#9138: Categories for polynomial rings
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Reporter: jbandlow | Owner: nthiery
Type: defect | Status: needs_review
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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Changes (by SimonKing):
* status: needs_info => needs_review
Comment:
With the latest patches, I obtain the following timings:
{{{
sage: R.<x> = ZZ[]
sage: timeit('(2*x-1)^2+5', number=10^4)
10000 loops, best of 3: 25.8 µs per loop
sage: R.<x> = QQ[]
sage: timeit('(2*x-1)^2+5', number=10^4)
10000 loops, best of 3: 27.8 µs per loop
sage: R.<x> = GF(3)[]
sage: timeit('(2*x-1)^2+5', number=10^4)
10000 loops, best of 3: 112 µs per loop
sage: R.<x> = QQ['t'][]
sage: timeit('(2*x-1)^2+5', number=10^4)
10000 loops, best of 3: 124 µs per loop
sage: R.<x,y> = ZZ[]
sage: timeit('(2*x-1)^2+5', number=10^4)
10000 loops, best of 3: 12.7 µs per loop
sage: R.<x,y> = QQ[]
sage: timeit('(2*x-1)^2+5', number=10^4)
10000 loops, best of 3: 15.7 µs per loop
sage: R.<x,y> = GF(3)[]
sage: timeit('(2*x-1)^2+5', number=10^4)
10000 loops, best of 3: 10.3 µs per loop
sage: R.<x,y> = QQ['t'][]
sage: timeit('(2*x-1)^2+5', number=10^4)
10000 loops, best of 3: 148 µs per loop
}}}
Without these patches:
{{{
sage: R.<x> = ZZ[]
sage: timeit('(2*x-1)^2+5', number=10^4)
10000 loops, best of 3: 22.7 µs per loop
sage: R.<x> = QQ[]
sage: timeit('(2*x-1)^2+5', number=10^4)
10000 loops, best of 3: 24.2 µs per loop
sage: R.<x> = GF(3)[]
sage: timeit('(2*x-1)^2+5', number=10^4)
10000 loops, best of 3: 87 µs per loop
sage: R.<x> = QQ['t'][]
sage: timeit('(2*x-1)^2+5', number=10^4)
10000 loops, best of 3: 113 µs per loop
sage: R.<x,y> = ZZ[]
sage: timeit('(2*x-1)^2+5', number=10^4)
10000 loops, best of 3: 13 µs per loop
sage: R.<x,y> = QQ[]
sage: timeit('(2*x-1)^2+5', number=10^4)
10000 loops, best of 3: 16.3 µs per loop
sage: R.<x,y> = GF(3)[]
sage: timeit('(2*x-1)^2+5', number=10^4)
10000 loops, best of 3: 10.5 µs per loop
sage: R.<x,y> = QQ['t'][]
sage: timeit('(2*x-1)^2+5', number=10^4)
10000 loops, best of 3: 237 µs per loop
}}}
In other words, there is a mild deceleration in the univariate case and a
mild (and in one case considerable) ''acceleration'' in the multivariate
case.
I don't understand why. But perhaps a reviewer has an idea, and can also
state his or her opinion how bad the deceleration is compared with the
acceleration?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9138#comment:18>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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