Objects
Functionality
Libraries
Examples
Availability
Contributors

Singularities of plane projective curves
Problem: 
Determine the type of the singularity
at (0,0) of 
f(x,y) =
y^{2}2x^{28}y4x^{21}y^{17}+4x^{14}y^{33}8x^{7}y^{49}+x^{56}+20y^{65}+4x^{49}y^{16} ,

and check whether this is the only singularity of the corresponding
complex plane projective curve C .

The algorithm proceeds as follows:
Step 1: 
Classify the singularity of f at (0,0) following Arnold's
classification scheme, in particular,
compute the local Tjurina number of f:
T_{local}(f) =
dim_{K}K[x,y]_{<x,y>}/< jacob(f), f
>

Step 2: 
Compute the global Tjurina number of f:
T_{global}(f) =
dim_{K}K[x,y]/< jacob(f), f
>
If T_{global}(f) = T_{local}(f) then there is no
further singularity in the affine part of C.

Step 3: 
Consider the singularities at infinity (coordinate change).

SINGULAR code
