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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Solving solvable quintics


Author: D. S. Dummit
Journal: Math. Comp. 57 (1991), 387-401
MSC: Primary 12E12; Secondary 12F10
Corrigendum: Math. Comp. 59 (1992), 309.
Corrigendum: Math. Comp. 59 (1992), 309.
MathSciNet review: 1079014
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Abstract: Let $ f(x) = {x^5} + p{x^3} + q{x^2} + rx + s$ be an irreducible polynomial of degree 5 with rational coefficients. An explicit resolvent sextic is constructed which has a rational root if and only if $ f(x)$ is solvable by radicals (i.e., when its Galois group is contained in the Frobenius group $ {F_{20}}$ of order 20 in the symmetric group $ {S_5}$). When $ f(x)$ is solvable by radicals, formulas for the roots are given in terms of p, q, r, s which produce the roots in a cyclic order.


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DOI: http://dx.doi.org/10.1090/S0025-5718-1991-1079014-X
PII: S 0025-5718(1991)1079014-X
Article copyright: © Copyright 1991 American Mathematical Society