Mon 2018-11-19 09:41:03 UTC+1, Simon King:
>
> If I recall correctly, there is a function that for *many* (not all) 
> interactively created objects in Sage tells how they can be constructed, 
> but I don't recall the name of that function. 

That is sage_input, which can be used as follows:

    sage: R.<x> = QQ[]
    sage: sage_input(R)
    QQ['x']
    sage: sage_input(x)
    R.<x> = QQ[]
    x

Note that it does not always work:

    sage: K = R.fraction_field()
    sage: sage_input(K)
    Traceback (most recent call last)
    ...
    ValueError: Can't convert Fraction Field of Univariate Polynomial Ring 
in x over Rational Field to sage_input form

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