On Feb 25, 2008, at 6:13 AM, David Harvey wrote:
>
> Currently in sage.rings.polynomial we have the following class
> hierarchy:
>
> Polynomial
> Polynomial_dense_modn
> Polynomial_dense_modn_ntl_zz
> Polynomial_dense_modn_ntl_ZZ
> Polynomial_dense_modp
>
> The implementations are via some weird combination of direct NTL
> access and libs.ntl.
>
> Is there eventually supposed to be Polynomial_dense_modp_ntl_zz and
> Polynomial_dense_modp_ntl_ZZ as well?
Yes. If there is not a trac ticket for it yet, there should be. It
shouldn't be that hard (just extend the modn polynomials and add some
functionality, e.g. gcd.
> Currently, if I do
> PolynomialRing(Integers(7)), it's apparently implemented via ZZ_pX
> (via libs.ntl!), but if I do PolynomialRing(Integers(1000)), it's
> implemented via zz_pX. So we get weird things like:
>
> sage: R.<x> = PolynomialRing(Integers(7))
> sage: f = R([ZZ.random_element() for _ in range(100)])
> sage: timeit("g = f*f")
> 625 loops, best of 3: 168 µs per loop
>
> but:
>
> sage: R.<x> = PolynomialRing(Integers(100))
> sage: f = R([ZZ.random_element() for _ in range(100)])
> sage: timeit("g = f*f")
> 625 loops, best of 3: 26.2 µs per loop
>
> i.e. it's six times faster if the modulus is composite.
>
> david
>
>
> >
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