#15801: Categories over a base ring category
-------------------------------+------------------------
Reporter: nthiery | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.2
Component: categories | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #10963 | Stopgaps:
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Comment (by nthiery):
Hi!
I started to work on this. We can now do:
{{{
sage: Algebras(Fields())
Category of algebras over Category of fields
}}}
(TODO: would be nicer as Category of algebras over fields)
and by default, polynomial rings are created in such categories:
{{{
sage: QQ['x'].category()
Join of Category of euclidean domains and Category of commutative
algebras over Category of quotient fields
}}}
All tests pass in the sage/rings/polynomial.
Here are the new timing for Simon's benchmark about creating lots of
polynomial rings:
With Sage 5.0.1:
{{{
sage: %time test()
CPU times: user 7.38 s, sys: 0.08 s, total: 7.46 s
Wall time: 7.48 s
}}}
With develop (6.2.beta7):
{{{
sage: %time test()
CPU times: user 9.31 s, sys: 125 ms, total: 9.44 s
Wall time: 9.47 s
}}}
With #10963:
{{{
sage: %time test()
CPU times: user 17.6 s, sys: 288 ms, total: 17.9 s
Wall time: 17.8 s
}}}
With #10963 and this ticket:
{{{
sage: def test():
....: for p in prime_range(10000):
....: P = GF(p)['t','x','z']
sage: %time test()
CPU times: user 2.99 s, sys: 127 ms, total: 3.11 s
Wall time: 3.03 s
}}}
Sounds like the time-performance issue for polynomials is indeed fixed for
polynomials :-)
Now, on to matrices!
--
Ticket URL: <http://trac.sagemath.org/ticket/15801#comment:10>
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