"Source: Text/Ring/FldFunG.text";
"Line: 8468";
"Date: Fri Sep 26 13:15:42 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/FldFunG.text, line: 8468
// Example: H46E47 ()
print "Example: H46E47";
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 := DifferentialSpace(F);
M7 := Module([Differential(3*F.1)], FieldOfFractions(Qx));
M8 := Module([Differential(F.1), Differential(F!BaseRing(F).1)], 
FieldOfFractions(Qx));
M12 := M7 meet M8;
M16 := M7 + M8;
assert M12 subset M7;
assert M12 subset M8;
assert M12 subset M16;
r := M7![&+[Random([-100, 100])/Random([1, 100])*x^i : i in [1 .. 5]]/
&+[Random([-100, 100])/Random([1,
100])*x^i : i in [1 .. 5]] : j in [1 .. Dimension(M7)]];
assert M7!D!r eq r;
r;
D!r;
SetEchoInput(ei);
