Newsgroups: sci.math.research
From: TangSimon@csc.cuhk.hk
Subject: Re: Computing roots from Galois group
Date: Wed, 5 Apr 1995 17:54:47 GMT

In article <95074.123024GSXGC@CUNYVM.CUNY.EDU> <GSXGC@CUNYVM.CUNY.EDU> writes:
>How does one go about computing roots of a polynomial when one knows
>the Galois group and it is solvable?  In particular, if I have a polynomial
>which splits in the base field then the Galois group is trivial, is there
>a straightforward way of discussing the roots of the polynomial in terms
>of radicals?  I happen to be interested in finite fields but I'm
>embarrassed that I don't know the answer to this question more generally.

Go to CD-Rom and find "Susan Landau". She has a paper on solvability by
radicals. Or see books by L. Gaal "Classsical Galois Theory" or
H.M. Edwards's "Galois Theory".

Regards,  TangSimon@cuhk.hk

List of papers authored by Landau, Susan

[Mod. note:  If you're too lazy to go to your library's MathSci on CD-ROM,
you can try http://www.ams.org/mathscinet/ instead.  The result of a
search for Susan Landau included the following:

   95d:11144 Landau, Susan How to tangle with a nested radical. (English)
   Math. Intelligencer 16 (1994), 49--55. (Jensen, Chr. U.) 11R06

   92k:12008 Landau, Susan Simplification of nested radicals. (English)
   SIAM J. Comput. 21 (1992), 85--110. (Mignotte, Maurice) 12Y05
   (11Y16 68Q40)

   92f:11181 Landau, Susan Erratum: ``Factoring polynomials over
   algebraic number fields'' [SIAM J. Comput. 14 (1985), no. 1, 184--195;
   MR 86d:11102]. (English) SIAM J. Comput. 20 (1991), 998. 11Y40 (11R09
   11Y05 68Q40)

   91c:13022 Kozen, Dexter (with Landau, Susan ) Polynomial decomposition
   algorithms. (English) J. Symbolic Comput. 7 (1989), 445--456. 13P05
   (68Q40)

-Greg]