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characteristic polynomial/zeta function of monodromy
https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1778		 Page 1 of 1
Author:  Dmitry [ Fri Oct 02, 2009 9:55 pm ]
Post subject:  characteristic polynomial/zeta function of monodromy
Dear Singular Users,

I tried to find a procedure to compute the characteristic polynomial/zeta function of monodromy for a surface singularity in C^3.

The only things I found are:
* procedure charPoly from hnoether.lib computes the characteristic polynomial of monodromy for plane curves only (i.e. for functions depending on two variables).

*in the manual of reszeta.lib is written:

the procedure zetaDL computes local Denef-Loeser zeta function. If string s1 or s2 has the value "A", additionally the characteristic polynomial of the monodromy is computed.


Being stupid I cannot understand how/where to specify the value "A" for the string s1 or s2. It does not appear in the example.


Could you help, giving some example to compute char.pol. e.g. for x^3+y^3+z^3 ?


many thanks!
Author:  Anne [ Thu Oct 15, 2009 8:29 am ]
Post subject:  Re: characteristic polynomial/zeta function of monodromy
Dear Dmitry,
I only saw your question today. Sorry.
Here is the example you asked about:

ring R=0,(x,y,z),dp;
ideal I=x^3+y^3+z^3;
list re=resolve(I,"K");
zetaDL(re,1,"A");

The output will then be:
Computing global zeta function
[1]:
1/(s+1)
[2]:
(s8+s7+s6-2s5-2s4-2s3+s2+s+1)

I hope this helps,
Anne
Author:  Dmitry [ Fri Oct 16, 2009 8:58 am ]
Post subject:  Re: characteristic polynomial/zeta function of monodromy
:D Thanks! :D

still another question.

I would like to compute the char. polynomial for several cases of the type

> ideal I=(x^p+y^q+z^r)^N+x^A+y^B+z^C;
> list re=resolve(I,"K");
> zetaDL(re,1,"A");

but already the first case:
> p=2;q=3;r=5;
> A=10;B=11;C=13;N=2;

takes indefinitely long time on my poor laptop (i.e. more than a couple of hours). The bottleneck is the resolution tree. Am I doing something wrong or the computation should take some time?


thanks again!
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