Returns the differential operator ring over the differential field F.
> F<z> := RationalDifferentialField(Rationals()); > R := DifferentialOperatorRing(F); > R; Differential operator ring over Differential Ring of Algebraic function field defined over Rational Field by $.2 - 4711 with derivation given by (1) d(z)
Given a differential operator ring R with n indeterminates and a sequence S of n strings, assign the elements of S to the names of the variables of R.This procedure only changes the names used in the printing of the elements of R.
The easiest way to create an element in a given ring is to use the angle bracket construction to attach a name to the indeterminate of the differential operator ring. Other constructions are given below.
The i-th indeterminate of the differential ring R, where i must be 1.
Coerce the element s into the differential operator ring R. Elements that are coercible into R are elements coercible into its underlying ring, sequences, and differential operators defined over the base ring of the coefficient ring of R.When the base ring of R is an algebraic differential field, elements of other differential operator rings over algebraic differential fields can be coerced into R so long as the underlying rings of the differential fields are the same.
The zero element of the differential operator ring R.
The identity element of the differential operator ring R.
> F<z> := RationalDifferentialField(Rationals()); > R<D> := DifferentialOperatorRing(F); > R.1; D > R!(1/z); 1/z; > R![1/2,0,5,z]; z*D^3 + 5*D^2 + 1/2 > S<T> := DifferentialOperatorRing(ChangeDerivation(F,z)); > R!T; z*D > S!D; 1/z*T