In a series of papers we develop symbolic computation algorithms to investigate finiteness of central configurations for the planar n-body problem. Our approach is based on Albouy-Kaloshin's work on finiteness of central configurations for the 5-body problems. In their paper, bicolored graphs called zw-diagrams were introduced for possible scenarios when the finiteness conjecture fails, and proving finiteness amounts to exclusions of central configurations associated to these diagrams. Following their method, the amount of computations becomes enormous when there are more than five bodies. In this paper we introduce matrix algebra for determination of possible diagrams and asymptotic orders, devise several criteria to reduce computational complexity, and determine possible zw-diagrams by automated deductions. For the planar six-body problem, we show that there are at most 86 zw-diagrams.

在一系列论文中，我们开发了符号计算算法来研究平面n体问题的中心配置的有限性。我们的方法基于 Albouy-Kaloshin 关于五体问题中心构型有限性的研究。在他们的论文中，为有限性猜想失败时的可能场景引入了称为zw图的双色图，并且证明有限性相当于排除与这些图相关的中心配置。按照他们的方法，当物体超过五个时，计算量就会变得巨大。在本文中，我们引入矩阵代数来确定可能的图和渐近阶，设计几个标准来降低计算复杂性，并通过自动推导确定可能的zw图。对于平面六体问题，我们证明最多有 86 个zw图。