Solving polynomials by radicals with roots of unity in minimum depth期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Solving polynomials by radicals with roots of unity in minimum depth

Authors:	Gwoboa Horng Ming-Deh Huang

Institution:	Department of Computer Science, University of Southern California, Los Angeles, CA90089-0781 ; Department of Computer Science, University of Southern California, Los Angeles, CA90089-0781

Abstract:	Let be an algebraic number field. Let $\alpha$ be a root of a polynomial $f\in kx]$ which is solvable by radicals. Let be the splitting field of $\alpha$ over . Let be a natural number divisible by the discriminant of the maximal abelian subextension of , as well as the exponent of , the Galois group of over . We show that an optimal nested radical with roots of unity for $\alpha$ can be effectively constructed from the derived series of the solvable Galois group of $L(\zeta _n )$ over $k(\zeta _n )$ .

Keywords:	Polynomials solvable by radicals

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