I mentioned that; Is it really strange though? It does not happen
implicitly through coercion. You have to explicitly ask to convert one
polynomial ring in two variables to another polynomial ring in two
variables (with mismatching generator names).
On Saturday, April 9, 2016 at 3:09:08 PM UTC+2, vdelecroix wrote:
>
> On 09/04/16 05:15, Volker Braun 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).
> >
> > 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
> > Conversion map:
> > From: Univariate Polynomial Ring in x over Rational Field
> > To: 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
> >
>
> Still, we have this strange (conversion) behavior
>
> sage: R.<x,y> = QQ[]
> sage: S.<y,t> = QQ[]
> sage: R(S('y'))
> x
> sage: S(R('x'))
> y
>
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