Norm1ToriHNP for GAP 4

Authors: Akinari Hoshi, Aiichi Yamasaki.
Needs: GAP, version >=4.8.7; GAP package HAP, version >=1.11.15;
Current version: ver.2020.03.19
(AlwaysHNPholds, KerResH3Z were improved to ver.2019.10.04
ChooseGiIterator, MaximalNormalSeries, ConjugacyClassSubgroupsNGHOrbitRep, ConjugacyClassesSubgroupsNGHOrbitRep, MinConjugacyClassesSubgroups, IsInvariantUnderAutG were added to ver.2019.10.04)
Old version: ver.2019.10.04
Contact: Akinari Hoshi, Aiichi Yamasaki.
URL: https://www.math.kyoto-u.ac.jp/~yamasaki/Algorithm/Norm1ToriHNP/index.html
Download: zip

Description

This code provides algorithms related to computations of total obstruction to the Hasse norm principle.

Installation

Download Norm1ToriHNP.zip and unpack it to some folder , e.g. C:\Users\username.
Then type "Read("HNP.gap");" on GAP.

Contents

Click the link below for further details.
Norm1ToriHNP.zip-+-FlabbyResolutionFromBase.gap
                 +-HNP.gap

References

[DP87] Yu. A. Drakokhrust, V. P. Platonov, The Hasse norm principle for algebraic number fields, (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 50 (1986) 946-968; translation in Math. USSR-Izv. 29 (1987) 299-322.
[HKY] A. Hoshi, K. Kanai, A. Yamsaki, Norm one tori and Hasse norm principle, arXiv:1910.01469, to appear in Math. Comp.
[HKY2] A. Hoshi, K. Kanai, A. Yamsaki, Norm one tori and Hasse norm principle, II: degree 12 case, arXiv:2003.08253.