The LinearOperators[DEToOrePoly] and LinearOperators[REToOrePoly] functions return an Ore operator K such that eq = K(f). The LinearOperators[OrePolyToDE], LinearOperators[OrePolyToRE], LinearOperators[FactoredOrePolyToDE], and LinearOperators[FactoredOrePolyToRE] functions apply the operator (L or M) to the function f. The LinearOperators[FactoredOrePolyToOrePoly] function converts an Ore polynomial in factored form, that is, a FactoredOrePoly structure, to an Ore polynomial in expanded form, that is, an OrePoly structure.

A completely factored Ore operator is represented by a structure that consists of the keyword FactoredOrePoly and a sequence of lists. Each list consists of two elements and describes a first degree factor. The first element provides the zero degree coefficient and the second element provides the first degree coefficient. For example, in the differential case with a differential operator D, FactoredOrePoly([-1, x], [x, 0], [4, x^2], [0, 1]) describes the operator .

An Ore operator is a structure that consists of the keyword OrePoly with a sequence of coefficients starting with the one of degree zero. The coefficients must be rational functions in x. For example, in the differential case with the differential operator D, OrePoly(2/x, x, x+1, 1) represents the operator .