Norm1ToriHNP for GAP 4 ver.2024.04.03

Authors: Akinari Hoshi, Aiichi Yamasaki.
Needs: GAP, version >=4.8.7; GAP package HAP, version >=1.11.15;
Current version: Norm1ToriHNP-2024.04.03.zip
(SchurCoverG, MinimalStemExtensions, AlwaysHNPholds in HNP.gap were improved;
AllSubgroups2, StemExtensions in HNP were added;
IsInvertible, SearchPRowBlocks, SearchP1, SearchPFilterRowBlocks, SearchPFilterRowBlocksRandomMT, SearchPMergeRowBlock, SearchPLinear, SearchPBilinear, SearchPQuadratic, Hcandidates, Norm1TorusJTransitiveGroup, Norm1TorusJPermutationGroup, Norm1TorusJCoset, Norm1TorusITransitiveGroup, Norm1TorusIPermutationGroup, TransformationMatPari, TransformationMatPerm, StablyPermutationCheckHPPari, StablyPermutationMCheckPPari, StablyPermutationFCheckPPari, StablyPermutationFCheckPFromBasePari in FlabbyResolutionFromBase.gap were added as in RatProbNorm1Tori for GAP 4 ver.2023.09.28;
FlabbyResolutionNorm1TorusJ in FlabbyResolutionFromBase.gap was added)
Old version 3: Norm1ToriHNPver.2022.10.17.zip
(AbelianInvariantsGoverH in HNP.gap was added)
Old version 2: Norm1ToriHNPver.2020.03.19.zip
(AlwaysHNPholds, KerResH3Z in HNP were improved;
ChooseGiIterator, MaximalNormalSeries, ConjugacyClassSubgroupsNGHOrbitRep, ConjugacyClassesSubgroupsNGHOrbitRep, MinConjugacyClassesSubgroups, IsInvariantUnderAutG in HNP were added)
Old version 1: Norm1ToriHNPver.2019.10.04.zip
Contact: Akinari Hoshi, Aiichi Yamasaki.
Repository: KURENAI (Kyoto University Research Information Repository) https://doi.org/10.57723/289563
URL:
http://mathweb.sc.niigata-u.ac.jp/~hoshi/Algorithm/Norm1ToriHNP/index.html
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-2024.04.03.zip and unpack it to some folder , e.g. C:\Users\username.
Then type "Read("HNP.gap");" on GAP.

Documentation

FlabbyResolutionFromBase [.html .pdf]
HNP [.html, .pdf]
README [.html, .pdf]

Content

Norm1ToriHNP-2024.04.03.zip-+-FlabbyResolutionFromBase.gap
                            +-FlabbyResolutionFromBase.pdf
                            +-FlabbyResolutionFromBasever.2018.11.05.gap
                            +-HNP.gap
                            +-HNP.pdf
                            +-HNPver.2019.10.04.gap
                            +-HNPver.2020.03.19.gap
                            +-HNPver.2022.10.17.gap
                            +-README.txt
                            +-README.pdf
                            +-Norm1ToriHNP-2024.04.03.pdf

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. AMS 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. ScienceDirect Extended version: arXiv:2003.08253.

[HKY25] A. Hoshi, K. Kanai, A. Yamsaki, Norm one tori and Hasse norm principle, III: Degree 16 case, J. Algebra 666 (2025) 794-820. ScienceDirect Extended version: arXiv:2404.01362.

[HKY] A. Hoshi, K. Kanai, A. Yamsaki, Hasse norm principle for $M_{11}$ and $J_1$ extensions, arXiv:2210.09119.