关于Pascal线的重构问题
On the reconstruction problem for Pascal lines
摘要：
给定一个圆锥曲线上的六个不同点$A, B, C, D, E, F$，排列成一个数组$\left[\begin{array}{ccc} A & B & C F & E & D \end{array}\right]$，帕斯卡定理说这些点$AE \cap BF, BD \cap CE, AD \cap CF$是共线的。包含它们的线被称为数组的帕斯卡，通过排列这些点，可以得到总共60条这样的线。在本文中，我们证明了初始的六元组可以明确地重建从四个具体选择帕斯卡。重建公式编码的一些transvectant身份证明使用二进制形式的图形演算。
英文摘要：
Given a sextuple of distinct points $A, B, C, D, E, F$ on a conic, arranged into an array $\left[\begin{array}{ccc} A & B & C F & E & D \end{array}\right]$, Pascal's theorem says that the points $AE \cap BF, BD \cap CE, AD \cap CF$ are collinear. The line containing them is called the Pascal of the array, and one gets altogether sixty such lines by permuting the points. In this paper we prove that the initial sextuple can be explicitly reconstructed from four specifically chosen Pascals. The reconstruction formulae are encoded by some transvectant identities which are proved using the graphical calculus for binary forms.
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