By an approximate numerical application of Galois theory it is proved that the sextic equation of anisotropic elasticity for cubic symmetry is in general unsolvable in radicals, elementary transcendental functions, or elliptic modular functions and that its group is the full symmetric group. This im
Explicit Galois resolvents for sextic equations
โ Scribed by A. C. Hurley; A. K. Head
- Book ID
- 104582089
- Publisher
- John Wiley and Sons
- Year
- 1987
- Tongue
- English
- Weight
- 597 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0020-7608
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
In this paper we show that some ideals which occur in Galois theory are generated by triangular sets of polynomials. This geometric property seems important for the development of symbolic methods in Galois theory. It may and should be exploited in order to obtain more efficient algorithms, and it e
It has previously been shown that the conventional algebraic Galois group of the sextic equation of anisotropic elasticity for cubic crystals is the symmetric group and the equation is therefore algebraically unsolvable in radicals. As an equation with four parameters it has also 15 monodromic Galoi
Let G be a transitive, solvable subgroup of S . We show that there is a common 6 ลฝ . w x formula for finding the roots of all irreducible sextic polynomials f x g Q x with ลฝ . Gal f s G. Moreover, once the roots r are calculated, there is an explicit i ลฝ . procedure for numbering them so that the G