as I was waiting for a Mac OS X-port to be
distributed soon. From time to time I checked the webpage at
but it seems that no one cared for OS X. For my “The book of
-project I need a system to make lots of examples so perhaps
one could just as well install the UNIX-version. Fortunately, I did a
last desperate Google on GAP OS X which brought me to the
Aachen-pages of the GAP-group where one seems to be more Macintosh
minded. The relevant page is the further notes for OS X on the
GAP-installation for UNIX-page. Here is what I did to get GAP running
under OS X. First go to the download page (btw. this page has
version 4.4 whereas St-Andrews is still distributing 4.3) and download


This will give you three tar-files on your Desktop. Fire
up the Terminal and make a new directory /usr/local/lib if
it doesn’t exist yet. Then, go to your Desktop folder and do

cp gap4r4.tar /usr/local/lib sudo cp xtom1r1.tar /usr/local/lib cd
/usr/local/lib sudo tar xvf gap4r4.tar sudo tar xvf

Then return to your Desktop Folder and copy the
remaining tar-file in the /usr/local/lib/gap4r4/pkg-folder which
is created by untarring the former two files and untar it as above.
Then, it is time to compile everything (assuming you have installed the
Developer’s tools) and there is one magic OS X-command which will
speedup GAP by 20%. Here is what to do

/usr/local/lib/gap4r4 sudo ./configure sudo make COPTS="-fast

and everything will compile nicely. If you
are so lucky as to have a G5-system, you should replace the last command
by sudo make COPTS=”-03″. Finally, get everything in the right

cd /usr/local/lib/gap4r4/bin sudo cp

and if /usr/local/bin is in
your $PATH then typing gap at the command line will give
you the opening GAP-banner :

Leave a Comment


COL is a map-coloring game invented by Colin Vout.
Two players Left (bLack) and Right (white) take turns in coloring the
map subject to the rule that no two neighboring regions may be colored
the same. The last player to be able to move wins the game. For my talk
on combinatorial game theory in two weeks, I choose for a simplified
version of COL, namely COLgo which is played with go-stoned on a
(partial) go-board. Each spot has 4 neighbors (North, East, South and
West). For example, the picture on the left is a legal COLgo-position on
a 5×5 board. COL is a simple game to illustrate some of the key features
of game theory. In sharp contrast to other games, one has a general
result on the possible values of a COL-position : each position has
value $z$ or $z+\\bigstar$ where $z$ is a (Conway)-number (that is, a
dyadic integer) and where $\\bigstar$ is the fuzzy game {0|0}. In
the talk I will give a proof of this result (there are not so many
results in combinatorial game theory one can prove from scratch in 50
minutes but this is one of them). Of course, to illustrate the result I
had to find positions which have counter-intuitive values such as 1/2.
The picture on the left is an example of such a position on a 5×5 board
but surely one must be able to find 1/2-positions on a 4×4 board
(perhaps even on a 3×3?). If you have an example, please tell me.

On a slightly different matter : I used the psgo.sty package in LaTeX to print the (partial)
go-boards and positions. If I ever write out the notes I’ll post them
here but they will be in Dutch.

Leave a Comment

the iTunes hack

If you
are interested in getting thousands of mp3-files on your computer
using only 128 Kb of ROM, read on! Yesterday I made my hands dirty and
with Jan’s help upgraded two 6 Gb colored iMacs (a blue and a
pink one) to potential servers for our home-network having a 80 Gb resp.
a 120 Gb hard disk. If you do the installation yourself such an upgrade
costs you roughly 1 Euro/Gigabyte which seems to me like a good
investment. Clearly, you need to know how to do this and be less
hardware-phobic than I am. Fortunately, the first problem is easily
solved. There is plenty of good advice on the net : for the colored
iMacs we used the upgrade an iMac-page of MacWorld. For possible
later use, there is also a page for replacing the hard disk in an old iBook
(which seems already more challenging) and in a flat screen iMac (which seems to be impossible
without proper tools). Anyway, we followed the page and in no time
replaced the hard disks (along the way we made all possible mistakes
like not connecting the new hard disk and then being surprised that the
Disk Utility cannot find it or not putting back the RAM-chips and
panicking when the normal start-up chime was replaced by an aggressive
beep). An unexpected pleasant surprise was that the blue iMac, which I
thought to be dead, revived when we replaced the hard disk.

