On Monday, August 17, 2020 at 6:04:41 AM UTC-7, John Cremona wrote:
>
> I'm sure this used to work: 
>
> sage: F = GF(2) 
> sage: r = 5/3 
> sage: F(1)*r 
> TypeError: unsupported operand parent(s) for *: 'Finite Field of size 
> 2' and 'Rational Field' 
>
> Of course I know that the could not be a coercion from QQ to GF(2) but 
> there is a conversion which works fine (when the denominator is odd): 
>

It would surprise me if this used to work. Perhaps a LONG time ago? It 
shouldn't work, because of the reason you mention [conversions aren't used 
for figuring out common parents]. What *does* work is

F(1)*5/3

because it's parsed as (F(1)*5)/3: dividing by integers is something that 
GF(2) allows.

If one would absolutely be intent on making it work, I guess one solution 
could be to have a (partial) multiplicative action of Q on GF(q); or more 
generally: on ZZ-modules. It would just have to be a lower priority 
solution than common parent finding.

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