Indeed, this is a bug.
It will (hopefully) be fixed in the next version of SINGULAR.
So far tau_es works only correct in the Newton nondegenerate case.
| Singular https://www.singular.uni-kl.de/forum/ |
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| modality of singularities https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1674 |
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| Author: | Dmitry [ Wed Jun 18, 2008 2:20 pm ] |
| Post subject: | modality of singularities |
I haven't found a command to calculate the modality of a singular point. In some simple cases this can be done by running classify(f); Guess this works for some lowest cases only. But it does not recognize (??) e.g. the case (x^5+y^6) |
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| Author: | Guest [ Fri Jun 20, 2008 5:59 pm ] |
| Post subject: | |
Computing the modality is a non-trivial task and there is no general algorithm available besides the classification, except for plane curve singularities. Moreover, we have to distinguish the modality for right- and contact-equivalence (the latter is even more complicated than the first). For curve singularities we can compute the right-modality with the help of an embedded resolution, cf. G.-M. Greuel, C. Lossen, E. Shustin: Introduction to Singularities and Deformations. Springer Verlag, Berlin, Heidelberg, New York (2006), p. 373, Remarks and Exercises. Or by the algorithm developed in A. Campillo, G.-M. Greuel, C. Lossen: Equisingular Calculations for Plane Curve Singularities. J. Symb. Comput. 42 (2007), 89-114. The latter is implemented in Singular in equising.lib. If mod denotes the right modality of an isolated hypersurface singularity f then mod = dimension of the mu-constant stratum of f in the base of the semiuniversal deformation of f, where mu is the Milnor number of f. Hence, if f is semi-quasihomogeneous or Newton-nondegenerate, it can be computed with the help of the Newton diagram of f. A discussion of this with examples about how to use the SINGULAR library equising.lib to compute the modality or, equivalently, the codimension tau_es of the mu-constant stratum for arbitrary plane curve singularities can be found at the above mentioned place too. Example: LIB "equising.lib"; ring r = 0,(x,y),ds; poly f = x5+y6; milnor(f) - tau_es(f); // -> 3 i.e. the right-modality is 3 (printlevel = 1; shows additional information) [/quote] |
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| Author: | Guest [ Sat Jun 21, 2008 6:58 am ] |
| Post subject: | |
Thanks! |
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| Author: | Dmitry [ Sat Jun 21, 2008 8:23 am ] |
| Post subject: | Something is strange with \tau^{es} !! |
The command poly f = (x2+y2)*(y2-(x-y)^3)*(x^3+y9); tau_es(f); returns: tau_es(f)=37 while the command poly f = ((x+y)^2+y2)*(y2-x3)*((x+y)^3+y9); tau_es(f); returns: tau_es(f)=23 note, however, that the polynomials differ by just a linear change of variables x->x+y A bug in Singular? |
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| Author: | greuel [ Mon Jun 23, 2008 2:00 am ] |
| Post subject: | |
Indeed, this is a bug. It will (hopefully) be fixed in the next version of SINGULAR. So far tau_es works only correct in the Newton nondegenerate case. |
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| Author: | hannes [ Tue Jul 08, 2008 4:00 pm ] |
| Post subject: | bug fix |
get a new version of the library hnoether.lib from ftp://www.mathematik.uni-kl.de/pub/Math ... oether.lib This should solve this issue. Hans Schoenemann |
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| Author: | Guest [ Thu Jul 10, 2008 7:25 am ] |
| Post subject: | thanks! |
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