It was recently conjectured that every component of a discrete rational dynamical system is a solution to an algebraic difference equation that is linear in its highest-shift term (a quasi-linear equation). Holonomic sequences are trivially seen as solutions to such dynamical systems. We prove that the conjecture holds for holonomic sequences and propose two algorithms for converting holonomic recurrence equations into such quasi-linear equations. The two algorithms differ in their efficiency and the minimality of orders in their outputs.

翻译：近来有猜想认为，离散有理动力系统的每个分量都是某个在其最高移位项上为线性的代数差分方程（拟线性方程）的解。全纯序列显然可视为此类动力系统的解。我们证明该猜想对全纯序列成立，并提出两种将全纯递归方程转化为此类拟线性方程的算法。这两种算法在效率及输出阶数的最小性上存在差异。