"Source: Text/Commut/RngDiff.text";
"Line: 1471";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Commut/RngDiff.text, line: 1471
// Example: H121E29 ()
print "Example: H121E29";
ei := GetEchoInput();
SetEchoInput(true);
S<t>:=DifferentialLaurentSeriesRing(Rationals());
_<T>:=PolynomialRing(S);
pol := T^4-5*t;
Sext<r>,mp := PurelyRamifiedExtension(pol);
IsDifferentialLaurentSeriesRing(Sext);
assert $1;
BaseRing(Sext) eq S and ConstantField(Sext) eq ConstantField(S);
assert $1;
RelativePrecision(Sext);
assert $1 eq 80;
RelativePrecisionOfDerivation(Sext);
Derivation(S)(t);
mp(t);
Derivation(Sext)(mp(t));
mp(Derivation(S)(t));
x := 4+6*t+O(t^6);
mp(x);
Derivation(Sext)(mp(x));
mp(Derivation(S)(x));
Inverse(mp)(r^4-r^8);
Inverse(mp)(r^4+O(r^5));
Derivation(Sext)(r);
SetEchoInput(ei);
