"Source: Text/Geometry/RieSrf.text";
"Line: 1362";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/RieSrf.text, line: 1362
// Example: H127E14 ()
print "Example: H127E14";
ei := GetEchoInput();
SetEchoInput(true);
Qxy<x, y> := PolynomialRing(Rationals(), 2);
f := 2*x^3*y^5 + x^2*y^6 - 1;
X := RiemannSurface(f);
m := X`Degree[1];
n := X`Degree[2];
f := ComplexPolynomial(X);
C<I> := BaseRing(Parent(f));
Ht := 10^5;
y1 := Random([-Ht..Ht])/Random([1..Ht]) + I*Random([-Ht..Ht])/Random([1..Ht]);
y2 := Random([-Ht..Ht])/Random([1..Ht]) + I*Random([-Ht..Ht])/Random([1..Ht]);
F1 := RootsNonExact(UnivariatePolynomial(Evaluate(f, [Parent(f).1, y1])));
F2 := RootsNonExact(UnivariatePolynomial(Evaluate(f, [Parent(f).1, y2])));
S1 := []; S2 := [];
for j in [1..n] do
  Append(~S1, X![F1[j], y1]);
  Append(~S2, X![F2[j], y2]);
end for;
D := &+S1 - &+S2;
A := AbelJacobi(D);
SetEchoInput(ei);
