These files provide an implementation of the DeConcini-Salvetti resolution in Sage, which in theory allow the computation of the cohomology of any finitely generated (possibly infinite) Coxeter group. Moreover, some methods are provided for computing the cohomology of the coroot lattices of root data.

The DeConcini-Salvetti resolution as such is implemented in DeConciniSalvetti.py. To use it, make it available in Sage by running

load("DeConciniSalvetti.py")

from within the Sage REPL. The you can e.g. run

W = CoxeterGroup(["E",8])
CS = DeConciniSalvettiResolution(W)
d2 = CS.d(2)
d2.kernel()

If you are specifically interested in computing the cohomology of all almost-simple semisimple root data up to rank eight, first edit Makefile and change the line

SAGE = /Applications/SageMath/sage

to reflect the location of your Sage executable; for example, if you installed Sage via a packet manager,

SAGE = sage

should be fine. After you've edited Makefile apppropriately, simply run

make

Note that this computation will probably take a day to finish. If you are interested in the cohomology of a specific root datum, e.g. do

sage main.py D 4
sage main.py A 2 3

etc.

At the moment, only finite Coxeter groups are supported, even though in principle all finitely generated Coxeter groups should be supported.