Hi Combinat folks!
I see on the Sage Combinat Road Map on trac that there are some tickets
dedicated to path algebras: #9889, #12630 and something which appears to
have no ticket yet, namely an interface to QPA in Gap.
What I'd need is: Path algebras over an arbitrary finite quiver
(loops will occur) with coefficients in a finite field (non-prime fields
will occur). The path algebras will be equipped with a monomial ordering
("monomials" corresponding to paths). And of course the implementation
should be very efficient in basic arithmetics, in comparison of monomials,
and in using monomials as cache keys.
- Am I right that those things are currently unavailable in Sage?
- Am I right that #12630 would not help me, since it is restricted to
the loop-less case?
- Am I right that #9889 would not help me, since it is pure Python and
thus not very efficient, and does not provide monomial orderings?
- I had a look at the QPA package - it looks like it would do the right
things for me (there is even talk about Gröbner bases and Ext
algebras, which is totally in my scope), but the package is not in the
list of "accepted packages" and not even in the list of "deposited
packages" of GAP. Do you know whether the implementation is
competitive? Is there a ticket to make it available in Sage?
So, what do you recommend to do? Try to use QPA in Sage via the new
libGAP (I guess the GAP pexpect interface would be too slow)? Or try and
write my own implementation?
Cheers,
Simon
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