D.6.1.11 charexp2poly

Assume:

v an intvec containing the characterictic exponents of an irreducible plane curve singularity. a a vector containing the coefficients of a parametrization given by x(t)=x^v[1], y(t)=a(1)t^v[2]+...+a[n-1]t^v[n], i.e. the entries of a are of type number.

Return:

A polynomial f in the first two variables of the basering, such that f defines an irreducible plane curve singularity with characteristic exponents v.

Note:

The entries in a should be of type number and the vector v should be the sequence of characteristic exponents of an irreducible plane curve singularity in order to get a sensible result,

LIB "alexpoly.lib";
ring r=0,(x,y),dp;
intvec v=8,12,14,17;
vector a=[1,1,1];
poly f=charexp2poly(v,a);
f;
==> -x17+8x16-20x15+17x14-16x13y+12x12y2-2x13+32x12y-16x11y2-8x10y3+x12-8x11y\
   +20x10y2-16x9y3-4x9y2+16x8y3-2x7y4-8x6y5+6x6y4-8x5y5-4x3y6+y8
invariants(f)[1][1];  // The characteristic exponents of f.
==> 8,12,14,17