[GAP Forum] Bruhat Orders

[Jay Taylor]

Dear Gary,

The CHEVIE package is what you really need to use but this can only be 
run in GAP 3. See the development version maintained by Jean Michel here

http://www.math.jussieu.fr/~jmichel/chevie/chevie.html

Alternatively this functionality is given in the new PyCox program 
written by Meinolf Geck, (this is written in Python and can be imported 
into Sage). The file can be downloaded on Geck's website here

http://www.abdn.ac.uk/~mth190/

A recent preprint of Geck's details some of its features

http://arxiv.org/pdf/1201.5566v1.pdf

This program is still quite new so it may not have all the functionality 
you need but the Bruhat order has certainly been implemented. There is 
also DuCloux's Coxeter program, written in C++, which can be found here

http://math.univ-lyon1.fr/~ducloux/coxeter/coxeter3/english/coxeter3_e.html

This will also compute the Bruhat order.

I hope some of these references help you.

-Jay