Working on ticket #15790 <http://trac.sagemath.org/ticket/15790>,¹ I've
noticed that coercion from Sparse Polynomial Ring over ZZ to Dense
Polynomial over ZZ with FLINT implementation is unexpectedly slow. It is
not the case with the NTL implementation, and it is actually not the
case either if we do not do coercion but simply define the same
polynomial directly:
sage: R.<x> = PolynomialRing(ZZ,sparse=True)
sage: S.<y> = PolynomialRing(ZZ,implementation="FLINT")
sage: T.<z> = PolynomialRing(ZZ,implementation="NTL")
sage: f=x^100000
sage: %time S(f) # Coercion, with FLINT
CPU times: user 8.83 s, sys: 96 ms, total: 8.92 s
Wall time: 8.94 s
y^100000
sage: %time T(f) # Coercion, with NTL
CPU times: user 32.1 ms, sys: 0 ns, total: 32.1 ms
Wall time: 32.1 ms
z^100000
sage: %time _= y^100000 # Direct input, with FLINT
CPU times: user 624 µs, sys: 4 µs, total: 628 µs
Wall time: 637 µs
Despite the fact that this is way faster with NTL, the time complexity
seems to be linear with NTL and quadratic with FLINT.
I haven't found where it may come from!
Cheers,
Bruno
¹ Btw, the ticket is ready to review, as well as #16516
<http://trac.sagemath.org/ticket/16516>. ;-)
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