Abstract
We propound a systematic and formal method to compute the Galois group of a non-necessarily irreducible polynomial: we proceed by successive inclusions, using mostly computations on scalars (and very few on polynomials). It is based on a formal method of specialization of relative resolvents: it consists in expressing the generic coefficients of the resolvent using the powers of a primitive element, thanks to a quadratic space structure; this reduces the problem to that of specializing a primitive element, which we are able to do in the case of the descending by successive inclusions. We incidentally supply a way to make separable a resolvent.
Research supported by the CNRS GDR 1026 (MEDICIS), the GDR-PRC 967 (MathInfo)t, and the CEC ESPRIT BRA contract 6846 (POSSO).
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Colin, A. (1995). Formal computation of Galois groups with relative resolvents. In: Cohen, G., Giusti, M., Mora, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1995. Lecture Notes in Computer Science, vol 948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60114-7_13
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DOI: https://doi.org/10.1007/3-540-60114-7_13
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