"Source: Text/Ring/FldFunG.text";
"Line: 8188";
"Date: Thu Jun 16 15:04:46 2022";
"Main: Thu May 25 10:02:38 2023";
// original file: Text/Ring/FldFunG.text, line: 8188
// Example: H45E45 ()
print "Example: H45E45";
ei := GetEchoInput();
SetEchoInput(true);
Q := Rationals();
Qx<x> := PolynomialRing(Q);
Qxy<y> := PolynomialRing(Qx);
f1 := y^2 - (x-1)*(x-2)*(x-3)*(x-5)*(x-6);
F := FunctionField(f1);
d := Divisor(F.1) + Divisor(F!BaseRing(F).1);
V1 := DifferentialSpace(d);
d := 2*Divisor(F.1) - Divisor(F!BaseRing(F).1);
V2 := DifferentialSpace(d);
V1;
V2;
V1 meet V2;
D := DifferentialSpace(F);
v := V1 ! [2/9, 4/9]; v;
D!v;
V1!$1;
BasisOfDifferentialsFirstKind(F);
SetEchoInput(ei);
