I just saw Robert's ticket about implementing / wrapping braid groups
in SAGE ( http://www.sagetrac.org/sage_trac/ticket/876 ) which is
pretty coincidental since I was thinking about the exact same thing
before I went to bed last night.  I wrote an email to Nikos
Apostolakis who had expressed interest in this on sage-support in June
to see if he was still interested.

GAP3 had support for braid groups provided by the "share package"
CHEVIE.  Unfortunately, when the change to GAP4 was made, this was
never ported over.  As David Joyner mentioned,  one possibility is to
have a (optional) GAP3 package from which the functionality could be
wrapped.  Another possibility is to port the GAP3 chevie code over to
GAP4.  I do not know how much of an undertaking this would be because
my familiarity with GAP programming is almost non-existent.  The third
possibility would be to port chevie directly over to SAGE; I looked at
the code for chevie, and this is definitely doable.  It would however
take a bit of time -- it's about 6000 lines of GAP code and about 2000
lines of comments.

It would be good to have a framework for root systems and the like
that all of these things can fit into.  This may be helpful in that
aspect: http://mupad-combinat.sourceforge.net/Wiki/RootSystems

--Mike

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