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D.6.1.12 tau_es2
Procedure from library alexpoly.lib (see alexpoly_lib).
- Usage:
- tau_es2(INPUT); INPUT poly or list
- Assume:
- INPUT is either a REDUCED bivariate polynomial defining a plane curve singularity,
or the output of
hnexpansion(f[,"ess"]), or the list hne in
the ring created by hnexpansion(f[,"ess"]), or the output of
develop(f) resp. of extdevelop(f,n), or a list containing
the contact matrix and a list of integer vectors with the characteristic exponents
of the branches of a plane curve singularity, or an integer vector containing the
characteristic exponents of an irreducible plane curve singularity.
- Return:
- int, the equisingular Tjurina number of f, i. e. the codimension of the mu-constant
stratum in the semiuniversal deformation of f, where mu is the Milnor number of f.
- Note:
- The equisingular Tjurina number is calculated with the aid of a Hamburger-Noether
expansion, which is the hard part of the calculation.
In case the Hamburger-Noether expansion of the curve f is needed
for other purposes as well it is better to calculate this first
with the aid of hnexpansion and use it as input instead of
the polynomial itself.
If you are not sure whether the INPUT polynomial is reduced or not, use
squarefree(INPUT) as input instead.
Example:
| | LIB "alexpoly.lib";
ring r=0,(x,y),ls;
poly f1=y2-x3;
poly f2=(y2-x3)^2-4x5y-x7;
poly f3=y3-x2;
tau_es2(f1);
==> 2
tau_es2(f2);
==> 14
tau_es2(f1*f2*f3);
==> 49
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See also:
develop;
equising_lib;
hnexpansion;
tau_es;
totalmultiplicities.
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