RatProbAlgTori for GAP 4 ver.2018.05.22

Authors: Akinari Hoshi, Aiichi Yamasaki.
Needs: GAP,version >=4.4.12; GAP package carat, version >=2.1b1; GAP package crystcat, version >=4.1.6; GAP package HAP, version >=1.10.6; GAP package SONATA, version >=2.4
Current version: RatProbAlgTori-2018.05.22.zip (Buildcarat.sh wad modified to ver.2017.06.18; BuildCarat.sh was added to ver.2012.10.08)
Contact: Akinari Hoshi, Aiichi Yamasaki.
Repository: KURENAI (Kyoto University Research Information Repository) https://doi.org/10.57723/289559
URL:
http://mathweb.sc.niigata-u.ac.jp/~hoshi/Algorithm/RatProbAlgTori/index.html
https://www.math.kyoto-u.ac.jp/~yamasaki/Algorithm/RatProbAlgTori/index.html

Description

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

Installation

  1. (for Windows) Install VMware (in suitable Language).
    (for Mac OSX) Install VMware Fusion (in suitable Language).
  2. Install Ubuntu (Japanese ver.) on VMware.
    Over 2GB memory on Ubuntu is recommended.
  3. Download GAP and unpack it on Ubuntu to ~/ (/home/username).
    Go to ~/gap4r8 (Type "cd ~/gap4r8") and type "./configure".
    If "Please install m4 or build without GMP." appeared, type "sudo apt install m4" then type "./configure" again.
    Type "make".
    Go to ~/gap4r8/pkg (Type "cd ~/gap4r8/pkg") and type "../bin/BuildPackages.sh".
  4. Download RatProbAlgTori.zip and unpack it to ~/ (/home/username).
    Go to ~/RatProbAlgTori (Type "cd ~/RatProbAlgTori") and type "chmod +x BuildCarat.sh".
    Go to ~/gap4r8/pkg (Type "cd ~/gap4r8/pkg") and type "~/RatProbAlgTori/BuildCarat.sh".
    Go to ~/RatProbAlgTori (Type "cd ~/RatProbAlgTori") and type "~/gap4r8/bin/gap.sh".
    If you can see "gap> ", the installation was successful.
    Then type "Read("RatProbAlgTori.gap");" on GAP.

Documentation

BuildCarat [.html, .pdf]
caratnumber [.html, .pdf]
cohomology [.html, .pdf]
crystcat [.html, .pdf]
crystdat [.html, .pdf]
crystlst [.html, .pdf]
FlabbyResolution [.html, .pdf]
GLnQ [.html, .pdf]
KS [.html, .pdf]
README [.html, .pdf]

Content

RatProbAlgTori-2018.05.22.zip-+-RatProbAlgTori-+-Bravais.gap
                                               +-BuildCarat.sh
                                               +-BuildCarat.pdf
                                               +-BuildCarat.old.2017.06.18.sh
                                               +-carat2crystcat.txt
                                               +-caratchpol.txt
                                               +-caratnumber.gap
                                               +-caratnumber.pdf
                                               +-cohomology.g
                                               +-cohomology.pdf
                                               +-cryst1.txt
                                               +-cryst2.txt
                                               +-cryst3.txt
                                               +-cryst4.txt
                                               +-cryst5.txt
                                               +-cryst6.txt
                                               +-crystcat.gap
                                               +-crystcat.pdf
                                               +-crystdat.zip (9 files included)
                                               +-crystdat.pdf
                                               +-crystlst.pl
                                               +-crystlst.pdf
                                               +-FlabbyResolution.gap
                                               +-FlabbyResolution.pdf
                                               +-GLnQ.zip (6 files included)
                                               +-GLnQ.pdf
                                               +-H1cryst.txt
                                               +-Hn.gap
                                               +-KS.gap
                                               +-KS.pdf
                                               +-RatProbAlgTori.gap
                                               +-README.txt
                                               +-README.pdf
                                               +-RatProbAlgTori-2018.05.22.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.