It was recently conjectured that every component of a discrete-time rational dynamical system is a solution to an algebraic difference equation that is linear in its highest-shift term (a quasi-linear equation). We prove that the conjecture holds in the special case of holonomic sequences, which can straightforwardly be represented by rational dynamical systems. We 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：最近有猜想提出，离散时间有理动力系统的每个分量都是某个代数差分方程的解，该方程在其最高位移项上是线性的（即拟线性方程）。我们证明该猜想在全纯序列这一特殊情形下成立，而全纯序列可以直接用有理动力系统表示。我们提出了两种将全纯递推方程转换为此类拟线性方程的算法。这两种算法在效率及输出方程阶数的最小性方面存在差异。