#11036: improve solve_mod performance
---------------------------+------------------------------------------------
Reporter: dsm | Owner: burcin
Type: enhancement | Status: new
Priority: minor | Milestone:
Component: symbolics | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by dsm):
This patch doesn't attempt to do anything sophisticated, it simply reaches
for the low-hanging fruit:
(1) It modifies solve_mod_enumerate so that if the modulus is `5^100`,
instead of iterating over `5^100` possibilities, it finds solutions mod 5,
then uses those to find solutions mod `5^2`, etc.
(2) It modifies solve_mod to short-circuit in some cases.
(3) It also makes an unrelated change: currently solve_mod(x==1, 1)
returns [()], but should probably return [(0,)].
The change has little effect for small moduli but wins easily on anything
nontrivial:
{{{
#OLD
sage: time solve_mod(x^2==41, 10^7)
CPU times: user 4.21 s, sys: 0.05 s, total: 4.27 s
Wall time: 4.33 s
[(3703821,), (1452429,), (3547571,), (1296179,), (8703821,), (6452429,),
(8547571,), (6296179,)]
}}}
{{{
# NEW
sage: time solve_mod(x^2==41, 10^7)
CPU times: user 0.04 s, sys: 0.00 s, total: 0.04 s
Wall time: 0.04 s
[(3703821,), (1452429,), (3547571,), (1296179,), (8703821,), (6452429,),
(8547571,), (6296179,)]
}}}
It still behaves very badly for large primes, but a lot better than the
current approach on powers of small primes. This
includes my use case of powers of 10-- there was an OEIS sequence I was
extending which I had to do manually because solve_mod was too slow, and
it irritated me that Mma could do it quickly..
Beyond the doctests I've tested it for small-coefficient univariate
polynomials of order <= 5 with modulus <= 12, and for lots of random
multivariate polynomials. Tests were against a four-line brute force
solver. Probably I've missed something, though, so more tests would be
appreciated!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11036#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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