Open AccessJournal Article
Dihedral quintic polynomials and a theorem of Galois
K B K Blair,Kenneth S. Williams +1 more
TLDR
In this article, it was shown how to determine the other three roots of a monic irreducible quintic polynomial in Q[X] with Galois group D5 in accordance with a theorem of Galois.Abstract:
Let r1 and r2 be any two roots of a monic irreducible quintic polynomial in Q[X] with Galois group D5. It is shown how to determine the other three roots as rational functions of r1 and r2 in accordance with a theorem of Galois.read more
Citations
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Journal ArticleDOI
Commentary on an unpublished lecture by G. N. Watson on solving the quintic
TL;DR: Watson's method applies to any solvable quintic polynomial whose Galois group is one of Z/5~, D5, or F2o.
Proceedings ArticleDOI
Computation of the splitting field of a dihedral polynomial
TL;DR: An algorithm is provided which returns a triangular set encoding the relations ideal of g which has degree 2€n since the Galois group of g
Journal ArticleDOI
Cyclic Galois Extensions for Quintic Equation
K. Yu. Gudkov,B. B. Lur’e +1 more
TL;DR: In this paper, the authors investigated cyclic Galois extensions for quintic equations and constructed the resolvent for real fields and fields containing the square root of −1, and proved a theorem which characterizes all the Galois extension for quintics.
References
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Book
A Course in Computational Algebraic Number Theory
TL;DR: The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods.
Journal ArticleDOI
Characterization of Solvable Quintics x5 + ax + b
TL;DR: In this paper, a characterisation of Solvable Quintics x5 + ax + b is presented. The American Mathematical Monthly: Vol. 101, No. 10, pp. 986-992.
Journal ArticleDOI
Polynomials with Frobenius groups of prime degree as Galois groups II
TL;DR: For polynomials of prime degree p ≥ 5 over Q with Frobenius groups of degree p: Fpl = Flp′, l| p − 1 as Galois groups as mentioned in this paper.