Returns the m-th symmetric power of the differential operator L as an element of the parent of L. The symmetric power is monic where possible. If n denotes the order of L, then the degree of the m-th symmetric power of L is at most (n + m - 1)choose(n - 1). The algorithm that is used is based on algorithms given in [BMW97].
> F<z> := RationalDifferentialField(Rationals()); > R<D> := DifferentialOperatorRing(F); > SymmetricPower(D^2, 3); D^4 > SymmetricPower(D^3-1, 2); D^6 + -7*D^3 + -8