Polynomial time algorithms for Galois groups
- Susan Landau
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In this paper we present several polynomial time algorithms for Galois groups. We show:
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.
- Polynomial time algorithms for Galois groups
- Book Title
- EUROSAM 84
- Book Subtitle
- International Symposium on Symbolic and Algebraic Computation Cambridge, England, July 9–11, 1984
- pp 225-236
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
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