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