Computation schemes for splitting fields of polynomials

@inproceedings{Orange2009ComputationSF,
  title={Computation schemes for splitting fields of polynomials},
  author={S. Orange and G. Renault and K. Yokoyama},
  booktitle={ISSAC '09},
  year={2009}
}
In this article, we present new results about the computation of a general shape of a triangular basis generating the splitting ideal of an irreducible polynomial given with the permutation representation of its Galois group G. We provide some theoretical results and a new general algorithm based on the study of the non redundant bases of permutation groups. These new results deeply increase the efficiency of the computation of the splitting field of a polynomial. 
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References

The Magma algebra system. I
  • The user language. J. Symbolic Comput
  • 1997