Doron Zeilbeger made a talk last Friday at CRM in Montreal during Sage Days 38 about \(n^{n-2}\). At the end of the talk, he propoed a contest to code Joyal's Bijection which relates double rooted trees on \(n\) vertices and endofunctions on \(n\) elements. I wrote an implementation in Sage. My code is available here : joyal_bijection.sage. It will certainly not win for the most brief code, but it is object oriented, documented, reusable, testable and allows introspection.

sage: load joyal_bijection.sage

sage: L = [7, 0, 6, 1, 4, 7, 2, 1, 5]
sage: f = Endofunction(L)
sage: f
Endofunction:
[0..8] -> [7, 0, 6, 1, 4, 7, 2, 1, 5]

sage: L = [(0,6),(2,1),(3,1),(4,2),(5,7),(6,4),(7,0),(8,5)]
sage: D = DoubleRootedTree(L, 1, 7)
sage: D
Double rooted tree:
Edges: [(0, 6), (2, 1), (3, 1), (4, 2), (5, 7), (6, 4), (7, 0), (8, 5)]
RootA: 1
RootB: 7

sage: f.to_double_rooted_tree()
Double rooted tree:
Edges: [(0, 6), (2, 1), (3, 1), (4, 2), (5, 7), (6, 4), (7, 0), (8, 5)]
RootA: 1
RootB: 7

sage: D.to_endofunction()
Endofunction:
[0..8] -> [7, 0, 6, 1, 4, 7, 2, 1, 5]

sage: D == f.to_double_rooted_tree()
True
sage: f == D.to_endofunction()
True

sage: E = Endofunctions(10000)
sage: f = E.random_element()
sage: time f == f.to_double_rooted_tree().to_endofunction()
True
Time: CPU 2.23 s, Wall: 2.24 s

On December 21 2011, version 0.12 of IPython was released with its own notebook. The differences with the Sage Notebook are explained by Fernando Perez, leader of IPython project, in the blog post The IPython notebook: a historical retrospective he wrote last January. One of the differences is that the IPython Notebook run in its own directory whereas each cell of the Sage Notebook lives in its directory.

The latest version of IPython is 0.12.1 and was released in April 2012 and I was curious of testing it. I followed the installations informations. I got into trouble some times but finally managed to install it. Below is how I did to install IPython 0.12.1 on my OSX 10.5.8 using Python 2.6.7.

Installing dependencies:

sudo easy_install-2.6 tornado
sudo easy_install-2.6 nose
sudo easy_install-2.6 pyzmq

The following command was broken for a while:

sudo easy_install-2.6 pyzmq

ending with error TypeError: 'NoneType' object is not callable. I managed to make it work by redoing the above install commands in the correct above order:

sudo easy_install-2.6 tornado
sudo easy_install-2.6 nose
sudo easy_install-2.6 pyzmq

Installing ipython-0.12:

sudo easy_install-2.6 ipython

To make ipython known from the command line, I added the following line to the file ~/.bash_profile:

# ipython
export PATH=/opt/local/Library/Frameworks/Python.framework/Versions/2.6/bin:$PATH

I tested the ipython installation with the iptest command. It finishes with Status: OK

iptest

I open the ipython notebook and it worked:

ipython notebook
[NotebookApp] Using existing profile dir: u'/Users/slabbe/.ipython/profile_default'
[NotebookApp] The IPython Notebook is running at: http://127.0.0.1:8888
[NotebookApp] Use Control-C to stop this server and shut down all kernels.

In safari, I get the following problem:

Websocket connection to
ws://127.0.0.1:8888/kernels/86fef706-f386-4116-b3e4-d6d7776afb0d could not
be established.  You will NOT be able to run code.  Your browser may not be
compatible with the websocket version in the server, or if the url does not
look right, there could be an error in the server's configuration.

But, in firefox, it works when I open a page at the above adress http://127.0.0.1:8888. It gives me the following dashboard page.

I created my first notebook and did some tests. I followed the documentation found here.

The next thing would be to try to use this with Sage. Some progress has been done and can be followed at ticket #12719.

En fin de semaine, les équipes de compétitions de Montréal (MUCC) et l'Association d'ultimate de Montréal (AUM) ont invité Ben Wiggins, longtemps entraîneur de l'équipe Sockeye de Seattle, à donner des ateliers pratiques et théoriques sur l'ultimate.

Comme j'étais occupé avec ma soutenance de thèse, j'ai pu assister à seulement un atelier que j'ai bien aimé. Voici les notes que j'ai prises.

Recently, a discussion on sage-devel mentionned the graph I did last year for the evolution of the overall doctest coverage of Sage. The graph was out of date, so I updated it with the recent data:

Sage 4.7:   May 26, 2011        85.4%   ~  23769 / 27833
Sage 4.7.1: August 16, 2011     85.7%   ~  24129 / 28155
Sage 4.7.2: November 03, 2011   86.0%   ~  24477 / 28462
Sage 4.8:   January 20, 2012    86.1%   ~  24601 / 28573

We are far from the +4.7% a year I was expecting...

Doctest coverage of Sage

I think we should now stop looking at this percentage for the 100% coverage goal, because the coverage is mostly influenced by the hundreds of new doctested functions that are added to every new version of Sage.

Instead we should consider the evolution of the number of undoctested functions (and maybe fix objectives about it):

Sage 4.7:   May 26, 2011        4064
Sage 4.7.1: August 16, 2011     4026  ->  38 old functions now 100% doctested
Sage 4.7.2: November 03, 2011   3985  ->  41 old functions now 100% doctested
Sage 4.8:   January 20, 2012    3972  ->  13 old functions now 100% doctested

Here is the graph of it:

Number of undoctested functions in Sage

Au cours de la dernière année, j'ai travaillé à l'élaboration d'un vocabulaire en français pour l'ultimate avec l'Office québécois de la langue française et avec des membres de la Fédération québécoise d'ultimate. Le résultat, qui vient de sortir, est intitulé Disque en jeu! et disponible sur le site de l'OQLF dans la section Lexiques et Vocabulaires. Plus d'informations sont disponibles sur la page Vocabulaire de la fédération.

Le vocabulaire contient soixante concepts et illustre différentes facettes du sport, telles que des stratégies, des types de lancers, des positions, des fautes, etc.