All sparse polynomials are implemented within Sage, in
sage.rings.polynomial.polynomial_generic_sparse. It would be good if the
constructor only used the implementation as part of the key for dense
polynomials.
David
On Wed, May 11, 2011 at 04:37, Simon King <simon.k...@uni-jena.de> wrote:
> Hi!
>
> When constructing a polynomial ring, one can provide arguments
> "sparse" and "implementation". But it seems that there is no sparse
> version based on NTL implementation:
>
> sage: R.<x> = PolynomialRing(ZZ, sparse=False, implementation='NTL')
> sage: R.is_sparse()
> False
> sage: R
> Univariate Polynomial Ring in x over Integer Ring (using NTL)
> sage: S.<x> = PolynomialRing(ZZ, sparse=True, implementation='NTL')
> sage: S.is_sparse()
> True
> sage: S
> Sparse Univariate Polynomial Ring in x over Integer Ring
>
> So, S is sparse, but the implementation is not mentioned (so, it seems
> to be the default, i.e. FLINT).
>
> However, providing "implementation" is not ignored, it is used for the
> cache key:
> sage: T.<x> = PolynomialRing(ZZ, sparse=True)
> sage: T
> Sparse Univariate Polynomial Ring in x over Integer Ring
> sage: S is T
> False
>
> Question 1:
> What is the underlying implementation of S? Is it NTL, as requested?
>
> Question 2, if the implementation of S is based on FLINT (the
> default):
> Should the "implementation" argument be silently ignored, so that "S
> is T" in the example above?
> Or should an error be raised instead ("explicit is better than
> implicit")?
>
> If the answer to question 1 is that it does use NTL, then of course it
> should be mentioned in the string representation.
>
> Best regards,
> Simon
>
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