Hey Salvatore,
   I would say this is the same problem as simplifying scalars of fraction 
fields of polynomials over QQ, that gcd(x, x) = 1 rather than x because x 
is a unit. I don't think we have a way around this currently other than 
doing some kind of explicit coercion.

Best,
Travis


On Friday, October 9, 2015 at 1:40:22 PM UTC-5, Salvatore Stella wrote:
>
> Dear all, 
> I just noted the following odd behaviour: 
>
> sage: L = LaurentPolynomialRing(ZZ, 'x').fraction_field() 
> sage: L.inject_variables() 
> Defining x 
> sage: x/x 
> 1 
>
> As one should expect but if we change the base ring then things get messy: 
> sage: L = LaurentPolynomialRing(LaurentPolynomialRing(ZZ,'t'), 
> 'x').fraction_field() 
> sage: L.inject_variables() 
> Defining x 
> sage: x/x 
> x/x 
> sage: _.denominator() 
> x 
>
> The fact that x/x is printed out as x/x is still ok if somewhat annoying. 
> But 
> the return value of denominator() is definitely not what I would expect. 
> Is this intentional? 
> Thanks 
> Salvatore 
>

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