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]
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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