论文标题
S2中的一些球形代码及其代数数字
Some spherical codes in S2 and their algebraic numbers
论文作者
论文摘要
对于3种电位，已获得了S2上1至65分的全局最小值的第一个195个球形代码：对数，库仑，称为汤姆森问题，分别为77、38和38位数字精度。已经发现，某些点集已嵌入多边形结构，限制了这些点，从而使它们被参数化并成功恢复了代数多项式。到目前为止，已经恢复了49个代数数集，但是从1,622个参数中恢复了另外109个代数数，为50,014位数字精度已知。这些最小多项式的代数非常高的代数程度可以从球形代码中找到代数数，并且需要新的数学工具来应对这一挑战。
The first 195 spherical codes for the global minima of 1 to 65 points on S2 have been obtained for 3 types of potentials: logarithmic, Coulomb, called the Thomson problem, and the inverse square law, with 77, 38, and 38 digits precision respectively. It was discovered that certain point sets have embedded polygonal structures, constraining the points, enabling them to be parameterized and to successfully recover the algebraic polynomial. So far 49 algebraic number sets have been recovered, but 109 more remain to be recovered from their 1,622 parameters, 983 known to 50,014 digit precision. The very high algebraic degree of these minimal polynomials eludes finding the algebraic numbers from the spherical codes and requires new mathematical tools to meet this challenge.
