Sitting at the PaCT conference in Novosibirsk.
There were some interesting talks, will summarize them later.
Met Sergei Gorlatch in person. It’s a nice feeling to talk to somebody, whos papers you cite and regard the basis for your own work. Oh, and SAC guys are also there.
Still near Linz, at the RISC/SCIEnce Summer School. Different courses, interesting people, no time to blog. ;)
We were yesterday in Linz for the sightseeing and the conference dinner. ‚T was nice.
And by the way, I have a new puzzle for you. It was told to me by Padraig Ó Catháin. You have two rectangles with one being 3 times the area of other and other being 3 times the perimeter of the one. Find their sides in integral numbers. More difficult question: how many solutions are there?
The afternoon lecture by Alexander Konovalov was a huge fun. Aside from all the algebraical goodness in GAP, he demonstrated something really amazing even to generic audience. It is actually easy to represent Rubik’s Cube as a group.
Let’s just unfold the cube and number the faces.
+--------------+
| |
| 1 2 3 |
| |
| 4 top 5 |
| |
| 6 7 8 |
| |
+--------------+--------------+--------------+--------------+
| | | | |
| 9 10 11 | 17 18 19 | 25 26 27 | 33 34 35 |
| | | | |
| 12 left 13 | 20 front 21 | 28 right 29 | 36 rear 37 |
| | | | |
| 14 15 16 | 22 23 24 | 30 31 32 | 38 39 40 |
| | | | |
+--------------+--------------+--------------+--------------+
| |
| 41 42 43 |
| |
| 44 bottom 45 |
| |
| 46 47 48 |
| |
+--------------+
Then you can represent the cube as
gap> cube := Group( > ( 1, 3, 8, 6)( 2, 5, 7, 4)( 9,33,25,17)(10,34,26,18)(11,35,27,19), > ( 9,11,16,14)(10,13,15,12)( 1,17,41,40)( 4,20,44,37)( 6,22,46,35), > (17,19,24,22)(18,21,23,20)( 6,25,43,16)( 7,28,42,13)( 8,30,41,11), > (25,27,32,30)(26,29,31,28)( 3,38,43,19)( 5,36,45,21)( 8,33,48,24), > (33,35,40,38)(34,37,39,36)( 3, 9,46,32)( 2,12,47,29)( 1,14,48,27), > (41,43,48,46)(42,45,47,44)(14,22,30,38)(15,23,31,39)(16,24,32,40) );
GAP can tell you, how many different positions the puzzle has:
gap> Size( cube ); 43252003274489856000
And that’s pretty damn much. But the best is: you can actually produce a solution from an arbitrary position just in three lines of GAP code. It looks like this: (mehr …)
Gröbner bases, OpenMP, MPI and parallel Haskells, oh my!
The First Day of the Training School is over. It was a long day and Alexander Konovalov and I kept sitting till half eight at the conference venue, because it was raining. Just got home from the dinner.
Also ICFP Contest ended today.
I arrived today in Linz, Austria. I’m staying here for two weeks. I attend the 4th RISC Summer School in Symbolic Computation. Should be tons of fun.
Meanwhile, I sit in my hotel room. I got my lunch, but have nothing for a dinner. And while fighting with headache I try for almost 24 hours now to find an ellipse equation from two tangents, tangential points and one focus. Analytically, of course. I have a repeated feal, I miss something very easy, but yet important. I really miss Marburgs‘ blackboards in such moments. And I really fight the thought that in few hours I’ll be hungry. to screw it all and to interpolate ellipse with splines.
Picture: a very tempting, but also a very wrong solution. (What’s wrong with it?)
