A question for coercion experts:
Currently we have:
sage: cm=get_coercion_model()
sage: cm.explain(ZZ,QQ['t'],operator.pow)
Coercion on left operand via
Composite map:
From: Integer Ring
To: Univariate Polynomial Ring in t over Rational Field
Defn: Natural morphism:
From: Integer Ring
To: Rational Field
then
Polynomial base injection morphism:
From: Rational Field
To: Univariate Polynomial Ring in t over Rational Field
Arithmetic performed after coercions.
Result lives in Univariate Polynomial Ring in t over Rational Field
Univariate Polynomial Ring in t over Rational Field
sage: cm.explain(QQ['t'],QQ,operator.pow)
Coercion on right operand via
Polynomial base injection morphism:
From: Rational Field
To: Univariate Polynomial Ring in t over Rational Field
Arithmetic performed after coercions.
Result lives in Univariate Polynomial Ring in t over Rational Field
Univariate Polynomial Ring in t over Rational Field
so if you do
sage: R.<t>=QQ[]
sage: 2^t
the latter gets evaluated by making coercing 2 into R and then trying to
raise to an element of R (which fails). Should we even be trying this? I
would think most valid cases of exponentiating are covered by actions. The
cases where it can be read as a binary operation on a single structure are
rare (and probably due to the structure acting on itself). (this comes up
on #20086)
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