A question on tex.stackexchange got me to play around with TikZ a little bit, which resulted in the following picture:

goboard

On the way, I produced some commands for quickly drawing similar pictures (note that there is already a LaTeX package for drawing black-and-white diagrams):

usepackage{tikz,amsfonts}
usetikzlibrary{calc,shadows}

% The basic environment that draws the board
newenvironment{partialgoboard}[2]{%
 begin{tikzpicture}[
 scale=0.5,
 stone/.style={drop shadow={shadow xshift=0.03, shadow yshift=-0.05}},
 black-stone/.style={black!80},
 black-highlight/.style={outer color=black!80, inner color=black!30},
 black-number/.style={white},
 white-stone/.style={white!70!black},
 white-highlight/.style={outer color=white!70!black, inner color=white},
 white-number/.style={black},
 gomark/.style={black,fill=brown!80}]
 clip (#1) rectangle (#2);
 fill[brown!80] (0,0) rectangle (20,20);
 draw[black] (1,1) grid (19,19);
 draw[thick,black] (1,1) rectangle (19,19);
 fill (4,4) circle (0.1);
 fill (4,10) circle (0.1);
 fill (4,16) circle (0.1);
 fill (10,4) circle (0.1);
 fill (10,10) circle (0.1);
 fill (10,16) circle (0.1);
 fill (16,4) circle (0.1);
 fill (16,10) circle (0.1);
 fill (16,16) circle (0.1);
 }{%
 end{tikzpicture}
 }

% A shortcut for drawing a full board
newenvironment{goboard}{begin{partialgoboard}{0,0}{20,20}}{end{partialgoboard}}

% A stone
newcommandgostone[4][]{%
 begin{scope}
 fill[stone,#2-stone] (#3,#4) circle (0.45);
 clip (#3,#4) circle (0.45);
 shade[#2-highlight] (-0.15+#3,0.5+#4) circle (0.7);
 end{scope}
 node[#2-number] at (#3,#4) {sffamilybfseries{#1}};
}

% Some markers
newcommandgotrig{(mathbftriangle)}
newcommandgobox{(mathbfBox)}
newcommandgodia{(mathbfDiamond)}

% Marking a position on the board
newcommandgomark[3]{%
 node[gomark] at (#2,#3) {sffamilybfseries{#1}};
}

The above example is then produced with:

begin{partialgoboard}{0,0}{10.5,10.5}
 gostone{white}{4}{9}
 gostone{white}{3}{4}
 gostone[gotrig]{white}{5}{3}
 gostone{white}{10}{4}
 gostone[1]{white}{2}{6}
 gostone[3]{white}{3}{3}
 gostone[5]{white}{4}{5}
 gostone[7]{white}{2}{3}
 gostone{black}{2}{4}
 gostone{black}{3}{5}
 gostone[2]{black}{4}{4}
 gostone[4]{black}{4}{3}
 gostone[6]{black}{3}{2}
 gostone[8]{black}{5}{4}
 gomark{A}{5}{5}
 gomark{B}{2}{2}
end{partialgoboard}

I finally finished typing my notes from the Algebraic Geometry course by Dr C. Birkar last Michaelmas term. As usual, they are available on the mathematics page. This is the first revision of the notes and they might still change a lot. Like most of my texts, the notes are under a Creative Commons license and you can also download the LaTeX source code. Additionally, I uploaded the Bazaar branch to Launchpad. So if you want to help me improve the text, you can just branch from lp:~caramdir/+junk/PartIII-AG. Of course, any feedback and corrections sent by e-mail (or any other way) are also always welcome.

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A written form of my talk on the Weil conjectures is available.

Today I finally submitted my diploma thesis. :) It is titled Mathematical Foundations of Elliptic Curve Cryptography and contains the following topics:

  • A short introduction to algebraic curves (including Riemann-Roch, but without proofs);
  • some parts of the general theory elliptic curves (including basics about the Tate module and the Weil and Tate pairings);
  • elliptic curves over the complex numbers;
  • elliptic curves over finite fields (Weil conjectured for elliptic curves);
  • elliptic curves over local fields (and the canonical lift);
  • division polynomials;
  • modular polynomials (also over finite fields);
  • an introduction to elliptic curve cryptography;
  • point counting (SEA and Satoh’s algorithm);
  • cryptoanalysis: MOV/Frey-Rück, anomalous curve and Weil descent attacks
  • and some connections to elliptic divisibility sequences.

Now all that is left to do is to prepare for the diploma examination…

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An der TU Wien ist für Juni ein Mathematik-Diplomandenkolloqium geplant. Wer mitmachen will, erhält auf der “Gebiete II”-Seite nähere Infos.

Ich habe das schöne Wetter heute für eine Besichtigung der Zürcher Altstadt genützt. Und dabei natürlich den Fotoapparat mitgenommen. Eine Auswahl der Fotos und ein paar weitere vom ETH Hauptgebäude gibt es wie immer auf Flickr.

Anmerkung: Da mein Laptop-Bildschirm für so gar nicht für Bildbearbeitung geeignet ist, sind alle Fotos direkt von der Kamera ohne (Farb-)Korrekturen.

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Zürich!

Bin am Sonntag in aller früh heil (aber müde) in Zürich. Inzwischen bin auch schon ganz gut in meinem Übergangsquartier (meine Wohnung habe ich erst ab März) eingerichtet und habe jetzt hoffentlich die meisten administrativen Tätigkeiten (Uni einschreiben, Aufenthaltsgenehmigung, etc.) erledigt. Dazu auch gleich: Wer meine österreichische Handy-Nummer hat, kann auf der Kontakt-Seite meine schweizer Nummer erfahren.

Das war’s einmal fürs erste, aber ich werde versuchen im Lauf des Semesters mich immer wieder einmal hier zu melden.

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Geschafft!

Ich bin durch Ulysses durch. Und das größtenteils auf Englisch! :)

You’d think companies like Mathworks and Waterloo Maple could at least afford to test their products on the most common Linux distros. But obviously they do not…

Installation instructions for Matlab R2007a (Vienna UT student version): Create a directory for Matlab, copy the license.dat into this directory and run the install executable from the dvd. The first two steps did of course work flawless, but

sudo /media/cdrom/install

only returned “Permission denied”.  Running

sudo sh /media/cdrom/install

also failed with a similar error. What did work, was coping the whole DVD to a temporary directory on the hard disk and running the install script from there. The installer even created symlinks in /usr/local/bin. Then Matlab did start and mostly work, but is did not display any menus when Compiz (Desktop Effects) is enabled. Google pointed me to this solution:

ln -s [matlabroot]/sys/java/jre/glnxa64/jre1.5.0/lib/amd64/motif21 [matlabroot]/sys/java/jre/glnxa64/jre1.5.0/lib/amd64/motif12

and start matlab with

AWT_TOOLKIT=3DMToolkit matlab

So I created /usr/local/bin/matlab with

#!/bin/sh
AWT_TOOLKIT=3DMToolkit [matlabroot]/bin/matlab

and core matlab now works fine. Only starting Simulink results in a segmentation fault, but I do not need that anyway.

Maple 11 (again Vienna UT student version) installation worked much better. I had anticipated to need workarounds like for the 10 and 9.5 versions, but simply running

sudo sh /media/cdrom/installMapleLinux64

worked. It did not create any symlinks though. But xmaple only displayed an empty window! This is again a compiz related problem and creating a similar start script as for Matlab worked.

Maßtheorie

Es ist erstaunlich, aber es haben sich wieder ein ganzer Haufen an Fehlern in der Zusammenfassung finden lassen. Also gibt es wieder einmal eine neue Version

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