Archive for the ‘RISC Summer’ Category

Business As Usual

Mittwoch, Juli 8th, 2009

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?

Rubik’s Cube and GAP

Mittwoch, Juli 1st, 2009

Rubik’s Cube
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 …)

Second Day in Short

Dienstag, Juni 30th, 2009

Gröbner bases, OpenMP, MPI and parallel Haskells, oh my!

First Day Over

Montag, Juni 29th, 2009

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.

RISC Summer School

Sonntag, Juni 28th, 2009

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?)