I haven't tried QPA but it seems to be a pure GAP script, so I would expect
that performance will be comparable to a pure Python implementation. But it
looks like a very nice project and its likely that it would be of some use
even if the core computations of a Sage quiver module were implemented
differently.
A C++/Cython implementation of the basic path algebra arithmetic with
bit-packed exponents and arbitrary coefficient rings would be a nice thing
to have though ;-)
On Wednesday, November 21, 2012 11:45:39 AM UTC, Simon King wrote:
>
> 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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