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| The integral closure of ideals (trying to use reesclos.lib) https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2327 |
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| Author: | Dmitry [ Thu Dec 19, 2013 11:05 am ] |
| Post subject: | The integral closure of ideals (trying to use reesclos.lib) |
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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| Author: | leonada [ Fri Dec 20, 2013 4:58 am ] |
| Post subject: | Re: The integral closure of ideals (trying to use reesclos.lib) |
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 www.dms.auburn.edu/~leonada 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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| Author: | Dmitry [ Sun Dec 22, 2013 9:45 am ] |
| Post subject: | Re: The integral closure of ideals (trying to use reesclos.lib) |
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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| Author: | Wolfram Decker [ Sun Jan 19, 2014 1:01 pm ] |
| Post subject: | Re: The integral closure of ideals (trying to use reesclos.lib) |
The library reesclos.lib was somewhat outdated since it relied on its own version of de Jong's normalization algorithm and not on the much faster algorithms by Greuel, Laplagne, and Seelisch respectively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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| Author: | Guest [ Tue Feb 11, 2014 7:43 am ] |
| Post subject: | Re: The integral closure of ideals (trying to use reesclos.lib) |
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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