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Solving polynomials by radicals
with roots of unity in minimum depth

Authors: Gwoboa Horng and Ming-Deh Huang
Journal: Math. Comp. 68 (1999), 881-885
MSC (1991): Primary 11R32; Secondary 11Y16, 12Y05
MathSciNet review: 1627793
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Abstract: Let $k$ be an algebraic number field. Let $\alpha$ be a root of a polynomial $f\in k[x]$ which is solvable by radicals. Let $L$ be the splitting field of $\alpha$ over $k$. Let $n$ be a natural number divisible by the discriminant of the maximal abelian subextension of $L$, as well as the exponent of $G(L/k)$, the Galois group of $L$ over $k$. 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 $k(\zeta _n )$.

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Additional Information

Gwoboa Horng
Affiliation: Department of Computer Science, University of Southern California, Los Angeles, CA90089-0781
Address at time of publication: Department of Computer Science, National Chung Hsing University, Taichung, Taiwan, R.O.C.

Ming-Deh Huang
Affiliation: Department of Computer Science, University of Southern California, Los Angeles, CA90089-0781

Keywords: Polynomials, solvable by radicals
Received by editor(s): April 24, 1996
Received by editor(s) in revised form: December 1, 1997
Additional Notes: The first author was supported in part by NSF Grant CCR 8957317.
The second author was supported in part by NSF Grant CCR 9412383.
Article copyright: © Copyright 1999 American Mathematical Society

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