"Source: Text/Commut/RngDiff.text";
"Line: 2651";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Commut/RngDiff.text, line: 2651
// Example: H121E47 ()
print "Example: H121E47";
ei := GetEchoInput();
SetEchoInput(true);
S<t> := DifferentialLaurentSeriesRing(Rationals());
R<D> := DifferentialOperatorRing(S);
_<T> := PolynomialRing(S);
Rext<Dext>, mp := PurelyRamifiedExtension(R, T^7-3*t);
Sext<text> := BaseRing(Rext);
Domain(mp) eq R and Codomain(mp) eq Rext;
assert $1;
IsDifferentialLaurentSeriesRing(Sext);
assert $1;
BaseRing(Sext) eq S;
assert $1;
RelativePrecision(Sext) eq 7*RelativePrecision(S);
assert $1;
D*t;
mp(D);
mp(R!t) eq Rext!(1/3*text^7);
assert $1;
Dext*text;
SetEchoInput(ei);
