"Source: Text/Commut/RngDiff.text";
"Line: 1443";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Commut/RngDiff.text, line: 1443
// Example: H121E28 ()
print "Example: H121E28";
ei := GetEchoInput();
SetEchoInput(true);
F<z> := RationalDifferentialField(Rationals());
_<X> := PolynomialRing(F);
Fext<v>, mp := PurelyRamifiedExtension(X^2-5*z);
IsAlgebraicDifferentialField(Fext);
assert $1;
mp(z) eq 1/5*v^2;
assert $1;
Parent(mp(z)) eq Fext;
assert $1;
Derivation(Fext)(mp(z));
assert $1 eq 1;
Derivation(Fext)(v);
Derivation(Fext)(v^2) eq Fext!5;
assert $1;
Inverse(mp)(v^2);
SetEchoInput(ei);
