#### D.6.1.11 charexp2poly

Procedure from library `alexpoly.lib` (see alexpoly_lib).

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,

Example:

    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

See also: charexp2multseq; multseq2charexp.

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