Related Maps#
This section is devoted to maps between differential operator rings.
- TranslationMap(R, e): RngDiffOp, RngElt -> Map#
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 \(e\).
- LiftMap(m, R): Map, RngDiffOp -> Map#
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 \(M\).
- Example Maps Between Diff Op Rings (ex-943ab0)#
> 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