Code

1. For the Hasse norm principle:

   • GAP code to calculate the cohomology group H^1(G,M), where G is a finite group and M a flasque module in a flasque resolution of the Chevalley module of G/H, as explained in Section 4 of [2].

   • GAP code to calculate the isomorphism class of the unramified Brauer group of norm one tori via a method of Drakokhrust and Platonov, as presented in Theorem 5.3 of [4].

   • GAP code to calculate the first obstruction to the Hasse norm principle for K/k corresponding to a tower N/K/k of number fields, as introduced in [1] and delineated in Remark 4.9 of [4].

   • GAP code to calculate the knot group of a Galois extension, given its Galois group and a list of the decomposition groups at the ramified places, as explained in Section 6.2 of [4].

2. For the multinorm principle:

   • GAP code to calculate the first obstruction to the multinorm principle for a finite number of extensions of a global field (as outlined in Remark 2.8 of [3]) and the total obstructions to the multinorm principle and weak approximation for multinorm one tori (as explained in Remark 3.8 of [3]).

References:

[1] Y.A. Drakokhrust, V.P. Platonov, The Hasse norm principle for algebraic number fields. Math. USSR-Izv. 29 (1987), 299-322.

[2] A. Macedo, The Hasse norm principle for A_n-extensions, Journal of Number Theory 211 (2020), 500-512 (arXiv).

[3] A. Macedo, On the obstruction to the Hasse principle for multinorm equations, to appear in Israel Journal of Mathematics (arXiv).

[4] A. Macedo, R. Newton, Explicit methods for the Hasse norm principle and applications to A_n and S_n extensions, to appear in Mathematical Proceedings of the Cambridge Philosophical Society (arXiv).