#5519: [with patch, positive review] Irreducibility test is slow for polynomials
over GF(2)
-------------------------+--------------------------------------------------
Reporter: rhinton | Owner: rhinton
Type: enhancement | Status: new
Priority: major | Milestone:
Component: algebra | Keywords:
-------------------------+--------------------------------------------------
Comment(by mvngu):
On Debian 5.0 Lenny with the following system info:
{{{
kernel: 2.6.24-1-686
CPU: Intel(R) Celeron(R) 2.00GHz
RAM: 1.0GB
}}}
here are some timing statistics:
{{{
# BEFORE
sage: P.<x> = GF(2)[]
sage: f = P.random_element(1000)
sage: %timeit f.is_irreducible()
10 loops, best of 3: 1.14 s per loop
sage:
sage: f = P.random_element(10000)
sage: %time f.is_irreducible()
CPU times: user 4972.13 s, sys: 2.83 s, total: 4974.95 s
Wall time: 5043.02 s
False
# AFTER
sage: P.<x> = GF(2)[]
sage: f = P.random_element(1000)
sage: %timeit f.is_irreducible()
10000 loops, best of 3: 40.7 µs per loop
sage:
sage: f = P.random_element(10000)
sage: %timeit f.is_irreducible()
1000 loops, best of 3: 930 µs per loop
sage:
sage:
sage: f = P.random_element(100000)
sage: %timeit f.is_irreducible()
10 loops, best of 3: 27.6 ms per loop
}}}
That is, a "before" 1.14 seconds vs. an "after" 40.7 microseconds,
resulting in a speedup of 28x:
{{{
sage: a = 1.14 * 1000 # convert to microseconds
sage: b = 40.7 # unit is microseconds
sage: (a - b) / a
0.964298245614035
sage: a / b
28.0098280098280
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5519#comment:15>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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