关于多项式乘法映射的X-Boardman符号
On the Thom-Boardman Symbols for Polynomial Multiplication Maps
摘要：
Thom在1956年首次引入了B-Boardman符号来对可微映射的奇点进行分类。后来，博德曼将其推广到更一般的环境中。虽然B-Boardman符号是由一系列非递增的非负整数来实现的，但一般来说，计算这些数字是非常困难的。在多项式乘法映射的情况下，罗伯特·瓦利（Robert Varley）指出，计算多项式乘法的B-Boardman符号简化为计算应用于两个多项式的次数的欧几里得算法的连续幂次和幂次。在本文中，我们证实了这个猜想。
英文摘要：
The Thom-Boardman symbol was first introduced by Thom in 1956 to classify singularities of differentiable maps. It was later generalized by Boardman to a more general setting. Although the Thom-Boardman symbol is realized by a sequence of non-increasing, nonnegative integers, to compute those numbers is, in general, extremely difficult. In the case of polynomial multiplication maps, Robert Varley conjectured that computing the Thom-Boardman symbol for polynomial multiplication reduces to computing the successive quotients and remainders for the Euclidean algorithm applied to the degrees of the two polynomials. In this paper, we confirm this conjecture.
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