RatProbNorm1Tori for GAP 4 ver.2024.08.21

Authors: Akinari Hoshi, Aiichi Yamasaki.
Needs: GAP,version >=4.4.12;
Current version: RatProbNorm1Tori-2024.08.21.zip
(Data files PSL28bpQ.dat, PSL28E8bpS.dat were added)
Old version 2: RatProbNorm1Toriver.2023.09.28.zip
(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)
Old version 1: RatProbNorm1Toriver.2018.11.05.zip
Contact: Akinari Hoshi, Aiichi Yamasaki.
Repository: KURENAI (Kyoto University Research Information Repository) https://doi.org/10.57723/289562
URL:
http://mathweb.sc.niigata-u.ac.jp/~hoshi/Algorithm/RatProbNorm1Tori/index.html
https://www.math.kyoto-u.ac.jp/~yamasaki/Algorithm/RatProbNorm1Tori/index.html

Description

This code provides algorithms for (stably, retract) rationality problem for norm one tori.

Installation

Download RatProbNorm1Tori-2024.08.21.zip and unpack it to some folder (e.g. C:\Users\username).
Then type "Read("FlabbyResolutionFromBase.gap");" on GAP.
In order to use the functions TransformationMatPari, StablyPermutationCheckHPPari, StablyPermutationMCheckPPari, StablyPermutationFCheckPPari, StablyPermutationFCheckPFromBasePari, an installation of PARI/GP [PARI2] is needed.
Then add the PARI/GP directory (e.g. C:\Program Files (x86)\Pari64-2-13-3) to PATH.

Documentation

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

Content

RatProbNorm1Tori-2024.08.21.zip-+-FlabbyResolutionFromBase.gap
                                +-FlabbyResolutionFromBase.pdf
                                +-FlabbyResolutionFromBasever.2018.11.05.gap
                                +-PSL28bpQ.dat
                                +-PSL28E8bpS.dat
                                +-README.txt
                                +-README.pdf
                                +-RatProbNorm1Tori-2024.08.21.pdf

References

[HY17] Akinari Hoshi and Aiichi Yamasaki, Rationality problem for algebraic tori, Mem. Amer. Math. Soc. 248 (2017) no. 1176, v+215 pp. AMS Preprint version: arXiv:1210.4525.

[HHY20] Sumito Hasegawa, Akinari Hoshi and Aiichi Yamasaki, Rationality problem for norm one tori in small dimensions, Math. Comp. 89 (2020) 923-940. AMS Extended version: arXiv:1811.02145.

[HY] Akinari Hoshi and Aiichi Yamasaki, Rationality problem for norm one tori for $A_5$ and ${\rm PSL}_2(\mathbb{F}_8)$ extensions, arXiv:2309.16187.

[PARI2] The PARI Group, PARI/GP version 2.13.3, Univ. Bordeaux, 2021, http://pari.math.u-bordeaux.fr/.