#9138: Categories for polynomial rings
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Reporter: jbandlow | Owner: nthiery
Type: defect | Status: needs_info
Priority: major | Milestone: sage-4.7
Component: categories | Keywords: introspection, categories
Author: Simon King | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by SimonKing):
Here are the test results:
Without all patches:
{{{
sage: R.<x> = ZZ[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 22.5 µs per loop
sage: R.<x> = QQ[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 24.5 µs per loop
sage: R.<x> = GF(3)[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 87.7 µs per loop
sage: R.<x> = QQ['t'][]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 114 µs per loop
sage: R.<x,y> = ZZ[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 21.9 µs per loop
sage: R.<x,y> = QQ[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 40 µs per loop
sage: R.<x,y> = GF(3)[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 26.3 µs per loop
sage: R.<x,y> = QQ['t'][]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 239 µs per loop
}}}
With the patches from #9944:
{{{
sage: R.<x> = ZZ[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 25.6 µs per loop
sage: R.<x> = QQ[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 26.7 µs per loop
sage: R.<x> = GF(3)[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 109 µs per loop
sage: R.<x> = QQ['t'][]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 121 µs per loop
sage: R.<x,y> = ZZ[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 31.4 µs per loop
sage: R.<x,y> = QQ[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 40 µs per loop
sage: R.<x,y> = GF(3)[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 26.8 µs per loop
sage: R.<x,y> = QQ['t'][]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 250 µs per loop
}}}
With the patches from #9944 and the patch from here:
{{{
sage: R.<x> = ZZ[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 25.7 µs per loop
sage: R.<x> = QQ[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 28.3 µs per loop
sage: R.<x> = GF(3)[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 115 µs per loop
sage: R.<x> = QQ['t'][]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 125 µs per loop
sage: R.<x,y> = ZZ[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 31 µs per loop
sage: R.<x,y> = QQ[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 17.5 µs per loop
sage: R.<x,y> = GF(3)[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 25.1 µs per loop
sage: R.<x,y> = QQ['t'][]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 256 µs per loop
}}}
Note, however, that the numbers arent't very stable
{{{
sage: R.<x,y> = QQ[]
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 20.9 µs per loop
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 20.8 µs per loop
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 22.6 µs per loop
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 37.9 µs per loop
sage: timeit('(2*x-1)^2+5')
625 loops, best of 3: 15.4 µs per loop
}}}
But there is a tendency: Things tend to be slower, both with #9944 and
with my patch.
So, it should be worth while to analyse the arithmetic with prun.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9138#comment:12>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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