RatProbAlgTori for GAP 4

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: 2017.06.18
Contact: Akinari Hoshi, Aiichi Yamasaki.
URL: https://www.math.kyoto-u.ac.jp/~yamasaki/Algorithm/RatProbAlgTori/index.html
Download: zip

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.

Contents

Click the link below for further details.
RatProbAlgTori.zip-+-RatProbAlgTori-+-Bravais.gap
                                    +-BuildCarat.sh
                                    +-caratnumber.gap
                                    +-cohomology.g
                                    +-crystcat.gap
                                    +-crystdat.zip (9 files included)
                                    +-crystlst.pl
                                    +-FlabbyResolution.gap
                                    +-GLnQ.zip (6 files included)
                                    +-Hn.gap
                                    +-KS.gap
                                    +-RatProbAlgTori.gap

References

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