We refine necessary and sufficient conditions for the generating series of a weighted model of a quarter plane walk to be differentially algebraic. In addition, we give algorithms based on the theory of Mordell-Weil lattices, that, for each weighted model, yield polynomial conditions on the weights determining this property of the associated generating series.

中文翻译：

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四分之一平面上行走的微分代数生成级数

我们将四分之一平面行走的加权模型的生成序列细化为微分代数的充分必要条件。此外，我们给出了基于 Mordell-Weil 格理论的算法，对于每个加权模型，在确定相关生成序列的此属性的权重上产生多项式条件。