Back home, I dumped a good part of our CD-collection on the blue
iMac (1440 songs, good for 4.3 days of music and taking up 7.11 Gb of
the vast 120 Gb hard disk) to test the iTunes Central hack
explained by Alan Graham in his six
great tips for homemade dot mac servers
. Would I manage to get the
entire collection on my old iBook which had only (after installing all
this WarWalking-software) 800 Mb of free disk space? Here is what
I did :

1. On the iBook (or any machine you want to
play this trick on) go to your Home/Music/iTunes-folder and drag
the two files and one directory it contains to the Trash. Do the
same for the two files and which are in the

2. On the
iBook, use the Finder/Network-icon to connect to the server
(iMacServer in my case) and browse to the iTunes-folder where you placed
all the music (still, on the iBook in the Finder-window opened when you
connect to iMacServer). Make an Alias of the two files and the
directory in it (click on one of them once, go to the
File-submenu of the Finder and choose Make Alias) which
results in three new entries in the iTunes directory : iTunes 4 Music
Library alias
, iTunes 4 Music Library.xml alias and iTunes
4 Music Library alias
. Drag these 3 aliases to the
Home/Music/iTunes-folder on the iBook and rename them by removing
the alias-addendum.

3. In the Finder-window on
the iBook corresponding to the iMacServer browse to the
Home/Library/Preferences-folder and drag the two files and to
the Home/Library/Preferences-folder of the iBook. Launch
iTunes and it will give you access to the whole iTunes-collection
of iMacServer! In all, the three aliases and the 2 copied files take up
128 Kb…

Leave a Comment

NOG master class update

Yesterday I made a preliminary program for the first two months
of the masterclass non-commutative geometry. It is likely that
the program will still undergo changes as at the moment I included only
the mini-courses given by Bernhard
and Markus Reineke but several other people have
already agreed to come and give a talk. For example, Jacques Alev (Reims),
Tom Lenagan (Edinburgh),
Shahn Majid (London),
Giovanna Carnovale (Padua) among others. And in
may, Fred assures me, Maxim Kontsevich will give a couple of talks.

As for the contents of the two courses I will be
teaching I changed my mind slightly. The course non-commutative
I teach jointly with Markus Reineke and making the program
I realized that I have to teach the full 22 hours before he will start
his mini-course in the week of March 15-19 to explain the few
he needs, like :

To derive all the
counting of points formulas, I only need from your course:

the definition of formally smooth algebras basic properties, like
– the definition of the component
– the fact that dim Hom-dim Ext is constant along
components. This I need
even over finite fields $F_q$, but I
went through your proof in “One quiver”,
and it works. The
key fact is that even over $F_q$, the infinitesimal lifting
property implies smoothness in the sense Dimension of variety =
dimension of
(schematic) tangent space in any $F_q$-valued
point. But I think it’s fine for
the students if you do all
this over C, and I’ll only sketch the (few)
modifications for
algebras over $F_q$.

So my plan is to do all of
this first and leave the (to me) interesting problem of trying to
classify formally smooth algebras birationally to the second
course projects in non-commutative geometry which fits the title
as a lot of things still need to be done. The previous idea to give in
that course applications of non-commutative orders to the resolution of
singularities (in particular of quotient singularities) as very roughly
explained in my three talks on non-commutative geometry@n I now
propose to relegate to the friday afternoon seminar. I’ll be
happy to give more explanations on all this (in particular more
background on central simple algebras and the theory of (maximal)
orders) if other people work through the main part of the paper in the
seminar. In fact, all (other) suggestions for seminar-talks are welcome
: just tell me in person or post a comment to this post.

