Travis Scrimshaw wrote:
> A casual user will almost certainly do
> 
> 1 / x^k
> 
> and then try to do a method on Laurent polynomials (say, iterate over
> such element). The rational functions code does not have many of the
> methods and features that Laurent polynomials have.

Yes, but is that really a problem? In many cases, the sooner you realize 
you missed a subtle point, the better...

Incidentally, couldn't we alleviate all these issues with parents by 
printing the (abbreviated name of) the parent by default when printing 
an Element as the result of a command in the REPL? I'm thinking of 
something like

sage: 1 + 1
2 : ZZ
sage: 2/1
2 : QQ
sage: 
sage: Pol.<x> = QQ[]
sage: x + 1
x + 1 : QQ[x]

and so on.

-- 
Marc

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