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? 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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