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D.6.1.1 resolutiongraph
Procedure from library alexpoly.lib (see alexpoly_lib).
- Usage:
- resolutiongraph(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:
- intmat, the incidence matrix of the resolution graph of the plane curve
defined by INPUT, where the entries on the diagonal are the weights of the
vertices of the graph and a negative entry corresponds to the strict transform
of a branch of the curve.
- Note:
- 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)^2-4x5y-x7;
poly f2=y2-x3;
poly f3=y3-x2;
resolutiongraph(f1*f2*f3);
==> 1,0,1,0,0,0,0,0,1,0,
==> 0,2,1,0,0,0,0,0,0,0,
==> 1,1,3,0,1,0,0,0,0,0,
==> 0,0,0,4,1,0,1,0,0,0,
==> 0,0,1,1,5,1,0,0,0,0,
==> 0,0,0,0,1,-2,0,0,0,0,
==> 0,0,0,1,0,0,-1,0,0,0,
==> 0,0,0,0,0,0,0,2,1,0,
==> 1,0,0,0,0,0,0,1,3,1,
==> 0,0,0,0,0,0,0,0,1,-3
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See also:
alexanderpolynomial;
develop;
hnexpansion;
totalmultiplicities.
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