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 Post subject: The integral closure of ideals (trying to use reesclos.lib)Posted: Thu Dec 19, 2013 11:05 am

Joined: Mon Jun 29, 2009 1:51 pm
Posts: 20
I need to compute the integral closures of ideals (ie.g. in k[[x,y]]). So, I'm playing with the following:

LIB "reesclos.lib";
ring r=0,(x,y),dp;
poly f=.....
ideal I=x*diff(f,x),y*diff(f,y);
list JJ=normalI(I);

for weighted homogeneous cases (e.g. f=x^p+y^q) the answer comes quickly. For non-weighted homogeneous, but Newton-non-degenerate (e.g. f=x^5+x^2*y^2+y^5) I could not get the answer in char=0, but at least the computation is successful for : >>>ring r=11,(x,y),dp;

In the simplest degenerate case, f=(x^2-y^3)^2+x*y^4;, I could not get the answer even in char=11. (After several minutes I just stopped Singular.)

Am I doing smth wrong/stupid?
Are there any faster ways to compute the integral closures of ideals?

Thanks!

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 Post subject: Re: The integral closure of ideals (trying to use reesclos.lib)Posted: Fri Dec 20, 2013 4:58 am

Joined: Mon Jan 31, 2011 9:50 pm
Posts: 8
Well I have had mixed timing results using either normalI in Singular's reesclos.lib or integralClosure(I) in Macaulay2.
I have posted a couple annotated examples on my website

If you have tried Macaulay2, I have some code for integral closures of ideals in positive charateristic
that I am testing, and a paper submitted to go along with it.

Doug

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 Post subject: Re: The integral closure of ideals (trying to use reesclos.lib)Posted: Sun Dec 22, 2013 9:45 am

Joined: Mon Jun 29, 2009 1:51 pm
Posts: 20
Thanks!

Indeed, in Macaulay it works unbelievably fast!!
(Or, rather: I'm doing smth very stupid in Singular, thus it goes very slowly)

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 Post subject: Re: The integral closure of ideals (trying to use reesclos.lib)Posted: Sun Jan 19, 2014 1:01 pm

Joined: Thu Apr 02, 2009 5:04 pm
Posts: 11
The library reesclos.lib was somewhat outdated since it relied on its own
version of de Jong's normalization algorithm and not on the much faster
algorithms by Greuel, Laplagne, and Seelisch respectively Boehm, Decker,
Laplagne, Pfister, Steenpass, and Steidel. The latter algorithms are implemented
in the libraries normal.lib respectively locnormal.lib.

We have now fixed the library reesclos.lib accordingly. The newest version can
be downloaded from our GIT respository and will be part of the next Singular
release. First tests show that Singular is now faster than Macaulay2.

For further tests, can you provide us with meaningful examples you are
interested in?

Thanks for informing us about the problem!

Wolfram

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 Post subject: Re: The integral closure of ideals (trying to use reesclos.lib)Posted: Tue Feb 11, 2014 7:43 am
Thanks for your help! (Sorry for the delay)

Regarding the meaningful examples (benchmarks), I guess already in the case of plane curve singularities with a few Puiseux pairs the computation (as above) can be quite non-trivial.

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