>From the answers to that thread, it seems that rule

(R0)  The parent of a / b should only depend on the parents 
         of a and b. 

has to be strict (7 people for and 2 vaguely against). The two
main reasons are consistency accross the different Sage rings
and the fact that coercion relies on it. The main argument
against is that it might be confusing for users.

To construct the element x^-1 one has to use 1 // x because //
stands for "internal division" in Sage (and not "floor division" as
Python defines it).

Now comes the last question where opinions were not clear. What
is the prefered behavior of powering: x^-1 and (1+x)^-1. There are
two and a half possibilities:

0) a^-1 should be equivalent to 1/a always (as a "Sage rule")

0') x^-1 and (1+x)^-1 should go to the fraction field for Laurent
  polynomials

2) x^-1 is a Laurent polynomial while (1 + x)^-1 raises an
  ArithmeticError

I am fine with all but I would like to get it right. Thanks for your
answers for getting this sorted out!

Vincent

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