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arXiv math/0005026math.GM
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最一般五次多项式的完全解

On the Complete Solution to the Most General Fifth Degree Polynomial

Richard J. Drociuk

摘要:

这篇文章背后的动机,是由于没有成功地找到一般五次方程的完整解。我们希望能找到一个解决方案,其中所有参数都是以直接的方式精确计算的。本文给出了一般五次方程五根的封闭形式解。它们可以在Maple V或新版本Maple VI上生成。在Maple的新版本Maple VI上,可以将本文中计算的所有替换插入到另一个中,并构造一个用于Tschirnhausian变换的大方程。该解决方案还使用了Maple V可以稳健计算的广义超几何函数。

英文摘要:

The motivation behind this note, is due to the non success in finding the complete solution to the General Quintic Equation. The hope was to have a solution with all the parameters precisely calculated in a straight forward manner. This paper gives the closed form solution for the five roots of the General Quintic Equation. They can be generated on Maple V, or on the new version Maple VI. On the new version of maple, Maple VI, it may be possible to insert all the substitutions calculated in this paper, into one another, and construct one large equation for the Tschirnhausian Transformation. The solution also uses the Generalized Hypergeometric Function which Maple V can calculate, robustly.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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