MultInvField 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 SONATA, version >=2.4
Current version: 2018.11.03 (MultInvFieldToNoetherProblem.gap was added to ver.2017.06.18)
Contact: Akinari Hoshi, Aiichi Yamasaki.
URL: https://www.math.kyoto-u.ac.jp/~yamasaki/Algorithm/MultInvField/index.html
Description
This code provides algorithms for multiplicative invariant fields.Installation
- (for Windows) Install VMware (in suitable Language).
(for Mac OSX) Install VMware Fusion (in suitable Language). - Install Ubuntu (Japanese ver.) on VMware.
Over 2GB memory on Ubuntu is recommended. - 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". -
Download MultInvField.zip and unpack it to ~/ (/home/username).
Go to ~/MultInvField (Type "cd ~/MultInvField") and type "chmod +x BuildCarat.sh".
Go to ~/gap4r8/pkg (Type "cd ~/gap4r8/pkg") and type "~/MultInvField/BuildCarat.sh".
Go to ~/MultInvField (Type "cd ~/MultInvField") and type "~/gap4r8/bin/gap.sh".
If you can see "gap> ", the installation was successful.
Then type "Read("MultInvField.gap");" on GAP.
Contents
Click the link below for further details.MultInvField.zip-+-MultInvField-+-AllSubdirectProducts.gap +-BuildCarat.sh +-caratnumber.gap +-cohomology.gap +-crystcat.gap +-crystdat.zip (9 files included) +-FlabbyResolution.gap +-KS.gap +-MultInvField.gap +-MultInvFieldToNoetherProblem.gap +-res.gap +-Glattice.dat +-Glattice5.dat +-Glattice6.dat +-NonInv.dat +-NonInv5.dat +-NSaltman.dat
References
[HY17] Akinari Hoshi and Aiichi Yamasaki,
Rationality problem for algebraic tori,
Mem. Amer. Math. Soc. 248 (2017) no. 1176, v+215 pp.
[HKY] Akinari Hoshi, Ming-chang Kang and Aiichi Yamasaki,
Multiplicative Invariant Fields of Dimension ≤ 6,
arXiv:1609.04142, to appear in Mem. Amer. Math. Soc.