
D.13.3.3 puiseuxExpansion
Procedure from library tropical.lib (see tropical_lib).
 Usage:
 puiseuxExpansion(f,n,#); f poly, n int, # list
 Assume:
 f is a nonconstant polynomial in two variables which is not
divisible by the first variable and which is squarefree
as a power series over the complex numbers;
the base field is either the field of rational numbers or a finite extension thereof;
monomial ordering is assumed to be local;
the optional parameter # can be the string 'subst'
 Return:
 list, where each entry of the list l describes the NewtonPuiseux
parametrisations of one branch of the plane curve singularity
at the origin defined by f; only the terms up to order n of each
parametetrisation are computed
l[i][1] = is a ring
l[i][2] = int
l[i][3] = string
WE NOW DESCRIBE THE LIST ENTRIES l[i] IN MORE DETAIL:
 the ring l[i][1] contains an ideal LIFT and the NewtonPuiseux
parametrisation of the branch is given by x=t^N and y=LIFT[1],
where N=l[i][2]
 if the base field had a parameter and a minimal polynomial, then
the new base field will have a parameter and a new minimal polynomial,
and LIFT[2] describes how the old parameter can be computed from the new one
 if a field extension with minimal polynomial of degree k was necessary,
then to the one extension produced acutally k extensions correspond by replacing
the parameter a successively by all zeros of the minimal polynomial
 if the option subst was set l[i][3] contains the polynomial where
y has been substituted by y(t^{1/N}) as a string
 Remark:
  it is best to use the procedure displayPuiseuxExpansion to
display the result
 the procedure requires the @sc{Singular} procedure absPrimdecGTZ to be
present in the package primdec.lib
 if f is not squarefree it will be replaced by its squarefree part
Example:
 LIB "tropical.lib";
printlevel=1;
ring r=0,(x,y),ds;
poly f=x2y4+x5y7;
puiseuxExpansion(f,3,"subst");
displayPuiseuxExpansion(puiseuxExpansion(f,3));

