Let $$\varPi _n$$ Π n be the set of bivariate polynomials of degree not greater than n . A $$\varPi _n$$ Π n -correct set of nodes is a set such that the Lagrange interpolation problem with respect to these nodes has a unique solution. A maximal line of a $$\varPi _n$$ Π n -correct set is any line containing exactly $$n+1$$ n + 1 nodes. Syzygy matrices can be used to find linear factors of the fundamental polynomials and detect maximal lines. We suggest to use matrix relations in order to generate syzygies, identify linear factors of fundamental polynomials and detect maximal lines. We interpret our results in the important case of GC sets trying to shed some light on the Gasca-Maeztu conjecture.

中文翻译：

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Radon 的构造和矩阵关系生成 syzygies

令 $$\varPi _n$$ Π n 是阶数不大于 n 的二元多项式的集合。$$\varPi _n$$ Π n -correct 节点集是这样的集合，使得关于这些节点的拉格朗日插值问题具有唯一解。$$\varPi _n$$ Π n -correct 集合的最大行是恰好包含 $$n+1$$ n + 1 个节点的任何行。Syzygy 矩阵可用于查找基本多项式的线性因子并检测最大值线。我们建议使用矩阵关系来生成syzygies，识别基本多项式的线性因子并检测最大值线。我们在 GC 集的重要案例中解释了我们的结果，试图阐明 Gasca-Maeztu 猜想。