Computing the rational parametrisations
Write f (x)(y) =
P
i,j ai,j xj
yi
, and draw the Newton polygon
of the (i, j) in the support of f .
i = degy
j = degx
Let pi + qj = r be a segment, with p, q coprime, q > 0. Write
f =
X
pi+qj=r
ai,j xj
yi
| {z }
f0(x,y)
+
X
pi+qj>r
ai,j xj
yi
| {z }
H.O.T.
.
Nicolas Mascot Algebraic curves