Symmetric Powers#
- SymmetricPower(L, m): RngDiffOpElt, RngIntElt -> RngDiffOpElt#
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 [Bronstein et al., 1997].
- Example Symmetric Power (ex-6160ae)#
> 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