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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