Leave a Comment

Bill Schelter’s Maxima

Schelter was a remarkable man. First, he was a top-class mathematician.
If you allow yourself to be impressed, read his proof of the
Artin-Procesi theorem. Bill was also among the first to take
non-commutative geometry seriously. Together with Mike Artin he
investigated a notion of non-commutative integral extensions and he was
the first to focuss attention to formally smooth algebras (a
suggestion later taken up by a.o. Cuntz-Quillen and Kontsevich) and a
relative version with respect to algebras satisfying all identities of
n x n matrices which (via work of Procesi) led to smooth@n
algebras. To youngsters, he is probably best know as the co-inventor of
Artin-Schelter regular algebras. I still vividly remember an
overly enthusiastic talk by him on the subject in Oberwolfach, sometime
in the late eighties. Secondly, Bill was a genuine Lisp-guru and
a strong proponent of open source software, see for example his
petition against software patents. He maintanind
his own version of Kyoto Common Lisp which developed into Gnu
Common Lisp
. A quote on its history :

GCL is
the product of many hands over many years. The original effort was known
as the Kyoto Common Lisp system, written by Taiichi Yuasa and Masami
Hagiya in 1984. In 1987 new work was begun by William Schelter, and that
version of the system was called AKCL (Austin Kyoto Common Lisp). In
1994 AKCL was released as GCL (GNU Common Lisp) under the GNU public
library license. The primary purpose of GCL during that phase of it’s
existence was to support the Maxima computer algebra system, also
maintained by Dr. Schelter. It existed largely as a subproject of

Maxima started as Bill’s version of
Macsyma an MIT-based symbolic computation program to which he
added many routines, one of which was Affine a package that
allowed to do Groebner-like computations in non-commutative
algebras (implementing Bergman’s diamond lemma) and which he
needed to get a grip on 3-dimensional Artin-Schelter regular
. Michel and me convinced Fred to acquire funds to
buy us a work-station (costing at the time 20 to 30 iMacs) and have Bill
flown in from the States with his tape of maxima and let him
port it to our Dec-station. Antwerp was probably for years
the only place in the world (apart from MIT) where one could do
calculations in affine (probably highly illegal at the time).
Still, lots of people benefitted from this, among others Michaela
and Kristel Van Rompay in their investigation
of 4-dimensional Artin-Schelter regular algebras associated to an
automorphism of a quadric in three-dimensional projective space.
Yesterday I ran into Bill (alas virtually) by browsing the
crypto-category of Fink. There it was, maxima, Bill’s package! I tried to install it
with the Fink Commander and failed but succeeded from the command line.
So, if you want to have your own version of it type

sudo fink
install maxima

from the Terminal and it will install without
problems (giving you also a working copy of common lisp). Unfortunately
I do not remember too much of Macsyma or Affine but there is plenty of
documentation on the net. Manuals and user guides can be obtained from
the maxima homepage and the University of Texas
(Bill’s university) maintains an online manual, including a cryptic description of
some Affine-commands. But probably I’ll have to send Michaela an
email asking for some guidance on this… Here, as a tribute to Bill who
died in july 2001 the opening banner

 iMacLieven:~ lieven$
/sw/bin/maxima Maxima 5.9.0 
Distributed under the GNU Public License. 
See the file COPYING. 
Dedicated to the memory of William Schelter. 
This is a development version of Maxima. 
The function bug_report() provides bug reporting information. 
Leave a Comment

