Computing Galois groups

[1] W. Bosma, J. Cannon and C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput., 24 (1997) 235 – 265.
[2] A. Bostan, P. Flajolet, B. Salvy and E. Schost, Fast computation of special resultants, J. Symbolic Comput., 41 (2006) 1 – 29.

[3] J. Cannon and D. Holt, Computing maximal subgroups of finite groups, J. Symbolic Comput., 37 (2004) 589 – 609.
[4] H. Cohen, A course in computational algebraic number theory, Springer, Berlin 1993.
[5] H. Derksen and G. Kemper, Computational invariant theory, Encyclopaedia of Mathematical Sciences, 130, Springer, Berlin, 2002.
[6] J. Dixon and B. Mortimer, Permutation groups, Graduate Texts in Mathematics, 163, Springer, New York, 1996.
[7] A.-S. Elsenhans, Invariants for the computation of intransitive and transitive Galois groups, J. Symbolic Comput., 47 (2012) 315 – 326.
[8] A.-S. Elsenhans, Improved methods for the construction of relative invariants for permutation groups, J. Symbolic Comput., 79 (2017) 211 – 231.
[9] A.-S. Elsenhans, A note on short cosets, Exp. Math., 23 (2014) 411 – 413.
[10] A.-S. Elsenhans and J. Klüners, Computing subfields of number fields and applications to Galois group computations, J. Symbolic Comput., 93 (2018) 1 – 20.
[11] C. Fieker and J. Klüners, Computation of Galois groups of rational polynomials, LMS J. Comput. Math., 17 (2014) 141 – 158.
[12] K. Geißler, Berechnung von Galoisgruppen über Zahl- und Funktionenkörpern, Dissertation, Berlin, 2003.

[13] W. Hart, M. van Hoeij and A. Novocin, Practical polynomial factoring in polynomial time, ISSAC 2011–Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation, New York, 2011 163 – 170.
[14] M. van Hoeij, J. Klüners and A. Novocin, Generating subfields, J. Symbolic Comput., 52 (2013) 17–34.
[15] B. Huppert, Endliche Gruppen. I, Springer, Berlin 1967.
[16] J. Klüners, On computing subfields. A detailed description of the algorithm, J. Théor. Nombres Bor-deaux, 10 (1998) 243 – 271.
[17] J. Klüners and G. Malle, A database for field extensions of the rationals, LMS J. Comput. Math., 4 (2001) 182-196.
[18] R. Stauduhar, The determination of Galois groups, Math. Comp., 27 (1973) 981-996.