RatProbNorm1Tori for GAP 4

Authors: Akinari Hoshi, Aiichi Yamasaki.
Needs: GAP,version >=4.4.12;
Current version: ver.2023.09.28
(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.2018.11.05)
Old version: ver.2018.11.05
Contact: Akinari Hoshi, Aiichi Yamasaki.
URL: 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.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.

Contents

Click the link below for further details. 
RatProbNorm1Tori.zip-+-FlabbyResolutionFromBase.gap
                     +-README.txt

References

[HY17] Akinari Hoshi and Aiichi Yamasaki, Rationality problem for algebraic tori, Mem. Amer. Math. Soc. 248 (2017) no. 1176, v+215 pp.
[HHY20] Sumito Hasegawa, Akinari Hoshi and Aiichi Yamasaki, Rationality problem for norm one tori in small dimensions, Math. Comp. 89 (2020) 923-940. 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/.