bandwidth measures

One day (hopefully) lots of MP3, JPEG and perhaps even
MPEG-files will be flying around our wireless home-network. But I
didn’t have any idea of how much data I could cram through the
Airport-connections. To estimate the available bandwith of a
network there is a nice free tool around, iperf of which you can download binaries for
almost any platform including OS X. So click on the MacOS X (Darwin 6.4)
binary button half way on the iperf-page and you get a Desktop
iperf-1.7.0-powerpc-apple-darwin6.4 Folder
which you may rename to
just iperf. Do this on two computers connected to the
Airport-network you want to measure. Now, decide which of the two will
play the ‘server’ and which the ‘client’ (the end result does not
depend on this choice). So fire up the Terminal of the serving
computer and type

sudo ~/Desktop/iperf/iperf -s

and you will
get a message saying that the server is listening on TCP port 5001. Go
to the SystemPreferences/Network to obtain the IP-address of the server
(say it is . Walk over to the ‘client’-computer and type
into its Terminal

sudo ~/Desktop/iperf/iperf -c

and after a few moments it will compute the bandwidth of the
connection for you. Here is a sample output of two Airport-card
iMacs connected to the same Airport-Extreme base station :

iMacLieven:~/Desktop/iperf lieven$ ./iperf
-s ------------------------------------------------------------\r\
nServer listening on TCP port 5001 TCP window size: 64.0 KByte
(default) -----------------------------------------------------------
- [  4] local port 5001 connected with port
49245 [ ID] Interval       Transfer     Bandwidth [  4]  0.0-10.3
sec  2.77 MBytes  2.27
Mbits/sec -----------------------------------------------------------
- Client connecting to, TCP port 5001 TCP window size:
65.0 KByte
(default) -----------------------------------------------------------
- [  4] local port 49515 connected with port
5001 [ ID] Interval       Transfer     Bandwidth [  4]  0.0-10.2
sec  2.73 MBytes  2.23 Mbits/sec indicating a bandwidth of approximately
2.25Mbits/sec. If we replay the same game with two
AirportExtreme-card iMacs on the same network we can nearly
triple (!) the bandwidth : 
[eMacAnn:~] lieven% cd
Desktop/iperf [eMacAnn:~/Desktop/iperf] lieven% ./iperf
-s ------------------------------------------------------------\r\
nServer listening on TCP port 5001 TCP window size: 64.0 KByte
(default) -----------------------------------------------------------
- [  4] local port 5001 connected with port
49314 [ ID] Interval       Transfer     Bandwidth [  4]  0.0-10.0
sec  8.50 MBytes  7.11
Mbits/sec -----------------------------------------------------------
- Client connecting to, TCP port 5001 TCP window size:
65.0 KByte
(default) -----------------------------------------------------------
- [  4] local port 49320 connected with port
5001 [ ID] Interval       Transfer     Bandwidth [  4]  0.0-10.9
sec  7.07 MBytes  5.45 Mbits/sec

However, if these two
AirportExtrame-card computers connect to each other via the
Graphite-Airport base station the bandwidth drops to a meagre 1.9
Mbits/sec which is roughly the same as two Airport-card computers
connecting (which gave me 2.45 Mbits/s). Anyway, there is no immediate
problem with bandwidth on either network for what I have in mind.
Another important number to know is the real speed of our
internet-connection (for instance if I want to replace our old router by
a better documented one and have a measure for the in/decrease of the
connection-speed). Here, a good URL is which offers two tests :
String and String SSI. The later one has a graphical
resulting page such as

Leave a Comment

google spammers

In the GoogleMatrix I tried to understand the concept
of the PageRank algorithm that Google uses to list pages according to
their \’importance\’. So, if you want your webpage to come out first in
a certain search, you have to increase your PageRank-value (which
normally is a measure of webpages linking to your page) artificially. A
method to achieve this is by link spamming, that is if page A is
to webpage of which you want to increase the PageRank value, take a page
B (either under your control or that of a friend webmaster) and add a
dummy link page B -> page A. To find out the effect of this on the
PageRank and how the second eigenvalue of the GoogleMatrix is able to
detect such constructs let us set up a micro-web consisting of
just 3 pages with links 1->2 and 1->3. The corresponding GoogleMatrix
(with c=0.85 and v=(1/3,1/3,1/3) is

