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.2024.04.03
(SchurCoverG, MinimalStemExtensions, AlwaysHNPholds were improved to ver.2022.10.17
FlabbyResolutionNorm1TorusJ, AllSubgroups2, StemExtensions were added to ver.2022.10.17 from ver.2024.04.03
IsInvertible, SearchPRowBlocks, SearchP1, SearchPFilterRowBlocks, SearchPFilterRowBlocksRandomMT, SearchPMergeRowBlock, SearchPLinea, SearchPBilinear, SearchPQuadratic, Hcandidates, Norm1TorusJTransitiveGroup, Norm1TorusJPermutationGroup, Norm1TorusJCoset, Norm1TorusITransitiveGroup, Norm1TorusIPermutationGroup, TransformationMatPari, TransformationMatPerm, StablyPermutationCheckHPPari, StablyPermutationMCheckPPari, StablyPermutationFCheckPPari, StablyPermutationFCheckPFromBasePari, were added to ver.2022.10.17 from ver.2024.04.03)
Old version 3: ver.2022.10.17
(AbelianInvariantsGoverH was added to ver.2020.03.19 from ver.2022.10.17)
Old version 2: 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 1: ver.2019.10.04
Contact: Akinari Hoshi, Aiichi Yamasaki.
URL: https://www.math.kyoto-u.ac.jp/~yamasaki/Algorithm/Norm1ToriHNP/index.html

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
                 +-README.txt

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.
[HKY22] A. Hoshi, K. Kanai, A. Yamsaki, Norm one tori and Hasse norm principle, Math. Comp. 91 (2022) 2431-2458. Extended version: arXiv:1910.01469.
[HKY23] A. Hoshi, K. Kanai, A. Yamsaki, Norm one tori and Hasse norm principle, II: Degree 12 case, J. Number Theory 244 (2023) 84-110. Extended version: arXiv:2003.08253,
[HKY] A. Hoshi, K. Kanai, A. Yamsaki, Norm one tori and Hasse norm principle, III: Degree 16 case, arXiv:2404.01362.