"Source: Text/Geometry/RieSrf.text";
"Line: 1303";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/RieSrf.text, line: 1303
// Example: H127E13 ()
print "Example: H127E13";
ei := GetEchoInput();
SetEchoInput(true);
Qx<x> := PolynomialRing(Rationals());
p := &*[ x - k : k in [1..10] ];
m := 4;
X := RiemannSurface(p,m : Precision:=100);
D := X![Random([1..5]),0] - X![Random([6..10]),0];
A := m * AbelJacobi(D:Reduction:="Real");
A := AbelJacobi(m * D : Reduction := "Complex");
D := Divisor( InfinitePoints(X), [1, 1] );
E := X![1] + X![2];
D eq E;
assert $1;
AJ := AbelJacobi(D : Reduction:="Real");
Coordinates(Random(InfinitePoints(X))) in SingularPoints(X);
assert $1;
X := RiemannSurface(LegendrePolynomial(4),4);
InfinitePoints(X);
[ X!Coordinates(P) : P in InfinitePoints(X) ] eq InfinitePoints(X);
assert $1;
SetEchoInput(ei);