1/3   1/20   1/20 1/3   9/10 
 1/20 1/3   1/20   9/10

which has eigenvalues 1,0.85 and 0.28.
The eigenvector with eigenvalue 1 (the PageRank) is equal to (0.15,1,1)
so page 2 and page 3 are equally important to Google and if we scale
PageRank such that it adds up to 100% over all pages, the relative
importance values are 6,9%,46,5% and 46,5%. In this case the eigenvector
corresponding to the second eigenvalue 0.85 is (0,-1,1) and hence
detects the two leaf-nodes. Now, assume the owner of page 2 sets up a
link spam by creating page 4 and linking 4->3, then the corresponding
GoogleMatrix (with v=(1/4,1/4,1/4,1/4)) is

77/240   3/80   3/80  
3/80 77/240   71/80   3/80   37/80 77/240   3/80   71/80  
3/80  3/80   3/80   3/80   37/80

which has eigenvalues
1,0.85,0.425 and 0.283. The PageRank eigenvector with eigenvalue 1 is
in this case is (0.8,8.18,5.35,1) or in relative importance % we have
(4.9%,50.1%,32.7%,6.1%) and we see that the spammer achieved his/her
goal. The eigenvector corresponding to the second eigenvalue is
(0,-1,1,0) which again gives the leaf-nodes and the eigenvector of the
third eigenvalue is (0,-1,0,1) and detects the spam-construct.

Leave a Comment

an even better LaTeX system

previous post the best LaTeX system was a commercial for Gerben
Wierda’s i-Installer to get a working tetex
distribution. I’ve been working happily with this TeX-system for two
years now but recently run into a few (minor) problems. In the process
of solving these problems I created myself a second tetex-system
more or less by accident. This is what happened. On the computer at the
university I once got fun packages running such as a chess-, go-
and Feynman diagrams-package but somehow I cannot reproduce this
on my home-machine, I get lots of errors with missing fonts etc. As I
really wanted to TeX some chess-diagrams I went surfing for the most
recent version of the chess-package and found one for Linux and
one under the Fink-project : the chess-tex package. So, I did a

sudo fink
install chess-tex

forgetting that in good Fink-tradition you can
only install a package by installing at the same time all packages
needed to run it, so I was given a whole list of packages that Fink
wanted to install including a full tetex-system. Did I want to
continue? Well, I had to think on that for a moment but realized that
the iTex-tree was living under /usr/local whereas Fink
creates trees under /sw so there should not really be a problem,
so yes let’s see what happens. It took quite a while (well over an hour
and a half) but when it was done I had a second full TeX-system, but how
could I get it running? Of course I could try to check it via the
command line but then I remembered that there is an alternative
front-end for TeXShop namely iTeXMac
which advertises that it can run either iTeX or the Fink-distribution of
tetex. So I downloaded it, looked in the preferences which indeed
contains a pane

where you can choose between using the standard
tetex-distribution or the Fink-distribution and iTeXMc finds
automatically the relevant folders. So I wrote a quick chess diagram ran
it trough iTeXMac and indeed it produced the graphics I expected! This
little system gave me some confidence in the Fink-distribution so I
fired up the Fink-Commander and looked under categories :
for other TeX packages I could install and there were plenty :
Latex2HTML, Latex2rtf, Feynman, tex4ht and so on. Installing them with
the commander is fun : just click on the package you want and click
‘Install’ under the Source-dropdown window

and in the lower part of the window you can follow the
installation process, whereas the upper part tells you what packages are
already installed and what their version-number is. I still have to
figure out how I will add new style files to this fink-tree and I have
to get used to the iTeXMac-editor but so far I like the robustness of
the system and the easy install procedure, so try it out!

Leave a Comment