CohomologyOfBorelVarieties
This is the homepage of the Macaulay 2 package CohomologyOfBorelVarieties, written by Baptiste Calmès and Viktor Petrov, and dedicated to the computation of the ring structure of an oriented cohomology theory applied to the variety of complete flags of a semi-simple linear algebraic group.
This package is experimental and should not be considered as a stable release. Please contact me (Baptiste Calmès) if you want to use it and run into problems.
Download
CohomologyOfBorelVarieties (version 0.2)
Installation
You first need a working version of Macaulay 2, at least version 1.4, available freely from here. You will also need to download the packages WeylGroups and FormalGroupLaws and install them first. Then, this package is installed by the standard procedure: for example, on a unix/linux or a Mac OS X system, lauch M2 from the directory where you have saved the package file, and within M2, type:
installPackage "CohomologyOfBorelVarieties"
This should install the package and the documentation files. This being done, the package can be loaded by typing:
loadPackage "CohomologyOfBorelVarieties"
in future M2 sessions. It should automatically load at the same time the packages WeylGroups and FormalGroupLaws needed for CohomologyOfBorelVarieties to work.
Documentation
All functions are documented in the usual Macaulay 2 documentation style and come with examples. For example, to view the documentation corresponding to the whole package, type
help "CohomologyOfBorelVarieties"
or
viewHelp "WeylGroups"
to open it in your web browser.
Here is an example of an M2 session that was used to compute the ring structure of the algebraic cobordism of the varieties of complete flags under simple groups of rank 2 (A2, B2, G2).
