Dear All,
sorry for the late reply: my todo list came knocking at my door and required
immediate attention.

I did a small test and it appears that both Polynomial and LaurentPolynomial
behave in the same way with respect to coercion. On the other hand their
behavior under conversion is different. 

Do we want the behavior under conversion to also be the same? If so, which
one should it be?
Best
S.





* David Roe <roed.m...@gmail.com> [2016-04-09 11:08:51]:

>    I think that this summary is right, including the explicit conversion
>    that relies on the index in gens().
>    David
> 
>    On Sat, Apr 9, 2016 at 4:15 AM, Volker Braun <[1]vbraun.n...@gmail.com>
>    wrote:
> 
>    Let me try to summarize the expected behavior: If there is a coercion
>    of the base rings, then there should be a coercion to the (laurent)
>    polynomial ring with additional variables. The variables in the
>    different rings are identified using their name (and not index in
>    gens() or any other rule).Â
>    sage: cm = get_coercion_model()
>    sage: R.<x> = QQ[]
>    sage: S.<x,t> = QQ[]
>    sage: cm.explain(R, S, operator.add)
>    Coercion on left operand via
>    Â  Â  Conversion map:
>    Â  Â  Â  From: Univariate Polynomial Ring in x over Rational Field
>    Â  Â  Â  To: Â  Multivariate Polynomial Ring in x, t over Rational
>    Field
>    Arithmetic performed after coercions.
>    Result lives in Multivariate Polynomial Ring in x, t over Rational
>    Field
>    Multivariate Polynomial Ring in x, t over Rational Field
>    No coercion if variable names are not strict subsets:
>    sage: T.<x,y> = QQ[]
>    sage: cm.explain(T, S, operator.add)
>    Unknown result parent.
>    But explicit conversion can still work, e.g. by falling back to the
>    index in gens():
>    sage: T(S.gen(0))
>    x
>    sage: T(S.gen(1))
>    y
> 
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> References
> 
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