We combine tools from homotopy continuation solvers with the methods of analytic combinatorics in several variables to give the first practical algorithm and implementation for the asymptotics of multivariate rational generating functions not relying on a non-algorithmically checkable `combinatorial' non-negativity assumption. Our homotopy implementation terminates on examples from the literature in three variables, and we additionally describe heuristic methods that terminate and correctly predict asymptotic behaviour in reasonable time on examples in even higher dimension. Our results are implemented in Julia, through the use of the HomotopyContinuation.jl package, and we provide a selection of examples and benchmarks.

翻译：我们把来自单调延续性求解器的工具与若干变量中的分析合成合成方法结合起来,为多变量合理生成功能的无源参数首次提供实际算法和实施方法,而不必依赖非逻辑性检验的“combinatory”非共性假设。 我们的同质执行以文献中三个变量中的例子结束,我们还描述了在合理时间内结束和正确预测更高层面实例中的无源行为的超自然方法。 我们的结果通过使用HiomotomyCsustain.jl 软件包在朱丽亚得到实施,我们提供了选择范例和基准。