Quotient for univariate Laurent polynomials

[kedlaya]

It would be nice if this worked rather than returning an error:

sage: F.<t> = LaurentPolynomialRing(GF(2))
sage: t // t
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/home/kedlaya/.sage/temp/kedlaya_laptop/18179/_home_kedlaya__sage_init_sage_0.py in <module>()

TypeError: unsupported operand type(s) for //: 'sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_mpair' and 'sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_mpair'

As it stands, I don't think univariate Laurent polynomial rings over a field support any division operation that stays within the ring:

sage: (t/t).parent()
Fraction Field of Univariate Laurent Polynomial Ring in t over Finite Field of size 2

except maybe if I access the internal representation (as a quotient ring) and implement it by hand.