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On computation of monodromy structure
https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1746		 Page 1 of 1
Author:  Dmitry Kerner [ Mon Jun 29, 2009 1:53 pm ]
Post subject:  On computation of monodromy structure
I'm trying to compute the monodromy in a specific example.
the simplest script:

LIB "gmssing.lib";
ring r = 0,(x,y,z),ds;
poly f=x*y*z*(x+y+z)+z^4*x+y^4*z+x^4*y;
monodromy(f);

(I need the Jordan block structure, not just the eigenvalues, hence I can't use e.g. spectrum(f) ).

Unfortunately my laptop is very slow (and not enough memory).

*Are there any ways to improve smth for this particular example?
*Or maybe somebody can just run this on a faster computer and put the results here?
Author:  levandov [ Sun Jul 19, 2009 4:08 pm ]
Post subject:  Re: On computation of monodromy structure
Hi Dmitry,

this example is tough (and interesting!) indeed. It took nearly 30 hours on a quite decent compute server and here's the data, which 'monodromy(f);' returns:
[1]:
_[1]=-1/4
_[2]=0
_[3]=1/9
_[4]=1/5
_[5]=2/9
_[6]=1/4
_[7]=1/3
_[8]=2/5
_[9]=4/9
_[10]=1/2
_[11]=5/9
_[12]=3/5
_[13]=2/3
_[14]=7/9
_[15]=4/5
_[16]=8/9
[2]:
1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1
[3]:
1,3,3,3,3,1,3,3,3,1,3,3,3,3,3,3

Why are you interested in this curve? Does it bear a special name? May I use it as benchmark for our collection?

With best regards,
Viktor Levandovskyy
Author:  Dmitry [ Sat Jul 25, 2009 3:02 pm ]
Post subject:  Re: On computation of monodromy structure
Thank you very much, this was very important for me!
Of course you can use this example for any purpose!


(We were particularly interested in this example as it seems to be a counterexample to some old question. Hopefully a short note will be posted to the arXiv next week.)
Author:  Dmitry [ Thu Jul 30, 2009 6:01 am ]
Post subject:  Re: On computation of monodromy structure
Finally the preprint is: arXiv:0907.5252

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