"Source: Text/Commut/RngDiff.text";
"Line: 1513";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Commut/RngDiff.text, line: 1513
// Example: H121E30 ()
print "Example: H121E30";
ei := GetEchoInput();
SetEchoInput(true);
F<z> := RationalDifferentialField(Rationals());
FF<z>:=ChangeDerivation(RationalDifferentialField(Rationals()),z);
RR<DD>:=DifferentialOperatorRing(FF);
RS<DS>, mpRRtoRS :=Completion(RR,Zeros(z)[1]);
S<t>:=BaseRing(RS);
IsDifferentialLaurentSeriesRing(S);
assert $1;
_<T> := PolynomialRing(S);
E<r>, mp := PurelyRamifiedExtension(T^3-5*t);
IsDifferentialLaurentSeriesRing(E);
assert $1;
RelativePrecision(E);
assert $1 eq 60;
RelativePrecisionOfDerivation(E);
assert $1 eq 60;
Derivation(E)(r);
mp(t);
Derivation(S)(t);
Derivation(E)(mp(t));
mp(Derivation(S)(t));
x:=t^(-2) +7+t^3 +O(t^15);
Derivation(S)(x);
Derivation(E)(mp(x));
mp(Derivation(S)(x));
y := 2*t+O(t^25);
Derivation(S)(y);
Derivation(E)(mp(y)) eq mp(Derivation(S)(y));
assert $1;
Derivation(E)(mp(y));
SetEchoInput(ei);
