It's the difference between conversion and coercion.

P = PolynomialRing(GF(2), "z", sparse=True); Q = PolynomialRing(ZZ, "z",
sparse=False)
sage: P.convert_map_from(Q)
Conversion map:
  From: Univariate Polynomial Ring in z over Integer Ring
  To:   Sparse Univariate Polynomial Ring in z over Finite Field of size 2
sage: P.convert_map_from(Q)(Q.gen())
z

David

On Wed, Oct 12, 2022 at 5:15 PM 'Martin R' via sage-devel <
sage-devel@googlegroups.com> wrote:

> Sorry, I don't understand your last sentence.  We have
>
> sage: P = PolynomialRing(GF(2), "z", sparse=True); Q = PolynomialRing(ZZ,
> "z", sparse=False)
> sage: P.has_coerce_map_from(Q)
> False
>
> How does this fit with
>
> "And of course you can convert even when Q is not sparse."?
>
> Martin
>
> On Wednesday, 12 October 2022 at 23:04:38 UTC+2 David Roe wrote:
>
>> Yes, that's expected.
>>
>> sage: P = PolynomialRing(GF(2), "z", sparse=True); Q = PolynomialRing(ZZ,
>> "z", sparse=True)
>> sage: P.has_coerce_map_from(Q)
>> True
>>
>> And of course you can convert even when Q is not sparse.
>> David
>>
>> On Wed, Oct 12, 2022 at 4:58 PM 'Martin R' via sage-devel <
>> sage-...@googlegroups.com> wrote:
>>
>>> I have no idea whether the following is to be expected:
>>>
>>> sage: P = PolynomialRing(GF(2), "z", sparse=False); Q =
>>> PolynomialRing(ZZ, "z")
>>> sage: P.has_coerce_map_from(Q)
>>> True
>>>
>>> sage: P = PolynomialRing(GF(2), "z", sparse=True); Q =
>>> PolynomialRing(ZZ, "z")
>>> sage: P.has_coerce_map_from(Q)
>>> False
>>>
>>> Martin
>>>
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