Polynomial time algorithms for Galois groups
There are polynomial time algorithms to determine:
If the Galois group of an irreducible polynomial over Q is a p-group.
the prime divisors of the order of a solvable Galois group
Using the classification theorem for finite simple groups, there is a polynomial time algorithm to determine whether an irreducible polynomial over Q has Galois group Sn or An.
We consider several techniques for computing Galois groups, including the Chebatorev Density Theorem, and their applicability to polynomial time computations.
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