Computation of Galois groups over function fields. (English) Zbl 0946.12002
Summary: Symmetric function theory provides a basis for computing Galois groups which is largely independent of the coefficient ring. An exact algorithm has been implemented over \(\mathbb{Q} (t_1,t_2,\dots ,t_m)\) in Maple for degree up to 8. A table of polynomials realizing each transitive permutation group of degree 8 as a Galois group over the rationals is included.
MSC:
| 12Y05 | Computational aspects of field theory and polynomials (MSC2010) |
| 12F10 | Separable extensions, Galois theory |
| 11R32 | Galois theory |
| 11R58 | Arithmetic theory of algebraic function fields |
| 12F12 | Inverse Galois theory |
| 11Y40 | Algebraic number theory computations |
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