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This section is devoted to maps between differential operator rings.
Returns a map on the differential operator ring R that replaces
R.1 by R.1 + e when applied to a
differential operator for some suitable ring element e.
Let m : F to M be a differential map on differential fields and
R a differential operator ring over F.
Then this routine lifts the given map to a map on
the differential operator rings R to S, where the
basefield of S is M.
> F<z> := RationalDifferentialField(Rationals());
> R<D> := DifferentialOperatorRing(F);
> transmap := TranslationMap(R, 2 + z);
> Codomain(transmap) eq R;
> transmap(D);
D + z + 2
> transmap(D^2);
D^2 + (2*z + 4)*D + z^2 + 4*z + 5
> P<T> := PolynomialRing(F);
> M<u>, mp := ext<F|T^2+z>;
> liftmap := LiftMap(mp, R);
> Rprime<Dprime> := Codomain(liftmap);
> IsDifferentialOperatorRing(Rprime);
true
> BaseRing(Rprime) eq M;
true
> liftmap(D);
Dprime
> liftmap(R!z);
z
> Derivation(Rprime)(liftmap(z));
1
> Derivation(Rprime)(u);
1/2/z*u
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