## Solving polynomials by radicals with roots of unity in minimum depth

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- by Gwoboa Horng and Ming-Deh Huang PDF
- Math. Comp.
**68**(1999), 881-885 Request permission

## 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 $k(\zeta _n )$.## References

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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.
- Email: gbhorng@cs.nchu.edu.tw
**Ming-Deh Huang**- Affiliation: Department of Computer Science, University of Southern California, Los Angeles, CA90089-0781
- Email: huang@cs.usc.edu
- 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. - © Copyright 1999 American Mathematical Society
- Journal: Math. Comp.
**68**(1999), 881-885 - MSC (1991): Primary 11R32; Secondary 11Y16, 12Y05
- DOI: https://doi.org/10.1090/S0025-5718-99-01060-1
- MathSciNet review: 1627793