Abstract
This study is a continuation of Yokoyama et al. [22], which improved the method by Landau and Miller [11] for the determination of solvability of a polynomial over the integers. In both methods, the solvability of a polynomial is reduced, in polynomial time, to that of polynomials, each of which is constructed so that its Galois group acts primitively on its roots. Then, by virtue of Pálfy’s bound [14], solvability of polynomials with primitive Galois groups can be determined in polynomial time. An effective method, thus, exists in theory. For practical computation, however, the most serious problem remains: How to determine solvability of each polynomial with primitive Galois group.
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© 1996 Birkhäuser Verlag Basel/Switzerland
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Anai, H., Noro, M., Yokoyama, k. (1996). Computation of the splitting fields and the Galois groups of polynomials. In: González-Vega, L., Recio, T. (eds) Algorithms in Algebraic Geometry and Applications. Progress in Mathematics, vol 143. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9104-2_3
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DOI: https://doi.org/10.1007/978-3-0348-9104-2_3
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