#17435: Cythonise path algebra elements
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Reporter: SimonKing | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.5
Component: algebra | Resolution:
Keywords: path algebra | Merged in:
elements | Reviewers:
Authors: Simon King | Work issues:
Report Upstream: N/A | Commit:
Branch: | b080629d373feb384750218e99b9f77286fd79b9
u/SimonKing/cythonise_path_algebra_elements| Stopgaps:
Dependencies: #16453 |
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Comment (by SimonKing):
According to [https://groups.google.com/forum/#!topic/sage-
devel/OdUGcRTtWc4 Nathann's comment on sage-devel], including timings is
ok, as long as the timings are consistent on different machines.
In this case, on openSUSE 32bit, arithmetic for path algebra elements is
faster than arithmetic for letterplace free algebra elements, which is
much faster than arithmetic for the default implementation of free algebra
elements. On openSUSE 64bit, it is the same ranking; while letterplace is
not faster in 64bit than in 32bit, the path algebra implementation becomes
20% faster in this example.
Of course, the purpose of the three implementations is different:
The letterplace implementation only allows to deal with homogeneous
elements, but in contrast to the default implementation for free algebras
it comes with standard basis computations, allowing to construct graded
algebra quotients.
Path algebras are more general then free associative algebras, and
homogeneity is not required. At the moment, standard bases are not
available---but in fact this should be the next step. I plan to finish
implementing a non-commutitive F5 algorithm, which can compute standard
bases for one and two-sided ideals of modules over path algebra quotients
(in particular, of ideals in path algebras, so that one can deal with
algebra quotients), provided of course that the computation terminates in
finite time. And moreover, it will be able to compute minimal generating
sets of modules over basic algebras.
So, in the long run, it might make sense to replace the current default
implementation of free algebra elements, modelling free associative
algebras as a special case of path algebras. But that's for future. I hope
that for now the comment on the relation of the three implementations is
fine.
--
Ticket URL: <http://trac.sagemath.org/ticket/17435#comment:20>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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